Diurnal land surface energy balance partitioning estimated from the thermodynamic limit of a cold heat engine

Abstract

Turbulent fluxes strongly shape the conditions at the land surface, yet they are typically formulated in terms of semiempirical parameterizations that make it difficult to derive theoretical estimates of how global change impacts land surface functioning. Here, we describe these turbulent fluxes as the result of a thermodynamic process that generates work to sustain convective motion and thus maintains the turbulent exchange between the land surface and the atmosphere. We first derive a limit from the second law of thermodynamics that is equivalent to the Carnot limit but which explicitly accounts for diurnal heat storage changes in the lower atmosphere. We call this the limit of a cold heat engine and use it together with the surface energy balance to infer the maximum power that can be derived from the turbulent fluxes for a given solar radiative forcing. The surface energy balance partitioning estimated from this thermodynamic limit requires no empirical parameters and compares very well with the observed partitioning of absorbed solar radiation into radiative and turbulent heat fluxes across a range of climates, with correlation coefficients r2 ≥ 95 % and slopes near 1. These results suggest that turbulent heat fluxes on land operate near their thermodynamic limit on how much convection can be generated from the local radiative forcing. It implies that this type of approach can be used to derive general estimates of global change that are solely based on physical principles.