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.