The findings of Briggs and Shantz have been confirmed repeatedly (Allison et al., 1958; Arkley, 1963; Chang, 1968; Hanks et al., 1969; Stanhill, 1960). Figure 7.1 shows the linear relationship between biomass produced and rainfall plus irrigation water used by Sart sorghum and Starr millet in Alabama, as adapted from data of Bennett et al. (1964). De Wit (1958) examined the relationships among climatic factors, yield, and water use by crops. He found the following general linear relationship to be true, especially in semiarid climates:
Y = yield component (e.g., total above-ground biomass or seed production)
T = cumulative actual transpiration
Tmax = maximum possible cumulative transpiration
m = constant dependent on yield component and species, especially on differences among photosynthetic mechanisms
Pan evaporation was used to represent Tmax, which is proportional to climatic factors, especially air vapor pressure deficit (VPD):
es = the saturation vapor pressure at a given air temperature
ea = the actual vapor pressure that exists in the air.
Combining these relationships, we see that yield is proportional to cumulative transpiration divided by vapor pressure deficit:
where k is a constant with units millibars • g (dry matter) • g-1 (water). Like m, k depends on yield component, species, and photosynthetic mechanisms.