Data Assimilation in strongly nonlinear geophysical systems
- When?
- Friday 12 March 2010, 16:00 to 17:00
- Where?
- 24AA04
- Open to:
- Staff, Students
- Speaker:
- Prof. Peter-Jan van Leeuwen (Reading)
Abstract: When simulating actual geophysical flows, inaccuracies in initial conditions, forcing fields and in the model equations themselves, both numerical and physical, lead to differences between the actual behavior of the system and the simulation. One way to address this problem is to try to incorporate the uncertainties in the simulations, e.g. in the form of probability density functions. The problem then is that for large-dimensional simulations in e.g. numerical weather prediction, the state space is so large, typically a million variables, that no computer is large enough to store these probability density functions.So, if we want to include these uncertainties we need an efficient representation of the pdf's.
However, just representing the uncertainties is not enough, we also want to reduce them. Direct observations of the system at hand is a possibility that we will explore here. Using Bayes Theorem on information transfer, we can update the pdf of the model with the pdf of the observations, in a procedure called data assimilation. Up to now, the use of Bayes Theorem has been simplified by assuming linear or linearized methods like the Kalman Filter and 4DVAR. In this contribution we will focus on efficient ways to do the fully nonlinear data assimilation problem using particle filters.
A particle filter based on exploiting the proposal density is used to solve the 'curse of dimensionality' that has hindered the use of particle filters in large-dimensional systems up to now. In short, the model equations obtain an extra term that pulls the model towards the future observations, and the weights are modified to take this change in model equations into account. Crucial is a modification to this scheme that ensures that the final weights are almost equal. The efficiency of this new method will be demonstrated in simple (up to 1000 dimensional) dynamical systems.
