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.

11 projects, 275 hands-on levels, run in your browser.

Syllabus

Foundations: code through climate science: Never written code before? Start here. You will learn the absolute basics of Python, output, variables, types, decisions, loops, and functions, using temperature readings, CO2 levels, energy balance, and sea level as your playground. By the end you are ready for Project 1.
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: Explore rotation, ideal geostrophic components, angular-momentum constraints and a nondimensional overturning model. Distinguish numerical demonstrations from forecasts of actual winds or circulation transitions.
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: Construct annual emissions pathways, examine conditional TCRE budgets and run a simplified response model. Compare common horizons and baselines, including explicit limits on removals and sea-level approximations.
Capstone: A Mini Earth-System Model: Compose annual emissions, a proportional carbon sink, logarithmic forcing, two additive thermal modes and illustrative impacts. Record shared baselines, units, initial conditions and completed-year timestamps before comparing conditional scenarios.

Key concepts

Aerosol forcing: Particles whose direct radiative and cloud effects can cool or warm; the aggregate anthropogenic aerosol forcing is generally cooling. Removing a negative forc…
Airborne fraction: Atmospheric carbon stock increase divided by emissions over the same interval. A value near 0.45 is an illustrative historical-scale diagnostic, not the fixed…
Albedo: The fraction of incident shortwave radiation reflected by a specified surface or planet. Planetary albedo includes clouds and atmosphere; illustrative ice and…
AMOC collapse: The Atlantic Meridional Overturning Circulation. The track uses a Stommel toy model to illustrate transitions and hysteresis; its reversed branch and fold valu…
Angular-momentum constraint: The ideal zonal wind Omega R sin(phi)²/cos(phi) follows from conserving angular momentum from a resting equator. It grows poleward and becomes unsuitable near…
Anomaly: A value minus a specified reference mean. Subtracting one constant removes an offset but does not remove a seasonal cycle; deseasonalization requires matching…
Autocorrelation: Statistical association between a series and lagged versions of itself. Several finite-sample estimators exist; this track divides adjacent centered products b…
Back-radiation: Downward longwave radiation emitted by the atmosphere and clouds. It is one gross surface energy flow; net radiative exchange also includes upward emission, so…
Baseline period: The reference period for an anomaly. Changing a constant reference mean shifts anomalies by the difference of means while leaving within-series linear slopes u…
Beer-Lambert law: For attenuation along a path, transmission is exp(-tau) and optical depths add. The elementary absorbed fraction 1-exp(-tau) assumes no scattering or additiona…
Bifurcation (tipping point): A qualitative change in a dynamical system as a parameter varies, such as the merger of stable and unstable equilibria at a fold. A coarse scan locates a sampl…
Budyko model: Here a toy energy balance model combines temperature-dependent albedo with linear OLR=A+B*(T-273.15). Its damped fixed-point iteration is numerical relaxation,…
Carbon budget: A cumulative emission amount associated with a temperature limit under specified uncertainty and non-CO2 assumptions. The toy inversion (target-current)/TCRE g…
Carbon cycle: Transfers of carbon among atmosphere, land, ocean and rocks on many timescales. Atmospheric stock change, annual emissions and the decay of a tagged pulse are…
Carbon sinks: Processes with net carbon uptake, including land and ocean exchange and slower geological removal. Uptake depends on concentration, climate and reservoir state…
Climate emulator (FaIR-lite): A computationally compact approximation to selected model responses. The track's two additive thermal modes illustrate fast and slow response; they are not…
Climate feedback: A response to a climate change that alters the original response. In the scalar linear model, warming=dT0/(1-f). A sum f approaching one removes stable linear…
Climatology: A mean seasonal cycle over a specified reference period, such as twelve calendar-month means. Subtracting the corresponding monthly value removes that estimate…
Committed warming: A conditional future temperature response under specified boundary conditions. At fixed forcing the linear equilibrium gap is F/lambda-T_now. Holding forcing,…
Coriolis effect: An apparent acceleration in a rotating frame. The traditional horizontal coefficient f=2 Omega sin(latitude) changes sign between hemispheres and vanishes at t…
Cos-latitude weighting: Cosine-latitude weighting approximates relative cell area on regular latitude-longitude grids with equal angular widths. Irregular grids require actual cell bo…
Critical slowing down: Critical slowing down can occur near some bifurcations, increasing recovery time and sometimes autocorrelation or variance. These indicators are neither necess…
Detection & attribution: Detection assesses whether a change is distinguishable from specified variability; attribution assesses causes while considering competing explanations and unc…
Earth-system model: An Earth-system model represents interacting physical and biogeochemical components. This track composes a simplified carbon-to-forcing-to-temperature-to-impac…
Effective sample size: An approximate number of independent observations conveying similar information for a specified statistic. n*(1-r)/(1+r) is a large-sample AR(1) rule often use…
Effective temperature: The blackbody temperature corresponding to outgoing flux. At radiative equilibrium, T_eff=[S*(1-albedo)/(4*sigma)]^(1/4). The illustrative 255 K versus 288 K s…
Emission scenario: A conditional pathway under stated assumptions, not a prediction. Compare common horizons, initial states, units and forcing conventions; simplified model rank…
Energy balance: Energy conservation for a defined system: incoming minus outgoing power changes stored energy. At the top of the atmosphere use absorbed shortwave minus outgoi…
Energy balance model (EBM): An energy balance model equates heat storage to forcing minus restoring radiation. For an anomaly T, C dT/dt=F-lambda T uses positive restoring lambda. Define…
ENSO: El Nino-Southern Oscillation is coupled tropical Pacific ocean-atmosphere variability. The track's damped, kicked two-state oscillator illustrates recharge…
Equilibrium climate sensitivity (ECS): Equilibrium climate sensitivity is the eventual global mean surface warming after a CO2 doubling under specified feedback conventions. The simple positive-rest…
Extremes & the shifted mean: Values beyond a specified threshold. Shifting a normal distribution's mean can greatly increase a fixed upper-tail probability, depending on threshold and…
Fingerprint: A modeled pattern associated with a specified response or forcing. Pattern correlation compares shape but is unchanged by positive scaling and additive offsets…
Geostrophic balance: Approximate balance between horizontal pressure-gradient and Coriolis accelerations, giving flow along isobars away from the equator. Friction, curvature, acce…
Greenhouse effect: Atmospheric infrared absorption and emission allow the surface to be warmer than the effective radiating temperature. The atmosphere also absorbs some sunlight…
GtC per ppm: Approximately 2.13 gigatonnes of carbon correspond to one ppm atmospheric CO2. One tonne of carbon corresponds to 44/12 tonnes of CO2. Convert the mass unit be…
Hadley cell: Tropical overturning with rising air and subtropical descent. Angular momentum, energy balance, eddies and seasonal structure constrain its extent. A chosen an…
Hysteresis: Dependence of the state on its history: forward and reverse parameter changes can follow different stable branches. Returning a parameter to an earlier value n…
Ice cores: Ice archives preserve isotopic and other proxies, while enclosed bubbles sample past atmospheric gases. Depth-age relationships require chronology; gas age can…
Ice-albedo feedback: Ice or snow loss can reduce reflectivity and increase absorbed sunlight, amplifying warming. A prescribed albedo change is not by itself proof of instability;…
Impulse response (the long tail): The response to an isolated input pulse. The supplied rounded carbon fit combines three exponentials and a constant 0.217 term, summing to 0.999 at age zero. I…
Inverse-square law: For isotropic luminosity L, flux at distance d is L/(4 pi d²). Doubling distance quarters the flux, not the temperature. Use compatible distance units and negl…
Layer models: An ideal shortwave-transparent column of N opaque infrared layers gives Ts=(N+1)^(1/4)*T_eff. The effective count inferred from a temperature ratio is a model…
Lead-lag analysis: Comparison of aligned series at time offsets. Define positive lag and time-axis orientation, retain enough nonconstant overlap and account for dating uncertain…
Mean insolation (S/4): The global mean incoming solar flux is S/4 because projected disk area pi R² is one quarter of spherical area 4 pi*R². This spatial average follows geometry wi…
Net zero: A balance between specified emissions and removals over a stated interval and scope. The code detects the first nonpositive annual entry, which is different fr…
Ocean acidification: Changes in carbonate chemistry as absorbed CO2 increases hydrogen-ion concentration and lowers pH. A 0.1 pH decrease increases hydrogen-ion concentration by ab…
Ocean heat uptake: Energy stored by the ocean from a planetary imbalance. Uptake delays surface warming while the ocean adjusts. An assumed uptake fraction in the joule conversio…
Optical depth (tau): Dimensionless integrated attenuation along a path. It depends on wavelength and absorber properties. This track prescribes gray surface and interior relations…
Overshoot: Exceedance of a selected threshold before later decline. The symmetric linear TCRE exercise assigns equal emitted and removed carbon amounts to opposite temper…
Planck response: Increased thermal emission as temperature rises. The derivative of blackbody emission is 4 sigma T³, but the actual climate Planck feedback involves atmospheri…
Polar amplification: A greater temperature change in polar regions than a chosen global reference, depending on period, variable and region. Multiple feedbacks contribute. The exer…
Pre-industrial: A reference before large industrial influence; 1850–1900 is commonly used as an approximation for global temperature comparisons. The model's 280 ppm CO2 r…
Proxy: An indirect indicator of an environmental quantity, requiring calibration and uncertainty assessment. Isotope-temperature slopes depend on location, moisture s…
Radiative forcing: A perturbation to net radiative energy input, expressed in W/m² with a specified reference and adjustment convention. It differs from the residual imbalance af…
Red noise (AR(1)): A process with relatively strong low-frequency variability. The AR(1) example x_next=r*x+shock models persistence for |r|<1 with independent innovations. It…
Return period: The inverse of a stationary event probability per interval, such as 100 years for annual p=0.01. It is an average recurrence interpretation, not a schedule; ch…
Revelle factor: The ratio of fractional seawater pCO2 change to fractional dissolved inorganic carbon change under specified chemical conditions. A factor ten means a small 10…
Rossby number: The usual magnitude U/(abs(f) L) compares inertial and rotational effects. Small values support rotation-dominated approximations under other suitable conditio…
Sea-level rise: Changes in global or local sea level from thermal expansion, land ice and other processes, with relative sea level also affected by land motion. The track'…
Snowball Earth: A hypothesis and evidence-based interpretation of severe ancient global glaciations, including Cryogenian episodes. The track explores an ideal bright-ice equi…
Solar constant: Solar irradiance on a surface perpendicular to the rays at Earth's mean distance, approximately 1361 W/m² at the top of the atmosphere. It is neither the g…
Stefan-Boltzmann law: An ideal blackbody emits sigma*T⁴ W/m² at absolute temperature T in Kelvin. A gray emitter adds emissivity. Mean emission is a mean of fourth powers, not gener…
Stommel two-box model: The nondimensional model q=1-S and dS/dt=H-abs(1-S)*S uses S as a salinity contrast. For 0<H<0.25 it has thermal and reversed stable branches separated b…
Surface energy budget: Surface shortwave absorption plus downward longwave, minus upward longwave and turbulent heat losses. Specify signs and consistent spatial and temporal averagi…
TCRE: Transient climate response to cumulative CO2 emissions: an approximately linear relation over a relevant range, with uncertain coefficient and pathway limitati…
The CO2 forcing law: The teaching approximation F=5.35*ln(C/C0) W/m² for positive concentrations in the same units. Equal concentration ratios give equal forcing changes, about 3.7…
The e-folding time: The time for a decaying departure to fall to 1/e of its initial value. In a stable linear EBM tau=C/lambda. Its value depends on the chosen heat capacity and r…
Thermal expansion: Water volume change with temperature depends on its thermodynamic state. The illustrative expansivity depth dT relation assumes uniform whole-ocean warming and…
Thermal wind: A relation between horizontal temperature gradients and vertical shear of geostrophic wind, with signs determined by coordinates. A weaker prescribed gradient…
Thermohaline circulation: Ocean circulation influenced by temperature and salinity effects on density. Actual overturning also involves winds, mixing and basin geometry; a two-box densi…
Time of emergence: The time when a specified signal exceeds a defined variability criterion. It depends on signal, noise, baseline, averaging and persistence. This track distingu…
Transient climate response (TCR): Transient climate response conventionally averages global warming over a 20-year period centered on CO2 doubling in a 1%-per-year concentration experiment. The…
Trend fitting (OLS): Ordinary least squares fits a slope and intercept by minimizing squared residuals. Annual sample indices give slope per year. Error estimates require assumptio…
Water-vapor feedback: Warming increases saturation vapor pressure by roughly 7% per K near typical surface temperatures. If relative humidity changes little, atmospheric water vapor…
Zero-emissions commitment (ZEC): Zero-emissions commitment is temperature change after CO2 emissions cease, over a specified horizon and initial state. Declining CO2 forcing and continuing the…
Zonal mean: An average along longitude at a given latitude. Arithmetic row means assume equal longitude widths and suitable valid-data coverage. The resulting vector retai…