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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.

Observations and climate model simulations consistently show a higher climate sensitivity of land surfaces compared to ocean surfaces. Here we show that this difference in temperature sensitivity can be explained by the different means by which the diurnal variation in solar radiation is buffered. While ocean surfaces buffer the diurnal variations by heat storage changes below the surface, land surfaces buffer it mostly by heat storage changes above the surface in the lower atmosphere that are reflected in the diurnal growth of a convective boundary layer. Storage changes below the surface allow the ocean surface–atmosphere system to maintain turbulent fluxes over day and night, while the land surface–atmosphere system maintains turbulent fluxes only during the daytime hours, when the surface is heated by absorption of solar radiation. This shorter duration of turbulent fluxes on land results in a greater sensitivity of the land surface–atmosphere system to changes in the greenhouse forcing because nighttime temperatures are shaped by radiative exchange only, which are more sensitive to changes in greenhouse forcing. We use a simple, analytic energy balance model of the surface–atmosphere system in which turbulent fluxes are constrained by the maximum power limit to estimate the effects of these different means to buffer the diurnal cycle on the resulting temperature sensitivities. The model predicts that land surfaces have a 50 % greater climate sensitivity than ocean surfaces, and that the nighttime temperatures on land increase about twice as much as daytime temperatures because of the absence of turbulent fluxes at night. Both predictions compare very well with observations and CMIP5 climate model simulations. Hence, the greater climate sensitivity of land surfaces can be explained by its buffering of diurnal variations in solar radiation in the lower atmosphere.

The global hydrologic cycle is likely to increase in strength with global warming, although some studies indicate that warming due to solar absorption may result in a different sensitivity than warming due to an elevated greenhouse effect. Here we show that these sensitivities of the hydrologic cycle can be derived analytically from an extremely simple surface energy balance model that is constrained by the assumption that vertical convective exchange within the atmosphere operates at the thermodynamic limit of maximum power. Using current climatic mean conditions, this model predicts a sensitivity of the hydrologic cycle of 2.2% K−1 to greenhouse-induced surface warming which is the sensitivity reported from climate models. The sensitivity to solar-induced warming includes an additional term, which increases the total sensitivity to 3.2% K−1. These sensitivities are explained by shifts in the turbulent fluxes in the case of greenhouse-induced warming, which is proportional to the change in slope of the saturation vapor pressure, and in terms of an additional increase in turbulent fluxes in the case of solar radiation-induced warming. We illustrate an implication of this explanation for geoengineering, which aims to undo surface temperature differences by solar radiation management. Our results show that when such an intervention compensates surface warming, it cannot simultaneously compensate the changes in hydrologic cycling because of the differences in sensitivities for solar vs. greenhouse-induced surface warming. We conclude that the sensitivity of the hydrologic cycle to surface temperature can be understood and predicted with very simple physical considerations but this needs to reflect on the different roles that solar and terrestrial radiation play in forcing the hydrologic cycle.