Seminar series
Date
Mon, 30 Oct 2006
14:15
14:15
Location
DH 3rd floor SR
Speaker
Dr Sarah Dance
Organisation
University of Reading
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.
/notices/events/abstracts/stochastic-analysis/mt06/dance.shtml