Discussion
Changes in rainfall-runoff relationship induced by
drought
Figure
3 and Figure 6 both show the consistent result that there was a shift in
the rainfall-runoff relationship during the post-drought period
(1997-2014) compared with the relationship during the historical period
(1970–1996). In this study, the increase in the catchment water storage
capacity and the decrease in soil moisture are considered to be the main
causes that induced the observed change in the hydrological process in
terms of the increase of parameters SC and C . The decline in soil
moisture means decreased groundwater recharge (Western, Grayson, &
Blöschl, 2002) leading to a decline in groundwater level and reduced
discharges to stream networks. Increased catchment water storage
capacity may also lead to a larger initial rainfall loss during the
drought and result in smaller runoff coefficient (Saft et al., 2016).
The increase in catchment water storage capacity may be caused by the
decline in groundwater level, which will be discussed in Section 5.2.
Many previous studies (Petrone et al., 2010; Petheram, Potter, Vaze,
Chiew, & Zhang, 2011; Hughes et al., 2012; Chiew et al., 2014) also
reported that declining groundwater level and deep soil moisture could
lead to changes in the rainfall-runoff relationship during the
Millennium drought in southeastern Australia. The pre-drought
groundwater level was close to the soil surface, and could amplify the
generation of surface runoff. However, this effect will be diminished
during drought with lower groundwater level and drier deep soil,
resulting in less rainfall becoming runoff.
Estimated time-variant model
parameters
SC represents the active water storage capacity (Xiong & Guo, 1999),
which is not a constant, but rather is a time-variant parameter in
contrast to the original parameter definition. There is also a
difference in the physical meaning of C compared with the
original definition given by Xiong & Guo (1999). In this study, a
change in C can reflect a change in the ratio between rainfall
and soil moisture in supplying actual evapotranspiration. The higherC value means that the ratio of rainfall to soil moisture is
smaller with regards to supplying actual evapotranspiration. That result
is due to Equation (1) of TWBM being based on the Budyko framework
(Xiong & Guo, 1999), where the mean variation of soil water content is
assumed to be zero on a multi-year scale. However, at a monthly scale,
the rainfall is sometimes not enough to provide water availability for
evapotranspiration, and soil water content in the deeper soil layer is
used to sustain evapotranspiration during drought (Cheng, Xu, Wang, &
Cai, 2011). If evapotranspiration is calculated using equation (1) when
TWBM is combined with the PF data assimilation method, then C is
calculated optimally at each time step rather than over the entire study
period. The time-variant parameter C reflects the variation of
the ratio of rainfall to soil moisture at each time step. Thus, the
increase in C can be attributed to the decrease of water supply
(including rainfall and soil moisture) available for actual
evapotranspiration. This can be inferred from Figure 2, which also
suggests that the Wee Jasper catchment experienced a wet period from
1983 to 1996). Average PET and precipitation were approximately equal
during this wet period. The PET and precipitation were 1174 mm and 1105
mm, respectively. However, during the period of 1997-2009, the average
PET became 403 mm larger than average precipitation. Due to changes in
the ratio of PET to precipitation (i.e., aridity index), more soil
moisture could be evaporated (Western et al., 2002) during period of
1997-2009. In addition, Figure 2 shows, the rainfall in this period
became lower. With higher evaporation of soil moisture and lower
rainfall, the ratio of rainfall to soil moisture in supplying actual
evapotranspiration was smaller.
More evaporated water from soil may come from deeper soil layers. During
prolonged drought, trees can access deep soil moisture and thereby
sustain transpiration. Loeb, Wang, Liang, Kato, & Rose (2017) found
that during the Millennium drought, the moisture in the top soil layer
stopped declining in 2002, while in the lower soil layer the moisture
continually declined until 2008 in central Australia, indicating that
the deep soil layer was capable of consistently supplying water for
evapotranspiration. The decrease in deep soil moisture may be due to the
transpiration of vegetation with deep roots during dry periods (Gao et
al., 2014; Loeb et al., 2017). The capacity of deep soil moisture to
consistently supply evapotranspiration is consistent with the
characteristics of the estimated parameter C time series.C maintained a higher value for a long time after the step change
point in the Millennium drought period (1997-2009) (see Figure 5).
Groundwater decline was considered to be the main reason for the shift
in SC. SC represents the active water storage capacity, which exhibited
large fluctuations at the monthly scale (Figure 6). The average
inter-monthly variation of SC was 43 mm. The large fluctuation of SC
indicated that it is sensitive to meteorological factors at the monthly
scale. Typically, there are two main factors that can lead to changes in
catchment water storage capacity, i.e., groundwater and soil properties.
Groundwater is considered to be the main factor because of the quicker
responses of groundwater to meteorological factors compared with
responses of soil properties (Hughes et al., 2012). Groundwater can also
vary at a monthly time scale (Jackson, Meister, & Prudhomme, 2011;
Adams et al., 2012). Relative to the interdecadal variation of soil
properties, such as hydraulic conductivity, water repellence, and
preferential flow pathways, groundwater is more sensitive to
meteorological factors in impacting catchment water storage capacity
(Saft, Peel, Western, & Zhang, 2016). Hughes et al. (2012) also found
that groundwater level declined about 3 m or more during the Millennium
drought in many catchments in southern Australia, including at the Del
Park, Bates, Lewis, Gordon, Cameron West, and Cameron Central
catchments. Many researchers also reported that the catchment
groundwater level dropped significantly during the Millennium drought in
southern Australia (Petrone et al., 2010; Petheram et al., 2011; Kinal
& Stoneman, 2012; Gao et al., 2014). Significant declines in
groundwater levels reported by these literature sources are consistent
with the findings in this study that SC was larger during the Millennium
drought period (1997-2009) than at other times (Figure 5 and Figure 6).
Data assimilation method for detecting drought
impacts
Many studies have reported that drought can alter catchment
rainfall-runoff relationships (Conway et al., 2004; Guardiola-Claramonte
et al., 2011; Petheram et al., 2011; Chiew et al., 2014). However,
reasons for changes in the relationship are still unclear, especially
regarding the driving factors at the process level. In this study, a new
method involving the combining of a data assimilation technique (PF)
with a process hydrological model (TWBM) was employed to detect and
attribute drought induced changes to the rainfall-runoff relationship in
the Wee Jasper catchment, which had experienced a 13-year prolonged
drought. Shifts in hydrological parameters adequately accounted for the
change in the rainfall-runoff relationship, as they represented
functional properties of hydrological behaviors. This new method not
only confirmed the fact that prolonged drought altered the
rainfall-runoff relationship, but also determined that increased
catchment water storage capacity and decreased soil moisture induced by
deep soil moisture depletion through persistent evapotranspiration of
deep-rooted woody vegetation during drought were the main factors
changing the rainfall-runoff relationship during the Millennium drought
in the Wee Jasper catchment. The results of this study demonstrated that
combining data assimilation with a process-level hydrological model is
an effective method for detecting and attributing drought impacts.
Due to a lack of long-term groundwater and soil moisture observations,
at this location, the relationship between the change in hydrological
parameters (SC and C) and observed groundwater and/or deep soil moisture
was not presented. Long-term groundwater data for such long-term drought
impact studies are typically very rare (Saft et al., 2016). However, the
decline of groundwater and deep soil moisture can still be inferred from
the meaning of the hydrological parameters, as described in Section 5.2.
This is one of the advantages of using time-variant parameters to detect
changes in the rainfall-runoff relationship (Deng et al., 2016;
Pathiraja et al., 2016).
The relationship between the hydrological parameters and runoff is
non-linear in TWBM. To obtain the parameters more accurately, the data
assimilation used in this study must be capable of handling a non-linear
system. For the capacity of retaining water balance, in contrast to the
to the Kalman filter-based recursive method, PF upgrades the probability
distributions of system states rather than changing the state ensemble
members, and thereby retains the water balance law of the hydrological
model. Therefore, PF was viewed as a suitable method for estimating the
hydrological parameters in this study.
However, in this study, modeling experiments were not carried out to
demonstrate the superiority of PF and/or TWBM compared with other data
assimilation methods and/or physical hydrological models. This study can
be viewed as an exploratory approach for detecting and attributing
changes in the rainfall-runoff relationship induced by prolonged drought
rather than a determination of the best combination of a data
assimilation method with a hydrological model. PF was selected because
of its ability to handle the non-linear characteristic (Arulampalam et
al., 2002; Moradkhani et al., 2005; Dumedah & Coulibaly, 2013) of the
rainfall-runoff relationship, which is widely recognized as a non-linear
type of function. TWBM was selected because of its successful
application with data assimilation (Deng et al., 2016) and its
capability to simulate the catchment rainfall-runoff relationship across
a wide range of climates, vegetation, and soil conditions. Because of
the limited number of parameters involved, combining TWBM with PF does
not afford the opportunity to obtain more information of impacted
hydrological behaviors. In the future, a more complex process-based
hydrological model with more parameters could be employed to detect the
impacted hydrological behaviors in a prolonged drought situation in
order to obtain a better understanding of the stationarity of the
catchment rainfall-runoff relationship, although this will likely
involve more uncertainties and/or computational costs.