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.