An Adjoint Sensitivity Study of Buoyancy- and Wind-Driven Circulation on the New Jersey Inner Shelf

Adjoint sensitivity analysis is used to study the New York Bight circulation for three idealized situations: an unforced buoyant river plume, and upwelling and downwelling wind forcing. A derivation of adjoint sensitivity is presented that clarifies how the method simultaneously addresses initial, boundary, and forcing sensitivities. Considerations of interpretation and appropriate definitions of sensitivity scalar indices are discussed. The adjoint method identifies the oceanic conditions and forcing that are ‘‘dynamically upstream’’ to a region or feature of interest, as well as the relative roles of the prior ocean state, forcing, and dynamical influences. To illustrate the method, which is quite general, the authors consider coastal sea surface temperature (SST) variability and define the adjoint scalar index as the temporal–spatial mean squared SST anomaly on a segment of the New Jersey coast at the conclusion of a 3-day period. In the absence of wind, surface temperature advection dominates the SST anomaly with two sources of surface water identified. Downwelling winds amplify upstream advective influence. Sensitivity to temperature is separated into direct advection and the dynamic effect on density stratification and mixing. For upwelling conditions, this decomposition shows that coastal SST is controlled by both advection from the south and subsurface, but above the 5-m depth, and temperature-related density stratification between 5 and 15 m to 10 km offshore. By identifying the timing and location of ocean conditions crucial to subsequent prediction of specific circulation features, the adjoint sensitivity method has application to quantitative evaluation of observational sampling strategies.