Error covariance tuning in variational data assimilation: application to an operating hydrological model
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ORIGINAL PAPER
Error covariance tuning in variational data assimilation: application to an operating hydrological model Sibo Cheng1,2
•
Jean-Philippe Argaud1 • Bertrand Iooss3,4 • Didier Lucor2 • Ange´lique Ponçot1
Accepted: 7 November 2020 Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract Because the true state of complex physical systems is out of reach for real-world data assimilation problems, error covariances are uncertain and their specification remains very challenging. These error covariances are crucial ingredients for the proper use of data assimilation methods and for an effective quantification of the a posteriori errors of the state estimation. Therefore, the estimation of these covariances often involves at first a chosen specification of the matrices, followed by an adaptive tuning to correct their initial structure. In this paper, we propose a flexible combination of existing covariance tuning algorithms, including both online and offline procedures. These algorithms are applied in a specific order such that the required assumption of current tuning algorithms are fulfilled, at least partially, by the application of the ones at the previous steps. We use our procedure to tackle the problem of a multivariate and spatially-distributed hydrological model based on a precipitation-flow simulator with real industrial data. The efficiency of different algorithmic schemes is compared using real data with both quantitative and qualitative analysis. Numerical results show that these proposed algorithmic schemes improve significantly short-range flow forecast. Among the several tuning methods tested, recently developed CUTE and PUB algorithms are in the lead both in terms of history matching and forecast. Keywords Data assimilation Error covariance Covariance modeling Hydrology Catchment modeling Flow forecast Precipitation-flow simulation
1 Introduction In order to improve the estimation of state variables, especially in dynamical systems, data assimilation (DA) techniques, originally developed for Numerical Weather Prediction (NWP) (Parrish and Derber 1992) and geosciences (Carrassi et al. 2018), have been widely applied in industrial problems, including hydrology (Houser et al. & Ange´lique Ponc¸ot [email protected] 1
EDF R&D, EDF Lab Paris-Saclay, 7 boulevard Gaspard Monge, Palaiseau 91120, France
2
LIMSI, CNRS, Universite´ Paris-Saclay, Campus Universitaire baˆt 507, Rue du Belve´de`re, Gif-sur-Yvette, Orsay Cedex 91405, France
3
Institut de Mathe´matiques de Toulouse, Universite´ Paul Sabatier, Toulouse, France
4
EDF R&D, EDF Lab Chatou, 6 quai Watier, Chatou 78400, France
2012), nuclear engineering (Gong et al. 2020b), biomedical applications (Rochoux et al. 2018), etc. The objectives of DA methods could be mainly divided into two groups:— field reconstruction and—parameter identification. The former aims at improving the estimation/forecast of a physical field of interest (e.g. temperature, velocity, usually multidimensional), while the latter consis
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