Applications of solutions to non-linear energy budget equations

Abstract

A fourth-order (quartic) and second-order equation is developed to solve the energy budget equation for latent energy flux density. The solutions are compared with conventional iterative techniques and the linearized Penman-Monteith form. The fourth-order and second-order equations are then used to show that the generally accepted expression for equilibrium evapotranspiration is theoretically incorrect, both for infinite aerodynamic resistance and for zero vapor pressure deficit. The new methods give new insights for the analysis of canopy-air temperature differences, interactions between canopy resistance and vapor pressure deficit, the Priestley-Taylor equation, and the Jarvis-McNaughton concept of atmospheric coupling.