One class of descriptions of landscape evaporation is based on the principle that actual evaporation E and atmospheric evaporative demand exhibit complementary behavior. A feature of some recent implementations of this approach is the need for the estimation of a free parameter, usually by calibration. In a different class of representations of landscape evaporation, several functional forms have been proposed in the past for the dependency of the annual evaporation precipitation ratio (E/P) on the annual aridity index - the Schreiber-Oldekop hypothesis, also known as the Budyko framework. While there is no general agreement in the literature on the optimal formulation of the “maximum possible evaporation” , the functional forms of appear to be quite insensitive to its exact nature. This observation allows to be equated with the evaporative demand , and this immediately leads to a blending of the annual evaporation precipitation ratio (E/P) with the complementary evaporation principle, and the prediction of its unknown free parameter. As this free parameter is found to be relatively insensitive to time scale, the complementary functions become not only calibration-free at the annual time scale, but also applicable even at daily time scales. The results are shown to be applicable worldwide with experimental data from 516 catchment water balance set-ups and 152 high quality eddy covariance flux stations. The present approach offers a practical tool for the prediction of daily evaporation using only routine meteorological data such as air temperature, humidity, wind speed, net radiation, and long-term average precipitation.