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Jean-Michel Brankart and Pierre Brasseur

Abstract

To study the Mediterranean general circulation, there is a constant need for reliable interpretations of available hydrological observations. Optimal data analyses (in the probabilistic point of view of objective analysis) are fulfilled using an original finite-element technique to minimize the variational principle of the spline procedure. Anyway, a prior statistical knowledge of the problem is required to adapt the optimization criterion to the purpose of this study and to the particular features of the system. The main goal of this paper is to show how the cross-validation methodology can be used to deduct statistical estimators of this information only from the dataset. The authors also give theoretical and/or numerical evidence that modified estimators–-using generalized cross-validation or sampling algorithms–-are interesting in the analysis optimization process. Finally, results obtained by the application of these methods to a Mediterranean historical database and their comparison with those provided by other techniques show the usefulness and the reliability of the method.

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Cyril Germineaud, Jean-Michel Brankart, and Pierre Brasseur

Abstract

A cross-validation algorithm is developed to perform probabilistic observing system simulation experiments (OSSEs). The use of a probability distribution of “true” states is considered rather than a single “truth” using a cross-validation algorithm in which each member of an ensemble simulation is alternatively used as the “truth” and to simulate synthetic observation data that reflect the observing system to be evaluated. The other available members are used to produce an updated ensemble by assimilating the specific data, while a probabilistic evaluation of the observation impacts is obtained using a comprehensive set of verification skill scores. To showcase this new type of OSSE studies with tractable numerical costs, a simple biogeochemical application under the Horizon 2020 AtlantOS project is presented for a single assimilation time step, in order to investigate the value of adding biogeochemical (BGC)-Argo floats to the existing satellite ocean color observations. Further experiments must be performed in time as well for a rigorous and effective evaluation of the BGC-Argo network design, though some evidence from this preliminary work suggests that assimilating chlorophyll data from a BGC-Argo array of 1000 floats can provide additional error reduction at the surface, where the use of spatial ocean color data is limited (due to cloudy conditions), as well at depths ranging from 50 to 150 m.

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Giovanni Abdelnur Ruggiero, Emmanuel Cosme, Jean-Michel Brankart, Julien Le Sommer, and Clement Ubelmann

Abstract

Most data assimilation algorithms require the inverse of the covariance matrix of the observation errors. In practical applications, the cost of computing this inverse matrix with spatially correlated observation errors is prohibitive. Common practices are therefore to subsample or combine the observations so that the errors of the assimilated observations can be considered uncorrelated. As a consequence, a large fraction of the available observational information is not used in practical applications. In this study, a method is developed to account for the correlations of the errors that will be present in the wide-swath sea surface height measurements, for example, the Surface Water and Ocean Topography (SWOT) mission. It basically consists of the transformation of the observation vector so that the inverse of the corresponding covariance matrix can be replaced by a diagonal matrix, thus allowing to genuinely take into account errors that are spatially correlated in physical space. Numerical experiments of ensemble Kalman filter analysis of SWOT-like observations are conducted with three different observation error covariance matrices. Results suggest that the proposed method provides an effective way to account for error correlations in the assimilation of the future SWOT data. The transformation of the observation vector proposed herein yields both a significant reduction of the root-mean-square errors and a good consistency between the filter analysis error statistics and the true error statistics.

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Sergey Skachko, Jean-Michel Brankart, Frédéric Castruccio, Pierre Brasseur, and Jacques Verron

Abstract

Bulk formulations parameterizing turbulent air–sea fluxes remain among the main sources of error in present-day ocean models. The objective of this study is to investigate the possibility of estimating the turbulent bulk exchange coefficients using sequential data assimilation. It is expected that existing ocean assimilation systems can use this method to improve the air–sea fluxes and produce more realistic forecasts of the thermohaline characteristics of the mixed layer. The method involves augmenting the control vector of the assimilation scheme using the model parameters that are to be controlled. The focus of this research is on estimating two bulk coefficients that drive the sensible heat flux, the latent heat flux, and the evaporation flux of a global ocean model, by assimilating temperature and salinity profiles using horizontal and temporal samplings similar to those to be provided by the Argo float system. The results of twin experiments show that the method is able to correctly estimate the large-scale variations in the bulk parameters, leading to a significant improvement in the atmospheric forcing applied to the ocean model.

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