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Accounting for correlated observation error in variational ocean data assimilation: application to altimeter data

ED SDU2E (Sciences de l’Univers, de l’Environnement, et de l’Espace)

https://youtube.com/live/_jxSAgNPjDM?feature=share

Data assimilation involves estimating the state of a system by combining observations from various sources with a background estimate of the state. For geophysical systems such as the ocean, the state would be defined as the values of physical variables (such as temperature or salinity) at every point on a three-dimensional ocean model grid. If we were trying to estimate the state of the ocean on a given day, the background state would typically be a forecast initiated the day before, which would then be corrected with the latest observations. Observations of the system can come from heterogeneous sources, such as satellites and in situ networks. The resulting corrected state of the system is called the analysis, and is typically used as the model initial condition for producing the forecast for the next day.

In order for the analysis to be an accurate representation of the state of the system, we need to have knowledge of the accuracy of the background state and observations. Both are affected by errors, which we assume can be described statistically by their covariance matrices: B for the background error, and R for the observation error. Variational data assimilation is a class of data assimilation methods where the analysis is obtained by minimising iteratively a cost function measuring the fit of a candidate state of the system to both the background and observations, with weights defined by B−1 and R−1. However, most of the complexity of data assimilation pertains to adapting these basic methods to the constraints of the real system, in order to obtain methods that are practical for real applications. In Numerical Weather Prediction, the background state of the system can often represent billions of degrees of freedom, which need to be combined with millions of observations every day.

In such a system, the explicit construction of the matrices B and R is too expensive to be done in practice. The construction of these matrices can be avoided using the iterative approaches of variational data assimilation, which only require operators that represent matrix-vectors products.

The assumption of uncorrelated observation errors (diagonal R) is commonly made to simplify the inverse covariance operator R−1, which is required by many minimisation algorithms. However, this assumption is problematic when dealing with certain observation types, notably high-resolution satellite data. Neglecting observation error correlations during assimilation often results in suboptimal analyses, where observations tend to be overfit at large spatial scales and underfit at small spatial scales. To address this issue, we have developed an observation error correlation model based on a diffusion operator for the ocean data assimilation system NEMOVAR. Diffusion operators — initially designed for modelling correlations in background error — offer a cost-effective and flexible framework for modelling R−1 (and R itself) with unstructured data. While accounting for observation error correlations should improve the accuracy of the solution, it also affects the convergence rate of the minimisation algorithms used to approximate the solution. In operational applications, where the minimisation process is usually truncated before full convergence, even correctly accounted for observation error correlations might compromise the accuracy of the analysis. Through analytical and numerical results, we explore the influence of the observation error correlations on both the sensitivity and convergence rate of variational data assimilation algorithms. In particular, we provide insight into how the choice of an observation error correlation model must reflect a balance between computational efficiency and accuracy.

Jury

M. Andrew MOORE	University of California, Santa Cruz	Reviewer
Mme Sarah DANCE	University of Reading	Reviewer
M. Arthur VIDARD	INRIA	Examiner
Mme Nadia FOURRIÉ	CNRM	Examiner
M. Massimo BONAVITA	European Centre for Medium-Range Weather Forecasts	Examiner
M. Anthony WEAVER	CERFACS / CECI UMR 5318	PhD supervisor
M. Oliver GUILLET	CNRM	PhD Co-supervisor
Mme Selime GÜROL	CERFACS/CECI UMR 5318	PhD Co-supervisor