Environmental Science A path through The Default Library ======================================== How the planet works as one system, how people are changing it, and what the evidence says about the choices ahead. Step 1. Earth Systems: Five Spheres, One Slow Machine ----------------------------------------------------- Why: Atmosphere, oceans, ice, rock and life, and the cycles that join them. The planet is not a rock with weather on it. It is a set of reservoirs of air, water, ice, rock and life, joined by flows that run at speeds from days to hundreds of millions of years. Earth-system science is the habit of asking: how big is the pool, how fast does it turn over, and what else is wired to it? Every year, at a mountaintop observatory on Hawaii, the carbon dioxide in the air goes up and down like breathing. It peaks in May and falls through the summer, by about 7 parts per million, as the forests and fields of the Northern Hemisphere inhale. Then it climbs again through the northern winter as they decay. That wiggle is the whole land biosphere, measured from the middle of the Pacific. Now look at where the wiggle sits from year to year. The annual average at Mauna Loa was 315.98 ppm in 1959 and 427.35 ppm in 2025 (NOAA). The breathing is still there. It is riding up a staircase. One graph holds two Earth-system ideas: fast cycles that repeat, and slow changes that accumulate. An Earth-systems course teaches you to read that graph and everything like it. This piece is the entry point to the Environmental Science major: spheres, cycles, deep time, and the carbon cycle across timescales. The physics of the greenhouse effect itself is in The Physics of the Greenhouse Effect (13/15), a good first read; here we look at the machinery around it. The course in one box Who takes itEveryone in environmental science, geography and Earth-science programmes, usually in year 1. Programmes differ in name (some call the whole degree "Earth Systems") but the UK subject benchmark for Earth and environmental sciences and the core of interdisciplinary programmes such as Stanford's and Yale's all begin with the planet as a connected system. What it is forGiving you a map of the planet's reservoirs and flows, so that later courses on climate, ecology, soils and pollution all have somewhere to attach. Comes afterNothing in this major. It helps to have met General Chemistry (35/36) and Statistics (34/05) at the same time. Leads toClimate Science (36/14), Conservation & Applied Ecology (36/15), Soils, Agriculture & Food Systems (36/18), Pollution & Environmental Health (36/17) and Environmental Data & GIS (36/20). What this piece gives youYou will not be able to map a rock formation or run a model. You will be able to ask, of any environmental claim, how big the pool is and how fast it turns over; to see why the poles and tropics behave as they do; and to place today's carbon on a ladder of timescales. Easier first reads: The Physics of the Greenhouse Effect (13/15), Entropy (13/12) and Ecology (35/48). Stocks, flows and residence time An Earth-system scientist sees the world as a set of bathtubs. Each reservoir is a stock (the water in the ocean, the carbon in soils). Each pipe is a flux (evaporation, photosynthesis). The one number that tells you how a bathtub behaves is the residence time, the average time an atom stays in the pool. residence time = size of the stock ÷ flux through itif inflow equals outflow the pool is in steady state; the residence time is also how quickly it responds to a change For water, the numbers are striking. About 505,000 km³ of water evaporate and fall again each year. The atmosphere holds only about 12,900 km³ at a time, so a water molecule spends roughly nine days there. The ocean holds about 1,338 million km³ and loses about 434,000 km³ a year to evaporation, which gives roughly 3,000 years (published values run to about 3,200). That is why weather changes in days and the deep ocean changes over millennia. Interactive · How fast does a pool respond? Water in the airWater in the ocean Stock size S Flux F through it Sliders are logarithmic (each step is a power of ten). Units are the same for S and F (km³ and km³ per year for water). Water values are rounded published figures (Wikipedia, "Water cycle", and the USGS value for the atmosphere); the response curve is the standard one-box model 1 − e−t/τ. With the default setting (the atmosphere's water), a rise in inflow is almost fully absorbed within a month. Slide the stock up to the ocean's and the same change takes the better part of ten thousand years to settle. This one idea explains why a spilled solvent clears from a stream in days but can linger in a lake for decades, and why fast reservoirs react and slow ones remember. Two more words matter. A negative feedback pushes a system back toward where it was (a warmer ocean radiates more heat to space). A positive feedback pushes it further (melting ice exposes dark water that absorbs more sunlight). Stable systems have mostly negative feedbacks; the interesting question is what happens when a slow reservoir is pushed past the point where one loop reverses. Sunlight, latitude and the engine of weather Everything starts with sunlight arriving unevenly. The tropics face the Sun nearly head-on all year. The poles get it at a slant, and not at all for months. You can calculate the sunlight at the top of the atmosphere from three things: the solar constant (about 1,361 W/m²), the tilt of Earth's axis (23.44°), and the day of the year. daily sunlight ∝ (1361 ÷ π) × [ H sin φ sin δ + cos φ cos δ sin H ]φ = latitude, δ = the Sun's declination that day, H = half-day length as an angle (it reaches π at the midnight-sun poles) Interactive · Sunlight by latitude and season June solsticeDecember solsticeMarch equinoxSeptember equinox Latitude (+ north) Day of year Top-of-atmosphere insolation with S0 = 1361 W/m², obliquity 23.44°, a circular-orbit declination plus the Earth–Sun distance term; good to a few percent. It ignores clouds, reflection and the atmosphere. Two things surprise nearly everyone. On the June solstice the North Pole receives about 524 W/m² a day, more than the equator's 385, because the Sun never sets. And the yearly average still runs from about 416 W/m² at the equator to about 168 W/m² at the North Pole. The poles are cold because the year is mostly night and because snow reflects most of what does arrive, not because summer is weak. That gradient drives the circulation. Heat moves poleward in the air and in the ocean; textbook estimates put the two together at roughly five petawatts across the mid-latitudes. In the tropics, warm air rises near the equator (the Intertropical Convergence Zone, a belt of towering storms), spreads out, and sinks at about 30° north and south. Falling air is dry, which is why so many deserts sit near that latitude: the Sahara, the Kalahari, the Atacama, Australia's interior. The rain belt follows the Sun north and south through the year. That seasonal swing is a monsoon, and it feeds more than a billion people: India's summer rains, the West African monsoon over the Sahel, and the rains of the Amazon and Congo basins. The Himalaya and Tibetan plateau are called the world's "water towers" because snow and glacier melt feed the great rivers of South and East Asia; how many people depend on them depends on how you count (a figure of well over a billion appears in regional assessments). Monsoons are not fixed. The same slow orbital changes that nudge ice ages also moved the rain belt: the Sahara was wet and green, with lakes, until about 5,500 years ago (the African Humid Period). The IPCC also finds that Northern Hemisphere aerosol pollution partly cut monsoon rain from the 1950s to the 1980s, with the Sahel and South Asia as examples, and that rain has partly recovered since (medium confidence). Hold that thought: in the Earth system, even air-quality laws can move rainfall. The ocean and ice: the planet's heat bank Water has an unusually high heat capacity, and there is a lot of it. The whole atmosphere has the same heat capacity as the top 3.5 metres of the ocean. So when the planet gains heat, almost all of it goes into the sea. The IPCC (AR6, 2021) puts the ocean's share of the extra heat stored in the climate system, 1971 to 2018, at 91%; land warming, ice melt and the air took about 5%, 3% and 1%. The air temperature we feel is the thin top of a very large heat store. That heat store has a clock. Surface water is mixed to depths of tens to hundreds of metres within years. Dense, cold, salty water sinks in the North Atlantic and around Antarctica and works its way along the deep ocean in a circuit of roughly a thousand years. Warm the surface, and the deep ocean takes centuries to catch up. This lag is why the planet is committed to more warming than has happened yet (the IPCC calls ocean warming "irreversible on centennial to millennial time scales"). Interactive · Where does the extra heat go? Energy imbalance at the top of the atmosphere Years Ocean layer that takes the heat Share going into the ocean Earth's area 5.101×1014 m², ocean 71% of it, seawater 1025 kg/m³ and 3990 J/kg/K, air 5.15×1018 kg at 1004 J/kg/K. The default 0.89 W/m² is Forster et al.'s estimate for 2005–2024; the share is the IPCC's 91%. A uniform layer is a simplification: real warming is concentrated near the surface. With the defaults, ten years of imbalance adds about 143 zettajoules, and a 2,000 m layer taking 91% of it warms by only about 0.04 °C. A small number on a thermometer is an enormous quantity of heat. Ice is the other heat bank. Greenland's ice would raise the sea about 7 metres if it all melted, and Antarctica's about 58 metres; neither is expected to vanish soon, but the sea has already risen about 0.20 m from 1901 to 2018 (IPCC), faster each decade: 1.3 mm a year early in the century, 3.7 mm a year in 2006 to 2018. Roughly half of the 1971–2018 rise came from the water expanding as it warmed, and half from melting land ice. Rock: the slow thermostat The solid Earth is a reservoir too, and the slowest. Plates of crust move a few centimetres a year, about as fast as your fingernails grow. In 1912 Alfred Wegener proposed continental drift, and it was rejected for lack of a mechanism; plate tectonics, with sea-floor spreading as the mechanism, became the mainstream view in the 1960s. Tectonics matters for climate because it runs a carbon cycle of its own. Volcanoes and ocean ridges release CO₂ from the interior. Rain, which is slightly acidic from dissolved CO₂, dissolves silicate rock and carries calcium and bicarbonate to the sea, where shellfish and plankton turn it into carbonate that sinks and is buried. The net effect removes CO₂ from the air over hundreds of thousands of years, and the process runs faster when the planet is warmer and wetter. That is a negative feedback with a very long delay, and it is the main reason the planet has stayed liveable for billions of years while the Sun grew about 30% brighter. It is also why volcanoes are not the cause of today's rise. Volcanic CO₂ is less than 1% of the CO₂ from burning fossil fuels; human emissions of roughly 40 Gt CO₂ a year dwarf the geological outgassing. The rock cycle is a slow thermostat, much too slow to cool a planet that is being warmed in decades. Deep time: Earth as a single calendar year The Earth is about 4.54 billion years old. That number defeats intuition, so geologists squeeze it into a year. Pick an event and see when it lands. Interactive · The calendar year of Earth Dates in million years ago are standard geological-timescale values and rounded estimates (earliest life and the Snowball episodes are the least precise). The calendar maps 4,540 million years onto 365 days. On that calendar, animals with shells arrive in mid-November, dinosaurs die out on 26 December, and Homo sapiens turns up in the last 40 minutes of 31 December. All of recorded history fits in the last minute. The point of the exercise is not to be impressed. It is to notice what the planet has already done. Oxygen from early photosynthesis rusted the oceans and then filled the air (the Great Oxidation, about 2.4 billion years ago). Ice reached the tropics in the Cryogenian "Snowball" episodes. Volcanic eruptions on a huge scale are linked to the end-Permian extinction, the worst the fossil record shows. About 56 million years ago a burst of carbon into the air, the Palaeocene–Eocene Thermal Maximum, warmed the planet by around 5 °C or more for tens of thousands of years; it is the best natural analogue for rapid carbon release, though it appears to have been much slower than the present rate. The last 2.6 million years are an ice-age world. The Serbian scientist Milutin Milanković worked out that wobbles in Earth's orbit and tilt change how sunlight is spread across latitudes and seasons, with beats of about 23,000, 41,000 and 100,000 years. Those wobbles are small, so something must amplify them, and ice cores show what: CO₂ moved between roughly 180 ppm in the cold phases and 280 ppm in the warm ones. Orbit sets the beat; ice, ocean and carbon amplify it. The IPCC notes that the most recent decade was warmer than the warmest multi-century period of the present interglacial, about 6,500 years ago, and that CO₂ in 2019 was higher than at any time in at least 2 million years (high confidence). The carbon cycle across timescales Carbon is the best single teacher of how reservoirs link up, because it moves on every timescale at once. Round figures for the main pools, in gigatonnes of carbon (GtC), are below. To turn carbon into carbon dioxide, multiply by 3.664. PoolGtC (approx.)Turns over in Atmosphere (about 427 ppm)about 910 (720 in 2000)years, with a long tail Land plants and soilsabout 2,000 to 2,500years to centuries Surface oceanabout 670years Deep oceanabout 36,700centuries to millennia Fossil fuels (resources)about 4,100; about 450 burned by 2020made over millions of years Sedimentary rocktens of millionshundreds of millions of years Fast: plants take up carbon and release it again, giving the seasonal wiggle. Slower: the surface ocean exchanges with the air within a year or so and mixes into the deep over centuries, and chemistry buffers it (extra CO₂ dissolving makes the sea more acidic, which the IPCC says is virtually certain to be mainly caused by human CO₂). Slowest of all: weathering and burial over hundreds of thousands of years, and tectonics over hundreds of millions. Interactive · The Keeling curve, with its breathing Year Annual means: NOAA Global Monitoring Laboratory, Mauna Loa (data downloaded November 2026). The monthly lines in the lower chart are the annual mean plus the average 2015–2025 seasonal shape, a reconstruction and not the measured months. Charles David Keeling began the record at Mauna Loa in 1958. Slide to the start of the record: 316 ppm in 1959, rising about 0.9 ppm a year in the 1960s, and about 2.4 ppm a year in the 2010s (annual means, 1960 to 1970 and 2010 to 2020). Now ask the bookkeeping question: of every tonne emitted, where does it go? Human CO₂ in 2024 was about 42 Gt (about 38.2 from fossil fuels and industry plus about 4.2 from land-use change; Forster et al., 2025). The air gained 3.76 ppm that year, which is 3.76 × 2.13 GtC per ppm × 3.664 = about 29 Gt CO₂. So about 69% stayed in the air in 2024, a high year; in 2025 the global rise fell to 2.06 ppm while energy-related emissions rose about 1.1% (Energy Institute). A swing that large with roughly flat emissions says the sinks changed, not the emissions. Land plants take up less in hot and dry years (2024 had a strong El Niño early in the year). Interactive · Where does a tonne of CO₂ go? 2024 (rise 3.76)A typical year (2.4)2025 growth (2.06) Human CO₂ that year Rise in the air Years after a one-off pulse Conversion 1 ppm = 2.13 GtC = 7.80 Gt CO₂. Rise in the air: NOAA global growth, 2024 and 2025; emissions are 2024's (Forster et al.), and 2025's total was not final when this was written, so the "2025" chip holds emissions at 2024's. The decay curve is the four-term fit of Joos et al. (2013), 0.2173 + 0.2240e−t/394.4 + 0.2824e−t/36.54 + 0.2763e−t/4.304. The second chart is the key lesson of the carbon cycle. Unlike a water molecule, a pulse of CO₂ does not simply leave with a single residence time. It spreads through ocean and land on several clocks at once, so roughly 40% of a pulse is still in the air after a century, a little over a quarter after five centuries, and about 22% is left for the very long tail that only rock weathering clears. Most of the carbon we burn is a loan with a very long repayment. That is the answer to the question "why does it matter if the sinks take up half?" The half they take is spread across the centuries. Numbers here describe how the system works; they are not forecasts, and the 2024 and 2025 figures are single years. What a graduate just sees Every reservoir has a residence time, stock divided by flux, and it sets how fast the pool responds and how long it remembers. Uneven sunlight is the engine: the tropics heat, the poles cool, and air and ocean carry heat between them. Almost all extra heat goes into the ocean, so the air temperature is the thin tip of a deep store. Volcanoes and rocks are a thermostat with a delay of hundreds of thousands of years, far too slow to offset a change made in decades. Deep time is large and eventful: Earth has been through snowballs, mass extinctions and warm spikes, and CO₂ is the common thread in the climate story. The seasonal wiggle on the Keeling curve is the Northern Hemisphere breathing; the staircase beneath it is us. A pulse of CO₂ has no single lifetime: some leaves in decades, a quarter lingers for centuries, and a fifth for ever on human timescales. Where it shows up next Climate Science (36/14) takes the energy-imbalance and carbon-pulse ideas here and builds the energy-balance model and carbon budget. Conservation & Applied Ecology (36/15) and Ecology (35/48): nutrient cycles are the same pools and fluxes with nitrogen and phosphorus. Soils, Agriculture & Food Systems (36/18): soils are the largest land carbon store and the link between the water and carbon cycles. Environmental Data & GIS (36/20): satellites and stations measure these fluxes; the Keeling record is the model for a good long-running dataset. In the world: reservoir operation, flood forecasting, monsoon forecasting for farmers in India and West Africa, carbon accounting, and the design of every climate model. If you want to go deeper 📘 Textbook. Tim Lenton, Earth System Science: A Very Short Introduction (Oxford University Press, 2016). A short, rigorous entry to the whole idea. 📘 Textbook. Kump, Kasting and Crane, The Earth System (Pearson, 3rd edition 2010). The widely used Earth-system course text, strong on cycles and feedbacks. 📘 Gentler. Bill Bryson, A Short History of Nearly Everything (2003), for deep time as a story. 🌐 Free course. MIT OpenCourseWare 1.018J Ecology I: The Earth System (Fall 2009). Also free: the IPCC AR6 WGI Summary for Policymakers, and NASA Earth Observatory. The takeaway The Earth system is a set of reservoirs joined by flows. Size divided by flux tells you how fast any pool moves; sunlight's unequal spread drives air and ocean; the ocean holds almost all the extra heat; and carbon moves on every clock from the seasons to the rock cycle. Learn the vocabulary of stocks, fluxes, residence times and feedbacks and later courses become applications of it. Try this: find any environmental figure in the news (litres of water, tonnes of waste, a pollutant in a lake) and ask what the pool is, what flux feeds and drains it, and what their ratio says about how long the effect would last. Sources & Further Reading Sources. IPCC AR6 WGI Summary for Policymakers (2021): 91% ocean heat share, sea-level figures, CO₂ at 2 million years, monsoon and aerosol statement, confidence language. NOAA Global Monitoring Laboratory, Mauna Loa annual and monthly means and global growth rates (downloaded November 2026). Forster et al., Indicators of Global Climate Change 2024, Earth System Science Data 17 (2025), for emissions and the 0.89 W/m² energy imbalance. Energy Institute, Statistical Review of World Energy 2026 (via DieselNet summary), for the 2025 emissions change. Water and carbon pools: Wikipedia, "Water cycle" and "Carbon cycle". Impulse response: Joos et al., Atmospheric Chemistry and Physics 13 (2013). Deep-time dates are standard geological-timescale values. All interactive numbers were computed in node. 🌐 IPCC AR6 WGI Summary for Policymakers 🌐 NOAA Global Monitoring Laboratory, Trends in CO₂ 🌐 MIT OCW 1.018J Ecology I: The Earth System 📘 Lenton, Earth System Science: A Very Short Introduction Step 2. General Chemistry: Electrons Decide Everything ------------------------------------------------------ Why: The chemistry under every environmental process. Every substance, from salt to proteins, is a pattern of electrons deciding to share, steal or keep their distance. Learn the pattern and the table, the shapes and the reactions start to look inevitable. Drop a pinch of salt into water and it vanishes. Drop a spoon of sugar in and it vanishes too. Yet the salt water conducts electricity and the sugar water does not, the salt can be pulled back out only by boiling the water away, and the two behave nothing alike in your cooking. Strike a match, and a stick of wood and a little powder become heat, light and smoke. Charge a phone, and something inside it moves from one side to the other and back again. A chemist looks at all of these and asks the same two questions. What are the atoms doing with their outer electrons? And where is the energy going? General Chemistry is the course that teaches you to ask those questions in your sleep. Almost every later chemistry course, and most of biology, is these two ideas applied to a bigger puzzle. The course in one box Who takes itChemistry, biology, chemical and materials engineering and pre-medical students, in year 1, almost everywhere in the world. Programmes shaped by the American Chemical Society, MIT's Course 5 or the Royal Society of Chemistry all start here. What it is forReading a formula as a picture of electrons, and predicting what will react, how much, and how much energy changes hands. Comes afterSchool algebra and physics. Calculus I (34/01) and Physics I: Mechanics (34/06) run alongside it. Leads toEquilibrium & Kinetics (35/37), Organic Chemistry: Structure & Mechanism (35/38), and through them Biochemistry (35/43) and Cell Biology (35/44). What this piece gives youYou will not be able to balance a hard redox equation under exam pressure. You will see why the periodic table has the shape it has, why a water molecule is bent, and how to turn grams into moles into energy. A kitchen-flavoured first read is The Science of Bread (14/07); for the chemistry of a battery see Batteries (29/08). This piece goes further. Atoms: the electrons are what chemistry sees An atom is a tiny nucleus of protons and neutrons with electrons around it. The nucleus almost never changes in a chemical reaction. That is the difference between chemistry and nuclear physics: chemistry is what happens when atoms trade, share or lend electrons and the nuclei stay put. (Radioactivity is the other business; Marie Curie won the 1903 Nobel Prize in Physics and the 1911 prize in Chemistry, the second for discovering radium and polonium, and her work sits on the border between them.) Electrons are not little planets. Quantum mechanics (see Quantum Mechanics, 34/83, for the real thing) says each electron occupies an orbital, a cloud-shaped region where it is likely to be found, and each orbital has a fixed energy. Orbitals come in shells numbered 1, 2, 3 and so on, and in shapes called s, p, d and f. An orbital holds at most two electrons. Fill them from the lowest energy up, and you get the atom's electron configuration. fill 1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p …lowest energy first · s holds 2, p holds 6, d holds 10 · only the outermost shell takes part in most chemistry Try it. Slide to carbon (6): 1s² 2s² 2p², so four electrons in the outer shell. Oxygen (8) has six. Sodium (11) has one, alone in a third shell. Sodium's single lonely outer electron and chlorine's seven, one short of a full eight, are why the two meet so eagerly. At 24 (chromium) and 29 (copper) you will see the table's first small exceptions: a half-full or full 3d subshell is slightly more stable than the tidy filling order predicts. Interactive · Build an atom, electron by electron Element (atomic number Z) Configurations by the Madelung filling order (1s 2s 2p 3s 3p 4s 3d 4p) with the chromium and copper exceptions; shell counts are the sum over subshells. Shells are drawn as rings for counting, not as orbits. The periodic table is a map of shell-filling In 1869 Dmitri Mendeleev presented a table that arranged the known elements by atomic weight and, crucially, left gaps where the pattern said an element should exist, and described what the missing ones would be like. The gaps were later filled by gallium, scandium and germanium. The modern table is the same idea, ordered by atomic number, and now we know what the rows are: each row is a shell filling up, and each column holds atoms with the same number of outer electrons, which is why they behave alike. (Mendeleev was not the only person to see the pattern; Lothar Meyer published a similar one around the same time. Mendeleev's gift was trusting the pattern enough to predict.) Three trends do most of the work, and one picture explains all three. An outer electron feels the nucleus's pull, partly cancelled by the electrons between. Move across a row and the nuclear charge grows while the new electrons go into the same shell, so the pull gets stronger and the atom shrinks. Move down a column and a whole new shell is added, so the atom is bigger and its outer electron is easier to remove. Interactive · Periodic trends from real data Ionisation energy Electronegativity Covalent radius Highlight element Data: first ionisation energies in kJ/mol from the NIST Atomic Spectra Database values (via Wikipedia's data page); Pauling electronegativities; covalent radii from Cordero et al., Dalton Trans. 2008 (carbon sp3; Mn, Fe, Co low-spin). Noble gases He, Ne and Ar have no Pauling value. Look at the ionisation energy plot: a sawtooth. Each peak is a noble gas, whose shell is full and which holds its electrons tightly; each trough is the alkali metal that follows, with one electron far out in a new shell. Sodium needs about 496 kJ per mole of electrons to lose one, neon needs 2081. That sawtooth is why sodium is violently reactive and neon is not reactive at all. Everything about metals, nonmetals and the families in between falls out of it. Bonds: a tug-of-war for electrons Atoms bond because the shared or transferred arrangement has lower energy than separate atoms. Which kind of bond forms depends on how unevenly the atoms pull. Electronegativity is a number for an atom's pull on the electrons it shares; Linus Pauling's scale runs from 0.82 for potassium to 3.98 for fluorine. If two atoms pull almost equally (hydrogen with hydrogen), the electrons are shared: a covalent bond. If one pulls vastly harder (chlorine versus sodium), it takes the electron outright, and the two resulting ions, one plus and one minus, stick together by plain electrical attraction: an ionic bond. In between lies the common case, the polar covalent bond, where the electrons are shared but sit closer to one atom. Water's O–H bond is the standard example. Δ(electronegativity) small → covalent · middling → polar covalent · large → ionic-likerough textbook cut-offs near 0.4 and 1.7. They are a guide, not a law: bonding is a continuum Interactive · What kind of bond? Na–Cl H–Cl O–H C–H H–H Na/Mg Atom A Atom B Pauling values (Z = 1 to 36, noble gases He, Ne and Ar omitted). Two metals are labelled metallic instead. The result matters outside the lab. Salt dissolves in water because water's polar O–H bonds make its oxygen end slightly negative and its hydrogen ends slightly positive, and those poles pry ions out of the crystal. Oil and water do not mix because oil has no poles to grip. "Like dissolves like" is bond polarity in one sentence. Shape: electron pairs repel, and that sets the geometry A molecule is not a flat diagram. Water is bent, not straight; ammonia is a little pyramid. One rule predicts most of it, the VSEPR rule (valence-shell electron-pair repulsion). Count the electron domains on the central atom, meaning each bond (single, double or triple counts as one) and each lone pair, since each domain is a cloud of negative charge. They repel, so they spread as far apart as they can on a sphere: two domains sit 180° apart, three at 120°, four at 109.5°, five and six in the arrangements below. The molecule's shape is then the arrangement of the atoms only; the lone pairs are invisible in the name but they still take up room. That is why water is bent: oxygen has four domains (two bonds and two lone pairs), arranged like a tetrahedron, but only two corners hold atoms. Lone pairs are slightly bulkier than bonds, so they squeeze the angle: 109.5° in methane, about 107° in ammonia, about 104.5° in water. Water's bend is why it is polar and why ice floats, which is why lakes freeze from the top down. Interactive · Build a molecule's shape CH₄ NH₃ H₂O CO₂ SF₆ XeF₄ Bonded atoms Lone pairs on the centre Directions are the ideal geometry for each number of domains; lone pairs fill the equatorial positions first in the five-domain case and opposite positions in the six-domain case, as VSEPR prescribes. Angles are textbook values; real molecules deviate by a few degrees. The tool stops at six domains (the common textbook range). The mole: counting atoms by weighing You cannot count atoms, but you can weigh them, and the mole turns one into the other. A mole is a fixed number of things, exactly 6.02214076 × 10²³ since the 2019 redefinition of the SI. The point of choosing that number is that one mole of any element weighs, in grams, its atomic weight: carbon about 12.011 g, oxygen 15.999 g (the IUPAC standard atomic weights, rounded). So grams become moles by dividing by the atomic or molar weight, and a balanced equation is a recipe in moles. C₃H₈ + 5 O₂ → 3 CO₂ + 4 H₂Oone mole of propane needs five moles of oxygen · the equation balances atoms, so mass in = mass out A worked number. One mole of propane (the gas in a camping stove) weighs 3 × 12.011 + 8 × 1.008 = 44.097 g. It needs five moles of oxygen, 159.99 g, and produces three moles of carbon dioxide (132.03 g) and four of water (72.06 g). In: 204.09 g. Out: 204.09 g. Nothing is lost. If there is less oxygen than five to one, the oxygen is the limiting reagent: the reaction stops when it runs out, some propane is left, and (in a real stove) you get soot and poisonous carbon monoxide, the reason you never burn a stove indoors without ventilation. Because air is about 21% oxygen, burning a volume of propane needs roughly 24 volumes of air. Interactive · Who runs out first? Propane Oxygen Molar masses from the IUPAC abridged standard atomic weights (C 12.011, H 1.008, O 15.999). Assumes complete combustion to CO₂ and H₂O. Energy in reactions: breaking costs, making pays Why does propane burn and release heat? Because the products' bonds are stronger than the reactants'. Breaking a bond always costs energy, since you pull two atoms against their attraction. Making a bond always releases it. A reaction's energy change is the bill for breaking all the old bonds minus the payment for making all the new ones. If you get paid more than you spent, heat comes out: exothermic. Otherwise it must be supplied: endothermic. ΔH ≈ (energy to break bonds) − (energy released making bonds)average bond enthalpies are estimates: they differ a little between tables and between molecules Methane burning: break four C–H and two O=O (2648 kJ), make two C=O and four O–H (3450 kJ), net −802 kJ per mole: exothermic. The measured value is −802.5. That match is partly luck, since the numbers are averages over many molecules, as the hydrogenation of ethene (−123 estimated against −136 measured) shows. Interactive · Bond ledger H₂ + Cl₂ CH₄ burning N₂ + H₂ Ethene + H₂ Average bond enthalpies in kJ/mol as in common textbook tables (the LibreTexts table lists e.g. C–H 415, H–Cl 432; C=O is the value for CO₂). Measured ΔH from standard enthalpies of formation, gaseous water. N₂ + 3H₂ → 2NH₃ is the Haber reaction (measured −92.28 kJ per mole of N₂ is the quoted standard value). Acids and bases: who gives up a proton An acid, at this level, is a molecule that hands a hydrogen ion (a proton) to water; a base takes one. The strength of an acid is not about how concentrated it is but about how readily it lets go. A strong acid such as hydrochloric acid gives up essentially all its protons. A weak one such as the acetic acid in vinegar gives up only a small fraction, which is why vinegar is safe to put on a salad and the same concentration of hydrochloric acid is not. The pH is minus the base-10 logarithm of the hydrogen-ion concentration, so each step down in pH is ten times more acidic. Worked number: 0.1 M hydrochloric acid has pH 1.00. 0.1 M acetic acid, with an acid constant of 1.75 × 10⁻⁵ (pKa 4.76), has pH 2.88, and only about 1.3% of its molecules have let go. Dilute it a thousand times and the fraction rises to roughly a third, an early hint of the equilibrium ideas of Equilibrium & Kinetics (35/37). And dilute even a strong acid to 10⁻⁸ M and the pH is 6.98, not 8: water itself supplies hydrogen ions, and you cannot make an acid into a base by adding water. Interactive · Strong versus weak Strong acid Acetic acid (vinegar) Concentration Solved exactly from the charge balance [H+] = [A-] + [OH-] with Kw = 10-14 and Ka = 10-4.756 for acetic acid at 25 °C. Ideal solution (activities ignored). What a graduate just sees A formula is an electron story: count the outer electrons first and the bonding follows. Position on the periodic table predicts size, reactivity and bond type; you rarely need to look anything up. Atoms bond to lower their energy, and unequal pulls make polar bonds, which make water, soap and proteins behave as they do. Count the electron pairs around an atom and you know the shape of the molecule. Equations are recipes in moles, not grams; the limiting reagent decides what you get. Atoms are neither created nor destroyed: if the equation does not balance, something is missing. Breaking bonds costs, making bonds pays, and the difference is the heat of the reaction. Strong is not concentrated: strength is how readily an acid lets go, concentration is how much you have. Where it shows up next Equilibrium & Kinetics (35/37): the weak acid you just met is the first reaction that does not go to completion, and the next course asks how far and how fast. Organic Chemistry (35/38): carbon's four bonds, the shapes above and electronegativity are the whole starting kit for curly arrows. Biochemistry (35/43): proteins fold because of polar bonds, water and pH; DNA holds together by hydrogen bonds you can now name. In the world: the lithium-ion battery in your phone (see Batteries, 29/08), fertiliser made from the Haber reaction, the reason a camping stove must be ventilated, and the pH label on a shampoo bottle. If you want to go deeper 📘 Free textbook. OpenStax, Chemistry 2e (Flowers, Theopold, Langley, Robinson et al.; free to read online, 2019). A full first-year course with worked problems. openstax.org 📘 Textbook. Brown, LeMay, Bursten, Murphy, Woodward and Stoltzfus, Chemistry: The Central Science (Pearson). One of the two or three books most universities assign, strong on the visuals. 📘 Gentler. Primo Levi, The Periodic Table (1975): twenty-one memoir chapters, each named for an element, by a chemist who survived Auschwitz. No equations, much meaning. 🌐 Free course. MIT OpenCourseWare 5.111 Principles of Chemical Science (Fall 2008): lectures on atoms, bonding, equilibrium and acids. The takeaway Chemistry is electron bookkeeping and energy bookkeeping. An atom's outer electrons set its place on the table, how it bonds and what shape its molecules take; the mole lets you weigh your way into those counts; and the balance between breaking and making bonds says whether a reaction gives heat or takes it. Try this: this week, look at the back of a food label or a bottle of vinegar and find one chemical name. Write its formula and count its outer electrons. (Kitchen-safe, and no mixing needed: just a pen.) Sources & Further Reading Sources. Electron configurations, VSEPR, the mole, bond enthalpies and pH are standard first-year textbook chemistry (OpenStax Chemistry 2e). Pauling electronegativities, first ionisation energies (NIST Atomic Spectra Database) and Cordero covalent radii (Dalton Trans. 2008, 2832) as tabulated on Wikipedia's data pages. Mendeleev presented his table to the Russian Chemical Society in 1869 (Wikipedia, Dmitri Mendeleev). Marie Curie: Nobel Prizes in Physics 1903 and Chemistry 1911 (nobelprize.org via Wikipedia). SI mole redefinition 2019 (BIPM). This is a textbook summary, not laboratory instruction. Go deeper. 🌐 OpenStax Chemistry 2e 🌐 MIT OCW 5.111 Principles of Chemical Science 📘 Primo Levi, The Periodic Table Step 3. Probability & Statistics: Reasoning with Uncertainty ------------------------------------------------------------ Why: The statistics behind every measurement and trend. Nothing you measure is exact, and no part comes out the same twice. Statistics is the discipline of knowing how much to trust a number. A machinist turns a hundred steel shafts to "10 millimetres". Measure them with a good micrometer and no two are the same: 9.981, 10.012, 10.004. Nothing is wrong. That scatter is a fact of every process, every material and every sensor. Now stack five of those parts end to end in a gearbox. Will the stack still fit the housing? A pollster calls a thousand people and says 52% will vote yes, give or take three. A drug trial says "significant". A forecast says 30% chance of rain. Every one of these is the same question: given scatter, how much should I trust this number? A graduate of probability and statistics doesn't see a single number any more. They see the shape of the scatter behind it. This piece builds that sight with eight things you can run: dice, tolerances, polls, a drug-trial trap, a belief that updates, and a gearbox stack. The course in one box Who takes it: almost every engineering and science student, usually in the second year; computer scientists meet it again before machine learning. What it's for: deciding what to believe, and how far to trust a measurement, when outcomes are uncertain. Comes after: Calculus I (34/01), which helps with continuous distributions, though the ideas here need little more than arithmetic. Leads to: Machine Learning (34/32) needs it directly. It also shows up in Materials Science & Manufacturing (34/13: process control and defects), Systems Engineering (34/22: reliability) and Computer Security (34/33: randomness and guessing). Honest line: you won't be able to design a clinical trial after this. You will see why "significant" doesn't mean "important", why a bigger sample beats a cleverer guess, and why most real quantities look like a bell curve. For easier first reads, see the library's Probability: How to Not Fool Yourself (12/03), Statistics for Reading the World (12/05) and Bayes' Theorem (12/17); this piece goes further into the engineering side. Random variables: a shape with a centre and a spread A random variable is a number that comes out of a process you can't predict one run at a time. The key move is to stop asking "what will it be?" and ask "what is the shape of what it could be?" Roll two dice and add them: 7 is six times as likely as 2 or 12, so the shape is a tent. Roll many times and the tent appears. Interactive · Roll dice, grow a shape Dice added together Roll 10 timesRoll 1,000 timesClear Without JavaScript: two dice add to 7 with probability 6/36 and to 2 or 12 with probability 1/36 each. The mean total is 7 and the standard deviation is about 2.42. Two numbers summarise a shape. The mean is its balance point: 7 for two dice. The standard deviation (the "spread") says how far values typically stray from the mean: about 2.4 for two dice, which means totals usually land between roughly 5 and 9. The variance is the standard deviation squared, and it is the one that adds up neatly when you combine independent things. standard deviation = √( average of (value − mean)² ) Now the shape that matters most. Measured quantities (shaft diameters, heights, sensor noise) tend to form the normal curve, the bell. Its great convenience is a fixed rule: about 68.3% of values fall within one standard deviation of the mean, 95.4% within two, and 99.7% within three. Engineers use it every day. Say the shaft's spec is 10.00 mm ± 0.05 mm. Slide the process around and see what share of parts get thrown away. Interactive · How many parts fail the spec? Average diameter Spread (standard deviation) Without JavaScript: a centred process with standard deviation 0.025 mm (the spec limits are exactly ±2 standard deviations) scraps about 4.55% of parts. Cut the spread to 0.01 mm and about 0.00006% are scrapped. Shift the average 0.02 mm off-centre with spread 0.02 mm and about 6.7% are scrapped. Two lessons graduates keep. First, spread, not average, decides quality: a process centred perfectly but wide still scraps parts. Second, being off-centre costs a lot even when the spread is fine. That is why factories track both. The central limit theorem: why the bell keeps appearing Why should so many things be bell-shaped? The answer is one of the most useful theorems in mathematics. Take almost any random process, however lopsided, and average a few dozen independent draws. The averages pile up in a bell, centred on the true mean, with spread shrinking like 1/√n. Early forms are due to de Moivre in 1733 (for coin flips) and Laplace, whose general version dates from about 1810. Pick a lopsided source and drag the sample size. Interactive · Average anything, get a bell Flat (0 to 1) Very lopsided Coin (0 or 1) Draws averaged together: n Without JavaScript: for the lopsided source (mean 1, standard deviation 1) the average of n = 30 draws has standard deviation 1/√30 = 0.183, and the 3,000 averages form a close-to-normal bell around 1. At n = 1 you see the raw source. By n = 30 even the lopsided one is a near-bell. The prediction (the curve) uses only two numbers from the source, its mean and its standard deviation. The shape of the source is forgotten. That is why a measurement made of many small independent errors is normal, and why so much of statistics can pretend things are bell-shaped. standard error of an average = σ / √n In words: the average of n draws wobbles less than one draw, by the square root of n. To halve the wobble you need four times the data, not twice. It is the quietest expensive fact in all of experimental science. Sampling and confidence intervals: how sure is a poll? You can't ask everyone, so you ask n people and treat the share saying yes as an estimate. How far off might it be? The standard error from the last section gives the answer. For a share p the wobble is √(p(1−p)/n), and a 95% confidence interval is the estimate plus and minus about two of those. For n = 1,000 and a share near half, that is ±3.1 percentage points: the familiar "margin of error". The wording is subtle, and the interactive makes it concrete. "95% confidence" is a statement about the method, not about one interval: if you ran the procedure again and again, about 95 intervals in 100 would capture the true value. Here the truth is secretly 52%. Run 100 polls. Interactive · 100 polls, one truth People asked in each poll Run 100 polls Without JavaScript: with 1,000 people per poll the margin of error is about 3.1 points; run 100 polls and about 95 of the intervals cover the true value. With 4,000 people the margin halves to about 1.5 points. Watch two things. Roughly five in a hundred intervals miss the truth even when everything is done correctly. And quadrupling the sample from 1,000 to 4,000 only halves the interval. A poll of a country and a poll of a town need the same sample size for the same precision, as long as the sample is random. The real danger is not the margin of error; it is a sample that isn't random at all, which no formula fixes. P-values and Bayes: two ways to weigh evidence A hypothesis test asks whether data are surprising if nothing is going on. The p-value is the probability, assuming nothing is going on, of seeing a result at least as extreme as yours. Flip a coin 100 times and get 60 heads: for a fair coin the chance of a split at least that lopsided in either direction is about 5.7%. It is not the probability that the coin is fair, and it is not the probability that the result was "due to chance". The American Statistical Association issued a rare formal statement on this in 2016, with six principles. Two of them: p-values do not measure the probability that a hypothesis is true, and a p-value does not measure the size or importance of an effect. The classic trap is testing many things. At the usual cut-off of 0.05, a test of a true "nothing" comes out "significant" one time in 20 by luck. Test twenty unrelated things and the chance that at least one lights up is 1 − 0.9520, about 64%. Try it: each press tests twenty effects that are, by construction, nothing. Interactive · Test twenty things that do nothing Run 20 testsReset the tally Without JavaScript: twenty tests of pure noise at the 0.05 level give at least one false "discovery" about 64% of the time, and one in 20 tests on average. If you report only the one that lit up, you have a headline and no finding. This is part of why many published results fail to repeat: in the Open Science Collaboration's 2015 attempt to replicate 100 psychology studies, 97% of the originals had statistically significant results but only 36% of the replications did. Bayes' rule answers a different question: given the data, how should my belief move? Start with a prior belief, multiply by how well each possibility explains the data, and renormalise. Say you test parts and want the defect rate. Know nothing at first (any rate from 0% to 100% equally likely) and add parts one at a time. Interactive · Learn a defect rate from parts Add a good partAdd 10 good partsAdd a defective partReset Without JavaScript: after 20 good parts and no defects, a flat starting belief gives a most-plausible defect rate near 0%, an average of 4.5%, and a 90% credible range of roughly a quarter of a percent to 13%. Twenty clean parts cannot rule out a defect rate near one in eight. Frequentists and Bayesians disagree about the philosophy: one treats probability as long-run frequency and never assigns it to a hypothesis, the other as degrees of belief that data update. In practice both are used, often on the same project, and on big data sets they usually agree. The Bayesian version has one practical advantage here: after twenty clean parts it honestly says "we still can't rule out one in eight". Correlation, regression and the trap of causation Correlation (called r) measures how tightly two quantities move together along a straight line, from −1 to +1. Regression fits the best line through the cloud (by least squares, as in Linear Algebra, 34/04). Both are summaries, and any summary can hide the story. In 1973 the statistician Francis Anscombe made four data sets with, to two decimals, the same mean, the same spread, the same r (0.82) and the same line (y = 3 + 0.5x). Look at each. Interactive · Four data sets, one set of numbers Set 1Set 2Set 3Set 4 Without JavaScript: all four Anscombe sets have mean x = 9, mean y = 7.50, correlation 0.816 and line y = 3.00 + 0.50x. Set 1 is a noisy line, set 2 a curve, set 3 a line with one outlier, and set 4 a single far point that creates the whole slope. The numbers agree and the stories do not: one noisy line, one curve, one line with a rogue point, one vertical stack held up by a single point. Always plot first. The other trap is the famous one. Ice-cream sales and drownings rise together, because summer heat drives both. A confounder (a hidden third factor) makes two things move together without either causing the other. The remedy graduates know is randomised assignment: if a coin decides who gets the treatment, nothing else can be systematically linked to it. Where you can't randomise, causal claims need much more than a line through a cloud. Engineering: tolerance stacks, reliability and Monte Carlo Five parts, each 10 mm ± 0.1 mm, line up in an assembly. What is the worst the total can be out? Worst-case stacking adds the tolerances: ±0.5 mm. It is safe and expensive, because it assumes every part is at its extreme in the same direction at once. If the parts vary independently, variances add, so the standard deviations add in quadrature: root-sum-square, √5 × 0.1 = ±0.224 mm. For five parts that is under half the worst-case figure. When the formulas get hard, engineers use Monte Carlo: let the computer build the assembly ten thousand times with random parts and count how often it fails. Here each part's tolerance is treated as three standard deviations. Choose how many parts are stacked. Interactive · Monte Carlo tolerance stack Parts in the stack Build 10,000 assemblies again Without JavaScript: five parts at ±0.1 mm (three standard deviations) give a worst-case limit of ±0.5 mm, a root-sum-square limit of ±0.224 mm, and in simulation only about 0.3% of assemblies exceed the root-sum-square limit; none come close to 0.5 mm. The honest caveat is that root-sum-square assumes the parts vary independently and are centred. A tool wearing in the same direction on every part breaks that assumption, and so does one supplier's batch. Engineers disagree about when to trust statistical stacking over worst-case; safety-critical designs often insist on worst-case. Reliability follows the same arithmetic. A system that needs all of its parts is a series system, and probabilities multiply: ten components that each work 99% of the time give 0.9910 ≈ 90.4% for the whole. Add a backup in parallel and failure needs both to fail: two units that each work 90% of the time give 1 − 0.1² = 99%. The two rules drive why aircraft duplicate systems and why complicated machines need very reliable components. What a graduate just sees Every number has a spread behind it; the first question is "how scattered?", not "what is it?". Spread, not the average, decides how many parts are scrapped, and centring matters too. Averages of many independent things are bell-shaped, whatever the source looked like. Halving the uncertainty costs four times the data. A 95% interval is a claim about a method: it misses one time in twenty by design. A p-value is "how surprising is this if nothing is going on", not "how likely is it true". Test twenty things and one will look significant; ask how many were tried. Plot the data; correlation is not causation, and only randomising breaks a confounder. Independent errors add in quadrature; series reliabilities multiply. Where it shows up next Machine Learning (34/32): training is fitting a model to noisy data; ideas of overfitting, error bars and Bayes are this course made bigger. Materials Science & Manufacturing (34/13): process capability and scrap rates are the normal curve against a spec limit. Mechanics of Materials (34/11) and Machine Design (34/19): safety factors exist because loads and strengths are distributions, not numbers. Systems Engineering (34/22): reliability budgets multiply series probabilities and add redundancy to push them back up. Computer Security (34/33) and Algorithms (34/24): good random numbers, randomised algorithms, and the odds of guessing a secret. If you want to go deeper 📘 Douglas Montgomery and George Runger, Applied Statistics and Probability for Engineers (Wiley; 7th edition). The standard engineering course text, with plenty of tolerance, quality and reliability problems. 📘 Joseph Blitzstein and Jessica Hwang, Introduction to Probability (CRC Press; 2nd edition, 2019). Best for deep intuition about probability itself, from Harvard's Stat 110. 📖 David Spiegelhalter, The Art of Statistics (2019): the most readable route for learning alone, built around real cases and honest about uncertainty. 🌐 MIT OpenCourseWare 18.05, Introduction to Probability and Statistics (Spring 2022): free notes and problem sets, with Bayesian and classical statistics side by side. The takeaway Nothing you measure is exact, so every number is a shape. Summarise a shape by its centre and its spread, trust averages more as the square root of the sample, read a confidence interval as a promise about a method, treat a p-value as a measure of surprise, and plot before you believe a correlation. Try this: next time you see a poll or a "significant" headline, find the sample size and ask how many things were tested. Then, in the dice widget above, add four dice and watch the tent turn into a bell. Sources & Further Reading Sources. The normal-curve rule (68.3%, 95.4%, 99.7%), the central limit theorem, confidence intervals, the binomial test, the Beta posterior, root-sum-square stacking and series/parallel reliability are standard textbook results (Montgomery and Runger; MIT 18.05); every number shown was recomputed in code. Wasserstein and Lazar, "The ASA's Statement on p-Values: Context, Process, and Purpose", The American Statistician (2016). Open Science Collaboration, "Estimating the reproducibility of psychological science", Science (2015): 97% of originals significant against 36% of replications. Anscombe, "Graphs in Statistical Analysis", The American Statistician (1973). Early forms of the central limit theorem: de Moivre (1733) and Laplace (c. 1810), as surveyed in recent histories such as Ulyanov, "From classical to modern central limit theorems" (arXiv 2405.19828). Go deeper. The books and course above; Wasserstein and Lazar's statement is free and short (doi.org/10.1080/00031305.2016.1154108). Step 4. Climate Science: A Heat Balance Sheet for the Planet ------------------------------------------------------------ Why: The greenhouse effect, feedbacks, the carbon budget and what models can tell us. A climate scientist keeps one ledger: energy in from the Sun, energy out as infrared, and what the difference does to the temperature. Nearly everything in the field, from the greenhouse effect to the carbon budget, is that ledger with more detail. Here is a number that sums up the problem. In 2025 the global average surface temperature was about 1.37 °C above the 1850–1900 level because of human activity, according to the annual "Indicators of Global Climate Change" update (reported in June 2026), and it is rising by about 0.27 °C each decade. At today's emissions, the remaining carbon budget for holding warming to 1.5 °C was estimated in the 2025 edition at about three years' worth. A budget in years, a trend in tenths of a degree per decade: those are the outputs of a very small set of ideas. This piece builds them from the bottom: a planet as one equation, the push from CO₂, the feedbacks that triple it, the ocean's delay, and the running total called the carbon budget. It ends with how the IPCC speaks about certainty, because reading a climate report means reading that language. This is the science. What societies should do with it is a question of values and trade-offs and is argued elsewhere in this major. The course in one box Who takes itEnvironmental, Earth and atmospheric science students, usually in year 2, and anyone in physics, economics or policy who wants the numbers behind the headlines. Programmes in the UK subject benchmark tradition and the interdisciplinary cores at Stanford and Yale all teach it, with the IPCC Sixth Assessment Report (2021–23) as the shared reference. What it is forExplaining why the climate changes, by how much, and how sure we are. Comes afterEarth Systems (36/13). The physics of the greenhouse effect is covered more gently in The Physics of the Greenhouse Effect (13/15), which is a good first read. Leads toEnergy Systems & Transitions (36/16), Environmental Economics & Policy (36/19) and Environmental Data & GIS (36/20). What this piece gives youYou will not be able to run a climate model. You will be able to build a one-equation planet, see why feedbacks give a lopsided range of warming, read a carbon-budget claim, and parse "very likely" and "high confidence". A planet as one equation Put the planet in a box. Sunlight comes in; the planet reflects some (its albedo, about 0.30) and absorbs the rest, spread over a sphere, which is a quarter of the area that faces the Sun. It must radiate the same amount out as infrared. The greenhouse gases make the planet a less efficient radiator, which we can represent with an effective emissivity ε less than 1. S(1 − α) ÷ 4 + F = ε σ T⁴S = 1361 W/m² · α = albedo · F = extra forcing · σ = 5.67×10⁻⁸ · T = surface temperature in kelvin Set ε = 1 (no greenhouse effect) and the planet sits at 255 K, which is −18 °C. Set ε to about 0.612 and you get 288 K, which is about 15 °C: the actual average. That single "knob" is the greenhouse effect. A forcing F, such as extra CO₂, is added on the left, and the temperature rises until the right-hand side catches up. Extra CO₂ gives a forcing that grows with the logarithm of the concentration: F = 5.35 × ln(C ÷ C₀) W/m², where C₀ is the pre-industrial 280 ppm. Doubling gives 3.7 W/m² from this formula; the IPCC's more detailed assessment of the effective radiative forcing of a doubling is 3.93 ± 0.47 W/m². At the 2025 annual mean of 427.35 ppm (NOAA, Mauna Loa) the formula gives 2.3 W/m². Interactive · One-equation planet Today (427 ppm)Doubled (560)No greenhouse (ε = 1)Brighter planet Albedo α Effective emissivity ε CO₂ concentration Zero-dimensional model with S = 1361 W/m² and σ = 5.670374×10−8. The forcing is added to absorbed sunlight, F = 5.35 ln(C/280); the model has no feedbacks. The curve is the radiated heat εσT⁴; the planet settles where it crosses the dashed line. Move the CO₂ slider from 280 to 560 and the model warms by 1.1 °C. That is the "no feedback" answer, set by how steeply a planet's radiation climbs with temperature (about 3.3 W/m² for each degree). It is almost exactly what the IPCC calls the Planck response, −3.22 W/m² per °C. If that were the whole story, doubling CO₂ would warm the planet by about 1.2 °C. It isn't, for the next reason. Feedbacks: why 1.2 °C becomes about 3 °C Warm the planet and other things change, and some of them change the energy balance again. The IPCC (AR6, Chapter 7) assesses the main ones, each as a number in W/m² per °C. A positive number amplifies warming. FeedbackBest estimateWhy Planck (warmer = radiates more)−3.22The stabiliser; always negative Water vapour + lapse rate+1.30Warmer air holds more vapour, itself a greenhouse gas Surface albedo+0.35Ice and snow melt, darker surface absorbs more Clouds+0.42 (−0.10 to +0.94)The largest uncertainty; depends on cloud height and type Net−1.16 (likely −1.54 to −0.78)Still negative, so the climate is stable, but the Planck response is multiplied by about 2.8 The equilibrium temperature rise for a doubling of CO₂ is the equilibrium climate sensitivity (ECS): ECS = forcing ÷ (−net feedback). Because the net feedback sits in the denominator, a small change in it makes a large change in ECS, and the uncertainty is lopsided. The AR6 assessment combines process understanding, the historical record, paleoclimate evidence and models into a best estimate of 3 °C, likely 2.5 to 4 °C, very likely 2 to 5 °C. This narrowed the old 1.5 to 4.5 °C range that stood for decades. Interactive · The feedback ledger AR6 best estimatesWeak cloudsStrong cloudsNo water vapour Water vapour + lapse rate Surface albedo Clouds Planck fixed at −3.22 W/m² per °C; forcing for doubled CO₂ 3.93 W/m² (IPCC AR6 Chapter 7, Table 7.10 and Table 7.4). Adding the AR6 feedbacks gives ECS of about 3.4 °C; AR6 notes the process-based net feedback is slightly less negative than the value implied by the overall ECS assessment, which is why the headline figure is 3 °C. Values past the last slider setting here are not assessed. Across the IPCC's likely range for the cloud feedback (+0.12 to +0.72) ECS moves from about 2.7 to 4.6 °C; remove the water vapour feedback and the sensitivity falls to about 1.6 °C. Cloud feedback is the largest source of uncertainty; the combined water-vapour and lapse-rate feedback is the largest single contributor to the warming. A caution from the IPCC: some CMIP6 climate models have a higher sensitivity than the assessed range, traced mainly to a stronger amplifying cloud feedback, and AR6 therefore does not simply average the models; it constrains its projections with observations. The ocean's delay: transient versus equilibrium The ECS is where the planet ends up after centuries. The warming we meet in a lifetime is less, because the ocean is still absorbing heat (see Earth Systems, 36/13). The transient climate response (TCR) is the warming at the moment CO₂ has doubled in a standard experiment where it rises 1% a year, about year 70. The IPCC's best estimate is 1.8 °C, likely 1.4 to 2.2 °C, below the ECS of 3 °C. A simple model captures it: a thin upper layer (air, land, the top of the ocean) exchanges heat with a huge deep ocean. Try it. Choose when the CO₂ stops rising. Interactive · Two-layer planet: stop the CO₂ and watch Stop at 1.5×Stop at 2×Stop at 3× Equilibrium sensitivity ECS Two-layer energy balance: upper layer 8 W·yr/m²/K, deep ocean 100, heat exchange 0.7 W/m²/K (illustrative values near published fits), forcing 3.93 W/m² per doubling, CO₂ rising 1% a year until the chosen multiple, then held constant. Stepped at 0.1 years. With ECS 3 °C the model warms about 2.0 °C at year 70 (the TCR; the IPCC's assessed value is 1.8 °C), but if CO₂ is merely held at that level the planet keeps warming for centuries, reaching about 2.7 °C by year 300, because the deep ocean is still catching up. Holding a concentration constant is not the same as stopping emissions. When emissions stop, the ocean and land keep pulling CO₂ out of the air. The IPCC concludes that achieving net zero CO₂ emissions, with non-CO₂ forcing declining, would be sufficient to prevent additional human-caused warming. The carbon budget: warming is a running total Here is the idea that turns the climate problem into a countdown. For CO₂, the warming is roughly proportional to the cumulative amount emitted, no matter how fast. The IPCC assesses each 1,000 gigatonnes of CO₂ to add 0.45 °C (likely range 0.27 to 0.63 °C), the TCRE, with high confidence in the near-linear relationship. It follows that to stop warming at any level you must reach net zero CO₂, and that any chosen limit comes with a fixed total, a remaining carbon budget. Limit (50% chance)IPCC AR6 budget from 1 Jan 2020 1.5 °C500 Gt CO₂ (400 for a 67% chance) 1.7 °C850 Gt CO₂ 2.0 °C1,350 Gt CO₂ (1,150 for a 67% chance) Human CO₂ is about 42 Gt a year (2024: about 38.2 from fossil fuels and industry plus about 4.2 from land use; Forster et al., 2025). Those AR6 budgets were set at the start of 2020. The annual update by Forster and colleagues re-bases them each year with new data: its 2025 edition put the 1.5 °C budget at about 130 Gt CO₂ from the start of 2025 (central estimate, 50% chance), a little over three years at current emissions. A June 2026 update was reported as showing the 1.5 °C budget gone in about three years and the 1.7 °C budget in about 12; those figures come from a news report, so check the latest edition of the paper. Interactive · Carbon-budget countdown 1.5 °C (Forster 2025)1.5 °C (AR6)1.7 °C (AR6)2 °C (AR6) Budget Emissions in the first year Change in emissions each year Budgets: IPCC AR6 SPM Table SPM.2 (from 1 Jan 2020, 50% chance) and Forster et al. 2025 (from 1 Jan 2025). Emissions: total CO₂ 2024, 42.4 Gt (38.2 fossil + 4.2 land use). The AR6 presets start at 42.4 for simplicity, not at 2020's actual emissions. A projection of arithmetic, not a forecast. Play with the sliders and a hard fact appears. Even if emissions fell by 7% a year from the start of 2025 (faster than the roughly 5% fall of the 2020 pandemic year), the sum of all future emissions would be about 600 Gt: far more than 130. To stay inside the 130 Gt budget, emissions would have needed to drop by about a third every year from the start of 2025. That is why climate scientists talk about overshoot: crossing the level and then using net-negative emissions to come back. It is also why the budget is an estimate with wide error bars, not a cliff. The AR6 table alone carries uncertainty of about ±550 Gt for historical warming and ±220 Gt for non-CO₂ gases, so the same limit can be read as a smaller or larger total. What has been measured, and what has not The measured record is where the theory meets the thermometer. Each figure below carries its date. Warming. IPCC AR6: 1.09 °C [0.95 to 1.20] above 1850–1900 in 2011–2020; the human-caused part for 2010–2019 was 1.07 °C [0.8 to 1.3], so almost all of it. In 2024, a record year, the observed value was 1.52 ± 0.13 °C, of which 1.36 °C was attributed to human activity (Forster et al., 2025). The 2015–2024 mean was 1.24 °C. The 2026 update reported 1.37 °C of human-induced warming in 2025. Rate. Human-induced warming rose at about 0.27 °C per decade over 2015–2024. Heat. The Earth's energy imbalance averaged 0.89 W/m² over 2005–2024 (0.79 for 2006–2018 in the IPCC, 0.50 for 1971–2006); the 2025 authors say the rate of heating has roughly doubled since the 1970s and 1980s. Sea level. Up about 0.20 m from 1901 to 2018 (IPCC); about 26 mm more in 2019–2024 alone (Forster et al.), more than double the long-run rate. CO₂. 427.35 ppm in 2025 (NOAA annual mean), the highest in at least 2 million years (IPCC, for 2019: high confidence). One point of care: a single year above 1.5 °C does not mean the Paris goal is broken. The IPCC reports global warming levels as 20-year averages, partly because one year includes natural swings such as El Niño (2023–24 was an El Niño period). Scientists do disagree about how much of the very warm 2023–24 was natural variability, how much was falling aerosol pollution (cleaner shipping fuel, falling emissions in China), and how much signals faster underlying warming; the 0.27 °C-per-decade human-induced rate is the cleaner number. How scientists talk about certainty Reading the IPCC means reading a defined language. Confidence has five levels (very low, low, medium, high, very high) and reflects how much evidence there is and how well it agrees. Likelihood is a probability scale for an outcome: virtually certain is 99 to 100%, very likely 90 to 100%, likely 66 to 100%, about as likely as not 33 to 66%, unlikely 0 to 33%, very unlikely 0 to 10%, exceptionally unlikely 0 to 1%. The ranges nest: if something is very likely it is also likely. In square brackets the IPCC gives the very likely range, a 90% interval, unless stated otherwise. Interactive · What does the IPCC mean by that? Probability of the outcome Likelihood scale from the IPCC AR6 WGI Summary for Policymakers, footnote 4. "More likely than not" is greater than 50%. Examples from AR6 show the language at work. It is unequivocal that human influence has warmed the atmosphere, ocean and land. It is virtually certain that human CO₂ is the main driver of surface-ocean acidification. ECS is very likely between 2 °C (high confidence) and 5 °C (medium confidence). On the Atlantic circulation: it is very likely to weaken this century, but there is medium confidence that it will not collapse abruptly before 2100. That last sentence marks the edge of the field. Known with high confidence: the planet has warmed, humans are the cause, CO₂ is the main control knob, and warming scales with cumulative emissions. Genuinely uncertain: the exact sensitivity (clouds), how aerosols have masked warming, the speed of ice-sheet loss, and tipping points such as the Amazon, ice sheets and the Atlantic circulation; AR6 says low-likelihood, high-impact outcomes cannot be ruled out. Reasonable scientists disagree at those edges. The science does not say what to do; carbon taxes, nuclear power, adaptation and degrowth are choices about values, argued in Environmental Economics & Policy (36/19) and Energy Systems & Transitions (36/16). Figures here are dated as shown and will be superseded by newer editions of the indicators and the IPCC's next report. What a graduate just sees A planet is an energy ledger: sunlight absorbed equals infrared emitted, and the greenhouse effect is a drop in how well it can radiate. CO₂'s push is logarithmic: each doubling adds about 3.7 to 3.9 W/m², however high you start. Feedbacks multiply the no-feedback 1.2 °C by about 2.8 to reach about 3 °C, and the uncertainty is lopsided because the net feedback is in the denominator. The ocean makes warming lag: TCR (about 1.8 °C) is less than ECS (about 3 °C). For CO₂, warming tracks the cumulative total: about 0.45 °C per 1,000 Gt, so limits mean budgets and a stable climate means net zero. Single hot years are not trends; look at 20-year means and the decadal rate. "Likely", "very likely" and "high confidence" are defined numbers and levels, not adjectives. Where it shows up next Energy Systems & Transitions (36/16): the budget is the reason the energy mix matters, and the cost curves decide how fast it can change. Environmental Economics & Policy (36/19): carbon prices turn the externality in the budget into a price. Environmental Data & GIS (36/20): satellites and ocean floats measure the energy imbalance and sea level. Thermodynamics (34/14) and Entropy (13/12): the same idea of a system exporting heat to cold space. In the world: national climate pledges, insurance and flood design, crop planning, and every climate headline you read. If you want to go deeper 📘 Textbook. Dennis Hartmann, Global Physical Climatology (Elsevier, 2nd edition 2015). The standard graduate-level text on the energy balance. 📘 Textbook. David Archer, Global Warming: Understanding the Forecast (Wiley, 2nd edition 2012) and Raymond Pierrehumbert, Principles of Planetary Climate (Cambridge, 2010) for the physics in depth. 📘 Gentler. Joseph Romm, Climate Change: What Everyone Needs to Know (Oxford, 2nd edition 2018), or the IPCC's own short Summaries for Policymakers, which are free. 🌐 Free course. MIT OpenCourseWare 12.340 Global Warming Science (Spring 2012). Also free: IPCC AR6 WGI Summary for Policymakers and Chapter 7, the energy-budget and sensitivity chapter. The takeaway Climate science is an energy ledger. CO₂ pushes on it logarithmically, feedbacks multiply the response to about 3 °C per doubling with a long upper tail, the ocean delays it, and for CO₂ the warming follows the cumulative total, which is what a carbon budget counts. The IPCC says which parts are known with high confidence and which are not, and a good reader holds both. Try this: take any climate headline with a number in it, and ask three questions: what is it measured against (which baseline years), over what period (one year or twenty), and which of the IPCC's likelihood or confidence words would fit. Sources & Further Reading Sources. IPCC AR6 WGI Summary for Policymakers (2021): warming, human-caused share, ECS, TCRE, Table SPM.2 budgets, sea level, confidence and likelihood scales, CMIP6 sensitivity note, Atlantic circulation statement. IPCC AR6 WGI Chapter 7: ERF of doubled CO₂ (3.93 ± 0.47), feedback values (Planck −3.22, water vapour + lapse rate +1.30, albedo +0.35, cloud +0.42, net −1.16, amplification 2.8), TCR 1.8 (1.4 to 2.2). Forster et al., Indicators of Global Climate Change 2024, Earth System Science Data 17 (2025): 1.52 and 1.36 °C for 2024, 0.27 °C per decade, 0.89 W/m², 130 Gt CO₂ from 2025, emissions; reported through the University of Leeds release (27 June 2025). The 2025 values (1.37 °C, about three years and about 12 years) are from a wire report of the June 2026 update (AAP, 10 June 2026), not from the paper itself. NOAA GML annual means. The two-layer model values and every interactive figure were computed in node. 🌐 IPCC AR6 WGI Summary for Policymakers 🌐 Forster et al., Indicators of Global Climate Change 2024 🌐 MIT OCW 12.340 Global Warming Science 📘 Hartmann, Global Physical Climatology Step 5. Ecology: Why Populations Boom, Crash and Balance -------------------------------------------------------- Why: Populations, food webs and nutrient cycles. Every species is a bank account with deposits (births) and withdrawals (deaths). Ecology is the course that learns what happens when thousands of accounts are tied together, and what people are doing to the whole ledger. In 1944 the US Coast Guard put 29 reindeer on St. Matthew Island, a treeless island in the Bering Sea with no predators, as an emergency food source. By summer 1963 there were about 6,000. The next winter or two the herd collapsed to 42 animals, and by the 1980s there were none. Nobody shot them. The island simply could not feed the number that compounding growth had produced. A wolf pack, a coral reef, a cornfield and a cod fishery are all the same kind of puzzle: living things that multiply, eat each other, compete for the same food, and pass the same atoms around. Ecology is the course that gives you the few equations that explain why numbers boom, why they crash, and why they sometimes balance for centuries. The course in one box Who takes itBiology, environmental science, forestry, fisheries and conservation students, usually in year 3 or 4. Medical and public-health students meet its population maths again in epidemiology. What it is forPredicting how populations and communities change, and which levers (harvest, habitat, predators, nutrients) move them. Comes afterEvolution (35/47) and Differential Equations (34/03). The models here are rates of change. Leads toConservation biology, fisheries science, epidemiology, climate and Earth-system science. In this series it sits beside Evolutionary Game Theory (34/45) and Bioinformatics & Genomics (35/52). What this piece gives youYou will not be able to manage a fishery. You will see why growth has a ceiling, why predator and prey chase each other round, why a food chain has about five links, and how to read a headline about wildlife decline. Easier first read: Entropy (13/12), for why energy only flows through. Growth compounds, then meets a ceiling A population grows the way money does at compound interest. If each individual leaves on average more than one surviving offspring, the next generation is bigger, and every extra individual adds to the next increase. Ecologists write the per-capita growth rate as r. With nothing in the way, the population follows a curve that doubles every ln 2 / r time units, about 0.69 / r. dN/dt = r Ngrowth per unit time = growth rate × number present  ·  doubling time = 0.693 ÷ r But food, space and disease do not scale up. Add a brake that gets stronger as the population nears what the place can support, the carrying capacity K, and you have the logistic equation, written by Pierre-François Verhulst in 1838. dN/dt = r N (1 − N/K)growth is fastest at N = K/2, and stops at N = K The curve is an S. Growth looks exponential at first, then slows, then flattens at K. The fastest absolute growth is at half of K, where the population adds r K / 4 individuals per unit time. That one fact runs fisheries, which we meet below. The St. Matthew reindeer show the limit of the model: they overshot K and crashed, because food recovers slowly. A study by Klein linked the crash to scarce food combined with an exceptionally severe winter. Real populations lag behind their own brakes. Interactive · Boom, brake, overshoot Growth rate r (per year)Carrying capacity KStarting number N00"> Illustrative numbers, not a species. Logistic closed form N(t) = K / (1 + ((K − N0)/N0) e−rt). The dashed line is unchecked exponential growth, clipped at the top of the chart. With r = 0.8 per year, K = 1,000 and a start of 10, the population takes about 5.7 years to reach half of K (ln 99 ÷ 0.8) and adds about 200 individuals a year at that moment. The same animals with no brake would pass 1,000 in about 5.8 years, then keep going. The two lines are almost indistinguishable at first. Early growth tells you nothing about the ceiling. Predators and prey chase each other Add a second species that eats the first. Prey multiply when predators are few; predators multiply when prey are plentiful; then predators over-eat, prey crash, predators starve, and prey recover. Alfred Lotka (1925) and Vito Volterra (1926) wrote this down independently, Volterra after fish-catch records from the Adriatic during the First World War. dx/dt = αx − βxy    dy/dt = δxy − γyprey x grow at α and are eaten at βxy · predators y grow by eating (δxy) and die at γ The model predicts something odd and testable: endless loops, with the predator peak lagging the prey peak by about a quarter cycle. Near equilibrium the period is about 2π / √(αγ). The famous real-world match is the Hudson's Bay Company's fur returns for snowshoe hare and Canada lynx, which cycle every ten years or so. But the model is a cartoon. It lets prey grow without limit and predators eat without limit, and its loops are fragile: small random dips can wipe a species out (the "atto-fox problem"). Ecologists still argue how much of the hare cycle is predators and how much is food and other factors. Interactive · Wolves and deer, simulated Prey growth αPredator death γStarting prey Lotka–Volterra with β = 0.04, δ = 0.02, solved by fourth-order Runge–Kutta for 40 time units; starting predators 9. Illustrative units. With α = 0.8 and γ = 0.6 the equilibrium is 30 prey and 20 predators, the loops orbit it, and a full cycle takes 9 to 10 time units (the small-loop formula gives 9.1; big loops run a little longer). Raise the predator death rate to 0.9, for instance by culling them, and the prey equilibrium climbs from 30 to 45 while the predator equilibrium stays at 20. The counter-intuitive lesson: in this model, the average number of predators depends on the prey's growth rate, and the average number of prey on the predators' death rate. Competition and niches Two species that need the same limited thing cannot both stay for ever. In the early 1930s Georgii Gause grew two Paramecium species, alone and together, in steady conditions: together, P. aurelia eventually drove P. caudatum out, though changing the conditions let the loser survive. The idea became the competitive exclusion principle: complete competitors cannot coexist. What lets many species share a forest is niches: each uses the resource differently enough that it limits itself more than it limits the others. Extend the logistic with competition coefficients: α12 is how much one individual of species 2 counts against species 1's room, and the reverse for α21. The rule falls out of the algebra: coexist if α12 < K1/K2 and α21 < K2/K1each species must hurt itself more than it hurts the other Interactive · Who stays? Different nichesSpecies 1 winsNeither can invadeα12 (species 2's effect on 1)12 (species 2's effect on 1)">α21 (species 1's effect on 2)21 (species 1's effect on 2)"> K1 = 100, K2 = 80, r = 0.5 for both, starting at 10 each; Euler steps of 0.05 to time 100. Illustrative. With the starting values the two settle at about 90 and 17: the weaker competitor survives only because each species crowds itself more than the other. Push either coefficient above its limit and one disappears. Push both over and the winner depends on who got there first. Food webs and energy pyramids Sunlight enters through plants, algae and some bacteria. Each time something is eaten, most of the energy is spent on living (respiration, heat), left as waste, or lies uneaten. The fraction passed from one level to the next is the trophic transfer efficiency. The textbook figure is "about 10%", from Raymond Lindeman's 1942 study of a Minnesota lake. Real values vary widely, from well under 1% to about 37% in his data, and marine plankton systems are often higher, near 15 to 20%. energy at level k = energy at the base × eke = transfer efficiency per step (about 0.1 as a rule of thumb) Because the energy shrinks geometrically, a food chain runs out after only a handful of links, and top predators are rare and need large territories. Webs are tangled, not chains, and removing one species can ripple: sea otters eat sea urchins that eat kelp (Estes and Palmisano, 1974), so otter loss opened the way for urchin-grazed kelp loss. The Yellowstone wolf story is famous but contested: wolves returned in 1995 and 1996, browsing of some trees fell in places, but bears, cougars, hunting and a changed stream channel also matter, and "wolves changed the rivers" overstates what the evidence shows. Interactive · The pyramid Transfer efficiency per stepEnergy fixed by plants (units) Illustrative units. A level counts as viable if it gets at least 1 unit. Bar width is on a log scale, the labels give the true energy. At 10% and 10,000 units from plants, herbivores get 1,000, small carnivores 100, bigger predators 10 and a top predator 1: five levels. At 5% the chain loses a level. That is the arithmetic behind "why are there no predators the size of a house". Nutrient cycles: the atoms go round, the energy does not Energy flows through an ecosystem once and leaves as heat. Atoms of carbon, nitrogen, phosphorus and water go round and round. Every cycle has pools (the atmosphere, plants, soil, ocean) and fluxes (photosynthesis, respiration, decay, runoff). The average time an atom stays in a pool, its residence time, is simply pool ÷ flux. A pool that is small compared with the flux through it turns over fast: the carbon in the atmosphere cycles through plants and oceans within a few years, while carbon in deep sediments and fossil fuels sits for millions. Humans are now a big flux. Burning fossil carbon moves carbon from a slow pool to a fast one; that is the climate story. Nitrogen is the other: the Haber process (met in Equilibrium & Kinetics, 35/37) lets factories turn atmospheric N2 into fertiliser, feeding billions, while the excess washes into rivers and coasts and fuels algal blooms that leave low-oxygen "dead zones". Which pool, which flux, and which way the arrow points answers most questions about a cycle. Biodiversity, islands and why species numbers matter Biodiversity is the variety of life at three levels: genes, species and ecosystems. About 8.7 million species is one estimate for all eukaryotes, most still unnamed, and diversity peaks in the tropics, which hold about half of species on less than a fifth of the land. Why does it matter? Three reasons, and a careful ecologist separates them. Function: long-running grassland experiments such as those at Cedar Creek, Minnesota, found that more diverse plots tend to be more productive and steadier, an "insurance" effect because different species do well in different years. Services: pollination, water filtering, fisheries. Value in itself: a claim about ethics, not data. How many species live somewhere depends strongly on area. Plotted on log axes, species number rises as a power of area, S = c Az, with z in textbooks usually quoted between about 0.15 and 0.35. A tenfold area gives 10z times the species: with z = 0.25, about 1.8 times. Run it backwards and cutting habitat to a tenth eventually loses about 44% of species. Some ecologists argue this method overstates extinctions from habitat loss, and extinctions lag behind the loss, an "extinction debt". In 1967 Robert MacArthur and E. O. Wilson explained islands with a balance: immigration of new species falls as an island fills up (fewer newcomers are new), extinction rises as it fills (more species, each with fewer individuals). Where the lines cross is the equilibrium number, and it is not static: species keep arriving and vanishing. Near islands get more immigrants; small islands lose species faster. Simberloff and Wilson tested it on tiny Florida Keys mangrove islands in 1969. Interactive · An island's balance, and what habitat loss costs Distance from mainland (km)Island area (km²)Species–area exponent zHabitat lost (%) Mainland pool P = 100 species; immigration rate 1·e−d/400·(1 − S/P) per year and extinction rate 0.25·(A/100)−0.5·S/P per year: illustrative shapes, not measured. Habitat lost uses Safter/Sbefore = (1 − lost)z. Try the preset-free defaults: a 100 km² island 200 km out settles near 70 of 100 mainland species; shrink it or move it far and the equilibrium falls. And with z = 0.25, losing 90% of the habitat leaves (0.1)0.25 = 56% of the species in the end. Human impact, measured honestly Headlines about nature are full of enormous numbers, so read the denominator. The WWF and the Zoological Society of London's Living Planet Report 2024 says monitored wildlife populations fell on average 73% between 1970 and 2020. That is an average change across a sample of vertebrate populations, not 73% of animals or species gone, and critics note the data lean toward birds and Europe and that a few populations with huge changes can drive the average. The direction is not in doubt; the exact size is. Insects are similar: a 2017 German study of 63 nature reserves found about three-quarters less flying-insect biomass over 27 years, and it is a real and alarming result for one region, not a global count. PlaceWhat happened North AmericaPassenger pigeons, once in the billions, were hunted out; the last one died in 1914. Atlantic cod off Newfoundland collapsed and Canada closed the fishery in 1992. South AmericaAmazon forest clearing is measured every year by Brazil's satellite programme (INPE); the rate has swung with policy. EuropeFarmland birds and insects have fallen; the Krefeld result above. AfricaThe Nile perch, introduced to Lake Victoria in the 1950s, was followed by the loss or collapse of many of the lake's cichlid fish species; the numbers are debated. AsiaThe Aral Sea shrank from the 1960s as rivers feeding it were diverted to irrigate cotton. OceaniaThe Great Barrier Reef has had repeated mass coral bleaching since 2016 as ocean heat waves hit. Antarctica20th-century whaling cut Southern Ocean whale populations to small fractions of their original size; some are slowly recovering. It is not all one-way. The 1987 Montreal Protocol cut ozone-damaging chemicals, and several whale populations are rebuilding. Management works when the model is right. The simplest case is a harvest: if you take a fraction h of the population each year from a logistic population, it settles at N = K (1 − h/r) and you take h N a year. That yield is highest at h = r/2, which gives the maximum sustainable yield r K / 4. Fish harder than r and the population falls to zero. Interactive · Harvest a fishery Growth rate rHarvest rate h (fraction taken per year) Schaefer-style surplus-production model with K = 1000 (illustrative). Equilibrium N = K(1 − h/r) and catch = h·N, valid for h < r; above r the stock goes to zero. Real fisheries add noise, age structure and uncertain stock estimates. At r = 0.5 and h = 0.25 the stock sits at 500 and the catch is 125 a year, the maximum. Push h to 0.4 and the catch is 80 while the stock is only 200: you work harder for less, and a bad year could tip it over. That is why managers target below the peak. Numbers here describe how ecologists think; they are not a forecast for any real place. What a graduate just sees Growth is multiplicative; every population is exponential until something pushes back. The fastest growth is half-way to the ceiling, which is also where harvest is most productive. Predator and prey numbers cycle; removing predators can make prey boom and crash instead of simply rise. Two species with the same needs cannot stay together; coexistence means different niches. About a tenth of energy passes up each step, so food chains are short and top predators are few. Atoms cycle, energy flows through once; check pools, fluxes and residence times. More area means more species, in a power law; losing habitat costs species slowly and then for good. Any decline statistic needs its denominator: what was counted, where, and over what years. Where it shows up next Evolution (35/47) feeds in: niches and competition are the selection pressures. Evolutionary Game Theory (34/45): cooperation and conflict in populations use the same coupled equations. Microbiology (35/50): a flask of bacteria is a population with exactly these curves. In the world: fishery quotas, wildlife reserves, invasive-species control, pest management, climate models and disease ecology (predator and prey become host and pathogen). If you want to go deeper 📘 Textbook. Michael Begon, Colin Townsend and John Harper, Ecology: From Individuals to Ecosystems (Wiley, 5th edition 2021). The standard upper-level text. 📘 Textbook. Robert Ricklefs and Rick Relyea, The Economy of Nature (W. H. Freeman). The widely assigned survey with a broad range of examples. 📘 Gentler. David Quammen, The Song of the Dodo (1996). Island biogeography as a travel story, from Wallace to modern extinction. 🌐 Free course. MIT OpenCourseWare 1.018J Ecology I: The Earth System (Fall 2009), covering cycles, populations and food webs. Also free: the ecology chapters of OpenStax Biology 2e. The takeaway Numbers of living things are set by a few ratios: how fast they can grow, how much room there is, who eats whom, and how much energy gets passed up. Learn those and you can read most ecological news. It also explains why saving a species is mostly about habitat and harvest, not good intentions. Try this: this week, find one population near you (pigeons, ants on a path, weeds in a crack) and ask what its ceiling K is and what sets it. You will usually find the answer is food, space or something that eats it. Sources & Further Reading Sources. Exponential and logistic growth (Verhulst, 1838), Lotka–Volterra (Lotka 1925, Volterra 1926), competition (Gause, early 1930s) and island biogeography (MacArthur and Wilson, 1967) are standard textbook ecology (Begon et al.; Ricklefs). St. Matthew Island reindeer, trophic transfer efficiency (Lindeman 1942), the Yellowstone dispute, the Living Planet Report 2024 figure and its criticisms, and the Krefeld insect study were checked against encyclopaedia summaries of the primary papers. Regional examples are well-documented cases given in outline. All interactive numbers were computed in node; model parameters are illustrative. 🌐 MIT OCW 1.018J Ecology I 🌐 OpenStax Biology 2e (free) 📘 Begon, Townsend & Harper, Ecology: From Individuals to Ecosystems 📘 Quammen, The Song of the Dodo Step 6. Conservation & Applied Ecology: What Counts as Saving Nature -------------------------------------------------------------------- Why: Biodiversity, protected areas and restoration. Everyone agrees nature should be saved. The course is about the harder questions: saved from what, measured how, protected where, and by whom. In 1992 Canada closed the Atlantic cod fishery off Newfoundland, putting about 30,000 fishing and plant workers out of a living. For years the catch had been "within quota". The quotas were set from stock estimates that were too high, and the fish had been dwindling underneath them. Nobody was breaking a rule. The rule itself was the problem. That is the pattern conservation science exists to catch. A protected area that protects the wrong ground, a "decline of 73%" that does not mean what it sounds like, a harvest plan that works until a bad year, a tree-planting pledge that counts seedlings rather than forests. Applied ecology takes the equations of Ecology (35/48) and asks what a government, a community or a fishing fleet should actually do with them. The course in one box Who takes itEnvironmental science, ecology, forestry, fisheries and geography students, usually in year 2 or 3, often with a field trip. Conservation biology grew up as its own discipline in the 1980s, and programmes in the UK, Europe, Latin America, Africa and Australasia teach versions of the same core. What it is forDeciding what to protect, restore or harvest, and checking whether it worked. Comes afterEcology (35/48), whose growth, harvest and island-biogeography models this piece uses and pushes further. Leads toSoils, Agriculture & Food Systems (36/18), Environmental Economics & Policy (36/19) and Environmental Data & GIS (36/20). What this piece gives youYou will not be able to write a management plan. You will see why species numbers fall slowly after habitat is cleared, why a "sustainable" quota can be one bad year from collapse, how to read a wildlife-decline index, why protecting 30% of the planet says little until you ask which 30%, and why who holds the land matters as much as how much of it is held. Easier first read: Ecology (35/48). Area, species and the extinction debt Clear most of a forest and you do not lose most of its species the next morning. The species-area relation of Ecology (35/48) says that, once things settle, the share of species that remain is the share of area that remains, raised to a small power z, usually about 0.15 to 0.35: Safter / Sbefore = (Aafter / Abefore)zwith z = 0.25, keeping 10% of the habitat keeps (0.1)0.25 = 56% of the species, eventually "Eventually" is the important word. A remnant forest starts with the species it had, then loses them as small populations blink out through bad luck, inbreeding and isolation, over decades or centuries. David Tilman and colleagues named the gap the extinction debt in 1994: species that are still present but already doomed, unless the habitat is restored or reconnected. Debt cuts two ways. It means counts made today understate what past clearance will cost, and it means there is still time to act on the species that are still hanging on. The method has critics. In 2011 Fangliang He and Stephen Hubbell argued in Nature that running the species-area curve backwards overestimates extinctions from habitat loss, because the curve counts species present in an area, while extinction needs species found only in the cleared part. Others answer that observed extinctions and the debt are real, and that the question is the size. Treat the 56% above as the textbook calculation, not a forecast for any real forest. Interactive · Habitat loss and the extinction debt Habitat lost (%)Species–area exponent zRelaxation time (years to lose 63% of the debt) Textbook model, illustrative: share of species = eq + (1 − eq)·e−t/τ, where eq = (1 − lost)z. Real relaxation times differ by species, patch size and isolation. With 90% cleared, z = 0.25 and a 40-year time constant, 83% of the species are still there after 20 years and 60% after 100, on the way down to 56%. The first photograph after clearing looks fine. That is the trap. Fisheries: the peak that is also a cliff The logistic model of Ecology (35/48) says growth is fastest at half the carrying capacity, so the largest steady catch, the maximum sustainable yield (MSY), is rK/4 and is taken by keeping the stock near K/2. That idea (Michael Schaefer's surplus-production work in the 1950s) became the backbone of fisheries law: the 1982 UN Convention on the Law of the Sea refers to maximum sustainable yield, and many national laws still do. It has been criticised from the start. William Larkin's 1977 paper was titled "An Epitaph for the Concept of Maximum Sustained Yield". The reasons are practical. Stock size is estimated, not counted. Fish species depend on one another. Recruitment swings with ocean conditions. And MSY sits right at the edge: the same arithmetic that gives the biggest catch gives the smallest safety margin. The Peruvian anchoveta, the biggest fishery in the world by weight in the 1960s, crashed in 1972–73 during an El Niño year after years of record catches. What matters is how you set the catch. A fixed quota (take 120 tonnes whatever you find) is easy to administer. A fixed fraction (take a quarter of the stock) falls automatically when the stock does. Try both with a bad year in year 10, where a fraction of the stock simply dies or leaves. Interactive · Quota or fraction, then a bad year Fixed quotaFixed fraction Growth rate r Quota (tonnes per year) Bad year in year 10: stock lost (%) Schaefer-style model, K = 1000, simulated in 0.05-year steps for 40 years from the equilibrium the rule would give. Illustrative; real fisheries add age structure, noise and uncertain estimates. Fixed fraction means the catch is that fraction of the current stock. At r = 0.5, MSY is 125 a year. A quota of 120 holds the stock at 600, with an unstable tipping point at 400. A 30% bad year drops it to 420, just above the line, and it recovers. A 50% bad year pushes it under, and the stock collapses by about year 17, while the quota keeps being taken. A quota of 125, the exact MSY, has no safety margin at all. A fixed fraction of 0.25 settles at 500, the same 125 a year, and survives a 50% bad year with a low point of 252, because the catch falls when the stock does. Where do the world's fisheries stand? FAO's 2024 report on the state of world fisheries put 37.7% of assessed marine stocks as overfished in 2021, up from 35.4% in 2019, with the remainder within biologically sustainable levels. Later FAO work using a finer list of stocks gives somewhat different shares, and by weight of landings the picture is better, around three-quarters of landings coming from sustainable stocks. Scientists disagree about how bleak that is. Daniel Pauly and others argue that official catch data hide declines and that many unassessed stocks are worse. Ray Hilborn and others reply that well-assessed fisheries in North America, Europe and Oceania have been recovering under strict limits, and the biggest problems are in poorly managed, unassessed fisheries, many of them in the tropics. Both camps agree that management works where there is data, enforcement and the will to cut catches. The Living Planet Index, with its caveats The headline everyone knows: the WWF and Zoological Society of London's Living Planet Report 2024 says monitored vertebrate populations fell on average by 73% between 1970 and 2020. The Living Planet Index (LPI) is built from tens of thousands of population time series, for several thousand species of mammals, birds, reptiles, amphibians and fish. For each population it takes the rate of change, then combines the rates with a (weighted) geometric mean, which is the average of the logarithms of the ratios. So it averages percentage changes, with every monitored population counting as one vote. index = exp( mean of ln(Nend / Nstart) )a population that falls 90% (ratio 0.1) pulls the average down as hard as one that rises tenfold pulls it up in the log That design has consequences, and reading the index well means knowing them. It is not "73% of animals" or "73% of species" gone. It is an average change in a sample, which is heavy with birds and with Europe and North America, where monitoring is easiest. Regions differ widely: the report puts Latin America and the Caribbean at declines above 90%, Europe and Central Asia far lower. Freshwater populations show the steepest fall of the three realms. And in 2020 a McGill University team (Leung and colleagues) showed that a small share of populations, under 3%, with extreme collapses, drove much of the earlier headline decline; other researchers criticised that re-analysis in turn, and more recent work has asked whether the index's mathematics exaggerates or hides trends. The direction of travel is not in dispute among the groups that studied it. The exact size is. Interactive · What does a 'decline index' say? 24 invented populations, sorted from worst to best. Grey bars are excluded. Remove the steepest decliners or risers and watch the index. Exclude the steepest declinersExclude the steepest risers Invented numbers, not data. Index = exp(mean of ln(end ÷ start)) over the populations kept; the real LPI adds smoothing and weighting by species and realm. In the toy set the index is 0.62, an average fall of 38%, even though the total number of animals has risen by about 3%: a few small populations have collapsed while the big ones are steady. Exclude the six steepest decliners and the index turns slightly positive. Neither number is "the truth". They answer different questions, and a good conservationist asks which one the decision needs: how many populations are in trouble, how many animals are left, or how many species are at risk. The IUCN Red List answers the last, by classifying species one at a time. Protected areas and 30×30 The Kunming–Montreal Global Biodiversity Framework, adopted in December 2022, set a target (Target 3) to conserve at least 30% of land, inland waters, coast and ocean by 2030, "30×30". The Protected Planet Report 2024 (UNEP-WCMC and IUCN) put coverage at 17.6% of land and inland waters and 8.4% of the ocean, with gains of under half a point since 2020 in either. Fewer than 5% of the world's land lies in protected areas whose management effectiveness has been assessed, and 51 countries and territories already exceed 30% on land. The target counts area, and area is easy to hit in the wrong way. Protected areas worldwide tend to sit on land that is high, steep, cold, dry and far from cities, because that is where it is cheap and politically easy to protect: "residual protection" (Joppa and Pfaff, 2009, is the classic paper). Species that live in fertile lowlands are the ones most likely to be left out. The better tool is systematic conservation planning: choose areas to cover as many species as possible at least cost, using complementarity (pick the next site that adds the most species not already covered), not richness alone. Interactive · Which 30%? RandomRemote and cheapComplementarity Share of the landscape protected Invented 16×16 landscape with 60 invented species whose ranges are small clusters, mostly in the lowlands on the left (darker cells, more species). Remote and cheap = the right-hand cells first. Illustrative: the point is the method, not the numbers. In this toy landscape, protecting 30% of the cells at random keeps some part of 54 of the 60 species and at least 30% of the range of 42 of them. Choosing the remote, cheap cells keeps part of 12 species and 30% of the range of 10, the same area for a fifth of the benefit. Choosing by complementarity covers all 60 and 30% of the range of 52. That gap is why the 30×30 text also asks for areas that are ecologically representative, well connected and equitably governed, and why whether the target works depends on which 30% is chosen. Indigenous land management Early national parks were often made by removing the people who lived there. Yellowstone (1872) was created on land used by Indigenous nations; the Maasai were moved from the Serengeti National Park when its boundaries were set in 1959. Critics of "fortress conservation" say the model is unjust and often fails, because it ignores local knowledge and turns neighbours into opponents. Defenders of strict protected areas answer that some places, and some species, do need people kept out, and that weak local governance can fail too. Most conservation scientists now take a middle position: both models work somewhere, and the question is which and where. The scale is large. A 2018 study in Nature Sustainability by Stephen Garnett and colleagues estimated that Indigenous Peoples manage or hold tenure rights over at least 38 million km² in 87 countries, more than a quarter of the world's land, and that these lands overlap about 40% of terrestrial protected areas and ecologically intact landscapes. Studies from the Amazon and elsewhere generally find lower forest loss inside recognised Indigenous territories, although how much of that comes from the title and how much from remoteness is argued. Management here is active, not absence. Aboriginal communities in northern Australia have used fire for tens of thousands of years, and since 2005 the West Arnhem Land Fire Abatement project has paired cool, early dry-season burning with carbon credits, reducing the large, hot late-season fires. In Namibia, communal conservancies (the first registered in 1998) give rural communities rights over wildlife, and wildlife numbers have risen in many of them. In Canada, Indigenous Protected and Conserved Areas, for example the Tribal Parks that the Tla-o-qui-aht declared in 1984 on Meares Island, are being used to count towards national targets. The 30×30 text itself recognises Indigenous and traditional territories, a change from the older, park-only view. Restoration: what grows back, and what does not The United Nations Decade on Ecosystem Restoration runs from 2021 to 2030, and the Bonn Challenge, launched in 2011, has a target of 350 million hectares of degraded land under restoration by 2030. The evidence says two things at once. Recovery can be fast and impressive: studies of tropical forests regrowing on abandoned land (Poorter and colleagues, 2016) found that soil fertility and biomass can approach old-growth levels within decades, though the species mix takes a century or more. Costa Rica's forest cover fell to roughly a quarter in the 1980s and has since recovered to more than half, helped by payments for ecosystem services, cattle-sector changes and protection. But the way planting is counted matters. Tree-planting pledges count seedlings; what ecosystems need is surviving, diverse, locally suited trees. Monoculture plantations store carbon but are poor habitat, planting trees on natural grassland or savanna can destroy a biome that was fine, and the African Union's Great Green Wall, launched in 2007 with a goal of 100 million hectares by 2030, has fallen well behind schedule. Often the cheapest and best method is to protect land and let it regrow by itself (natural regeneration), which is also what farmer-managed regrowth in Niger did. Ask three questions of any restoration claim: what was the reference ecosystem, how many survive, and who owns and keeps it. What a graduate just sees Species are lost slowly after habitat is lost; today's counts miss the extinction debt. The peak of a yield curve is also where there is no margin for a bad year; the harvest rule matters more than the target. A decline index is an average of percentage changes across a sample: ask what was counted and which populations drive it. "Percent protected" means little without "which percent": representation, connectivity, and management matter. Protected areas are cheapest where they matter least; planning for complementarity beats grabbing the easy land. Who holds and manages land is a conservation variable, not a side issue. Restoration is judged by survival and diversity decades later, not by planting day. Where it shows up next Environmental Economics & Policy (36/19): payments for ecosystem services, quotas as property rights, and the cost of protection. Environmental Data & GIS (36/20): the maps, satellite counts and range data that planning like the toy above runs on. Soils, Agriculture & Food Systems (36/18): the biggest driver of habitat loss is farmland. In the world: fisheries councils, national park agencies, community conservancies, Indigenous ranger programmes, and the IUCN Red List. If you want to go deeper 📘 Textbook. Richard Primack, Essentials of Conservation Biology (Oxford University Press / Sinauer; use the latest edition). The standard undergraduate course text. 📘 Textbook. Ray Hilborn and Ulrike Hilborn, Overfishing: What Everyone Needs to Know (Oxford University Press, 2012). A clear, fair-minded case on fisheries from one side of the debate; read Daniel Pauly's papers beside it. 📘 Gentler. Elizabeth Kolbert, The Sixth Extinction (2014), a reporter's tour of extinction science; and Callum Roberts, The Unnatural History of the Sea (2007), on what the ocean used to hold. 🌐 Free. Protected Planet (UNEP-WCMC and IUCN) for the live protected-area data; IUCN Red List; and MIT OpenCourseWare 1.018J Ecology I for the population and biodiversity background. The takeaway Conservation is measurement under pressure. The same few ideas answer most of it: species vanish with a lag, harvests need margins, indices need denominators, targets need locations, and land needs its keepers. This is information, not a verdict on any policy; choosing between protection, use and restoration also involves values that the numbers cannot settle. Try this: find a local protected area or nature reserve and ask what it was chosen for and what is left out of it. Then check who lives or works around it. The answers say more than the percentage on a map. Sources & Further Reading Sources. The species-area relation and extinction debt (Tilman and colleagues, Nature, 1994) and its critique (He and Hubbell, Nature, 2011); Schaefer's surplus-production model; Larkin, "An Epitaph for the Concept of Maximum Sustained Yield" (1977); FAO State of World Fisheries and Aquaculture 2024 (37.7% of assessed stocks overfished in 2021) and later FAO assessments; Living Planet Report 2024 (WWF and ZSL) and Leung and colleagues (Nature, 2020); Protected Planet Report 2024 (UNEP-WCMC and IUCN) and the Kunming–Montreal framework (December 2022); Garnett and colleagues, Nature Sustainability 2018; Joppa and Pfaff, 2009; Poorter and colleagues, Nature 2016. Statements about Costa Rica, the Great Green Wall, Namibia, Arnhem Land and Canada are given in outline and should be checked against current reports before being quoted. All interactive numbers were computed in node; the models and data in them are illustrative. 🌐 Protected Planet 🌐 IUCN Red List 📘 Primack, Essentials of Conservation Biology 📘 Hilborn & Hilborn, Overfishing: What Everyone Needs to Know Step 7. Energy Systems & Transitions: What a Kilowatt-Hour Really Costs ----------------------------------------------------------------------- Why: Where energy comes from and what changing it costs. Changing the world's energy is not one problem but four: what we burn and generate, what it costs, whether it is there at 7 p.m. on a still winter night, and how fast any of it can be built. The subject is the habit of keeping all four in view at once. In 2025 the world made more solar electricity than ever: about 2,780 terawatt-hours, 30% more than the year before. In the same year it burned more coal, oil and gas than ever too. The Energy Institute's 2026 Statistical Review (published 30 June 2026) found that total energy supply passed 600 exajoules, up 1.7%, with fossil fuels still supplying about 86% of it, and renewables the biggest source of growth. Both headlines are true. A transition is not a switch that replaces one thing with another; so far it has been a pile that keeps growing. An energy-systems course teaches you to hold both facts, and to ask of any proposal: how much energy, at what cost, delivered when, and built by when. The climate reason for caring (the carbon budget) is in Climate Science (36/14). The physics is in Energy: The One Currency of the Universe (13/02), How a Nuclear Reactor Works (13/14) and Thermodynamics (34/14). The course in one box Who takes itEnvironmental science, energy and engineering students, usually in year 3, and anyone in economics, policy or geography who deals with power. Interdisciplinary programmes teach it alongside climate science, with data from the Energy Institute, the IEA, IRENA and Ember. What it is forUnderstanding where energy comes from, what changing it costs, and why the engineering and the economics are as hard as the politics. Comes afterClimate Science (36/14), and through it Earth Systems (36/13). Leads toEnvironmental Economics & Policy (36/19) and Pollution & Environmental Health (36/17); for the engineering side, Power Systems & Electric Machines (34/39) and Thermodynamics (34/14). What this piece gives youYou will not be able to plan a grid. You will be able to read an energy-mix chart without being fooled, compute a levelised cost, see why storage and flexibility matter more than raw cost, and state the best case for and against nuclear, hydro and biofuels. Easier first reads: Batteries (29/08), Nuclear Energy (29/09) and How Electricity Reaches Your Wall (13/04). Where energy comes from, and how it is counted The Energy Institute's 2026 review, covering 2025, gives the mix. Of world primary energy (the fuel and flows going into the system), fossil fuels supplied about 86%, nuclear 5.2%, hydro 2.7%, and other renewables (wind, solar, biofuels, geothermal) 5.9%, of which solar was 1.7% and wind 1.6%. Electricity is a different slice, because it is only part of final energy use, which also includes oil for transport and gas for heat. In electricity, renewables passed one-third of world generation for the first time in 2025 (33.8%), overtaking coal (33.0%), according to Ember's 2026 review. Solar reached 8.7% of power, passing wind at 8.4%; nuclear was 8.8% (Energy Institute). Interactive · Two slices of the same world Primary energy 2025Electricity 2025 How wind and solar are counted Primary energy shares: Energy Institute, Statistical Review of World Energy 2026 (as reported by DieselNet, July 2026); "other renewables" is the 5.9% for renewables excluding hydro minus solar and wind. Electricity: coal and renewables from Ember (2026) and nuclear, wind, solar from the Energy Institute; "hydro, bio & other" (16.7%) and "gas, oil & other" (24.4%) are derived by subtraction, and the two sources differ slightly. Counting demo: wind 9.77 EJ + solar 10.12 EJ, total supply taken as 595 EJ. Drag the counting slider. Primary-energy tables count fuel burned, and a typical fossil plant wastes more than half the heat. If wind and solar electricity is counted at face value, it is about 3.3% of the world's primary energy. If instead it is credited with the fuel a 40%-efficient fossil plant would have burned to make the same electricity (the "substitution" convention), the same wind and solar become about 8.0%. Neither is wrong; they answer different questions. When you read a share, ask which convention and which slice. Who emits and who uses it matters as much as the global total. In 2025, fossil-fuel generation fell in China (down 0.9%, its first fall since 2015) and in India (down 3.3%) as record wind and solar came online, while coal use in the United States rose about 10% (Energy Institute and Ember). Hundreds of millions of people, mostly in sub-Saharan Africa, still have no electricity at all, so "the world's energy problem" also includes adding supply, not only changing it. What a kilowatt-hour costs: LCOE and its limits The standard way to compare power plants is the levelised cost of electricity (LCOE): all the costs of building and running a plant over its life, divided by all the electricity it will produce, both discounted to the present. The spreadsheet version is short. LCOE = (capital cost × capital-recovery factor + fixed O&M) ÷ (8.76 × capacity factor) + fuel and variable cost$ per MWh · capital cost in $/kW · capacity factor in % of the year the plant runs at full-power equivalent Three things dominate. Capital cost is almost everything for solar, wind and nuclear, which have no fuel bill. Capacity factor is how much of the year the plant produces: roughly a quarter for solar, a third to 40% or more for wind, and above 90% for a well-run nuclear plant. And the discount rate (the cost of money) matters because capital-heavy plants must borrow for years before they earn anything. Interactive · Build a power plant's price Solar PVOnshore windOffshore windGas (CCGT)New nuclear Capital cost Capacity factor Cost of money (discount rate) Life Fixed operating cost Fuel and variable cost Illustrative inputs chosen so each preset lands inside the published US range; they are not Lazard's or anyone's actual assumptions. Gas preset: fuel at about $4 per MMBtu with a heat rate of 6.5 MMBtu/MWh ($26) plus $3 variable O&M. Ranges: Lazard, LCOE+ (19th edition, July 2026), unsubsidized, United States. Computed in node. Two data points help calibrate. In the United States, Lazard's 2026 analysis puts unsubsidized new utility-scale solar at $40 to $98 per MWh, onshore wind $37 to $99, gas combined-cycle $51 to $129, offshore wind $105 to $167 and new nuclear $175 to $255; it noted that costs rose across technologies and that the cost of gas generation was at a 15-year high. Globally, IRENA's Renewable Power Generation Costs in 2024 found weighted-average costs of $43 per MWh for utility-scale solar and $34 for onshore wind, with China's solar at $33, and reported that 91% of newly commissioned utility-scale renewables were cheaper than the cheapest new fossil alternative. Costs differ by country mostly because capital is cheaper in some places and sun and wind are better in others. Now the limits of LCOE, which analysts of every view accept in some form. It treats a megawatt-hour at noon on a sunny day the same as one in a still January dusk. It leaves out the cost of the grid, backup and storage a variable source needs, and it leaves out what a firm source saves the grid. Supporters of wind and solar point out that LCOE already favours them and that the system cost is falling fast; supporters of nuclear and firm power respond that the true comparison is cost of a reliable system, where LCOE is the wrong yardstick. Both sides are describing real costs. The next section is the part LCOE leaves out. Balancing a grid, hour by hour Electricity cannot be stored for free, so supply must match demand every second, and demand has a daily shape: a trough at night, a morning rise, and an evening peak. Solar produces only in daylight and peaks at midday, when demand is middling; the gap in the evening, as the sun sets and people come home, is the "duck curve" that grid operators describe. Wind has its own rhythm. And weather can take both away at once: a windless, overcast spell in winter, which Germans call a Dunkelflaute ("dark doldrums"), can last days. Interactive · One day on a grid Ordinary dayCalm, cloudy day Solar share of daily electricity Wind share Firm clean power (nuclear, hydro) as a flat share Battery size (hours of average demand) Stack, bottom to top: firm clean (gold), solar (red), wind (green), battery (blue), gas (grey). Invented demand, solar and wind shapes for a generic grid, scaled so average demand is 100; gas can always meet the shortfall. Battery power is capped at 40% of average demand with 88% round-trip efficiency. The "calm" day scales solar to 25% and wind to 10% of normal. Illustrative, not a forecast. Try it. With 30% solar, 20% wind and 10% firm power and no battery, about 5.7% of wind and solar is wasted at midday and gas supplies about 43% of the day, with its output swinging between low and high. Add four hours of battery and the waste vanishes and the evening peak is shaved (gas falls only to about 40%). Then switch to a calm, cloudy day: gas jumps to about 80%, and four hours of battery barely moves it. That is the core system lesson: batteries solve the daily problem, not the weekly one. Averaged over a year, cheap wind and solar can supply a lot; the hard cases are the few days when they supply little. Storing energy: batteries, water and molecules Storage comes in a few forms, each with a niche. Lithium-ion batteries are the fast-falling-cost option: BloombergNEF's December 2025 survey put the average pack price at $108 per kWh, down 93% in real terms since 2010; stationary-storage packs averaged $70 per kWh (LFP chemistry about $81). Pumped hydro (pump water uphill with spare electricity, run it back down later) has historically been the large majority of grid storage, returning roughly 70 to 85% of the energy and lasting decades. Hydrogen and other chemical fuels can store energy for weeks or seasons, but make-and-burn round trips return only roughly a third to a half. And flexibility without storage, such as moving demand (charging cars at midday, running industrial loads when power is cheap), long transmission lines that link different weather, and spare dispatchable plants, matters as much as batteries. Scale gives perspective. World electricity use is about 31,700 TWh a year, so one hour of it is 3.6 TWh. Packs for just that hour, at $70 per kWh, would cost about $250 billion, before power electronics, land, and installation. A few hours of storage per grid is realistic and valuable. Weeks of it is a different order of cost, which is why the debate between "mostly renewables with storage and grids" and "also keep firm sources such as nuclear, hydro and gas with capture" is about the cost of the last 10 to 20% of a system, not the first 80%. Nuclear, hydro and biofuels: the arguments Three technologies split opinion. The point is not to pick; it is to hear each side at its strongest. Compare them on two numbers first: life-cycle emissions (IPCC 2014 medians) and deaths per unit of energy (from accidents and air pollution; Our World in Data, drawing on Markandya and Wilkinson 2007 and Sovacool et al. 2016, with the caveat that the coal, oil and gas rates are from European plants and probably understate the global figure). Interactive · Design a grid mix World 2025 (approx.)No coalClean mixAll gas Coal Gas Nuclear Hydro Wind Solar Sliders are weights, normalised to 100%. Life-cycle gCO₂e/kWh, IPCC 2014 medians: coal 820, gas 490, nuclear 12, hydro 24, onshore wind 11, solar PV (utility) 48. Deaths per TWh (OWID): coal 24.6, gas 2.8, nuclear 0.03 (an estimate dominated by Chernobyl and Fukushima), hydro 1.3 (0.04 without the 1975 Banqiao failure), wind 0.04, solar about 0.02. The "World" preset puts gas, oil and other at gas's value, so it is an index, not a measurement. Costs, storage and backup are not included. Nuclear. The case for: it makes low-carbon electricity day and night, from a small footprint, at a death rate per TWh close to wind and solar and far below fossil fuels, and plants can run 60 years or more. Without it, supporters say, a firm clean backbone is much harder and costlier to find. The case against: new plants in the West have run years late and billions over (the American Vogtle 3 and 4 went from about $14 billion to more than $30 billion), Lazard's 2026 range for new nuclear ($175 to $255) is far above solar, wind or gas combined-cycle, long-lived waste has an operating permanent repository in very few countries, and the technology is linked to weapons proliferation. The honest summary: both the safety record and the cost record are real, and the dispute is mostly about whether costs reflect the technology or the way the West builds. The full story is in Nuclear Energy (29/09). Hydro. For: it is the largest renewable source (2.7% of primary energy), usually cheap once built, dispatchable, and the source of most grid storage. Against: big dams flood land and move people (China's Three Gorges Dam, 22.5 GW, displaced an estimated 1.1 to 1.4 million), hold back sediment, harm migratory fish, and reservoirs in warm places can emit methane. Output follows rainfall, so a drought can cut supply on a hydro-dependent grid. Most of the best sites in rich countries are already used, and the remaining growth is in Asia, Africa and Latin America, where the trade-offs are sharpest. Biofuels. For: liquid fuels from plants are one of the few options for aviation, shipping and heavy transport, where batteries struggle, and sugarcane ethanol in Brazil gives roughly 8 to 10 units of energy out per unit of fossil energy in. Against: US corn ethanol gives only about 1.3 to 1.6, and the argument turns on land: a 2008 Princeton-led study counted the emissions from clearing other land to replace the crops diverted to fuel and found corn ethanol worse than gasoline (+93%), while the US EPA's 2010 analysis projected a 21% saving by 2022. Researchers still dispute how to model that indirect land use. Biofuels also compete with food: during the 2007–08 price spike the World Bank first attributed 70 to 75% of the rise to biofuels and related factors, and later studies found a smaller share. Biofuels from wastes and residues avoid most of the land problem but are limited in amount. Transitions are slow, and so far they have added up History offers a caution. Coal did not replace wood in the 19th century; oil did not replace coal; the world burns more of both than ever. The energy historian Vaclav Smil has argued that energy transitions take decades because the machines, pipes and habits built around a fuel last decades. The optimists' reply is that solar and batteries follow a different path: they are manufactured goods whose costs fall as the total built doubles, and the numbers in this piece (batteries down 93% since 2010; solar growing 30% in a year) show that curve at work. The two views are not exclusive: solar is growing very fast, and it is growing from a small base. Interactive · How fast can a share grow? Same additions each yearAdditions grow 5% a yearSmaller start Solar added in 2025 (first year) Growth of those yearly additions Growth of total electricity demand Start: 2,778 TWh of solar in 2025 (Ember, +636 TWh, +30% on 2024) out of world generation of about 31,700 TWh (derived from coal's 10,476 TWh at 33.0%); demand growth of 3% matches the Energy Institute's 2025 figure. Pure arithmetic: not a forecast, and it ignores curtailment, storage and the other sources. Play with it. If the world simply adds the same 636 TWh of solar every year while demand grows 3%, solar's share creeps to about 28% by 2050. If the yearly additions themselves grow by 5% a year, the share reaches roughly half by 2050. The point is not the number: it is that a share is a ratio, and the answer depends on the growth of both the numerator and the denominator. The decision-makers who matter in the next two decades are the ones building: China, which added the most wind and solar, India, which in 2025 installed more new solar capacity than the United States for the first time, and the countries that mine and refine the materials, such as the lithium-rich salt flats of Chile, Argentina and Bolivia and the cobalt mines of the Democratic Republic of Congo. Whether and how fast to change is a matter for Environmental Economics & Policy (36/19). What the engineering and the numbers say is that it is a build-out problem as much as an invention problem. Figures here are dated as shown; energy statistics are revised each year. What a graduate just sees An energy share depends on the slice (primary or electricity) and on the counting convention. For solar, wind and nuclear, cost is capital cost and the cost of money; fuel is almost irrelevant. LCOE compares plants, not systems: a megawatt-hour's value depends on when it arrives. Batteries fix the daily cycle, not the cloudy week; the last 10 to 20% of a clean grid is the expensive part. Every low-carbon source has a hard problem: nuclear its cost and waste, hydro its land and rivers, biofuels their land, wind and solar their variability. Energy transitions have so far been additions; growth in demand can absorb a lot of clean supply. Shares are ratios: ask what is growing in the numerator and in the denominator. Where it shows up next Environmental Economics & Policy (36/19): carbon prices, subsidies and regulation are the tools for changing the cost columns in the LCOE calculator. Pollution & Environmental Health (36/17): the deaths-per-TWh column is mostly air pollution. Climate Science (36/14): the carbon budget sets the deadline the energy system is racing. Power Systems & Electric Machines (34/39) and Thermodynamics (34/14): the engineering behind the grid-balancing demo. In the world: utility planning, energy ministries, investment banks, and every household choice about heating, cooking and transport. If you want to go deeper 📘 Textbook. Vaclav Smil, Energy and Civilization: A History (MIT Press, 2017) for the long view; and Jefferson Tester et al., Sustainable Energy: Choosing Among Options (MIT Press, 2nd edition 2012), the textbook for MIT's introductory energy course. 📘 Gentler. David MacKay, Sustainable Energy - Without the Hot Air (2009), free to read online, which does the arithmetic of energy supply and demand in everyday units. Written for the UK, so the numbers are dated, but the method is the point. 🌐 Free course. MIT OpenCourseWare 22.081J Introduction to Sustainable Energy (Fall 2010). Also free: Our World in Data's energy pages and Ember. The takeaway Energy is four questions at once: what mix, what cost, when delivered, how fast built. Wind and solar are now the cheapest new electricity in many places, and growing quickly, but fossil fuels also hit records in 2025; cost per megawatt-hour is not the same as the cost of a reliable system; and nuclear, hydro and biofuels each have a real best case and a real worst case. Try this: look at your own electricity bill or your country's grid page and find two numbers: the source of power at this hour, and the source at the evening peak. Then ask what would have to change to make the second one cleaner. Sources & Further Reading Sources. Energy Institute, Statistical Review of World Energy 2026 (75th edition, 30 June 2026), read through the DieselNet summary of 2025 data (primary-energy shares, EJ figures, electricity shares, emissions, coal by country). Ember, Global Electricity Review 2026 (renewables 33.8%, coal 33.0%, solar 2,778 TWh, China and India). Lazard, LCOE+ (19th edition, July 2026), through the Utility Dive report (16 July 2026). IRENA, Renewable Power Generation Costs in 2024 (2025). BloombergNEF battery price survey (9 December 2025). Life-cycle emissions: IPCC (2014) medians as summarised on Wikipedia. Death rates: Our World in Data, "What are the safest and cleanest sources of energy?" Three Gorges figures, US ethanol and land-use debates: Wikipedia summaries of primary sources (including Searchinger et al., Science, 2008). Vogtle costs and nuclear status: this library's Nuclear Energy (29/09). Storage round-trip efficiencies are rounded textbook ranges. Every interactive figure was computed in node; the plants' inputs are illustrative. 🌐 Our World in Data: Energy 🌐 MIT OCW 22.081J Introduction to Sustainable Energy 📘 MacKay, Sustainable Energy - Without the Hot Air Step 8. Hydraulics & Water Resources: Moving Water Where People Need It ----------------------------------------------------------------------- Why: Rivers, floods, dams and water supply. Pipes, pumps, rivers, floods, dams and levees: the part of civil engineering that decides where water goes, and what happens on the day it goes somewhere else. Turn on a tap on the tenth floor and water comes out. Somebody had to lift it there, and somebody had to decide how wide the pipe should be so it would not come out as a trickle. Now look at a river after a storm. It was ankle-deep last week and now it is brown, fast and over the car park. Same water, same laws, a different job: in the pipe, the engineer is delivering it; in the river, the engineer is surviving it. This is the course where fluid mechanics goes to work on whole landscapes. The graduate does not solve Navier–Stokes. They keep a short list of habits: count water in and water out, think in "head" (energy as a height), ask how often the bad day comes, and remember that every barrier has a way to fail. The course in one box Who takes it: civil and environmental engineers (and agricultural and some mechanical engineers), usually in year 3, as one course in hydraulics and often a second in hydrology. Civil programmes shaped by the ASCE Body of Knowledge all include it; geoscience and public-policy programmes teach the hydrology half. What it's for: sizing the pipes, pumps, channels, reservoirs and flood defences that move and store water, and judging the risk that they are overwhelmed. Comes after: Fluid Mechanics (34/15), Probability & Statistics (34/05). Leads to: Environmental Engineering (34/68) for the water once it is dirty, Geotechnical Engineering (34/66) for dams and levees as soil structures, and Corporate Finance (34/51), the engineering-economics course, for deciding what protection is worth paying for. Honest line: you won't be able to design a dam or a drainage network after this. You will see why narrowing a pipe is so costly, why a "100-year flood" can strike twice in a decade, and what went wrong at New Orleans, Teton and Vajont. This piece picks up where Fluid Mechanics (34/15) stops. Pressure, Bernoulli and the Reynolds number are assumed; if they are rusty, read 34/15 first. Pipes and pumps: where two curves cross Engineers measure the energy in water as a height: head, in metres. Bernoulli's three terms (pressure, speed, elevation) each become a height, and they add up to the total head. In a real pipe the total slowly drops along the way, because friction turns it into heat. That drop is the head loss. hf = f · (L / D) · v² / 2ghead lost = friction factor × (length ÷ diameter) × speed-head This is the Darcy–Weisbach relation. The friction factor f comes from the Reynolds number and the roughness of the pipe wall (the Moody chart, or a formula such as Swamee–Jain). The part to keep in your head is the diameter. For a fixed flow, the speed goes as 1/D², so v² goes as 1/D⁴, and the extra 1/D makes it about 1/D⁵. Halve the diameter and the loss is roughly 32 times bigger. In the model below, 30 litres a second through 1,500 m of 200 mm pipe loses about 7 m of head; through 100 mm it would lose about 233 m, which no pump would supply. Pipe diameter is the cheapest dial in the whole system. A pump adds head, but less of it the more water you ask for. Plot the pump's head against flow and the line falls. Plot what the pipe needs (the lift in height, plus the friction loss) and the line rises. The pump runs where the two curves cross. Everything else in a pumping design is moving one curve to put that crossing where you want it. Whole networks follow the same logic as an electric circuit: head is voltage, flow is current, and at every junction the flows add up to zero (see Circuit Analysis, 34/34). The classic hand method for loops of pipe, by Hardy Cross (1936), is just that. Interactive · Find the operating point Pipe diameter Lift (static head) A made-up pump (50 m of head at zero flow, 35 m at 60 L/s) feeding 1,500 m of pipe, roughness 0.1 mm, plus 5 velocity heads of fittings. Water at 20 °C. Try 250 mm and 15 m, then shrink the pipe to 150 mm and watch the flow fall. Open channels: when water outruns its own waves In a pipe, pressure pushes the water. In a river, a canal or a storm drain flowing part-full, only gravity does, and the water has a free surface that can wave. That surface decides everything. A small ripple on shallow water travels at √(g·y), where y is the depth. Compare the water's speed with the ripple speed and you get the Froude number. Fr = v / √(g · y)flow speed ÷ speed of a surface wave Below 1 the flow is subcritical: calm, deep, and ripples can travel upstream, so a downstream gate or bridge pier "tells" the water far behind it. Above 1 the flow is supercritical: fast, shallow, and ripples are swept away downstream, so nothing downstream can warn it. For uniform flow in a long channel the working rule is Manning's equation (from the Irish engineer Robert Manning, 1890s): speed grows with the slope's square root and with the channel's "hydraulic radius" to the power 2/3, and falls with roughness. When fast shallow water meets slow deep water, it cannot change gently. It jumps: a sudden rise in surface, a roaring, churning roller, and a large share of the energy burned off as turbulence. The depths on the two sides are linked by one formula, and the energy lost is a large fraction of what the flow carried. That is useful: below a spillway, a concrete stilling basin forces a jump so the water leaves the dam slowly instead of scouring the river bed. You can see the small version in your kitchen: the circular ring around where a tap's stream hits the sink is a hydraulic jump. Interactive · The hydraulic jump Depth before the jump Speed before the jump Rectangular channel, horizontal bed, no friction on the bed. Sequent depth y₂ = (y₁/2)(√(1 + 8Fr₁²) − 1); energy lost = (y₂ − y₁)³ / (4y₁y₂). The jump is drawn to a made-up scale. A catchment: rain in, flood out Hydrology starts with an accounting identity: rain that falls on a catchment either soaks in, evaporates, or runs off. Only the runoff makes the river rise, and how fast it arrives decides how high. Dry, bushy ground soaks up the first part of a storm. A roof, a road and a car park do not. A standard classroom model (the Curve Number method from the US Soil Conservation Service, now NRCS, with a triangular "unit hydrograph" for timing) captures this in a few lines. Land cover sets a curve number from about 30 (very absorbent) to 100 (a paved surface). The more paved, the bigger the runoff for the same rain, and the water reaches the river sooner, because pipes and gutters carry it faster than meadow does. Both effects stack on the peak. This is the reason developers are now asked for detention ponds and permeable paving: to give back some of the storage the pavement took. Interactive · Pave the catchment Share of land paved Storm: rain in 3 hours Illustrative 10 km² catchment: rural land CN 70, paved CN 98, area-weighted. Lag falls from 3 h (unpaved) to 1.2 h (fully paved). 80 mm in 3 h is a very heavy storm. Dashed line: the same storm on unpaved land. Return periods: why a 100-year flood isn't once a century Engineers cannot say "it will flood in 2031". They say how likely a given flood is in any one year. A "100-year flood" is the flow that has a 1-in-100 chance, or 1%, of being equalled or beaten in any year. That is all it means. It is a probability per year, not a schedule, and not a promise that 99 quiet years must follow. P(at least one in n years) = 1 − (1 − 1/T)nT = return period in years Over a 30-year mortgage the chance of meeting a 100-year flood at least once is 1 − 0.99³⁰ = 26%. Over a 100-year life it is 63%. That also means there is a 37% chance of none in a century, and a 26% chance of two or more. The independence is the key: the river does not remember last year's flood. Floods in successive years are rare but entirely possible. Two cautions belong in every graduate's head. First, the 100-year flow is estimated, usually by fitting a distribution to a record of perhaps 50 to 100 years, then extrapolating. The tail is uncertain. Second, the method assumes the climate and the catchment are the same as in the record. Paving, deforestation and a warming climate all break that assumption, which is why many agencies now say "1% annual exceedance probability" and revise their maps. Interactive · The flood odds calculator Return period T Years you are exposed Roll one random period Independent years, constant chance. The strip shows one random run with a fixed starting seed, then a new one each press. Red cell: a flood at least this big. Dams and reservoirs: moving water through time Rivers flood in spring and run dry in late summer, while people need water all year. A dam is a machine for shifting water through time: store the surplus, release it when it is short. Dams also make electricity, hold back floods and raise a water level for navigation or irrigation. Their costs are real too: sediment slowly fills reservoirs, evaporation loses water, and a valley, its people and its fish are changed for ever. The engineering of storage is bookkeeping, a mass balance for the whole reservoir: storage today = storage yesterday + inflow − release − losses. The surprise is the limit. A reservoir cannot supply more than the river brings in on average, however big. Below that limit, bigger storage buys reliability, but with sharply diminishing returns. Play with it below. Interactive · Size the reservoir Storage capacity Yearly demand One hundred invented years of river flow (mean 100 units, varying by about ±40% and with some dry runs), not a real river. No evaporation, no sediment, no environmental release. When barriers fail: New Orleans, Teton and Vajont A levee is a wall of earth or concrete that keeps a river or the sea off land it would otherwise cover. It does one job: hold a water level up to a design height. It moves risk rather than removing it: land behind it develops, and the day the design is exceeded or the structure fails the losses are larger. The 100-year idea matters here: a levee built to the 100-year level is overtopped, on average, once in a hundred years. Hurricane Katrina struck on 29 August 2005. The storm surge overtopped some levees and floodwalls, notably on the eastern side of the city, and that part was a question of design height. The disaster came from where defences failed below their design level. The 17th Street and London Avenue canals and part of the Industrial Canal broke while water was below the top of the walls. By 31 August about 80% of the city was flooded, some areas under up to 15 feet of water. Published death counts for Louisiana differ, roughly 1,000 to 1,500. The US Army Corps of Engineers, which had designed and built the system, acknowledged in a June 2006 report faulty design, incomplete sections and substandard construction. A 2007 American Society of Civil Engineers review called it the worst engineering catastrophe in US history, and concluded about two-thirds of the flooding could have been avoided if the levees had held. The lesson is the one every graduate keeps: a defence is a system of links, and what matters is the weakest one (here soil under the walls and the walls' foundations; see Geotechnical Engineering, 34/66). It also shows how a "protected" city can be misled into thinking it is safe. Two dam failures make the same point from other angles, and both are often told wrong. Teton Dam, Idaho, 5 June 1976. It was a 93 m earth-fill dam, finished in November 1975, failing during its first filling. Seepage found a path through or beneath the dam and began carrying soil away: internal erosion, called piping. The leak grew from a trickle to a breach within hours; the reservoir emptied and 11 people died. An independent panel named internal erosion the most probable cause, but could not say whether it began through fissured rock under the grout seal or through cracks in the dam's core. Neither a flood nor an earthquake overwhelmed it. A dam can be strong and still lose to the water seeping through and under it. Water in soil, and what it can carry off, is the subject of Geotechnical Engineering (34/66). Vajont, Italy, 9 October 1963. The concrete arch dam, at 262 m among the tallest in the world, did not fail. It stood. About 260 million cubic metres of mountainside slid into the reservoir, the displaced water went over the crest, and the flood killed about 2,000 people in the valley below (the official count is 1,917; estimates run up to roughly 2,500). The warning signs on the slope had been disregarded, and a handful of engineers were convicted in a trial moved to L'Aquila. Experts still debate how much rain, reservoir level and earthquakes each contributed. The lesson: the engineer designs the dam, but the dam sits in a landscape, and the landscape must be understood too. Water scarcity: the same equations, worldwide On the planet as a whole, water is not scarce; fresh water is badly placed and timed. The hydrology graduate thinks in balances, region by region and season by season. Where demand approaches the renewable supply, extra demand is met by drawing down stored water: aquifers, glaciers, reservoirs. Irrigated agriculture is the largest user worldwide, by most estimates around two thirds to 70% of withdrawals, so most of the water problem is a food problem. The Joint Monitoring Programme of WHO and UNICEF reported in August 2025 that, in 2024, about 2.1 billion people (roughly one in four) still lacked safely managed drinking water, including 106 million who drank directly from untreated surface water. Those figures describe services, not rainfall. Scarcity is as often a pipe, a pump, a price and a government as it is a drought. Engineers also disagree about the cure: big dams and transfers versus recycling, efficiency, demand management and small local systems. The right mix depends on the place, and civil engineers inherit the argument. What a graduate just sees Head is energy as a height; pipes lose it to friction, and the loss is roughly 1/D⁵: a skinny pipe is expensive to push through. A pump works where its falling curve crosses the pipe's rising one. Change either curve and the flow moves. Fast shallow water outruns its own ripples; where it meets slow deep water it jumps, and the jump is a free energy-burner. Pavement raises the runoff and shortens the delay, so the flood peak grows twice over. A 100-year flood is a 1% chance each year. Over a mortgage, one in four. A reservoir can never yield more than the average inflow, and each extra bit of storage buys less. Defences fail at their weakest link, often below their design load: soil, seepage, foundations. Failures happen to dams and levees as parts of a landscape: Teton leaked, Vajont slid, New Orleans' walls gave way. Where it shows up next Environmental Engineering (34/68): the same pipes and channels now carry sewage and treated water; the river's flow sets how much pollution it can take. Geotechnical Engineering (34/66): seepage, slope stability and foundations are what decided Teton, Vajont and New Orleans. Probability & Statistics (34/05) and Engineering Economics (34/51): choosing the return period is a decision about money and lives. The real world: city drainage, irrigation schemes, hydropower, flood maps and insurance, port and canal design, and the water utility in every town. If you want to go deeper 📘 Textbook: Larry W. Mays, Water Resources Engineering (Wiley): the broad standard, covering hydraulics and hydrology together. 📘 Textbook: David A. Chin, Water-Resources Engineering (Pearson): strong on worked design problems. 📘 Classic for the river half: Ven Te Chow, Open-Channel Hydraulics (1959), and Chow, Maidment and Mays, Applied Hydrology (McGraw-Hill). 📘 Gentler: John McPhee, The Control of Nature (1989): essays, including a long one on the Army Corps' fight to hold the Mississippi in its channel. ▶️ Free course: MIT OpenCourseWare 1.72 Groundwater Hydrology (Fall 2005), a graduate course for the water-underground side; for the surface side, the fluid mechanics course linked in 34/15 is the base. 🌐 Easier first read in this library: Fluid Mechanics (34/15). The takeaway Water engineering is accounting plus risk. In a pipe, head is lost to friction, the pump sits where two curves cross, and diameter is the strongest lever. In a river, speed against wave speed decides whether the flow is calm or jumps. A catchment turns rain into a flood, and paving makes that flood bigger and quicker. A 100-year flood is a 1% chance a year, not a schedule. Dams shift water in time, can never beat the average inflow, and fail through seepage, slopes and weak links in the chain, as at Teton, Vajont and New Orleans. Try this: after the next heavy rain, find where the water on your street goes and what it runs over. Then look up the flood map for your town and see what its "1%" line is. Is your house inside it? Sources & Further Reading Sources. Darcy–Weisbach, Swamee–Jain, Froude number, Manning's equation, the hydraulic jump relations, the SCS Curve Number method and the return-period formula are standard textbook material (Mays; Chin; Chow; NRCS National Engineering Handbook Part 630). All interactive numbers were computed in node. Teton Dam: US Bureau of Reclamation fact sheet and the 1976 Independent Panel report (hosted at damfailures.org): 11 deaths, internal erosion the most probable cause, exact initiation not determined; construction and failure dates from the Teton Dam article on Wikipedia. Vajont: Wikipedia article (260 million m³, 262 m dam, official toll 1,917, range up to about 2,500, trial at L'Aquila). New Orleans 2005: Wikipedia, Effects of Hurricane Katrina in New Orleans (80% flooded by 31 August, failures below design height, June 2006 Corps acknowledgement, ASCE review). Water access: WHO/UNICEF Joint Monitoring Programme, report of August 2025 (2.1 billion lack safely managed drinking water in 2024; 106 million use untreated surface water). Hardy Cross (1936), the Dutch 1953 flood and the irrigation share of withdrawals are cited from standard texts and FAO figures, not re-checked for this piece. 🌐 WHO/UNICEF JMP: household water, sanitation and hygiene, 2025 update 🌐 Dam Failures: Teton Dam (Idaho, 1976) 🌐 MIT OpenCourseWare 1.72 Groundwater Hydrology 📘 John McPhee, The Control of Nature Step 9. Soils, Agriculture & Food Systems: Feeding Eight Billion From a Thin Skin of Earth ------------------------------------------------------------------------------------------ Why: Soil, farming and feeding eight billion people. Almost every calorie you eat passed through a few centimetres of soil, a bag of nitrogen made from air, and a decision about how to use the land. This is the course that follows the food back to those three things. In April 1935 a dust storm from the Great Plains reached Washington, DC, while a US Senate committee was hearing evidence about soil erosion. Hugh Bennett, who led the new Soil Conservation Service, is said to have pointed out of the window at the darkening sky. The Dust Bowl had stripped topsoil from millions of hectares of ploughed prairie in a decade of drought, and within weeks Congress passed the Soil Conservation Act. Soil that took centuries to build had been lost in seasons. Now run the film forward. Since the 1960s world cereal yields have roughly tripled, and the number of people has gone from about three billion to eight (the United Nations marked the eight-billionth person in November 2022). Much of that came from fertiliser made with the Haber–Bosch process, which takes nitrogen out of the air. Farming also covers about half of the world's habitable land and produces about a quarter of its greenhouse gas emissions. This is a course about a system with huge successes and huge costs, and a graduate's job is to tell the two apart. The course in one box Who takes itEnvironmental science, agronomy, geography, food-system and development students, usually in year 3. Soil science and agroecology are taught from Wageningen to Nairobi, Embrapa in Brazil, Cornell and China Agricultural University. What it is forUnderstanding how land, water, nutrients and people combine into food, and what each way of farming and eating costs the planet. Comes afterPlant Biology (35/53), which covers photosynthesis, domestication and the Green Revolution. This piece does not repeat them. Leads toEnvironmental Economics & Policy (36/19), Environmental Data & GIS (36/20) and Conservation & Applied Ecology (36/15). It also draws on Pollution & Environmental Health (36/17), since fertiliser is a pollutant when it leaves the field. What this piece gives youYou will not be able to plan a farm. You will see why soil is a stock lost faster than it forms, what Haber–Bosch changed and what it costs, why higher yields do not automatically save land, what a plate of food emits, and how to read the organic and GM arguments without picking a team. Easier first reads: The Science of Bread (14/07) and The Cultures on Your Plate (14/04). Soil is made slowly and lost quickly Soil is rock turned into a living material. Vasily Dokuchaev in Russia and, later, Hans Jenny in California described it as the product of five things: climate, organisms, relief (the slope), parent material and time. Jenny's 1941 equation puts it in one line. The point of the five factors is that they act slowly. Under most conditions a centimetre of topsoil takes decades to centuries to form. Losing it takes far less. Raindrops knock particles loose, and running water carries them away; wind does the same on dry ground. The standard tool for water erosion is the Universal Soil Loss Equation (Wischmeier and Smith, in use since the 1960s and 1970s): A = R × K × LS × C × Prain erosivity × soil erodibility × slope length and steepness × crop cover × conservation practice, in tonnes per hectare per year The last two factors are the ones a farmer controls. Keep the ground covered (C) and break up the slope with contour rows or terraces (P), and loss falls by factors of ten. David Montgomery's 2007 review of more than 1,600 measurements found that erosion from conventionally ploughed fields averaged one to two orders of magnitude faster than soil is produced, while no-till fields lost soil at rates close to formation. He estimated the net loss from ploughed fields at around a millimetre a year, enough to strip a typical hillslope soil over spans like the lifetime of a civilisation, and the book that followed, Dirt, argued that this is why some societies declined. Archaeologists disagree about how much of any one collapse soil explains. FAO's 2015 report on the world's soil resources estimated about a third of soils as moderately to highly degraded by erosion, salt, compaction, acidity and pollution. Interactive · How fast does a field lose its soil? Bare groundPloughed maizeNo-till maizeGrass No practiceContour rowsTerraces Slope (%) Slope length (m) Rain erosivity R (MJ·mm per ha·h·yr) USLE with K fixed at 0.03 t·ha·h per ha·MJ·mm. The cover factors (bare 1, ploughed maize 0.3, no-till 0.08, grass 0.01) and practice factors (contour 0.6, terraces 0.15) are round illustrative values; real ones depend on crop stage, residue and region. 1 mm of soil over 1 ha is about 13 tonnes at 1.3 t per cubic metre. The model cannot see gullies or tillage erosion. At the defaults, ploughed maize on an 8% slope loses about 29 tonnes per hectare a year, 2.2 mm, so 20 cm of topsoil would last about 90 years. No-till with contour rows loses about 4.6 tonnes (0.35 mm), enough for about 570 years, and grass loses under 1 tonne. Natural soil formation is usually estimated at under about 0.1 mm a year, or roughly a tonne per hectare, so only the grass case sits near it. Raise the slope to 20% and every number climbs, which is why steep land is terraced in the Andes, in the Philippines, in Yemen and in southern China. Not all soils are the same story. The Amazon's terra preta, dark earths rich in charcoal and pottery, were built up by Indigenous farmers over centuries and stay fertile today, evidence that people can make soil as well as lose it. Soil organic matter holds carbon, water and nutrients, which is why cover crops, mulch and manure matter. Nitrogen: the bottleneck, and Haber–Bosch Plants need nitrogen more than any other nutrient except what the air and water provide, and nitrogen is everywhere: 78% of the atmosphere. But the N2 molecule has a triple bond that almost no organism can break. Bacteria can, including those in the root nodules of beans, peas and clover, and lightning breaks a little. For most of history this set a ceiling on food: farmers rotated legumes, spread manure, mined guano and Chilean nitrate, and populations stayed under the limit. Fritz Haber showed in the summer of 1909 that ammonia could be made from nitrogen and hydrogen, and Carl Bosch scaled it up at BASF's Oppau plant, which began production in 1913. The reaction runs at high pressure and temperature over an iron catalyst, and the hydrogen comes mostly from natural gas, so ammonia production uses roughly 1–2% of the world's energy. Haber won the Chemistry Nobel in 1918, Bosch in 1931. Haber's other legacy was leading Germany's chemical-weapons programme in the First World War, the first use of chlorine gas at Ypres in 1915. The same chemistry fed and killed. Erisman and colleagues estimated in 2008 that synthetic nitrogen fertiliser feeds nearly half the world's people, about 48%. The rest of the story is that much of it never reaches a plant. Global assessments put the share of applied nitrogen that ends up in the harvested crop at roughly half; the rest is lost as nitrate in water, ammonia and nitrous oxide in air. Nitrous oxide is a greenhouse gas about 273 times as strong as carbon dioxide per tonne over 100 years (IPCC AR6), and nitrate in rivers feeds the dead zones seen in Ecology (35/48). yield rises fast, then flattens at a plateauthe last kilogram of nitrogen buys almost no grain, but it all leaves the field if the crop cannot use it Interactive · How much nitrogen is enough? Nitrogen applied (kg per ha) Price ratio: kg of N costs this many kg of grain Quadratic-plateau response, a standard agronomic form, with invented round parameters: 5 t/ha with no fertiliser (soil supply), plateau 11 t/ha at 200 kg N/ha. Grain is taken as 1.5% nitrogen (15 kg per tonne). Real responses differ by crop, soil, weather and previous crop. At 100 kg the field yields 9.5 tonnes and each extra kilogram of nitrogen still buys 30 kg of grain. At 150 kg it buys 15. At 200 kg it buys none, and every kilogram above that is surplus: at 250 kg, 85 kg per hectare is left over. With nitrogen costing the equivalent of 5 kg of grain a kilogram, the profit-maximising dose is about 183 kg, a little under the plateau. Farmers who add a safety margin, because a bad year costs more than the extra bag, aren't foolish. This is why policies on fertiliser pricing, timing, precision application and legume rotations work on the slope of this curve. Worldwide the picture is lopsided. Parts of China, India and Europe have applied far more than crops can use, while much of sub-Saharan Africa applies far too little and has the largest yield gaps. Yields, land and the sparing-or-sharing argument Higher yields should spare land: if you grow twice as much per hectare you need half the land for the same food, leaving the rest for forest. This was Norman Borlaug's argument, and in crude terms it has held (see Plant Biology, 35/53). But economists have long noted a rebound: a more profitable crop can lead farmers to clear more land, which researchers have argued happened with soy and cattle in South America and oil palm in Southeast Asia. Yield gains spare land only if something else (law, price, enforcement, the cost of clearing) holds the frontier. A second argument is about what kind of farming to put on the land. In 2005 Rhys Green and colleagues set out the choice. Land sharing farms the whole landscape in a wildlife-friendly, lower-yield way. Land sparing farms a smaller area intensively and keeps the rest wild. Which wins depends on how fast a species' numbers fall as yield rises. Make a simple model: the density of a species is 1 on wild land and 1 − yp at relative yield y, and the landscape must produce a fraction P of the maximum. Farming a fraction P/y of the land at yield y leaves total species density: S = 1 − P × yp − 1if p > 1 the best choice is the lowest yield (sharing); if p < 1 it is the highest (sparing) Interactive · Share the land or spare it? Food needed (share of maximum output) Curve shape p (below 1: species fall fast at low yields) Yield on the farmed land A teaching model from the Green et al. (2005) set-up, with a made-up density curve. Yield is limited to at least P (all land farmed). Real species differ: some thrive on farms, others vanish at the first plough. With half the food needed and p = 0.5 (species fall quickly at first), the best landscape farms half the land at full yield and spares the other half: species density 0.50, against 0.29 when the whole landscape is farmed gently. Change p to 2 and the answer reverses: sharing gives 0.75 and sparing 0.50. Field studies point both ways. Phalan, Balmford and colleagues (2011) found that most of the species they counted in Ghana and India did better under sparing, but other places, and other groups such as birds on traditional farms, favour sharing, and the sparing argument needs the spared land actually to be protected. What we eat: diets and emissions The biggest lever on food's footprint is what is on the plate. The most-cited data set is Joseph Poore and Thomas Nemecek's 2018 analysis in Science, which pulled together data from about 38,700 commercial farms in 119 countries and around 40 products. They estimated that food produces about 26% of global greenhouse gas emissions, with livestock and fisheries contributing about 31% of food emissions. Animal products, they found, use about 83% of farmland while providing about 18% of calories and 37% of protein. About 80% of agricultural land, counting grazing and feed crops, serves meat and dairy; only about half of the world's cereal goes directly to people, while about 41% goes to animal feed. Food (average)kg CO2e per kgm² of land per kg Beef (beef herd)99.5326 Lamb and mutton39.7370 Cheese23.988 Pork12.317 Poultry9.912 Eggs4.76.3 Rice4.52.8 Tofu3.23.5 Peas1.07.5 Wheat and rye1.63.9 Potatoes0.50.9 Poore and Nemecek (2018), via Our World in Data, reference year 2010. Global averages: the same food varies widely between producers, and the paper stresses that how a food is produced can matter as much as which food it is. Three honest complications. First, the unit changes the ranking: per kilogram, per calorie and per gram of protein give different orders for foods like nuts, rice and pulses. Second, the average hides the system: beef from deforested Amazon pasture and beef from dairy herds on Irish grassland are very different products, and Poore and Nemecek's table lists a separate figure for beef from dairy herds (33 kg CO2e per kg). Third, grazing land is often unsuitable for crops, so a defender of pasture-based livestock can fairly argue that removing the animals does not turn that land into farmland, and defenders of herding economies in the Sahel, the Andes and Mongolia point out that livestock is a livelihood there, not a luxury. The reply is that most of the land in the data is spent on a small fraction of food. Methane is also treated differently by different accounting methods, and the 100-year metric used here is itself debated by scientists. Poore and Nemecek's headline was that a global shift away from animal products could cut food's land use by about three-quarters and its emissions by about half; whether and how much people should change is a values question that this piece does not decide. Interactive · A year on a plate Meat at most mealsMixed, modest meatVegetarianVegan Beef (g per day) Cheese (g per day) Poultry (g per day) The diets are invented round examples, not surveys; the other foods follow the preset. Emissions and land use per kg are the Poore and Nemecek averages in the table above (and for other foods in the same data set); processing, transport and waste are inside those figures only partly, and the figures are 2010 global means. With the "mixed" preset, the year's food comes to about 1.9 tonnes of CO2e and about 4,800 m² of land. The "meat at most meals" diet is about 3.5 tonnes and 10,000 m², and the vegan one about 0.5 tonnes and 960 m². Move only the beef slider and you will find that it dominates. The list can mislead, so remember the scale: these are model averages, and what a real person emits depends on where and how their food is grown. Cutting waste helps too: the UN Environment Programme's Food Waste Index 2024 put waste at around a billion tonnes in 2022, roughly a fifth of food available to consumers, and Poore and Nemecek estimate waste as about a quarter of food emissions. Organic versus conventional, argued fairly "Organic" is a set of production rules (no synthetic fertilisers or most synthetic pesticides) and not a measure of health or environmental impact. The evidence is mixed because the claims are about different things. The case for. Organic fields hold more soil carbon and support more species on the farm. A 2012 meta-analysis (Tuomisto and colleagues) found about 30% higher species richness on organic farms. Organic systems that rely on legumes and manure avoid the energy cost of Haber–Bosch and lower the risk of pesticide pollution in water. The case against. Yields are lower. Seufert, Ramankutty and Foley (2012) found organic yields about 25% below conventional on average, with the gap anywhere from 5% to 34% depending on crop and conditions. A 2015 re-analysis by Ponisio and colleagues put it at about 19%, shrinking to about 8–9% with rotations and multi-cropping. Lower yields mean more land for the same food, and because land conversion releases carbon, the per-kilogram emissions advantage shrinks or reverses for some crops. Without synthetic nitrogen, supplying enough nutrients is the limit. The middle. Modelling by Muller and colleagues (2017) suggested that a fully organic world could feed 9 billion people in 2050, but only if food waste fell by half and animals ate far less crop feed, which is a diet change by another name. Many agronomists favour options that borrow from both camps: legume rotations, integrated pest management, precision fertiliser and cover crops. Interactive · What a yield gap costs in land Organic yield gap (%) Share of cropland converted to organic (%) Arithmetic: land needed = 1 + share × (1 ÷ (1 − gap) − 1), for the same total output and no change in diet or waste. The range 5–34% is from Seufert et al. (2012); 19% is the Ponisio et al. (2015) average. At a 19% gap, converting all cropland to organic needs about 24% more land for the same output; converting 30% needs about 7% more. Whether that is a good trade depends on what the extra land would have been, which is a judgement about biodiversity, carbon and food prices, not a number from a model. GM crops, argued fairly Genetic modification inserts one or a few genes into a crop. The two big commercial traits are insect resistance (the Bt gene from a soil bacterium) and herbicide tolerance. The science and the politics have moved apart. What the evidence says about safety. The US National Academies' 2016 report on genetically engineered crops found no substantiated evidence that approved GE foods are less safe to eat than conventional ones, and major scientific bodies worldwide have said much the same, while stressing that each new product should be assessed on its own traits, not on the technique. The public is far less convinced than scientists. What the evidence says about farms. A 2014 meta-analysis (Klümper and Qaim) found that GM adoption cut chemical pesticide use by about 37%, raised yields by about 22% and farmer profits by about 68% on average, with the largest gains in developing countries; yield gains were bigger for insect-resistant crops (about 25%) than for herbicide-tolerant ones (about 9%). Critics point to results that vary by place and year, to the use of some non-peer-reviewed studies, to the evolution of resistance (glyphosate-resistant weeds, and pests that adapt to Bt), and to seed prices and corporate concentration. India's Bt cotton raised yields and cut insecticide sprays in the years after its 2002 approval, though how much and for whom has been disputed. Where regulation differs. The European Union authorises GM crops case by case and grows almost none, while the United States, Brazil, Argentina, Canada and India grow large areas (India only cotton). Nigeria approved a pest-resistant Bt cowpea in 2019. Golden Rice, engineered to supply beta-carotene against vitamin A deficiency, was approved for cultivation in the Philippines in 2021, but in April 2024 a Philippine court of appeals halted its commercial propagation and that of a Bt eggplant on safety and legal grounds, and the case has gone on appeal. Newer gene-editing techniques such as CRISPR raise the same questions in new legal forms. Farming systems from every continent Most of the textbook examples come from the temperate North. Farmers have developed other answers, adapted to local water, soil and labour. PlaceSystemWhat it shows AfricaNiger and Burkina Faso: farmer-managed natural regeneration and zaï planting pitsFarmers have restored degraded drylands by protecting tree stumps that resprout, and by digging pits that catch rain and manure; reported to have re-greened millions of hectares in Niger. AsiaHani rice terraces (Yunnan, China, UNESCO 2013); paddy rice-fish cultureWater, fish, ducks and rice in one managed landscape; terraces turn steep ground into level fields. South AmericaAndean terraces and potato diversity; Amazonian terra pretaAltitude zones, thousands of potato varieties and soils built by people. North AmericaThe Haudenosaunee "three sisters" (maize, beans, squash); the mechanised Great PlainsCompanion planting where beans fix nitrogen for maize, and the opposite scale: huge farms, big machines, ploughing lessons from the Dust Bowl. Central AmericaMilpa; the chinampas of the Valley of MexicoMixed maize fields, and raised garden beds on lake shallows still farmed at Xochimilco. EuropeIberian dehesa and montado; Dutch greenhousesOak-pasture agroforestry for pigs, cattle and cork; and the opposite: high-tech, high-yield protected horticulture. OceaniaKuk Swamp (Papua New Guinea, UNESCO 2008); Aboriginal fire managementDrained garden plots dating back thousands of years, among the world's earliest agriculture sites; land managed by fire, not the plough. AntarcticaNo farming; a test greenhouse (EDEN-ISS) at the German Neumayer III stationFood grown with no soil, in a closed system, to practise for places where soil does not exist. The common thread is that every system is a bundle of choices about water, nutrients and labour, tuned over generations. The modern argument is less "tradition against technology" than which parts of each bundle fit which landscape and market. What a graduate just sees Soil is a stock built over centuries and lost over decades; cover and slope decide the rate. Haber–Bosch feeds nearly half of humanity, and roughly half of what is applied does not reach the crop. Crop response to nitrogen flattens; the last bags buy little grain and pollute a lot. Higher yields spare land only when something stops the frontier from moving. Sparing or sharing depends on the shape of the species-yield curve, so the answer is empirical and local. Food's emissions are dominated by a few animal products; the unit (kg, kcal, protein) changes the ranking, and producers vary widely. Organic and GM are each a bundle of claims; check which claim, for which crop, in which country. Farming systems from every continent are solutions to local constraints, not stages on one ladder. Where it shows up next Environmental Economics & Policy (36/19): fertiliser taxes, subsidies, payments for soil carbon and the price of food. Environmental Data & GIS (36/20): satellite crop maps, drought indices and the land-use data behind the numbers here. Conservation & Applied Ecology (36/15): sparing versus sharing is the same debate seen from the wildlife side. In the world: agricultural extension services, the CGIAR research centres, soil-testing labs, food companies' supply-chain claims and the FAO's hunger statistics. If you want to go deeper 📘 Textbook. Ray Weil and Nyle Brady, The Nature and Properties of Soils (Pearson, 15th edition, 2017). The standard soil-science text. 📘 Textbook. Stephen Gliessman, Agroecology: The Ecology of Sustainable Food Systems (CRC Press; use the latest edition). The farm-as-ecosystem view. 📘 Gentler. David Montgomery, Dirt: The Erosion of Civilizations (University of California Press, 2007), and Vaclav Smil, Enriching the Earth (MIT Press, 2001), on nitrogen and the Haber–Bosch story. 🌐 Free course. MIT OpenCourseWare 1.74, Land, Water, Food, and Climate (Fall 2020), a graduate course with lecture notes on land, nutrients, agroecology and genetic engineering. Also free: Our World in Data on food and emissions. The takeaway Food is soil, nitrogen and land, in that order of hidden importance. Soil is a slow stock; nitrogen is a fast and leaky flow; land is where the two meet wildlife. Most debates in the field are about which trade-off to accept, so check which claim a speaker is making and what it is measured per. This describes how the system works, not what anyone should eat or farm. Try this: pick one food you ate today and trace it back: where it grew, what fed it (fertiliser, manure, feed), and how far it travelled. Then look up its number in the table and ask what the average hides. Sources & Further Reading Sources. Soil-forming factors (Jenny, 1941); the USLE (Wischmeier and Smith); Montgomery, "Soil erosion and agricultural sustainability", PNAS 2007; FAO Status of the World's Soil Resources (2015); Haber and Bosch dates and Nobel years; Erisman and colleagues, Nature Geoscience 2008; IPCC AR6 for the nitrous oxide warming potential; Green and colleagues, Science 2005, and Phalan and colleagues, Science 2011; Poore and Nemecek, Science 2018, with per-kilogram figures from Our World in Data (reference year 2010); Seufert and colleagues, Nature 2012; Ponisio and colleagues, 2015; Tuomisto and colleagues, 2012; Muller and colleagues, 2017; National Academies 2016; Klümper and Qaim, PLoS ONE 2014; Philippine Court of Appeals rulings on Golden Rice (April and August 2024); UNEP Food Waste Index 2024. Regional farming-system examples and some dates are given in outline and should be checked against UNESCO and FAO pages before being quoted. The Dust Bowl anecdote is the usual telling and details vary between accounts. All interactive numbers were computed in node; the models are illustrative. 🌐 Our World in Data: food and emissions 🌐 MIT OCW 1.74 📘 Weil & Brady, The Nature and Properties of Soils 📘 Montgomery, Dirt; Smil, Enriching the Earth Step 10. Pollution & Environmental Health: The Dose, the Plume and the Count ---------------------------------------------------------------------------- Why: Air, water and chemical pollution, and what it does to health. Pollution is a dose delivered to people. Learn how a dose becomes a harm, how a chimney becomes a concentration, and how anyone counts the dead, and most of the argument becomes readable. On 5 December 1952 a cold, still fog settled over London and stayed for four days. Coal smoke from millions of chimneys had nowhere to go. Hospitals filled with people who could not breathe, and undertakers ran out of coffins. Contemporary counts put the deaths at about 4,000, and later analyses of the death records suggest it was several times that, up to roughly 12,000. The Clean Air Act of 1956 followed. The smog came from a fuel, a chimney and the weather, and what it did to people could be counted. All of environmental health is that chain: a source, a path, a dose and a count. The chain is still running. The Lancet Commission on Pollution and Health estimated that pollution caused about 9 million deaths in 2015, and its 2022 update, using 2019 data, found about 9 million again, around one death in six worldwide. It put air pollution at about 6.7 million of those, water pollution at about 1.4 million and lead at about 0.9 million, with most of the burden in low- and middle-income countries. These are modelled estimates with wide uncertainty, built the way Epidemiology & Evidence-Based Medicine (35/58) teaches, and this piece shows you how. This piece explains how environmental health works. It is not medical advice. For a health question, see a clinician; in an emergency, call your local emergency number. The course in one box Who takes itEnvironmental science, public-health, civil and environmental engineering students, in year 3 or 4. Toxicology and exposure assessment are the heart of it, and programmes from the UK to Brazil, India and South Africa teach the same chain. What it is forLinking emissions to concentrations, concentrations to doses, and doses to disease, so that limits and clean-ups can be set sensibly. Comes afterGeneral Chemistry (35/36) and Epidemiology & Evidence-Based Medicine (35/58). Leads toEnvironmental Economics & Policy (36/19), Environmental Data & GIS (36/20) and Public & Global Health (35/61). Beside it: Environmental Engineering (34/68), on how water is cleaned. What this piece gives youYou will not be able to do a risk assessment. You will see why the shape of a dose–response curve is a live argument, what PM2.5 and the WHO guideline mean, why a taller chimney can move a problem rather than remove it, why some chemicals climb food chains, how lead became the best-studied pollutant in history, and why plastics are hard to count. Easier first reads: Entropy (13/12), for why waste never goes away, and Food Safety at Home (14/06). The dose makes the poison, and the curve's shape matters "All things are poison, and nothing is without poison; only the dose makes a thing not a poison", wrote Paracelsus in the 1530s. Water, salt and vitamin A can all harm in excess. Toxicology turns the saying into a graph, the dose–response curve: dose along the bottom, the chance or size of harm up the side. What a graduate remembers is that the whole argument is at the left-hand end, where doses are low and effects are too rare to see in any one study. There are three common shapes. A threshold model says nothing happens until a dose is passed (the body repairs or clears small amounts). A linear no-threshold (LNT) model says every bit adds risk in proportion. A saturating curve rises fastest at low doses and flattens later. Regulators typically assume no threshold for substances that damage DNA and for the dose levels they cannot measure, as a precaution. Critics, including supporters of hormesis (a claim that low doses of some agents are beneficial), say this overstates low-dose risk; supporters of precaution reply that the data at the low end are too sparse to rule it out. For fine particles the WHO states that no safe level has been identified, and the curves used in global burden studies are typically concave: steepest at low levels. expected cases = people exposed × (extra risk at their dose)a tiny risk times a huge population is a large count The multiplication at the bottom is the second lesson. Epidemiologist Geoffrey Rose pointed out in 1981 that most cases of a disease come from the many people at moderate risk, not the few at high risk, simply because there are more of them. Try it below. Interactive · Three curves, one population No thresholdThresholdSaturating Dose (arbitrary units) Threshold (used by the threshold curve) People exposed (millions) Invented curves for a fictional pollutant, not data. No threshold: 2 extra cases per 100,000 per unit. Saturating: 220·d ÷ (d + 55). Threshold: 2 per unit above the threshold. The last line compares 1% of people at dose 80 with the other 99% at the dose you chose. With the no-threshold curve, a dose of 10 gives 20 extra cases per 100,000, so 10 million people give 2,000. The 1% at dose 80 (100,000 people) produce 160 cases; the other 99% at dose 10 produce 1,980. The few high-dose people are the visible emergency, but the many at lower doses are most of the count. With a threshold of 20, dose 10 produces none, which is why the shape of the left-hand end is worth arguing about. Air: PM2.5, the guideline and who breathes what PM2.5 is particulate matter 2.5 micrometres across or smaller: soot, smoke, sulphate and nitrate droplets, and dust, from burning fuel in engines, power stations, cooking fires and wildfires, and formed in the air from gases such as sulphur dioxide. A hair is about 70 micrometres wide, so particles this small slip past the nose and throat, reach deep into the lungs and carry some of their material into the blood. They are linked to heart disease, stroke, lung disease and cancer, which is why fine particles, not the more visible coarse dust, dominate the death counts. ultrafine ≤0.1PM2.5 ≤2.5PM10 ≤10hair ≈70log scale, micrometres The World Health Organization's Global Air Quality Guidelines of September 2021 cut the annual PM2.5 guideline from 10 to 5 µg/m³ and the 24-hour value from 25 to 15 µg/m³, and cut the annual nitrogen dioxide guideline from 40 to 10 µg/m³. Guidelines are not laws. Countries set legal limits that balance health against cost and feasibility, and the legal limits differ widely: the annual PM2.5 figures are 9 µg/m³ in the United States (set in 2024), 10 µg/m³ from 2030 in the European Union's revised air quality directive, 35 µg/m³ in China's standard for most areas (a stricter 15 for the cleanest zones), and 40 µg/m³ in India's national standard. Each can be justified, and none is the WHO number. The State of Global Air programme's 2025 report linked air pollution to roughly 7.9 million deaths in 2023, about 4.9 million from outdoor air and 2.8 million from household air pollution, mostly from cooking with solid fuels. These are estimates from a different group with a different method from the Lancet Commission's, and the totals differ for that reason. How do we know the particles themselves are the cause, not the smoking, income or climate of the places that have them? That is the confounding problem of Epidemiology & Evidence-Based Medicine (35/58). The Harvard Six Cities study (Dockery and colleagues, 1993) followed adults in six US cities for about 15 years and found that, after adjusting for smoking and other factors, mortality in the most polluted city was about a quarter higher than in the cleanest. Natural experiments reinforce it: studies of a steel-mill closure in Utah's valleys in 1986 and 1987 found fewer admissions for children's respiratory disease, and cities that cleaned their air saw life expectancy rise. Interactive · How many times the guideline? At the WHO guidelineEU 2030 limitIndia's standardA heavily polluted year Annual mean PM2.5 (µg/m³) Annual limits as described in the text (WHO 2021 guideline; US 2024; EU from 2030; China, most areas; India). Check the current official texts. The 'heavily polluted' value is an illustration, not a particular city. At 100 µg/m³ the air is 20 times the WHO guideline, and even India's standard, the loosest here, is exceeded 2.5 times. At 8 µg/m³ the air meets every limit in the table but the WHO's. Because the curve has no known safe floor, the guideline is not a line between safe and unsafe. It is a point on a slope that the WHO judged achievable and protective. How far a plume goes A concentration in the air depends on how much is released, how high, and how fast it mixes. Turbulence spreads a plume sideways and upward in a bell-shaped (Gaussian) pattern, and the widths grow with distance at rates that depend on the weather. Meteorologists sort the weather into stability classes: unstable (sunny, with rising thermals), neutral (overcast, windy) and stable (clear night, still, often with an inversion). At ground level, directly under the plume, the concentration is: C = Q / (π u σy σz) × exp( − H² / 2σz² )Q = emission rate · u = wind speed · H = effective release height · σ = how wide the plume has spread sideways (y) and upward (z) Read it as two ideas. Dilution: more wind, or a wider plume, means a lower concentration. Height: the exponential term keeps the plume off the ground until it has spread to about the height H. Tall stacks were built to exploit this, and they worked locally, but taller stacks without cleaner fuel moved sulphur from nearby towns to far-away forests and lakes, one source of the acid rain that polluted Scandinavia and eastern North America from the 1970s. And on a stable night a lofted plume can stay aloft for kilometres and then come down far away. Interactive · A chimney and the weather Sunny and unstableOvercast, neutralClear night, stable Wind speed (m/s) Effective release height (m) Gaussian plume for a continuous source of 100 g/s on flat ground, centreline at ground level, with Briggs's open-country spread formulas for classes B, D and F (Briggs 1973, as tabulated in standard dispersion handbooks). No chemistry, no buoyant rise, no buildings: a teaching model, not a regulatory tool. With a 50 m effective height and a 3 m/s wind, the overcast case peaks at about 1,600 µg/m³ about 800 m away. In sunny, unstable air the same chimney peaks higher (about 2,400) but closer (about 300 m), because turbulence brings the plume down quickly. On a clear night the peak is lower (about 600) but 4 km away, and at 1 km the ground sees almost nothing: the people nearest to the stack are spared and those farther off are not. Raise the wind to 8 m/s and the peak falls to about 600 for the neutral case. Dilution is the cheapest pollution control there is, and it fails when the air will not move. Persistent chemicals and the food-chain ladder Some chemicals vanish in days; others stay for decades. Two properties decide which become problems: persistence (the half-life in soil, water or bodies) and fat-solubility, measured by log Kow, the octanol–water partition coefficient. A fat-loving chemical leaves water for the fat of living things. A rule of thumb from the 1970s relates the two: log BCF ≈ 0.85 log Kow − 0.70, where the bioconcentration factor (BCF) is how many times more concentrated the chemical is in a small aquatic organism than in the water. Then, because fat-bound chemicals are not excreted, each meal passes them to the next consumer along with the food, so the concentration rises up the chain, biomagnification, by a factor per step (a biomagnification factor, BMF). top predator = water × BCF × BMF³four rungs in a food chain: plankton, small fish, large fish, fish-eating bird The classic case is DDT. Rachel Carson's Silent Spring (1962) argued that it thinned the eggshells of birds of prey and killed songbirds, and the United States banned most uses in 1972. DDT is also a reminder that the story has a second side: it saved huge numbers from malaria, and the Stockholm Convention (adopted in 2001, in force from 2004) still allows it for disease-vector control in some countries. Mercury is the other textbook case, with the Minamata disease of the 1950s in Japan and the global Minamata Convention (adopted 2013, in force from 2017). The modern concern is PFAS, the "forever chemicals": thousands of compounds that resist breakdown. In 2024 the US EPA set drinking-water limits of 4 nanograms per litre for two of them, PFOA and PFOS, though the schedule has been under review since. Interactive · Up the food chain Fat-solubility, log Kow Biomagnification factor per step Half-life in the water (years) Years since the release stopped Fictional chemical, water starting at 1 nanogram per litre; concentration in organisms in nanograms per kilogram. The BCF rule of thumb is a rough regression, the factors per step are invented, and real chemicals are metabolised by some animals and not others. Bar lengths are on a log scale. At log Kow 6, BCF is about 25,000, and a factor of 3 per step puts the top bird at about 680,000 times the water concentration. A chemical with log Kow of 3 and the same factors is magnified only about 2,000 times. After 20 years with a 5-year half-life the water is at 6% of the start and the whole ladder with it, which is why banned persistent chemicals take generations to clear and why a short half-life is the best property a new chemical can have. Lead: one metal, a century of evidence Lead is the best-studied pollutant in history, and its lesson is about speed. Thomas Midgley Jr., at General Motors, found tetraethyl lead to be an effective anti-knock additive for petrol on 9 December 1921, and leaded petrol spread across the world. The geochemist Clair Patterson, measuring the age of the Earth in the early 1950s, found his samples contaminated by environmental lead, traced it in ice cores to the arrival of leaded petrol, and became an early and effective campaigner against it. The US phased down lead in petrol from 1976 and banned it for on-road vehicles from 1 January 1996, and Algeria, the last country to sell it, stopped in July 2021; the UN Environment Programme declared the end of leaded petrol on 30 August 2021. The harm is well documented, and it falls hardest on children. Lead damages the developing brain, and the World Health Organization states that no level of exposure has been identified as safe. In the US the CDC's blood lead reference value, the level at which children are flagged for follow-up, was lowered to 3.5 micrograms per decilitre in 2021, from 5. A 2020 UNICEF and Pure Earth report estimated that around one child in three, up to 800 million worldwide, has a blood lead level at or above 5 micrograms per decilitre, with the main sources including battery recycling, old paint, spices, cookware and pipes. In Flint, Michigan, the city switched its water source in April 2014 without adding corrosion control, and lead leached from old pipes: a failure of treatment, covered further in Environmental Engineering (34/68). Two points matter for the rest of the course. First, lead was an enormous natural experiment: blood lead fell with the phase-out in the countries that did it, which is strong evidence that policy works. Second, the evidence kept hardening for decades at lower and lower doses, as measurement improved, and each time the "safe" level moved down. That is what a no-threshold-in-practice pollutant looks like. Plastics: counting what is hard to count The scale is counted best in a 2017 paper by Roland Geyer, Jenna Jambeck and Kara Lavender Law in Science Advances: about 8.3 billion tonnes of plastic produced from 1950 to 2015, of which about 6.3 billion tonnes became waste. Of that waste, roughly 9% was recycled, 12% incinerated, and 79% accumulated in landfills or in the natural environment. In an earlier paper, Jambeck and colleagues estimated that 4.8 to 12.7 million tonnes entered the oceans from land in 2010; a 2021 study of river inputs (Meijer and colleagues) estimated 0.8 to 2.7 million tonnes a year, concentrated in a thousand or so rivers. The estimates differ because plastic leaks in many ways and is measured in few. Fate of plastic waste to 2015ShareBillion tonnes (of 6.3) Recycled9%0.57 Incinerated12%0.76 Landfill or the environment79%4.98 What this does to health is the open question. Microplastics (under 5 mm) and nanoplastics have been found in human blood, placentas and arteries; a 2024 study in the New England Journal of Medicine found plastic particles in the fatty deposits of the carotid artery in many patients, and the patients who had them had more heart attacks, strokes and deaths over about three years. That is an association, not proof of cause, and methods for measuring tiny plastic particles in tissue are being challenged. The additives in plastics (some phthalates, bisphenols and flame retardants) have clearer evidence of harm than the plastic itself. Governments are negotiating a treaty. The talks in Geneva in August 2025 ended without agreement on a text, so check the UN Environment Programme for where the talks stand now. What a graduate just sees Every pollution story is a chain: source, path, dose, harm. Break any link and the harm stops. The shape at the low-dose end of the curve is the real argument, and it is hard to measure. A small risk times a large population is a big number; most cases come from the many at moderate risk. Guidelines (WHO) and legal limits differ; a limit is a judgement about cost, not a line between safe and unsafe. Dilution works until the air stops moving, and a taller stack moves a problem. Persistent plus fat-soluble means it builds up along food chains; half-life decides the clean-up time. For lead, safe levels were revised down again and again; the best evidence for regulation is the fall after bans. Death counts for pollution are modelled estimates from several groups, with different methods and wide ranges. Where it shows up next Environmental Economics & Policy (36/19): pollution is the textbook externality; limits, taxes and trading schemes put a price on the dose. Public & Global Health (35/61): burden-of-disease counting and the household-air-pollution programmes behind the cooking-fire numbers. Soils, Agriculture & Food Systems (36/18): fertiliser and manure are the largest source of water pollution in many places. In the world: air-quality alerts, drinking-water standards, chemical regulation (REACH in the EU, TSCA in the US) and the engineers who run treatment works. If you want to go deeper 📘 Textbook. Gilbert Masters and Wendell Ela, Introduction to Environmental Engineering and Science (Pearson, 3rd edition 2008). A standard undergraduate text for dispersion, risk and water. 📘 Textbook. Howard Frumkin (ed.), Environmental Health: From Global to Local (Jossey-Bass/Wiley, 3rd edition 2016). The public-health view of exposures from air to climate. 📘 Gentler. Rachel Carson, Silent Spring (1962), the book that began modern environmental regulation, still readable as science writing. 🌐 Free course. MIT OpenCourseWare 20.104J / BE.104J, Chemicals in the Environment: Toxicology and Public Health (Spring 2005), covering toxicology, epidemiology and risk assessment. The takeaway Pollution is a chain from chimney to body, and each link has a rule: dilution and weather for air, persistence and fat-solubility for chemicals, dose and population for health. The numbers are estimates and the shape of the low-dose curve is argued, but the direction is clear: less exposure, less harm. Whether to pay for it is a matter of values as well as evidence. Try this: look up your city's air-quality reading for today and compare it with the WHO annual guideline of 5 µg/m³ for PM2.5. Then ask where the nearest big source is and which way the wind is blowing. Sources & Further Reading Sources. Lancet Commission on Pollution and Health (2017) and Fuller and colleagues, "Pollution and health: a progress update", Lancet Planetary Health, 2022 (deaths in 2019); WHO Global Air Quality Guidelines (2021); State of Global Air (2023 estimates, as summarised); Dockery and colleagues, New England Journal of Medicine, 1993; the 1952 London smog and the Clean Air Act 1956 (encyclopaedia summaries; death estimates range from about 4,000 to about 12,000); Briggs (1973) dispersion formulas and the Gaussian plume as in standard textbooks; Paracelsus on dose; Rose (1981) on prevention; Midgley, Patterson, the US phase-out and Algeria's end of leaded petrol (UNEP, 2021); CDC blood lead reference value (2021); UNICEF and Pure Earth (2020); Geyer, Jambeck and Law (2017); Jambeck and colleagues (2015); Meijer and colleagues (2021); Marfella and colleagues, New England Journal of Medicine (2024). The legal limits in the PM2.5 table, the PFAS rule and the plastics-treaty status change and should be checked against current official texts. All interactive numbers were computed in node; models and data in them are illustrative. 🌐 WHO Global Air Quality Guidelines 2021 🌐 MIT OCW 20.104J 📘 Masters & Ela, Introduction to Environmental Engineering and Science 📘 Carson, Silent Spring Step 11. Environmental Economics & Policy: Putting a Price on What Nobody Was Charged For ----------------------------------------------------------------------------------------- Why: Externalities, carbon prices, regulation and international agreements. Smoke, carbon and noisy neighbours share one economic problem: someone pays a cost that never appears on a bill. Economists have a toolkit for it, an argument about how to use it, and a few numbers that decide a lot. A diesel lorry drives past a school. The owner paid for the lorry, the fuel and the driver. Nobody paid for the exhaust that the children breathe, or for the extra tonne of carbon dioxide that will stay in the air for centuries. Those costs are real, they are large, and they have landed on people who were not in the deal. That gap between what a decision costs the decision-maker and what it costs everyone is the starting point of environmental economics. The second half of the subject is harder: once you see the gap, what do you do? Charge for the damage, let people negotiate, cap the total, ban the worst practice, or build a treaty? Reasonable people, and reasonable economists, pick differently. A graduate keeps both the tools and the arguments. This piece is about how the world works, not a recommendation for any country's policy. The course in one box Who takes itEnvironmental science and environmental studies students, usually in the final year; economics students take it as an elective (MIT teaches it as 14.42, Environmental Policy and Economics). Programmes in public policy, development and energy teach versions of it too. What it is forJudging environmental policies by their costs and benefits, and understanding why pricing, trading, regulation and treaties each work in some places and fail in others. Comes afterMicroeconomics (34/42), where externalities first appear, and Public Economics (34/49), on taxes, public goods and government failure. Leads toIt sits beside Climate Science (36/14), Energy Systems & Transitions (36/16) and Pollution & Environmental Health (36/17), and feeds How problems become policies, Public Policy (35/16). What this piece gives youYou will not be able to design a carbon market. You will see why a tax and a cap are cousins, why the discount rate can matter more than the science, and why "who pays?" is a separate question from "what is efficient?". It goes further than the externality section of Microeconomics (34/42), which is the easier first read. Figures here are illustrative unless dated. Externalities: the cost nobody was billed Arthur Cecil Pigou, in The Economics of Welfare (1920), described the gap with a smoking factory chimney and the neighbours' laundry. His idea is still the core: if each extra tonne of pollution does damage that the polluter does not pay, charge them the damage and they will pollute to the point where cutting one more tonne costs more than the harm it prevents. Not zero pollution, which would be absurdly expensive, but the right amount. The picture has two lines. Marginal damage rises with emissions: the first tonnes do little harm, later ones more. Marginal abatement cost falls as emissions rise: the cheap cuts come first and the last 5% costs the most. They cross at the efficient level of pollution, and the height of the crossing is the Pigouvian tax. tax = marginal damage at the efficient quantitycut emissions until the next tonne of cutting costs more than the harm it avoids Interactive · Where the lines cross How fast damage rises with emissions How fast cutting gets dearer marginal damage   marginal abatement cost An invented economy that would emit 100 million tonnes a year if left alone. Damage per tonne = slope × emissions; cost of the next cut = slope × (100 − emissions). Money in arbitrary units. Without JavaScript: with both slopes equal to 1 the efficient level is 50 million tonnes, the tax is 50 per tonne, and the policy is worth 2,500 units a year over doing nothing. Steeper damage or cheaper cutting both lower the efficient quantity. And the efficient level is almost never zero, which many students find uncomfortable and critics attack. Defenders answer that the same arithmetic tells you to cut hard when damage is high. Coase: when people can simply bargain In 1960 Ronald Coase asked what happens if there is no tax and the two sides can talk. His example came from English law: in Sturges v Bridgman (1879) a confectioner's noisy machinery disturbed a doctor next door. Coase noticed that whoever the court sides with, if the parties can bargain cheaply, the outcome that is worth most gets chosen. If the confectioner's business is worth more than the doctor's quiet, the doctor sells the right to make noise; if not, the confectioner pays to stop. The law decides who pays, not which outcome happens. The catch is the word "cheaply". Bargaining costs money and effort: finding the other party, agreeing the facts, enforcing the deal. With two neighbours that is small. With a river, a city's air or the atmosphere, the number of parties is huge and the cost of striking a deal swamps the gain. Pigou's tax and Coase's bargain answer the same gap in different settings. Interactive · A factory and a laundry Factory may polluteLaundry has clean air Factory's gain from running Laundry's damage if it runs Cost of striking a deal Invented numbers. The best outcome is for the factory to run only if its gain beats the damage. A deal is struck only if its gain is bigger than the cost of making it. Without JavaScript: with a gain of 60, damage of 80 and a deal cost of 5, the factory stops whichever side holds the right; the laundry pays if the factory holds it. If the deal cost is 30, the factory holding the right keeps polluting even though that is the worse outcome. Price or quantity: carbon taxes versus cap-and-trade For carbon, the two famous instruments are cousins. A carbon tax fixes the price and lets the quantity of emissions follow. A cap-and-trade system, or emissions trading system (ETS), fixes the quantity, issues that many permits, lets firms trade them and lets the price follow. In both, a firm with cheap cuts cuts more and a firm with dear cuts pays. That is the big gain over telling every firm to cut 10%: the same total reduction at lower total cost, because the cuts happen where they are cheapest. Interactive · Same cut, different bill Total reduction wanted (units) Surprise: cutting turns out dearer by Three invented firms whose cost of cutting the next unit rises at 1, 2 and 4 per unit already cut. Every number is computed from those slopes. Without JavaScript: to cut 30 units, a uniform rule (10 each) costs 350 while a price or permit market costs about 257, around 27% less. If cutting turns out 50% dearer, a cap keeps the cut at 30 and the permit price rises by half; a tax stays put and the cut falls to 20. The second half of the demo is Martin Weitzman's 1974 point (Prices vs. Quantities): when you are unsure of costs, a tax gives price certainty and quantity uncertainty, a cap the reverse. Which matters more depends on the shape of the damage. If damage rises sharply past a threshold, certainty about quantity is worth a lot, which favours a cap. If damage is spread evenly over decades, as it is for carbon accumulating in the air, an error in any one year's quantity matters little and price certainty has the edge. InstrumentTypeWhat is known (dated) EU ETSCap-and-trade, since 2005About €82 per tonne on 5 October 2026 (S&P Global). Fell from about €30 in April 2006 to €0.10 in September 2007 when too many permits were issued; under €3 in 2013; above €100 in 2023. SwedenCarbon tax, since 1991Among the longest-running and highest carbon taxes in the world. British ColumbiaCarbon tax, since 2008Returned revenue through tax cuts and credits; studies found modest emission cuts. Canada (federal)Consumer fuel chargeEnded in spring 2025 by the new government; the carbon price on large industry continues. ChinaNational ETS, since 2021Began with the power sector, set against output rather than a fixed total cap, and has been widened to more industries. WorldAll instrumentsWorld Bank (May 2026): 87 carbon pricing instruments, just over 29% of global emissions covered, more than $107 billion raised in 2025, average price near $21 per tonne. The sides, in their own terms. Tax advocates (many economists; in 2019 thousands of US economists signed a statement backing a carbon tax with dividends) say it is simple, hard to game, gives firms a predictable price and raises revenue that can cut other taxes or be returned. Cap advocates say the point of climate policy is a quantity, the carbon budget, so fix it; trading systems have also proved easier to pass politically because permits can be handed out. Regulation and subsidy advocates point out that some barriers are not about price (landlords who do not pay the heating bill, grids that take a decade to build, research that benefits rivals), so standards and public investment do work a price alone cannot. Sceptics of pricing note that it can be reversed overnight (France's fuel-tax rise in 2018 set off the gilets jaunes protests and was dropped) and that markets can leave pollution hotspots. The evidence shows each working somewhere; the field has not declared one the winner. The social cost of carbon: a price in search of a number To set a Pigouvian tax, or to decide whether a new rule is worth its cost, you need the damage from one more tonne of CO₂: the social cost of carbon (SCC). It is built in steps. Emit a tonne; estimate the extra warming; estimate the damage to farms, health, coasts and labour that warming causes in every future year; convert those damages to money; add them up, with later years counted for less. Integrated assessment models such as Nordhaus's DICE do this arithmetic. The answer swings hugely with the choices. The US government's interim estimate in 2021 was $51 per tonne (2020 dollars, 3% discount rate). In 2023 the Environmental Protection Agency published an update of $190 per tonne (2020 dollars, 2% discount rate, for emissions in 2020), reflecting newer science and a lower discount rate. In January 2025 an executive order disbanded the interagency group that produced the figures, and later that year the agency moved to overhaul the method. Other governments and researchers use their own numbers. Notice the range: a factor of four within a few years of one country's own work. Critics come from two directions. Robert Pindyck argued in 2013 that the models' key inputs, such as climate sensitivity, the damage function and the chance of catastrophe, are so poorly known that the output gives a false sense of precision. Others, including Martin Weitzman, argued that the tail risks (low-probability, very bad outcomes) mean standard calculations understate the case for action. Defenders reply that policy needs some number, and a transparent range beats a default of zero. Discounting: the Stern–Nordhaus argument Carbon's damage arrives over a century or more, and that makes the discount rate the most powerful dial in the model. At 5% a year, $1,000 of damage in 100 years is worth about $8 today. At 1.4%, it is worth about $250. A thirty-fold difference from one assumption that is about ethics as much as finance. The standard framework is the Ramsey rule: the rate is the pure rate of time preference ρ (do we value a future person's welfare less just because they are later?), plus the elasticity of marginal utility η (how much less an extra dollar matters to someone richer) times the growth rate g of consumption (the future will be richer). In symbols r = ρ + η·g. r = ρ + η × gdiscount rate = impatience + (aversion to inequality × growth) In 2006 Nicholas Stern's review, written for the UK government, took ρ = 0.1% (only to allow for the small chance humanity does not exist) and η = 1, giving an average discount rate near 1.4% and an estimate that unchecked warming would cost at least 5% of global GDP every year, perhaps 20% or more. William Nordhaus (Nobel 2018) replied that these choices contradict how people actually save and invest: policy should use rates close to what markets pay, and doing so supports a gentler, slower rise in the carbon price. Stern's side answers that choosing a discount rate is an ethical decision, and that treating future people as worth less is hard to defend. Weitzman called Stern's conclusion "right for the wrong reasons", arguing the real case rests on tail risks. A survey of about 200 experts by Drupp, Freeman, Groom and Nesje (2018) found a median recommended rate of 2%, and most thought rates from 1% to 3% acceptable. Interactive · What is a distant harm worth today? Stern-likeMiddle (about 2%)Market-based Pure time preference ρ (% per year) Elasticity of marginal utility η Growth of consumption g (% per year) The presets are illustrations of each camp's kind of choice, not their exact parameters, which change from model to model. The per-tonne damages are an invented stream (50 cents in year 1, rising 4 cents a year for 200 years), not a real social cost of carbon. Without JavaScript: at 1.4%, $1,000 of damage in 100 years is worth about $250 today; at 2%, about $138; at 4.5%, about $12. An invented damage stream (50 cents in year 1, rising 4 cents a year, for 200 years) sums to about $192 a tonne at 1.4% and about $32 at 4.5%. Paris: a treaty with no police Climate is the extreme case of Coase's problem: nearly 200 countries, no world government, and a benefit (a stable climate) that everyone shares whether or not they pay. Economists call that a free-rider problem: each country does better if others cut and it does not. The Montreal Protocol (1987) beat a similar problem for ozone-depleting gases, helped by cheap substitutes and trade penalties for non-members. Carbon has no equally cheap substitute for everything. Interactive · Should this country cut? Countries in the game Global benefit of one country's cut Home benefit (cleaner air, cheaper energy) Each country's cut costs it 10 units. The benefit of its cut is shared equally among all countries. An invented, simplified game: the real payoffs differ by country and over time. Without JavaScript: with 10 countries, a global benefit of 30 per cut, a private cost of 10 and no home benefit, each country gains only 3 from its own cut, so none cuts, though all cutting would give each 20. A home benefit above 7 makes cutting worthwhile alone. The Paris Agreement was adopted on 12 December 2015 and entered into force on 4 November 2016; 194 parties as of January 2026. Its design takes the game seriously. Instead of the top-down targets of the 1997 Kyoto Protocol, which bound mainly rich countries, each country submits its own nationally determined contribution (NDC), updated every five years and expected to progress. The aim is to hold warming "well below 2 °C" and pursue 1.5 °C. Nothing forces a country to meet its pledge. The enforcement is transparency, a global stocktake (the first reported in 2023) and reputation, plus the hope that cheap clean energy turns the "home benefit" slider in your favour. Article 6 allows countries to trade emission reductions, with rules settled at the Glasgow conference in 2021 to prevent double counting. Money is the live dispute. Under the 1992 framework convention, richer countries accept "common but differentiated responsibilities" because they emitted most of the carbon already in the air. At COP29 in Baku (2024), developed countries agreed to lead on at least $300 billion a year of climate finance by 2035; developing countries had asked for much more. The United States gave notice of withdrawal from Paris in January 2025, effective 27 January 2026, having left once before (2017 notice, effective 2020) and rejoined in 2021. The EU's carbon border adjustment (CBAM), which takes effect from 2026, is called a trade barrier by some exporters and a fairness measure by its backers. Environmental justice: who pays and who breathes it "Efficient" does not mean "fair", and environmental harms are rarely spread evenly. In 1982, residents of Warren County, North Carolina, a poor county with a large Black population, protested a landfill for soil contaminated with PCBs; more than 500 people were arrested in six weeks. A 1987 report by the United Church of Christ found that race was the strongest predictor of where hazardous-waste sites stood in the US. The 1991 People of Color Environmental Leadership Summit adopted 17 principles of environmental justice. The movement is worldwide: in Nigeria's Ogoniland, the writer Ken Saro-Wiwa campaigned against oil pollution and was executed in 1995. Economists give two partly separate analyses. One is exposure: poorer people often live nearer to roads, plants and dumps because land is cheaper there, and Coase would say the poor sell their quiet at a low price because they have fewer alternatives; critics note that a bargain between unequal parties is not a free one. The second is the incidence of the policy itself. A carbon price falls hardest, as a share of income, on households that spend the most on fuel and heating, which is why revenue use matters. A cap-and-trade system has a local twist: a national cap does not stop emissions of harmful local pollutants rising at a particular plant. A 2018 study of California's programme (Cushing and colleagues) found that in 2013–15, more than half of regulated facilities reported higher in-state greenhouse gas emissions than before, and that increases were more common near neighbourhoods with more residents of colour and more poverty; the authors called the results preliminary. Interactive · A carbon price, and what you do with the money Carbon price (per tonne) Share of revenue paid back equally to every household Ten invented income groups with invented fuel and goods spending, built so the burden is a bigger share of income at the bottom. Real results vary by country, climate and how the money is spent. The bars show the net effect as a percentage of income. Without JavaScript: at $50 per tonne with no rebate, the poorest tenth loses about 3.2% of income and the richest tenth about 1.0%. If all the revenue is returned equally, the poorest tenth gains about 4.0% net and the richest tenth loses about 0.5%. Climate justice adds a global version: the countries that emitted least, many in Africa, suffer much of the damage, and a fund for "loss and damage" was agreed at the 2022 conference in Sharm el-Sheikh. What counts as fair is a question of values; economics supplies the costs and the tools. A tax on carbon can be made progressive; a ban on a polluting plant can protect a neighbourhood a price would not; neither is automatic. What a graduate just sees An environmental problem is a cost landing on someone who was not in the decision. The efficient amount of pollution is where the next cut costs as much as the harm it prevents, almost never zero. A tax and a cap-and-trade system are cousins: one fixes the price, the other the quantity. Letting the cheap cuts happen first is where the savings come from. Bargaining fixes the problem only when the parties are few and the deal is cheap. The discount rate is an ethical choice that can swing the answer thirty-fold. A free-rider problem will not solve itself; treaties work through self-interest, transparency and, sometimes, trade penalties. "Who pays?" and "what is efficient?" are different questions; the answer to the first can be built into the policy. Where it shows up next Climate Science (36/14) and Energy Systems & Transitions (36/16): the carbon budget and the cost curves that make a price work. Pollution & Environmental Health (36/17): the damage side of the graph, from air pollution deaths to lead in water. Public Policy (35/16): how a carbon price or a ban survives a legislature, and why some are dropped. In the world: the permit price in the news, a congestion charge, a plastic-bag fee, an offset on a flight, a company's internal carbon price, and every debate about who bears the cost of the energy transition. If you want to go deeper 📘 Textbook. Tom Tietenberg and Lynne Lewis, Environmental and Natural Resource Economics (Routledge, many editions), or Charles Kolstad, Environmental Economics (Oxford University Press). Both are standard undergraduate texts; check for a recent edition. 📘 Gentler. William Nordhaus, The Climate Casino (Yale University Press, 2013), or Gernot Wagner and Martin Weitzman, Climate Shock (Princeton University Press, 2015); they disagree usefully on the risks. 🌐 Free reports. The World Bank's State and Trends of Carbon Pricing (yearly, free) and the Stern Review (2006, free online). 🌐 Free course. MIT OpenCourseWare 14.42 Environmental Policy and Economics (Spring 2011). The takeaway Environmental economics starts from a missing bill. Prices, caps, bargains, standards and treaties are different ways of putting the bill back, and each works in the setting it fits. The numbers that decide the most, the social cost of carbon and the discount rate, rest on ethical choices that no measurement can settle. Efficiency says what a policy costs and who gains; it does not say who deserves to pay. Try this: pick one thing you did today that has an external cost (a drive, a flight, a plastic wrapper), and write down who bears that cost and what price, tax or rule would put it on your bill. Sources & Further Reading Sources. Pigou, The Economics of Welfare (1920); Coase, "The Problem of Social Cost," Journal of Law and Economics 1960, with Sturges v Bridgman (1879); Weitzman, "Prices vs. Quantities," Review of Economic Studies 1974. EU ETS history and the 2013 low: Wikipedia, "European Union Emissions Trading System" (read 2 November 2026); EU ETS price of about €82 on 5 October 2026: S&P Global Commodity Insights report of that date; the reading of "above €100 in 2023" is from the same Wikipedia page. World Bank, State and Trends of Carbon Pricing 2026 (press release of 19 May 2026). Canada: Wikipedia, "Carbon tax," on the March 2025 declaration ending the consumer charge. Social cost of carbon: Resources for the Future primer on the EPA's 2023 estimates ($190 per tonne, 2020 dollars, 2% discount rate); Executive Order 14154 (January 2025); Wikipedia, "Social cost of carbon"; Pindyck, "Climate Change Policy: What Do the Models Tell Us?" Journal of Economic Literature 2013; Weitzman, "Fat-Tailed Uncertainty in the Economics of Catastrophic Climate Change" (2011) and "Fat Tails and the Social Cost of Carbon" (2014). Stern Review (30 October 2006); Nordhaus, "A Review of the Stern Review" (2007); Drupp, Freeman, Groom and Nesje, American Economic Journal: Economic Policy 2018. Paris Agreement: UNFCCC text and Wikipedia, "Paris Agreement" (194 parties as of January 2026; US withdrawal effective 27 January 2026). COP29 finance goal and COP27 loss-and-damage fund: UNFCCC decisions. Environmental justice: Wikipedia, "Environmental justice"; United Church of Christ, Toxic Wastes and Race in the United States (1987); Cushing et al., PLOS Medicine 2018 (data 2011–2015). 📘 Tietenberg and Lewis, Environmental and Natural Resource Economics 🌐 MIT OpenCourseWare 14.42 🌐 World Bank Carbon Pricing Dashboard Step 12. Environmental Data & GIS: Reading the Planet from Orbit ---------------------------------------------------------------- Why: Satellites, maps and environmental data. A satellite never sees a forest. It sees numbers: how much light of each colour came back from a square of ground. Turning those numbers into a map, a trend and an honest error bar is a craft with its own traps. .px{min-height:0;padding:0;border:0;border-radius:3px;aspect-ratio:1/1;width:100%} On most web maps, Greenland looks about as big as Africa. It is not. Africa is about fourteen times larger: roughly 30.4 million square kilometres against 2.17 million. Nobody lied; the map made a choice that is excellent for navigation and poor for comparing sizes, and the choice is invisible unless you know to ask. Environmental data is full of choices like that. A satellite picture of a field becomes a green-brown map through a formula. A "twenty-year trend" depends on which years you pick. A forest-loss figure comes from a map that is itself an estimate. A graduate of this course does not distrust every map; they ask four questions of any one: what was measured, at what pixel size, in which projection, and with what error? The course in one box Who takes itEnvironmental science, geography and earth science students, often in the final year as a lab-based course. Geographic information science (GIS) and remote sensing are taught in geography departments, in environmental programmes and increasingly in data science. What it is forCollecting, mapping and checking environmental data: what a satellite measures, how it becomes a map, and how sure you can be of the answer. Comes afterProbability & Statistics (34/05), for the idea of an interval and why noisy data fools us. Leads toIt feeds Conservation & Applied Ecology (36/15), Soils, Agriculture & Food Systems (36/18), Climate Science (36/14), Hydraulics & Water Resources (34/67) and any dissertation that uses a map. What this piece gives youYou will not be able to process a Sentinel image. You will see why a healthy leaf is bright in near-infrared, how a pixel can hide a small wood, why a map's area is not the real area, and how to read a trend and its error bar. All the landscapes and time series here are invented. Statistics (34/05) is the easier first read. Remote sensing: reading light from orbit Every surface reflects some fraction of the sunlight that hits it, and the fraction changes with the colour (wavelength) of the light. That pattern is its spectral signature. Chlorophyll in a leaf absorbs red and blue light for photosynthesis, so a healthy leaf reflects little red. The spongy cells inside the leaf scatter near-infrared light (just past what our eyes see), so a healthy leaf reflects a lot of it. Water absorbs nearly everything beyond red. Snow is bright in visible light and dark in the short-wave infrared. A sensor that measures a handful of bands can therefore tell crops, water, soil and snow apart even where they look alike to the eye. The long data record is public. Landsat 1 launched on 23 July 1972, and Landsat 9 on 27 September 2021, carrying on a record with 30 m multispectral pixels. The European Sentinel-2 pair launched on 23 June 2015 and 7 March 2017 (a third, 2C, on 5 September 2024), with 13 bands and pixels down to 10 m, covering a 290 km swath. Interactive · Spectral signatures Stylised, textbook-shaped curves, not measured spectra. The five dashed lines mark band centres like those of Sentinel-2 (blue 490, green 560, red 665, near-infrared 842 and short-wave infrared 1610 nm). Without JavaScript: a healthy crop reflects about 0.04 in red and about 0.50 in near-infrared; water reflects almost nothing in near-infrared; bare soil rises slowly from red to infrared. NDVI: one number for how green The simplest and most used trick is the normalised difference vegetation index. Take the near-infrared (NIR) and red reflectances, subtract, and divide by the sum. Healthy plants are dark in red and bright in NIR, so the answer is high; bare soil is nearly equal in both, so it sits near zero; water is darker in NIR than red, so it is negative. Rouse and colleagues at Texas A&M reported it from Landsat data in 1973–74, and Compton Tucker of NASA published early uses in 1979. NDVI = (NIR − red) ÷ (NIR + red)always between −1 and +1; dividing by the sum cancels some lighting differences Interactive · One formula, two uses Red reflectance Near-infrared reflectance A dry spell hits the crops: severity Brown is low NDVI, green is high, blue is water. Forest top-left, a river, a town, bare patches, crops elsewhere. An invented 12 × 12 scene with typical reflectances for each cover and a little random noise. Under a dry spell the crops lose near-infrared and gain red. Without JavaScript: healthy crops near 0.76 fall to about 0.39 under severe stress; forest is about 0.86, town about 0.1 and water below zero. NDVI is a proxy. It saturates in dense canopy (a rainforest and a lush field can both read near 0.9), wet soil darkens, haze and clouds shift it, and different sensors define "red" and "NIR" slightly differently. It tracks greenness, not yield or health. Its great strength is that it is computed the same way across fifty years of images. Resolution: four ways a pixel can be too coarse A pixel records one average for the whole square, so anything smaller than the square is blended into its surroundings. Remote-sensing courses distinguish four kinds of resolution. Spatial: the size of the square (10 m for Sentinel-2's visible bands, 30 m for Landsat, 250 m to 1 km for the MODIS instruments that watch the whole planet daily). Spectral: how many bands, and how narrow. Temporal: how often the same spot is revisited (about 5 days for Sentinel-2 with two satellites; 16 days for one Landsat). Radiometric: how finely brightness is divided, the bit depth. You rarely get all four at once; fine pixels cost a narrow swath and fewer visits. Interactive · Zoom out and lose the small things 10 m20 m40 m80 m160 m An invented 640 m × 640 m landscape: a large wood, a smaller wood, five 40 m copses and a 10 m hedgerow. A pixel is labelled forest if more than half of it is trees. Which small woods survive depends on how the grid happens to fall on them. Without JavaScript: at 10 m all five copses and the hedgerow are visible; at 20 m the hedgerow is gone and the forest area is about 14% low; at 40 m only two of the five copses remain. This is the mixed-pixel problem. A 30 m Landsat pixel straddling a road and a field reads as neither. It also explains why a deforestation map from 30 m data cannot see selective logging of a few trees, and why the same landscape gives different area figures at different resolutions. Map projections: flattening a sphere A globe cannot be flattened without tearing or stretching; Gauss proved this in 1827. Every flat map makes a trade. The Mercator projection (Gerardus Mercator, 1569) keeps angles right, so a straight line on the map is a steady compass course, which is why sailors used it. The price is that scale grows with latitude: at 60° everything is drawn twice as wide and twice as tall, four times the area. Web maps use a variant, Web Mercator (EPSG:3857, introduced by Google Maps in 2005), which cuts off at about 85°. An equal-area projection keeps sizes right and bends shapes; the Gall–Peters map is one, and the Equal Earth projection (Šavrič, Patterson and Jenny, 2018) is a newer, rounder one. The practical rule for data work: the coordinate system is part of the data. Latitude and longitude (WGS 84, EPSG:4326) are angles, not distances: a degree of longitude is 111.32 km at the equator and half that at 60°. To measure area or distance, use a projection suited to the region, such as a UTM zone (the world is cut into 60 zones, each 6° wide) or an equal-area projection for areas. Mixing two coordinate systems quietly shifts features by metres to kilometres. Interactive · How a circle is drawn MercatorEqual-area cylindricalPlate carrée (lat/lon) Latitude Scale factors come from the standard formulas on a sphere (Mercator: 1 ÷ cos φ both ways; equal-area cylindrical: 1 ÷ cos φ east-west and cos φ north-south; plate carrée: 1 ÷ cos φ east-west, 1 north-south). Areas: Greenland 2.166 million km², Africa about 30.4 million km². Without JavaScript: at 60° Mercator draws everything 2 times too wide and 2 times too tall, so 4 times the area; the equal-area projection keeps area but draws a circle as a flat ellipse. Greenland is truly 0.07 of Africa and is drawn at about 0.75 of it in Mercator. Layers and overlay: what is near what A geographic information system stores the world as layers. In the vector model, a feature is a point (a well), a line (a river) or a polygon (a district), each with a table of attributes. In the raster model, a feature is a grid of cells with a value in each, like the NDVI scene above. The questions a GIS answers are almost always spatial ones: what is inside this boundary, what is within 2 km of that river, which polygons overlap, and what is the population of the overlap? The method is old. In 1854 John Snow plotted cholera deaths in Soho against water pumps; Roger Tomlinson led the Canada Geographic Information System in the 1960s, often called the first true GIS. Interactive · Buffer a river Buffer distance from the river village inside the buffer   outside; circle size grows with population Sixteen invented villages and one invented river on a 32 km × 20 km map. Distances are straight-line to the nearest part of the river. Without JavaScript: within 2 km of the river there are 2 of 16 villages (about a third of the people); within 4 km, 10 villages and about 81% of the people. A caution that shows up here: the answer jumps. Moving the buffer from 3 to 4 km adds seven villages. Results from overlay depend on the distance, the boundaries and the units chosen, a family of effects geographers call the modifiable areal unit problem: redraw the district lines and the statistics change, though the people have not moved. Time series and trends: signal, season and noise One image is a snapshot; a series of images is evidence of change. The record of NDVI from the AVHRR instruments begins in 1981. A study by Zhu and colleagues (2016) using satellite leaf-area data for 1982–2009 found greening over 25% to 50% of the world's vegetated land and browning on under 4%, and a model-based attribution of about 70% of it to rising CO₂; others stress land use and water. Regional stories are just as real: much of the Sahel has become greener since the mid-1980s drought, with scientists debating how much is rainfall recovery and how much is land management. Three things hide inside any such series: a trend, a seasonal cycle (NDVI rises and falls every year, so compare like months, or use annual means) and noise (weather, clouds, sensor drift). The usual tool is a straight line fitted by least squares, with an interval around the slope from Probability & Statistics (34/05). Two traps are specific to time series. The window matters: a short window ending in a drought can slope the other way from the long-term line. And neighbouring years are correlated (a wet year is often followed by a wet year), so there are fewer independent points than it seems and the simple interval is too narrow. Interactive · Choose your window First year used Last year used With the dry year (year 18)Dry year replaced Twenty invented yearly NDVI-like values: a true slope of 0.03 per decade, correlated noise, and a dry year in year 18. Red line: fit over your window. Dashed line: all 20 years. Intervals use the t distribution; the second interval uses a standard adjustment for lag-1 autocorrelation. Without JavaScript: all 20 years give a trend of +0.032 per decade ± 0.016. Years 13–18, ending in the dry year, give −0.099 ± 0.184, and years 14–20 give −0.007 ± 0.166: both are consistent with no trend and neither refutes the long one. Years 1–10 give +0.036 ± 0.025, widening to ± 0.038 once autocorrelation is allowed for. Uncertainty: a map is an estimate A land-cover map is a classification, and classifications are wrong somewhere. The standard check is an accuracy assessment: pick sample locations, find out what is really there (from higher-resolution images or the field), and tabulate map class against reference class in a confusion matrix. User's accuracy says how many pixels mapped as "cleared" really were. Producer's accuracy says how much of the really cleared land was mapped. A single headline, overall accuracy, hides both. The trap, set out in the good-practice guide by Olofsson and colleagues (2014), is that counting mapped pixels gives a biased area. If a rare class is mapped from a huge area of stable land, even a tiny leak of true change into the "stable" class adds up. The remedy is to estimate area from the sample, stratified by map class, with an interval. Interactive · A map says 1,000 hectares were cleared Share of mapped-as-cleared pixels truly cleared Share of mapped-as-stable land that was truly cleared An invented 100,000 ha region: 1,000 ha mapped as cleared, 99,000 ha as stable. Reference samples: 100 in the cleared class and 400 in the stable class. Estimate = area × share in each class, summed; the interval comes from the stratified-sample standard error. Without JavaScript: with 85% user's accuracy and 0.8% missed clearing in the stable class, overall accuracy is 99.1%, yet the sample-based estimate of cleared land is about 1,642 ha, give or take about 870 ha, against 1,000 ha mapped. The same thinking applies to everything a graduate meets: a weather station network that is dense in cities, a model that fills gaps between stations, a published figure for global forest loss, a population grid built by splitting census totals over a land-cover map. Each hides a method and an error. Ask for the confusion matrix, the interval and the reference data. What a graduate just sees A pixel is an average, so anything smaller than the pixel is blended into its neighbours. Healthy vegetation is dark in red and bright in near-infrared; NDVI compresses that into one number, which saturates in dense canopy. Fine pixels, wide coverage and frequent visits trade off against each other. Every flat map distorts something: Mercator keeps angles and inflates area toward the poles. Latitude and longitude are angles; measure areas and distances in a projected coordinate system. "Near" in a GIS means a number you chose, and the answer can jump when you change it. A trend depends on its window, and neighbouring years are not independent. A map with 99% overall accuracy can still miss most of a rare class. Where it shows up next Conservation & Applied Ecology (36/15): protected-area boundaries, habitat maps and deforestation alerts. Soils, Agriculture & Food Systems (36/18): crop monitoring from NDVI, drought watches and yield forecasts. Climate Science (36/14) and Hydraulics & Water Resources (34/67): gridded temperature and rainfall, snow cover, floodplain maps. In the world: the flood-risk map on a property listing, a wildfire perimeter, a ship-routing app, a city's tree-canopy audit, and how an insurer or a government checks that a "protected" forest still stands. If you want to go deeper 📘 Textbooks. Thomas Lillesand, Ralph Kiefer and Jonathan Chipman, Remote Sensing and Image Interpretation (Wiley, 7th edition, 2015), and Paul Longley, Michael Goodchild, David Maguire and David Rhind, Geographic Information Science and Systems (Wiley, 4th edition, 2015). Check for a newer edition. 📘 Gentler. Mark Monmonier, How to Lie with Maps (University of Chicago Press, 3rd edition, 2018), a short and entertaining tour of projections, scale and persuasion. 🌐 Free training. NASA's Applied Remote Sensing Training (ARSET) offers courses on satellite data for environmental applications. 🌐 Free hands-on. The QGIS Training Manual works through vector and raster analysis in the free QGIS software, in 20 modules. The takeaway A satellite gives numbers per pixel, and everything after that is a choice: which bands to combine, what pixel size to live with, which projection to measure in, which years to fit, and how to estimate the error. Good environmental data work is mostly making those choices explicit and putting an interval on the answer. Try this: open a web map and compare the apparent sizes of Greenland and Africa, then look up each country's real area; or find a "forest lost" figure in the news and look for its method and its uncertainty. Sources & Further Reading Sources. Landsat 1 (23 July 1972) and Landsat 9 (27 September 2021) launch dates and 30 m multispectral pixels: Wikipedia, "Landsat program"; Sentinel-2 launches (23 June 2015, 7 March 2017, 5 September 2024), 13 bands, 10/20/60 m, 290 km swath and 5-day combined revisit: Wikipedia, "Sentinel-2". NDVI formula, typical values and history (Rouse et al. 1973/1974; Tucker, Remote Sensing of Environment 1979): Wikipedia, "Normalized difference vegetation index." Web Mercator (EPSG:3857, Google Maps 2005, about 85.05° limit): Wikipedia, "Web Mercator projection". Equal Earth (2018) and the Greenland-Africa comparison: Wikipedia, "Equal Earth projection". Greenland 2,166,086 km² and Africa about 30.37 million km²: Wikipedia country and continent articles. Gauss, Disquisitiones generales circa superficies curvas (1827), and Mercator (1569), standard history of cartography. Zhu et al., "Greening of the Earth and its drivers," Nature Climate Change 6 (2016), 791–795. Sahel re-greening debate: Herrmann, Anyamba and Tucker (2005), Olsson et al. (2005). Olofsson et al., "Good practices for estimating area and assessing accuracy of land change," Remote Sensing of Environment 148 (2014). John Snow, 1854; Tomlinson and the Canada Geographic Information System, 1960s (standard GIS history). The reflectance curves, scenes, landscape and time series are invented and computed in the page. 📘 Lillesand, Kiefer and Chipman, Remote Sensing and Image Interpretation 📘 Monmonier, How to Lie with Maps 🌐 NASA ARSET Step 13. Public & Global Health: Health Beyond the Clinic --------------------------------------------------------- Why: Health beyond the clinic. Medicine treats the person in front of it; public health asks why that person is the one in the chair, and what would have kept the next thousand out of it. Its tools are counting, water, laws, money and vaccines. In August 1854, cholera hit Broad Street in Soho, London. The doctor John Snow marked the deaths on a map, saw them cluster around one water pump, and persuaded officials to remove its handle. He did not know about bacteria; he had a map, a hunch and a count. That is public health in one picture: no cure, no drug, a change made to a shared thing, and a drop in deaths among people who never knew they had been at risk. A hundred and seventy years later the shared things are tobacco taxes, vaccination schedules, clean air, seat belts and how a country pays for its hospitals. This piece explains how public health works; it is not medical advice. For a health question, see a clinician; in an emergency, call your local emergency number. The course in one box Who takes itMedical students (often as "community medicine" or "population health", in the later clinical years), nursing and public-health students, and anyone in health policy. Master of Public Health degrees draw on epidemiology, biostatistics, health policy, environmental health and social science. What it is forPreventing disease and prolonging life across whole populations, and deciding what a society should spend its health money on. Comes afterEpidemiology & Evidence-Based Medicine (35/58), for how causes are found, and Public Policy (35/16), for how problems become policies. Leads toHealth-policy and global-health careers; and it connects back to Medical Ethics & Law (35/60), where rationing and mandates are argued. What this piece gives youYou will not be able to design a vaccination programme. You will see why most disease is made outside hospitals, why the mix of diseases changes as countries grow richer, how health is counted, the four ways health systems are paid for, what herd immunity really is, and what tobacco and pandemics taught the field. Easier first reads: Your Immune System, Day by Day (01/10) and Where Public Money Goes (18/08). Health is made outside the clinic Ask what keeps a population healthy and doctors are, to the surprise of many, only part of the answer. Clean water and sewers, food, housing, work, education, income and the air all matter more for most diseases than treatment. A famous argument by the historian Thomas McKeown (1976) said that Britain's death rate fell in the nineteenth century mainly because people ate better, not because medicine improved. Later historians such as Simon Szreter credited public works and sanitation as well. The two sides disagree about the mix, not about the point: a society's health is mostly made upstream. The same is true today. In the Whitehall studies, led by Michael Marmot from the late 1960s, British civil servants, all with secure jobs and access to the same health service, showed a gradient: each step down the grade ladder came with worse health. The WHO's Commission on Social Determinants of Health (2008) put the lesson in its title, Closing the Gap in a Generation. Social position, not only germs and genes, gets under the skin. A second lesson comes from the epidemiologist Geoffrey Rose (1981, 1985): a population approach shifts everyone a little; a high-risk approach finds and treats the people at the top of the distribution. The high-risk approach is efficient for each person treated, but most cases come from the large middle group, because there are so many more people there. Rose called the result the prevention paradox: a measure that brings large benefits to the community offers little to each individual. Interactive · The prevention paradox Risk doubles every (score units) Shift achieved (score units lower) High-risk group (top % of scores) Illustrative model, not real data: 100,000 people with a bell-shaped risk score (mean 100, spread 15); yearly risk is 0.5% at a score of 100 and doubles every set number of units. "Population" lowers everyone's score by the shift; "High-risk" lowers only the top group's. With the starting values there are about 858 cases a year among 100,000 people. The top 10% of scores produce only 41% of them, so 59% of cases occur in people nobody would call high-risk. Shifting everyone by 5 units prevents 29% of cases but needs about 398 person-years of effort per case prevented; treating only the top 10% prevents 12% but needs about 99. The narrow approach is four times as efficient and prevents less than half as much. The transition from infection to chronic disease As countries get richer, the diseases that kill them change. Abdel Omran named this the epidemiological transition in 1971: first an age of pestilence and famine, then of receding pandemics as sanitation and food improve, then of degenerative and man-made diseases such as heart disease, cancer and diabetes. Later writers added stages, and critics point out that it does not run in a straight line: many low- and middle-income countries carry a double burden of infections and chronic disease together, and some "chronic" diseases turn out to have infectious causes. The latest World Health Organization data (for 2023) show it clearly. About 61 million people died that year; the top causes worldwide were ischaemic heart disease (9.5 million), stroke (6.8 million), chronic obstructive pulmonary disease (3.6 million), lower respiratory infections (2.7 million), Alzheimer's and other dementias (2.1 million), diabetes (2.0 million) and lung cancers (1.8 million). WhereWhat the top ten causes of death look like, WHO 2023 Low-income countriesSeven of ten are communicable. Lower respiratory infections lead; diarrhoeal diseases are fifth; malaria, tuberculosis and HIV/AIDS appear. High-income countriesNine of ten are noncommunicable. Heart disease and stroke are in the top three; dementia is third and lung cancer fourth; lower respiratory infections (sixth) are the only infection. Counting the burden: deaths, years and DALYs Deaths alone mislead: a death at 30 costs more years than one at 90, and a disease that disables without killing does not appear. The disability-adjusted life year (DALY) counts one lost year of healthy life, whether lost by early death or by living with illness. It is the main unit of the Global Burden of Disease (GBD) study, run by the Institute for Health Metrics and Evaluation (IHME) in Seattle, and WHO publishes its own estimates; the two differ in methods and sometimes in numbers. DALY = YLL + YLDyears of life lost to early death + years lived with disability (cases × weight × duration) A disability weight runs from 0 (full health) to 1 (equivalent to death) and comes from surveys of how people rank states of health. The weights are debated: the GBD revised many between 2004 and 2010 (blindness fell from 0.594 to 0.195), dropped the early age-weighting that valued young adults' years more, and dropped discounting of future years. Critics say any such weighting hides value judgments; defenders say that without a common unit, we cannot compare a heart attack with a lifelong back problem. Interactive · Which condition costs more? Sudden and fatalChronic and mildDisabling for life Deaths Years of life lost per death People living with it Disability weight Years lived with it Invented conditions with round numbers. The presets are not real diseases. The first preset gives 1,000 deaths × 30 years = 30,000 years of life lost, and no disability. The second has no deaths at all but 50,000 people living for 10 years at weight 0.2: 100,000 years lived with disability. By deaths alone the first looks worse; by DALYs the quiet, chronic one is more than three times as big. That is why lower back pain, depression and hearing loss rank high in burden tables even though they rarely kill. Who pays: four ways to run a health system Every health system answers the same question: who pays, and who provides? Four patterns recur, and most countries mix them. Beveridge model (named after William Beveridge's 1942 report): tax-funded, government-run. The UK's National Health Service, founded in 1948, is the classic example; Spain and the Nordic countries are close. Bismarck model: insurance funds paid by employers and workers, with private providers. It began with Germany's sickness insurance law of 1883; Germany, France and Japan work this way in different forms. National health insurance: one public insurer paying private providers. Canada's provinces and South Korea use it. Out-of-pocket: patients pay when they are sick. It is the main route where public systems are weak, and it pushes families into poverty. Real systems vary: Switzerland requires everyone to buy regulated private insurance; the United States combines employer plans, public programmes (Medicare, Medicaid) and the uninsured; Brazil's tax-funded Sistema Único de Saúde was set up by the 1988 constitution; Thailand introduced a tax-funded universal coverage scheme in 2002; Rwanda built community insurance funds with donor money. Interactive · Spending around the world % of GDPPer personOut-of-pocket % Data: WHO Global Health Expenditure Database as republished by Our World in Data, retrieved 1 November 2026; GDP share is for 2023, per-person spending (international dollars, adjusted for prices) and out-of-pocket share for 2023 or 2024 depending on the country. "Out-of-pocket" is the share of all health spending paid directly by patients. System labels are simplified. The United States spent 16.7% of its GDP on health in 2023, about $13,500 per person; Germany 11.7%, the UK 11.0%, Japan 10.7%. In Nigeria 72% of health spending was out of pocket, in India 44%, in Mexico 41%; in Thailand, which spends only 4.5% of GDP, it was about 10%. Spending, coverage and health are three different things. Vaccines, herd immunity and eradication The central number of infectious-disease dynamics is R0, the average number of people one case infects in a fully susceptible population. If R0 is above 1, an outbreak grows. Immunity shrinks the number: when a fraction v of people are immune, each case infects R0(1 − v) others, and the outbreak dies when that falls below 1. The needed fraction is the herd immunity threshold. threshold = 1 − 1 ÷ R0divided by vaccine effectiveness if it is below 100%; assumes people mix randomly The usual figures are 71 to 83% for smallpox, 80 to 86% for polio and 92 to 94% for measles (R0 about 12 to 18). Real populations mix unevenly, so pockets of low coverage can keep a disease alive even when the national average looks high. Interactive · Run an epidemic R0 of the disease Vaccinated (%) Vaccine effectiveness (%) A simple model (SIR) with everyone mixing equally, an infectious period of 5 days, and 1 in 10,000 infected at the start. The vaccine is "all-or-nothing" on a fraction of people. Real epidemics are messier. Set R0 to 2.5 with no vaccination: the model gives a peak of about 24% of people infected at once and about 89% infected in total. Vaccinate 60% with a 95%-effective vaccine and 57% are immune, just under the 60% threshold: the effective R is 1.08 and only about 5% are ever infected. At 70% coverage, 66% are immune, the effective R is 0.84 and the outbreak barely starts. For measles the coverage needed is above 90%, which is why a few unvaccinated schools can bring it back. Eradication is the extreme case: drive the number to zero everywhere. Smallpox is the only human disease so far. The WHO began an intensified programme in 1967, the last natural case was diagnosed in October 1977 (Ali Maow Maalin, in Somalia), and eradication was certified in May 1980; the last death was a laboratory accident in Birmingham in 1978. Stocks of the virus still exist at two WHO-approved laboratories, in the United States and Russia. Rinderpest, a cattle disease, was declared eradicated in 2011. Polio is near: the global programme began in 1988, wild poliovirus types 2 and 3 were declared eradicated in 2015 and 2019, and the African region was certified free of the wild virus in 2020. Type 1 persists in Pakistan and Afghanistan: 99 cases in 2024 (74 and 25), and about 38 reported by October 2025 (the full-year count is not verified here). The oral vaccine can also, rarely, seed outbreaks in under-vaccinated communities. Tobacco: a long fight with a known cause Smoking is the great proof that prevention works slowly. In 1950 Richard Doll and Austin Bradford Hill published a case-control study linking cigarettes to lung cancer, followed by their British doctors' cohort in 1954 (see Epidemiology & Evidence-Based Medicine, 35/58). The industry's response, documented in later litigation and in books such as Merchants of Doubt, was to manufacture doubt. Today WHO says tobacco kills more than 7 million people a year, of whom over 1.6 million are non-smokers exposed to smoke (2023 data). The response was the first treaty negotiated under WHO: the Framework Convention on Tobacco Control, adopted in 2003 and in force since 2005, with 183 parties by WHO's count. It is backed by the "MPOWER" package (2007): monitor use, protect people from smoke, offer help to quit, warn about dangers, enforce bans on advertising, raise taxes. Raising tobacco taxes is widely regarded as one of the most effective measures. Australia introduced plain packaging in 2012; others followed. Newer products such as e-cigarettes divide experts: some health bodies see them as a route off cigarettes, others as a route on to nicotine for young people, and the evidence is still developing. Pandemics and preparedness An epidemic is more cases than expected in a place; a pandemic is one that spreads across continents; a disease is endemic when it circulates steadily. The 1918 influenza is the benchmark, with estimates of deaths spanning a wide range, commonly put near 50 million. HIV/AIDS is a pandemic that is still going; the 2014 to 2016 Ebola outbreak in West Africa caused more than 11,000 deaths; the 2009 H1N1 influenza spread worldwide. COVID-19 showed how hard it is to count a pandemic. WHO estimated 14.9 million excess deaths (range 13.3 to 16.6 million) in 2020 and 2021, far more than officially recorded; an IHME-led study published in 2022 estimated more than 18 million. The difference comes from different methods and the fact that many countries record few deaths at home. Lessons the field drew included early surveillance, fast testing, supply stocks, trust and clear communication, and fair access to vaccines, which was unequal between rich and poor countries. The International Health Regulations (2005) require countries to report events; in May 2025 the World Health Assembly adopted a Pandemic Agreement, though as far as I could verify its annex on sharing pathogens and benefits was still being negotiated. What a graduate just sees Most health is made upstream (water, food, housing, income); a clinic treats what upstream failed to prevent. A small shift across a whole population can prevent more cases than a large shift in the few at highest risk. Deaths undercount burden; years lost and years lived with disability change the ranking. As countries grow richer the leading causes of death move from infections to chronic disease, often leaving a double burden in between. Health systems differ in who pays and who provides; spending, coverage and outcomes are three different things. Herd immunity is 1 − 1/R0, and it protects those who cannot be vaccinated only while coverage stays high everywhere. Every statistic about a pandemic depends on who counted and how; ask for the method. The best public-health measures are often boring: taxes, laws, pipes and schedules. Where it shows up next Epidemiology & Evidence-Based Medicine (35/58) supplies the methods (cohorts, trials, bias) that public-health claims rest on. Public Policy (35/16) and Political Economy (35/17): who pays, and why reforms stall. Medical Ethics & Law (35/60): rationing, mandates and consent at population scale. Microbiology (35/50) and Immunology (35/57): the biology behind R0, vaccines and resistance. In the world: ministries of health, WHO and national disease-control agencies, NGOs and foundations, health insurers, and every school-vaccination schedule. If you want to go deeper 📘 Textbook. Michael Marmot, The Health Gap (2015) for the social-determinants view, and a standard introduction such as Bernard Turnock's Public Health: What It Is and How It Works (Jones & Bartlett), widely used in public-health schools. 📘 Textbook. Detels et al., Oxford Textbook of Global Public Health (Oxford University Press). The reference work for the global picture. 📘 Gentler. Hans Rosling, Factfulness (2018), and Steven Johnson, The Ghost Map (2006), the story of John Snow and the Broad Street pump. 🌐 Free course and data. OpenWHO hosts free WHO courses; Our World in Data's health pages and the IHME GBD Compare tool let you explore the numbers. The takeaway Public health is medicine's other half: counting who falls ill and why, then changing the shared conditions (water, laws, prices, vaccines, money) so fewer do. Its arithmetic is simple: a threshold of 1 − 1/R0, a DALY as years lost plus years lived with disability, and a paradox that the biggest gains go to people who never knew they were at risk. Try this: this week, pick one thing near you that protects public health without you noticing (tap water, a food-safety rule, a vaccination record, a smoke-free sign). Find who decided it and when. (This is curiosity, not medical advice.) Sources & Further Reading Sources. Causes of death 2023: WHO, "The top 10 causes of death" fact sheet. Health spending: WHO Global Health Expenditure Database via Our World in Data (retrieved 1 November 2026). DALY definition and weights: encyclopaedia summaries of the Global Burden of Disease method. Omran (1971, Milbank Memorial Fund Quarterly) and later criticism. Herd immunity thresholds: encyclopaedia summary of standard figures. Smallpox: WHO; polio: GPEI, WHO and news reports (2024 and 2025 counts differ by source and date). Tobacco: WHO tobacco fact sheet (2023 data; FCTC adopted 2003, in force 2005, 183 parties). COVID excess deaths: WHO, 5 May 2022 (14.9 million, range 13.3 to 16.6); IHME estimate from memory of the 2022 Lancet paper. Snow, McKeown, Whitehall, Beveridge (1942), Bismarck (1883) and Rose (1981, 1985) as standard history. Interactive numbers computed in node. Not medical advice. 🌐 OpenWHO (free courses) 🌐 Our World in Data: Health 📘 Rosling, Factfulness 📘 Johnson, The Ghost Map Step 14. Public Policy: How Problems Become Policies, and What Then Goes Wrong ------------------------------------------------------------------------------ Why: How problems become policies. A city charges fifteen cents for a plastic bag and the bags nearly vanish. A famous job-training scheme is announced with fanfare and fizzles in a maze of approvals. Public policy is the study of why the first happens, why the second is more common, and how to tell which is which. In March 2002 Ireland began charging shoppers 15 cents for every plastic bag at the till. Reports at the time, from the government and the press, said use fell by about 90 percent within weeks. Notice what did not happen: no inspector visited homes, no one was jailed, and nobody forbade bags. A small price, collected by the shop, changed what millions of people did without thinking about it. Now picture the opposite. A national programme is announced to create jobs in a poor district. Years later the money has been spent on meetings and approvals, and almost no jobs exist. Nobody lied, nobody stole. Every office that had to agree did agree, slowly and partly. A good idea met a long chain of people who each had other priorities. Public policy as a subject asks four things about any such case. Why did this problem get attention when others did not? What tool did the government choose, and why that one? Did the plan survive contact with the people who had to carry it out? And did it work, which means: compared with what would have happened anyway? The course in one box Who takes itPolitical science and public-affairs majors, usually in year 3. Schools of public policy (the Kennedy School, LSE, Sciences Po, the Hertie School and others) teach the same core as the heart of a master's degree, mixed with economics and statistics. What it is forUnderstanding how a social problem becomes a law, a tax or a programme, and judging whether that policy worked. Comes afterComparative Politics (35/13) and Public Economics (34/49). Leads toNo later subject in the curriculum requires it. It sits beside Administrative Law (35/09), which asks how governments are held to the law, and Research Methods in Political Science (35/18), whose tools judge whether a policy worked. What this piece gives youYou will not be able to write a cost-benefit analysis. You will be able to read a news story about a new tax, ban or scheme and ask the five questions a policy analyst asks. Easier first reads: How a Law Gets Made (18/07), How Government Actually Works (18/01) and Where Public Money Goes (18/08). The policy cycle: a useful map that is not the territory Textbooks draw policy as a loop: a problem is noticed, put on the agenda, a solution is designed, a decision is made, the decision is carried out, and the results are evaluated, which sends you back to the start. The idea goes back to Harold Lasswell's 1956 account of the "decision process" in stages, and nearly every introduction to public policy still opens with some version of it. Its value is that it gives you questions to ask at each point. Its weakness is that real policy does not happen in order. Charles Lindblom argued in 1959 that officials do not survey all options and pick the best; they "muddle through", making small changes from where they already are. Solutions often exist before problems: a team has a programme in a drawer and waits for a crisis to attach it to. The cycle is a checklist, not a law of nature. Interactive · The cycle, walked through one real case The case is Ireland's 2002 plastic bag levy. The stages are the textbook ones; the case details are simplified. Sources differ on exact usage figures, so treat "about 90 percent" as the figure reported at the time. Without JavaScript: Ireland's 2002 levy moved from visible litter, to a design choice (a fee at the till rather than a ban), to implementation by shops, to a reported fall of about 90 percent in use, and a later increase of the fee after use crept up. Agenda setting: why some problems get attention and others wait Thousands of real problems exist at any time. Only a few get a minister's, a legislator's or the public's attention. John Kingdon, in Agendas, Alternatives, and Public Policies (1984), described three streams flowing separately. The problem stream: indicators, crises, a disaster on the news. The policy stream: ideas floated by experts and officials, most of which go nowhere. The politics stream: the national mood, elections, lobbying, a change of government. When the three meet, a "policy window" opens, and a policy entrepreneur who has a solution ready can push it through. Windows close again, often within months. A second account, by Frank Baumgartner and Bryan Jones in Agendas and Instability in American Politics (1993), says policy is mostly stable and then changes suddenly, a pattern they call punctuated equilibrium. Attention is scarce, so a problem can be ignored for years and then, when its image changes (from "a medical matter" to "a threat to children", say), move from one committee to a very different one. Interactive · Three streams and a window Problem: how loud is the crisis Policy: how ready is a workable solution Politics: how receptive are decision-makers A metaphor, not a measured model: the threshold of 6 is invented to make the idea playable. Kingdon himself describes the streams as largely independent and the window as partly chance. Play with it. A loud crisis with no ready solution gets hearings and hand-wringing; a ready solution with no crisis waits in a drawer. The practical lesson is Kingdon's: people who want change prepare the policy stream in the quiet years, so that when a window opens they are not drafting from scratch. Instruments: regulation, taxes, spending, information and nudges Once a problem is on the agenda, the government chooses a tool. Political scientists group them roughly as: regulation (a rule, a ban, a standard), taxes and prices (change what a choice costs), spending and subsidies (pay for a service or reward a behaviour), information (warnings, labels, campaigns) and nudges (changing the default or the way choices are shown, without banning anything). Each acts on a different lever, and the same goal can be pursued with any of them. To cut sugar intake, Mexico taxed sugary drinks from January 2014 at one peso per litre; a study in the BMJ estimated purchases fell about 6 percent over 2014 and about 12 percent by December relative to earlier trends. The UK chose a levy on manufacturers' sugary drinks, in force from April 2018, which pushed producers to reformulate. Others rely on labels or school-meal rules. The core economic point about price instruments is that a tax lets each firm or person choose where to cut, and so reaches the same target more cheaply than a uniform rule. Suppose three factories must together cut pollution by a fixed amount, and cutting costs each of them a different amount. A uniform standard makes each cut the same share, including the one for whom it is dearest. A tax makes everyone cut until the last unit costs the same as the tax, so the cheap cutters cut more. Try it. Interactive · Same target, two instruments Total cut required (units) How different the factories' costs are Three factories whose cost of the next unit cut rises in proportion to how much they have already cut: slopes 4/r, 4 and 4r (r is the slider). Costs are in arbitrary money units. Textbook model; real regulators do not know these slopes, which is the standard argument for prices and tradable permits. With r = 1 the factories are identical and the two tools cost the same. As the spread grows, the tax pulls ahead. The caveats matter as much as the result: the model assumes the regulator can set the right tax without knowing costs (it cannot, so it adjusts), and it ignores who pays. A flat tax on fuel hits a poor household harder, which is why many carbon taxes come with rebates. Nudges are the cheapest instrument and the most oversold. A well-known 2003 study by Eric Johnson and Daniel Goldstein found that countries where people must opt out of organ donation reported far higher consent than those where they must opt in. Later work cautions that consent is not donation: hospital systems and family permission matter as much as the default. Implementation: the gap between a law and what happens Jeffrey Pressman and Aaron Wildavsky's 1973 book Implementation (subtitled "How Great Expectations in Washington Are Dashed in Oakland; or, Why It's Amazing That Federal Programs Work at All") followed a federal job-creation scheme in Oakland, California. Their lesson: a programme that needs agreement from many separate offices has many chances to fail. Each "clearance" is a point where someone can delay or veto. If each has a high chance of agreement, the chain still frays, because probabilities multiply. P(success) = p × p × … × p = pnn clearances, each passed with chance p; 0.9 ten times gives about 35 percent Interactive · The clearance chain Chance each office agrees Offices that must agree A simple multiplication that assumes the offices decide independently. Real offices are not independent, and later scholars argued that coordination and bargaining can raise the odds. Pressman and Wildavsky's own point was the warning, not the exact number. A second source of gaps is the person at the counter. Michael Lipsky's Street-Level Bureaucracy (1980) argued that teachers, police officers, caseworkers and nurses make policy in practice: they have more cases than time, so they ration attention and bend rules. Policy on paper is what the capital writes. Policy in practice is what thousands of workers do when the line outside is long. Good designers ask: who has to do this, with what time, and what happens if they simply cannot? Evaluation: what would have happened anyway? The evaluator's central question is about a world nobody saw: what would have happened without the policy? This unseen outcome is the counterfactual. Comparing a group before and after a policy is the obvious test, and it is often badly wrong, because things change on their own: the economy grows, a disease wanes, a school year ends. Mexico's Progresa programme, begun in 1997, gave poor families cash if their children went to school and clinics. Because it could not reach every community at once, the government drew lots for the first wave: of 506 communities in the evaluation, about 320 got the money first and about 186 waited (sources differ by one). Surveys every six months compared the two groups. Enrolment, especially in secondary school, rose in the treated communities. The programme was renamed Oportunidades in 2002 and later Prospera, and cash-transfer schemes with conditions spread to many other countries, Brazil's among them. The 2019 economics Nobel prize, shared by Abhijit Banerjee, Esther Duflo and Michael Kremer, honoured this style of experimental evaluation of anti-poverty policy. Interactive · Before-and-after versus a comparison group True effect of the programme (points of enrolment) What would have happened anyway (trend, points) Invented, illustrative numbers: both groups start at 60 percent enrolment and both are hit by the same background trend. Real estimates carry sampling error, which this toy leaves out. Set the trend to +5 and the effect to 4. A naive before-and-after comparison claims a 9-point success. The comparison group reveals that 5 of those points would have come anyway. Set the trend negative and a working programme looks like a failure. The lesson is the one Progresa's designers acted on: a policy is judged against a counterfactual, and the best counterfactual is a comparison group chosen by chance. The methods piece (Research Methods in Political Science, 35/18) takes this much further. Evidence-based policy, and its limits "Evidence-based policy" means choosing policies because rigorous evaluations found they work. Governments have built institutions for it: in the UK, the What Works Network was launched in 2013 as a set of centres that synthesise evidence for areas such as crime, education and ageing. A cautionary example is "Scared Straight", a programme that takes at-risk teenagers into prisons to frighten them. It was popular and seemed obviously sensible. Systematic reviews of randomised trials found it did not reduce offending and, on average, probably increased it. Evidence overturned common sense. The approach has limits, and its own defenders list them. Published results overstate. Journals prefer significant findings, and small studies that happen to land high are the ones that get published. Stefano DellaVigna and Elizabeth Linos (Econometrica, 2022) compared 126 trials run by two US "nudge units" with 26 academic papers: the academic papers averaged an effect of 8.7 percentage points on take-up, and the units' own trials 1.4 points. Publication bias, they estimated, explains much of the gap. Other researchers disagree on how large the true effect of nudges is: one 2022 meta-analysis found a moderate effect, and a reanalysis argued that after correcting for publication bias there is no clear evidence of any. What worked there may not work here. A result from Kenyan schools or a New Haven neighbourhood tells you about that place; whether it carries to Lagos, Lima or Leeds depends on how the programme works and who delivers it. Angus Deaton and Nancy Cartwright made this argument forcefully in 2018. Even the famous Kenyan school-deworming study (Miguel and Kremer, 2004) has been re-examined and argued over by later researchers, with reviews disagreeing about its size. And what is measured gets gamed. Where a number becomes the target, people optimise the number. Interactive · Why published effects run high True effect (percentage points) People per group in each trial 600 simulated trials of a programme that raises take-up from 10 percent. Only trials that are positive and significant at the usual 5 percent level count as "published". Illustrative simulation with a fixed random seed. With a true effect of 1 point and 400 people per group, the few trials that clear the bar overstate the truth by several times. Make the trials bigger and the exaggeration fades. This is why evaluators ask for pre-registered trials, large samples and replications, and why a single dramatic study is a reason for interest, not a policy. What a graduate just sees The policy cycle is a checklist of questions, not a description of how things happen. Solutions often wait for problems. A problem gets attention when a crisis, a ready solution and a receptive government line up. Prepare in the quiet years. The same goal can be pursued with a rule, a price, a payment, a label or a default. Ask which lever is being pulled and who pays. A price lets people who find cutting cheap do more of it, which usually reaches a target more cheaply than a uniform rule. Probabilities multiply: a plan that needs many separate yeses is far less likely to survive than each yes suggests. Policy is made at the counter as well as the capital. Ask who has to do this, and with what time. "It worked" means "it did better than what would have happened anyway". Ask for the comparison group. Published effects are inflated. One striking study is a lead, not proof; and what worked in one place may not work in another. Where it shows up next Research Methods in Political Science (35/18): the tools for finding a counterfactual, from field experiments to natural experiments. Administrative Law (35/09): the courts' side of implementation, asking when an agency's rule or decision can be challenged. Public Economics (34/49) and Behavioral Economics (34/46): the economics behind taxes, public goods and nudges. In the world: a city councillor deciding between a ban and a fee, a ministry of health asking for a pilot before a national rollout, an NGO choosing which programme to fund. Congestion charges (Singapore began its scheme in 1975, London in 2003) are the same story again: a price chosen, an agenda window, an implementation challenge, an evaluation. If you want to go deeper 📘 Textbook. Thomas Birkland, An Introduction to the Policy Process (Routledge): the standard undergraduate text on the cycle, agenda setting and theories of change. 📘 Textbook. Paul Cairney, Understanding Public Policy (Palgrave): short, critical, and strong on why the cycle is a simplification. 📘 Gentler. Abhijit Banerjee and Esther Duflo, Poor Economics (PublicAffairs, 2011): policy evaluation told through stories from India, Kenya, Mexico and elsewhere. 🌐 Free course. MIT OpenCourseWare 14.73, The Challenge of World Poverty (Banerjee and Duflo, Spring 2011): lectures that apply evaluation to real programmes. The takeaway Policy is a chain: a problem gets attention, a tool is chosen, many people carry it out, and someone asks what would have happened anyway. Each link can break, and each can be examined. Read any new policy by asking which link you are being asked to take on trust. Try this: this week, take one policy in the news, a tax, a ban or a scheme, and write down its goal, its instrument, who has to carry it out, and what comparison would show whether it worked. Sources & Further Reading Sources. Policy cycle: Lasswell, The Decision Process (1956); Lindblom, "The Science of Muddling Through", Public Administration Review (1959). Agendas: Kingdon (1984); Baumgartner and Jones (1993). Ireland's levy: introduced 2002 at 15 cents, a drop of about 90 percent reported by the government at the time (BBC News, 2002 and other reports; per-person figures differ between sources, and critics note bags are reused as bin liners). Mexico's soda tax: Colchero et al., BMJ (2016), about 6 percent fall in 2014 and about 12 percent in December 2014. UK Soft Drinks Industry Levy: announced 2016, in force 6 April 2018. Nudges: Johnson and Goldstein, Science (2003); DellaVigna and Linos, Econometrica 90(1), 2022, 81-116 (1.4 vs 8.7 points; 126 trials vs 26 papers); the Mertens et al. meta-analysis and the Maier et al. correction, PNAS (2022). Implementation: Pressman and Wildavsky (1973); Lipsky (1980). Progresa: renamed Oportunidades 2002; evaluation of 506 communities, about 320 treatment (J-PAL and Attanasio, Meghir and Santiago, Review of Economic Studies); 2019 Nobel to Banerjee, Duflo and Kremer. What Works Network: launched 2013 (UK government). Scared Straight: Cochrane systematic review of randomised trials (Petrosino and colleagues). Deaton and Cartwright, "Understanding and misunderstanding randomized controlled trials", Social Science & Medicine (2018). Miguel and Kremer, Econometrica (2004). Sections on the nudge-unit and trial simulation are the author's own illustrations. This piece describes how policy works; it is not advice on any particular policy. 🌐 MIT OpenCourseWare 14.73 📘 Banerjee & Duflo, Poor Economics 📘 Kingdon, Agendas, Alternatives, and Public Policies