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.
[Please insert Figure 3 here]
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.
[Please insert Figure 4 here]
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.
[Please insert Figure 5 here]
[Please insert Figure 6 here]