{"Bibliographic":{"Title":"An Evaluation of NESDIS TOVS physical retrievals using data impact studies","Authors":"","Publication date":"1989","Publisher":""},"Administrative":{"Date created":"08-20-2023","Language":"English","Rights":"CC 0","Size":"0000103827"},"Pages":["Berir\nQC\n996\n.T33\nOF\nCOMMUNITY\nno.69\nA\nTECHNICAL MEMORANDUM NWS NMC 69\n*\n*\nWITH\nAvenue\nSTATES\nOF\nAN EVALUATION OF NESDIS TOVS PHYSICAL RETRIEVALS USING DATA\nIMPACT STUDIES\nNATIONAL METEOROLOGICAL CENTER\nWASHINGTON, D.C.\nJUNE 1989\nU.S. DEPARTMENT OF\n/\nNational Oceanic and\n/\nNational Weather\nCOMMERCE\nAtmospheric Administration\nService","NOAA TECHNICAL MEMORANDUMS\nNational Meteorological Center\nNational Weather Service, National Meteorological Center Series\nThe National Meteorological Center (NMC) of the National Weather Service (NWS) produces weather\nanalyses and forecasts for the Northern Hemisphere. Areal coverage is being expanded to include the\nentire globe. The Center conducts research and development to improve the accuracy of forecasts, to\nprovide information in the most useful form, and to present data as automatically as practicable.\nNOAA Technical Memorandums in the NWS NMC series facilitate rapid dissemination of material of\ngeneral interest which may be preliminary in nature and which may be published formally elsewhere at a\nlater date. Publications 34 through 37 are in the former series, Weather Bureau Technical Notes (TN),\nNational Meteorological Center Technical Memoranada; publications 38 through 48 are in the former series\nESSA Technical Memoranda, Weather Bureau Technical Memoranada (WBTM). Beginining with 49, publications\nare now part of the series, NOAA Technical Memoranadums NWS.\nPublications listed below are available from the National Technical Information Service (NTIS),\nU.S. Department of Commerce, Sills Bldg., 5285 Port Royal Road, Springfield, VA 22161. Prices on\nrequest. Order by accession number, (given in parentheses).\nWeather Bureau Technical Notes\nTN 22 NMC 34\nTropospheric Heating and Cooling for Selected Days and Locations over the United States\nDuring Winter 1960 and Spring 1962. Philip F. Clapp and Francis J. Winninghoff, 1965, 18\npp. (PB-170-584)\nTN 30 NMC 35\nSaturation Thickness Tables for the Dry Adiabatic, Pseudo-adiabatic, and Standard Atmos-\npheres. Jerrold A. LaRue and Russell J. Younkin, January 1966, 18 pp. (PB-169-382)\nTN NMC 36\nSummary of Verification of Numerical Operational Tropical Cyclone Forecast Tracks for\n1965. March 1966, 6 pp. (PB-170-410)\nTN 40 NMC 37\nCatalog of 5-Day Mean 700-mb. Height Anomaly Centers 1947-1963 and Suggested Applica-\ntions. J. F. O'Conner, April 1966, 63 pp. (PB-170-376)\nESSA Technical Memoranda\nWBTM NMC 38\nA Summary of the First-Guess Fields Used for Operational Analyses. J. E. McDonell,\nFebruary 1967, 17 pp. (AD-810-279)\nWBTM NMC 39\nObjective Numerical Prediction Out to Six Days Using the Primitive Equation Model--A\nTest Case. A. J. Wagner, May 1967, 19 pp. (PB-174-920)\nWBTM NMC 40\nA Snow Index. R. J. Younkin, June 1967, 7 pp. (PB-175-641)\nWBTM NMC 41\nDetailed Sounding Analysis and Computer Forecasts of the Lifted Index. John D. Stackpole,\nAugust 1967, 8 pp. (PB-175-928)\nWBTM NMC 42\nOn Analysis and Initialization for the Primitive Forecast Equations. Takashi Nitta and\nJohn B. Hovermale, October 1967, 24 pp. (PB-176-510)\nWBTM NMC 43\nThe Air Pollution Potential Forecast Program. John D. Stackpole, November 1967, 8 pp.\n(PB-176-949)\nWBTM NMC 44\nNorthern Hemisphere Cloud Cover for Selected Late Fall Seasons Using TIROS Nephanalyses.\nPhilip F. Clapp, December 1968, 11 pp. (PB-186-392)\nWBTM NMC 45\nOn a Certain Type of Integration Error in Numerical Weather Prediction Models. Hans\nOkland, September 1969, 23 pp. (PB-187-795)\nWBTM NMC 46\nNoise Analysis of a Limited-Area Fine-Mesh Prediction Model. Joseph P. Gerrity, Jr.,\nand Ronald D. McPherson, February 1970, 81 pp. (PB-191-188)\nWBTM NMC 47\nThe National Air Pollution Potential Forecast Program. Edward Gross, May 1970, 28 pp.\n(PB-192-324)\nWBTM NMC 48\nRecent Studies of Computational Stability. Joseph P. Gerrity, Jr., and Ronald D. McPherson,\nMay 1970, 24 pp. (PB-192-979)\nNOAA Technical Memorandums\nNWS NMC 49\nA Study of Non-Linear Computational Instability for a Two-Dimensional Model. Paul D.\nPolger, February 1971, 22 pp. (COM-71-00246)\nNWS NMC 50\nRecent Research in Numerical Methods at the National Meteorological Center. Ronald D.\nMcPherson, April 1971, 35 pp. (COM-71-00595)\nNWS NMC 51\nUpdating Asynoptic Data for Use in Objective Analysis. Armand J. Desmarais, December\n1972, 19 pp. (COM-73-10078)\nNWS NMC 52\nToward Developing a Quality Control System for Rawinsonde Reports. Frederick G. Finger\nand Arthur R. Thomas, February 1973, 28 pp. (COM-73-10673)\n(continued on inside back cover)","QC\n996\n,T33\nLIBRARY\nno, 69\n1990\n3\nMAR\nCommerce\nof\nDept.\nU.S\nNOAA Technical Memorandum NWS NMC 69\nAN EVALUATION OF NESDIS TOVS PHYSICAL RETRIEVALS USING DATA\nIMPACT STUDIES\nClifford H. Dey, Ralph A. Petersen, Bradley A. . Ballish,\nPeter M. Caplan, Lauren L. Morone, H. Jean Thiebaux, and\nGlenn H. White\nNational Meteorological Center\nHenry E. Fleming, Anthony L. Reale, and Donald G. Gray\noffice of Research and Applications, NESDIS\nand\nMitchell D. Goldberg and Jamie M. Daniels\nST Systems Corporation, Lanham, Maryland\nATMOSPHERIC\nDESCRIVE\nNOAA\nWashington, D. C.\nJune 1989\nDEPARTMENT\nCOMMERCE\nOF\nUNITED STATES\nNational Oceanic and\nNational Weather\nDEPARTMENT OF COMMERCE\nAtmospheric Administration\nService\nNOAA\nRobert A. Mosbacher, Sr.\nWilliam E. Evans\nElbert W. Friday, Jr.\nSecretary\nUnder Secretary\nAssistant Administrator","2\nABSTRACT\nA new NESDIS technique to produce temperature profiles from\nradiance information measured by satellite-born sensors has been\nevaluated. The new procedure relies on explicit knowledge of the\nphysical processes involved, while the previous operational procedure\nrequired only a set of a priori statistics. The evaluation was\nperformed using data impact studies, a departure from the previous NMC\npractice of using only collocation statistics to make such\nevaluations. Two real-time data impact studies were performed. The\nresults of the second data impact study led to operational use of\ntemperature retrievals produced by the new method, beginning on\nSeptember 20, 1988. The experiments demonstrate the necessity for a\nclose cooperation between a data producer (NESDIS) and a data user\n(NMC) as the meteorological community moves toward an era of\nconsolidated data assimilation procedures.\nI. INTRODUCTION\nTOVS (TIROS Operational Vertical Sounder) temperature profiles\nproduced by the National Environmental Satellite and Data Information\nService (NESDIS) currently provide the only operational source of\natmospheric profile observations over the entire globe. The profiles\nare derived from raw radiance information that satellite-born sensors\nmeasure through a complex retrieval process. The retrieval procedure\nused prior to these experiments had been based on a linear\nmultivariate regression using a large number of radiosonde reports\nwith collocated TOVS radiance measurements (Smith, et. al, 1979,\nMcMillin and Dean, 1982). Temperature profiles produced by this\nprocedure were referred to as statistical retrievals. While this\ntechnique served the meteorological community well over the years, the\napproach has the deficiency that it did not allow the retrievals to\ndepart far from mean conditions, and therefore tended to underestimate\ngradients. In an attempt to alleviate this deficiency, NESDIS has\nrecently developed an alternative technique -- the NESDIS TOVS\nPhysical Retrieval System -- which utilizes a priori physical\nknowledge of the atmosphere but still requires a reduced number of\nradiosonde reports with colocated TOVS radiance measurements.\nRetrievals produced in this way are hereafter referred to as physical\nretrievals.\nIn the past, the acceptance by the National Meteorological Center\n(NMC) of major modifications to the retrieval process made by NESDIS\nhas been based primarily on evidence from radiosonde collocation\ncomparisons. However, recent increases in the computational resources\navailable to NMC now permit a more thorough evaluation via a data\nimpact study. Data impact studies have two significant advantages:\n(1) they measure the true effect of the revised retrieval process on\nour operational NWP products, and (2) they provide far more revealing\ninformation than collocation statistics alone, information that can be\nused by NESDIS to further improve their retrieval technology.","3\nThis paper presents the results of two data impact studies of the\nphysical retrievals which ultimately led to a decision by NMC to use\nthe retrievals operationally. The benefits of close cooperation\nbetween a data producer (NESDIS) and a data user (NMC) are readily\napparent. The next section describes the physical retrieval process\nand contrasts it with the previously-used statistical retrieval\nmethod. The third section presents the experimental design. The\nresults of the first data impact study, the modifications made\nfollowing it, and the results of the second data impact study are\ndetailed in Section 4. A comparison of observational error statistics\nfor retrievals produced by the statistical and physical systems is\ncontained in Appendix A.\nII. THE PHYSICAL RETRIEVAL ALGORITHM\nII.1 Definitions\nThere are two generic approaches to retrieving temperature pro-\nfiles from satellite data. One general approach is \"statistical\" in\nthat the temperature profile is derived by a multivariate regression\nprocedure with the satellite radiances used as predictors. This\napproach requires only a priori, coincident temperature and radiance\ndata to derive the regression coefficients. The retrieval algorithm\nused by NESDIS throughout the time period of the TIROS-N/NOAA 6-10\nSatellite Series has been this approach. Details can be found in\nPhillips, et al. (1979) Smith, et al. (1979) and Smith and Woolf\n(1976).\nThe other general approach is \"physical\" in that explicit knowl-\nedge of the physical processes involved is required. That is, the\nrelationship between temperature and radiance is modeled by the\nradiative transfer equation and the model is inverted to obtain the\ntemperature profile from the radiances. (The only exception to these\ntwo general categorizations is the synthetic regression method, which\nis a combination of the two methods, whereby the a priori radiances\nare calculated from the a priori temperature profiles using the\nradiative transfer equation.)\nIn the subsequent subsections, the particular physical retrieval\nmethod that was used for the NWP model impact studies is described.\nNot only is the retrieval algorithm a physical one, but it also is a\nsimultaneous one. This means that the atmospheric temperatures, the\nsurface temperature, and the water vapor mixing ratios are retrieved\nsimultaneously as a single solution vector.\nII.2 Retrieval Method\nSince the preliminary processing steps of the physical retrieval\nalgorithm remain the same as they were for the statistical retrieval\nalgorithm, they are not repeated here. It will be assumed that the\nsatellite data have been calibrated as radiances, earth located, and","4\ncarry appropriate identifying information. We assume further that (1)\nthe infrared radiances have been cloud cleared, when not too cloudy,\nand converted to brightness temperatures, (2) the microwave brightness\ntemperatures are free of precipitation effects and have been corrected\nfor antenna side lobe and surface emissivity effects, and (3) the\nbrightness temperatures viewed along a slant path have been converted\nto equivalent nadir-viewing brightness temperatures.\nThere are three parts to our physical retrieval algorithm. The\nretrieval operator must be assembled and inverted, an initial\napproximation to the solution (i.e., a first guess profile) must be\nobtained, and the simultaneous temperature/moisture profile retrieved\nfrom the brightness temperatures. The retrieved profile has 50\natmospheric temperatures (t1 at 0.02 hpa through 50 at 1000 hpa), the\nsurface (skin) temperature Es, and 16 water vapor mixing ratios (q1 at\n300 hpa through 916 at 1000 hpa), which can be written in the column-\nvector form:\nq16]\n(1)\nV = [t1\nt50'\nts,\nwhere the superscript T represents the vector transpose.\nThe particular physical retrieval method used is the minimum\nvariance method, whose theory and derivation can be found in Rodgers\n(1976). Since our retrieval method is also a simultaneous one, it is\nreferred to as the minimum variance simultaneous (MVS) method (see\nFleming, et al. 1986b, for details).\nII.3 Tuning Data Sets\nA tuning data set is a set of radiosonde temperature/moisture\nprofiles that are coincident in time and in place with the satellite\nradiance data. These data are collected globally for a period of 28\ndays and are updated on a rotating file on a daily basis. A tuning\ndata set contains no matchups from overcast conditions or from situa-\ntions that are sufficiently cloudy that the radiances cannot be cloud\ncleared. Furthermore, there are three tuning sets: one for ocean\nconditions, one for land-day conditions, and one for land-night\nconditions.\nThe purposes of the tuning data sets are threefold. First, their\nname is derived from the fact that they are used to tune the retrieval\nalgorithm for uncertainties in the physical model. Second, they are\nused to linearize the retrieval operator, which is nonlinear in its\ntrue form. Finally, the tuning sets provide libraries from which the\nretrieval first guess profile is selected. These functions are ela-\nborated upon in subsequent subsections.\nIn order to construct the tuning sets, a predetermined list of\napproximately 200 radiosonde stations is used to determine the pairs\nof coincident radiosonde temperature/moisture profiles and satellite\nbrightness temperature vectors that are used in the 28-day file from\nwhich the tuning sets are constructed. Criteria that the matched\nvector pairs must meet are as follows:","5\na) The time window is + or - 2 hrs., except over oceans where it\ncan be time-interpolated up to 6 hrs.\nb) The space window varies with geographical region, being\nlarger in data sparse regions than in data dense regions, but it\naverages about 1 deg. in both latitude and longitude.\nc) The radiosonde report must be complete at least between 850\nand 100 hpa.\nd) Matched vector pairs whose terrain heights differ too\ngreatly, because the satellite and radiosonde locations are too far\napart, are deleted from the file.\ne) Several gross screening tests also are performed to eliminate\ninconsistencies among the temperatures and brightness temperatures.\nThe actual number of matched pairs in the 28-day file is less\nthan the 5,600 pairs that 200 stations would yield in 28 days because\nof cloud contamination and the failure of many matched pairs to meet\ncriteria (a) through (e) above. The 28-day file typically contains\naround 3,500 matched pairs of radiosonde/satellite data.\nII.4 Retrieval Operator\nThe explicit form of our minimum variance simultaneous retrieval\noperator C is given by:\nC = S T (A S AT+N)-1\n(2)\nwhere the superscripts T and -1 denote matrix transpose and inverse,\nrespectively. Matrices S and N are solution and noise covariance\nmatrices, respectively, while A is the radiative transfer matrix.\nThe matrix S is the covariance matrix of the vector V of (1) has\ndimensions 67x67, and has the following block matrix form:\nS1\nS4\nS5\nS =\nS2\nS6\n(3)\nS5T\nS6\nS3\nThe component matrices S1, S2, S3 are, respectively, the 50x50\ntemperature covariance matrix, the 1x1 surface temperature scalar, and\nthe 16x16 water vapor mixing ratio covariance matrix. The three\nremaining block matrices are the rectangular cross-covariance matrices\nof the various possible paired mixtures of the parameters just cited.\nOne hundred eight covariance matrices of the type shown in (3)\nhave been generated for use in the MVS retrieval method and are\ndescribed in Crosby et al. (1973) These matrices are based on 12\nbimonthly groupings of a combination of radiosonde, rocketsonde and\ngrenadesonde data to cover the full year. In other words, even though\nthe data for these matrices cover a two-month period, they are applied","6\nto only a one-month period, centered on the two month period, so that\nthere is a half-month overlap at each end of the monthly period to\nsmooth the transition from month to month. The covariance matrices\nalso are categorized by one of five latitudinal belts: 60 to 90N, 45\nto 60N, 30 to 45N, 15 to 30N, and 15N to 15S. Finally there is one\nmatrix each for land and ocean conditions, except for the equatorial\nbelt where there is a single combined land/ocean case. This accounts\nfor the total of {12 [ (4 X 2) + 1]} = 108 matrices. In addition,\ncorresponding to each of the 108 matrices is a mean profile of the\nform given in (1) These same 108 matrices and mean profiles are used\nin the Southern Hemisphere by applying them symmetrically across the\nequator and displacing them in time by six months.\nThe elements of the radiative transfer matrix A in (2) are prod-\nucts of: a weighting function or transmittance function value, a\nPlanck function linearization factor, a radiance scaling factor, a\nnumerical quadrature weight, and for the water vapor elements, a\nderivative of the Planck function with respect to temperature. This\nmatrix has dimensions nx67 where n is the number of channels (or\nbrightness temperatures) used, which depends on the cloud conditions\nand the operating condition of each channel. The matrix A also has a\nblock matrix form, namely,\n(4)\nA = [A1, A2, A3]\nIn (4) the matrices A1, A2, and A3 are the retrieval operators for\natmospheric temperature, surface temperature, and moisture, respec-\ntively, and have dimensions nx50, nx1, and nx16.\nFinally, N is the nxn covariance matrix of the system total\nnoise, which includes instrumental noise and all other noise generated\nby the system such as residual cloud contamination of the radiances,\ncalibrations errors, etc. A tridiagonal matrix normally is used for N\nbecause the noise is correlated among adjacent channels. Correlations\namong additional channels are known to exist, but they are assumed to\nbe sufficiently small that they can be ignored.\nII.5 Retrieval Bins\nThe 67xn dimensional retrieval operator C in (2) is nonlinear in\nthe sense that the covariance matrix S of (3) and the radiative\ntransfer matrix A of (4) depend upon the temperature and moisture\nconditions of the atmosphere that is being sensed by the satellite\nradiometer. In other words, both S and A depend upon the solution.\nHowever, they can be treated as being linear if the operator C is\napplied over a sufficiently restricted domain. This is accomplished\nby creating retrieval bins.\nThere are a total of 27 bins; one for each of 9 latitudinal belts\n(90 to 60N, 60 to 45N, 45 to 30N, 30 to 15N, 15N to 15S, 15 to 30S, 30\nto 45S, 45 to 60S, and 60 to 90S) and one each for the three condi-\ntions: (1) ocean, day and night, (2) land, day only, and (3) land,\nnight only. Each of these 27 bins contains one of the 108 covariance","7\nmatrices cited above, linearized matrices A and C, a mean tempera-\nture/moisture vector V, and a mean brightness temperature vector b,\nwhich are determined by the following schemes. (Note that the terms\n\"profile\" and \"vector\" are used interchangeably.)\nFirst, each bin is filled with data from the tuning sets that are\nappropriate for its latitudinal, land-ocean, and day-night\ncharacteristics. A bin is considered full when it contains a sample of\n100 matched pairs of temperature/moisture and brightness temperature\nvectors. This typically is achieved within the most recent 2-week\nperiod for most bins. However, there are data-sparse regions where the\nmaximum bin size of 100 is not attained, in which case a minimum size\nof 20 matched vector pairs over the 28-day period is required. For\nthose rare exceptions in which even this minimum requirement cannot be\nmet, the bin is filled with the matched data from the most appropriate\nneighboring bin. After the tuning set vector pairs have been distrib-\nuted among the 27 bins, mean temperature/moisture and brightness tem-\nperature vectors are calculated from the collection of vector pairs in\neach bin and are called bin means.\nNext, each of the 108 mean temperature profiles associated with\nthe 108 covariance matrices is compared with the bin mean temperature\nprofile, and then the covariance matrix S corresponding to the covar-\niance mean profile closest to bin mean is entered into that bin. The\nmeasure of closeness is the ordinary Euclidean norm applied to the\nmean temperature vectors at pressure levels p to 1000 hpa, where p is\nthe lowest pressure level attained by any of the radiosondes. Radio-\nsondes over high terrain are not used. This process is repeated until\neach of the 27 bins contains a covariance matrix S from the set of\n108, along with the bin mean temperature/moisture vector V and bin\nmean brightness temperature vector b. Because of the nature of this\nselection process, the same covariance matrix can be used to fill more\nthan one retrieval bin. The bin components are updated weekly by\nrepeating the process just described.\nThe linearization of the matrix A proceeds by using all of the\nindividual bin temperature/moisture vectors that were used to generate\nthe bin temperature/moisture mean vector and evaluating a separate\nmatrix A for each individual vector in the bin. This produces a set\nof individual matrices Aj, which are temperature and moisture\ndependent. The linearized matrix A is obtained from the average of\nthese individual matrices, i.e.,\n(5)\nA\n(1/I)\nAi\n=\ni=1\nwhere I is total number of profiles in the tuning subset.\nThe averaging procedure (5) is repeated for every retrieval bin.\nThus, every bin now contains matrices S, A, and the corresponding bin\nmean vectors V and b. By applying S and A to (2) , one obtains a 67xn\nlinearized retrieval operator C, given explicitly by","8\n(6)\nHowever, this retrieval operator is not stored as such; it is stored\nas two components C1 and C2, where\nC1 = S AT\n(7a)\nC2 = A S AT + N\n(7b)\nThis allows one to use any channel combination during the retrieval\nprocess; otherwise, separate matrices C would have to be generated and\nstored for every conceivable channel combination. The vectors V and\nb, and the retrieval operator components C1 and C2, are stored on a\nfile that is updated weekly, and they are accessed routinely by the\nonline retrieval processing system.\nII.6 The Retrieval Solution\nTo retrieve a solution vector V of the type (1) , given a measured\nsatellite brightness-temperature vector b, one uses the equation\nV = V + (b - b)\n(8)\nIn (8) V and b are the first guess vectors and C is the linearized\nretrieval operator, which is constructed online from the component\nmatrices C1 and C2 of (7a) and (7b).\nTheoretically, only a first guess for V is required in (8)\nbecause the first guess for b can be gotten from the radiative trans-\nfer matrix A and V, i.e.,\nb=AV\n(9)\nHowever, as mentioned previously, A is not known with certainty. This\nmeans that not only is b in error in (9), but so is C because of (6) ®\nThe paper by Fleming, et al. (1986a) discusses this problem in great\ndetail and offers the following simple solution. Instead of using (9)\nto determine b, one should derive it from the same data from which V\nwas calculated. In other words, whenever radiosonde tempera-\nture/moisture data are collected to calculate V, collocated satellite\nradiance data also should be collected from which to calculate b. This\nis the reason that both b and V are carried in all of the retrieval\nbins.\nNow in order to actually obtain the retrieval solution V from\n(8) one must first extract a retrieval operator C and mean vectors V\nand b from one of the bins. A reasonable selection would be to use\nthat bin whose latitudinal, land-ocean, and day-night characteristics\nare most like that of the satellite measurement at hand. However,\nthere are two problems with that approach. First, the air mass\nrepresented by the satellite measurement may not coincide with the\nclimatological one of the bin. Second, (8) is the solution of an\nequation of the first kind; therefore, it is strongly dependent on the","9\nfirst guess vector V. Thus, the choice of V is crucial. In order to\nensure that the choices of V, b, and C used in (8) are the ones that\nare most consistent with the measured b, we have developed the\n\"library search technique\" which is described next.\nII.7 First Guess Vector\nThe library search technique, Goldberg, et al. (1988), is one in\nwhich the brightness temperature vector from which the retrieval is to\nbe calculated is compared for closeness (i.e. similarity) with each\nbrightness temperature vector in one of the two tuning sets described\nin Subsection II. 3, depending upon whether the satellite measurement\nis over land or ocean. In this context the tuning set serves as a\nlibrary and will be called that. A vector norm, weighted by the\ninverse of the covariance matrix calculated from all the brightness\ntemperatures in the library, is used as the measure of closeness. The\n20 brightness temperature vectors in the library that are closest to\nthe given brightness temperature vector are saved and averaged. The\nresulting average vector is used as the first guess brightness\ntemperature vector, and is denoted b*.\nNext, the 20 radiosonde temperature/moisture profile vectors\nmatched to the 20 averaged brightness temperature vectors in the\nlibrary also are averaged. This second average vector is used for the\nsolution first guess profile, and is denoted V. This technique for\n*\nobtaining b and V is what we mean by a library search. The number\n20 was found in practice to be a good compromise between having enough\nvectors to average out noise and anomalous structures, and not having\ntoo many vectors so that the representativeness and fine structure of\na good first guess are washed out. Note that both b and V are\nobtained from measurements, thereby satisfying the requirements\nestablished in Subsection II. 6.\nWe now must resolve the question of which first guess tempera-\nture/moisture vector to use in the final solution (8) : the bin mean V\nor the library mean v\"? Also, from which bin should the mean vectors\nand retrieval operator components be extracted? These issues are\nresolved by using the first guess and bin selection procedures\ndescribed next.\nII.8 Selection Procedure\nFirst it is necessary to give the explicit formula for the clo-\nseness (or distance) measure, denoted d, which was described in the\nprevious subsection. Let B be the covariance matrix of the brightness\ntemperature vectors in either one of the two tuning sets (libraries)\ndescribed in Subsection II. 3, and let K be the number of such vectors\nin the library. Then the scalar distance between the given single\nbrightness temperature vector b from which the current retrieval is to\nK, of the library is\nbe made and each vector member (k), k = 1,\n,\ngiven by the formula\nd (k) = [b - b(k) T [b - (k)\n(10)","10\nDenote the smallest 20 of these values by d' (j), j = 1,\n20.\nIn\nconformity with the discussion of the library search technique in the\nprevious subsection, the 20 b(k)'s associated with the d'(j)'s are\naveraged to form b*, as are the 20 corresponding V's to form v*.\nAlso, compute the scalar distance d from the formula\na* = (b - b*) TB-1(b - b*)\n(11)\nNext, select the bin whose mean vector is most closely associated\nwith the current vector b by first reducing the selection to the 4\nmost likely bin candidates based on their latitudinal, land-ocean, and\nday-night characteristics. In some geographical regions, such as the\npolar regions, the number of candidate bins is reduced. The final bin\nselection is based on a comparison of temperatures. That is, let t\nrepresent the atmospheric temperature portion of the vector v* and let\nt(j) represent the same portion of the vectors v(j), j = 1,\n4,\nwhere the v(j) 's are the mean vectors of the 4 bins just cited. Find\nthat index jo for which the inner product\n[t* - E(j)]T (t* - E(j)), j = 1,\n4\n(12)\nis a minimum, where these temperature vectors include only the pres-\nsure levels between 50 and 1000 hpa over oceans and the pressure\nlevels between 50 and 700 hpa over land (because of terrain height\nproblems). The bin associated with the index is known as the\nretrieval bin. Extract b from the retrieval bin and use it and the\ncurrent b to calculate d from the formula\nd = (b - - b)T B-1 (b - b)\n(13)\nIf d apply the current b, and C, b, and V from the\nretrieval bin with index jo' to (8) in order to retrieve the solution\nvector V. (Note that this step will be exercised, at the very most,\n5% of the time.) Otherwise, apply the current b, and b*, v\", and the\njust-selected C to (8) in order to retrieve the solution vector V.\nFinally, move to the next retrieval location and repeat the selection\nand retrieval procedures just described to compute the next retrieval.\nII.9 Stratospheric First Guess\nThe essentials of the physical retrieval algorithm have been\npresented. All that remains to be discussed are the details of what\nis done in the middle and upper stratosphere where no radiosonde\ntemperature data are available. The combined\nstratospheric/tropospheric retrieval procedure is as follows.\nThe first step is to assemble the first guess temperature/\nmoisture profile, which is given explicitly by\nV = [E1,\n20,\nt50'\n-\n91\n(14)\nts","11\nThis vector has the form of vector (1) , except that the atmospheric\ntemperature portion of vector (14) has three explicit segments. To\nunderstand these temperature segments, recall that there are three\nkinds of mean temperature profiles: those associated with the 108\ncovariance matrices which are described in Subsection II. 4, the bin\nmean profiles obtained from the tuning data sets as described in Sub-\nsection II.5, and the library mean profiles which are described in\nSubsection II.7.\nThe mean temperature profiles associated with the covariance\nmatrices are based on rocketsondes and grenadesondes, as well as\nradiosondes, and so they extend to the top of the atmosphere at 0.02\nhpa. Consequently, they are used to fill in the first 15 elements of V\nin (14), which terminate at 18.4 hpa. Temperature elements 16 through\n20, i.e., 22.6 through 46.6 hpa, are filled in with the bin mean pro-\nfiles because they are based on the tuning set mean profiles which are\nmore accurate than those associated with the covariance matrices.\nNote\nthat the number of radiosonde temperature profiles that reach these\nmiddle pressure levels is too limited to use the library means. On the\nother hand, temperature elements 21 through 50 of V, which run from\n54.7 to 1000 hpa, are filled in with either the library mean or the bin\nmean, depending on the outcome of the first guess selection procedure\ndescribed in the previous subsection. This same selected profile also\nprovides the surface temperature and moisture first guess values for V\nin (14)\nof the three kinds of mean temperature profiles just discussed,\nthe bin and library mean profiles always have a mean brightness tem-\nperature vector associated with them. This paired correspondence was\nestablished when these mean vectors were first discussed. Only the\nmean profiles associated with the covariance matrices have no corre-\nsponding mean brightness temperature vectors. But these brightness\ntemperature vectors can be synthesized (i.e., calculated) from the\ncovariance matrix mean profile using (9) In other words, for each\nbin the mean temperature profile associated with the bin S matrix,\ncoupled with the surface temperature and moisture mean values associ-\nated with the bin, is applied to the radiative transfer equation to\nproduce the mean brightness temperatures. Even though these calcula-\ntions will be in error because A is in error, they are the only\nbrightness temperatures available that can be associated with the\ncovariance matrix mean profile.\nII. 10 Final Retrieval Process\nAll three of the mean brightness temperature vectors cited above,\neach of whose dimension is equal to n, are used in the final retrieval\nprocess as follows. Subtract each of the three mean vectors from the\nsingle, measured brightness temperature vector from which the\nretrieval is to be made. Arrange the resulting three difference vec-\ntors into an nx3 matrix and call it D. Then replace the difference\nvector (b - b) in (8) with the matrix D and form the matrix product","12\n(15)\nE = C D\nwhere E has dimensions 67x3.\nNow treat the three columns of the matrix E as three separate\nvectors and extract the top 15 elements from the first vector, the\nmiddle 5 elements from the second vector, and the bottom 47 elements\nfrom the last vector. Assemble the these three vector segments into a\nsingle 67-element vector and call it e. Then the final retrieval\nsolution is that given by\n(16)\nV = + e\nwhich follows from (8), (15), and the composition of e.\nA shortened, but less precise, way of describing the procedures\nof the last two paragraphs is to say that (8) was used three times to\nretrieve the final V of (16). In other words, in the first retrieval\nthe measured b, and the mean b and V vectors associated with the\ncovariance matrix, were used to retrieve the first 15 elements of V.\nIn the second retrieval the same measured b, and the bin mean b and V\nvectors were used to retrieve the next 5 elements of V. Finally, in\nthe third retrieval the same measured b, and the bin mean or the\nlibrary mean b and V vectors (depending on the outcome of the selec-\ntion procedure), were used to retrieve the last 47 elements of V.\nThis completes the description of our physical retrieval method.\nfinal retrieval solution of 50 atmospheric temperatures, the sur-\nThe\nface temperature, and 16 water vapor mixing ratios is given by V in\n(16). Not only is the emphasis of the retrieval method on the physi-\ncal aspects of the problem, but also on finding the optimal first\nguess profile for the solution. Finally, in order to minimize the\nsolution errors arising from an incomplete knowledge of the physics of\nthe problem, we stressed the fact that the first guess brightness\ntemperature vector must come from measurements collocated with the\nmeasured temperature/moisture profiles, not from model calculations.\nIII. EXPERIMENTAL DESIGN\nSince a global data set was to be examined in these impact\nstudies, the NMC Global Data Assimilation System (GDAS, Dey and\nMorone, 1985) and Medium Range Forecast Model (MRF, Sela, 1982) were\nselected as the test vehicles. The GDAS is an analysis/6-hour\nforecast cycle run operationally four times daily which produces first\nguesses for all NMC objective analyses, provides initial conditions\nfor 10-day MRF forecasts, and serves as the NMC analyses of record.\nThe analysis procedure used in the GDAS is a multivariate optimum\ninterpolation procedure that calculates corrections of height, wind,\nand relative humidity on 12 mandatory pressure surfaces from 1000 to\n50 hpa. The MRF is a global spectral model with a sophisticated\npackage of physical parameterizations, currently configured with 80-\nwave (triangular truncation) horizontal resolution and 18-layers in","13\nthe vertical. The model is used both to make the 6-hour forecasts in\nthe GDAS and to make a 10-day forecast once each day (from the 0000\nGMT GDAS analysis)\nThe GDAS and MRF are a major part of the operational suite run on\nCDC CYBER 205 computers. An experimental GDAS/MRF system can also be\nrun in parallel with the operational suite in order to perform more\nsystematic tests of proposed analysis/forecast changes prior to\nimplementation. The data impact studies described in this paper were\nperformed using such a parallel GDAS/MRF system, in this case\nidentical to the operational GDAS/MRF system in all respects except\nthat physical retrievals were used in the parallel GDAS analyses,\nwhile statistical retrievals were used in the operational GDAS\nanalyses. As a time saving measure, the parallel MRF forecast was\nintegrated only to 5 days instead of 10.\nThe first experiment began at 0000 GMT on September 11, 1987,\nusing the operational first guess for both operational and parallel\nanalyses. The experiment then ran without interruption until being\nterminated at 1800 GMT on October 1, 1987, for a total of 21 days,\nwith each system producing its own analyses and forecasts from its own\nfirst guesses. Because the number of non-TOVS observations available\nto the operational and parallel analyses were identical at every\nindividual analysis time during the 21 days, we can safely conclude\nthat differences between the operational and parallel GDAS/MRF results\nare due solely to the different sets of TOVS data used.\nAs will be discussed in the next section, the results of the\nfirst test showed positive impact in some regions, but also identified\na number of deficiencies with the retrievals in others. During part\nof the ensuing 6 months, NESDIS made various improvements to the\nphysical retrieval system. These improvements are also described in\nthe next section. When collocation statistics indicated that the\nperformance of the physical retrieval system had improved, a second\ndata impact study was performed, beginning at 0000 GMT on April 6,\n1988 and ending at 1800 GMT on April 18, 1988. Although several\nchanges had been made to the operational GDAS/MRF system during the 6-\nmonth improvement period (Sela, 1988), precautions were taken to\ninsure that differences between the operational and parallel GDAS/MRF\nsystems in the second impact test were again due solely to differences\nin the TOVS data. The results of the second data impact study\njustified operational use of the physical retrievals, which occurred\non September 20, 1988.\nIV. EXPERIMENTAL RESULTS\nIV.1 The First Impact Study\nIV.1. Subjective Results\nSubjective comparisons of 500 hpa height forecasts were made each\nday throughout the study period to examine the relative accuracy of\nthe two retrieval data sets at predicting synoptic scale waves.","14\nSpecifically, forecast error fields were obtained from each forecast\nsystem for the 00, 24, 48, and 72 hour forecast periods. Fields of\nthe differences of the forecast errors were also used to determine if\nsignificant analysis differences could be identified and traced\nthrough the forecast period and to determine if the forecast error\ndifferences indicated a persistent forecast improvement or\ndegradation. In all cases, the operational analyses were used as a\nverification standard.\nIn the Northern Hemisphere, differences in the analyses rarely\nexceeded 25 m in magnitude, with forecast differences at 72 h seldom\nlarger than 50 m. In the Southern Hemisphere, however, the impact of\nthe physical retrieval scheme was much larger, with the magnitude of\nsynoptic scale differences in the 500 hpa height analyses often\nexceeding 100 m. The largest differences were concentrated along the\nbaroclinic zones. The example shown in Figure 1 is fairly typical of\nthe analysis and forecast differences observed during the test period.\nIn the analyses, the details of the wave southwest of South America\nare treated quite differently by the two sets of satellite data.\nHeights in the center and to the east of the wave crest have been\nraised by from 50 to 90 m in the parallel analysis, while heights in\nthe short wave to the southwest of the ridge have been reduced by 140\nm. This pattern of differences remains remarkably intact during the\n72 h forecast when compared to the operational analyses. At 24 h, the\nlarge operational error in the positioning of the ridge south of Cape\nHorn has been almost completely eliminated in the physical system.\nThe pattern of improvement in the treatment of the ridge persists\nthrough 48 hours. By 72 h, another area of improvement with the\nphysical system appears in the southwest of the display area.\nThroughout the test, synoptic scale patterns of analysis\ndifference were observed over the entire band from 10°S to 80°S.\nOverall, a correspondence persists between areas of negative forecast\nheight errors in the operational system and positive forecast error\ndifferences (and vice versa), indicating a general improvement in the\nforecast using the physical retrievals. The difference in the\nforecast errors through 48 hours often represented 20% to 40% of the\nforecast errors themselves and, subjectively, favored the physical\nsystem.\nThe effect of the two retrieval systems on time-averaged\natmospheric fields was examined by calculating and comparing time\nmeans of analyzed and forecast fields from the two systems over the\nperiod September 11 - October 1, 1987. The two retrieval systems\nproduce larger differences in the Southern Hemisphere than in the\nNorthern Hemisphere and larger differences over the oceans, where the\nsatellite data have the major influence.\nFigure 2 displays the vertical cross-section of zonal mean\ndifference in analyzed height between the parallel system using\nphysical retrievals and the operational system using statistical\nretrievals. The largest differences occur at upper levels in the\nSouthern Hemisphere over the southern ocean and the edge of Antarctia.\nFor reference, the magnitude of the differences between analyses is","15\nlarger than that noted between the MRF86 (version of the MRF\noperational at the end of 1986) system and the higher resolution MRF87\n(version of the MRF now operational) system during the 1987\npreimplementation test period. The differences between 5 day\nforecasts by the two systems (not shown) are similar in pattern and\nmagnitude, although larger over Antarctia.\nThe mean differences in initialized zonal wind produced by the\nmodifications to the mass field made by the two sets of retrievals is\nshown in Figure 3. In general, differences in the Northern Hemisphere\nare less than 1 m/s. The largest differences, as expected, are\ncoincident with the largest gradient of height change, with\ndifferences of 2.5 m/s observed in the stratospheric jet in the\nSouthern Hemisphere.\nTo study the regional effects of these zonal difference patterns,\nthe mean analyzed 250 hpa height over the Southern Hemisphere is\nexhibited in Figure 4. The physical retrievals produce lower heights\nover the tropical oceans, particularly off the west coast of South\nAmerica. Initialization, however, reduces notable differences between\nthe two systems here. Over the southern oceans, the physical\nretrievals produce higher heights by as much as 24 m and lower heights\nover the coast of Antarctia by up to 31 m. Five day forecasts by the\ntwo systems show similar patterns of systematic differences.\nIV.1. Objective Results\nObjective assessments were made based on the fit of individual\ntypes of data to the GDAS first guess, analysis, and initialization\n(the sense of the fit is observation minus field value) The fit to\nthe analyses is an indication of the spatial coherence of the\nobservations, while the fit to the first guesses is a measure of\nwhether the analysis changes led to an improvement or degradation in\nthe ensuing 6 h forecasts. The statistics are tabulated for 10°x10°\nlatitude/longitude boxes and averaged over the entire 21-day period.\nThe statistics include the number of reports, the mean fit, and the\nstandard deviation of the fit. The values were further averaged over\ngroups in order to obtain a sample size sufficient to insure\nstatistical reliability. In all the first impact study graphs, the\nsolid line represents the operational (statistical) retrieval system\nand the dotted line shows the parallel (physical) retrieval system.\nAlthough all time periods are available, the fits described here are\nonly to data valid from 2100 GMT to 0300 GMT (i.e., 0000 GMT data)\nalthough they are representative of the other times as well.\nFigure 5 presents the fit of radiosonde data over Antarctica, the\nshaded area in Figure 5 (a), to the first guesses valid at 0000 GMT (It\nshould be noted that the GDAS analyses use satellite profile data\nthroughout the atmosphere over water, but only above 100 mb over\nland.) The height standard deviations from the physical retrieval\nsystem are improved over those from the statistical retrieval system\nthroughout the full depth of the atmosphere (Figure (b)) implying\nthat the physical retrievals at any given analysis time are more\ntemporally consistent with the satellite and conventional data used in","16\nthe previous analyses. The mean fit of the radiosonde heights to the\nfirst guess fields (Figure 5c), however, shows that the physical\nretrievals caused the first guesses to have an increased cold bias\nabove 500 hpa. Figures 5 (d) and 5 (f) indicate the standard deviation\nof the fit of the radiosonde data to the first guess wind fields was\nalso improved by using the physical retrievals. The decrease in the\nstandard deviations is important because it indicates the first guess\naccuracy has been improved with the physical retrievals.\nFigure 6 depicts the fit of the TOVS retrievals over the South\nPacific Ocean, the shaded area in Figure 6 (a) to the analyses. In\nproducing these plots, the statistical TOVS retrievals were fit to the\nanalyses from the statistical system, while the physical TOVS\nretrievals were fit to the analyses from the physical system. The\nstandard deviations of the fits of paths A (clear) B (partly cloudy),\nand C (cloudy) TOVS retrievals, Figures (b), 6(d), and 6(f),\nrespectively, were poorer in the physical system. This suggested that\nthe physical retrievals possessed more information on scales not\nrepresented in the guess fields than did the statistical ones. This\nwas especially apparent for path C retrievals. The mean fit of the\nTOVS retrievals to the analyses, Figures (c), 6(e), and (g),\nindicated both path B and path C physical retrievals were warmer\nrelative to their respective analyses than their statistical\ncounterparts.\nIn the Northern Hemisphere, there was very little difference in\nthe performance of the statistical and physical systems over land.\nOver oceanic areas, however, the picture was different. Figures 7\npresents the fit of the TOVS retrievals over the North Pacific Ocean,\nthe shaded area in Figure 7 (a), to the analyses. The standard\ndeviations of the fits of paths A, B, and C TOVS retrievals, Figures\n(b), 7 (d), and (f) respectively, were very close for both\nstatistical and physical retrievals, although there was a slight edge\nfor path C physical retrievals. However, the mean fits of the TOVS\nretrievals to the analyses, Figures 7 (c), 7 (e), and 7 (g), suggested\nthe presence of a problem with the path C physical retrievals. Here,\nthe mean fits suggest the presence of a warm bias in the path C\nphysical retrievals that is substantially larger than that observed in\nthe corresponding path C statistical retrievals. In an area\ncontaining a mixture of paths A, B, and C retrievals, this would\nmanifest itself in a rather noisy depiction of the atmosphere, and\ncould cause the development of anomalous baroclinicity around areas of\ncloudy soundings.\nVerification scores for the MRF forecasts integrated from the\nparallel and operational GDAS analyses are compared in Tables 1 and 2.\nIn Table 1, Southern Hemisphere anomaly correlation scores for the 5-\nday forecasts are compared. The statistical system analyses were used\nas the standard in calculating the anomaly correlation. The\ncalculations were done for the area from 20°S to 80°s. Scores for\n4\nof the 21 days were not available. of the remaining 17 comparisons,\n10 cases favored the physical retrievals while 7 favored the\noperational retrievals. The overall average favored the physical\nsystem.","17\nIn Table 2, the 72-hour forecasts are verified against 3 networks\nof rawinsonde stations: 102 Northern Hemisphere stations, 110 North\nAmerican stations, and 31 Southern Hemisphere stations. The mean of\nthe height errors, the standard deviation of the height errors, and\nthe RMS of the vector wind errors were calculated for 850 hpa, 500\nhpa, 250 hpa, and 100 hpa and averaged over the 20 days of the 21-day\nthe test period for which verification scores were available. In the\nSouthern Hemisphere, the MRF forecasts made from the analyses using\nphysical retrievals verified consistently better than from those using\nthe statistical retrievals, especially with respect to height. A two-\ntailed student-T test indicated the differences in the Southern\nHemisphere mean height scores were significant at the 5% level.\nIn\nthe Northern Hemisphere, however, the verification scores favored the\nforecasts from the statistical system in 19 of the 24 possible\ncomparisons, while only one comparison favored the forecast from the\nphysical retrievals. Although the same test for statistical\nsignificance indicated only one of these differences was statistically\nsignificant at the 5% level, the consistency of the Northern\nHemisphere comparisons was troublesome.\nIV.1.3 Conclusions from the First Test\nBoth subjective and objective comparisons showed the system using\nthe physical retrievals performed consistently better in the Southern\nHemisphere. There is some evidence this may be due, in part, to\nphysical retrievals performing better in the winter hemisphere.\nHowever, because of the degradation in the Northern Hemisphere\nverification scores and the problems with the path C physical\nretrievals, it was recommended that NESDIS examine the problems\nrevealed in the first impact study.\nIV.2 Retrieval System Weaknesses Identified by the First Impact\nStudy\nIV.2.1 Bin Selection Procedure\nThe first impact study identified several weaknesses in the\nphysical retrieval processing system used to produce the temperature\nprofiles submitted to NMC for evaluation. This led to system changes\nwhich resulted in the final configuration of the physical retrieval\nalgorithm described in Section II.\nThe retrieval algorithm weaknesses were related primarily to the\nprocedure for selecting the operator for a given temperature/moisture\nretrieval. The earlier system determined the retrieval bin (and hence\nthe retrieval operator) on the basis of the similarity between the\nobserved satellite brightness temperature vector and the corresponding\nbin mean brightness temperature vector. However, the channel\ncombination used for cloudy retrievals differed from that used under\nclear conditions. This resulted in a systematic difference in the\nchoice of the retrieval bins, and hence in the retrieval operators\n(and in some cases the first guess profiles) used for neighboring","18\ncloudy and clear retrievals. Consequently, in areas having a mixture\nof cloudy and clear conditions, neighboring cloudy and clear\nretrievals could have significant differences between them.\nAnother deficiency related to the selection of the retrieval\noperator was the small number of candidate bins (as described in\nSubsection II. 8) This affected the appropriateness of the selected\nretrieval operator under anomalous weather conditions.\nThe two deficiencies cited were resolved by the following\nchanges. First, the bin selection procedure was changed from\ncomparing brightness temperature vectors to that of comparing\natmospheric temperature profiles, using the scalar distance criteria\nof (12) This change unified the criterion for the bin selection\namong the clear and cloudy retrievals; it also increased the\nsensitivity of the selection criterion. Second, the number of\ncandidate bins from which to choose was increased from 2 to a maximum\nof 4 and software was introduced to ensure that the same retrieval\noperator is used for neighboring clear and cloudy soundings.\nThese changes essentially removed all of the systematic\ndifferences previously observed between neighboring clear and cloudy\nretrievals, and improved the quality of the retrieval products in\nunstable weather situations as well.\nIV.2.2 Other Minor Difficulties\nA logistical problem concerned the transfer of cloudy retrievals\nto NMC for use in the Northern Hemisphere mid-latitudinal zone (from\n30 to 60N over the oceans) To satisfy its own needs, NMC has\nroutinely generated its own statistical retrievals in this\ngeographical region. Normally, these retrievals would automatically\nreplace those computed by the NESDIS. This procedure was erroneously\ncontinued in the software used to transfer the NESDIS physical\nretrieval products to NMC during the first impact study. The mixture\nof the NESDIS clear and cloud-cleared physical retrievals with the NMC\ncloudy statistical retrievals caused additional systematic differences\nbetween the clear and cloudy retrieval products which were clearly\nevident in the impact study results. The corrected transfer procedure\nremoved the retrieval-related systematic differences.\nFurther study of the cloudy physical retrievals over the oceans\nrevealed that the sea surface temperatures (SST's) that are appended\nto these retrievals were excessively noisy. Because the SST's have a\nstrong impact on cloudy retrievals, deviations between neighboring\ncloudy retrievals near the surface were observed to be related to the\ndeviations between the appended SST values. The source of the noisy\nSST values was traced to the TOVS window channel values, which were\npoorly adjusted for atmospheric water vapor attenuation. This problem\nwas corrected by replacing the TOVS SST field with data from the NMC\n15-day SST file which are available operationally. Since these NMC\nSST's are much less noisy, there was a proportional reduction in noise\nin the cloudy oceanic retrievals.","19\nThe ensuing review and corrective actions following the first\nimpact study also resulted in a modification to the mean temperature\nvectors in the pressure interval 20 to 50 hpa. Recall from Subsection\nII.9 that the bin mean is used in this pressure interval for the first\nguess temperature profile and that the corresponding bin mean bright-\nness temperature vector is used in a second retrieval cycle as\ndescribed in Subsection II.10. Originally, retrievals based on the\ngiven geographical bin were combined with neighboring ones as a\nweighted average to avoid retrieval jumps across geographical\nboundaries. The present procedure of using only the current single-\nbin means resulted in a noticeable reduction in error of the retrieved\ntemperatures above 50 hpa. This was due not only to the change just\nmentioned, but also to the changes in the bin selection procedure\nmentioned in Subsection IV.2.1.\nIV.3 The Second Impact Study\nIV.3.1 Subjective Results\nAfter the new retrieval procedures described above were\ninstalled, the second impact study was conducted beginning at 0000 GMT\non April 6, 1988 and ending at 0000 GMT on April 18. The results from\nthis study again show the largest differences in the analyses and\nforecasts in the southern hemisphere, with the region of largest\ndifferences shifted south with the mean position of the baroclinic\nzone. On 13 April, for example (Fig. 8), the initialized 500 hpa\nheight fields show a difference of over 120 m over the Antarctic\nPeninsula. The question remains as to which of these analyses is more\ncorrect. In this case, the fact that the 24-hour forecast based on\nthe physical retrievals shows a marked decrease in the large negative\nerror forecast operationally with this wave provides strong evidence\nto support the superiority of the physical retrieval analysis. The\nimprovement in the definition of this short wave ridge persists\nthroughout the 72-hour forecast period as the wave propagates\nnortheastward through the longer wave regime. Although improvements\nare noted elsewhere, the differences in the analyses also lead to\ndegradations in the forecasts in some areas. However, these\ndegradations are generally smaller than the forecast improvements.\nAs in the first impact test, the differences in the analyses are\nrather small in the northern hemisphere, with the largest\nmodifications again associated with details of the short waves moving\nalong the mid-latitudinal baroclinic zone. Several of the larger\nanalysis differences persist during the forecast cycle and lead to an\nimprovement in the subsequent downstream definition of the waves as\nthey approach the west coast of North America.\nThe systematic behavior of analyses and forecasts during the\nsecond impact study was also investigated by examining differences in\natmospheric fields time-averaged over the impact study period of April\n6-18, 1988. Figure 9 (top) displays the difference in zonal mean\nheight between time-averaged NMC initialized analyses using physical\nand statistical retrievals. The largest differences appear near 50","20\ndeg. in the Southern Hemisphere, where the physical retrievals produce\nlower heights above 600 mb. The physical retrievals also produce\nslightly lower heights in the tropics. In the Northern Hemisphere,\ndifferences between the two analyses are generally less than 5 m.\nTime-averaged five-day forecasts (Fig. 9 - bottom) from the two\nsystems appear more similar than the analyses.\nFigures 10 and 11 compare zonal mean systematic errors in zonal\nwind and temperature from the two systems for five-day forecasts\nverifying April 11-18, 1988. Forecasts from each system are verified\nagainst initialized analyses from that system. The errors are quite\nsimilar in the two systems, but the analysis-forecast system using\nphysical retrievals shows slightly less westerly bias in zonal wind\nnear 30 deg. in both hemispheres, a decreased cold bias near 55 deg.\nat 700 hpa in the Southern Hemisphere, and a decreased warm bias in\nthe upper tropical troposphere. Figure 10 implies that these changes\nin systematic error reflect changes in the analyses more than changes\nin the forecasts.\nFigure 12 displays differences in analyzed 250 hpa geopotential\nheight between the two systems over the Southern Hemisphere. Physical\nretrievals produce lower heights west of Peru, over the tropical\nAtlantic, and around Antarctia, and slightly higher heights near 30\ndeg. Initialization (not shown) decreases differences between the two\nsystems in the tropics. The corresponding map for 1000 - 850 hpa\nthickness (Figure 13) displays colder temperatures over the tropical\noceans with physical retrievals. Large differences appear in mid-\nlatitudes between time-averaged five-day height forecasts from the two\nsystems (Figure 14) ; these appear much less zonally symmetric than\ndifferences in the initial state and show very little difference in\nthe tropics. Five-day forecasts of 1000 - 850 hpa thickness from the\nsystem using physical retrievals display less cold bias over the\ntropical oceans (Figure 15) ; this appears to be more the result of\nchanges in the analyses than in the forecasts themselves.\nIn the Northern Hemisphere, physical retrievals tend to produce\ncolder low-level temperatures (Figure 16) and lower 250 hpa heights\n(Figure 17) over the tropical oceans in the analyses. Elsewhere, the\ndifferences are considerably smaller than in the Southern Hemisphere,\nas are the differences between time-averaged five-day forecasts\n(Figure 18) .\nIV.3.2 Objective Results\nFigure 19* depicts the fits of the radiosonde observations over\nAntarctia, the shaded area in Figure 19 (a), to the first guesses.\n* In all graphs in Figures 19 - 21, the dotted line is from the\nstatistical retrieval system and the solid line from the physical\nretrieval system - the reverse of Figures 1 - 3. However, the abcissa\nof each of these graphs is the same scale as the corresponding graph\nin Figures 5 - 7.","21\nThe standard deviations of the fits, Figures (b), 9(d), and (f)\nall favor the physical retrieval system by about the same margin as in\nthe first impact study. The mean fit, Figure (c) indicates the\nfirst guesses now both have a pronounced warm bias instead of the\ncold one observed in the first impact study. As in the first test,\nthe physical retrieval system is warmer than the statistical system,\nbut in this case leads to smaller mean errors.\nFigure 20 shows the fits of the retrievals over the South Pacific\nOcean, the shaded area in Figure 20 (a) , to the analyses. The standard\ndeviations of the fits of path A and path C retrievals to the analyses\nare now equivalent, and the fits of path B retrievals favors the\nphysical retrieval system. This is a distinct improvement over the\nfirst impact study. The mean fits of path C retrievals, however,\nindicate the physical retrievals are warmer compared to their analyses\nthan are their statistical counterparts. The path B physical\nretrievals show almost no bias at all.\nFigure 21 presents the fits of retrievals over the North Pacific\nOcean, the shaded area in Figure 1(a), to the analyses. The standard\ndeviations of the fits are again very close, but this time, there is a\nslight advantage for the path A statistical retrievals. As before,\nthe mean fits of path A and B retrievals are rather close, while the\npath C retrievals again have a larger warm bias than the statistical\nretrievals. However, the difference is much smaller than in the first\nimpact study, with the warm bias confined to the bottom levels of the\nretrievals.\nThe subjective evaluations indicated that in a majority of the\ncases investigated the use of the physical retrievals in the analyzes\nled to a larger improvement in the subsequent forecasts. An objective\nmeasure of the overall impact of the retrievals on the forecasts can\nbe seen in the comparative plots of anomaly correlation shown in Figs.\n22 and 23. The 4-day forecast range was chosen for this comparison\nsince a majority of the operational forecasts for this period\nbracketed the 60% \"utility\" criterion. Points plotted above the dark\ncentral diagonal denote improvements by the physical scheme and visa\nversa (Approximations of the temporal forecast improvement are given\nby the dashed diagonals). Any forecasts in the upper left quadrant of\nthe diagram indicate cases of poor statistical retrieval based\nforecasts which were made \"useful\" with the physical retrieval system,\nwhile forecasts falling in the lower right quadrant represent\nforecasts which were made \"unusable\" by the physical retrieval system.\nof the southern hemisphere winter cases (the dots in Figure 22)\n,\nthe quality of the best forecasts was changed very little using the\nnew retrievals. However, marked improvement (10% and more) was noted\nfor the cluster of forecasts which had been only slightly better than\nthe 60% confidence criterion operationally. In fact, improvements of\ngreater than 10% (1 day) were noted in 6 of the 15 forecast cases,\nwith two of the 5 unuseful cases becoming useful. Overall, an\nimprovement of nearly 8 hours in forecast skill was observed. In the\nnorthern hemisphere winter (the crosses in Figure 23) the impact was\nmuch less pronounced, probably due to the overriding impact of the","22\nhigh quality conventional data sets. However, the largest impacts of\nthe physical retrievals were toward improving forecasts which had been\nonly marginally useful using the operational data, with a slight net\nimprovement overall. (It should be noted that this was a period when\nall operational models performed very poorly.) In summer, the results\nwere less pronounced in both hemispheres, with the northern hemisphere\ntests (the dots in Figure 23) showing no net impact and the `southern\nhemisphere (the crosses in Figure 22) results showing a small, but\npositive impact. It should also be noted that all 4 of the southern\nhemisphere cases in which the physical retrievals decreased the\nutility of the forecasts occurred during a single five day period (as\nnoted by numbered points on fig. 22) indicating the possibility of a\nsystematic, regime dependent behavior in the physical retrieval\nsystem.\nIn Table 3, the 72-hour forecasts from the second retrieval study\nare verified in the same manner as the ones from the first impact\nstudy were in Table 2. This time, however, the forecasts from the\nphysical system were better 7 times out of 12 possible comparisons for\nthe NH102 network, and 11 times out of 12 for the NA110 network. Only\nthe mean 850 hpa height field from the physical retrieval system\nverified worse than its counterpart from the statistical retrieval\nsystem. In the Southern Hemisphere, on the other hand, the\nverification scores are rather mixed. This is in contrast to the\nresults from the first impact study, and supports the previous\nconclusion that the improvement of the physical retrieval system over\nthe statistical retrieval system is greater in the winter than in the\nsummer hemisphere. This is related to the improved definition of\nbaroclinic zones by the physical retrievals and the fact that the\nbaroclinic zones are stronger in the winter hemisphere.\nIV.3.3 Conclusions from the Second Test\nThe results from the second impact study were more promising than\nwere those from the first. The Northern Hemisphere verification\nscores were considerably better in the second study, while the\nSouthern Hemisphere scores were mixed. The fits of the analyses to\nthe TOVS retrievals over the Northern and Pacific oceans were somewhat\nimproved in the second study, although there was evidence that the\npath C physical retrievals still have a warm bias in the lowest\nlevels. In view of these findings, NMC decided in favor of\noperational use of the physical retrievals.\nSummary and Conclusions\nV.\nA new NESDIS technique to produce temperature profiles from\nradiance information measured by satellite-born sensors has been\nevaluated. The new procedure relies on explicit knowledge of the\nphysical processes involved, and is therefore referred to as the\nNESDIS TOVS Physical Retrieval System, or more simply, the physical\nretrieval method. The previous operational procedure required only\na\nset of a priori statistics, and is therefore referred to as the\nstatistical retrieval method. The evaluation was performed using data","23\nimpact studies, a departure from the previous NMC practice of using\nonly collocation statistics to make such evaluations.\nTwo real-time data impact studies were performed. The first was\nfor the period September 11 - October 1, 1987. This study showed the\nphysical retrieval system to perform generally better in the Southern\nHemisphere, but slightly worse in the Northern Hemisphere. 'In\naddition, the northern hemisphere path C retrievals were found to have\na significant warm bias. Because of these deficiencies, NESDIS\nreexamined the physical retrieval algorithms. After several\nimprovements had been made, a second data impact study was performed\nfor the period April 7 - 18, 1988. In this study, the physical\nretrieval system performed better in both hemispheres, although the\nimprovement in the Southern Hemisphere was less pronounced. This may\nbe due to the physical retrievals system performing relatively better\nin the winter hemisphere. The warm bias in the path C physical\nretrievals in the Northern Hemisphere remained, although it was\nreduced and confined to the lowest levels. The results of the second\ndata impact study were sufficiently encouraging to justify operational\nuse of temperature retrievals produced by the new method. This\noccurred on September 20, 1988.\nSeveral advantages of this type of data evaluation were\ndemonstrated. First, data impact studies provide more useful\ninformation about the meteorological influence of satellite data than\ndo collocation statistics alone. Second, the effect of retrievals\nproduced by the new procedure specifically on the operational NMC\nanalysis/forecast systems can be evaluated. These experiments have\nalso demonstrated the necessity for a close cooperation between a data\nproducer (NESDIS) and a data user (NMC) as the meteorological\ncommunity moves toward an era of consolidated data assimilation\nprocedures. While it is not always possible to perform a data impact\nstudy such as this because of the substantial resources required, it\nshould be encouraged whenever it is possible, for the potential\nresults are substantial.","24\nREFERENCES\nCrosby, D. S, H. E. Fleming, and D. Q. Wark, 1973: Covariance matrices\nand means of atmospheric Planck profiles for application to tem-\nperature sounding from satellite measurements. J. Atmos. Sci.,\n30, 141-144.\nDey, C. H. and L. L. Morone, 1985: Evolution of the National\nMeteorological Center Global Data Assimilation System: January\n1982 - December 1983. Mon. Wea Rev., 113, 304-318.\nFleming, H. E. D. S Crosby, and A. C. Neuendorffer, 1986a: Correction\nof satellite temperature retrieval errors due to errors in\natmospheric transmittances. J. Appl. Meteor., 25, 869-882.\nFleming, H. E. , M. D. Goldberg, and D. S Crosby, 1986b: Minimum vari-\nance simultaneous retrieval of temperature and water vapor from\nsatellite radiance measurements. Preprints, Second Conf. on\nSatellite Meteorology/Remote Sensing and Applications (Williams-\nburg, Va.) Amer. Meteor. Soc., Boston, pp. 20-23.\nGoldberg, M. D., J. M. Daniels, and H. E. Fleming, 1988: A method for\nobtaining an improved initial approximation for the tempera-\nture/moisture retrieval problem. Preprints, Third Conf. on\nSatellite Meteorology and Oceanography (Anaheim, Calif.) Amer.\nMeteor. Soc., Boston, pp. 20-23.\nMcMillin, L. M., and C. Dean, 1982: Evaluation of a new operational\ntechnique for producing clear radiances. J. Appl. Meteor., 12,\n1005-1014.\nPhillips, N., L. McMillin, A. Gruber, and D. Wark, 1979: An evaluation\nof early operational temperature soundings from TIROS-N. Bull.\nAmer. Meteor. Soc. 60, 1188-1197.\nRodgers, C. D., , 1976: Retrieval of atmospheric temperature and compo-\nsition from remote measurements of thermal radiation. Rev.\nGeophys. Space Phys., 14, 609-624.\nSela, J. G. , 1982: The NMC Spectral Model. NOAA Technical Report\nNWS30, National Meteorological Center, Washington, DC 20233\nSela, J. G. 1988: The new T80 NMC operational spectral model.\nPreprints, Eighth Conference on Numerical Weather Prediction\n(Baltimore, Md. ) , Amer. Meteor. Soc., 312 - 313.\nSmith, W. L., and H. M. Woolf, 1976: The use of eigenvectors of stat-\nistical covariance matrices for interpreting satellite sounding\nradiometer observations. J. Atmos. Sci., 33, 1127-1140.","25\nSmith, W. L. , H. M. Woolf, C. M. Hayden, D. Q. Wark, and L. M. McMil-\nlin, 1979: The TIROS-N operational vertical sounder. Bull. Amer.\nMeteor. Soc., 60, 1177-1187.\nVerzal, P., H. J. Thiebaux, and L. L. Morone, 1988: Observation error\nvariance estimates. Impact of their use on observed spatial\ncorrelation structure. Preprints, Eighth Conference on Numerical\nWeather Prediction (Baltimore, Md. ) Amer Meteor Soc., Boston, pp\n214-218.","APPENDIX A\nPhysical Retrieval Observational Error Estimation\nIn order to most profitably use the physical retrievals in\nstatistical analysis schemes, the observational error of the new\nretrievals must be estimated. Such studies have been initiated, but\nthey are beyond the scope of this paper. However, an estimate of the\nerror associated with both the instrument and the retrieval process\ncan be obtained by examining differences between observations and 6-hr\nforecast values. The technique used is based on the fact that the\ntotal forecast error variance (computed from the difference between\nthe observation and the forecast) includes both the prediction error\nvariance and the observation error variance. The prediction error is\ndefined as the true error in the forecast. The observation error\naccounts for errors from imperfect instrument and transmission\nsystems, and \"errors of unrepresentativeness\" to the extent that the\ninstrument measures features in the atmosphere which are not\nappropriate to the grid- or time-scale of the forecast model. Using\nthese definitions, coupled with the assumption that prediction and\nobservation errors are statistically independent of one another, the\nsmallest value of the total forecast error variance sets an upper\nbound on the value of the observation error variance on any level and\nwithin any region.\nSix-hour height forecast-error standard deviations were computed\nfor the physical retrievals at mandatory pressure levels. Standard\ndeviations are shown instead of variances because the values are more\neasily related to observed increments. Table A.1 presents upper\nbounds on observation error standard deviations, where each value is\nthe smallest forecast error standard deviation within a ten degree\nlatitude band for each retrieval type.\nThe data used for these computations are Pacific Ocean retrievals\nfrom a thirty day period extending from July 20 to August 18, 1988.\nOnly 00Z and 12Z measurements were used. The thickness measurements\nwere anchored to each day's 1000 hpa analysis to produce observed\nheights at 11 mandatory pressure levels from 850 to 50 hpa. The\nphysical retrievals were excluded from the anchoring analysis. The\nforecast error was computed as the difference between the observed\nsatellite height and the 6-hour forecast from NMC's global spectral\nmodel horizontally interpolated to the observation location. The data\nwas then subjected to a gross quality check. Typically, only a\nfraction of a percent of the measurements were discarded.\nThe forecast error variance was computed for 2.5 degree boxes\nwithin each latitude band. A minimum of 10 observations for a\nparticular retrieval type was required before a variance was computed.\nAs can be seen in Table A.1, in some latitude bands no boxes had the\nrequired 10 observations during the 30 day period. This is","particularly evident with partly cloudy soundings. As a measurement\nof the reliability of these minimum standard deviations, Table A. 2\nshows the number of boxes for which a standard deviation was\ncalculated in each latitude band. The reliability of our computation\nof forecast error standard deviations, as well as our selection of a\nmeaningful minimum, is dependent on the number and distribution of the\nsatellite-minus-forecast differences. Our results suggest that this\ntype of study should use data from a longer period than thirty days.\nThe variation of minimum-standard-deviation with latitude is\nstriking. This latitudinal variation was also evident in a similar\nstudy on three months of forecast errors computed from radiosonde\nobservations (Verzal et al. , 1988) . While it is probable that some of\nthe increase with latitude is due to the increase of the prediction\nerror variance, the proportion of the observation error that describes\nunrepresentativeness error is also likely to increase with latitude.\nUsing the same method described above, the statistical retrievals\nfor the same time period were also studied. Figure 24 shows a\ncomparison of 11 levels of minimum forecast error standard deviations\nfor physical and statistical retrievals. Values are presented for\nthree latitude bands for which the largest number of standard\ndeviations were calculated for each retrieval type. The statistical\nretrievals may have an advantage because they were used in the\nanchoring analysis. However, this comparison does not show any\nsystematic differences between the two retrieval methods.","Valid Date\nStatistical System\nPhysical System\n16 Sept. , 1987\n0.414 *\n0.350\n17 Sept., 1987\n0.285\n0.517 *\n18 Sept., 1987\n0.494\n0.531 *\n19 Sept., 1987\n0.653 *\n0.629\n20 Sept., 1987\n0.383\n0.589 *\n21 Sept., 1987\n0.320\n0.528 *\n22 Sept., 1987\n0.533\n0.554 *\n23 Sept., 1987\n0.353 *\n0.317\n24 Sept., 1987\n0.327\n0.404 *\n25 Sept., 1987\n0.650\n0.774 *\n27 Sept., 1987\n0.796 *\n0.717\n28 Sept., 1987\n0.797\n0.817 *\n29 Sept., 1987\n0.804 *\n0.749\n30 Sept., 1987\n0.665\n0.690 *\n1 Oct.,\n1987\n0.665\n0.706 *\n3 Oct.,\n1987\n0.715 *\n0.699\n4 Oct.,\n1987\n0.674 *\n0.624\nTable 1.\n500 hPa Anomaly Correlation Scores for the 5 Day\nForecasts from the first data impact study for the\nArea 20°S to 80°s. The better score is indicated\nby an asterisk (*).","102 Northern Hemisphere Stations\nStandard Deviation\nRMS Vector\nMean\nWind Error\nHeight Error (m)\nHeight Error (m)\n(m/s)\nStatistical\nPhysical\nStatistical\nPhysical\nStatistical\nPhysical\n7.3\n850 hPa\n- 0.1 *\n- 0.5\n34.3 *\n35.0\n7.3\n500 hPa\n-17.8 *\n-18.5\n44.8\n44.8\n8.8\n8.8\n64.0 *\n13.5 *\n13.7\n250 hPa\n-14.5 *\n-16.0\n64.2\n6.6 *\n6.7\n100 hPa\n-46.3 *\n-47.4\n55.4 *\n56.4\n110 North American Stations\nStandard Deviation\nRMS Vector\nMean\nHeight Error (m)\nHeight Error (m)\nWind Error (m/s)\nStatistical\nPhysical\nStatistical\nPhysical\nStatistical\nPhysical\n850 hPa\n- 6.0 *\n- 7.0\n26.2 *\n26.4\n6.5\n6.5\n500 hPa\n-27.8 *\n-29.0\n35.9 *\n36.6\n8.3 *\n8.4\n250 hPa\n-27.3 *\n-28.2\n58.3 *\n59.5\n14.9 *\n15.0\n100 hPa\n-42.1 *\n-42.5\n41.8 *\n43.5\n7.6 *\n7.8\n31 Southern Hemisphere Stations\nStandard Deviation\nMean\nRMS Vector\nHeight Error (m)\nHeight Error (m)\nWind Error (m/s)\nStatistical\nPhysical\nStatistical\nPhysical\nStatistical\nPhysical\n850 hPa\n- 8.0\n- 4.0 *\n36.9\n36.3 *\n8.9 *\n9.0\n500 hPa\n-24.3\n- -20.9 *\n52.0\n51.3 *\n11.0 *\n11.1\n250 hPa\n-10.4\n- 3.4 *\n71.7\n70.6 *\n16.3\n16.3\n100 hPa\n-31.1\n-23.4 *\n66.0\n64.6 *\n10.5\n10.3 *\nVerification of 3 Day Forecasts from the First Data Impact Study,\nTable 2.\nSeptember 11, 1987 - October 1, 1987. The better score is\nindicated by an asterisk (*) .","102 Northern Hemisphere Stations\nMean\nStandard Deviation\nRMS Vector\nHeight Error (m)\nHeight Error (m)\nWind Error\n(m/s)\nStatistical\nPhysical\nStatistical\nPhysical\nStatistical\nPhysical\n850 hPa\n- 1.1 *\n- 1.3\n43.8\n43.2 *\n8.5\n8.4 *\n500 hPa\n-24.2\n-24.2\n58.2\n57.0 *\n11.1\n11.0 *\n250 hPa\n-24.0\n-23.1 *\n77.2\n75.8 *\n14.4\n14.2 *\n100 hPa\n-49.3 *\n-49.4\n66.3 *\n66.7\n8.0\n8.0\n110 North American Stations\nMean\nStandard Deviation\nRMS Vector\nHeight Error (m)\nHeight Error (m)\nWind Error (m/s)\nStatistical\nPhysical\nStatistical\nPhysical\nStatistical\nPhysical\n850 hPa\n3.9 *\n4.3\n34.3\n34.0 *\n7.7\n7.6 *\n500 hPa\n-22.1\n-21.4 *\n51.2\n49.4 *\n11.1\n10.8 *\n250 hPa\n-14.8\n-11.8 *\n73.6\n70.7 *\n16.1\n15.5 *\n100 hPa\n-35.9\n-33.7 *\n48.4\n48.0 *\n8.1\n8.0 *\n31 Southern Hemisphere Stations\nMean\nStandard Deviation\nRMS Vector\nHeight Error (m)\nHeight Error (m)\nWind Error (m/s)\nStatistical\nPhysical\nStatistical\nPhysical\nStatistical\nPhysical\n850 hPa\n- 0.4 *\n- 1.3\n29.1\n28.1 *\n7.5 *\n7.6\n500 hPa\n-14.4 *\n-15.8\n38.8 *\n40.7\n9.7\n9.5 *\n250 hPa\n- 4.1 *\n- 5.6\n58.7 *\n59.3\n16.4\n15.6 *\n100 hPa\n- 0.0 *\n1.6\n53.0\n51.1 *\n10.1\n9.8 *\nTable 3. Verification of 3 Day Forecasts from the Second Data Impact\nStudy, April 6, 1988 - April 18, 1988. The better score is\nindicated by an asterisk (*) .","Clear Physical Retrievals\nPressure (mb)\n150\n100\n70\n50\n850\n700\n500\n400\n300\n250\n200\n70.6\n92.2\n39.5\n46.5\n50.7\n63.3\n60-70S\n20.8\n25.9\n26.9\n28.3\n35.6\n50-60S 12.3 19.6 23.1 26.1 29.8 27.8 31.1 24.7 34.2 37.4 40.2\n18.8\n21.9\n23.9\n26.4\n33.5\n40-50S\n9.6\n10.2\n12.9\n14.9\n18.4\n19.7\n19.9\n15.8\n20.8\n17.0\n19.4\n23.3\n25.7\n24.2\n30-40S\n7.6\n11.9\n12.5\n18.8\n14.1\n16.7\n12.5\n11.1\n20-30S\n9.4\n12.1\n12.6\n13.2\n12.8\n12.0\n12.5\n13.5\n21.2\n8.7\n8.4\n10.3\n11.6\n7.7\n10-20S\n5.4\n7.5\n8.1\n21.9\n5.6\n6.9\n8.4\n11.0\n13.8\n14.3\n13.8\n14.3\n11.7\n0-10S\n4.3\n20.3\n16.3\n22.5\n8.7\n10.9\n12.6\n13.4\n15.4\n0-10N\n6.3\n5.6\n7.7\n10-20N\n---\n21.1\n18.0\n19.6\n8.3\n12.0\n15.0\n16.4\n17.6\n20-30N\n5.2\n8.0\n7.8\n15.5\n15.1\n16.3\n14.2\n15.0\n18.0\n30-40N\n6.0\n6.0\n7.6\n7.8\n12.4\n19.2\n15.7\n19.2\n11.9\n14.1\n14.2\n14.5\n14.8\n40-50N\n7.3\n7.7\n9.4\n30.0\n21.3\n20.6\n27.3\n34.2\n31.6\n50-60N\n11.2\n9.4\n17.3\n21.7\n23.0\n60-70N\n---\nTable A.: 1 (a) Minimum forecast error standard deviations by ten degree\nlatitude band for Pacific Ocean clear physical retrievals.","Partly Cloudy Physical Retrievals\nPressure (mb)\n850\n700\n500\n400\n300\n250\n200\n150\n100\n70\n50\n60-70S\n50-60S\n40-50S\n30-40S\n20-30S\n10-20S\n10.6\n10.9\n12.1\n17.7\n17.8\n19.5\n21.7\n22.1\n21.1\n18.7\n28.4\n0-10S\n6.0\n7.9\n8.9\n12.2\n14.7\n14.8\n16.5\n19.2\n19.7\n18.3\n23.3\n0-10N\n5.4\n10.7\n12.9\n12.2\n13.6\n15.8\n18.2\n22.6\n17.8\n14.9\n23.4\n10-20N\n7.1\n9.0\n10.3\n10.7\n11.6\n13.5\n16.0\n16.6\n21.0\n17.1\n24.0\n20-30N\n8.2\n9.1\n9.1\n7.9\n9.9\n10.3\n13.3\n17.9\n23.1\n18.1\n24.4\n30-40N\n10.6\n13.5\n17.5\n17.6\n15.4\n15.5\n21.6\n19.8\n19.6\n13.6\n14.1\n40-50N\n50-60N\n60-70N\nTable A.1(b). Same as (a) except for partly cloudy retrievals","Cloudy Physical Retrievals\nPressure (mb)\n100\n70\n50\n850\n700\n500\n400\n300\n250\n200\n150\n60-70S\n19.1\n17.2\n20.1\n27.6\n31.3\n30.5\n44.3\n43.5\n54.9\n70.0\n88.3\n50-60S\n17.0\n19.2\n28.3\n30.0\n29.4\n28.4\n36.9\n39.3\n36.6\n43.0\n61.7\n40-50S\n9.6\n14.6\n18.5\n21.1\n23.1\n23.8\n26.7\n27.7\n24.3\n27.4\n41.1\n30-40S\n6.2\n10.1\n15.5\n20.1\n23.1\n20.4\n25.7\n27.2\n31.0\n25.1\n26.1\n20-30S\n12.2\n16.4\n21.5\n26.8\n28.9\n26.6\n22.6\n25.1\n21.2\n17.0\n26.1\n10-20S\n10.1\n12.3\n15.6\n13.8\n13.8\n13.6\n14.0\n14.6\n19.9\n17.5\n25.6\n0-10S\n---\n---\n---\n0-10N\n6.2\n8.5\n9.4\n11.4\n14.4\n16.8\n20.5\n21.6\n18.3\n19.2\n27.2\n10-20N\n6.2\n7.3\n7.4\n9.0\n8.7\n9.2\n12.9\n19.1\n21.9\n20.7\n23.1\n20-30N\n9.9\n9.8\n11.2\n13.1\n17.9\n21.3\n22.5\n24.5\n23.6\n18.0\n20.7\n30-40N\n8.0\n9.4\n12.1\n13.5\n16.0\n19.5\n24.2\n23.4\n26.6\n25.2\n25.9\n40-50N\n13.0\n19.2\n20.1\n23.3\n24.6\n24.8\n26.1\n31.9\n39.9\n32.2\n26.6\n50-60N\n5.7\n8.8\n10.9\n27.3\n31.3\n33.1\n36.8\n48.1\n49.1\n47.1\n52.2\n60-70N\n---\n---\nTable A.1(c). . Same as (a) except for cloudy retrievals","Physical Retrieval Type\nClear\nPartly Cloudy\nCloudy\n60-70S\n18\n0\n18\n50-60S\n60\no\n60\n40-50S\n25\n0\n125\n30-40S\n51\n0\n82\n20-30S\n74\n0\n42\n10-20S\n93\n7\n27\n0-10S\n21\n32\n0\n0-10N\n13\n35\n10\n10-20N\no\n31\n5\n20-30N\n10\n18\n4\n30-40N\n15\n5\n6\n40-50N\n8\n0\n4\n50-60N\n5\n0\n2\n60-70N\n0\no\no\nTable A. 2. . Number of 2.5 degree boxes for which a minimum of 10 retrievals\nany particular type were available during the period of July 20 - August\nof\n18, 1988.","500 MB HEIGHT DIFFERENCE (M) -- (MRFX-MRF6)\nVALID 00Z 19 SEP 87\n00-HR MRFS FORECAST\nFigure 1. A forecast comparison from\nsee\nthe first data impact study. 500\n589\n989\nhPa geopotentials (thin lines, dam)\n37388\nH\nare from the verifying operational\nanalyses. Left column - forecasted\n0\nerrors (m, negative values dashed)\nH\nS\nfrom the operational MRF at 24-,\n48-, and 72-hours. Right Column -\ndifferences between experimental\n60\nand operational MRF initialized\nH\n500 hPa heights (top, m, negative\n20\nvalues dashed) and forecasted error\non\nBS\ndifference fields (m, negative\nvalues dashed) at 24-, 48-, and\n20\n-12.\n72-hours. A positive error\n40\ndifference indicates higher heights\nin the experimental system.\n500 MB HEIGHT DIFFERENCE (M) -- (MRFX-MRFS)\nOPERATIONAL MRFS -- 500 MB HEIGHTS (DM) / ERROR (H)\nVALID 00Z 20 SEP 87\n24-HR MRFS FORECAST\nVALID 00Z 20 SEP 87\n24-HR MRFS FORECAST\nH\n58G\n586\n588\n586\n586\n588\n588\n$\n77\n28\nIS\n26\nb\nsa\n564\n37\n1\n-31\n8\nH\n24\n95\n20\n-53\n-58490\n119\n80s\n492\n488\n489\nT60\n720 -80\n40\n500 HB HEIGHT DIFFERENCE (M) -- (MRFX-HRFS)\nOPERATIONAL MRFS -- 500 MB HEIGHTS (DM) / ERROR (H)\nVALID 002 21 SEP 87\n48-HR HRFS FORECAST\n48-HR MRFS FORECAST\nVALID 00Z 21 SEP 87\n-12\n585)\nLAC\nto 586\ns85\n584\n586 586\n585\n585\nIS\nTO\n576\n-ZO\n38\n20\n20\n55)\n80\n30\nTCO\n100\n200\nso\n50\n91\n-CO\n-100\n-20\n120\n80\n480\n480\nan\n500 MB HEIGHT DIFFERENCE (M) -- (MRFX-HRFS)\nOPERATIONAL MRFS -- 500 HB HEIGHTS (DH) / ERROR (M)\nVALID 00Z 22 SCP 87\n72-HR MRFS FORECAST\n72-HR MRFS FORECAST\nVALID 00Z 22 SEP 87\n584\n587\n10\nZ676\n$7.6\n88\n-160\n534\n3\n140\n50\n110\n240\ndo\n-100\n200\nuper\n480\n160\n20","50\n50\n8.\n5.1\n200\n200\nL\nL\n-1.7\n5.5\n400\n400\n600\n600\n600\n800\n1000\n1000\n90S\n602\n30S\no\nSON\n60N\n90N\nLATITUDE\nFigure 2 . Zonal mean difference in height\nbetween analyses with physical retrievals\nand analyses with statistical retrievals\nduring the first data impact study.\nContour interval 5 m.\n50\n50\n