## Abstract

An idealized, linear model of the coastal ocean is used to assess the domain of influence of surface type data, in particular how much information such data contain about the ocean state at depth and how such information may be retrieved. The ultimate objective is to assess the feasibility of assimilation of real surface current data, obtained from coastal radar measurements, into more realistic dynamical models. The linear model is used here with a variational inverse assimilation scheme, which is optimal in the sense that under appropriate assumptions about the errors, the maximum possible information is retrieved from the surface data. A comparison is made between strongly and weakly constrained variational formulations. The use of a linear model permits significant analytic progress. Analysis is presented for the solution of the inverse problem by expanding in terms of representer functions, greatly reducing the dimension of the solution space without compromising the optimization. The representer functions also provide important information about the domain of influence of each data point, about optimal location and resolution of the data points, about the error statistics of the inverse solution itself, and how that depends upon the error statistics of the data and of the model. Finally, twin experiments illustrate how well a known ocean state can be reconstructed from sampled data. Consideration of the statistics of an ensemble of such twin experiments provides insight into the dependence of the inverse solution on the choice of weights, on the data error, and on the sampling resolution.

*Corresponding author address:* Dr. John S. Allen, College of Oceanographic and Atmospheric Sciences, Oregon State University, 104 Ocean Admin. Bldg., Corvallis, OR 97331-5503.