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: