Turbulent viscosity optimized by data assimilation

As an alternative approach to classical turbulence modelling using a first or second order closure, the data assimilation method of optimal control is applied to estimate a time and space-dependent turbulent viscosity in a th ree-dimensional oceanic circulation model. The optimal control method, desc ribed for a 3-D primitive equation model, involves the minimization of a co st function that quantifies the discrepancies between the simulations and t he observations. An iterative algorithm is obtained via the adjoint model r esolution. In a first experiment, a k + L model is used to simulate the one -dimensional development of inertial oscillations resulting from a wind str ess at the sea surface and with the presence of a halocline. These results are used as synthetic observations to be assimilated. The turbulent viscosi ty is then recovered without the k + L closure, even with sparse and noisy observations. The problems of controllability and of the dimensions of the control are then discussed. A second experiment consists of a two-dimension al schematic simulation. A 2-D turbulent viscosity field is estimated from data on the initial and final states of a coastal upwelling event.