Technical note: Analytical sensitivity analysis and uncertainty estimation of baseflow index calculated by a two-component hydrograph separation method with conductivity as a tracer

Abstract

Abstract. The two-component hydrograph separation method with conductivity as a tracer is favored by hydrologists owing to its low cost and easy application. This study analyzes the sensitivity of the baseflow index (BFI, long-term ratio of baseflow to streamflow) calculated using this method to errors or uncertainties in two parameters (BFC, the conductivity of baseflow, and ROC, the conductivity of surface runoff) and two variables (yk, streamflow, and SCk, specific conductance of streamflow, where k is the time step) and then estimates the uncertainty in BFI. The analysis shows that for time series longer than 365 days, random measurement errors in yk or SCk will cancel each other out, and their influence on BFI can be neglected. An uncertainty estimation method of BFI is derived on the basis of the sensitivity analysis. Representative sensitivity indices (the ratio of the relative error in BFI to that of BFC or ROC) and BFI′ uncertainties are determined by applying the resulting equations to 24 watersheds in the US. These dimensionless sensitivity indices can well express the propagation of errors or uncertainties in BFC or ROC into BFI. The results indicate that BFI is more sensitive to BFC, and the conductivity two-component hydrograph separation method may be more suitable for the long time series in a small watershed. When the mutual offset of the measurement errors in conductivity and streamflow is considered, the uncertainty in BFI is reduced by half.