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

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.)

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

(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”.

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)).

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

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.

Nominal height for radiance obs.

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

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)

In situ and radiance observations Geopotential height Relative humidity Tropics 0.38 0.13 Extratropics 0.93 0.20 AMSUA AMSUB5 StdDev 0.60-0.80 0.30-0.40 Standard deviation in LogP Vertical correlation length scale in LogP

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.)

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

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

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.

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)

Thank you