On the estimation of circulation from density observations in coastal and shelf regions

This paper investigates aspects of determining coastal and shelf circulation using observa tions of the density field. The diagnostic method is first examined, and its associated barotropic indeterminacy and sensitivity to the joint effect of baroclinicity and bottom relief (JEBAR) are highlighted. Next, the dynamic consequences of adding an additional equation for the advec tion of density to the diagnostic equations are considered. This allows the input density field to adjust to the circulation, meaning that dynamically consistent density and velocity estimates can be obtained from density observations. It is argued that such an approach is useful in coastal and shelf regions to properly account for the role of JEBAR, and the control exerted on the circulation and density fields by buoyancy fluxes across open lateral boundaries found in limited-area models. An inverse method is investigated for estimating the buoyancy fluxes across the open boundaries into the model domain, using interior point observations of the density field (i.e. a boundary control approach). The methodology is explored using a limitedarea model of an idealized shelf. Numerical experiments are used to illustrate the issues arising in this joint estimation problem, for both barotropically and baroclinically dominated situations.