### Variational data assimilation for missing data interpolation in SST images

Sileye O. Ba, Thomas Corpetti, Bertrand Chapron, Ronan Fablet
2010 2010 IEEE International Geoscience and Remote Sensing Symposium
THE PROBLEM Because of the cloud coverage, sea surface temperature (SST) images produced from satellite recordings contain missing data. Usually, a preliminary step before any processing on the SST images is the missing data interpolation. Many algorithms have already been proposed for missing data interpolation. Up to our knowledge, most of the proposed methods are based on the Kalman Filtering or smoothing framework [1] . The Kalman filters are probabilistic methods to estimate the optimal
more » ... mate the optimal state sequence of a linear system defined by uni-modal Gaussian distributions. Together with the optimal states, covariance matrices representing confidence about the states are estimated. The main drawback of the Kalman filtering methods is that, because of the large dimensionality of SST images, estimating the covariance matrix of the states tends to be computationally expensive, as it requires the inversion of very large matrices. In this paper, we propose a method based on the variational data assimilation framework ([2]) to assimilate missing data in SST images. Mainly, variational data assimilation has two advantages with respect to Kalman filtering techniques. First, it naturally deals with nonlinear state dynamics, and observation operator. Secondly, it does not require the estimation of the covariance matrix to measure the confidence about the optimal states, thus reducing the computational cost of the estimation. We proposed two types of methods. The first type is based on the minimization of a cost function involving a term about the observations composed of the observed SST image with missing data, and a term about the regularity of the final estimate. The second type of method is based on the minimization of a cost function composed of a term involving an entire sequence of SST images and a term about the temporal regularity of the sequence of desired outputs. Section 2 presents the methodology we developed for missing data interpolation, Section 3 provides preliminary results. METHODOLOGY Static image assimilation