Representer-based analyses in the coastal upwelling system

The impact of surface velocity and SSH data assimilated in a model of wind-driven upwelling over the shelf is studied using representer and observational array mode analyses and twin experiments, utilizing new tangent linear (TL) and adjoint (ADJ) codes. Bathymetry, forcing, and initial conditions are assumed to be alongshore uniform reducing the problem to classical two-dimensional. The model error is attributed to uncertainty in the surface wind stress. The representers, analyzed in cross-shore sections, show how assimilated observations provide corrections to the wind stress and circulation fields, and give information on the structure of the multivariate prior model error covariance. Since these error covariance fields satisfy the dynamics of the TL model, they maintain dominant balances (Ekman transport, geostrophy, thermal wind). Solutions computed over a flat bottom are qualitatively similar to a known analytical solution. Representers obtained with long cross-shore decorrelation scale for the wind stress errors l_x (compared to the distance to coast) exhibit the classical upwelling structure. Solutions obtained with much smaller l_x show structure associated with Ekman pumping, and are nearly singular if l_x is smaller than the grid resolution. The zones of maximum influence of observations are sensitive to the background ocean conditions and are not necessarily centered around the observation locations. Array mode analysis is utilized to obtain model structures (combinations of representers) that are most stably observed by a given array. This analysis reveals that for realistic measurement errors and observational configurations, surface velocities will be more effective than SSH in providing correction to the wind stress on the scales of tens of km. In the DA test with synthetic observations, the prior nonlinear solution is obtained with spatially uniform alongshore wind stress and the true solution with the wind stress sharply reduced inshore of the upwelling front, simulating expected ocean–atmosphere interaction. Assimilation of daily-averaged alongshore surface currents provides improvement to both the wind stress and circulation fields.