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.
Highlights
Hydrograph separation, aims to identify the proportion of water in different runoff pathways in the export flow of a basin, which helps in identifying the conversion relationship between groundwater and surface water; in addition, it is a necessary condition for optimal allocation of water resources (Cartwright et al, 2014; Miller et al, 2014; Costelloe et al, 2015)
Where fbf is the ratio of baseflow to streamflow in a single calculation process, Wfbf is the uncertainty in fbf at the 95 % confidence interval, WBFC and WROC are the standard deviations of the BFC and ROC multiplied by the t value (α = 0.05; two-tail) from the Student’s distribution, and WSC is the analytical error in conductivity multiplied by the t value (α = 0.05; two-tail) (Miller et al, 2014)
The absolute value of the sensitivity index for BFC is generally greater than that for ROC, indicating that baseflow index (BFI) is more affected by BFC – for example, if there are 10 % uncertainties in both BFC and ROC, BFC leads to −1.40 times 10 % of uncertainty in BFI (−14.0 %), while ROC leads to −0.89 times 10 % (−8.9 %)
Summary
Hydrograph separation ( called baseflow separation), aims to identify the proportion of water in different runoff pathways in the export flow of a basin, which helps in identifying the conversion relationship between groundwater and surface water; in addition, it is a necessary condition for optimal allocation of water resources (Cartwright et al, 2014; Miller et al, 2014; Costelloe et al, 2015). The two parameters BFC and ROC represent the electrical conductivity of baseflow and surface runoff, respectively. The determination of the parameters (BFC, ROC) of the conductivity two-component hydrograph separation method involves some uncertainties (Miller et al, 2014; Okello et al, 2018). The uncertainty in the separation results of the CMB method is mainly estimated using an uncertainty transfer equation based on the uncertainty in BFC, ROC, and SCk (Genereux, 1998; Miller et al, 2014). The main objectives of this study are as follows: (i) analyze the sensitivity of long-term series of baseflow separation results (BFI) to parameters and variables of the CMB equation The derived solutions were applied to 24 basins in the US, and the parameter sensitivity indices and BFI uncertainty characteristics were analyzed The derived solutions were applied to 24 basins in the US, and the parameter sensitivity indices and BFI uncertainty characteristics were analyzed (Sect. 4)
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