# 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.