The two-parameter recursive digital filter method
(Eckhardt) and the conductivity mass balance (CMB) method are two
widely used baseflow separation methods favored by hydrologists. Some
divergences in the application of these two methods have emerged in recent
years. Some scholars believe that deviation of baseflow separation results
of the two methods is due to uncertainty of the parameters of the Eckhardt
method and that the Eckhardt method should be corrected by reference to the
CMB method. However, other scholars attribute the deviation to the fact that
they contain different transient water components. This study aimed to
resolve this disagreement by analyzing the effectiveness of the CMB method
for correcting the Eckhardt method through application of the methods to 26
basins in the United States by comparison of the biases between the
generated daily baseflow series. The results showed that the approach of
calibrating the Eckhardt method against the CMB method provides a “false”
calibration of total baseflow by offsetting the inherent biases in the
baseflow sequences generated by the two methods. The baseflow sequence
generated by the Eckhardt method usually includes slow interflow and bank
storage return flow, whereas that of the CMB method usually includes
high-conductivity water flushed from swamps and depressions by rainfall, but
not low-conductivity interflow and bank storage return flow. This difference
results in obvious peak misalignment and periodic deviation between the
baseflow sequences obtained by the two methods, thereby preventing
calibration. However, multi-component separation of streamflow can be
achieved through comparison. Future research should recognize the deviations
between the separation results obtained by the different methods, identify
the reasons for these differences, and explore the hydrological information
contained therein.
Introduction
Streamflow usually contains components originating from different sources,
such as surface runoff, interflow, groundwater runoff, bank storage return
flow, and water flushed out from wetlands or depressions by rainfall
(Cartwright et al., 2014; Schwartz, 2007; McCallum et al., 2010; Lin et al.,
2007). These components from different sources are usually characterized by
different residence times and chemical and isotopic characteristics
(Cartwright et al., 2018). Collectively, these components control the runoff
process and water chemistry characteristics of a river and consequently
affect the ecosystem along the river (Howcroft et al., 2019; Saraiva Okello
et al., 2018). For example, the existence of transient water sources
(interflow and bank storage return flow) will result in different
concentration vs. discharge relationships during the rising and falling
limbs, thus forming a hysteresis loop (Cartwright et al., 2014; Cartwright
and Miller, 2021). Quantitative estimation of the relative proportions and
the temporal resolutions of these components is a prerequisite for
accurately predicting hydrological processes and protecting the river
ecosystem (Duncan, 2019).
Since it is almost impossible to directly measure the different components
of streamflow, they are usually indirectly determined through separation of
the runoff process (Hagedorn, 2020; Lin et al., 2007). Since the task of
accurately separating the runoff process into individual components presents
a difficult challenge, hydrologists generally separate streamflow into two
components, namely surface runoff and baseflow (Chapman, 1999; Eckhardt,
2005; Schwartz, 2007; Tallaksen, 1995). Surface runoff is the rapid flow
that occurs on the catchment surface during a rainfall event, whereas
baseflow is long-term “slow” runoff regulated by regional groundwater and
other delayed stores of water, such as interflow and bank storage return
flow (Cartwright et al., 2018; Cartwright and Miller, 2021; Nathan and
McMahon, 1990). However, some recent studies have taken the approach of
simply generalizing the baseflow to be equivalent to the regional
groundwater discharge, thereby ignoring the influence of transient water
sources (Lott and Stewart, 2016; Lyu et al., 2020; Stewart et al., 2007;
Zhang et al., 2017). Using the above generalization, hydrologists have
developed a variety of two-component hydrograph separation methods, also
called “baseflow separation methods”, which have been reviewed in detail
by Nathan and McMahon (1990) and Chapman (1999). These methods can be
broadly placed into three categories: (1) graphical methods; (2) filtering
methods, and (3) mass balance methods (Lott and Stewart, 2016; Rammal et
al., 2018; Xie et al., 2020; Hagedorn, 2020; Yang et al., 2019c). Graphical
methods, such as the hydrograph separation program (HYSEP) (Sloto and
Crouse, 1996), United Kingdom Institute of Hydrology (UKIH) (Piggott et al.,
2005), and streamflow partitioning method (PART) (Rutledge, 1998), are
automated versions of the traditional manual separation method. The majority
of baseflow series generated by these methods consist of broken lines and do
not reflect the natural transition of baseflow (Duncan, 2019; Eckhardt,
2008).
Lyne and Hollick (1979) proposed the earliest single-parameter filtering
algorithm based on the principle of signal processing, which typically
requires multiple forward and backward filtering passes. There is a great deal of
randomness associated with the determination of the number of filtering
passes, which often increases uncertainty in the separation results.
Boughton (1993) proposed an improved two-parameter filtering algorithm
following which Jakeman and Hornberger (1993) proposed a three-parameter
filtering algorithm; however, no clear physical explanations for the
parameters of either algorithm were provided (Chapman, 1999). Eckhardt (2005) derived a new two-parameter recursive filtering algorithm, referred
to as the Eckhardt method in the present study, based on the linear
reservoir theoretical framework. The two parameters included in this
algorithm are the recession coefficient (α) reflecting the recession
characteristics of baseflow and the BFImax reflecting the long-term
baseflow proportion. Although the recession coefficient (α) of the
Eckhardt method can be easily determined by recession analysis, empirical
analysis is required to determine the BFImax (Eckhardt, 2012).
Collischonn and Fan (2013) proposed a method to estimate BFImax based
on the linear reservoir theory. The Eckhardt method has been widely applied
due to its clear physical basis and easy operation (Guzmán et al., 2015;
Hagedorn, 2020; Li et al., 2014; Xie et al., 2020; Zhang et al., 2017).
However, some scholars have pointed out that there is a certain amount of
uncertainty associated with the selection of the BFImax value in the
Eckhardt method, which requires correction by other methods (Lott and
Stewart, 2016; Rammal et al., 2018; Saraiva Okello et al., 2018; Zhang et
al., 2013), such as the mass balance method based on environmental tracers.
The mass balance method calculates the proportions of total streamflow of
different streamflow components based on the distinct chemical compositions
of these components (Blumstock et al., 2015; Genereux, 1998; Hagedorn,
2020). Since a single tracer can only separate two flow components,
achieving the separation of multiple flow components requires the concurrent
use of multiple different tracers. The earliest tracers used included inert
ions such as chloride, stable isotopes, and radioactive isotopes (Burns,
2002; Genereux, 1998; Stewart et al., 2007). The heavy resource costs of
water sample collection and detection limits the application of the mass
balance method for long-sequence baseflow separation. Alternately,
hydrologists proposed a mass balance method using conductivity as a tracer
(CMB), thereby reducing the cost of the mass balance method and facilitating
the application of the method to separation of long-sequence baseflow
(Pinder and Jones, 1969; Yu and Schwartz, 1999; Stewart et al., 2007). The
CMB method has since been widely applied by researchers (Cartwright et al.,
2014; Hagedorn, 2020; Kronholm and Capel, 2015; Lott and Stewart, 2013, 2016; Lyu et al., 2020; Miller et al., 2014; Saraiva Okello et
al., 2018; Yang et al., 2019a; Zhang et al., 2013).
The majority of studies have concluded that the tracer-based CMB method has
a clear physical basis and is therefore one of the most objective baseflow
separation methods. The CMB method is therefore often used as a reference
within the analysis of the effects of other baseflow separation methods or
within the correction of the parameters of other methods (Lott and Stewart,
2013, 2016; Saraiva Okello et al., 2018; Stewart et al.,
2007; Zhang et al., 2017). Stewart et al. (2007) applied the CMB method for
the correction of the window length of the HYSEP method, whereas Lott and
Stewart (2016) used the CMB method within the correction of the BFImax
parameter of the Eckhardt method so as to obtain BFI values or cumulative
baseflow consistent with that of the CMB method. Zhang et al. (2013) used
the CMB method to correct two parameters of the Eckhardt method. Saraiva
Okello et al. (2018) used discrete conductivity values for the correction of
the BFImax of the Eckhardt method. The main objective of these
corrections was to obtain a consistent BFI or cumulative baseflow, but they
do not spend too much time analyzing the fitting degree or deviation of
daily baseflow. In other words, these studies only proved that the CMB
method can be used to correct the BFI separated by the Eckhardt method on a
multi-year scale, but they could not explain the effect of calibration on the
intra-year (daily) scale. However, other studies have found that the
baseflow sequence generated by the CMB method may contain different flow
components compared to that generated by the Eckhardt method (Cartwright et
al., 2014; Rammal et al., 2018). The correction of the Eckhardt method based
on the CMB method should only be performed under the condition of both
methods containing the same flow components (Hagedorn, 2020). Cartwright et
al. (2014) analyzed the contribution of different sources of water to
streamflow by comparing the differences in the results of baseflow
separation by the Eckhardt and CMB methods. Since these two types of
applications appear to be quite different, their joint application can cause
great confusion to hydrologists, mainly related to whether they can be used
for calibration or comparison and weather calibration on the daily scale is
truly possible. As mentioned above, streamflow consists of many flow
components, which are generalized into two broad types for the convenience
of separation. The ultimate goal of streamflow separation should be to
determine the contribution of each component to streamflow and not merely
to determine the contribution of these two generalized components.
Therefore, it is more meaningful to determine the contribution of various
components by comparing different baseflow separation methods than to use
one method to calibrate another.
In fact, some studies have shown that the baseflow sequences generated by
the CMB method usually include some high-conductivity water flushed out
from swamps or depressions by rainfall and do not include transient water
with low conductivity, such as bank storage return flow and interflow
(Cartwright et al., 2014; McCallum et al., 2010; Yang et al., 2019b).
However, to date, no research has clearly identified whether these transient
water sources are included or excluded in the baseflow sequences generated
by the Eckhardt method. Unlike these studies, the present study attempted to
resolve this confusion by conducting a detailed analysis of the effect of
correcting the Eckhardt method against the CMB method and further analysis
of whether the Eckhardt method is truly corrected by the CMB method. The
present study focused not only on the consistency of cumulative baseflow or
the BFI value, but also on the degree of fit and deviation of the daily
baseflow sequence after correction. In addition, the present study discussed
in detail the effects of transient water sources on streamflow and
conductivity and the different transient water sources included in the
separation results of the two methods.
MethodsTwo-parameter recursive digital filter method (Eckhardt)
The filtering method uses the basic principle of baseflow constituting the
low-frequency component of streamflow that reacts relatively slowly to
precipitation, whereas surface runoff constitutes the high-frequency
component of streamflow that reacts quickly to precipitation (Xie et al.,
2020). Eckhardt (2005) combined the basic principles of the filtering method
with the linear reservoir model, which reflects the linear relationship
between discharge and storage of groundwater in a basin to derive the
Eckhardt filter equation (Eq. 1):
bk=1-BFImaxαbk-1+(1-α)BFImaxyk1-αBFImax.
Equation (1) is limited by bk≤yk, α is the recession
constant, BFImax is the maximum baseflow index (the long-term ratio of
baseflow to total streamflow), bk is the baseflow, and yk is the
streamflow for the time step k.
Eckhardt (2008) proposed a recession analysis method for the calculation of
the recession coefficient (α). Under conditions of the streamflow
recession phase satisfying Eq. (2) and persisting over an extended period,
yk+1 and yk can be considered equal to the baseflow. Equation (3) can
then be established if the theoretical assumption of a linear reservoir is
true.
2yk-3>yk-2>yk-1>yk>yk+1>yk+23yk+1=αyk
The slope of the upper boundary of the scatter plot of all yk+1 and
yk that meet the above conditions can be considered α, which
usually has a random error of less than 2 % (Eckhardt, 2008).
Eckhardt (2005) suggested the selection of
BFImax≈0.80 for perennial streams with
porous aquifers, BFImax≈0.50 for ephemeral
streams with porous aquifers, and BFImax≈0.25
for perennial streams with hard-rock aquifers. Collischonn and Fan (2013)
proposed a reverse iterative algorithm (Eq. 4) for estimating BFImax
based on the linear reservoir assumption. Equation (4) is iterated in the reverse
direction to obtain the maximum daily baseflow, following which the sum can
be divided by the total streamflow to obtain the BFImax. The present
study used this approach to estimate the BFImax before correction.
bk-1=bkα(bk-1≤yk-1)
Conductivity mass balance method (CMB)
The two-component mass balance method using conductivity as a tracer (CMB)
has been proposed by Pinder and Jones (1969) and Yu and Schwartz (1999). Equation (5) shows the general form of the CMB, which is based on three implicit
assumptions: (1) apart from baseflow and surface runoff, the contributions
of other flow components can be ignored; (2) the conductivities of surface
runoff and baseflow are constant or change in a predicted manner and show
obvious differences during the separation period; and (3) in-stream processes
such as evaporation do not significantly change the conductivity (Miller et
al., 2014; Yang et al., 2019a).
bk=yk(SCk-ROC)BFC-ROC
In Eq. (5), SCk, BFC, and ROC are the conductivities of
streamflow, baseflow, and rainfall runoff, respectively. Generally,
conductivity reflects the total salinity or the concentration of charged
ions of streamflow. Some studies have pointed out a positive correlation
between conductivity and chloride ion content (Cartwright et al., 2014). A
field study by Stewart et al. (2007) showed that the maximum and minimum
streamflow conductivities of a basin can be used as an estimate of BFC and ROC, respectively. However, the maximum conductivity of
streamflow may be a function of the combined effects of evaporation, human
activities, and baseflow, whereas estimation of the minimum conductivity may
be affected by instrument errors. Therefore, Miller et al. (2014), Yang et
al. (2019a), and Lyu et al. (2020) recommend the use of the conductivity
value at 99 % probability of each year as an estimate of baseflow
conductivity, whereas gaps in the yearly baseflow conductivity time series
can be obtained by linear interpolation. They also recommended the use of
the conductivity value at 1 % probability in all records as an estimate of
surface runoff conductivity. The present study followed the strategy of
Miller et al. (2014). It should be noted that in some humid regions, the
maximum value of streamflow conductivity may be lower than that of regional
groundwater (Cartwright and Irivine, 2020; McCallum et al., 2010). This may
be caused by the continuous discharge of transient water sources into the
river during the dry season. Due to the lack of regional groundwater
conductivity data, the present study assumed that this phenomenon was not
existent in each basin in which the CMB method was applied.
Calibration of the Eckhardt method
Similar to Lott and Stewart (2016), Zhang et al. (2013), and Saraiva Okello
et al. (2018), the present study calibrated the BFImax by minimizing
the deviation between the baseflow series separated by the CMB and Eckhardt
methods. During the correction, the absolute relative bias (PBIAS) between
the daily baseflow series calculated by the Eckhardt and CMB methods was
used as the objective function, and BFImax was gradually adjusted at
intervals of 0.01 until a minimum absolute PBIAS was obtained.
Evaluation of the calibration effect
This present study calculated the Nash–Sutcliffe (Nash and Sutcliffe, 1970)
efficiency coefficient (NSE) and relative bias (PBIAS) between the
cumulative baseflows obtained by the Eckhardt and CMB methods, and also the
NSE, PBIAS, PBIAS(–), PBIAS(+), and P(|daily bias|>50 %) between the daily baseflows (Eqs. 6–10) to evaluate the
calibration effect.
6NSE=1-∑i=1nQoi-Qmi2∑i=1nQoi-Qoi‾27PBIAS=∑i=1nQmi-Qoi∑i=1nQoi×100%8PBIAS-=∑i=1nQmi-Qoi∑i=1nQoi×100%(Qmi<Qoi)9PBIAS+=∑i=1nQmi-Qoi∑i=1nQoi×100%(Qmi>Qoi)10P(|dailybias|>50%)=ThenumberofbkECK-bkCMBbkCMB>0.5Thenumberoftotaltimesteps×100%
In Eqs. (6) to (10), Qo is the reference standard value or
observation value, Qm is the simulation or calculation value, the NSE
reflects the degree of fit of the two series, the PBIAS reflects the total
relative deviation between the two series, PBIAS(–) reflects the total
negative relative deviation between two series, PBIAS(+) reflects the
total positive relative deviation between two series, and P(|daily
bias|>50 %) reflects the proportion of the sequences
with >50 % absolute daily bias between the two series. The
closer the NSE is to 1, the better the fit between the simulated and
observed values, whereas the closer the PBIAS value is to 0, the smaller the
deviation between the simulated and observed values. The larger the value
of P(|daily bias|>50 %), the greater the
proportion of the sequences with obvious deviations between the two baseflow
series.
Data
Lyu et al. (2020) showed that a negative correlation between streamflow and
conductivity is an indicator of the applicability of the CMB method and
emphasized that the CMB method has better applicability when the correlation
coefficient is less than -0.5. The adoption of this criterion also
eliminates those basins which are clearly affected by human activities such
as reservoirs and sewage discharge, since the impact of human activities
will reduce the negative correlation between streamflow and conductivity
(Miller et al., 2014). Since the estimation of the parameters (BFC,
ROC) of the CMB method may have greater uncertainty when the time
series is short, Lyu et al. (2020) suggested that the time series should
exceed 6 months, whereas Lott and Stewart (2016) suggested that the time
series should exceed 2 years. Therefore, the present study randomly selected
26 hydrological stations from the United States Geological Survey (USGS)
National Water Information System (NWIS) website:
http://waterdata.usgs.gov/nwis (last access: September 2020). The negative
correlation between conductivity and streamflow at each site was less than
-0.5, and the sequence length of each site exceeded 2 years. The areas of
the basins gauged by these hydrological stations range from 46 to
110 973 km2, and the lengths of the measured streamflow time series among
the stations range from 2 to 9 years. The streamflow data of all stations
are continuous and complete, and no station has missing conductivity data
exceeding 10 % of total data. The present study performed linear
interpolation based on the conductivity values at both ends of the missing
period to infill missing data. Table S1 shows a summary of the hydrological
stations used. The present study used the Eckhardt and CMB methods to
separate the baseflow of these 26 stations, following which the BFImax
of the Eckhardt method in each station was calibrated with reference to the
CMB method. Finally, the effect of the correction was evaluated and
discussed.
Results
Table S1 shows the results for the estimation of the parameters (α,
BFImax). The α values of the 26 stations ranged from 0.978 to
0.998 with an average of 0.991. Before calibration, the BFImax ranged
from 0.19 to 0.86 with an average of 0.39, whereas after correction, the
BFImax ranged from 0.17 to 0.67 with an average of 0.39. Although the
average value of BFImax did not change after calibration, the range of
fluctuation was reduced.
Table 1 shows the baseflow separation results of the CMB and Eckhardt
methods before and after correction. The baseflow index
(BFI=∑bk∑yk) calculated by the CMB
method was between 0.15 and 0.64 with an average of 0.29. The BFI calculated
by the Eckhardt method before calibration was between 0.14 and 0.81 with an
average of 0.31, whereas that after calibration was between 0.15 and 0.63
with an average of 0.29. As shown in Fig. 1, there was an element of random
deviation between the BFI values calculated by the Eckhardt and CMB methods
before calibration, with that of the Eckhardt method showing no obvious
trend of overestimation or underestimation, whereas the BFI values
calculated by the two methods were basically identical after calibration.
Table 1 shows the NSE and PBIAS values for the comparison of the cumulative
baseflow series by the Eckhardt and CMB methods after calibration. The NSE
ranged from 0.91 to 1.00 with an average value of 0.97, whereas the PBIAS
ranged from -12 % to 13 % with an average of -1 %. The cumulative
baseflow obtained by the Eckhardt method after calibration showed a good fit
with that of the CMB method, indicating that the two methods generated
consistent estimates of total baseflow after calibration.
Comparison of BFI of the Eckhardt and conductivity mass balance
(CMB) methods before and after calibration.
Table 1 also shows the NSE, PBIAS, PBIAS(–), PBIAS(+), and P(|daily
bias|>50 %) obtained through the comparison of daily
baseflow series generated by the corrected Eckhardt and CMB methods. The
NSEs of daily baseflow ranged from -2.35 to 0.45 with an average of
-0.30. The NSEs of 20 of the 26 stations were less than zero, indicating
that the daily baseflow series generated by the two methods showed major
differences. The PBIAS ranged from -11 % to 2 % with an average of
0 %, the PBIAS(–) ranged from -47 % to -13 % with an average of
-28 %, and the PBIAS(+) ranged from 14 % to 48 % with an average of
28 %. Figure 2 shows the variations in PBIAS, PBIAS(–), and PBIAS(+) with
BFImax using station 02297100 as an example, where it is evident that
an increase in BFImax results in a gradual increase in total relative
deviation (PBIAS) from negative to positive. The total deviation (PBIAS) is
zero when the absolute values of PBIAS(–) and PBIAS(+) are equal and
offset each other. In other words, although the two methods obtain the same
total baseflow after calibration, some obvious biases between the daily
baseflow series persist, although the positive and negative biases offset
each other. The P (|daily bias|>50 %) ranged
from 13 % to 84 % with an average of 44 %. On average, nearly half of
the daily baseflow series obtained by the two methods after calibration
showed a daily absolute bias exceeding 50 %. Therefore, it can be argued
that the calibration of the Eckhardt method against the CMB method obtains a
“false” correction under which the same total baseflow series obtained by
the two methods was due to the offsetting of inherent deviation in the
baseflow series.
The results of baseflow separation of streamflow from 26
hydrological stations of the United States Geological Survey (USGS) National
Water Information System (NWIS) before and after calibration. “Eck.”
represents the uncalibrated Eckhardt method whereas “Cali.” represents the
calibrated Eckhardt method.
The biases between daily baseflow series calculated by the
Eckhardt and CMB methods for the United States Geological Survey (USGS)
station 02297100 varied with BFImax. PBIAS is total relative bias,
PBIAS(–) is the total negative relative bias, and PBIAS(+) is the total
positive relative bias.
Bias between daily baseflow series generated by the conductivity
mass balance (CMB) and Eckhardt methods after calibration for the United
States Geological Survey (USGS) station 02298202. BF represents baseflow.
The lines beyond the coordinate range are not shown to show the details more
clearly.
Figure 3 shows the bias between the daily baseflow series generated by the
CMB and Eckhardt methods after calibration using station 02298202 as an
example. As shown in Fig. 3, the peak of the baseflow sequence generated
through the Eckhardt method usually appeared during the recession stage,
whereas that through the CMB method usually appeared during the rising
stage. This misaligned peak resulted in obvious periodicity in deviation
between the baseflow sequences obtained by the Eckhardt and CMB methods. The
baseflow generated by the Eckhardt method was usually significantly lower
than that generated by the CMB method during the rising stage, whereas it
was significantly higher during the recession stage. This phenomenon was
also reflected in other stations, as shown for an additional five stations
in the Supplement (Figs. S1–S5). The examples mentioned above focused on
periodic deviation in the rising and falling limbs during the wet season,
and the corresponding deviation during the dry season tended to be smaller
(Figs. 3, S1–S5). As discussed by Cartwright et al. (2014), this
phenomenon may be due to a higher contribution of transient water sources to
streamflow during the wet season. In addition, the calibration process may
aggravate the deviation observed during the dry season, with Fig. S5 being
an obvious example. Before calibration, the two methods obtained basically
the same separation results for the dry season, whereas after calibration,
although the total deviation was minimized, there was a significant increase
in the deviation during the dry season, which is logically incorrect.
DiscussionThe influence of transient water on streamflow and conductivity
As mentioned in the introduction, streamflow includes not only surface
runoff and baseflow, but also a variety of different transient water
sources, such as interflow, bank storage return flow, and high-conductivity
water flushed out from depressions or wetlands by rainfall (Cartwright et
al., 2014; Schwartz, 2007; McCallum et al., 2010; Lin et al., 2007). These
transient water sources flow into the river at different spatiotemporal
resolutions, thereby affecting streamflow and conductivity. Figure 4 is a
conceptual diagram of the influence of different transient water sources on
streamflow and conductivity during the late dry season, rainfall, and
post-rain recession periods.
Ideally, streamflow is mainly dominated by groundwater discharge after a
long period of drought during which the conductivity of streamflow in the
basin is close to that of groundwater (Lott and Stewart, 2013; Stewart et
al., 2007). The conductivity of streamflow needs to be compared with that of
regional groundwater to determine whether or when this state is reached in a
basin. In addition, continual evaporation will result in a gradual increase
in the total dissolved solids (TDSs) and conductivity of wetland water, depression water, and shallow
groundwater in the valley (Liu et al., 2019).
During a rainfall event, a portion of rainfall forms surface runoff, a
portion infiltrates the soil to recharge groundwater, and a portion of the
infiltrated water returns to the surface runoff to form interflow (Nathan
and McMahon, 1990; Nejadhashemi et al., 2007; Tallaksen, 1995). Surface
runoff formed during the early stage of rainfall will flush out
high-conductivity wetland or depression water in the valley or quickly
mobilize high-conductivity soil water, forming a pulse of high-conductivity
water (Cartwright et al., 2014; Yang et al., 2019b). This phenomenon is
essentially part of the “old-water” paradox: the early flood events in
most basins usually contain a lot of old water with chemistry or
isotopic characteristics different from those of precipitation (Kirchner, 2003), and
there remains no accepted mechanism to explain this phenomenon (Bishop et
al., 2004; Kirchner, 2003). However, the flushing of wetlands or depression
water and the rapid mobilization of soil water are the two most likely
mechanisms to explain this phenomenon (Cartwright and Morgenstern, 2018;
Kienzler and Naef, 2008; Xiao et al., 2020). This pulse of high-conductivity
water can lead to an overestimation of the conductivity of streamflow at the
rising stage and even the estimation of an abnormal increase in
conductivity with an increase in streamflow (Aubert et al., 2013; Cartwright
et al., 2014; Zhi et al., 2019). This abnormal increase in conductivity with
increasing streamflow can be easily screened out from the conductivity
sequences. Figure 5 shows part of the screening results for two stations
(06296120 and 03201980) where it is evident that the point of abnormal
increase in conductivity is usually distributed during the initial rising
stage and usually corresponds to the peak in baseflow of the CMB method.
Continuous rainfall will subsequently result in the flow of a large amount
of low-conductivity water into the river, resulting in a significant
decrease in conductivity of streamflow approaching that of rainfall. At the
same time, the rapid rise in the river water level will result in recharge
of the aquifer by part of the low-conductivity streamflow to form bank
storage water (Howcroft et al., 2019; McCallum et al., 2010).
During the recession stage after rainfall, surface runoff quickly recedes
and stops, whereas interflow gradually decreases and finally stops. The
proportion of groundwater in streamflow gradually increases, resulting in a
gradual rise in conductivity. At the same time, the low-conductivity bank
storage water formed during the rainy season is also gradually returned to
the stream (Cartwright et al., 2014; McCallum et al., 2010). There have been
many studies on the influence of bank storage and return flow on streamflow
and solutes (Cartwright and Irivine, 2020; Chen and Chen, 2003; McCallum et
al., 2010; McCallum and Shanafield, 2016). The general consensus among these
studies is that low-conductivity river water generated during the flood
stage will seep into the aquifer under the action of the hydraulic gradient
and will continue to be discharged for several months after the flood,
eventually leading to a significantly delayed solute discharge process.
Cartwright et al. (2014) emphasized that interflow is influenced by the same
mechanism as that of bank storage return flow. Both interflow and bank
storage return flow result in the conductivity of streamflow during the
recession stage being lower than that during the rising stage, thereby
forming a clockwise hysteresis loop between conductivity and streamflow. The
existence of this hysteresis loop between solute and streamflow has been
confirmed by many other studies (Aubert et al., 2013; Evans and Davies,
1998; Wagner et al., 2019; Winnick et al., 2017; Zhi et al., 2019). As shown
in Fig. 6, this hysteresis loop was evident in all 26 stations examined in
the present study. There were usually differences in the shapes of the
hysteresis loops among the different stations or different flood events for
the same station, which reflects the different effects of bank storage
return flow or interflow in different watersheds or in the same watershed at
different periods. Cartwright and Miller (2021) analyzed the temporal and
spatial variations in river conductivity in Australian (the Barwon, Glenelg,
and Campaspe rivers) and North American (the upper Colorado River) basins
and similarly attributed these variations to the temporal and spatial
fluctuations of transient water sources.
In addition to these transient water sources, human impacts such as
reservoirs, abstraction of water for irrigation and sewage discharge will
also affect streamflow and conductivity. Reservoirs have a direct influence
on streamflow and solute transport processes (Lehner et al., 2011), and
abstraction of river water for irrigation disturbs streamflow. On the other
hand, irrigation return flow water tends to have a higher TDS, which results
in an increase in the conductivity of streamflow (Kronholm and Capel, 2015).
Domestic sewage usually contains a large amount of inorganic salts, and the
discharge of sewage can result in a significant increase in the conductivity
of streamflow (Osode and Okoh, 2009). Although different basins may be
affected by different human activities to different degrees, it is clear
that human activities significantly reduce the negative correlation between
streamflow and conductivity. The negative correlation coefficients between
streamflow and conductivity of the basins examined in the present study were
all less than -0.5; therefore, basins that were obviously affected by human
activities have been excluded. For this reason, the present study only
briefly discussed the impact of human activities.
A conceptual diagram illustrating the influence of different
transient water sources on streamflow over different periods. For the
streamline arrows in the figures, color reflects the relative conductivity
whereas width reflects the relative flow. The equation shown represents the
linear reservoir model describing the relationship between groundwater
storage (S) and discharge (Q).
The abnormal increase in conductivity resulting from the flushing
out of concentrated high-conductivity water from wetlands or depressions
during the initial rising stage evident in the streamflow sequences of two
United States Geological Survey (USGS) stations. (a) Station 06296120. (b)
Station 03201980. It was assumed that this abnormal increase in conductivity
was present when an increase in streamflow exceeding 10 % was accompanied
by an increase in conductivity. BF: baseflow; SC: conductivity.
Clockwise hysteresis loops between conductivity and streamflow
during flood events evident in the streamflow sequences of six United States
Geological Survey (USGS) stations. (a) Station 02298202; (b) station
02207120; (c) station 03106000; (d) station 06089000; (e) station 03072655;
(f) station 08068275. The arrows reflect the direction of time.
The transient water components are different among the baseflow
sequences generated by the CMB and Eckhardt methods
The results of the present study (Sect. 4) confirmed that it is not
possible to calibrate the Eckhardt method against the CMB method as the
baseflow series generated by these two methods show inherent deviations.
These inherent deviations are mainly due to the baseflow series generated by
the two methods containing different transient water sources (Cartwright et
al., 2014; Hagedorn, 2020; Rammal et al., 2018) as the two methods are
constructed based on different theoretical assumptions (Sect. 2).
The Eckhardt method subscribes to the linear reservoir model (S=kQ)
between discharge (Q) and storage (S) of groundwater in a basin, where k is the
recession constant and its relationship with the filtering parameter
α is k=-1ln(α) (Chapman,
1999). The linear reservoir model can be derived based on the Boussinesq
equation and Darcy's law of porous media (Brutsaert and Nieber, 1977; Furey
and Gupta, 2000). Many studies based on recession analysis have confirmed
the universal existence of this linear reservoir relationship (Brutsaert,
2008; Tallaksen, 1995; Thomas et al., 2013). The baseflow sequence obtained
based on the linear reservoir theoretical assumption usually has the
following characteristics (Duncan, 2019): (1) the recession of baseflow will
continue for an extended period after the rise of streamflow; (2) the
baseflow peak usually appears after the streamflow peak due to the
storage-routing effect of underground reservoirs; and (3) baseflow recession is
likely to follow an exponential decay function, i.e., the linear reservoir
model. Therefore, the baseflow sequence separated by the Eckhardt method
theoretically does not generally include high-conductivity water flushed out
from wetlands or depressions by rainfall at the beginning of the rising
stage, but does include the majority of water flowing through the porous
medium to satisfy the linear reservoir assumption, including groundwater
flow, slow interflow, and bank storage return flow.
The CMB method subscribes to a chemical mass balance under which separated
baseflow usually comprises components with high conductivity, regardless of
whether these components flow through a porous medium or whether they meet
the linear reservoir assumption. Therefore, the baseflow sequence generated
by the CMB method will include high-conductivity water flushed out of
wetlands or depressions by rainfall, but will not include interflow and bank
storage return flow with low conductivity (Cartwright et al., 2014; Rammal
et al., 2018). The flushing out of high-conductivity water from wetlands or
depressions mainly occurs during the initial rising stage, while interflow
and bank storage return flow mainly occur during the recession stage.
Therefore, the baseflow sequences generated by the Eckhardt and CMB methods
include different transient water sources and show obvious misaligned peaks
and periodic deviation during the wet season (Figs. 3, S1–S5). Although
the deviation between the two methods is relatively small during the dry
season, some inherent deviation between them may persist. The Eckhardt
method usually recognizes many segments as fully baseflow segments when they
meet the recession characteristics, but the CMB method only recognizes a
full baseflow segment when the conductivity reaches the maximum for 1 or 2 d. The BFImax calibration process will only change the total
baseflow and will not significantly change the position of the baseflow
peak and the frequency of the full baseflow segment. Therefore, the use of
the CMB as a reference to calibrate the Eckhardt method is not recommended,
even if it is only carried out during the dry season.
Given that the results of baseflow separation by the two methods show
inherent deviations, future research should avoid investing a lot of time in
using one method to calibrate the other and instead focus on analyzing the
underlying causes of these inherent deviations and their significance for
the study of hydrological processes. For example, by comparing the baseflow
sequences calculated by these two methods, streamflow can be separated into
multiple components, or the contribution of different transient water sources
to streamflow can be identified. Figure 7 is a schematic of different
streamflow components reflected by inherent deviations between the two
baseflow sequences. The intersection of the baseflow sequences of the two
methods reflects high-conductivity deep circulating groundwater with a long
residence time. The portion of the baseflow sequence generated by the
Eckhardt method that is situated above that generated by the CMB method
reflects low-conductivity transient water with a short residence time such
as bank storage return flow and interflow. The portion of the baseflow
sequence generated by the CMB situated above that by the Eckhardt method
reflects high-conductivity transient water such as high-conductivity water
from wetlands or depressions. The complementary set of the two baseflow
separation results reflects surface runoff.
Schematic diagram showing the inherent deviation between baseflow
sequences generated by the Eckhardt and conductivity mass balance (CMB)
methods which reflects different streamflow components using the United
States Geological Survey (USGS) station 06037500 as an example. BF:
baseflow.
Conclusions
The present study evaluated the effectiveness of calibrating the Eckhardt
method against the CMB method for 26 basins in the United States by
comparing biases between the daily baseflow sequences generated by the two
methods and attempted to resolve the confusion resulting from the combined
application of the two methods from a new perspective. Compared with
previous studies, the basins examined in the present study cover a wider
range of climate and basin characteristics. The areas of the basins studied
ranged between 46 and 110 973 km2, with the latitudes of the
hydrological stations ranging between 26.98 and 47.52∘ N. Therefore, the basins examined in the present study were representative
of most climate zones from Florida to Montana. The main conclusions drawn
from the present study are summarized below.
The calibration of the Eckhardt method against the CMB method represents a
“false” correction based on only the total baseflow by offsetting inherent
biases in the baseflow sequences generated by the two methods. The use of
the two-component CMB method as a reference to calibrate the Eckhardt method
is not recommended, even if it is only performed during the dry season.
The present study verifies and extends the conclusions obtained in previous
research (McCallum et al., 2010; Cartwright et al., 2014) under a wider
range of watershed characteristics. These conclusions include that different
transient water sources may contribute to baseflow separated by methods
based on different basic assumptions. The baseflow sequence generated by the
Eckhardt method usually includes slow interflow and bank storage return
flow, whereas that of the CMB method usually includes high-conductivity
water flushed from swamps and depressions by rainfall but excludes
low-conductivity interflow and bank storage return flow. The differences in
transient water sources contributing to baseflow between these two methods
result in differences in the baseflow sequences obtained, particularly in
terms of an obvious misalignment of flow peaks and periodic deviation.
Therefore, the one method cannot be used to calibrate the other (Fig. 3).
However, the four-component separation of streamflow can be achieved through
comparison (Fig. 7).
These results of the present study can also provide some hydrological
insight: (a) the application of two-component baseflow separation methods
based on different theoretical assumptions is likely to produce baseflow series
containing different components. In application, there should be careful
analysis of whether the components contained in the separation results are
consistent with the research objectives. (b) The adoption of the definition
of baseflow as the amount of discharge of regional groundwater to a river
(which is used to evaluate surface water and groundwater interactions)
within the CMB and Eckhardt methods can result in large errors in the rising
and falling limbs, respectively. Therefore, the use of the Eckhardt method
and CMB method for the rising and falling limbs, respectively, may be more
reasonable. (c) Future research should consider the existence of deviations
between the separation results produced by different baseflow separation
methods, try and identify the reasons for these differences, and explore the
hydrological information contained therein. In addition, it should be
recognized that mutual correction cannot be used to obtain consistent daily
results between different baseflow separation methods.
Data availability
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:
http://waterdata.usgs.gov/nwis (NWIS, 2020).
The supplement related to this article is available online at: https://doi.org/10.5194/hess-25-1747-2021-supplement.
Author contributions
WY, CX, ZZ, and XL developed the research
train of thought. WY and ZZ collected and processed all research data. CL
and XL applied for funding for this research. WY prepared the manuscript
with contributions from all coauthors.
Competing interests
The authors declare that they have no conflict of interest.
Acknowledgements
We are grateful to the Jilin Jingyu Field Scientific Observation and Research Base of the Volcanic and Mineral Springs for supporting our research. We also thank the reviewers for their comments.
Financial support
This research has been supported by the National Natural Science Foundation of China (grant no. 41572216), the Provincial School Co-construction Project Special – Leading Technology Guide (grant no. SXGJQY2017-6), the China Geological Survey Shenyang Geological Survey Center “Hydrogeological Survey of Songnen Plain” project (grant no. [2019]DD20190340-W09), and the Geological Survey Foundation of Jilin Province (grant no. 2018-13).
Review statement
This paper was edited by Stacey Archfield and reviewed by Ian Cartwright and one anonymous referee.
ReferencesAubert, A. H., Gascuel-Odoux, C., and Merot, P.: Annual hysteresis of water
quality: A method to analyse the effect of intra- and inter-annual climatic
conditions, J. Hydrol., 478, 29–39, 10.1016/j.jhydrol.2012.11.027,
2013.Bishop, K., Seibert, J., Köhler, S., and Laudon, H.: Resolving the
Double Paradox of rapidly mobilized old water with highly variable responses
in runoff chemistry, Hydrol. Process., 18, 185–189, 10.1002/hyp.5209,
2004.Blumstock, M., Tetzlaff, D., Malcolm, I. A., Nuetzmann, G., and Soulsby, C.:
Baseflow dynamics: Multi-tracer surveys to assess variable groundwater
contributions to montane streams under low flows, J. Hydrol., 527,
1021–1033, 10.1016/j.jhydrol.2015.05.019, 2015.
Boughton, W. C.: A hydrograph based model for estimating the water yield of
ungauged catchments, Inst. Engs. Aust., Nat. Conf. Publ., 93, 317–324,
1993.Brutsaert, W. and Nieber, J. L.: Regionalized drought flow hydrographs from
a mature glaciated plateau, Water Resour. Res., 13, 637–643, 10.1029/WR013i003p00637, 1977.Brutsaert, W.: Long-term groundwater storage trends estimated from
streamflow records: Climatic perspective, Water Resour. Res., 44,
W02409, 10.1029/2007wr006518, 2008.
Burns, D. A.: Stormflow-hydrograph separation based on isotopes: the thrill
is gone – what's next?, Hydrol. Process., 16, 1515–1517, 2002.Cartwright, I. and Morgenstern, U.: Using tritium and other geochemical
tracers to address the “old water paradox” in headwater catchments,
J. Hydrol., 563, 13–21, 10.1016/j.jhydrol.2018.05.060, 2018.Cartwright, I. and Irivine, D.: The spatial extent and timescales of bank
infiltration and return flows in an upland river system: Implications for
water quality and volumes, Sci. Total. Environ., 743, 140748, 10.1016/j.scitotenv.2020.140748, 2020.Cartwright, I. and Miller, M. P.: Temporal and spatial variations in river specific conductivity: Implications for understanding sources of river water and hydrograph separations, J. Hydrol., 593, 125895, 10.1016/j.jhydrol.2020.125895, 2021.Cartwright, I., Gilfedder, B., and Hofmann, H.: Contrasts between estimates of baseflow help discern multiple sources of water contributing to rivers, Hydrol. Earth Syst. Sci., 18, 15–30, 10.5194/hess-18-15-2014, 2014.Cartwright, I., Atkinson, A. P., Gilfedder, B. S., Hofmann, H., Cendón,
D. I., and Morgenstern, U.: Using geochemistry to understand water sources
and transit times in headwater streams of a temperate rainforest, Appl.
Geochem., 99, 1–12, 10.1016/j.apgeochem.2018.10.018, 2018.Chapman, T.: A comparison of algorithms for stream flow recession and
baseflow separation, Hydrol. Process., 13, 701–714, 10.1002/(Sici)1099-1085(19990415)13:5<701::Aid-Hyp774>3.0.Co;2-2, 1999.Chen, X. and Chen, X.: Stream water infiltration, bank storage, and storage
zone changes due to stream-stage fluctuations, J. Hydrol., 280,
246–264, 10.1016/s0022-1694(03)00232-4, 2003.Collischonn, W. and Fan, F. M.: Defining parameters for Eckhardt's digital
baseflow filter, Hydrol. Process., 27, 2614–2622, 10.1002/hyp.9391,
2013.Duncan, H. P.: Baseflow separation – A practical approach, J. Hydrol., 575, 308–313, 10.1016/j.jhydrol.2019.05.040, 2019.Eckhardt, K.: How to construct recursive digital filters for baseflow
separation, Hydrol. Process., 19, 507–515, 10.1002/hyp.5675, 2005.Eckhardt, K.: A comparison of baseflow indices, which were calculated with
seven different baseflow separation methods, J. Hydrol., 352,
168–173, 10.1016/j.jhydrol.2008.01.005, 2008.Eckhardt, K.: Technical Note: Analytical sensitivity analysis of a two parameter recursive digital baseflow separation filter, Hydrol. Earth Syst. Sci., 16, 451–455, 10.5194/hess-16-451-2012, 2012.Evans, C. and Davies, T. D.: Causes of concentration/discharge hysteresis
and its potential as a tool for analysis of episode hydrochemistry, Water Resour. Res., 34, 129–137, 10.1029/97wr01881, 1998.Furey, P. R. and Gupta, V. K.: Space-time variability of low streamflows in
river networks, Water Resour. Res., 36, 2679–2690, 10.1029/2000wr900136, 2000.Genereux, D.: Quantifying uncertainty in tracer-based hydrograph
separations, Water Resour. Res., 34, 915–919, 10.1029/98wr00010, 1998.Guzmán, P., Batelaan, O., Huysmans, M., and Wyseure, G.: Comparative
analysis of baseflow characteristics of two Andean catchments, Ecuador,
Hydrol. Process., 29, 3051–3064, 10.1002/hyp.10422, 2015.Hagedorn, B.: Hydrograph separation through multi objective optimization: Revealing the importance of a temporally and spatially constrained baseflow solute source, J. Hydrol., 590, 125349, 10.1016/j.jhydrol.2020.125349, 2020.Howcroft, W., Cartwright, I., and Cendón, D. I.: Residence times of bank
storage and return flows and the influence on river water chemistry in the
upper Barwon River, Australia, Appl. Geochem., 101, 31–41, 10.1016/j.apgeochem.2018.12.026, 2019.Jakeman, A. J. and Hornberger, G. M.: How much complexity is warranted in a
rainfall-runoff model?, Water Resour. Res., 29, 2637–2649, 10.1029/93WR00877, 1993.Kienzler, P. M. and Naef, F.: Subsurface storm flow formation at different
hillslopes and implications for the “old water paradox”, Hydrol. Process., 22, 104–116, 10.1002/hyp.6687, 2008.Kirchner, J. W.: A double paradox in catchment hydrology and geochemistry,
Hydrol. Process., 17, 871–874, 10.1002/hyp.5108, 2003.Kronholm, S. C. and Capel, P. D.: A comparison of high-resolution specific
conductance-based end-member mixing analysis and a graphical method for
baseflow separation of four streams in hydrologically challenging
agricultural watersheds, Hydrol. Process., 29, 2521–2533, 10.1002/hyp.10378, 2015.Lehner, B., Liermann, C. R., Revenga, C., Vörösmarty, C., Fekete,
B., Crouzet, P., Döll, P., Endejan, M., Frenken, K., Magome, J.,
Nilsson, C., Robertson, J. C., Rödel, R., Sindorf, N., and Wisser, D.:
High-resolution mapping of the world's reservoirs and dams for sustainable
river-flow management, Front. Ecol. Environ., 9, 494–502, 10.1890/100125, 2011.Li, L., Maier, H. R., Partington, D., Lambert, M. F., and Simmons, C. T.:
Performance assessment and improvement of recursive digital baseflow filters
for catchments with different physical characteristics and hydrological
inputs, Environ. Modell. Softw., 54, 39–52, 10.1016/j.envsoft.2013.12.011, 2014.Lin, K., Guo, S., Zhang, W., and Liu, P.: A new baseflow separation method
based on analytical solutions of the Horton infiltration capacity curve,
Hydrol. Process., 21, 1719–1736, 10.1002/hyp.6357, 2007.Liu, B., Zhao, W., Wen, Z., Yang, Y., Chang, X., Yang, Q., Meng, Y., and
Liu, C.: Mechanisms and feedbacks for evapotranspiration-induced salt
accumulation and precipitation in an arid wetland of China, J. Hydrol., 568, 403–415, 10.1016/j.jhydrol.2018.11.004, 2019.Lott, D. A. and Stewart, M. T.: A power function method for estimating base
flow, Ground Water, 51, 442–451, 10.1111/j.1745-6584.2012.00980.x, 2013.Lott, D. A. and Stewart, M. T.: Base flow separation: A comparison of
analytical and mass balance methods, J. Hydrol., 535, 525–533, 10.1016/j.jhydrol.2016.01.063, 2016.
Lyne, V. and Hollick, M.: Stochastic Time-Variable Rainfall-Runoff
Modeling, Australian National Conference Publication, Australian, Canberra,
1979.Lyu, H., Xia, C., Zhang, J., and Li, B.: Key challenges facing the application of the conductivity mass balance method: a case study of the Mississippi River basin, Hydrol. Earth Syst. Sci., 24, 6075–6090, 10.5194/hess-24-6075-2020, 2020.McCallum, J. L. and Shanafield, M.: Residence times of stream-groundwater
exchanges due to transient stream stage fluctuations, Water Resour. Res., 52, 2059–2073, 10.1002/2015wr017441, 2016.McCallum, J. L., Cook, P. G., Brunner, P., and Berhane, D.: Solute dynamics
during bank storage flows and implications for chemical base flow
separation, Water Resour. Res., 46, W07541, 10.1029/2009wr008539,
2010.Miller, M. P., Susong, D. D., Shope, C. L., Heilweil, V. M., and Stolp, B.
J.: Continuous estimation of baseflow in snowmelt-dominated streams and
rivers in the Upper Colorado River Basin: A chemical hydrograph separation
approach, Water Resour. Res., 50, 6986–6999, 10.1002/2013wr014939,
2014.Nash, J. E. and Sutcliffe, J. V.: River flow forecasting through conceptual
models part I – A discussion of principles, J. Hydrol., 10,
282–290, 10.1016/0022-1694(70)90255-6, 1970.Nathan, R. J. and McMahon, T. A.: Evaluation of automated techniques for
base flow and recession analyses, Water Resour. Res., 26, 1465–1473, 10.1029/WR026i007p01465, 1990.National Water Information
System (NWIS): Streamflow and conductivity data, available at: http://waterdata.usgs.gov/nwis, last access: 23 September 2020.Nejadhashemi, A. P., Sheridan, J. M., Shirmohammadi, A., and Montas, H. J.:
Hydrograph Separation by Incorporating Climatological Factors: Application
to Small Experimental Watersheds 1, J. Am. Water Resour. As., 43, 744–756, 10.1111/j.1752-1688.2007.00059.x, 2007.Osode, A. N. and Okoh, A. I.: Impact of Discharged Wastewater Final
Effluent on the Physicochemical Qualities of a Receiving Watershed in a
Suburban Community of the Eastern Cape Province, CLEAN – Soil, Air, Water,
37, 938–944, 10.1002/clen.200900098, 2009.Piggott, A. R., Moin, S., and Southam, C.: A revised approach to the UKIH method for the calculation of baseflow, Hydrolog. Sci. J., 50, 911–920, 10.1623/hysj.2005.50.5.911, 2005.
Pinder, G. F., and Jones, J. F.: Determination of the ground‐water component of peak discharge from the chemistry of total runoff, Water Resour. Res., 5, 438–445, 1969.Rammal, M., Archambeau, P., Erpicum, S., Orban, P., Brouyère, S.,
Pirotton, M., and Dewals, B.: Technical Note: An Operational Implementation
of Recursive Digital Filter for Base Flow Separation, Water Resour. Res., 54, 8528–8540, 10.1029/2018wr023351, 2018.
Rutledge, A. T.: Computer programs for describing the recession of ground-water discharge and for estimating mean ground-water recharge and discharge from streamflow records-update, U. S. Geological Survey, Reston, Report 98-4148, 1998.Saraiva Okello, A. M. L., Uhlenbrook, S., Jewitt, G. P. W., Masih, I.,
Riddell, E. S., and Van der Zaag, P.: Hydrograph separation using tracers
and digital filters to quantify runoff components in a semi-arid mesoscale
catchment, Hydrol. Process., 32, 1334–1350, 10.1002/hyp.11491, 2018.Schwartz, S. S.: Automated Algorithms for Heuristic Base-Flow Separation1,
J. Am. Water Resour. As., 43, 1583–1594, 10.1111/j.1752-1688.2007.00130.x, 2007.
Sloto, R. A. and Crouse, M. Y.: HYSEP: A Computer Program for Streamflow Hydrograph Separation and Analysis, U. S. Geological Survey, Reston, Report 96-4040, 1996.Stewart, M., Cimino, J., and Ross, M.: Calibration of Base Flow Separation
Methods with Streamflow Conductivity, Groundwater, 45, 17–27, 10.1111/j.1745-6584.2006.00263.x, 2007.Tallaksen, L. M.: A review of baseflow recession analysis, J. Hydrol., 165, 349–370, 10.1016/0022-1694(94)02540-R, 1995.Thomas, B. F., Vogel, R. M., Kroll, C. N., and Famiglietti, J. S.:
Estimation of the base flow recession constant under human interference,
Water Resour. Res., 49, 7366–7379, 10.1002/wrcr.20532, 2013.Wagner, S., Fair, J. H., Matt, S., Hosen, J. D., Raymond, P., Saiers, J.,
Shanley, J. B., Dittmar, T., and Stubbins, A.: Molecular Hysteresis:
Hydrologically Driven Changes in Riverine Dissolved Organic Matter Chemistry
During a Storm Event, J. Geophys. Res.-Biogeo., 124,
759–774, 10.1029/2018jg004817, 2019.Winnick, M. J., Carroll, R. W. H., Williams, K. H., Maxwell, R. M., Dong,
W., and Maher, K.: Snowmelt controls on concentration-discharge
relationships and the balance of oxidative and acid-base weathering fluxes
in an alpine catchment, East River, Colorado, Water Resour. Res., 53,
2507–2523, 10.1002/2016wr019724, 2017.Xiao, X., Zhang, F., Li, X., Zeng, C., Shi, X., Wu, H., Jagirani, M. D., and
Che, T.: Using stable isotopes to identify major flow pathways in a
permafrost influenced alpine meadow hillslope during summer rainfall period,
Hydrol. Process., 34, 1104–1116, 10.1002/hyp.13650, 2020.Xie, J., Liu, X., Wang, K., Yang, T., Liang, K., and Liu, C.: Evaluation of typical methods for baseflow separation in the contiguous United States, J. Hydrol., 583, 124628, 10.1016/j.jhydrol.2020.124628, 2020.Yang, W., Xiao, C., and Liang, X.: Technical note: Analytical sensitivity analysis and uncertainty estimation of baseflow index calculated by a two-component hydrograph separation method with conductivity as a tracer, Hydrol. Earth Syst. Sci., 23, 1103–1112, 10.5194/hess-23-1103-2019, 2019a.
Yang, W., Xiao, C., Liang, X., and Zhang, Z.: Study on the influence of
water-rock interaction on streamflow conductivity based on hydrograph
separation, E3S Web Conf., 98, 11005, 10.1051/e3sconf/20199811005, 2019b.Yang, W., Xiao, C., Liang, X., and Zhang, Z.: Two baseflow separation
methods based on daily average gage height and discharge, Water Supply, 19,
1978–1985, 10.2166/ws.2019.074, 2019c.
Yu, Z. and Schwartz, F. W.: Automated calibration applied to
watershed-scale flow simulations, Hydrol. Process., 13, 191–209, 1999.Zhang, J., Zhang, Y., Song, J., and Cheng, L.: Evaluating relative merits of
four baseflow separation methods in Eastern Australia, J. Hydrol.,
549, 252–263, 10.1016/j.jhydrol.2017.04.004, 2017.Zhang, R., Li, Q., Chow, T. L., Li, S., and Danielescu, S.: Baseflow
separation in a small watershed in New Brunswick, Canada, using a recursive
digital filter calibrated with the conductivity mass balance method,
Hydrol. Process., 27, 2659–2665, 10.1002/hyp.9417, 2013.Zhi, W., Li, L., Dong, W., Brown, W., Kaye, J., Steefel, C., and Williams,
K. H.: Distinct Source Water Chemistry Shapes Contrasting
Concentration-Discharge Patterns, Water Resour. Res., 55, 4233–4251, 10.1029/2018WR024257, 2019.