Improved analytical expressions for transient specific yield in shallow groundwater drainage

Abstract

This paper presents the new analytical expressions to improve the description of transient specific yield (Sy) in shallow groundwater drainage. A new expression of the transient Sy (i.e. Sy,G (t)) that only considers the gravity effect is first derived based on the modified van Genuchten model. This analytical expression is still valid when water table depth (WTD) is less than the soil air-entry pressure head, and thus completes the lack of description in the near-saturated segment in previous expressions. Further, we propose an approximate method to dealing with the diffusivity (capillary) effect, and derive an improved approximate expression of Sy with both considering the gravity and diffusivity (capillary) effects. The accuracy of the improved expression of Sy,GD (t) is evaluated with the test cases that cover all of soil types (under the USDA soil classification system) and different changes in water table, also compared with the expression derived with only considering the gravity effect. The comparisons show that the Sy,GD (t) expression could more accurately capture the dependence of the transient Sy on time and WTD, and significantly reduce the errors of ignoring the diffusivity effect. In addition, the analytical expression of ultimate Sy and the final time td required to reach its ultimate value are both derived based on the initial and final equilibrium states. Results indicate that our improved expressions can expand the application range of analytical expression and significantly improve the calculation accuracy of transient Sy in the shallow groundwater environments.