Optimal observations for variational data assimilation

An important part of ocean state estimation is the design of an observing system that allows for the efficient study of climate related questions in the ocean. A solution to the design problem is presented here in terms of optimal observations that emerge as singular vectors of the modified data resolution matrix. The actual computation is feasible only for scalar quantities and in the limit of large observational errors. Identical twin experiments performed in the framework of a 18 North Atlantic primitive equation model demonstrate that such optimal observations, when applied to determining the heat transport across the Greenland - Scotland ridge, perform significantly better than traditional section data. On seasonal to interannual time scales, optimal observations are located primarily along the continental shelf and information about heat transport, wind stress, and stratification is being communicated through boundary waves and advective processes. On time scales of about 1 month, sea surface height observations appear to be more efficient in reconstructing the cross-ridge heat transport than hydrographic observations. Optimal observations also provide a tool for understanding changes of ocean state associated with anomalies of integral quantities such as meridional heat transport.