Deutscher Wetterdienst Vertical localization issues in LETKF Breogan Gomez, Andreas Rhodin, Hendrik Reich
Dec 13, 2015
Deutscher Wetterdienst
Vertical localization issues in LETKF
Breogan Gomez, Andreas Rhodin, Hendrik Reich
Deutscher Wetterdienst
Perform single observation experiments and study the vertical impact. In situ observations and radiances.
First attempt to understand the behavior of the LETKF.
Explore the fundamental limitations of EnKF or LETKF algorithms (i.e. un-localized obs. such as radiance obs.)
Objectives
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LETKF – Localized Ensemble Transform Kalman Filter
Horizontal
VerticalIntegral gives one number, but where to apply it!
Vloc
Similar to a Gaussian but function equals 0 at aprox. 3 times Vloc
Localization function
Analysis are independent for every grid point
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Background Ensemble
B-matrix 128 random perturbations
3DVAR first guess
128 ensemble members. (Same error covariance
statistics as 3DVAR)+
3DVAR and LETKF should give equal results for a large (infinity) number member of ensemble members. This means that, for comparison purposes, 3dvar can be regarded as the reference to match.
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Objective is to study the impact of a surface pressure observation on a vertical profile.
A single surface observation from a rawinsonde is chosen at a random location.
Single sfc pressure observation
LETKF and 3DVAR allows to select the prognostic variable to analyze. (geopot. height or temperature).
Finally different vertical localization values are chosen to see the different impacts: 1.00, 0.60, 0.30, 0.15 (Those are eq. to the sigma of a gaussian distribution in log(P)).
Parameters to study
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Assimilated in Geopot. height
Assimilated in Temperature
Geopot. height increments Temperature increments
Assimilation in Geop. height or Temperature values Single sfc pressure Obs
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Objective is to study the impact of a radiance observation on a vertical profile.
A single random location is chosen and only some channels are studied. AMSUA: 5, 7 and AMSUB: 3, 4, 5.
Different vertical localization values: 10.0, 1.2, 0.6, 0.3. Only geopotential height values are used this time.
Radiance observations
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Nominal height values for radiances
AMSUA7 Sensitivity functions for temperature and relative humidity
AMSUB4 Sensitivity functions for temperature and relative humidity
L
irhbirhtbit
L
iirhbirhtbit
rht
HH
zHHz
1
1,
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Standard Deviation
AMSUA5 - Temperature Increments match 3dvar between 0.6 and 1.2
AMSUB4 - RH Increments already have a good agreement with 3dvar between 0.3 and 0.6
AMSUA5 AMSUA7 AMSUB3 AMSUB4 AMSUB5
StdDev 0.65 0.82 0.45 0.34 0.33
StdDev is higher for AMSUA than AMSUB(Values in LogP comparable to Vloc)
rhbirhtbit HH
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In situ and radiance observations
Geopotential height /
Temperature
Relative humidity
Tropics 0.38 0.13
Extratropics 0.93 0.20
Vertical correlation length scale in LogP
AMSUA AMSUB5
StdDev 0.60-0.80 0.30-0.40
Standard deviation in LogP
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In situ and radiance observations
Objective is to study the impact of a radiance observation on a vertical profile.
We want to threat this observations with different vlocs values as they are of a different physical kind.
Different vertical localization values (10.0, 1.2, 0.6, 0.3, 0.15) are used for an in-situ obs. meanwhile a radiance observation has a fixed value of 1.2. (Fertig et al. 2007)
AMSUA5 and an artificial rawinsonde measurement at 800HPa were used. (We impose a obs. minus first guess equal to the standard error of each observation.)
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Temperature increments
AMSUA5
AMSUA5 +
Temp 800HPa
Temp 800HPa
The over-shooting is reduced, while still matching the in-situ observation.
But still we can have some balance problems when Vloc is small for in-situ observations.
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Some problems found
AMSUB3
Noisy increments.
Many member are close to zero!AMSUB5
Relative Humidity Increments
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One should consider which diagnostic variables are used in the analysis. (In this case geopotential height or temperature, may be others)
A method to estimate the nominal height of radiance observations has been proposed. Satisfactory results so far.
Summary and Conclusions
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Summary and Conclusions
Localization of non local observations (radiances)
Non linearity (relative humidity increments)
Localization of variables of very different length scales.
Single location experiments: need to do global experiments with a full set of observation and perform some statitistics (e. g. RMSE)
Aspects not handled satisfactorily yet.