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Joseph Smagorinsky developed numerical experiments on atmospheric circulation and was a central figure in the early modeling work at the Geophysical Fluid Dynamics Laboratory. Its institutional history credits his work with Syukuro Manabe in building atmospheric models for climate research during the 1950s and 1960s.^[ref]

His 1963 General Circulation Experiments with the Primitive Equations: I. The Basic Experiment by Joseph Smagorinsky integrated a simplified atmospheric model over an extended period and examined its momentum and heat transport. The model represented winds at two internal levels and a single temperature, with specified radiative forcing and dissipative mechanisms. Its lateral exchange coefficient depended on the local horizontal strain rate.^[ref]

The motivating difficulty is scale. A computational grid can represent large circulation patterns while failing to resolve smaller eddies that still transport momentum and heat. The Smagorinsky model represents some effects of those unresolved motions by an eddy viscosity, linking the closure to the resolved deformation rather than tracking every small eddy directly.

The original experiment also illustrates scientific restraint: Smagorinsky reported aspects of agreement with observed circulation while judging the modeled small-scale diffusion to play too large a role. A model can reproduce broad patterns yet misallocate the processes producing them. Comparing transport mechanisms and energy budgets therefore supplies a stronger test than visual resemblance alone.^[ref]

Syukuro Manabe and Klaus Hasselmann each received one quarter for physical climate models quantifying variability and predicting global warming. Giorgio Parisi received one half for discovering how disorder and fluctuations interact in physical systems from atomic to planetary scales.^[ref]

A radiative-convective climate column applies a radiative-convective equilibrium model to the vertical thermal structure relevant to climate change. Radiative transfer determines heating and cooling; convective adjustment represents unresolved vertical redistribution when the chosen atmospheric lapse rate is too steep. Radiative equilibrium alone need not give a physically admissible lower-atmospheric profile.

In 1967, Syukuro Manabe and Richard T. Wetherald computed equilibrium with prescribed relative humidity, allowing atmospheric water vapor to change with temperature. Their average-cloud case warmed by $2.36\mathrm{K}$ for carbon dioxide increasing from 300 to 600 parts per million, versus $1.33\mathrm{K}$ with fixed absolute humidity. These are model outputs, not measured warming. The comparison isolates an important water-vapor feedback.^[ref]

An original two-temperature calculation exposes the bookkeeping. Let an opaque surface absorb solar irradiance $Q$ and emit blackbody thermal radiation $\sigma T_s^4$. A single isothermal atmospheric layer transmits all sunlight and absorbs a fraction $ϵ$ of surface infrared emission, emitting $ϵ\sigma T_a^4$ both upward and downward. This is a grey thermal-band emissivity, with $0<ϵ\le 1$. Let $H$ be upward nonradiative heat flux, and let $C_s,C_a>0$ be heat capacities per unit area. Then conservation of energy givesThe two equations sum toHere $L$ is outgoing longwave radiation. Both $H$ and downward atmospheric emission cancel internally: they redistribute energy without creating it. The factor two in atmospheric emission counts two faces. Dropping the downward face would spoil the surface budget. Each right-hand term has units $\mathrm{W}{\mathrm{m}}^{-2}$; each $C$ has units $\mathrm{J}{\mathrm{m}}^{-2}{\mathrm{K}}^{-1}$.

Choose $Q=240\mathrm{W}{\mathrm{m}}^{-2}$, $H=80\mathrm{W}{\mathrm{m}}^{-2}$ and $ϵ=1$. At equilibrium, $L=\sigma T_a^4=240\mathrm{W}{\mathrm{m}}^{-2}$ and $\sigma T_s^4=400\mathrm{W}{\mathrm{m}}^{-2}$, giving $T_a\simeq 255.06\mathrm{K}$ and $T_s\simeq 289.81\mathrm{K}$. Direct substitution gives surface balance $240+240-400-80=0$ and atmospheric balance $400-480+80=0$. These deliberately chosen fluxes illustrate the model; they are not an observed global budget or a reconstruction of the 1967 calculation. Prescribing $H$ illustrates heat transfer accounting but does not close a realistic convection law.

For fixed $Q,H,ϵ$, the positive-temperature equilibrium is locally stable. Put $a=4\sigma T_s^3>0$ and $b=4ϵ\sigma T_a^3>0$. The Jacobian matrix of the temperature equations has trace $-a/C_s-2b/C_a<0$ and determinant $ab(2-ϵ)/(C_s{C}_a)>0$. Thus both eigenvalues have negative real part. Temperature-dependent climate feedbacks alter this test. A single grey layer also omits the optical spectrum, cloud structure and the independent thermal behavior of the troposphere and stratosphere.

Richard T. Wetherald and Syukuro Manabe calculated atmospheric radiative-convective equilibrium with a prescribed relative humidity distribution. Allowing the water-vapour content to adjust with temperature changed the sensitivity compared with fixing absolute humidity.^[ref]

The calculation demonstrates why a humidity constraint is a physical modelling assumption: it controls part of the radiative feedback as the atmosphere warms.

Syukuro Manabe and Richard T. Wetherald modelled an atmosphere relaxing toward radiative-convective equilibrium and studied its response to changes in factors including carbon dioxide. Their prescribed relative humidity lets water vapour change with temperature.^[ref]

This couples radiative transfer with vertical thermal adjustment, making the feedback assumptions explicit. A simpler dry or fixed-water-content atmosphere need not predict the same equilibrium response.