Premium
State and parameter estimation of hydrologic models using the constrained ensemble Kalman filter
Author(s) -
Wang Dingbao,
Chen Yuguo,
Cai Ximing
Publication year - 2009
Publication title -
water resources research
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.863
H-Index - 217
eISSN - 1944-7973
pISSN - 0043-1397
DOI - 10.1029/2008wr007401
Subject(s) - kalman filter , projection (relational algebra) , ensemble kalman filter , computer science , constraint (computer aided design) , data assimilation , state space , mathematical optimization , nonlinear system , state (computer science) , filter (signal processing) , algorithm , mathematics , extended kalman filter , artificial intelligence , statistics , meteorology , physics , geometry , quantum mechanics , computer vision
Data assimilation techniques, such as the Kalman filter (KF) and its extensions, update state variables based on the KF type of algorithms, but state‐space models usually have relevant physical laws or settings. The updated states by the KF may violate some physical constraints, which can be equality or inequality, and linear or nonlinear constraints. This paper presents three methods, the naive method, the projection method and the accept/reject method, to incorporate constraints into the ensemble Kalman filter (EnKF). Essentially, the projection method projects the updated ensemble members from the unconstrained EnKF to the feasible space characterized by the constraints. The accept/reject method tries to enforce the updated states to obey the constraints by resampling the observation error and model error. The three methods are applied to a conceptual hydrologic model for state estimation and sequential parameter learning, with specific treatment of inequality constraints. Both the reject/accept and projection methods perform better than the naive method which treats the hard constraint in a simple way and ignores other constraints. It is easy to implement the accept/reject method, the performance of which is comparable to the projection method regarding both the estimation quality and the computational time with the case study.