Thu, 02 Nov 2006
16:30
DH 1st floor SR

Granular Mechanics

George Mullenger
(University of Canterbury, NZ)
Thu, 02 Nov 2006

14:00 - 15:00
Comlab

Multivariate highly oscillatory integration

Mr Sheehan Olver
(University of Cambridge)
Abstract

The aim of this talk is to describe several methods for numerically approximating

the integral of a multivariate highly oscillatory function. We begin with a review

of the asymptotic and Filon-type methods developed by Iserles and Nørsett. Using a

method developed by Levin as a point of departure we will construct a new method that

uses the same information as the Filon-type method, and obtains the same asymptotic

order, while not requiring moments. This allows us to integrate over nonsimplicial

domains, and with complicated oscillators.

Tue, 31 Oct 2006
17:00
L1

Phan theory

Prof. S. Shpectorov
(University of Birmingham)
Mon, 30 Oct 2006
15:45
L3

Topology of moduli spaces I

Ulrike Tillmann
Abstract

1. Introduction and survey of the cohomological results

This will be a relatively gentle introduction to the topologist's point of view of Riemann's moduli space followed by a description of its rational and torsion cohomology for large genus.

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.

 /notices/events/abstracts/stochastic-analysis/mt06/dance.shtml