How to construct recursive digital filters for baseflow separation

Abstract

Recursive digital filtering of hydrographs is a baseflow separation method that can easily be automated and has been recommended for providing reproducible results. In the past, different formulations of the most simple filter type, the so‐called one‐parameter filter, have been proposed. In this paper, a theoretical framework is developed for filter algorithms that were constructed under the assumption that the outflow from an aquifer is linearly proportional to its storage. It is shown that these one‐parameter filters describing an exponential baseflow recession are all special cases of a two‐parameter filter whose equation is specified. Its parameters are the recession constant—which can be objectively determined by a recession analysis—and BFI max, the maximum value of the baseflow index that can be modelled by the algorithm. This introduces a subjective element into the baseflow calculation, since BFI max is not measurable. A preliminary analysis based on the results of conventional separation techniques shows that it might be possible to find typical BFI max values for classes of catchments that can be unequivocally distinguished by their hydrological and hydrogeological characteristics. Copyright © 2004 John Wiley & Sons, Ltd.