**Nonlinear Data Assimilation for Satellite Observations in High-Dimensional Models**
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Ades, Melanie ^{1}; van Leeuwen, Peter Jan^{2}
^{1}Reading University, UNITED KINGDOM; ^{2}University of Reading, UNITED KINGDOM
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Observations of the earth are incredibly important for the numerical prediction of environmental processes. The information gained from a diverse range of instruments is combined with numerical model information on the environmental process, to provide initial conditions for forecasting. There is much debate over how best to combine the two sources of information, however most current schemes rely on certain assumptions being made. Potentially, the two most significant assumptions are that the numerical model and the observation operator are linear or close to linear. The observation operator gives the relationship between what is observed by instruments such as satellites and the variables of the numerical models. As technological advances allow for increasingly higher resolution models and more complex observations, these linear assumptions become less justifiable. For example the relationship between the radiances observed by satellites and the temperature and relative humidity used in numerical weather prediction models is clearly not straightforward. Hence new schemes are required for combining the information from the observations and numerical model under less restrictive assumptions.

Particle filters are a class of methods that make no assumptions about either the linearity of the model or the observation operator. They work by representing the probability density function (pdf) of the information coming from the numerical model by an ensemble of particles or model states. The particles are then weighted by their proximity to the observations to give the pdf of the model state given the observations. Although they make no linear assumptions, their applicability for the numerical prediction of geophysical systems is limited by the high dimension of most environmental processes. In high dimensions many more particles are required, in order to gain useful combined information from the observations and numerical model, than there is currently the computing power to run. The equivalent weights particle filter is an adaptation to the basic particle filter designed to reduce the number of particles required and it has been shown to be extremely effective in a 65,500 variable Barotropic Vorticity model.

In this presentation we look at the performance of the scheme in a high dimensional, single layer Primitive Equation model that represents the active layer in an idealised ocean. The parameters have been chosen to ensure as realistic a representation of the ocean as possible since the ultimate aim is to use the scheme for actual geophysical systems. We look at how well the equivalent weights particle filter is able to capture the evolution of the system in twin experiments. In particular we study how this is effected by using realistic satellite sampling strategies to be able to judge their effectiveness for ocean nowcasting and forecasting. This work forms part of an ESA Data Assimilation project.