The last step is resampling. Resampling is conducted in PF to reduce the particle degeneracy problem (Arulampalam et al., 2002). The basic idea of resampling is to eliminate the low-weighted particles in favor of concentrating on high-weighted particles. The resampling particles are generated by the system dynamic function\(x_{1}^{i}=f\left(x_{0}^{i},v_{0}\right)\). The obtained new collection of equally-weighted particles \(\left\{x_{1}^{i}\right\}\)is used for another reweighting under the condition of subsequent observation \(y_{1}\). As the procedure continues at time step k (k =1, 2, 3….), the subsequent estimated states\(\hat{x_{1}}\), \(\hat{x_{2}}\),\(\ \hat{x_{3}}\),… will be obtained analogously to Equation (7) until the final observation is used. A more detailed description of the PF method can be found in Arulampalam et al. (2002).

In this study, the Particle filter is combined with hydrological model (i.e. , TWBM), to estimate the soil moistures S , parameterC and parameter SC at each time step. The state vector\(x_{k}=[SC,C,S\ ]^{\prime}\), includes both state and parameters. The observed runoff is the observation in the Particle filter. The parameters C and SC are set to range from 0.2-2.0 and 100-4000 (mm), respectively. The system state-transition equation for the SC, C and S are as follows: