Ensemble Kalman Filter Algorithmic Questions3_potthast... · EnKF Angorithmic Questions...

Roland.potthast@dwd.de EnKF Angorithmic Questions 1

Ensemble Kalman Filter

Algorithmic Questions

KENDA Mini Workshop

Roland Potthast

Deutscher Wetterdienst, Offenbach, Germany

28.02.2014, LMU Munich

Roland.potthast@dwd.de EnKF Angorithmic Questions 2

Contents (Speed Dating)

1. EnKF Migration Concept and BACY Testbed

Schraff, Reich, Rhodin, Cress, Anlauf, Köpken-

Watts, Faulwetter, Stiller, …

2. Adaptive Localization – Analytical Approach

Perianez, Reich, P. (PhD Uni Reading)

3. Multistep Analysis for EnKF

Rhodin, Perianez, Reich, P. (DWD)

4. Transformed Localization

Rhodin (his talk); Nadeem and P. – PhD Project

Uni Göttingen

5. Analysis of a Multi-Scale Localization

Perianez, Reich, P.

6. Analysis of Retrieval Assimilation, Tomography

+ EDA

Altuntac and P. – PhD Project with Uni Göttingen

7. Nonlinearity, Zero Gradient and EnKF

Schomburg, Schraff, Perianez, P.

Roland.potthast@dwd.de EnKF Angorithmic Questions 3

1. BACY Basic Cycling Testbed

Roland.potthast@dwd.de EnKF Angorithmic Questions 4

• The optimal localization radius

depends on

– The density of observations

– The observation error

– The background covariances

– The number of ensemble

members

• Analytical estimates of the

assimilation error

• Analytical formula to calculate the

localization radius

2. Adaptive Localization – Analytical Approach

Publications in Progress: Perianez, Reich, P. • Adaptive Localization: Formula with Instructive Examples

• Estimate Localization Error: mathematical paper

Roland.potthast@dwd.de EnKF Angorithmic Questions 5

• Carry out the analysis in several

steps = successive assimilation or

multistep analysis

• Equivalence of this approach based

on Bayes’ Formula

• B Matrix stays the same after

multistep analysis

• Equivalence of Analysis Ensemble

under certain conditions (in general

the analysis ensemble is changed)

3. Multistep Analysis

Work/Publications in Progress: Perianez, Reich, Rhodin, P. • Multistep Analysis: basic mathematics paper being finished

• Application in NWP: algorithmical issues implemented in KENDA

Roland.potthast@dwd.de EnKF Angorithmic Questions 6

• Employ a transformation of the state

space or/and the observation space

before localization

• Algebraic Properties of this

approach

• Efficient localization of B Matrix via

wavelet space transformation

• Transformation of Nonlocal

Operators (e.g. Radiances)

4. Transformed Localization

Work/Publications in Progress: Rhodin; Aamir Nadeem and P. • Transformed Localization: basic mathematics paper in progress

• Application to Localization of B Matrix: implementation in progress

• Application to NWP: radiance assimilation in a second step

U H x = U y

U H T T-1 x = U y

Transformed equation

H‘ x‘ = y‘

Roland.potthast@dwd.de EnKF Angorithmic Questions 7

• Analysis of

multi-scale

localization with

error estimates

• Showing

improvement for

instructive

Examples

• Application to

ENKF for NWP

5. Analysis of Multi-Scale Localization

Work/Publications in Progress: • Analysis of Multiscale Localization: basic mathematics paper in

progress

Roland.potthast@dwd.de EnKF Angorithmic Questions 8

• Investigate the assimilation of

retrievals in contrast to direct

assimilation of the observations

• Equivalence of this approach based

on Bayes’ Formula

• Equivalence for full EnKF

• Instructive negative Examples:

what goes wrong with retrievals

assimilation

• GPS/GNSS Tomography as a key

application

6. Retrieval Assimilation and Tomography

Publications in Progress: Altuntac and P.; Bender et al • Retrieval Assimilation: basic mathematics paper being finished

• Direct GNSS Tomography: KENDA implementation by Bender

• GNSS Tomography: Total Variation Regularization by Altuntac

Roland.potthast@dwd.de EnKF Angorithmic Questions 9

Basic Questions:

• Analyse the treatment of

strong nonlinearities in the

EnKF: linear method right?

• Zero Gradient Question: is it

a “problem”?

• Examples: cloudy radiances,

positive quantities, …

• Cloud Products and the right

observation operator?

• Non-local Norms and the

stochasticity of processes

7. Nonlinearity, Zero Gradient and EnKF

Work/Publications in Progress: Schomburg, Schraff, P., Perianez • Seviri Cloud Products in NWP: see Annikas talk

• Seviri direct radiances: Perianez, Schomburg, Schraff, Otkin, P., …

RTTOV

with

opaque

cloud at

height h

Roland.potthast@dwd.de EnKF Angorithmic Questions 10

Many Thanks!

Roland.potthast@dwd.de EnKF Angorithmic Questions 11

(1) 1st Step: ICON replaces GME

(2) Refined Region over Europe

2nd step: ICON replaces COSMO-EU

(3) VarEnKF replaces 3dVAR

(4) KENDA replaces Nudging for Cosmo-DE

(5) 3rd step: ICON replaces COSMO-DE

1. Background Migration Concept

Roland.potthast@dwd.de EnKF Angorithmic Questions 12

VarEnKF Migration

Roland.potthast@dwd.de EnKF Angorithmic Questions 13

KENDA Migration