Results

Rainfall-runoff relationships during pre- and post-drought periods

In order to verify whether there was a change in the rainfall-runoff relationship in the Wee Jasper catchment due to multi-year drought, a statistical examination used by Saft et al. (2015) was employed. The observed annual rainfall-runoff relationships for the Wee Jasper catchment during the pre- and post-drought periods are shown in Figure 3. The entire study period (1970-2014) was divided into the pre- and post-drought periods using the beginning year of the Millennium drought (1997) (CSIRO, 2012), as the catchment behaviors were assumed to change during the Millennium drought and to not recover in the more normal last five years (2010-2014). The runoff data were transformed by the Box-Cox transformation (Box & Cox, 1964) to make them follow an approximately normal distribution and to become approximately linear with rainfall data as done by (Saft et al., 2015). Figure 3 demonstrates that during the pre-drought period, the slope and intercept of the rainfall-runoff relationship are 0.016 and 4.35, respectively. During the post-drought period, the slope was the same (0.016), but the intercept was 2.19. The significant decrease in the intercept (p < 0.05) suggests that the rainfall-runoff relationship between the pre- and post-drought periods were significantly different. The small intercept means that the reduction in runoff with decreasing rainfall during the post-drought period was smaller than expected for the same reduction of rainfall during the pre-drought period.
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Simulated runoff by combining a data assimilation method with a hydrological model

Observed and simulated monthly runoff are shown in Figure 4. The simulated monthly runoff was calculated by TWBM with ensemble mean parameters from 100 runs using the PF data assimilation method. Figure 4 shows that the simulated monthly runoff agreed well with observed monthly runoff over the entire period from 1970 to 2014 except March 2012. The NSE between the simulated and observed runoff was 0.94. High NSE values indicated that the simulated runoff was almost the same as the observed runoff at every time step. The BIAS between the simulated and observed runoff was −0.05, which indicated that the total volume of simulated runoff was slightly less than the volume of observed runoff. Both NSE and BIAS values suggested that the long-term monthly rainfall-runoff relationship of the Wee Jasper catchment was well captured by the combination of the PF data assimilation method with TWBM. Thus, assimilated time-variant parameters of the hydrological model (i.e., SC and C ) can be used to infer the long-term dynamic state of the catchment hydrological behavior.
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Changes in the state variables (SC andC )

Anomalies of the annual values of SC and C from 1970 to 2014 are shown in Figure 5. The anomalies were calculated using ensemble mean parameters from 100 runs using the PF data assimilation method. Annual anomalies of SC (Figure 5a) were generally seen to increase from negative to positive over the 1970-2014 period, with some variability. Annual anomalies of SC varied from −40.7% around 1976 to 22.4% around 2004. The entire study period can be divided into three different but consecutive periods (1970-1984, 1985–1992, 1993–2014) by the three-year moving window curve. The three-year moving window of SC anomalies was negative during the 1st period (1970-1984). The moving window curve alternated between negative and positive values during the 2nd period (1985–1993). And moving window curve was all positive during the 3rd period (1994–2014) except for 2013. The Millennium drought period (1997–2009) lies in the 3rdperiod (1994–2014), indicating that during the Millennium drought period, SC was larger than the mean SC value cacluated over the entire study period (1970-2014).
Figure 5b shows inter-annual fluctuations of the anomalies of C . Annual anomalies of C showed a similar increasing time trend as seen for SC. Basically, anomalies of C were negative at the beginning of the study period, and mostly positive at the end of study period. The C anomaly fluctuated more frequently and had shorter and more consecutive positive and negative periods than seen for SC (Figure 5a). Annual anomalies ranged from −23.5% to 21.7%, and could be divided into three periods (1970-1979, 1980-1997, 1998-2014) using the three-year moving window curve. The three-year moving window ofC anomalies was always negative during the 1stperiod (1970-1979). It then alternated between negative and positive values during the 2nd period (1980-1997), similar to what was observed for SC, but with more fluctuation cycles. The three-year moving window of C anomalies was always positive during the 3rd period (1997-2014) except for 2013. The Millennium drought period (1997–2009) fell in the 3rdperiod (1997–2014), during which the three-year moving window ofC anomalies were all positive, indicating the during the Millennium drought period C was larger than the mean Cvalue calculated for the entire study period (1970-2014).
Figure 6 presents of SC and C at the monthly time scales over the 1970-2014 study period with the 5.0%–95.0% prediction uncertainty range (grey ribbon) estimated from 100 model runs. Step changes in the time-variant series of SC and C were detected using the Pettitt-test and are also shown in Figure 6 (red dashed line). In Figure 6a, the step change for SC was identified as occurring in April 1997. The average values of SC before and after the step change were 2606.4 and 3217.4 mm, respectively. The average value of SC increased 23.4% after the step change. The estimated monthly time series of C is shown in Figure 6b. The step change for C was identified as occurring in November 1996. The average values of C before and after the step change point were 1.08 and 1.19, respectively. The meanC value increased about 10.2% after the step change. Figure 6 shows that TWBM parameters shifted significantly around the beginning of the Millennium drought (i.e., 1997), which is consistent with the statistical examination described in Section 4.1, and indicates a significant shift in the rainfall-runoff relationship in the Wee Jasper catchment due to the prolonged drought.
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