The conductivity mass balance (CMB) method has a long history of application to baseflow separation studies. The CMB method uses site-specific and widely available discharge and specific conductance data.
However, certain aspects of the method remain unstandardized, including the
determination of the applicability of this method for a specific area,
minimum data requirements for baseflow separation and the most accurate
parameter calculation method. This study collected and analyzed stream
discharge and water conductivity data for over 200 stream sites at large
spatial (2.77 to 2 915 834 km
Baseflow is the groundwater contribution to total streamflow (Hewlett and Hibbert, 1967), which plays a critical role in sustaining streamflow during dry periods (Rosenberry and Winter, 1997). Quantitative estimates of stream baseflow can be used to determine baseflow response to environmental conditions, thereby improving understanding of the water budget of a watershed and facilitating the estimation of groundwater discharge and recharge (Tan et al., 2009; Dhakal et al., 2012; Ran et al., 2012).
Given the importance of baseflow, many methods have been proposed for baseflow separation. Although these methods can be categorized according to various conditions (Stewart et al., 2007; Zhang et al., 2013; Miller et al., 2014; Lott and Stewart, 2016), they can generally be divided into two groups, namely non-tracer-based and tracer-based separation methods (Li et al., 2014). Non-tracer methods mainly include graphical and low-pass filter methods which only require stream discharge data (Nathan and McMahon, 1990; Eckhardt, 2008). Given the wide availability of stream discharge records, these approaches can readily be applied to a large number of sites (Miller et al., 2014). However, since these methods are typically applied without reference to any hydrological basin variables, the objective assessment of their accuracy remains a challenge (Nathan and McMahon, 1990; Arnold and Allen, 1999; Arnold et al., 2000; Furey and Gupta, 2001; Huyck et al., 2005; Eckhardt, 2008). In contrast, tracer-based baseflow separation methods adhere to the principle of mass balance (MB). Tracers such as stable isotopes, major ions and specific conductance (SC) have been used to quantify surface runoff and groundwater discharge to streamflow (Miller et al., 2014). The advantage of these methods relates to their use of site-specific variables, such as concentrations of chemical constituents, which are a function of actual physical processes and flow paths in the basin responsible for generation of different flow components. Therefore, chemical mass balance estimates of baseflow are often considered to be more reliable than those from graphical hydrograph separation estimates (Stewart et al., 2007). The principal disadvantage of mass-balance methods relates to their requirements of both observed discharge and chemical concentration data, which are not widely available, especially over a long period. This makes the application of the MB method in large basins impractical over a long period. For example, while stable isotopes are generally considered to be the most accurate chemical tracers for hydrograph separation (Kendall and McDonnell, 2012), the analytical costs associated with these constituents often limit their use in large studies (Miller et al., 2014).
In an analysis of hydrograph separation conducted using different geochemical tracers, Caissie et al. (1996) demonstrated that SC was the most effective single variable for quantifying the runoff and groundwater components of total streamflow since SC is a natural environmental tracer that can be inexpensively measured concurrently with streamflow (Kunkle, 1965; Matsubayashi et al., 1993; Arnold et al., 1995; Caissie et al., 1996; Cey et al., 1998; Heppell and Chapman, 2006; Stewart et al., 2007; Pellerin et al., 2008).
The conductivity mass balance (CMB) method converts specific conductance to a baseflow value using a two-component mass balance calculation (Pinder and Jones, 1969; Nakamura, 1971; Stewart et al., 2007):
Certain questions need to be addressed before the CMB method can be considered for separating baseflow in a watershed. These include whether the
CMB method is applicable to a watershed, how to more accurately determine
the key parameters SC
The present study conducted a comprehensive qualitative and quantitative analysis of data from more than 200 hydrological sites widely distributed in the Mississippi River basin, United States of America. Based on the results of statistical analysis, the present study had the following objectives: (1) determine the criteria and main factors influencing the applicability of the CMB method; (2) identify the best method for determining the parameters of the CMB method; (3) determine data requirements for the CMB method. The conclusions of the present study can help to determine whether the CMB method is applicable to a particular river reach and can provide a reference standard for use of the method.
The Mississippi River basin is located on the western side of the continental divide. The basin encompasses five states and has a drainage area of 320 000 km
Map showing the Mississippi River basin and the locations of the 201 stream gauging sites included in the present study.
The CMB method assumes that the two main recharge sources in any particular river section, streamflow runoff and baseflow have relatively stable conductivity values (Stewart et al., 2007; Lott and Stewart, 2012). Under natural conditions, streamflow conductivity reaches a maximum value under the dry season minimum discharge, indicating the dominant contribution of baseflow to streamflow (Miller et al., 2014). In contrast, streamflow conductivity will decrease during the high-flow period when the contribution of direct runoff through rainfall or snowmelt to discharge increases. This relationship between stream conductivity and the discharge persists through intermediate-state streamflows, with an inverse power function between streamflow discharge and conductivity identified (Miller et al., 2014). Conditions under which the above general relationship does not apply indicate the influence of other external factors on the river which the CMB method would be unable to represent. Therefore, during the process of baseflow separation, the applicability of the CMB method to a particular river section can be determined by identifying the relationship between stream discharge and conductivity.
In the present study, to identify the applicability of the CMB method to the
201 different site locations in the Mississippi River basin, the relationships between conductivity and streamflow discharge at the sites were quantitatively evaluated by correlation analysis. Stream sites were
grouped into four categories according to the strength of the relationship,
as indicated by the inverse correlation coefficient (
As according to the CMB equation (Eq. 1), the key parameters that are needed to calculate the baseflow index of total flow are the conductivities
of baseflow (SC
Several approaches are currently used to determine SC
Since Stewart et al. (2007) have pointed out that longer conductivity records are more likely to contain low conductivity values associated with high discharge, the present study used the minimum or 1st percentile (ordered by decreasing conductivity) method to estimate SC
The sensitivities of BFI to SC
Monitoring data of 26 stream sites with long-term records of stream discharge and water conductivity were analyzed to study the influence of different monitoring durations on the accuracy of parameter determination and baseflow separation results. Among the 26 sites, 5 had monitoring periods longer than 14 years, whereas the remainder had monitoring periods longer than 5 years. Continuous sampling periods within the five longer stream monitoring records included 3, 6, 9, 12, 15, 18, 21 and 24 months, whereas those in the remaining stream monitoring records included 3, 6, 9 and 12 months. To reduce the sampling error caused by the small number of samples, overlapping of monitoring data was allowed when sampling. In addition, each segment for a specific sampling duration was randomly chosen due to the variability in water quality measurements (Li et al., 2014). SC
As mentioned above, the sensitivities of BFI measurement to SC
The dimensionless sensitivity index of BFI (output) with SC
There is uncertainty associated with the estimation of true means from finite samples, which is regarded as a type of error in statistical inference (Lo, 2005). This uncertainty in the CMB method was estimated based on the uncertainties in SC
On the other hand, Yang et al. (2019) found that random measurement errors in
Given that the determination of the parameters involves sensitivity analysis and that the sampling period of the shortest time series might not exceed 1 year, both the uncertainty estimation methods of BFI proposed by Yang et al. (2019) and Genereux and Hooper (1998) were used to determine the parameters and the shortest time series in the present study.
The analysis of the 201 stations across the major Mississippi River basin showed a high variation in response of conductivity to stream discharge. Most sites (157) showed an inverse correlation between streamflow discharge and conductivity, with the number of sites with the high, medium, and low inverse correlations being 47, 72 and 38, respectively. The goodness of fit (
Inverse correlation between stream discharge and conductivity
An analysis of the spatial distribution of inverse correlations between stream discharge and conductivity in the basin showed that the correlations were related to various factors, including topography, altitude, stream
discharge and location. In general, most stations located in stream headwater areas with a steep terrain and high elevation showed inverse correlations between flow and conductivity, with
Spatial distribution of data analysis points within the Mississippi River basin according to the correlation between conductivity and stream discharge.
Values and variations of SC
The sensitivity analysis results (Table 1) showed that the sensitivity indices of BFI for SC
A comparison of results for different methods used to obtain parameters for baseflow separation methods.
1 and 2 represent yearly dynamic max and yearly dynamic 99th, respectively.
On this basis, the uncertainty values
The SC
Values and variations of mean BFI and
Temporal variation in discharge, specific conductance and baseflow for a typical site in the Mississippi River basin.
The results of the present study suggested that the applicability of the CMB method to a particular site can be determined by the presence of an inverse correlation between streamflow discharge and conductivity within monitoring data. Baseflow separation showed unreasonable results for sites in which there was no significant inverse correlation between stream conductivity and discharge. Taking site 01636315 as an example (Fig. 6), an increase in river flow from 28 August to 16 December 2006 was accompanied by a consistently high level of conductivity over the entire monitoring period. The calculated baseflow for this site using Eq. (1) was too large, with a significantly higher ratio during the flood process which clearly did not conform with the mechanism of the baseflow recharge process. During periods of recession (for example, 23 July–6 November 2007, 9 June–24 August 2008, 30 June–21 October 2009, and 23 May–11 August 2010), a gradual decrease in discharge was accompanied by a gradual decrease in conductivity, which is an opposite trend to what would be expected, and resulting in the calculated baseflow hydrograph being significantly lower than the runoff hydrograph. During the dry season, the only source of water in the river was baseflow, and therefore the separation results were clearly incorrect. In fact, for sites in which there was no significant inverse correlation between stream discharge and conductivity, they tended to show a positive relationship. Under these conditions, baseflow separation will generate inaccurate baseflow estimates. Therefore, the present study confirmed the value of an inverse correlation between conductivity and discharge as an indicator of the suitability of the CMB method.
The presence of an inverse correlation between stream conductivity and discharge is dependent on a strong hydraulic connection between groundwater and surface water in a reach and on the major direction of surface water–groundwater interaction being from groundwater to surface water. The CMB method should not be applied to sites in which there is interference in this relationship through anthropogenic activities and other external factors. In this way, conductivity and streamflow data can accurately reflect the natural spatial and temporal variation in baseflow and in the baseflow index. The present study further analyzed the characteristics of factors influencing the inverse correlation between stream conductivity and discharge, including location, topography, surrounding environmental conditions and anthropogenic interferences. By combining the inverse correlation and baseflow separation results, the present study provides a discussion of the key factors influencing the applicability of the CMB method.
Ground elevation and spatial distribution of correlation coefficients for the correlation between stream conductivity and discharge in the Mississippi River basin.
Scatterplot of the correlation coefficient against the elevation of the Mississippi River basin monitoring sites.
More than 90 % (
Catchment area and correlation coefficient of each site in the Mississippi River basin.
The present study analyzed and compared site data for the mainstem and tributaries of the Missouri River basin, Arkansas River basin, upper Mississippi River basin and other sub-basins. The results showed that a higher proportion of sites in the tributaries met the requirements of the CMB method. For example, the proportions of tributary and mainstem sites which met the requirements of the CMB method in the Missouri River, Ohio River and upper Mississippi River were 51.6 % and 36.4 %, 70.5 % and 50 %, and 54.5 % and 50 %, respectively. Tributary sites were generally characterized by a high altitude and steep terrain, whereas the mainstem sites fell within plain and low-altitude areas. Therefore, in general, the CMB method is more likely to be applicable to tributary sites.
In theory, streamflow discharge should be a strong determinant of the feasibility of the CMB method. Within a specific watershed, sites with high
discharge are mostly located along the mainstems and downstream area, and as
discussed above, few are suitable for application of the CMB method. On the
other hand, sub-basins with lower flow are likely to be more susceptible to
temporal variations in water quantity and the influences of external factors, resulting in distorted results of baseflow separation. However, the results of the present study showed no consistent mathematical relationship between streamflow discharge and correlation coefficient
Human activities can significantly affect stream discharge and water quality, thereby disrupting their natural relationship and invalidating the application of the CMB method. Human activities can result in dramatic changes to river conductivity, and the major impact processes include agricultural irrigation, mining activity, the use of salts as road de-icing agents and groundwater pumping (Kaushal et al., 2005; Crosa et al., 2006; Zume and Tarhule, 2008; Dikio, 2010; Palmer et al., 2010; Bäthe and Coring, 2011; Miguel et al., 2013). Other anthropogenic factors can also result in artificial variations in conductivity, such as industrial wastewater discharge (Piscart et al., 2005; Dikio, 2010), discharge of sewage wastewater (Silva et al., 2000; Williams et al., 2003; Lerotholi et al., 2004) or reduced river discharge due to river impoundment (Mirza, 1998).
Irrigation and the resulting rise in groundwater tables have been reported as one of the main factors leading to significant changes in electrical conductivity of river water, particularly in arid and semi-arid regions in which crop production consumes large quantities of water. Since crops absorb only a fraction of salt introduced through irrigation water, the remaining salt concentrates in the soil, leading to saline soil (Lerotholi et al., 2004). These salts may be leached out through run-off, ultimately ending up in rivers. Therefore, agriculture practices such as fertilizer application can influence the concentrations of conductivity and hence affect the accuracy of the CMB method. In contrast, Li et al. (2018) showed that conductivity of baseflow and surface runoff did not change over time in forest watersheds.
Mining activity is another major source of salts in rivers. Large quantities of potash salts are extracted each year for the manufacture of agricultural fertilizers. During the process of manufacturing of crude salt, which contains not only potash, but also NaCl and other salts, huge amounts of solid residues are stockpiled. The salts are dissolved during precipitation events and may enter surface waters. Mountaintop mining is a mining technique which involves removing 150 or more meters of a mountain to gain access to coal seams and has been blamed for large-scale stream salinization (Pond et al., 2008). The exposure of coal seams to weathering and percolation during coal mining provides many opportunities for the leaching of sulfate from coal wastes into surface waters (Fritz et al., 2010; Bernhardt and Palmer, 2011).
Significant changes in electrical conductivity in the cold regions has often
been reported to be the result of the use of salts as road de-icing agents (Löfgren, 2001; Ruth, 2003; Williams et al., 2003). The amount of
salts used to de-ice roads in North America increased from 909 000 to
1 347 000 t per winter from 1961 to 1966 (Hanes et al., 1970). During the
1980s, the amount of salts applied to roads increased to 10 million t yr
Groundwater pumping can reduce groundwater discharge to streams and affect the hydraulic connection between groundwater and surface water and then invalidates the application of the CMB method. When a well is pumped at a constant rate, initially most of the groundwater comes from storage, eventually reaching the river, inducing a leakage of stream water to adjacent aquifer and depleting streamflow significantly (Bredehoeft and Kendy, 2008; Gleeson and Ritcher, 2018). This change in relationship between groundwater and surface water renders CMB method less applicable.
Typically, a monitoring site is located adjacent to a reservoir or other water conservancy infrastructure, which may contribute to significantly
increased evaporation and higher conductivity. On the other hand, the reservoir/dam can also provide substantial sources of water in low-flow periods. This may decrease conductivity in streams, thereby undermining the
groundwater contribution to streams and leading to an underestimation of
baseflow conductivity. In the present study, such affected stream sites
included 07130500, 05116000, 06058502, 03400800 and 05370000 located in the
upstream part of the Mississippi River basin, and these sites showed relatively poor inverse correlations between stream conductivity and discharge, with correlation coefficients of
Since the Mississippi River basin encompasses almost two-thirds of the entire area of the United States and streamflow occurs through large areas of plain in the Midwest and densely populated areas in the east, the impacts of anthropogenic factors in these areas are great, resulting in limited applicability of the CMB method.
The present study found that, in general, for the entire Mississippi River basin, the CMB method was more applicable for headwater sites, tributaries and high-altitude regions of
A related study in the upper Colorado River basin suggests higher-elevation watersheds typically have greater baseflow yield (Rumsey et al., 2015), and Dyer (2008) found that high flows in upper streams are mainly stimulated by the snowmelt process and whether the impacts of altitude and site location are mainly due to differences in hydrological regimes, i.e., snow-dominated in upper streams and rain-dominated in lower watersheds. From these findings which are based on the major river basins in North America, we still cannot establish a relationship between hydrological regimes and the applicability of the CMB method. On the other hand, as a large watershed, the Mississippi River basin has sizeable spatial heterogeneity of climate. The role of climate in hydrology, particularly for low flows, is more pronounced in larger watersheds. The influence of hydrological processes on baseflow is complex, particularly when taking climate change into consideration. Therefore, specialized research will be required in the future.
The comparison of sensitivity analysis results indicated that the influence of parameter SC
Comparison of baseflow calculation results of the main parameter determination methods for a site (07097000) in the Mississippi River basin.
Over a long-term monitoring period, river water quality is often influenced
by anthropogenic processes such as release of water from upstream reservoirs
and sewage discharge, which can result in extremely high conductivity and
underestimated baseflow. The use of the 99th percentile of conductivity
as SC
However, it must be stressed that although the applicability of the CMB method has been verified for a site before determining parameters, it cannot be guaranteed that there will be no anthropogenic disturbance to parameters of a site in which the CMB method has been found to be applicable and that the parameters correspond to the lowest flows very well. For example, leakage of an underground storage tank may last for a long time, which may result in many observations of extremely high conductivities that cannot be avoided by the 99th percentile method. So there is a possibility that the 99th percentile conductivity does not correspond to the lowest flows. Therefore, parameters should be assessed after calculation by the 99th percentile method to further avoid abnormal phenomena and errors within separation results.
Determining the shortest monitoring periods appropriate for calculating SC
Differences between the baseflow index (BFI) obtained from 3, 6, or 9 months of data and the BFI obtained from standard sampling durations.
Through comprehensive qualitative and quantitative analysis of stream discharge and conductivity data for more than 200 hydrological stations in
the Mississippi River basin, the present study systematically addressed key
questions related to the application of the CMB method to particular sites
for baseflow separation. In general, the CMB method was found to be more
applicable to tributaries, headwater sites, sites at high altitude and sites
with little influence from anthropogenic activities. The applicability of
the CMB method can be determined by analyzing the inverse correlation
between stream discharge and conductivity. Continuous monitoring of flow and
conductivity of longer than 6 months in duration are required to ensure the reliability of baseflow separation results within the CMB method. Within a long series of monitoring data, the 1st percentile method and dynamic
99th percentile method are recommended to determine the parameters of SC
Further study is required to determine which 6 months should be selected for continuous monitoring after the shortest sampling period is determined, as this could be closely related to the geographical location and meteorological conditions of each station. In addition, future research should address whether monitoring should occur during the wet season, dry season, or both. Future research should also consider large watersheds in other latitudes and climates so as to compare and verify the conclusions of the present study and to establish more generalized methods. The present study can act as a reference for the identification of parameters of baseflow separation methods so as to improve the accuracy of these methods.
All streamflow and conductivity data can be retrieved from the US Geological Survey's (USGS) National Water Information System (NWIS) website using the special site number:
The supplement related to this article is available online at:
HL developed the research train of thought. CX completed the data requirement analysis. JZ carried out the CMB method suitability assessment. BL compared different parameter determination methods. HL prepared the manuscript with contributions from all the coauthors.
The authors declare that they have no conflict of interest.
This work is supported by the project funded by the National Key R & D Program of China (2018YFC0406503) and the National Natural Science Foundation of China (U19A20107, 41702252) special funds for basic scientific research-operating expenses of central universities. We would like to express our sincere thanks to the editor and the anonymous reviewers for the constructive and positive advice and comments which helped improve the manuscript.
This research has been supported by the National Key R & D Program of China (grant no. 2018YFC0406503), the National Natural Science Foundation of China (grant nos. U19A20107 and 41702252), and special funds for basic scientific research-operating expenses of central universities (grant no. 202010).
This paper was edited by Stacey Archfield and reviewed by two anonymous referees.