1. Vertical localization issues in LETKF
Breogan Gomez, Andreas Rhodin, Hendrik Reich

2. Objectives
Perform single observation experiments and study the vertical impact. Set up some simple experiments using one observation to study the impact in the profiles. (i. e. in situ observations and radiances)
Understand in detail the behavior of the LETKF.
Find practical solutions for some of the issues found.
Explore the fundamental limitations of EnKF or LETKF algorithms (i.e. un-localized obs. such as radiance obs.)

3. LETKF – Localized Ensemble Transform Kalman Filter
Vloc
Similar to a Gaussian but function equals 0 at aprox. 3 times Vloc
Horizontal
Localization function
Analysis are independent for every grid point
Integral gives one number, but where to apply it!
Vertical

4. (Same errocovariance statistics as 3DVAR)
Outlook
128 random perturbations
B-matrix
128 ensemble members.
(Same errocovariance statistics as 3DVAR) +
3DVAR
first guess
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 truth”.

5. Single sfc pressure observation
Objective is to study the impact of a surface pressure observation on a vertical profile.
A single surface observation from a rowinsonde is chosen at a random location.
Parameters to study
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)).

6. Single sfc pressure Obs
Assimilation in Geop. height or Temperature values
Single sfc pressure Obs
Assimilated in Geopot. height
Assimilated in Temperature
Geopot. height increments
Temperature increments

7. Radiance observations
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.
Vertical position of the observation
We test a method to select automatically a nominal height for radiance observations.
Only geopotential height values are used this time.
Different vertical localization values: 10.0, 1.2, 0.6, 0.3.

8. Nominal height for radiance obs.

9. Nominal height values for radiances
AMSUA7 Sensitivity functions for temperature and relative humidity
AMSUB4 Sensitivity functions for temperature and relative humidity

10. 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)

11. In situ and radiance observations
Geopotential height
Relative humidity
Tropics
0.38
0.13
Extratropics
0.93
0.20
AMSUA
AMSUB5
StdDev
Standard deviation in LogP
Vertical correlation length scale in LogP

12. 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.)
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.)

13. Temperature increments
AMSUA5
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.
AMSUA5 +
Temp 800HPa

14. Many member are close to zero! Relative Humidity Increments
Some problems found
AMSUB3
Noisy increments.
Many member are close to zero!
AMSUB5
Relative Humidity Increments

15. Summary and Conclusions
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.

16. Summary and Conclusions
Aspects not handled satisfactorily yet.
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)

17. Thank you