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Appl. Math. Stat."],"abstract":"<jats:p>Practical data assimilation algorithms often contain hyper-parameters, which may arise due to, for instance, the use of certain auxiliary techniques like covariance inflation and localization in an ensemble Kalman filter, the re-parameterization of certain quantities such as model and\/or observation error covariance matrices, and so on. Given the richness of the established assimilation algorithms, and the abundance of the approaches through which hyper-parameters are introduced to the assimilation algorithms, one may ask whether it is possible to develop a sound and generic method to efficiently choose various types of (sometimes high-dimensional) hyper-parameters. This work aims to explore a feasible, although likely partial, answer to this question. Our main idea is built upon the notion that a data assimilation algorithm with hyper-parameters can be considered as a parametric mapping that links a set of quantities of interest (e.g., model state variables and\/or parameters) to a corresponding set of predicted observations in the observation space. As such, the choice of hyper-parameters can be recast as a parameter estimation problem, in which our objective is to tune the hyper-parameters in such a way that the resulted predicted observations can match the real observations to a good extent. From this perspective, we propose a hyper-parameter estimation workflow and investigate the performance of this workflow in an ensemble Kalman filter. In a series of experiments, we observe that the proposed workflow works efficiently even in the presence of a relatively large amount (up to 10<jats:sup>3<\/jats:sup>) of hyper-parameters, and exhibits reasonably good and consistent performance under various conditions.<\/jats:p>","DOI":"10.3389\/fams.2022.1021551","type":"journal-article","created":{"date-parts":[[2022,10,28]],"date-time":"2022-10-28T07:58:06Z","timestamp":1666943886000},"update-policy":"https:\/\/doi.org\/10.3389\/crossmark-policy","source":"Crossref","is-referenced-by-count":4,"title":["Continuous Hyper-parameter OPtimization (CHOP) in an ensemble Kalman filter"],"prefix":"10.3389","volume":"8","author":[{"given":"Xiaodong","family":"Luo","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Chuan-An","family":"Xia","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1965","published-online":{"date-parts":[[2022,10,28]]},"reference":[{"key":"B1","doi-asserted-by":"publisher","first-page":"35","DOI":"10.1115\/1.3662552","article-title":"A new approach to linear filtering and prediction problems","volume":"82","author":"Kalman","year":"1960","journal-title":"Trans ASME Ser D J Basic Eng"},{"key":"B2","doi-asserted-by":"crossref","DOI":"10.1002\/0470045345","volume-title":"Optimal State Estimation: Kalman, H-Infinity, and Nonlinear Approaches","author":"Simon","year":"2006"},{"key":"B3","first-page":"1628","article-title":"A new approach for filtering nonlinear systems","volume-title":"The Proceedings of the American Control Conference","author":"Julier","year":"1995"},{"key":"B4","doi-asserted-by":"publisher","first-page":"107","DOI":"10.1049\/ip-f-2.1993.0015","article-title":"Novel approach to nonlinear and non-Gaussian Bayesian state estimation","volume":"140","author":"Gordon","year":"1993","journal-title":"IEEE Proc Radar Signal Process"},{"key":"B5","doi-asserted-by":"publisher","first-page":"4089","DOI":"10.1175\/2009MWR2835.1","article-title":"Particle filtering in geophysical systems","volume":"137","author":"Van Leeuwen","year":"2009","journal-title":"Mon Weath Rev"},{"key":"B6","doi-asserted-by":"publisher","first-page":"465","DOI":"10.1016\/0005-1098(71)90097-5","article-title":"Recursive Bayesian estimation using Gaussian sums","volume":"7","author":"Sorenson","year":"1971","journal-title":"Automatica"},{"key":"B7","doi-asserted-by":"publisher","first-page":"1783","DOI":"10.1002\/qj.49712455002","article-title":"The ECMWF implementation of three-dimensional variational assimilation (3D-Var). 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