Climate Model Resolution Lab

Model Grid

Latitude bands (resolution) 24

Forcing

CO₂ concentration 420 ppm

Solar constant 100%

Meridional heat diffusion D 0.60

Ice-albedo feedback

Live Readouts

Global mean T

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Equator−Pole ΔT

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Ice line

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Grid error vs N=90

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Temperature vs Latitude

How it works

This is a genuine 1-D latitudinal energy-balance climate model (Budyko–Sellers / North type), the same family of equations used as the low-order backbone of real climate models. Each latitude band φ obeys:

C·∂T/∂t = S(φ)·(1−α(T)) − (A + B·T − ΔF_CO2) + ∇·(D·cosφ·∂T/∂φ)/cosφ

S(φ) = (S₀/4)·(1 − 0.477·P₂(sinφ))     insolation by latitude
ΔF_CO2 = 5.35·ln(CO2/280)               CO2 radiative forcing (IPCC formula)
α(T) = 0.62 if T < −10°C else 0.30      ice-albedo switch
A + B·T                                  linearized outgoing longwave (Budyko)

The equation is solved with an implicit (backward-Euler) tridiagonal solve every step, so it stays numerically stable at any grid resolution or diffusion strength — exactly the kind of solver real climate codes use for diffusive terms.

Latitude bands — the model's spatial grid. Coarser grids blur the ice line and smear the equator-to-pole gradient; a hidden N=90 reference model runs in parallel so you can read the actual discretization error this introduces.
CO₂ / Solar constant — external forcing knobs, exactly as in scenario runs of a real GCM.
Diffusion D — how efficiently the atmosphere/ocean mix heat poleward; low D produces a cold, ice-heavy planet with a steep gradient, high D flattens it.
Ice-albedo feedback — toggling it off removes the nonlinear runaway that gives these models their famous multiple equilibria (Snowball-Earth-type bifurcations).

−40°C40°C

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