Transcript Allgemein - uni

KENDA and the LETKF
Christoph Schraff, Hendrik Reich, Andreas Rhodin
contributions related to specific observation types also from
Klaus Stephan, Annika Schomburg; Uli Blahak
Km-scale ENsemble-based Data Assimilation

Priority project in COSMO consortium (CH, D, GR, I, PL, ROM, RU)

Local Ensemble Transform Kalman Filter (LETKF) ,
(because of its relatively low computational costs)

provide perturbed initial conditions for COSMO-DE EPS
KENDA / LETKF
FE12 Presentation, DWD (OF), 17 June 2011
[email protected]
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Local Ensemble Transform Kalman Filter
LETKF (Hunt et al., 2007)
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ensemble
mean
forecast
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k perturbed ensemble
forecasts mean fcst.
forecast perturbations
0.9 Pert 1
-0.1 Pert 2
-0.1 Pert 3
-0.1 Pert 4
local
transform
matrix w
Xb
flow-dep background error cov.
Pb
= (k – 1 )
x  xb  Xb w
X b (X b )T
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+(
analysis mean
wa
analysis error
covariance
(computed only in
ensemble space)
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analysis
Wa(i)
perturbations
w a ( i )  w a  Wa ( i )
perturbed
analyses
set up cost function J(w) in ((k-1) -dimensional !) ensemble space,
explicit solution for minimisation (Hunt et al., 2007)
KENDA / LETKF
FE12 Presentation, DWD (OF), 17 June 2011
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[email protected]
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LETKF for COSMO :
technical implementation
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analysis step (LETKF) outside COSMO code (included in 3DVAR pack. of DWD)
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obs operators in COSMO,
ensemble of independent COSMO runs collect obs – f.g.  4D -LETKF
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basically for verification purposes, COSMO obs operators incl. quality control
will be implemented in 3DVAR / LETKF environment
 future: hybrid 3DVAR-EnKF approaches in principle applicable to COSMO
KENDA / LETKF
FE12 Presentation, DWD (OF), 17 June 2011
[email protected]
3
LETKF:
status and current work
•
LETKF fully implemented, deterministic analysis implemented recently
•
LETKF not yet included in NUMEX
 preliminary LETKF experiments, using Hendrik’s scripts:
– 3-hourly cycles, up to 2 days (7 – 8 Aug. 2009: quiet + convective day)
– 32 ensemble members
– LBC: perturbed (COSMO-SREPS, 3 * 4 members), or unperturbed (C-EU)
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examime spread / skill ratio , noise , structure of analysis increments …
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vertical localisation
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hydrostatic balancing of analysis increments
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adaptive methods (obs errors R , covariance inflation)
KENDA / LETKF
FE12 Presentation, DWD (OF), 17 June 2011
[email protected]
4
LETKF (COSMO) , example:
zonal wind at lowest model level
after 1 day of 3-hrly cycling of LETKF
nudging analysis (reference)
front
= area with large spread,
i.e. assumingly with
large forecast errors
first guess ensemble spread
analysis mean – f.g. mean
analysis mean – nudging ana.
= area with large analysis
increments
= area with differences
to nudging analysis
KENDA / LETKF
FE12 Presentation, DWD (OF), 17 June 2011
[email protected]
5
LETKF (km-scale COSMO) :
scientific issues / refinement
(forecast / analysis) ensemble spread ‘characterises’ (forecast / analysis) error, but
•
limited ensemble size, ensemble can only sample but not fully represent errors
•
model error (key issue, also for 4DVAR !) is not accounted for by algorithm
 ensemble spread / LETKF is blind to model errors
 lack of spread
to account for it:
covariance inflation, what is needed ?
 multiplicative Xb   · Xb
(tuning, or adaptive (y – H(x) ~ R + HTPbH))
KENDA / LETKF
FE12 Presentation, DWD (OF), 17 June 2011
[email protected]
6
LETKF experiments for COSMO-DE:
adaptive multipl. covariance inflation 
LETKF first guess mean
(inner domain average, ensemble lateral BC)
zonal wind, at ~ 500 hPa
 = 1.2 constant
 adaptive, variable in space
 spread / skill ratio only slightly improved,
spread still too small
RMSE
however:  is used inside LETKF,
direct effect not shown in these plots
spread
7 Aug.
8 Aug.
KENDA / LETKF
FE12 Presentation, DWD (OF), 17 June 2011
[email protected]
7
LETKF experiments for COSMO-DE:
adaptive multipl. covariance inflation 
LETKF first guess mean
(inner domain average, ensemble lateral BC)
zonal wind, at ~ 500 hPa
 = 1.2 constant
 adaptive, variable in space
RMSE (vs. determ. analysis)
f.g. spread
f.g. spread, scaled with
adaptive inflation factor 
f.g. spread, ‘filtered’ adaptive 
zonal wind, ~ 850 hPa
RMSE
spread
 spread still too small
7 Aug.

8 Aug.
7 Aug.
8 Aug.
inflation ‘filtered’ (temporally, by upper & lower limits) as ‘seen’ by LETKF:
spread improved, but still too small (LBC; upper limit (1.7) too low ?)
KENDA / LETKF
FE12 Presentation, DWD (OF), 17 June 2011
[email protected]
8
LETKF (km-scale COSMO) :
scientific issues / refinement
to account for lack of spread:
covariance inflation, what is needed ?
 multiplicative Xb   · Xb
(tuning, or adaptive (y – H(x) ~ R + HTPbH))
 additive :
– perturbing the NWP model
– fixed perturbations of model physics parameters (COSMO-DE EPS)
 leads to non-Gaussian distributions, appears unsuitable
– stochastic physics (revised ECMWF scheme, by Torrisi, I (2011/06) )
– statistical (climatological) 3DVAR-B  hybrid schemes !
– additive inflation which reflects model error as estimated by statistics
(comparing forecast tendencies with observed tendencies, Gorin & Tsyrulnikov)
KENDA / LETKF
FE12 Presentation, DWD (OF), 17 June 2011
[email protected]
9
LETKF (km-scale COSMO) :
scientific issues / refinement
•
localisation
•
update frequency at ?
(multi-scale data assimilation,
successive LETKF steps with different obs / localisation ?)
1 hr  at  15 min
non-linearity vs. noise / lack of spread / 4D property ?
•
perturbed lateral BC (LBC)
(  source of noise )
(distort implicit error covariances in filter  limit use of obs ?)
note: shorter data cut-off & higher analysis frequency
for COSMO-DE than for driving global system ICON
•
ensemble size (40 ?)
•
non-linear aspects, convection initiation (outer loop , (latent heat nudging) ?)
KENDA / LETKF
FE12 Presentation, DWD (OF), 17 June 2011
[email protected]
10
LETKF (km-scale COSMO) :
current work : new observation types
•
radar : radial velocity and (3-D) reflectivity
 extramural research
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ground-based GPS slant path delay : humidity
 PhD
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cloud information
 Eumetsat Fellow Annika
based on satellite and conventional data
(Issues in LETKF:
non-Gaussian distribution of obs increments, non-linear obs opr,
non-local obs, obs error correlations / thinning …)
KENDA / LETKF
FE12 Presentation, DWD (OF), 17 June 2011
[email protected]
11
LETKF (km-scale COSMO) :
plans
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< 2011 / 10 :
– implement ensemble LBC using GME ensemble from LETKF
– implement refined treatment of LBC
– implement KENDA + GME LETKF + LBC from GME LETKF in NUMEX
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2011 / 11 – 2012 / 10 :
– experiments > 2 days (Nens = 40) with NUMEX !
system evaluation !
– use radar obs (1st: wind) , finer tuning, tackling scientific issues
– efficiency, technical robustness (cope with crashes of few ensemble memb.)
– perturbations of lower BC (maybe later ?)
– ensemble verification (upper-air: end of 2011; rest: later)
•
> 2012 / 11 : pre-operational :
more tuning / refinements, more obs (GPS, cloud; screen-level obs), ICON LBC
KENDA / LETKF
FE12 Presentation, DWD (OF), 17 June 2011
[email protected]
12
KENDA
thank you for your attention
KENDA / LETKF
FE12 Presentation, DWD (OF), 17 June 2011
[email protected]
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