Climate Modeling

Learn how climate science actually works by building its models from scratch in Python: the planetary energy budget, the greenhouse effect layer by layer, radiative forcing and feedbacks, snowball-Earth bifurcations, the carbon cycle, ocean tipping points, trends versus noise, and a mini Earth-system model that turns emission scenarios into warming. The physics inside every projection, not the headlines.

10 projects, 250 hands-on levels, run in your browser.

Syllabus

Earth's Energy Budget: All of climate science starts from one ledger: sunlight in, infrared out. This project builds that ledger from scratch, the inverse-square law that sets the solar constant, the albedo that throws part of it back, the Stefan-Boltzmann law that radiates the rest away, and the famous effective temperature of 255 K whose 33-degree gap to the real surface is the greenhouse effect waiting to be explained.
The Greenhouse Effect: The atmosphere is nearly transparent to sunlight and nearly opaque to infrared, and that asymmetry is worth 33 kelvin. This project builds the greenhouse effect from layer models: how absorption stacks up along a path, why a single glass layer forces the surface to 2^(1/4) times the effective temperature, what N layers do (and why Venus is an oven), and the emissivity and optical-depth knobs that tune the real planet.
Radiative Forcing & Feedbacks: Push the energy budget and the climate pushes back. This project quantifies both sides: radiative forcing, the logarithmic CO2 law worth 3.7 W/m^2 per doubling, and the feedbacks that amplify or damp the response, the Planck restoring force, water vapor, ice-albedo, and clouds, combining into the single most consequential number in the field: equilibrium climate sensitivity.
Energy Balance Models: Give the planet a heat capacity and it remembers; give it reflective ice and it can tip. This project builds the workhorse models of conceptual climate science: the transient response with its ocean-set e-folding time, committed warming in the pipeline, and the ice-albedo feedback that hands the same Sun two stable climates, one temperate, one snowball, with a hysteresis loop between them that once trapped the real Earth for millions of years.
The Carbon Cycle: Between the smokestack and the thermometer sits the carbon cycle: of every tonne emitted, the ocean and land quietly take roughly half, and what stays airborne stays for centuries. This project builds the accounting, the GtC-to-ppm exchange rate, box models of the reservoirs trading carbon, the airborne fraction, the famous long tail of a CO2 pulse, and the seawater chemistry that throttles the ocean sink.
Circulation: Heat arrives at the equator and must get to the poles, and the machinery that moves it is rotating. This project builds the dynamics: the Coriolis parameter and when rotation matters, geostrophic balance (why wind follows isobars), the angular-momentum argument that pins the Hadley cell at 30 degrees, and the Stommel two-box model of the Atlantic overturning, complete with the saddle-node bifurcation that makes 'AMOC collapse' a precise mathematical statement.
Climate Variability: The climate record is a trend wearing a costume of noise: El Nino spikes, volcanic dips, and the red wander of a system with memory. This project builds the statistical toolkit, anomalies and climatology, the AR(1) model that explains why climate noise is red, a toy ENSO oscillator, honest trend fitting, and the tail arithmetic showing how a small shift of the mean multiplies heat extremes.
Climate Data Analysis: Between raw station and satellite grids and a headline like 'warmest year on record' sits careful arithmetic. This project builds it in numpy: the cos-latitude weighting without which global means are wrong, zonal averages, anomaly baselining, per-gridcell trend maps and the Arctic's amplified warming, the lead-lag correlations read from ice cores, and the signal-to-noise ratio that decides when a change has officially emerged from the noise.
Scenarios & Projections: Every climate projection is an if-then machine: IF emissions follow this path, THEN warming follows that one. This project builds the machine, pathway construction and net-zero arithmetic, the astonishingly linear TCRE relationship that turns cumulative carbon into degrees, the remaining carbon budget, a two-timescale temperature model, sea-level rise that lags centuries behind, and the head-to-head comparison of policy futures.
Capstone: A Mini Earth-System Model: Everything this track built, bolted into one machine: emissions enter, the carbon module decides what stays airborne, the forcing module turns concentration into watts, the two-box temperature module turns watts into degrees, and the impacts module turns degrees into sea level and threshold-crossing years. Then the payoff: run rival policy futures through the whole chain and write the report that says what each one costs in degrees and decades.

Key concepts

Aerosol forcing: Pollution particles reflect sunlight and brighten clouds: a NEGATIVE forcing near -1 W/m^2 that currently masks a third of the greenhouse forcing. Cleaning the…
Airborne fraction: The share of emitted carbon that stays in the atmosphere, observed near 45 percent for decades. The rest is the ocean and land sinks working for free.
Albedo: The fraction of sunlight reflected straight back to space, about 0.30 for Earth. Ice is bright ( 0.6), ocean dark ( 0.06), which is what arms the ice-albedo fe…
AMOC collapse: Push freshwater forcing past the Stommel fold and the Atlantic overturning jumps to its reversed mode, and easing the forcing back does NOT restore it. Irrever…
Angular-momentum constraint: Air conserving angular momentum from a resting equator must spin up zonal wind Omega R sin^2(phi)/cos(phi) as it moves poleward, the arithmetic that pins the H…
Anomaly: Departure from a reference-period mean. Anomalies strip away absolute offsets and the seasonal cycle, which is why global datasets agree on anomalies even when…
Autocorrelation: The correlation of a series with its own past. Lag-1 autocorrelation calibrates the AR(1) model and sets the decorrelation time -1/ln(r).
Back-radiation: The atmosphere's downward infrared glow, about 340 W/m^2 at Earth's surface, more than arrives directly from the Sun. The greenhouse effect made measur…
Baseline period: The reference years an anomaly is measured against (1951-1980, 1991-2020, pre-industrial...). Switching baselines shifts every number by one constant, a perenn…
Beer-Lambert law: Radiation crossing an absorber survives as exp(-tau): optical depths add along the path, and absorption saturates as a layer thickens, the reason CO2's ban…
Bifurcation (tipping point): A parameter value where an equilibrium appears or vanishes, often by saddle-node collision. Past it, the system has no choice but to jump to a different state,…
Budyko model: An EBM with linearized outgoing radiation, OLR = A + B(T - 273.15), the greenhouse hidden inside A and B. Add an albedo ramp and it exhibits the snowball bifur…
Carbon budget: TCRE inverted: (target minus current warming) / TCRE tonnes may still be emitted. For 1.5 C the remainder is under two decades of current emissions, the arithm…
Carbon cycle: The flow of carbon between atmosphere (~880 GtC), ocean, land, and rocks. Of each tonne emitted, roughly half is quietly removed by ocean and land sinks within…
Carbon sinks: Ocean uptake (CO2 dissolving against the Revelle buffer) and land uptake (forests fertilized by CO2 itself). Both weaken as the planet warms, which raises the…
Climate emulator (FaIR-lite): A two-timescale impulse-response model (fast ~4 yr, slow ~240 yr boxes) that reproduces a full GCM's global temperature at a billionth of the cost. The eng…
Climate feedback: A response to warming that changes the warming itself: water vapor and ice-albedo amplify, extra emission damps. With feedback factor f, warming becomes dT0/(1…
Climatology: The expected value for each calendar month or day, averaged over a reference period. Subtracting it deseasonalizes a series, exposing the interannual signal.
Committed warming: The warming still owed at today's forcing: F/lambda minus what has already arrived, roughly half a degree. It arrives even if concentrations are frozen now.
Coriolis effect: On a rotating planet, moving air and water curve: right in the north, left in the south, not at all at the equator. f = 2 Omega sin(latitude) is the coefficien…
Cos-latitude weighting: Gridcell area shrinks as cos(latitude), so honest global means weight each band accordingly. Skip it and your 'global mean' is polar-biased, a classic…
Critical slowing down: Near a fold, recovery from small kicks takes visibly longer: rising autocorrelation and variance are measurable early-warning signals of an approaching tipping…
Detection & attribution: Detection: the change is outside natural variability (signal-to-noise above 2). Attribution: its spatial fingerprint matches the forced pattern, not the Sun&#3…
Earth-system model: The full chain in one machine: emissions -> carbon cycle -> concentrations -> forcing -> temperature -> impacts. This track's capstone build…
Effective sample size: Correlated data carry fewer independent points: n(1-r)/(1+r). A century of strongly red annual data is worth about eleven independent samples, trend tests must…
Effective temperature: The temperature at which absorbed sunlight balances emitted infrared: (S(1-albedo)/4 sigma)^(1/4), about 255 K for Earth. The 33 K gap to the observed 288 K su…
Emission scenario: An if-then future: a complete emission pathway fed through the climate machine. Scenarios are not predictions; they are the menu of choices, priced in degrees.
Energy balance: The planet's ledger: absorbed solar in, infrared out, and warming whenever the books do not close. Earth currently runs about +0.9 W/m^2, the imbalance dri…
Energy balance model (EBM): Climate's hydrogen atom: C dT/dt = forcing - lambda T. One heat capacity, one feedback parameter, and most of the conceptual results in this track.
ENSO: El Nino-Southern Oscillation: the Pacific's recharge oscillator, where warm-water volume and surface temperature chase each other in a damped, wind-kicked…
Equilibrium climate sensitivity (ECS): The eventual warming from doubled CO2: F_2x divided by the net feedback parameter, assessed at roughly 2.5-4 K with 3 K canonical. The single most consequentia…
Extremes & the shifted mean: Shift a Gaussian climate one degree warmer and the exceedance of a fixed high threshold multiplies several-fold: the deadly part of warming lives in the tails,…
Fingerprint: The spatial pattern a forcing produces (greenhouse: tropospheric warming WITH stratospheric cooling). Pattern correlation against observations is how causes ar…
Geostrophic balance: Pressure gradient against Coriolis: the wind ends up flowing ALONG isobars at speed (1/rho f) dp/dn. One pressure map yields the whole large-scale wind field.
Greenhouse effect: The atmosphere passes sunlight but absorbs infrared, so the surface must warm above the effective temperature for the same energy to escape from higher, colder…
GtC per ppm: The atmosphere's exchange rate: 2.13 gigatonnes of carbon per ppm of CO2 (and 3.67 tonnes of CO2 per tonne of carbon). Unit errors here have embarrassed ma…
Hadley cell: Hot air rises at the equator, drifts poleward, and sinks near 30 degrees, where angular-momentum conservation would otherwise demand impossible 134 m/s winds.…
Hysteresis: The way down and the way back differ: the forcing that breaks a state is not the forcing that restores it. Snowball Earth needs a far brighter Sun (or far more…
Ice cores: Fossil air in bubbles and an isotope thermometer in the ice itself, 800,000 years deep. They give the CO2-temperature lockstep of the glacial cycles and the pr…
Ice-albedo feedback: Melting ice darkens the surface, which absorbs more sunlight, which melts more ice. Wire it into an energy balance model and the same Sun supports two stable c…
Impulse response (the long tail): A pulse of CO2 decays as a sum of exponentials: about 41 percent left after a century, 22 percent after millennia. There is no single 'lifetime of CO2'…
Inverse-square law: Flux falls as 1/distance^2 because the same power crosses ever larger spheres. It sets each planet's solar constant from one number, the Sun's luminosi…
Layer models: Treat the atmosphere as IR-opaque panes: one layer forces the surface to 2^(1/4) times the effective temperature, N layers to (N+1)^(1/4). Venus behaves like r…
Lead-lag analysis: Scan the correlation of two series across time offsets to see who moves first. In glacial cycles, orbital wobbles lead, with CO2 as the amplifying middleman.
Mean insolation (S/4): The planet intercepts sunlight as a disk (pi R^2) but spreads it over a sphere (4 pi R^2), so the average input is a quarter of the solar constant, about 340 W…
Net zero: The year emissions minus removals reach zero. Because warming tracks CUMULATIVE carbon, temperature stops rising (roughly) when emissions stop, not when they m…
Ocean acidification: Dissolved CO2 makes carbonic acid: surface pH has fallen about 0.1 since pre-industrial times, a 30 percent rise in acidity, hard on anything that builds a she…
Ocean heat uptake: About 91 percent of the energy imbalance ends up in the ocean, zettajoules per decade. While the deep ocean still draws heat, the surface stays below its equil…
Optical depth (tau): The dimensionless thickness of an absorber: transmission is exp(-tau). In the gray-atmosphere model the surface warms as (1 + 3 tau/4)^(1/4); Earth's effec…
Overshoot: Exceeding a temperature target before coming back down. TCRE makes the debt explicit: every tonne over budget must later be removed by net-negative emissions.
Planck response: The fundamental restoring force: warming raises emission by ~4 sigma T^3 per kelvin (about 3.8 W/m^2/K at 255 K). Alone it would limit a CO2 doubling to about…
Polar amplification: The Arctic warms 2-4 times faster than the globe: retreating ice and snow uncover dark surfaces, and stable polar air traps the warming near the ground.
Pre-industrial: The reference climate before fossil emissions, conventionally 1850-1900 (CO2 at 280 ppm). The Paris targets of 1.5 and 2 degrees are measured from here, not fr…
Proxy: An indirect thermometer: isotope ratios, tree rings, corals, sediments. Calibrated against the instrumental era, proxies extend the record thousands of times b…
Radiative forcing: The change a perturbation makes to the planet's net energy input, in W/m^2, before the temperature responds. The common currency that lets CO2, methane, ae…
Red noise (AR(1)): Noise with memory: x_t = r x_(t-1) + shock. Climate variability is red because the ocean integrates weather, which inflates variance, stretches excursions, and…
Return period: The inverse of an event's annual probability: a '100-year' flood has p = 0.01. Warming shrinks return periods, yesterday's century event become…
Revelle factor: Seawater chemistry's buffer (~10): a 10 percent rise in atmospheric CO2 raises dissolved carbon only ~1 percent. It throttles the ocean sink and stiffens f…
Rossby number: U/(fL): the ratio of inertia to rotation. Small for weather systems (rotation rules), enormous for bathtubs (it does not), the test for when Coriolis matters.
Sea-level rise: Expansion plus melt, currently 4 mm/yr and accelerating. The multi-century commitment ( 2.3 m per degree from paleo) dwarfs the 2100 numbers; local rise adds s…
Snowball Earth: The ice-albedo feedback's deep end: a fully frozen, brilliantly reflective planet, stable under the same Sun as our temperate one. Earth fell in around 700…
Solar constant: The Sun's flux at Earth's distance, about 1361 W/m^2: the luminosity spread over a sphere one astronomical unit in radius. Every energy budget starts h…
Stefan-Boltzmann law: A body at temperature T radiates sigma T^4 W/m^2. The fourth power is climate's pressure valve: warm the planet a little and it radiates a lot harder.
Stommel two-box model: Temperature drives the overturning one way, salinity the other: q = 1 - S in nondimensional form. One quadratic later, the circulation has TWO stable modes, an…
Surface energy budget: What the ground gains (sunlight + back-radiation) and loses (its own emission + evaporation + convection). It closes separately from the top-of-atmosphere budg…
TCRE: The transient climate response to cumulative emissions: warming is LINEAR in total carbon ever emitted, about 1.65 K per trillion tonnes. The most policy-usefu…
The CO2 forcing law: F = 5.35 ln(C/C0) W/m^2: forcing grows with the logarithm of concentration, so each DOUBLING adds the same ~3.7 W/m^2. Ratios matter, not ppm.
The e-folding time: An EBM relaxes toward equilibrium with timescale C/lambda, about 7 years for the ocean mixed layer. One reason the thermometer always lags the forcing.
Thermal expansion: Warm water takes more room: the steady, certain part of sea-level rise, with an equilibrium of order 0.7 m per kelvin once the whole ocean has warmed, centurie…
Thermal wind: Horizontal temperature contrast forces vertical wind shear: the equator-to-pole gradient builds the jet stream with height. Arctic amplification weakens the gr…
Thermohaline circulation: The ocean's density-driven overturning: cold salty water sinks at high latitudes and creeps back at depth, the Atlantic limb (AMOC) carrying about a petawa…
Time of emergence: The year a warming signal climbs decisively above local noise (S/N > 2). The quiet tropics emerge FIRST despite warming slower, noise, not trend, sets the d…
Transient climate response (TCR): The warming at the MOMENT of doubling under a 1 percent/yr ramp, smaller than ECS because the ocean is still swallowing heat. The number that governs this cent…
Trend fitting (OLS): The least-squares slope through a time series, with a standard error that must be inflated for autocorrelation before declaring significance. Modern global war…
Water-vapor feedback: Warmer air holds ~7 percent more water per kelvin (Clausius-Clapeyron), and water vapor is itself a greenhouse gas: the largest amplifying feedback, roughly do…
Zero-emissions commitment (ZEC): The warming drift AFTER emissions reach zero: falling concentrations roughly cancel the ocean's lag, so best estimates sit near zero. Stopping works.
Zonal mean: The average along a latitude circle: climate collapsed to one curve per latitude, where the equator-pole gradient, the deserts, and polar amplification all sho…