3 Baseflow recession analysis
method
The process of baseflow recession analysis can be divided into three
stages: 1) extracting the baseflow recession segment; 2) Selecting an
appropriate theoretical model; 3) Determining the optimal model
parameters (Tallaksen, 1995). Each stage has different methods. Stoelzle
et al. (2013) points out that different combinations of methods will get
different recession characteristics, and the parameter optimization
method has the most obvious effect on the results. Therefore, based on
the power function relationship of -dQ/dt and Q (Sect. 3.2), this study
adopts 12 combinations of four recession segment extraction methods
(Sect. 3.1) and three parameter optimization methods (Sect. 3.3) to
carry out the baseflow recession analysis. Finally, the difference of
mean value of recession coefficient under different parameter
optimization methods is analyzed. The Matlab toolbox developed by
Arciniega-Esparza, Breña-Naranjo, Pedrozo-Acuña, and Appendini (2017)
facilitates the automated analysis and comparative analysis of recession
analysis.
3.1 Baseflow recession segment extraction
methods
There are four commonly used methods for extracting recession segments:
Kir method (Kirchner, 2009), Vog method (Vogel & Kroll, 1992), Bru
method (Brutsaert & Nieber, 1977) and Aks method (Aksoy & Wittenberg,
2011). See Table 1 for a summary. The Vog method selects recession
segments from the decreasing parts of 3-day moving averages of
streamflow. Kir, Bru and Aks methods all select the recession segment in
the parts of \(dQ/dt\) < 0. Kir method includes all the parts
of \(dQ/dt\) < 0, while Bru and Aks methods exclude the
segments affected by rainfall or surface runoff based on different
criteria. Stoelzle et al. (2013) and Arciniega-Esparza et al. (2017) has
discussed these methods in detail, and this paper will not repeat them.
Table 1. Recession segment extraction methods.
3.2 Theoretical model
Hydrologists have provided a
variety of theoretical models for baseflow recession analysis based on
different assumptions, see Tallaksen (1995), Smakhtin (2001), and Thomas
et al. (2015) for details. The current widely used theoretical models
are: linear reservoir model, \(S=kQ\) (Maillet, 1905), nonlinear
reservoir model,\(\ S=kQ^{\beta}\) (Hartmut Wittenberg, 1999) and
power law relationship between \(-dQ/dt\) and Q,\(-\frac{\text{dQ}}{\text{dt}}=aQ^{b}\) (Brutsaert & Nieber, 1977).
These three models are essentially based on the power law relationship
between storage and discharge (also named nonlinear reservoir). The
linear reservoir model presents a particular feature as it has a power
exponent of 1. The power function relationship of \(-dQ/dt\) and Q can
be obtained by substituting the power law relationship between storage
and discharge into the basin continuity equation(Wang & Cai, 2009),k and β are constants and the corresponding relationships
with a and b are \(k=\frac{1}{\left(2a-ab\right)}\)and \(\beta=2-b\) (Thomas et al., 2015). Therefore, this study uses
the power function model of \(-dQ/dt\) and Q to analyze the recession.
It should be pointed out that the water storage (S) here refers to the
active water storage in the basin that can be discharged to the river.
3.3 Parameter optimization
methods
There are three widely used parameter optimization methods: linear
regression, lower envelope, and binning (Stoelzle et al., 2013).
According to the scatter plot of
log(|dQ /dt |) vs. log(Q ), the
three parameter optimization methods determine the fitting line with
different forms. The slope of the line is b , and the intercept is
log(a ),\(\log\left(-\frac{\text{dQ}}{\text{dt}}\right)=\log\left(a\right)+b*\log(Q)\).
The linear regression method is to fit the line with the least square of
all scattered points. The lower envelope method uses the lower boundary
(or lower 5% critical line) of the scatter points to determine the
fitting line. The binning method is to segment the scattered points
according to the streamflow, then calculate the average value of each
segment, and finally make the least square fitting line of these average
values. Stoelzle et al. (2013) and Thomas et al. (2015) have discussed
these methods in detail.