where SC is a parameter in mm. SC can be regarded as catchment active water storage capacity, which regulates the response of catchment monthly runoff to rainfall.
By combining TWBM with the PF data assimilation method, monthly time-variant series of SC and C were obtained, reflecting the dynamic variation of catchment hydrological behaviors to climate variability. Shifts in C reflect the changes in catchment evapotranspiration mechanisms resulting from the impacts of drought on catchment water and the energy balance. Trends and/or step changes in SC indicate the influences of drought on catchment water yields through the control of catchment soil water dynamics (e.g., groundwater storage, interaction between surface water and groundwater, etc. ) on runoff generation.

The Particle filter

PF was used in this study to trace the variation of C and SC. It is a sequential data assimilation method, using many independent random samples, called particles, to simulate posterior distribution (Arulampalam et al., 2002; Moradkhani & Weihermüller, 2011). PF was selected for two main reasons in this study: superiority in handling non-linear processes (Moradkhani, Hsu, Gupta, & Sorooshian, 2005; Moradkhani, 2008) and capacity in retaining the water balance (Pan & Wood, 2006; DeChant & Moradkhani, 2012; Moradkhani, DeChant, & Sorooshian, 2012). Two equations (i.e., state-transition and measurement equations) were the fundamental equations of PF at each time step \(t_{k}\) (k = 0, 1, 2, …) (Moradkhani et al., 2005).
The state-transition equation is: