Improving Treatment of Noise Specification of Kalman Filtering for State Updating of Hydrological Models: Combining the Strengths of the Interacting Multiple Model Method and Cubature Kalman Filter

“Filtering methods have been widely used to improve the forecast performances of hydrological models. Although extensive research has been carried out on filtering methods in the hydrology literature, researchers have not treated the noise statistics of filtering methods in much detail. Wrongly specified noise statistics can lead to degraded state estimates and even filter divergence. A powerful approach for state estimation in the presence of unknown noise statistics is the interacting multiple model method (IMM), which solves the noise specification problem by combining the strengths of multiple filters with different noise statistics. The IMM method has received little to no attention in the hydrologic context. This paper proposes a novel approach (IMM-CKF) for updating the states of hydrological models in the presence of unknown noise statistics by combining the cubature Kalman filter (CKF) with the IMM. The CKF is a popular nonlinear filter that has received little attention in the hydrology literature. The method is tested using a lumped hydrological model. The results of the synthetic case suggest the IMM-CKF can yield an accurate estimate for the switch as well as the changed states when there are abrupt changes in the noise statistics of true noises, even if sub-filter noise statistics are not equal to the real ones. The real case results (a forecast experiment) show that the IMM-CKF has successfully combined the strengths of different sub-filters and associated noise statistics. The IMM-CKF can be useful for hydrological forecasting, especially when useful information about the true noise statistics is unavailable.”

(Citation: Sun, Y., Tian, X., Bao, W., et.al. – Improving Treatment of Noise Specification of Kalman Filtering for State Updating of Hydrological Models: Combining the Strengths of the Interacting Multiple Model Method and Cubature Kalman Filter – Water Resources Research 59(2023)7, art. no. e2022WR033635 – DOI: 10.1029/2022WR033635)