Sampling strategies based on the Singular Value Decomposition for ocean analysis and forecast

Abstract. In this article we discuss some possible optimal sampling strategies for a simplified ocean model, used as a preliminary tool to understand the observation needs for real analysis and forecasting systems. Indeed, observations are mostly useful for improving the reliability of forecasting models, which require upstream an analysis model in which Data Assimilation techniques are used. In addition, observation networks and in particular in-situ networks are expensive and require careful positioning of a limited number of observation instruments. As in other literature studies, the Singular Value Decomposition has been adopted, which has many advantages, especially when we dispose of a variational assimilation method like the 4D-Var, also because the calculation of Singular Vectors and Singular Values is linked to the availability of tangent linear and adjoint models. SVD has been adopted here as a method for identifying areas where maximum error growth occurs, within which sampling gives particular advantages. However, a SVD-based sampling strategy may not be unique, and we need to introduce other criteria, based on the correlation between points, since the information observed on neighbouring points can be redundant. The criteria adopted are easily replicable in practical applications, and require rather standard studies to obtain prior information (for example, climatological and correlation studies), to be carried out in order to properly design observation networks.