A Formula to Express Evapotranspiration as a Function of Soil Moisture and Evaporative Demands of the Atmosphere

A mathematical expression was developed and tested which describes the relation between evapotranspiration and soil moisture. A general premise of this mathematical model is that the evapotranspiration-soil moisture relationship is determined by interaction of climatic, soil and plant factors. The basic model is dETa/dYs = -ke[1-(ETa/ETmx)] in which ETa is the actual evapotranspiration, Ψs is the total soil water potential, k is a proportionality coefficient, ∈ is the soil moisture extraction capacity of the atmosphere , and ETmx is the evapotranspiration that would occur from a particular crop-soil unit when soil moisture was not limiting. From this model the following expression was derived: ETa = (1/1+(Ys/Ys’)^[2.56/log (Ymi/Ymx)])g E0 where Ψmx\u27, Ψs\u27, Ψmi are the soil potentials at which ETa is equal to 95%, 50% and 5% of ETmx\u27 respectively; EO is the evaporation from a free water surface and expressed the evaporative demands of the atmosphere. The term g is a proportionality coefficient equal to ETmx/EO. A second formula was developed that expresses the same relationship in terms of soil water content, and was derived from the former by assuming a hyperbolic relationship between soil water potential and water content. These formulas, as well as various other models which are described in the literature, were tested using experimental data covering a wide range of climatic, soil and plant variables. It was concluded that: (a) Most models advocated in the literature are only adequate to describe the relation between evapotranspiration and soil moisture under particular climatic , soil and plant conditions. (b) The formulas derived from the proposed model provide a good fit for the evapotranspiration-soil moisture relationship under widely different circumstances. If proper values are chosen for the coefficients, these formulas yield relations that are similar to several of the models taken from the literature. Consequently, the proposed mathematical expression appears to be a general model of the manner in which plants use soil water under different vegetative and environmental conditions. (c) It seems possible to predict in a comparative way the pattern of soil water utilization in a soil-plant-atmosphere system . This may be done from a knowledge of the relations between the coefficients of the formulas and climatic, soil and plant factors influencing evapotranspiration