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 (BF

Hydrograph separation (also 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). Some researchers indicated that tracer-based hydrograph separation methods yield the most realistic results because they are the most physically based methods (Miller et al., 2014; Mei and Anagnostou, 2015; Zhang et al., 2017). Many hydrologists have suggested that electrical conductivity can be used as a tracer in hydrograph separation (Stewart et al., 2007; Munyaneza et al., 2012; Cartwright et al., 2014; Lott and Stewart, 2016; Okello et al., 2018). Conductivity is a suitable tracer because its measurement is simple and inexpensive, and it has distinct applicability in long-series hydrograph separation (Okello et al., 2018).

The two-component hydrograph separation method with conductivity as a tracer
(also called conductivity mass balance (CMB) method; Stewart et al., 2007)
calculates baseflow through a two-component mass balance equation. The
general equation is shown in Eq. (1), which is based on the following assumptions:

contributions from end-members other than baseflow and surface runoff are negligible;

the specific conductance of runoff and baseflow are constant (or vary in a known manner) over the period of record;

in-stream processes (such as evaporation) do not change specific conductance markedly;

baseflow and surface runoff have significantly different specific conductance.

Stewart et al. (2007) conducted a field test in a drainage basin of
12 km

Most existing parameter sensitivity analysis methods are empirical methods that usually substitute varying values of a certain parameter into the separation model and then compare the range of the separation results produced by these varying parameter values (Eckhardt, 2005; Miller et al., 2014; Okello et al., 2018). Eckhardt (2012) indicated that “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”. Eckhardt (2012) derived sensitivity indices of equation parameters by the partial derivative of a two-parameter recursive digital baseflow separation filter equation. Until now, the parameters' sensitivity indices of the CMB equation have not been derived.

At present, the uncertainty in the separation results of the CMB method is
mainly estimated using an uncertainty transfer equation based on the
uncertainty in BF

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 (Sect. 2); (ii) derive the uncertainty in BFI (Sect. 3). The derived solutions were applied to 24 basins in the US, and the parameter sensitivity indices and BFI uncertainty characteristics were analyzed (Sect. 4).

In order to calculate the sensitivity indices of the parameters, the partial
derivatives of

Then, the partial derivatives of BFI to BF

The dimensionless sensitivity index is also called the “elasticity index”,
and it reflects the proportional relationship between the relative error in
BFI and the relative error in parameters (e.g., if

In addition to the two parameters, there are two variables (SC

Basic information, parameter sensitivity analysis, and uncertainty estimation results for 24 basins in the US. The asterisk in the “area” column indicates that the values are estimated based on data from adjacent sites.

Small errors in SC

The analysis of

According to previous studies, in the case where a variable

According to Genereux (1998), “While any set of consistent uncertainty (

Based on the above principle, Genereux (1998) substituted Eq. (18) into
Eq. (17) to derive the uncertainty estimation equation (Eq. 19) of the CMB method:

Better estimates of the uncertainty in

BFI is a function of BF

The above sensitivity analysis and uncertainty estimation methods were
applied to 24 catchments in the US (Table 1). All basins used in
this study are perennial streams, with drainage areas ranging from
10 to 1 258 481 km

The daily baseflow of each basin was calculated using Eq. (1). The
99th percentile of the conductivity of each year was used as BF

Finally, the uncertainty in

Scatterplots of sensitivity indices vs. time series (

The calculation results are shown in Table 1. The average baseflow index of
the 24 watersheds is 0.34, the average sensitivity index of BFI for mean BF

The sensitivity index of BFI for BF

Scatterplot of uncertainty in BFI (

The sensitivity index of BFI for RO

Estimation results of

Genereux's method (Eq. 19) estimates the average uncertainty in BFI in the
24 basins (average of mean

The conductivity of shallow subsurface and soil flow in real watersheds is sensitive to climatic conditions and usually shows obvious fluctuations (Miller et al., 2014). The CMB method classifies high-conductivity flow (e.g., deep subsurface flow) as baseflow and low-conductivity flow (e.g., local shallow soil flow) as surface runoff (Cartwright et al., 2014). Therefore, in the watershed containing a large number of low-conductivity soil flows, the BFI calculated by the CMB method comprised only the baseflow index of the deep subsurface flow. The parameter sensitivity indices and uncertainty in the deep subsurface flow were also calculated by the methods of this paper. Cartwright et al. (2014) showed that the ratio of low-conductivity soil flow to high-conductivity subsurface flow in the Barwon Basin in southeastern Australia is close to 1. If only the BFI doubles and other parameters remain unchanged, then the sensitivity indices calculated by Eqs. (9) and (10) are halved, whereas the uncertainty calculated by Eq. (23) remains unchanged. Therefore, nonconstant soil flow conductivity may lead to an overestimation of sensitivity, but it has less impact on uncertainty estimates.

To better understand the effects of low-conductivity soil flow on BFI,
parameter sensitivity, and the uncertainty estimation results, this study
assumed that the high-conductivity baseflow is constant and the ratio of
low-conductivity soil flow to high-conductivity baseflow (SF

This study analyzed the sensitivity of BFI, calculated using the CMB method,
to errors or uncertainties in the parameters BF

Systematic errors in specific conductance and streamflow as well as temporal and spatial variations in baseflow conductivity may be the main sources of BFI uncertainty. Better rating curves are probably more important than better loggers, and understanding the specific conductance of baseflow is likely more important than understanding that of surface runoff.

The above conclusions were drawn only from the average of the studied 24 basins, and further research in other countries or in more watersheds is thus required. This study focused on the two-component hydrograph separation method with conductivity as a tracer, but parameter sensitivity analysis and uncertainty analysis methods involving other tracers are similar. Therefore, similar equations can easily be derived by referring to the findings of this study.

All streamflow and conductivity data can be retrieved from
the US Geological Survey's (USGS) National Water Information System (NWIS)
website using the special gage number:

The supplement related to this article is available online at:

WY, CX, and XL developed the research train of thought. WY and CX completed the parameters' sensitivity analysis. XL completed the uncertainty estimate of BFI. WY carried out most of the data analysis and prepared the manuscript with contributions from all coauthors.

The authors declare that they have no conflict of interest.

This work is supported by the National Natural Science Foundation of China (41572216), the Provincial School Co-construction Project Special – Leading Technology Guide (SXGJQY2017-6), the China Geological Survey Shenyang Geological Survey Center “Changji Economic Circle Geological Environment Survey” project (121201007000150012), and the Jilin Province Key Geological Foundation Project (2014-13). We thank the anonymous reviewers for useful comments to improve the manuscript. Edited by: Markus Hrachowitz Reviewed by: three anonymous referees