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# Contemporary American Society SOC 125

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This 6 page Class Notes was uploaded by Deron Effertz on Thursday September 17, 2015. The Class Notes belongs to SOC 125 at University of Wisconsin - Madison taught by Staff in Fall. Since its upload, it has received 9 views. For similar materials see /class/205176/soc-125-university-of-wisconsin-madison in Sociology at University of Wisconsin - Madison.

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Date Created: 09/17/15

Assimilation of AMSUA Microwave Radiances with an Ensemble Kalman Filter EnKF Herschel L Mitchell P L Houtekamer G rard Pellerin Mark Buehner and Bjarne Hansen Service M t orologique du Canada Meteorological Service of Canada Dorval Quebec Canada Introduction The ensemble Kalman lter EnKF is a 4D data assimilation method that uses a MonteCarlo ensemble of shortrange forecasts to estimate the covariances of the forecast error Evensen 1994 Burgers et al 1998 Houtekamer and Mitchell 1998 It is a close approximation to the standard Kalman lter The approximation becomes more accurate as the ensemble size increases The EnKF is conceptually simple It does not depend strongly on the validity of hypotheses about the linearity of the model dynamics and requires neither a tangent linear model nor its adjoint In addition it parallelizes well Like most modern data assimilation methods the EnKF directly assimilates observed radiance data This aspect of the EnKF and in particular the assimilation of AMSU A microwave radiances is the focus of this presentation First the EnKF and the experimental environment are brie y described Then we focus on how the EnKF assimilates the AMSU A microwave radiances and show some results indicating their impact with the EnKF including a comparison with similar results from a 3D Var system The present text ends with some concluding remarks and a brief outline of our future plans in this area The EnKF For ensemble member 2 the EnKF equations can be written as w w KltorHltw gtgt lt1 ijt1gtMIIgtq 2 where KI analysis eld Ilf rst guess forecast eld 0239 vector of perturbed observations H interpolation operator may be nonlinear K gain matrix t1 the next analysis time M full nonlinear forecast model 1239 representation of model error The gain matrix K determines how much weight is given to the innovation oi 7 vis a vis the forecast or rst guess eld Ilf As in the standard Kalman lter the gain matrix is de ned as K PfHTHPfHT R 1 3 where R is the observational error covariance matrix Unlike the standard Kalman lter the EnKF uses a random ensemble to estimate error covariances ie PfHT 2 Wf 7 WHICH 7 HM lt4 2 1 HPfHT 2 111M gt H1IfgtlH1If gt 7 HUN 5 2 1 Note that since H is applied to each background eld individually rather than to the covariance matrix Pf it is possible to use nonlinear operators For example H can be a radiative transfer model if radiance observations are available Localization Correlations associated with remote observations tend to be small and di cult to estimate using small ensembles To lter covariances at long distances we use a Schur product ie an elementwise product of two matrices as described in Houtekamer and Mitchell 2001 That is instead of directly using covariances calculated from the ensemble we lter any such covariances using Pfnrj p0 L OPf MW 6 ans emble where p is a correlation function with compact support and 0 denotes the Schur product This leads to a positive de nite matrix Pf Gaspari and Cohn 1999 Here r is the distance between points n and Ti and L is the distance beyond which the correlation function 0 is zero Our rationale is that as ensemble sizes increase in the future for example with increases in the available computational power it will be possible to increase L and thereby relax the localization In fact the EnKF never computes the covariance matrix Pf to calculate the gain matrix K only PfHT and HPfHT are required By applying covariance localization separately in the horizontal and in the vertical we are effectively using the following modi ed de nition of the gain matrix KpvOpHOPfHTlVOpHOHPfHTgtRl 1r 7 Here 0 H and pV are the correlation functions used for horizontal and vertical localization respectively and PfHT and HPfHT are computed from the ensemble using eqs 4 and 5 respectively Actually rather than using a single ensemble we use a con guration consisting of a pair of ensembles as proposed in Houtekamer and Mitchell 1998 Having two ensembles allows the Kalman gain used for the assimilation of data into one ensemble to be computed from the other ensemble Currently the vertical localization forces covariances to zero in 2 units of ln pres sure Thus for example the covariances associated with a 1000 hPa observation fall to zero at 135 hPa while those associated with a 10 hPa observation fall to zero at 74 hPa The Experimental Environment The EnKF used here has been developed in a series of studies in increasingly realistic environments starting with the 3 level quasigeostrophic model used by Houtekamer and Mitchell 1998 and Mitchell and Houtekamer 2000 For the past few years we have been using the Canadian Global Environmental Multiscale GEM primitive equation model Cote et al 1998 initially a dry 21 level version to assimilate simulated ob servations Mitchell et al 2002 and more recently a 28 level version that includes a complete set of physical parameterizations to assimilate real observations Houtekamer et al 2003 Our approach with the EnKF has been to use those observations accepted by the Canadian operational global 3D Var As discussed in Houtekamer et al 2003 this facilitates comparisons with the operational system and allows the EnKF to make use of the operational background check77 and QCVAR ii TOVS monitoring and bias correction and iii horizontal thinning of TOVS observations Currently of the observations assimilated by the 3D Var the EnKF assimilates the following o from radiosondes uvTqpsmfaceg o from aircraft uvT o from satellites cloud track winds u1 and AMSU A microwave radiances 0 surface observations T psmface The EnKF uses the same observational error statistics as the operational 3D Var This too facilitates comparisons with the operational system Assimilation of AMSUA Microwave Radiances For the calculation of simulated radiances from a model state vector the EnKF like the Canadian operational 3D Var procedure uses the RTTOV radiative transfer model RTTOV 6 Saunders et al 1999 Saunders 2000 was used for the experiments presented here although we have subsequently converted to RTTOV 7 Our implementation of RTTOV is very much based on its use in the operational 3D Var Chouinard et al 2002 Since it uses eqs 1 4 5 and 7 to assimilate observations the EnKF requires neither the tangent linear nor the adjoint of the radiative transfer model Using only observations accepted by the operational 3D Var the EnKF assimilates AMSU A channels 3710 over open ocean and from three to ve of these channels over land and ice depending on the height of the topography as described by Chouinard et al 2002 In addition the AMSU A observations used operationally are thinned to a horizontal resolution of N 250 km The results shown below are from data assimilation cycles over a 2 week period in May June 2002 During this period AMSU A observations were available from two polar orbiters NCAA 15 and NCAA 16 Due to the horizontal thinning of the AMSU A observations approximately 3000 pro les were available for assimilation every 6 h from each of these two satellites Results from Two Experiments The rst experiment is a TOVSNOTOVS experiment Results are evaluated by verifying 6 h forecasts against radiosonde observations The evaluation is performed over a 5 day period after a 5 day spin up In this experiment the horizontal grid is 144 X 72 the EnKF uses a total of 96 ensemble members and the correlation function used for localization in the horizontal falls to zero at 2300 km Results show a neutral to modest improvement in the Northern Hemisphere not shown A more substantial positive impact of the AMSU A observations is observed in the tropics and in the Southern Hemisphere The Southern Hemisphere results are presented in Fig 1 It can be seen that assimilation of the AMSU A pro les results in generally smaller biases and standard deviations std dev for all ve variables The second experiment is a 3D VarEnKF comparison Both methods have been used to assimilate exactly the same set of observations using the same observational error statistics The same forecast model resolution physical parameterizations etc has been used for both methods For this experiment the horizontal grid is 240 X 120 the EnKF uses a total of 128 ensemble members and the correlation function used for horizontal localization in the EnKF falls to zero at 2800 km Houtekamer et al 2003 present veri cations of 6 h forecasts and analyses against radiosonde observations for this experiment Here we examine veri cations against the AMSU A data Figs 2 and 3 show 0 P and O A statistics for each AMSU A radiance channel for the 3D Var and EnKF assimilation cycles respectively A comparison of corresponding panels from the two gures indicates that the current version of the EnKF yields larger std dev values than the 3D Var especially for channels 3 9 and 10 The EnKF also produces larger biases than the 3D Var system perhaps because the AMSU A data is bias corrected using the latter system The results while encouraging indicate that there is considerable room for improvement with respect to the EnKF assimilation of the AMSU A data Conclusions An EnKF has been developed for atmospheric data assimilation It is to be used as the data assimilation component of the Canadian operational medium range Ensemble Prediction System Results with real observations indicate that the EnKF can be used to assimilate AMSU A microwave radiances Work is continuing aimed at improving the assimilation of the AMSU A microwave radiances in the EnKF Among the aspects that we intend to examine are the effect of the verticalhorizontal localization the necessity for EnKF speci c a QC b moni toring and c bias correction procedures the desirability of adjusting the observational error speci cation including the possible inclusion of observational error correlations We also intend to assimilate other types of radiance data eg AMSU B with the EnKF Acknowledgments The development of a new data assimilation algorithm is a com plex project We are grateful to our many colleagues at Direction de la recherche en meteorologie and the Canadian Meteorological Centre for their help suggestions and encouragement We thank Clement Chouinard and Jacques Halle for their help and ad vice regarding the assimilation of the AMSU A radiances We also thank Chantal Cote for generating Figs 2 and 3 l 2 mS GZ 5 Tl an in l l is w l 5n 7 2 1 m 2 7 39Z 2 72 EU 7 7 3 In 7 7 1 an I us so 7 7 m an 7 I 7 m 37 3m 7m 7 m m 7 V an mu7 7313 mu7 733 7 an mu 7 r 7 m mu 7 7 m l m 91 zuu 7 an gm 7 k 3 250 7 7 32 250 7 i r 7 3 3mm 7 7 i5 3mm 7 7 i5 ADD 7 7 32 400 7 7 3 37 1 315 Emu 7 7 97 sun 7 m m l l nu ma 7 U 7 an 7mm 7 J I 7 an 550 7 7 3 550 7 7 33 925 7 ii 92 7 gt 7 i3 mnn l l g mnn r l g 72 n z 4 5 72 u z 4 5 dam degree ES um 12 U l r m mu 7 7 m 320 Sun 7 7 3w 7mm 7 gt 7 ll 550 7 7 i l m 925 7 V 7 m mnn v 75 m 7 n 2 4 s a degree Type E7T mua020524ou02052812300mm2 10 Regina emisphere Sud ElAlS mmuomsmoonnszstLonomimm Lat7ion 905 130w zus 160E E7T mua020524ou02052812300mmo 10 j SLaL ElAlS mmuozosmoonnszstLonomimm Figure 1 Veri cation scores for the ensemble mean for the rst experiment The mean value7 ie7 bias7 dashed and std dev solid of the observed minus interpolated 6 h forecasts are shown for the assimilation cycle with AMSU A data in red and Without AMSU A data in blue for the region south of 200 South

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