Role of complementary relationship in Budyko framework from water-limited to energy-limited environments

Abstract:

The complementary relationship and Budyko curve are two kinds of approaches for describing the relationship between catchment-scale actual and potential evaporation. According to a nonlinear complementary relationship model, it was derived that, with constant energy input (denoted by constant radiation term (E_rad) of potential evaporation), the changes in aerodynamic term (E_aero) are accompanied with opposite changes in actual evaporation under water-limited conditions, but same direction changes in actual evaporation under energy-limited conditions. As a result, the radiation term and aerodynamic term play different roles in the Budyko curve. In other words, complementary relationship plays a role in the Budyko framework, which should be seriously considered.

The role of complementary relationship on the Budyko curve from water-limited to energy-limited environments was schematically analyzed, considering the different correlations between actual evaporation and the radiation and the aerodynamic terms. Under water limited conditions, the catchment with a higher E_rad/E_aero would be wetter, and characterized with higher evaporation efficiency and larger properties parameter of Budyko curve. Under energy limited conditions, the role of complementary relationship may be different.

E_rad/E_aero is found to be connected with the variations of catchment parameter in the Budyko curve, and an exponential relationship between the catchment parameter and E_rad/E_aero was derived through dimensional analysis and mathematical reasoning.

The analysis will be evaluated using water balance data of a number of catchments from non-humid to humid environments over China.