Introduction

Drought is one of the most frequently occurring environmental disasters, and both historical observations and future climate projections show increasing frequency of drought worldwide (Dai, 2013; Feng & Fu, 2013; Trenberth et al., 2013). Droughts are mostly triggered by a reduction in seasonal or annual precipitation (Mishra & Singh, 2010). Droughts can have devastating impacts on regional food production, water resources management, drinking water supply, and even the stability of governments (Mishra & Singh, 2010; Dai, 2011; Zhang, Zhang, Cui, & Zeng, 2011). Although drought usually has dire environmental and socio-economic consequences, drought prediction is still a grand challenge (Dai, 2011; Mishra & Singh, 2011; Chiew et al., 2014). Drought involves complex interactions amongst different dimensions including meteorological conditions, vegetation water demand, hydrological conditions,etc . (Wang, Basia, & Arie, 2003; Nalbantis & Tsakiris, 2009; Dai, 2011; Zhang et al., 2011; Buttafuoco, Caloiero, & Coscarelli, 2015) hat can induce shifts in regional hydrological regime or rainfall-runoff relationship, leading to failures in predicting the onset, duration, severity, and termination of drought (Guardiola-Claramonte et al., 2011; Mishra & Singh, 2011; Zhang et al., 2011; Chiew et al., 2014; Huijgevoort, Lanen, Teuling, & Uijlenhoet, 2014; Yang et al., 2017).
Determining whether drought can lead to shifts in catchment hydrological behaviors is critical for future accurate hydrological prediction (Huijgevoort et al., 2014; Saft, Western, Zhang, Peel, & Potter, 2015). Previously, many studies have reported that drought can violate the assumption of stationarity in the catchment rainfall-runoff relationship (Conway et al., 2004; Guardiola-Claramonte et al., 2011; Cheng et al., 2012; Hughes, Petrone, & Silberstein, 2012; Chiew et al., 2014). Chiew et al. (2014) found that the rainfall-runoff relationship during drought periods was simulated poorly and overestimated significantly (up to 150%) by a hydrological model previously calibrated under normal period. Petrone, Hughes, Niel, & Silberstein (2010) found a significant decline in the runoff coefficient and a shift in hydrological regime in the headwater regions of southwest Western Australia after a long-term decline in rainfall from the mid-1970s to 2008. Based on the long-term rainfall-runoff observations of 228 catchments in south-eastern Australia, Saft et al. (2015) showed that prolonged drought during 1997-2009 led to a statistically significant shift in the rainfall-runoff relationship in about 46% of the studied catchments. Although many studies have statistically demonstrated that long-term drought can lead to shifts in catchment hydrological regimes based on observations and modelling, there is still great uncertainty in detecting and predicting whether drought can induce changes in catchment hydrological behaviors and in understanding why the rainfall-runoff relationship can change at the process level.
Insights into this challenge can be gained by combining a data assimilation method with process-based hydrological models. This approach accounts for hydrological non-stationarity in the rainfall-runoff relationship for capturing shifts in the flow regime induced by long-term drought. It also accounts for time-variant parameters in the hydrological model. Accounting for both factors leads to identification of possible mechanisms that cause the changes in catchment hydrological behaviors. Parameters in a process-based hydrological model represent catchment functional properties, and thus can be used to detect catchment hydrological behaviors and their changes (Pathiraja, Marshall, Sharma, & Moradkhani, 2016). Parameters in hydrological models are traditionally assumed to be stationary (i.e., time-invariant), and are calibrated against observed runoff (Coron et al., 2012). There is an accumulated body of literature showing that hydrological systems can be non-stationary, and that parameters in hydrological models should be time-variant. This is because substantial anthropogenic changes of climate have occurred outside of the historically measured mode of natural variability, and direct alteration of local water cycles has occurred as a result of land and water management practices including deforestation (Destouni, Jaramillo, & Prieto, 2013; Lima et al., 2014; Cheng et al., 2017; Guimberteau et al., 2017), groundwater extraction (Kinal & Stoneman, 2012; Miguez-Macho & Fan, 2012), and damming of rivers for hydroelectricity (Botter, Basso, Porporato, Rodrigueziturbe, & Rinaldo, 2010; Xue, Liu, & Ge, 2011). Recent studies have recognized that models with time-variant parameters can reasonably account for shifts in the catchment rainfall-runoff relationship or catchment behaviors under changing environments (Merz, Parajka, & Blöschl, 2011; Chiew et al., 2014; Deng, Liu, Guo, Li, & Wang, 2016). Based on time-variant parameters obtained by a data assimilation method, not only can changes in the catchment rainfall-runoff relationship can be detected (Deng et al., 2016), but also the causes of the changes can be identified from hydrological parameters (Pathiraja et al., 2016; Xiong et al., 2019). For example, (Deng et al., 2016) combined a two-parameter monthly water balance model to obtain time-variant hydrological parameters, and successfully detected the impacts of land-use changes on catchment water storage capacity in the Wudinghe Basin, which led to changes in the catchment rainfall-runoff relationship. Pathiraja et al. (2016) demonstrated that land cover changes can lead to significant step changes in estimated parameters in hydrological models using an ensemble Kalman filter with a locally evolutionary linear parameter in two paired experimental catchments in the Western Australia. They identified changes in the excess runoff generation process that resulted from land use changes. Based on previous successful studies for detecting and understanding hydrological non-stationarity under changing environments using a data assimilation method, we employed a similar methodology to investigate the non-stationarity in hydrological behavior induced by long-term drought.
In this study, the Particle filter (PF) data assimilation technique was combined with a two-parameter monthly water balance model (TWBM) to obtain time-variant parameter series, and then to identify changes caused by drought at the process level. The PF data assimilation technique is one of a general class of ensemble-based statistical data assimilation methods that is more suitable for nonlinear data assimilation problems and retaining the water balance (Arulampalam, Maskell, Gordon, & Clapp, 2002; Moradkhani & Weihermüller, 2011; Field, Tavrisov, Brown, Harris, & Kreidl, 2016) , and thus was selected in this study. The TWBM model is a widely used monthly hydrological model that has been successfully applied to simulate the catchment rainfall-runoff relationship in a wide range of climates, soils, and vegetation conditions (Guo, Wang, Xiong, Ying, & Li, 2002; Guo et al., 2005; Xiong & Guo, 2012; Shuai, Xiong, Dong, & Zhang, 2013; Zhang, Liu, Liu, & Bai, 2013; Xiong, Yu, & Gottschalk, 2015). The specific objectives of this study were to (1) demonstrate whether the PF data assimilation method can be used to detect changes in catchment hydrological behaviors induced by drought; (2) detect whether prolonged drought can cause changes in the catchment rainfall-runoff relationship; and (3) identify the mechanisms responsible for drought induced changes in catchment hydrological behavior at the process level.