Particle Filters for Numerical Weather Prediction Peter Jan van - - PowerPoint PPT Presentation

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Apr 25, 2023 140 likes •297 views

Particle Filters for Numerical Weather Prediction Peter Jan van Leeuwen + PF group (Mel Ades, Javier Amezcua, Phil Browne, David Livings, Alison Fowler, Matt Lang, Michael Goodliff) Data-Assimilation Research Centre DARC University of

SLIDE 1

Particle Filters for Numerical Weather Prediction

Peter Jan van Leeuwen + PF group

(Mel Ades, Javier Amezcua, Phil Browne, David Livings, Alison Fowler, Matt Lang, Michael Goodliff)

Data-Assimilation Research Centre DARC University of Reading, UK

SLIDE 2

What is a particle filter?

Write the prior pdf as
Then the posterior pdf is given as

with the weights wi related to the distance to the observations and the model equations

SLIDE 3

Curse of dimensionality

The weights are degenerate with a large number of

bservations: one particle gets weight 1, rest weight 0.

This problem has largely been solved:

Particle filters have enormous freedom via proposal density:
Relaxation to observations between observation times
E.g. Equivalent-Weights Particle Filter is not degenerate by

construction

ONLY APPROXIMATION IS FINITE ENSEMBLE SIZE
Example: 65,000 dimensional highly nonlinear barotropic

vorticity model, observations every 50 timesteps, 32 particles

SLIDE 4

Equivalent-Weights Particle Filter

Force model towards observations between
bservation times
Ensure that weights are equivalent at
bservation times:

t=0 t=50 t=100 y y

SLIDE 5

Fully observed system

SLIDE 6

Half-observed system

Observe 1/16 of the grid points within the red square

nly.

SLIDE 7

The relaxation step

b=0.05 b=0.4

SLIDE 8

The Equivalent-weights step

SLIDE 9

Convergence of the pdf

32 particles 128 particles 512 particles

SLIDE 10

Rank histograms

Full state observed

SLIDE 11

Between observations

Relaxation (nudging)
4DVar on each particle: Initial condition fixed

Model error essential

X X X X

SLIDE 12

Why Particle Filters?

PF solve fully nonlinear data-assimilation problem
No state covariances !!!

4DVar: B matrix, EnKF’s localisation+inflation

Model errors essential, so we have to work on them:

natural way to model improvement

Particles are independent random draws from

posterior pdf

Perfect for forecasting!

SLIDE 13

Conclusions + Outlook

Particle filters do not need state covariances.
Proposal density allows enormous freedom
We can solve the curse-of-dimensionality problem by

construction, e.g. Equivalent-weights scheme

Other efficient schemes are being derived.
We have to work on model error covariances
We are working on applications to ECMWF system and

HadCM3 climate model

SLIDE 14