The model facilitates a new generalization of the asymmetric complementary relationship with the asymmetry parameter b analytically predicted for a wide range of meteorological conditions with initial tests yielding good agreement between measured and predicted actual evaporation. Evaporation rates predicted based on the steady state reference temperature hypothesis were in good agreement with class A pan evaporation measurements suggesting that evaporation from pans occurs with negligible sensible heat flux. The feedback between drying land surfaces and overlaying air properties, central in the Bouchet (1963) complementary relationship, is implicitly incorporated in the hypothetical steady state where the sensible heat flux vanishes and the available energy is consumed by evaporation. We employed an analytical pore-scale representation of evaporation from terrestrial surfaces to define potential evaporation using a hypothetical steady state reference temperature that is common to both air and evaporating surface. The definition of potential evaporation remains widely debated despite its centrality for hydrologic and climatic models.

Results suggest that any model can be used with similar precision, since they show similar errors, although the MLR method allows analyzing and quantifying the errors introduced by the variables. The accuracy of the model estimates represents 10 % of the observed measured values of SM and is in line with state of the art algorithms. The resulting models were obtained with precipitation (PP), air temperature ( Ta) and relative humidity (RH) observations and with SAR data from the Sentinel-1A satellite mission. The water balance equation was solved with Multiple Linear Regression (MLR), Multivariate Adaptive Regression Splines (MARS) and Artificial Neural Network (ANN) statistical models, fed with readily available data over Comisión Nacional de Actividades Espaciales (CONAE) core site located in Cordoba province, Argentina.

The procedure presented in this paper takes into account water input and output processes of the soil system and represents them with different hydro-environmental variables and SAR data.

These models require soil information such as soil physical properties and mineral composition, not readily available in Argentina and many other remote areas of the world. Thus, a variety of methodologies with different levels of complexity are available nowadays. In recent years, remotely sensed data with Synthetic Aperture Radar (SAR) and radiometer sensors have been used to develop different methodologies to obtain SM maps. A procedure for soil moisture (SM) estimation over flat lands in the Argentinian Pampas region, using the water balance equation that considers SM to be the result of water inflows and outflows to the soil system, is presented.

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