Dynamically constrained projection for subsurface current velocity

Abstract

An approach is described that projects surface current observations downward to obtain subsurface current structure consistent with the interior current dynamics. The projection approach is unrestricted by water depth. However, this study emphasizes well-mixed constant density flow in water depths appropriate for mid and outer shelf, where viscous and inertial processes are comparably important. By means of twin experiments, in which the projected current profiles are compared to the known simulated current profiles, it is shown that both the projection time step and the time domain affect the accuracy of the projection. At minimum, the time domain needs to span the dominant period of current oscillation while the time step resolves this oscillation. When both are achieved, the projected current profiles converge to the simulated profiles, and this convergence can be faster than that by assimilating surface observations to correct model spin-up from an inaccurately known initial condition. Furthermore, the projection is shown to be robust in the presence of data noise, and with appropriate weighting of the data constraints, the effect of noise on the projection accuracy can be minimized. In the present projection problem, the sea surface slope is assumed unknown and obtained together with the current profile. The use of variable eddy viscosity in velocity projection is illustrated as well with an iterative procedure.