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

Deutscher Wetterdienst LETKF – Localized Ensemble Transform Kalman Filter Horizontal Vertical Integral 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

Deutscher Wetterdienst 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.

Deutscher Wetterdienst  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

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

Deutscher Wetterdienst  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

Deutscher Wetterdienst Nominal height values for radiances AMSUA7 Sensitivity functions for temperature and relative humidity AMSUB4 Sensitivity functions for temperature and relative humidity

Deutscher Wetterdienst 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 AMSUA5AMSUA7AMSUB3AMSUB4AMSUB5 StdDev StdDev is higher for AMSUA than AMSUB (Values in LogP comparable to Vloc)

Deutscher Wetterdienst In situ and radiance observations Geopotential height / Temperature Relative humidity Tropics Extratropics Vertical correlation length scale in LogP AMSUAAMSUB5 StdDev Standard deviation in LogP

Deutscher Wetterdienst 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.)

Deutscher Wetterdienst 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.

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

Deutscher Wetterdienst  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

Deutscher Wetterdienst 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.

Deutscher Wetterdienst Thank you

Deutscher Wetterdienst Apendix - Nominal height for radiance obs.