Entropy Budget of the Global Climate System Under Radiative Forcing

Abstract

The global climate system behaves as a nonequilibrium heat engine that converts the entropy flux imposed by
incoming solar radiation and outgoing terrestrial radiation into material entropy production through atmospheric and
oceanic motion, latent-heat transport, and turbulent mixing, yet how this material entropy production responds to
sustained radiative forcing remains only coarsely quantified. We used a two-dimensional latitudinal energy balance
model with 36 latitude bands, forced by CO2-equivalent radiative perturbations from 0 to 8.5 W/m^2 following four
forcing scenarios, to compute the planetary radiative entropy budget and its partition into sensible-heat, latent-heat,
and mechanical (kinetic-energy dissipation) transport channels across 240 simulated years per scenario. At the
unforced baseline, material entropy production stabilized at 54.8 mW/(m^2 K), consistent with prior
maximum-entropy-production estimates, and rose to 61.3 mW/(m^2 K) under the 8.5 W/m^2 forcing scenario, a
11.9% increase driven disproportionately by the latent-heat channel, whose share of total material entropy
production grew from 32% to 41% as forcing increased. Meridional temperature gradient weakened by 18% under
maximum forcing, yet total meridional entropy transport increased by 9.4%, because enhanced latent-heat transport
more than compensated for the reduced sensible-heat gradient (r = -0.91, p < 0.001, across the four scenarios). A
sensitivity analysis varying the assumed longwave feedback parameter by ±25% shifted equilibrium material
entropy production by only 3.1 mW/(m^2 K), while varying the meridional diffusivity coefficient by the same margin
shifted it by 7.8 mW/(m^2 K), identifying diffusive heat transport efficiency, rather than radiative feedback strength,
as the dominant control on the simulated entropy budget's sensitivity. The model's radiative entropy production,
computed directly from the difference between absorbed shortwave and emitted longwave photon entropy fluxes,
exceeded material entropy production by more than an order of magnitude at every forcing level, confirming that the
climate system remains far from the state of maximum material entropy production even under strong forcing.
These results indicate that anthropogenic radiative forcing systematically increases the entropy-production burden
carried by the hydrological cycle specifically, rather than by atmospheric and oceanic sensible-heat circulation
broadly, with implications for how maximum-entropy-production closure schemes are calibrated in
reduced-complexity climate models.