“General Coldness of Climate Models” and the Second Law: Implications for Modeling the Earth System

Abstract

Motivated by the circumstantial evidence of the pervasive nature of the ?general coldness? of climate model simulations, a theoretical analysis is made of the model response expected from the presence of both physical and aphysical sources of entropy under the joint conditions that the net flux of energy through the upper and lower boundaries of the atmosphere and the isentropic temporally, areally integrated entropy source must vanish. These joint conditions are essential for a simulated global climate state to be without drift. The application of these conditions in the presence of positive definite aphysical entropy sources leads to the conclusion that the model-simulated climate state will be characterized by a general coldness, in particular in the upper polar troposphere and lower tropical troposphere as observed in 104 out of 105 possible outcomes from 35 different simulations by 14 climate models. In assessing the magnitude of this effect, a 10°C bias in mean temperature corresponds with a relatively small error of 4% in the mean heat addition of an isentropic layer. This correspondence reveals the extreme sensitivity of a climate model?s temperature response to aphysical entropy sources introduced by spurious numerical dispersion/diffusion, Gibbs oscillations, parameterizations, and other factors. In accurately simulating hydrologic and chemical processes, this difficulty is compounded in the sense that the saturation specific humidity doubles for each additional 10°C increase in temperature and the inherent strong dependence of both processes on temperature, pressure, and amount of water substances?vapor, liquid, and ice. A strategy that makes climate simulations tractable is that numerical trade-offs occur among the various parameterizations of the components of heat addition. These trade-offs allow models to be tuned to simulate a reasonable state achievable for given resolution, numerics, and parameterizations. Oreskes et al. label this step ?calibration? and suggest that in such situations, ?empirical adequacy is forced.? The results of this analysis in combination with Carathéordary?s statement of the Second Law reveals in the strict sense that the presence of positive definite aphysical sources of entropy in a climate model precludes the simulation of unbiased distributions of the heat addition and temperature. Since in the strict sense the true state cannot be simulated, several questions follow: are reasonable states of global and regional climate change simulated for the right reasons; just what are reasonable states; and how are the right reasons to be determined in view of the trade-offs among the several components of parameterized heat addition?