The Water Budget Myth and Its Recharge Controversy: Linear vs. Nonlinear Models

The water budget myth, which is the idea that safe pumping must not exceed the initial recharge, gave rise to a controversy about the role of recharge in assessing the sustainability of groundwater development. To refute the concept of safe yield, a simplified water budget equation is used, which equals the total pumping rate to the sum of capture and storage change. Since initial recharge and discharge are canceled out from this equation, it is concluded that sustainable pumping has nothing to do with recharge. Investigating the assumptions underlying this equation, it is seen that it expresses the superposition principle, which implicitly assumes the groundwater reservoir can be depleted indefinitely and boundary conditions are an infinite source of water. To evaluate sustainability, however, the limits of the aquifer system must be examined accurately. Theoretically, this can only be accomplished applying nonlinear models, in which case setting up the simplified water budget equation is impossible without knowing the initial conditions. Hence, excluding recharge when assessing sustainable pumping may not be done inconsiderately, which is illustrated by two examples. An analytical solution, developed by Ernst in 1971 to simulate flow to a well in a polder area with a nonlinear function for drainage, even shows that it is not necessarily a misconception to assume the cone of depression stops expanding when the pumping rate is balanced by the infiltration rate.