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Sequential ensemble‐based optimal design for parameter estimation
Author(s) -
Man Jun,
Zhang Jiangjiang,
Li Weixuan,
Zeng Lingzao,
Wu Laosheng
Publication year - 2016
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 - 10.1002/2016wr018736
Subject(s) - sampling (signal processing) , computer science , estimation theory , mathematical optimization , entropy (arrow of time) , ensemble kalman filter , kalman filter , optimal design , algorithm , sample size determination , focus (optics) , optimal estimation , data mining , mathematics , statistics , machine learning , filter (signal processing) , extended kalman filter , artificial intelligence , physics , quantum mechanics , optics , computer vision
The ensemble Kalman filter (EnKF) has been widely used in parameter estimation for hydrological models. The focus of most previous studies was to develop more efficient analysis (estimation) algorithms. On the other hand, it is intuitively understandable that a well‐designed sampling (data‐collection) strategy should provide more informative measurements and subsequently improve the parameter estimation. In this work, a Sequential Ensemble‐based Optimal Design (SEOD) method, coupled with EnKF, information theory and sequential optimal design, is proposed to improve the performance of parameter estimation. Based on the first‐order and second‐order statistics, different information metrics including the Shannon entropy difference ( SD ), degrees of freedom for signal ( DFS ) and relative entropy ( RE ) are used to design the optimal sampling strategy, respectively. The effectiveness of the proposed method is illustrated by synthetic one‐dimensional and two‐dimensional unsaturated flow case studies. It is shown that the designed sampling strategies can provide more accurate parameter estimation and state prediction compared with conventional sampling strategies. Optimal sampling designs based on various information metrics perform similarly in our cases. The effect of ensemble size on the optimal design is also investigated. Overall, larger ensemble size improves the parameter estimation and convergence of optimal sampling strategy. Although the proposed method is applied to unsaturated flow problems in this study, it can be equally applied in any other hydrological problems.