Abstract. A filter for separating base flow from streamflow in a river basin is derived from a mass balance equation for base flow from a hillside. Unlike other existing filters, this filter is physically based both during streamflow recession and rise, and each of the parameters in it has a well-defined physical meaning. Unlike other approaches to base flow separation, the filter is applied without any calibration or constraints. Yet, using two criteria as measures of filter performance, it performs as well as or better than two existing filters that require calibration. Using the same two criteria, weaknesses in the filter are identified and attributed mainly to a ratio of two parameters that are related to groundwater recharge and overland flow. This ratio is estimated using precipitation and streamflow data, and its estimate is conjectured to be inaccurate because of the poor spatial resolution of the precipitation data. Moreover, this ratio is assumed to be constant in time, yet, on physical grounds, it should be treated as a time-dependent quantity.
IntroductionBase flow time series are needed to understand the spatial and temporal variability of runoff processes in river basins, to extrapolate runoff processes to ungauged locations [Gupta and Waymire, 1998], and, in practice, to manage water quantity and quality. However, there is no direct way to continuously measure base flow throughout a basin or processes that affect base flow such as overland flow, evapotranspiration, interflow, and groundwater recharge. Consequently, many approaches have been developed to estimate or separate base flow from streamflow continuously in time [e.g., see Wittenberg, 1999;Chapman, 1999;Birtles, 1978]. None of these approaches are physically based under all streamflow conditions and consist of only a few parameters. As a result, they rely heavily on calibration which masks the physics behind base flow estimation particularly during times when streamflow is rising. In this paper, a mathematical filter for continuous base flow separation is developed that is physically based under all streamflow conditions. It consists of four well-defined physical parameters, three of which can be estimated using both rainfall and streamflow data. Our filter is physically based both during streamflow recession and rise, and its physical basis requires that it be applied once and only forward in time to produce an estimate of base flow. By contrast, application of some other filters to streamflow data appears arbitrary [e.g., Nathan and McMahon, 1990; Chapman, 1991]. Unlike other filters, our filter is not founded on the assumption that base flow and overland flow are the low-and high-frequency components of streamflow, respectively [Spongberg, 2000]. Thus it accounts for the possibility that low-frequency variations exist in overland flow because of those in precipitation. The filter consists of four physical constants that must be evaluated before using it. Three of these are estimated from streamflow and precipitation data, and the filter...
