Thermodynamics of an idealized hydrologic cycle

The diurnal hydrologic cycle, a sequence of evapotranspiration, boundary layer growth, moist convection, and precipitation, is described in a thermodynamic framework, assuming an atmosphere composed solely of water. This idealized cycle is shown to be equivalent to an abbreviated version of the classical Rankine cycle where not all the water vapor is condensed. Energy and entropy fluxes of the processes involved in the cycle are quantified using the reversible approximation as a function of the quality of the liquid-vapor mixture (the ratio of the residual background vapor and the total mass of water) and the different temperatures at which evaporation and condensation take place. The proposed framework allows quantitative estimates of the net work (which is used by the cycle to drive the atmospheric circulation and dissipated by various frictional forces and nonidealities) as well as of the thermodynamic efficiency of the cycle. Possible extensions of the idealized framework relating to the role of dry air and the inclusion of various irreversible processes are also discussed.