Year 0CO2 - ppmWarming - KEquilibrium - KGain 1/(1-f) -fps -

Drag to orbit, wheel or pinch to zoom. The bars on the right are the heat-flux budget in W/m2 at the chosen year: forcing and every feedback response (up = adds energy, down = removes it). The last bar, the imbalance, shrinks to zero as the planet reaches equilibrium. Polar ice and glow are schematic.

Climate Feedback Gain Budget Lab

A zero-dimensional Earth: CO2 adds a forcing, the planet warms, and every feedback adds or removes energy in response. Their sum decides how much warming the forcing finally causes and how fast.

Forcing scenario

Feedback parameters (W/m2 per K)

Live readouts

Warming against time (K)

Orange: all feedbacks. Blue: Planck response only. Dashed: analytic equilibrium. White line: year shown on the globe.

Experiment: how the gain blows up

Sweeps the water-vapour feedback and plots the equilibrium warming for 2x CO2. As the feedback factor f approaches 1, sensitivity grows without bound: a small uncertainty in f means a large one in warming.

Uncertainty: seeded Monte Carlo

Independent numerical checks

Controls

Pick a CO2 pathway and a final CO2; the year slider (or Play) moves through 100 years. Each feedback slider can be changed; the presets set typical or extreme combinations.
Drag to orbit the globe, wheel or pinch to zoom.

The science

Forcing. F = 5.35 ln(C/280 ppm) W/m2, so doubling CO2 gives about 3.7 W/m2. Energy balance. C_eff dT/dt = F(t) + λ T, where the net feedback parameter λ = λ_Planck + λ_wv + λ_lapse + λ_albedo + λ_cloud is negative for a stable climate.

Gain. Without feedbacks the warming is ΔT₀ = F/|λ_P| ≈ 1.2 K for 2x CO2. With the feedback factor f = Σλ_i/|λ_P| (all non-Planck terms) each loop adds a fraction f of the previous one, so ΔT = ΔT₀ (1 + f + f² + …) = ΔT₀/(1 − f) = F/(−λ). If f reaches 1 the linear model has no equilibrium. The warming timescale is τ = C_eff/|λ|.

Simplifications, stated honestly. The default values are typical, rounded central values from published assessments (water vapour about +1.8, lapse rate about -0.5, surface albedo about +0.35, cloud about +0.45, Planck about -3.2 W/m2/K); treat them as illustrative, not as exact measurements. The model is global-mean and linear: no ocean heat uptake beyond one effective heat capacity (real warming is slower and has a long tail), no pattern effects, no state-dependent feedbacks, no tipping points, aerosols or carbon cycle. Uncertainty widths in the Monte Carlo are rough illustrative values with independent Gaussians. The ice caps and glow on the globe are a schematic of the warming number, not a projection.

Made for learning; models are simplified.