Sensitivity of a Barotropic Ocean Model to Perturbations of the Bottom Topography

In this paper, we look for an operator that describes the relationship between small errors in representation of the bottom topography in a barotropic ocean model and the model's solution. The study shows that the model's solution is very sensitive to topography perturbations in regions where the flow is turbulent. On the other hand, the flow exhibits low sensitivity in laminar regions. The quantitative measure of sensitivity is influenced essentially by the error growing time. At short time scales, the sensitivity exhibits the polynomial dependence on the error growing time. And in the long time limit, the dependence becomes exponential

Optimal boundary conditions at the staircase-shaped coastlines

A 4D-Var data assimilation technique is applied to the rectangular-box configuration of the NEMO in order to identify the optimal parametrization of boundary conditions at lateral boundaries. The case of the staircase-shaped coastlines is studied by rotating the model grid around the center of the box. It is shown that, in some cases, the formulation of the boundary conditions at the exact boundary leads to appearance of exponentially growing modes while optimal boundary conditions allow to correct the errors induced by the staircase-like appriximation of the coastline.Comment: Submitted to Ocean Dynamics. (27/02/2014

Boundary conditions control for a Shallow-Water model

A variational data assimilation technique was used to estimate optimal discretization of interpolation operators and derivatives in the nodes adjacent to the rigid boundary. Assimilation of artificially generated observational data in the shallow-water model in a square box and assimilation of real observations in the model of the Black sea are discussed. It is shown in both experiments that controlling the discretization of operators near a rigid boundary can bring the model solution closer to observations as in the assimilation window and beyond the window. This type of control allows also to improve climatic variability of the model.Comment: arXiv admin note: substantial text overlap with arXiv:1112.4293, arXiv:1112.3503, arXiv:0905.470

Sensitivity of the attractor of the barotropic ocean model to external influences: approach by unstable periodic orbits

International audienceA description of a deterministic chaotic system in terms of unstable periodic orbits (UPO) is used to develop a method of an a priori estimate of the sensitivity of statistical averages of the solution to small external influences. This method allows us to determine the forcing perturbation which maximizes the norm of the perturbation of a statistical moment of the solution on the attractor. The method was applied to the barotropic ocean model in order to determine the perturbation of the wind field which provides the greatest perturbation of the model's climate. The estimates of perturbations of the model's time mean solution and its mean variance were compared with directly calculated values. The comparison shows that some 20 UPOs is sufficient to realize this approach and to obtain a good accuracy

Data Assimilation and Sensitivity of the Black Sea Model to Parameters

An adjoint based technique is applied to a Shallow Water Model in order to estimate influence of the model's parameters on the solution. Among parameters the bottom topography, initial conditions, boundary conditions on rigid boundaries, viscosity coefficients and the amplitude of the wind stress tension are considered. Their influence is analyzed from different points of view. Two configurations have been analyzed: an academic case of the model in a square box and a more realistic case simulating Black Sea currents. It is shown in both experiments that the boundary conditions near a rigid boundary influence the most the solution. This fact points out the necessity to identify optimal boundary approximation during a model development.Comment: Hydrodynamical Modelling of the Black Sea (2011

Identification of Optimal Topography by Variational Data Assimilation

The use of data assimilation technique to identify optimal topography is discussed in frames of time-dependent motion governed by non-linear barotropic ocean model. Assimilation of artificially generated data allows to measure the influence of various error sources and to classify the impact of noise that is present in observational data and model parameters. The choice of assimilation window is discussed. Assimilating noisy data with longer windows provides higher accuracy of identified topography. The topography identified once by data assimilation can be successfully used for other model runs that start from other initial conditions and are situated in other parts of the model's attractor.Comment: Ocean Modelling (2008

Variational Data Assimilation for Optimizing Boundary Conditions in Ocean Models

International audienceThe review describes the development of ideas Gury Ivanovich Marchuk in the field of variational data assimilation for ocean models applied in particular in coupled models for long-range weather forecasts. Particular attention is paid to the optimization of boundary conditions on rigid boundaries. As idealized and realistic model configurations are considered. It is shown that the optimization allows us to determine the most sensitive model operators and bring the model solution closer to the assimilated data

Optimizing Lateral Boundary Conditions at Staircase-shaped Coastlines: Variational Approach

International audienceA 4D-Var data assimilation technique is applied to the rectangular-box configuration of the NEMO in order to identify the optimal parametrization of boundary conditions on lateral boundaries. The case of the staircase shaped coastlines is studied by rotating the model grid around the center of the box. It is shown that, in some cases, the formulation of the boundary conditions on the exact boundary leads to appearance of exponentially growing modes while optimal boundary conditions allow to correct the influence of the stair-case-like boundaries

Optimal Boundary Discretization by Variational Data Assimilation

International audienceVariational data assimilation technique applied to the identification of the optimal discretization of interpolation operators and derivatives in the nodes adjacent to the boundary of the domain is discussed in frames of the linear shallow water model. The advantage of controlling the discretization of operators near boundary rather than boundary conditions is shown. Assimilating data produced by the same model on a finer grid in a model on a coarse grid, we have shown that optimal discretization allows us to correct such errors of the numerical scheme as under-resolved boundary layer and wrong wave velocity

Parameterizing subgrid scale eddy effects in a shallow water model

Basing on the maximum entropy production principle, the influence of subgrid scales on the flow is presented as the harmonic dissipation accompanied by the backscattering of the dissipated energy. This parametrization is tested on the shallow water model in a square box. The closure problem is analyzed basing on the balance between the dissipation of energy and its backscattering. Results of this model on the coarse resolution grid are compared with the reference simulation at four times higher resolution. It is shown that the mean flow is correctly recovered, as well as variability properties, such as eddy kinetic energy fields and its spectrum