Ensemble Kalman Filter Algorithmic Questions
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1 Ensemble Kalman Filter Algorithmic Questions KENDA Mini Workshop Roland Potthast Deutscher Wetterdienst, Offenbach, Germany , LMU Munich EnKF Angorithmic Questions 1
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. EnKF Angorithmic Questions Roland.potthast@dwd.de 2
3 1. BACY Basic Cycling Testbed EnKF Angorithmic Questions 3
4 2. Adaptive Localization Analytical Approach 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 Publications in Progress: Perianez, Reich, P. Adaptive Localization: Formula with Instructive Examples Estimate Localization Error: mathematical paper EnKF Angorithmic Questions 4
5 3. Multistep Analysis 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) Work/Publications in Progress: Perianez, Reich, Rhodin, P. Multistep Analysis: basic mathematics paper being finished Application in NWP: algorithmical issues implemented in KENDA EnKF Angorithmic Questions Roland.potthast@dwd.de 5
6 4. Transformed Localization 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) U H x = U y U H T T -1 x = U y Transformed equation H x = y 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 EnKF Angorithmic Questions Roland.potthast@dwd.de 6
7 5. Analysis of Multi-Scale Localization Analysis of multi-scale localization with error estimates Showing improvement for instructive Examples Application to ENKF for NWP Work/Publications in Progress: Analysis of Multiscale Localization: basic mathematics paper in progress EnKF Angorithmic Questions 7
8 6. Retrieval Assimilation and Tomography 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 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 EnKF Angorithmic Questions Roland.potthast@dwd.de 8
9 7. Nonlinearity, Zero Gradient and EnKF 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 RTTOV with opaque cloud at height h Work/Publications in Progress: Schomburg, Schraff, P., Perianez Seviri Cloud Products in NWP: see Annikas talk Seviri direct radiances: Perianez, Schomburg, Schraff, Otkin, P., EnKF Angorithmic Questions Roland.potthast@dwd.de 9
10 Many Thanks! EnKF Angorithmic Questions 10
11 1. Background Migration Concept (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 EnKF Angorithmic Questions 11
12 VarEnKF Migration EnKF Angorithmic Questions 12
13 KENDA Migration EnKF Angorithmic Questions 13
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