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.