1. PP Kenda : Status Report christoph. schraff@dwd
PP Kenda : Status Report Deutscher Wetterdienst, D Offenbach, Germany
Contributions / input by:
Klaus Stephan, Andreas Rhodin, Hendrik Reich, Werner Wergen (DWD)
Daniel Leuenberger (MeteoSwiss)
Marek Lazanowicz (IMGW)
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

2. ( - ) + = ( - ) + = ( - ) + = ( - ) + = ( - ) + =
LOCAL Ensemble Transform Kalman Filter (LETKF) (graphs by Neil Bowler, UK MetOffice)
( ) =
0.9 Pert 1
-0.1 Pert 2
-0.1 Pert 3
-0.1 Pert 4
-0.1 Pert 5
( ) =
( ) =
( ) =
( ) =
Xb(i) =
xb(i) xb
(local *, inflated) transform
matrix
k perturbed forecasts
ensemble mean forecast
analysis mean
(computed only in S)
perturbed analyses
flow-dependent
background 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)
*: localisation: set of obs and hence wa(i) depends on location

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

4. 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))

5. – :
air-mass convection
00 UTC runs
06 UTC runs
IEU (coarse IC)
IDE (fine-scale IC)
ETS
0.1 mm
FBI

6. – :
air-mass convection
00 UTC runs
06 UTC runs
IEU (coarse IC)
IDE (fine-scale IC)
ETS
1.0 mm
FBI

7. – :
air-mass convection
12 UTC runs
18 UTC runs
IEU (coarse IC)
IDE (fine-scale IC)
ETS
0.1 mm
FBI

8. – :
air-mass convection
12 UTC runs
18 UTC runs
IEU (coarse IC)
IDE (fine-scale IC)
ETS
1.0 mm
FBI

9. – :
frontal period
00 UTC runs
12 UTC runs
IEU (coarse IC)
IDE (fine-scale IC)
ETS
0.1 mm
FBI

10. model:
2 x
6 – 18 h fcst =
24-h sum of
precipitation
radar (24-h sum)
IEU (coarse IC)
IDE (fine-scale IC)
2 – 3 June 07
11 – 12 June 07

11. 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
Past experiments (Leuenberger):
environment affects impact of fine-scale
details in analysis from LHN
Radar
With LHN
Without LHN
(dashed:
determininistic)

12. 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 !
9-UTC runs
OBS
with LHN
without LHN
– 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)

13. Task 2: Technical implementation of an ensemble data assimilation framework / LETKF
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 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)
COSMO
ensemble
exp.
system
 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.)
LETKF

14. 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 observations
that 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 data
structure and vice versa required for new COSMO obs operators.

15. 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

16.  set up (G-) SIRF test with COPS period
time
Weighting +
Resampling
Guiding steps
final weighting
after free forecast is computed
SREPS (ass.)
SREPS (pred.)
radar / satellite / in-situ obs.
free forecast …
HRES
select best
members
( ≤10 )
Evaluate classical and spatial (object oriented, fuzzy) metrics
for weighting mesoscale (SREPS) and km-scale
ensemble members (DLR, MCH)
• assess correlation of metrics betw. models of different res.
• assess persistence of skill in different metrics
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

17. thank you for your attention

18. Sequential Importance Re-Sampling
Sequential Importance Re-Sampling
Ensemble members
Observation
PDF
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 h