3.2 Recession fitting method
At first, the previous master recession curve method (Barnes, 1939) was replaced by overlapping individual recession events. It can avoid to ignore the variability of groundwater storage depletion and interference caused by the transition points between direct runoff and low-flow (Anderson & Burt, 1980). However, the filtered data points had a discontinuous time series due to the strict criteria for excluding the influence of precipitation and evapotranspiration. Therefore, to reduce the uncertainty for the definition of the initial time, the widely-used method is to plot the relationship between the flow variation (-dQ/dt ) and the streamflow (Q ) function to reveal the average recession behavior without the need for continuous data.
When Brutsaert and Nieber (1977) initially developed the analysis method, it was noted that evapotranspiration largely accelerated the flow variation during the recession process. In addition, the groundwater storage discharges from the aquifer had a lower flow variation than the other components of the observed streamflow, such as surface runoff and interflow. This indicates that the minimum flow variation dQ/dt corresponding to the given streamflow Q , that is, the lower envelope for the data points, can reduce the evapotranspiration influence and ensure that the streamflow value is only low-flow. In previous studies, the position of the lower envelope was manually fitted. To avoid observation and calculation errors, the fitting line placed 5% of the data points below the lower envelope (Brutsaert, 2008), however the precise location of the fitting line has been continuously debated because of the subjectivity and uncertainty (Ajami, Troch, Maddock, Meixner, & Eastoe, 2011; Stoelzle, Stahl, & Weiler, 2013). In addition to the lower envelope, many other fitting methods have been proposed since the development of the low-flow recession analysis. For example, Brutsaert (2005) proposed that soil heterogeneity may eliminate the evaporative effect in basins with large areas and hillslopes, so it is recommended that the fitting line should pass through the entire data point cloud instead of the lower envelope. Kirchner (2009) proposed a transformation method to reduce the noise and error of the original data by binning the threshold value of the streamflow and then calculating the average recession behavior. In this study, to reduce the disparity in the range of flow variation corresponding to a given streamflow, Kirchner’s (2009) binning method was used. The method bins the screened data points into at least a 1% logarithmic range of the streamflow and then calculates the mean and standard deviation for each bin. Bins which were one-half of the mean flow variation higher than the flow variation of the standard deviation were selected. Finally, weighted regression analysis was performed using the inverse variance of the selected bins. Through this method, data points with high uncertainty have a lesser influence and data noise which reduces accuracy can be avoided to ensure the fitting result is more representative of the recession parameters at the overall catchment. A schematic diagram of the relationship between the streamflow and flow variation is presented in Figure 3.