Interrelations of yield, evapotranspiration, and water use efficiency from marginal analysis of water production functions

The study uses the concepts of marginal water use efficiency (MWUE), and elasticity of water production (EWP) to reveal the dynamic interrelations of crop yield (Y), seasonal evapotranspiration (ET), and water use efficiency (WUE) based on the functional relation of an ET production function (ETPF). When the ETPF is linear, the changing trend of WUE with ET is directly affected by the intercept of the function, and the EWP will be numerically equivalent to a yield response factor (KY) when ET reaches maximum ET (ETm). When the ETPF is quadratic, the ET needed to maximise WUE is less than the ET for maximum yield (Ym), and the ET value that occurs at maximum WUE equals the arithmetic square root of the ratio of the intercept of the function to the coefficient of function quadratic term. The interrelationships of Y, ET, and WUE are demonstrated using a quadratic ETPF developed for maize from data obtained in a field experiment.