Marie-Claude Bourque

A Wind-Driven Upwelling System Analyzed with an Adjoint Model

Thesis Approved July 1993

Satellite images of the Gulf of St-Lawrence show a persistent band of cold water along the north coast of Jacques-Cartier Strait in the summer. A possible explanation for this feature is that bottom water is being upwelled by the predominantly north-westerly, or alongshore, winds. This area of the Gulf of St-Lawrence is important for fisheries and wind-driven upwelling processes would be expected to influence the local ecosystem dynamics. This thesis tests this hypothesis by comparing wind stress and upwelling velocity time series.

Two approaches were used to infer the upwelling velocity from moored thermistor temperature records. The first method is a simple regression model. The model dynamics assume that temporal variations in temperature are caused by vertical advection. The second method is a data assimilation technique based on the adjoint method. A review of the adjoint method is included, first for the general case and then in a more specific way for a simple upwelling model. Five different test cases were assessed, each varying slightly in the dynamics or the vertical grid. Along with solving for the vertical velocity, the adjoint model resolved the vertical diffusion and a residual term accounting for horizontal exchanges and local heating.

The results from both the regression model and the adjoint model support the upwelling hypothesis. For periods longer than 1.5 days, corresponding to periods over which storms occur, the coherence between the wind stress and the vertical velocity was found to be 0.7, which exceeds the 5 percent significance level. The cross- shore length scale on which upwelling occurs, L, was inferred from the transfer function between the upwelling velocity, w, and the wind stress, tau. Using the upwelling model, tau = w/rho f L, the length scale was found to be 6 to 10 km. Because of its similarity to the Rossby radius, this further supports the upwelling hypothesis.