Space-time structure and dynamics of the forecast error in a coastal circulation model of the Gulf of Lions

Abstract

The probability density function (pdf) of forecast errors due to several possible error sources is investigated in a coastal ocean model driven by the atmosphere and a larger-scale ocean solution using an Ensemble (Monte Carlo) technique. An original method to generate dynamically adjusted perturbation of the slope current is proposed. The model is a high-resolution 3D primitive equation model resolving topographic interactions, river runoff and wind forcing. The Monte Carlo approach deals with model and observation errors in a natural way. It is particularly well-adapted to coastal non-linear studies. Indeed higher-order moments are implicitly retained in the covariance equation. Statistical assumptions are made on the uncertainties related to the various forcings (wind stress, open boundary conditions, etc.), to the initial state and to other model parameters, and randomly perturbed forecasts are carried out in accordance with the a priori error pdf. The evolution of these errors is then traced in space and time and the a posteriori error pdf can be explored. Third- and fourth-order moments of the pdf are computed to evaluate the normal or Gaussian behaviour of the distribution. The calculation of Central Empirical Orthogonal Functions (Ceofs) of the forecast Ensemble covariances eventually leads to a physical description of the model forecast error subspace in model state space. The time evolution of the projection of the Reference forecast onto the first Ceofs clearly shows the existence of specific model regimes associated to particular forcing conditions. The Ceofs basis is also an interesting candidate to define the Reduced Control Subspace for assimilation and in particular to explore transitions in model state space. We applied the above methodology to study the penetration of the Liguro-Provençal Catalan Current over the shelf of the Gulf of Lions in north-western Mediterranean together with the discharge of the Rhône river. This region is indeed well-known for its intense topographic and atmospheric forcings.