Analytical expressions for drainable and fillable porosity of phreatic aquifers under vertical fluxes from evapotranspiration and recharge

In shallow unconfined aquifers, the response of the water table (WT) to input and output water fluxes is controlled by two distinct storage parameters, drainable and fillable porosity, which are applicable for WT drawdown and rise, respectively. However, only the drainable porosity estimated from the hydrostatic soil moisture profile is in common use. In this study, we show that under conditions of evapotranspiration and/or recharge from or to a shallow water table, drainable and fillable porosity have different values. Separate analytical expressions are developed for drainable and fillable porosity accounting for dynamic soil moisture conditions through the assumption of successive steady state fluxes in the unsaturated zone. The equations are expressed in terms of soil hydraulic parameters and matric suction at the soil surface. Parametric evapotranspiration and recharge functions are used to estimate the suction at the soil surface. The final expressions are independent of evapotranspiration or recharge function, thus allowing the use of any appropriate function to estimate the storage parameters. It is shown that the occurrence of unsaturated zone fluxes can result in significantly different values of drainable and fillable porosity, even when hysteresis is neglected. Application of the two parameters in a Boussinesq-type groundwater model resulted in significantly improved estimates of field-measured water table dynamics compared to the hydrostatic, single-parameter model.