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.
Highlights
A universal but very challenging problem in earth science modelling and prediction is the characterisation of both conceptual and numerical model errors
Error covariances are explored by means of their Central Empirical Orthogonal Functions (Ceofs), leading to physical characterisation of the forecast error subspace in model state space
We have studied the penetration of the LPC current over the shelf of the Gulf of the Lion in the north-western Mediterranean
Summary
A universal but very challenging problem in earth science modelling and prediction is the characterisation of both conceptual and numerical model errors. This is true concerning both Ensemble assimilation techniques and Ensemble predictability and observability studies Even if they do not give a complete picture of the forecast error statistics in non-linear cases, the first- and second-order moments are yet giving the “mean forecast” path and the associated uncertainties in model state space. The study of the first- to fourth-order moments of the forecast errors gives both focus and limitations to this paper Under such limitations, error covariances are explored by means of their Central Empirical Orthogonal Functions (Ceofs), leading to physical characterisation of the forecast error subspace in model state space. Error covariances are explored by means of their Central Empirical Orthogonal Functions (Ceofs), leading to physical characterisation of the forecast error subspace in model state space This qualitative and quantitative error characterisation can help reducing the order of an assimilation problem, a suitable control subspace being chosen within this forecast error subspace.
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