Inverse Adjoint Estimation of Eddy Viscosity for Coastal Flow Models

Abstract

Tuning a three‐dimensional (3‐D) coastal circulation model for vertical eddy viscosities can be a laborious task. An efficient alternative is to use adjoint inverse estimation methods, and one such method is developed here. A cost functional that consists of two terms is formulated: The first describes the lack of fit between model results and available data, and the second measures the variance of the eddy viscosity with depth. This latter term has been introduced with a view to eliminate the instabilities commonly associated with inverse methods. Weights are used to vary the relative influence of each term. The “optimized” eddy viscosity estimate is obtained by a variational minimization of the functional. The procedure is tested using velocity data at the center of a rectangular sea domain. Wind and tidal forcing are considered along with known eddy viscosity profiles. The inverse model retrieves extremely good estimates of the eddy viscosities in all cases, even when data are sparse. The estimates are all smooth, and the method and the solutions exhibit no sign of instability.