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[email protected] EnKF Angorithmic Questions 1
Ensemble Kalman Filter
Algorithmic Questions
KENDA Mini Workshop
Roland Potthast
Deutscher Wetterdienst, Offenbach, Germany
28.02.2014, LMU Munich
[email protected] 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.
[email protected] 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
[email protected] 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
[email protected] 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‘
[email protected] 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
[email protected] 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
[email protected] 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
[email protected] 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
![Combining analog method and ensemble data assimilation ......The Analog Ensemble Kalman Filter and Smoother 5 [7]. Here, we exploit the low-computational ensemble Kalman recursions](https://img.dokumen.tips/doc/110x75/60ba54885e0f0a256565f9d9/combining-analog-method-and-ensemble-data-assimilation-the-analog-ensemble.jpg)
