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Abstract
Abstract. 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.
Highlights
Many separation methods have been proposed, amongst them the two parameter recursive digital filter of Eckhardt (2005), which has since been applied in numerous studies, sometimes under the name of “Eckhardt filter”
As a measure for the sensitivity of the baseflow index BFI with respect to the parameters a and BFImax, a dimensionless sensitivity index S is calculated as the ratio between the relative error of BFI and the relative error of the respective parameter
The analytical sensitivity analysis shows that the recession constant a influences the calculated baseflow index BFI more than the filter parameter BFImax
Summary
The aim of baseflow separation is to distinguish two streamflow components: baseflow (groundwater discharging into the stream) and quick flow (surface runoff and interflow). Many separation methods have been proposed, amongst them the two parameter recursive digital filter of Eckhardt (2005), which has since been applied in numerous studies, sometimes under the name of “Eckhardt filter”. The equation of this low-pass filter is bk. An empirical sensitivity analysis consists of three steps, which are repeated several times: 1. An empirical sensitivity analysis is only a makeshift if an analytical sensitivity analysis, that is an analytical calculation of the error propagation through the model, is not feasible.
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