A proposed composite Boussinesq equation for estimating baseflow recessions and storage-outflow relationship

Abstract

Baseflow recession analysis characterizes the interactions between ground and surface water, and many studies have focused on estimating the mathematical form of the relationship and its parameters. The Boussinesq equations can estimate baseflow recession and storage-outflow relationship. However, these equations assume either linear or nonlinear behavior, depending on the streamflow conditions. The linear equation cannot represent the nonlinear behavior of the baseflow, and the nonlinear equation cannot fit the lowest discharge values. In addition, the nonlinear equation is oversimplified and does not include baseflow from groundwater storage below the stream’s water level. Therefore, we propose a composite Boussinesq equation that includes the linear portion of baseflow below the stream’s water level, includes a nonlinear storage, and fits low discharge values. The performance of the linear, nonlinear, and composite methods are assessed using 1561 USGS stream gaging stations across the contiguous US (CONUS). The regression constants, which represent the aquifer characteristics, are estimated for all gages using the three methods. Results show that the composite equation results in smaller errors for estimating baseflow recession events and the storage-outflow relationship. Finally, four different variables, precipitation, evapotranspiration, average discharge, and drainage area, were analyzed to find the relationship between the watershed conditions and baseflow analysis in terms of the regression constants and the relative errors of the best fit curves. Results show that the nonlinearity increases in drier regions, and the relative error for all three methods increases in wet climate regions with high precipitation and evapotranspiration. The composite equation is a well-performing alternative to linear or nonlinear equations across all basin characteristics, allowing for estimating the full range of baseflow behavior.