Mon, 11 Feb 2008
14:45
Oxford-Man Institute

Stochastic competition models from ecology to society

Prof. Yuri Kondratiev
(University of Reading)
Abstract

We describe individual based continuous models of random evolutions and discuss some effects of competitions in these models. The range of applications includes models of spatial ecology, genetic mutation-selection models and particular socio-economic systems. The main aim of our presentation is to establish links between local characteristics of considered models and their macroscopic behaviour

Mon, 30 Oct 2006
14:15
DH 3rd floor SR

The ensemble Kalman filter: a state estimation method for hazardous weather prediction

Dr Sarah Dance
(University of Reading)
Abstract
Numerical weather prediction models require an estimate of the current state of the atmosphere as an initial condition. Observations only provide partial information, so they are usually combined with prior information, in a process called data assimilation. The dynamics of hazardous weather such as storms is very nonlinear, with only a short predictability timescale, thus it is important to use a nonlinear, probabilistic filtering method to provide the initial conditions. 

Unfortunately, the state space is very large (about 107 variables) so approximations have to be made.

 The Ensemble Kalman filter (EnKF) is a quasi-linear filter that has recently been proposed in the meteorological and oceanographic literature to solve this problem. The filter uses a forecast ensemble (a Monte Carlo sample) to estimate the prior statistics. In this talk we will describe the EnKF framework and some of its strengths and weaknesses. In particular we will demonstrate a new result that not all filters of this type bear the desired relationship to the forecast ensemble: there can be a systematic bias in the analysis ensemble mean and consequently an accompanying shortfall in the spread of the analysis ensemble as expressed by the ensemble covariance matrix. This points to the need for a restricted version of the notion of an EnKF. We have established a set of necessary and sufficient conditions for the scheme to be unbiased. Whilst these conditions are not a cure-all and cannot deal with independent sources of bias such as modelling errors, they should be useful to designers of EnKFs in the future.

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