contributions / input by: klaus stephan, andreas rhodin, hendrik reich, werner wergen (dwd)

KENDA (Km-Scale Ensemble-based Data Assimilation)

COSMO General Meeting, Cracow, 15 – 19 Sept. 2008KENDA [email protected]

Contributions / input by:

Klaus Stephan, Andreas Rhodin, Hendrik Reich, Werner Wergen (DWD)

Daniel Leuenberger (MeteoSwiss)

Marek Lazanowicz (IMGW)

PP Kenda : Status Report [email protected]

Deutscher Wetterdienst, D-63067 Offenbach, Germany

• short introduction to LETKF (Hunt et al., 2007)

• general issues in the convective scale first experiments on trying to assess the importance of km-scale details versus larger-scale conditions in the IC

• implementation (task 2)

• DAQUA SIRF



k perturbed forecasts

ensemble mean forecast

(local *, inflated) transform

matrix

( - ) + =

( - ) + =

( - ) + =

( - ) + =

( - ) + =analysis mean

(computed only in S)perturbed analyses

0.9 Pert 1-0.1 Pert 2-0.1 Pert 3-0.1 Pert 4-0.1 Pert 5

LOCAL Ensemble Transform Kalman Filter (LETKF)(graphs by Neil Bowler, UK MetOffice)

flow-dependentbackground error covar.

analysis error covariance(computed only in S)

in the (k-dimensional) sub-space S spanned by background perturbations :(approx: implicitly linearise observation operator about the background mean ensemble)

explicit solution for minimisation of cost function (Hunt et al., 2007, Physica D)

)( wXxx bba

)()( iabbia wXxx

*: localisation: set of obs and hence wa(i) depends on location

Xb(i) = xbxb(i)



Task 1: General issues in the convective scale and evaluation of COSMO-DE-EPS

Purpose: Guides decision how resources will be spent on/ split betw. LETKF and SIR

(COSMO-NWS and universities); part of the learning process

main disadvantage of LETKF: assumes Gaussian error distributions

Task 1.1.A: investigate non-Gaussianity by means of O – B statistics (convective / larger scales, different forecast lead times): provides an upper limit estimate of the non-Gaussianity to deal with

talk by Daniel Leuenberger:Statistics of COSMO observation increments in view of data assimilation

Task 1.2: investigate non-Gaussianity by examining perturbations of very-short range(2009) forecasts from COSMO-DE-EPS

Task 1.1.C: assess influence of non-Gaussianity by examining balance (spin-up) of(2009) linear combinations of COSMO-DE-EPS forecast members

Task 1.4: Review on Hunt et al. implementation of LETKF(2009, by M. Tsyrulnikov)



LOCAL Ensemble Transform Kalman Filter (LETKF)

Task 1.1 D: assess importance of km-scale details versus larger-scale conditions in the IC

(do we have to analyse the small scales, or is it sufficient to analyse the large scales, as e.g incremental 4DVAR (ECMWF) would do ?)

Comparison: ‘IEU’: IC from interpolated COSMO-EU analysis of ass cycle (no LHN, nudging on coarse scales, same correlations scales in nudging)

‘IDE’: IC from (opr.) COSMO-DE analysis of ass cycle

(COSMO and LHN versions as operational at experiment time (old grid pt. search, old ref. precip))



00 UTC runs 06 UTC runs

ETS

FBI

IEU (coarse IC)IDE (fine-scale IC)

31.05. – 13.06.07: air-mass convection

0.1 mm




ETS

FBI


1.0 mm





ETS

FBI


0.1 mm





ETS

FBI


1.0 mm




ETS

FBI



14.06. – 20.07.07: frontal period

0.1 mm



model:2 x

6 – 18 h fcst=

24-h sum ofprecipitation

radar (24-h sum) IDE (fine-scale IC)IEU (coarse IC)

2 – 3 June 07

11 – 12 June 07



Task 1.1.D: assess importance of km-scale details

Results of comparison ‘IEU’ – ‘IDE’:

─ ‘IDE’ better (ETS with similar bias) than ‘IEU’ for 12- and 18-UTC runs, similar for 0- and 6-UTC runs.

─ ‘IDE’ clearly better in some cases

Want to: rule out influence of different soil moisture compare ‘IEU’ with:

─ COSMO-DE ass with LHN, soil moisture from C-EU

─ COSMO-DE ass without LHN, soil moisture from C-EU

RadarWith LHN Without LHN (dashed: determininistic)

Past experiments (Leuenberger):environment affects impact of fine-scaledetails in analysis from LHN



with LHNwithout LHN

many experiments: – different initial conditions (IDE, IEU, no LHN, no RS-q,…)– different lateral boundary cond. (opr (delayed), actual, analysis)

largest impact on daily cycle of precip. from variation of initial time of forecast !

OBS

9-UTC runs

– the closer the initial time is to 9 UTC, the less (increase of) convection in afternoon– not significantly affected by LHN, little affected by RS-humidity

model climate differs from ‘climate’ introduced by observations (nudging)

experiments: – without ass of upper-air T, (q)– without ass of ps (incl. T-correction)



Task 2: Technical implementation of an ensemble data assimilation framework / LETKF

LETKF

COSMO

read obs (NetCDF) + Grib analysis of ensemble member

compute obs–fg (obs. increm.) + QC (contains obs operator)

write NetCDF feedback files (obs + obs–fg + QC flags) + Grib files (model)ensemble

analysis step (LETKF) outside COSMO code ensemble of independent COSMO runs up to next analysis time separate analysis step code, LETKF included in 3DVAR code of DWD

read ensemble of NetCDF feedback files + ensemble of COSMO S-R forecast Grib files

perform LETKF (based on obs–fg values around each grid pt.,calculate transformation matrices and analysis (mean & pert.)(adapt: C-grid, specific var (w) (,efficiency))

write ensemble of COSMO S-R analysis Grib files + NetCDF feedback files with additional QC flags ( verif.)

exp.system



Task 2: Technical implementation of an ensemble data assimilation framework / LETKF

‘stat’-module: compute model (forecast) – obs for verification :

want to have capability of computing distance of model (ensemble member) to observationsthat have not been used previously in a COSMO run ( SIRF) need to include obs operators + QC in ‘stat’-module 2 options:

1. adapt separate program ‘lmstat’ (by NetCDF feedback / obs interface, QC)

2. adapt verification mode of 3DVar/LETKF package( include full COSMO observation operators with QC,

translate COSMO data structure into 3DVAR data structure and vice versa,extend flow control (e.g. reading several Grib files and temporal interpolation)

Advantages:

– COSMO obs operators available in 3DVAR/LETKF environment 3DVar/ EnKF approaches requiring 3DVar in principle applicable to COSMO LETKF for ICON will require COSMO obs operators in the future

– 1 common code for GME/ICON and COSMO to produce input for diagnostics / verif..

Disadvantages:

– more complex code for this diagnostic task

– possibly additional transformation from COSMO data structure into 3DVAR datastructure and vice versa required for new COSMO obs operators.



Task 3: Evaluate and optimise LETKF (needs to be detailed further)(after 2009)

Issues: Model perturbations, covariance inflation, localisation (multi-scale DA ?), convection initiation (warm bubbles, LHN), etc.

Resources required totally: 3



set up (G-) SIRF test with COPS period

time

Weighting +

Resam

pling

Guiding steps

Weighting +

Resam

pling

final weightingafter free forecast is computed

SREPS (ass.) SREPS (pred.)

radar / satellite / in-situ obs.

free forecast

… …

HRES

select bestmembers( ≤10 )

Set up standard and G-SIRF with and without standard data assimilation (MIUB, DWD)

• assess impact of conventional DA (LHN, PIB) on ensemble development (spread generation, keeping ensemble on track)

• implement optimal stepping to a new driving mesoscale ensemble

Evaluate classical and spatial (object oriented, fuzzy) metricsfor weighting mesoscale (SREPS) and km-scaleensemble members (DLR, MCH)• assess correlation of metrics betw. models of different res.• assess persistence of skill in different metrics



thank you for your attention



Sequential Importance Re-SamplingEnsemble members

PDF

h

Observation

Prior PDF 1. take an ensemble with a prior PDF

Obs. PDF 2. find the distance of each member to the obs (using any norm / H)

Posterior PDF 3. combine prior PDF with distance to obs to obtain posterior PDF

Members after re-sampling 4. construct new ensemble reflecting posterior PDF

Forecast from re-sampled members

5. integrate to next observation time

weighting of ensemble members by observations and redistribution according to posterior PDF

no modification of forecast fields

contributions / input by: klaus stephan, andreas rhodin, hendrik reich, werner wergen (dwd)

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