Technical Note: Analytical sensitivity analysis of a two parameter recursive digital baseflow separation filter

A sensitivity analysis for a well-established baseflow separation technique, a two parameter recursive digital filter, is presented. The sensitivity of the calculated baseflow index to errors or uncertainties of the two filter parameters and of the initial baseflow value is analytically ascertained. It is found that the influence of the initial baseflow value is negligible for long time series. The propagation of errors or uncertainties of the two filter parameters into the baseflow index is expressed by a dimensionless sensitivity index, the ratio between the relative error of the baseflow index and the relative error of the respective parameter. Representative index values are derived by application of the resulting equations to 65 North American catchments. In the mean the parameter a, the recession constant, has a stronger influence on the calculated baseflow index than the second filter parameter BFImax. This is favourable in that a can be determined by a recession analysis and therefore should be less uncertain. Whether this finding also applies for a specific catchment can easily be checked by means of the derived equations.