The Budyko and complementary relationships in an idealized model of large-scale land–atmosphere coupling

Abstract. Two well-known relationships in hydrology and hydrometeorology, the Budyko and complementary relationships, are examined within an idealized prototype representing the physics of large-scale land–atmosphere coupling developed in prior work. These relationships are shown to hold on long (climatologic) timescales because of the tight coupling that exists between precipitation, atmospheric radiation, moisture convergence and advection. The slope of the CR is shown to be dependent on the Clausius–Clapeyron relationship between saturation-specific humidity and temperature, with important implications for the continental hydrologic cycle in a warming climate; e.g., one consequence of this dependence is that the CR may be expected to become more asymmetric with warming, as higher values of the slope imply a larger change in potential evaporation for a given change in evapotranspiration. In addition, the transparent physics of the prototype permits diagnosis of the sensitivity of the Budyko and complementary relationships to various atmospheric and land surface processes. Here, the impacts of anthropogenic influences, including large-scale irrigation and global warming, are assessed.