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.
Deep Dive into 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.
1 Introduction.
It is now well known, even the best model is not sufficient to make a forecast. Any model depends on a number of parameters, it requires initial and boundary condition and other data that must be collected and used in the model. However, interpolating data from observational points to the model grid or smoothing of observed data is not an optimal way to incorporate these data in a model. Lorenz, in his pioneering work [Lorenz, (1963) ] has shown that a geophysical fluid is extremely sensitive to initial conditions. This fact requires Email address: kazan@imag.fr ( Eugene Kazantsev).
Preprint submitted to Ocean Modelling to bring the model and its initial data together, in order to work with the couple “model-data” and identify the optimal initial data for the model taking into account simultaneously the information contained in the observational data and in the equations of the model.
Optimal control methods [Lions, (1968) ] and perturbations theory [Marchuk, (1975) ] applied to the data assimilation technique ([Le Dimet, (1986) ], [Le Dimet and Talagrand, (1986) ]) show ways to do it. They allow to retrieve an optimal initial point for a given model from heterogeneous observation fields. Since early 1990’s many mathematical and geophysical teams have been involved in the development of the data assimilation strategies. One can cite many papers devoted to this problem, as in the domain of development of different techniques for the data assimilation such as nudging ( [Verron, (1992) ], [Verron and Holland, (1989) ], [Blayo et al., (1994) ], [Auroux and Blum, (2008) ]) ensemble methods and Kalman filtering ( [Bennett and Budgell, (1987) ], [Cohn, (1997) ], [D.T. Pham and Roubaud, (1998) ], [Brusdal et al., (2003) ]), variational data assimilation (3DVAR and 4DVAR) ([Le Dimet and Talagrand, (1986) ], [Lewis and Derber, (1985) ], [Thépaut and Courtier, (1991) ], [Navon et al., (1992) ]) and in the domain of its applications to the atmosphere and oceans.
These methods have proved capable of combining information from the model and the heterogeneous set of available observations. They have supported a remarkable increase in forecast accuracy (see, for example [Kalnay et al., (1990) ]) The success of the data assimilation stipulates the development of modern models together with methods allowing to integrate all available data in the model. Thus, in 1997 acknowledging the need for better ocean observations and ocean forecasts and with the scientific and technical opportunity that readily available satellite data had delivered, the Global Ocean Data Assimilation Experiment (GODAE) was initiated to lead the way in establishing global operational oceanography. Another example, the Mercator Ocean Group was founded in 2002 to set up an operational system for describing the state of the ocean, an integral part of our environment. Input for the Mercator system comes from ocean observations measured by satellites or in situ observations through measurements taken at sea. These measurements are assimilated by the analysis and forecasting model. The assimilation of observation data in a model is used to describe and forecast the state of the ocean for up to 14 days ahead of time.
However, majority of the data assimilation methods are now intended to identify and reconstruct an optimal initial point for the model. Since Lorenz [Lorenz, (1963) ], who has pointed out on the importance of precise knowledge of the starting point of the model, essentially the starting point is considered as the control parameter and the target of the data assimilation.
Of course, the model’s flow is extremely sensitive to its initial point. But, it is reasonable to suppose that an ocean model is also sensitive to many other parameters, like bottom topography, boundary conditions, forcing fields and friction coefficients. All these parameters and values are also extracted in some way from observational data, interpolated on the model’s grid and can neither be considered as exact, nor as optimal for the model. On the other hand, due to nonlinearity and intrinsic instability of model’s trajectory, its sensitivity to all these external parameters may also be exponential.
Numerous studies show strong dependence of the model’s flow on the boundary data ( [Verron and Blayo, (1996) ], [Adcroft and Marshall, (1998) ]), on the representation of the bottom topography ( [Holland, (1973) ], [Eby and Holloway, (1994) ], [Losch and Heimbach, (2007) ]), on the wind stress ( [Bryan et al., (1995) ], [Milliff et al., (1998) ]), to diffusivity coefficients [Bryan, (1987) ] and to fundamental parametrisations like Boussinesq and hydrostatic hypotheses [Losch et al., (2004) ].
Despite the bottom topography and the boundary configuration of the ocean are steady and can be measured with much better accuracy than the model’s initial state, it is not obvious how to represent them on the model’s grid because of the limited resolution. It is known
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