Abstract

Abstract. The hydrologic cycle results from the combination of energy conversions and atmospheric transport, and the laws of thermodynamics set limits to both. Here, we apply thermodynamics to derive the limits of the strength of hydrologic cycling within the Earth system and about the properties and processes that shape these limits. We set up simple models to derive analytical expressions of the limits of evaporation and precipitation in relation to vertical and horizontal differences in solar radiative forcing. These limits result from a fundamental trade-off by which a greater evaporation rate reduces the temperature gradient and thus the driver for atmospheric motion that exchanges moistened air from the surface with the drier air aloft. The limits on hydrologic cycling thus reflect the strong interaction between the hydrologic flux, motion, and the driving gradient. Despite the simplicity of the models, they yield estimates for the limits of hydrologic cycling that are within the observed magnitude, suggesting that the global hydrologic cycle operates near its maximum strength. We close with a discussion of how thermodynamic limits can provide a better characterization of the interaction of vegetation and human activity with hydrologic cycling.

Highlights

  • The global hydrologic cycle plays a critical role in the Earth system (Chahine, 1992)

  • Several studies indicate that the atmospheric circulation operates near its thermodynamic limit (Paltridge, 1975, 1978; Lorenz et al, 2001; Kleidon et al, 2003, 2006), so that we can infer the strength of the associated heat and moisture transport by atmospheric motion from the assumption of maximum thermodynamic efficiency

  • The optimum heat fluxes depend solely on the difference in solar absorption, Jin,t − Jin,p, which reflect the same properties as those stated by Stone (1978), but in addition it explicitly makes use of the assumption that atmospheric motion operates at its thermodynamic limit

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Summary

Introduction

The global hydrologic cycle plays a critical role in the Earth system (Chahine, 1992). In this study we ask about the fundamental factors that limit the strength of hydrologic cycling within the Earth system. A general result of thermodynamics is the Carnot limit, which describes the maximum rate by which a heating difference can be converted into mechanical work. This mechanical work is needed to maintain atmospheric motion, and motion is needed to maintain the ability to transport moisture. The derivation of the maximum strength of hydrologic cycling requires some background on the relevant constraints on the processes that are shown, by the conservation of energy, and how thermodynamics sets limits.

Thermodynamics of hydrologic cycling within the Earth system
The laws of thermodynamics
Vertical heating gradient
Horizontal heating gradient
Atmospheric motion
Hydrologic cycling
Maximum strength of hydrologic cycling
Maximum power limit
3.21 Maximum sptorwenegrtlhimofithydrologic cycling by vertical convection
Global estimates
Sensitivities
B A vegetation activity
Summary and conclusions
Entropy exchange in a steady state system
Findings
Linear approximations
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