C£S'. is: Mb 5>s r ^rcs o* NOAA Technical Report NESS 73 Evaluation of a Balanced 300-mb Height Analysis as a Reference Level for Satellite-Derived Soundings WASHINGTON, D.C. JANUARY 1976 UNITED STATES DEPARTMENT OF COMMERCE National Oceanic and Atmospheric Administration National Environmental Satellite Service NOAA TECHNICAL REPORTS National Environmental Satellite Service Series The National Environmental Satellite Service (NESS) is responsible for the establishment and operation of the environmental satellite systems of NOAA. Publication of a report in NOAA Technical Report NESS series will not preclude later publication in an expanded or modified form in scientific journals. NESS series of NOAA Technical Reports is a continua- tion of, and retains the consecutive numbering sequence of, the former series, ESSA Technical Report National Environmental Satellite Center (NESC) , and of the earlier series, Weather Bureau Meteorological Satellite Laboratory (MSL) Report. Reports 1 through 39 are listed in publication NESC 56 of this ser- ies. Reports 1 through 50 in the series are available from the National Technical Information Service (NTIS), U.S. Department of Commerce, Sills Bldg., 5285 Port Royal Road, Springfield, Va. 22151, in pa- per copy or microfiche form. Order by accession number, when given, in parentheses. Beginning with 51, printed copies of the reports are available through the Superintendent of Documents, U.S. Government Printing Office, Washington, D.C. 20402; microfiche available from NTIS (use accession number when available). Prices given on request from the Superintendent of Documents or NTIS. ESSA Technical Reports NESC 40 Cloud Measurements Using Aircraft Time-Lapse Photography. Linwood F. Whitney, Jr., and E. Paul McClain, April 1967, 24 pp. (PB-174-728) NESC 41 The SINAP Problem: Present Status and Future Prospects; Proceedings of a Conference Held at the National Environmental Satellite Center, Suitland, Maryland, January 18-20, 1967. E. Paul McClain, October 1967, 26 pp. (PB-176-570) NESC 42 Operational Processing of Low Resolution Infrared (LRIR) Data From ESSA Satellites. Louis Rubin, February 1968, 37 pn. (PB-178-123) NESC 43 Atlas of World Maps of Long-Wave Radiation and Albedo — for Seasons and Months Based on Measure- ments From TIROS IV and TIROS VII. J. S. Winston and V. Ray Taylor, September 1967, 32 pp. (PB-176-569) NESC 44 Processing and Display Experiments Using Digitized ATS-1 Spin Scan Camera Data. M. B. Whitney, R. C. Doolittle, and B. Goddard, April 1968, 60 pp. (PB-178-424) NESC 45 The Nature of Intermediate-Scale Cloud Spirals. Linwood F. Whitney, Jr., and Leroy D. Herman, May 1968, 69 pp. plus appendixes A and B. (AD-673-681) NESC 46 Monthly and Seasonal Mean Global Charts of Brightness From ESSA 3 and ESSA 5 Digitized Pic- tures, February 1967-February 1968. V. Ray Taylor and Jay S. Winston, November 1968, 9 pp. plus 17 charts. (PB-180-717) NESC 47 A Polynomial Representation of Carbon Dioxide and Water Vapor Transnission. William L. Smith, February 1969 (reprinted Anril 1971), 20 pp. (PB-183-296) MFSC 48 Statistical Estimation of the Atmosphere's Geopotential Height Distribution From Satellite Radiation Measurements. William L. Smith, February 1969, 29 pp. (PB-183-297) NESC 49 Synoptic/Dynamic Diagnosis of a Developing Low-Level Cyclone and Its Satellite-Viewed Cloud Patterns. Harold J. Brodrick and E. Paul McClain, May 1969, 26 pp. (PB-184-612) NESC SO Estimating Maximum Wind Speed of Tropical Storms From High Resolution Infrared Data. L. F. Hubert, A. Timchalk, and S. Fritz, May 1969, 33 pp. (PB-184-611) NESC 51 Application of Meteorological Satellite Data in Analysis and Forecasting. Ralph K. Anderson, Jerome P. Ashman, Fred Bittner, Golden R. Farr, Edward W. Ferguson, Vincent J. Oliver, Arthur H. Smith, James F. W. Purdom, and Ranee W. Skidmore, March 1974 (reprint and revision of NESC 51, September 1969, and inclusion of Supplement, November 1971, and Supplement 2, March 1973), pp. 1 — 6C-18 plus references. NESC 52 Data Reduction Processes for Spinning Flat-Plate Satellite-Borne Radiometers. Torrence H. MacDonald, July 1970, 37 pp. (COM-71-00132) (Continued on inside back cover) „ ATMQSP^ *'r ^MENJ 0* G ° NOAA Technical Report NESS 73 Evaluation of a Balanced 300-mb Height Analysis as a Reference Level for Satellite-Derived Soundings ALBERT THOMASELL, JR. WASHINGTON, D.C. JANUARY 1976 a o *i UNITED STATES DEPARTMENT OF COMMERCE Rogers C.B. Morton, Secretary .■a National Oceanic and Atmospheric Administration V Robert M. White, Administrator O «/> National Environmental Satellite Service t3> David S. Johnson, Director CONTENTS Abstract 1 1.0 Introduction 1 2.0 The analysis method 3 2.1 Height analysis 3 2.2 Wind analysis 4 2.3 Data error checking 4 2.4 Aircraft wind editing 5 3.0 Experimental results 7 3.1 Details of the experiment 7 3.2 Evaluation of the balanced height analysis with observed heights ... 8 3.3 Evaluation of the final analysis with observed heights 12 3.4 Comparison of the CRAM analyses with the NMC analysis 18 3.4.1 Numerical comparison 18 3.4.2 Graphical comparison 20 4.0 Summary and conclusions 23 Acknowledgments 24 References 24 ii EVALUATION OF A BALANCED 300-MB HEIGHT ANALYSIS AS A REFERENCE LEVEL FOR SATELLITE -DERIVED SOUNDINGS Albert Thomasell, Jr. Meteorological Satellite Laboratory National Environmental Satellite Service NOAA, Washington, D.C. ABSTRACT. A technique is developed and evaluated for using wind observations through application of the balance equation to improve the accuracy of objective height analysis in regions between height observations to provide reliable reference heights for satellite derived soundings. At upper levels (near 300 mb) , numerous aircraft winds and satellite observed cloud vector winds are available for this purpose. In regions of moderate size, where the height analysis is determined primarily by winds and where the winds are deemed sufficiently dense and accurate, the technique produces interpolated height values with an estimated rms error of 30 m or less 80 to 851 of the time. Where these conditions are met it is concluded that the technique provides reliable reference heights. 1.0 INTRODUCTION To obtain height profiles from satellite measured radiances, it is neces- sary to specify the height accurately at some arbitrary reference level (Smith, Woolf, and Fleming, 1972). These reference heights are usually obtained from an analysis at some specified constant pressure level : where observations are plentiful, there is no particular problem in obtaining a height analysis that is accurate within the noise limit of the data. In regions devoid of height observations, however, values must be interpolated to obtain a continuous analysis. In such regions, wind observations may be used in the interpolation process by the use of any one of several wind- height relationships. It is the goal of this study to develop a technique that makes full use of wind observations for height interpolation in the analysis, and to eval- uate the accuracy of such values with regard to their suitability as reference heights. The objective analysis technique developed and tested here uses the wind-height approximation embodied in the balance equation (e.g., Haltiner and Martin, 1957) to incorporate winds into the analysis of height. The technique was applied to data at the 300-mb level to exploit the normally abundant aircraft winds that are available at or near this level in otherwise data sparse regions over the oceans. The study was motivated primarily by the availability of these winds and the expected increase in high level satellite derived winds. Calculations performed on the polar stereographic grid provide an analysis for most of the Northern Hemisphere. The basic technique used is the Conditional Relaxation Analysis Method (CRAM) (Thomasell and Welsh, 1963) . Observations are used to define inter- nal boundary point values on the grid, and then values interpolated for all nonboundary points require that the interpolated values satisfy the solution of a Poisson equation. The forcing function, the right-hand side of the Poisson equation, determines the shape of the resulting analysis at non- boundary points, and is calculated from whatever information is available for the problem at hand. The magnitude of the analyzed values is determined by peripheral boundary conditions and internal boundary values. The method thus permits nonlinear interpolation among data points accurate to the extent that the forcing function defines the true shape of the field. The balance equation, written as a Poisson equation in height, has been used by Phillips (1959) , Rosenthal (1960) , and Endlich, Mancuso and Shigeishi (1971) to obtain height fields from wind fields, primarily in the tropics where direct height observations tend to be inadequate for accurate analysis. These investigators have shown that for an area comprising most of the United States, where data are dense and relatively consistent, the balance equation produces a height field that differs from a conventional height analysis by approximately 15 to 30 meters rms. Rosenthal (1960) showed that the largest differences tended to occur in low center where the balanced heights were too high. In general, however, there was quite good agreement between the shapes of the balanced and the conventional height analyses. Because of its ability to define shape well in regions where winds are plentiful, the balance equation is used in CRAM to calculate the required forcing function from winds for interpolation among height observa- tions. Here, the use of the balance equation differs from that used by the above investigators in two important aspects. First, the analysis area is much larger; it covers most of the Northern Hemisphere, rather than just the United States. Second, the concept of internal boundary points defined by the height observations is introduced to limit the size of regions requiring interpolation. The balanced forcing function used for the height analysis is evaluated from a wind analysis. In the CRAM technique, wind is analyzed by components where the first guess is a geostrophic wind field with ageostrophic correc- tions obtained from a first-guess height field. Edited wind observations define internal boundary points and the Laplacian of the wind first guess comprises the forcing function. It is solely in the definition of the wind analysis that wind observations influence the subsequent height analysis. For each case on which the analysis method was tested, two different CRAM height analyses were produced. One, the balanced-height analysis, was con- structed entirely from the balanced forcing function and peripheral boundary conditions. This corresponds to the type of analysis produced by the above- mentioned investigators. The other, the final analysis, uses the same balanced forcing function, plus internal boundary values defined by observed heights. In both analyses, regions between boundary values contain inter- polated heights that conform to the balance equation. These interpolated heights may ultimately serve as reference heights for satellite derived soundings, so their accuracy is of prime concern, a priori one may assume this accuracy is a function of region size between boundary points, thus, the final analysis would be the better of the two. The basic reason for calculating the balanced-height analysis is to provide, where possible, direct measurements of the accuracy of balanced interpolated heights, using independent height observations, for a limited range of region size and wind quality. These measurements are then used to infer the accuracy in regions of the final analysis where no height observations are available. 2.0 THE ANALYSIS METHOD 2.1 Height Analysis CRAM requires that the analysis of height Z at non-boundary points satisfy the Poisson equation V 2 Z = F, CI) where F is a forcing function that defines the shape of the Z field. To incorporate the balanced wind law into the analysis, we use the balanced forcing function for the polar stereographic grid (Deutscher Wetterdienst 1960) given by F = £-£ c - - (V x Vf) • k - ?m 2 J(V,U) g g g 1 2 K 2 2 - - VK * Vm - - V m g g . i cv 88 . u % ^ 2 (2) g 8y 9y 9x 1 m 3V 8U 8m 2 " g LU 8x " v 8x J By > where <5 is the reference grid increment C381 km) , m is the local map factor, f isJJie coriolis parameter, and g is the acceleration of gravity. The vector V and its components U and V are scaled winds (Stackpole 1969) and are the true winds divided by the local map factor. The other symbols of (2) are defined by r - 1¥ iy g " 3x ' Dy' JC ,, U)E 5Y^.SV3U 3x 8y 3y 3x U 2 + V 2 K = Equation 2 shows that F is a function only of the wind field and latitude. Equation 1 is here solved by the implicit alternating-direction relaxation method, described by Mancuso (1967), which iterates on complete rows and col- umns rather than point by point. The method is applied with normal derivative boundary conditions obtained from the NMC operational 300-mb height analysis. For the final analysis, those observations of height which define internal boundary points are not permitted to change value during the relaxation solu- tion of (1). Since observations normally do not coincide with gridpoints, their information must in some way be translated to gridpoints for subsequent use in the analysis technique. In this study, a value from the first-guess field is interpolated at the location of the observation and the difference between the observation and the interpolated first guess value is added to the first guess at the nearest gridpoint. If more than one observation affects a gridpoint, an average difference is used to define the internal boundary value. The relaxation procedure forces the remaining gridpoints to assume values dictated by the forcing function, the internal boundary values, and the peripheral boundary conditions. To eliminate small scale irregulari- ties, a mild smoothing filter is applied to the analysis as a final step. 2.2 Wind Analysis In wind analysis, each component is analyzed separately. A first-guess field is obtained for each wind component by calculating a geostrophic wind field from a moderately smoothed version of the NMC height analysis. Smooth- ing was found necessary to suppress spurious, large geostrophic winds at low latitudes. Smoothing also has the deleterious effect of attenuating small scale features and of reducing the height gradient, and, hence, the geo- strophic wind speed throughout the analysis area. The geostrophic wind field is modified to include ageostrophic corrections as outlined by Arnason, et al* (1962). Each wind component is analyzed by the CRAM method in which the forcing function is defined as the Laplacian of the modified first -guess field. All available edited wind observations are used to define internal boundary values, and the Poisson equation is solved by relaxation with fixed periph- eral and internal boundary values. As a final step, the wind analysis is smoothed lightly with a filter (Thomasell et aU 1966) to remove small scale irregularities. For one series of tests, the analyzed winds were used in unmodified form to calculate F in equation (1) . These winds are later referred to as divergent winds. In another series, the winds were made non-divergent by Endlich's (1967) method of altering wind fields. 2.3 Data Error Checking Because the MC analysis, itself the product of a comprehensive error checking procedure, is readily available, it is used as the basis for de- tecting errors in both the height and wind observations used in this study. Height error checking is simple. If a height observation differs from the NMC analysis by more than 100 meters, it is discarded. With this discard limit, surviving heights agree with the NMC analysis within 30 meters rms. Wind vectors are checked by comparing them with geostrophic wind vectors interpolated from the NMC analysis at the locations of the wind observations. The error detection method is essentially the same as that devised by Endlich et at. ^(1971) . Let v\represent the larger of the two wind vectors and V , the smaller, ihen the ratio of the dot product of the two vectors to £he square of the larger wind speed , v s ' V L |V a | R = * , L - ±J± Cos 0, provides a useful decision index for error checking. The angle between the two winds is given by 0. The ratio R expresses the projection of the smaller vector on the larger vector as a percentage of £he larger, wind speed. The maximum value of R is +1, which results when V s and V_ are identical. When the vectors are equal in magnitude but opposite in direction, (6=180°) , a minimum value R=-l is obtained. Orthogonal vectors produce R=0. An observed wind vector is discarded if R < R min ' where R^ is a parameter that controls the maximum, angular departure and the maximum difference in wind speed for a given Vt . In practice, this method of wind error checking and, in particular, the value Rjnin =0.3 appears to be satisfactory. 2.4 Aircraft Wind Editing The observations used in the wind analyses are synoptic rawinsonde and bogus winds at 300 mb, and aircraft winds that are usually both asynoptic and off- level. The raw aircraft winds generally present a chaotic picture and require some editing and modification. First, the aircraft winds are screened and all observations outside the altitude interval 25,000 ft to 38,000 ft and the time interval + 6 hours from map time are discarded. Then, the aircraft winds are made quasi - synoptic by advecting them in a smooth steering flow- -forward for early data and backward for late data--for a distance proportional to the steerir-cr flow and the age of the report. Large-scale steering flows have been de- scribed by Thomasell and Welsh (1968) and Nagle and Hayden (1971) . The steering flow used here was obtained by smoothing the first guess height field to eliminate features of synoptic scale and smaller. After the aircraft winds are edited and modified, they are subjected to the wind error checking method described in the previous section. Figure la, for January 18, 1970 at 0000 GMT, shows a typical set of un- edited winds available for analysis at the 300 -mb level. The larger barbs represent rawinsonde and bogus winds; the smaller barbs, found only over ocean regions, are aircraft winds. Figure lb shows the same set of winds after O O o •-a CO V) h3 O in -i 1 o o to o o to u Ctj 7 under the assumption that the true analysis error at a data point is uncorrelated with the data noise there. A useful interpretation of C7 is that, within an equivalent region, it represents the difference between a balanced height analysis with zero bias and an analysis (assumed perfect) constructed from a dense network of height observations. In this sense, a-p is directly comparable to the verification statistic used by Phillips (1959), Rosenthal (1960), and Endlich et at. (1971) for evaluating their balanced height analyses. Tables 1 and 2 give values of on and ag for three separate cases for the Europe and the United States verification areas. It is evident from these tables that both o>j and ag undergo significant changes from case to case and from one area to another. To help describe this variability with greater certainty, values of a^, a^, and or were calculated for 28 cases. Their frequency distributions, for 5-meter intervals, are given in table 3 for the United States and Europe areas. Table 3 shows that the distributions for 14 Table 3, -Frequency distribution of the verification parameters o^, a-j, and o^ obtained from 28 cases Value of o parameter (5-m intervals) Frequency of occurrence (%) United States Eurooe °E a T a N a E a T a N 5.0 10.0 15.0 20.0 25.0 30.0 35.0 40.0 45.0 4.9 9.9 14.9 19.9 24.9 29.9 34.9 39.9 44.9 49.9 0.0 0.0 0.0 0.0 0.0 0.0 0.0 7.1 0.0 0.0 0.0 0.0 3.6 10.7 46.4 0.0 3.6 0.0 10.7 39.3 42.9 0.0 17.9 46.4 32.1 10.7 10.7 7.1 32.1 5.0 28.6 17.9 0.0 17.9 17.9 3.6 10.7 7.1 0.0 42.9 10.7 0.0 7.1 3.6 0.0 3.6 14.3 0.0 3.6 0.0 0.0 25.0 0.0 3.6 3.6 0.0 3.6 3.6 0.0 Table 4. --Mean and standard deviation (a) of the verification parameters a E , a-p, and a^ obtained from 28 cases Verification Verification area parameters united States Europe Mean a Mean a Cm) Cm) Cm) Cm) a E 26.9 8.0 34.0 6.4 Orn 21.3 8.6 26.7 7.4 a N 15.8 3.2 20.5 2.4 15 ag and ox are not gaussian, but, rather, are skewed with peak frequencies tending toward the lower values. The means and standard deviations of the three verification parameters ag, o^r, and o^ for the United States and Europe verification areas are given in table 4. Data noise, on, is seen in tables 3 and 4 to be greater in Europe than in the United States; however, in both areas the values of noise are restric- ted to a relatively narrow range. For the United States area, about 901 of the noise values lie in the range 10 to 20 meters; in Europe, over 951 of the noise values are in the range 15 to 25 meters. The mean noise level in the United States area is 15.8 meters and in Europe is 20.5 meters. The greater noise level in the Europe area may be attributed to the use there of a relatively large number of different types of radiosonde instruments. Whether oe or err is chosen as a measure of interpolation error in equiv- alent regions of the final analysis, it is apparent from the wide distri- bution of these parameters in tables 3 and 4 that no single value is representative of the interpolation error. The error may be meaningfully expressed only in terms of a probability statement. Toward this end, esti- mated probability distribution functions constructed from the data in table 3 are presented in figure 4. Each function gives the probability that a, now treated as a continuous random variable, will be equal to or less than some prescribed value 0}$\x. Functions are given for oj and 0£ for the Europe and United States verification areas. By coincidence, the functions for erg in the United States and for cr in Europe were so nearly alike that they are given as a single curve in figure 4. 1.0 1 — -i 1 1 — — i — i— — ' — J»«^5jS5 PT 0.9 - 0.8 - 0.7 1 0.6 i b. 0.5 UNITED/ STATES / fa i /UNITED! 1 STATES J Ft / EUROPE / he EUROPE - CO O £ 0.4 - 0.3 - 0.2 - - 0.1 - - 0.0 y i / 1 1 1 1 1 1 10 20 30 cr (meters) 40 50 Figure 4. --Estimated probability distribution functions for oj and aj£ for Europe and the United States. 16 The Oj function for the Europe area for most probability levels is roughly only 5 meters larger than that for the United States and one half the difference between the corresponding erg functions. Thus, ov is some- what more independent of area than Qg. The slightly lower values of a T for the United States area, compared with those for Europe, may be mainly ascribed to the smaller size of the United States area, although some of the difference may be due to slightly more accurate or consistent winds in the United States. The large range of values associated with eg and a^ within a given veri- fication area is directly related to two factors, wind quality and intensity of curvature in the height field. The high values of a are associated with wind sets of inferior quality, marked curvature, or both, and the low values with unusually good wind sets or smooth height contours with little curvature. The practical determination of equivalent regions is made difficult by the lack of reliable measures of wind accuracy. For this study they were estab- lished by subjective comparisons of wind sets. The equivalent regions, of course, may occur at any locations throughout the analysis area where the required conditions are met. On the other hand, no estimate of the inter- polation error can be made for the final analysis where the region is too large or where the wind data are insufficient. Figure 5. --Zones A and B containing equivalent interpolation regions for which estimated probability distribution functions o>r are given in figure 6. Asterisks indicate the locations of radiosonde stations from which height observations are normally available. 17 Figure 5 shows two different zones within which it was deemed possible to estimate interpolation error; within each of these are a number of individual interpolation regions that, subjectively, are judged to be approximately homogeneous. The asterisks in figure 5 indicate the locations of rawinsonde stations where height observations (used as internal boundary points) are normally available. The spaces between the height observations are the interpolation regions for which estimates of analysis error are desired. In the oceanic regions excluded from zones A and B in figure 5, in particular the large mid-Pacific area, there normally are not enough wind observations to qualify these areas as equivalent regions. 10 20 30 40 cr T (meters) Figure 6. --Estimated probability distribution functions for 07 for the interpolation regions in zones A and B shown in figure 5. 18 Figure 6 shows estimated probability distribution functions for the param- eter cr-p for zones A and B. The interpolation regions in zone B were judged to be equivalent to the Europe area; the B curve in figure 6 is identical to the Europe area a-p curve in figure 4. The interpolation regions in zone A, based on a trade-off between region size and wind quality, were judged to be slightly inferior to the United States area, primarily because of the con- sistently high wind quality available in the United States area. For lack of numerical measures of quality, the zone A curve in figure 6 was arbi- trarily placed midway between the United States area and the Europe area Of curves shown in figure 4. No error functions for ag are given in figure 4 because this parameter is data -noise dependent, and the geographical distribution of data noise is generally unknown. Figure 6 shows a rather small difference in interpolation error between zones A and B; further, approximately 80 to 851 of the time ax is less than 30 meters. Experience with measured errors in Europe and the United States shows that errors less than 30 meters represent analyses in the good-to- excellent category. Errors between 30 and 40 meters rms represent marginal analyses, and errors greater than 40 meters rms represent poor analyses. Thus, in this study for zones A and B, the interpolation error associated with aircraft winds and the balanced wind law is quite acceptable most of the time. 3.4 Comparison of the CRAM Analyses With the NMC Analysis Numerical and graphical comparisons of the CRAM analyses with the NMC analysis are given here to illustrate to what degree the balanced height and final analyses agree with an accepted, widely used, standard analysis. These comparisons with the NMC analysis substantiate the large scale bias and the large -amplitude, synoptic-scale difference (noted earlier in table 1) that are present in the balanced height analyses. They also show the dramatic reduction of these differences effected by the final analysis. The synoptic scale difference patterns, which are mirrored in the final analysis, but with much smaller amplitude, show a systematic loss of amplitude of synoptic scale features in the balanced height analysis. Most significantly, the comparisons show that the final analysis, except for no-data regions, is virtually equivalent to the NMC analysis. 3.4.1 Numerical Comparison Verification statistics for the balanced height analysis compared with the NMC analysis are presented in the upper half of table 5. These statistics are calculated for the entire analysis area. Here the mean error has little significance because the relaxation procedure for producing the balanced height analysis forces it to be small. With the exception of the relatively good divergent wind analysis case for 27 March 1971, the rms differences are seen to be quite large. In contrast, the final analysis comparisons with the NMC analysis, shown in the lower half of Table 5, indicate markedly smaller rms differences, map for map. 19 Table 5 .- -Hemispheric comparison of balanced-height and final analyses with the NMC analysis Non-divergent wind Divergent wind Analysis Case analysis errors (meters) analysis errors (meters) comparison Mean rms a Mean rms a Balanced-height 18 Jan -3.3 60.8 60.7 -1.8 57.1 57.0 analysis minus 1970 NMC analysis 00Z 27 Mar -3,0 57.0 56.9 -1.1 41.8 41.8 1971 12Z 15 Jun -2.7 77.8 77.8 -1.5 81.8 81.8 1972 12Z Final height 18 Jan 7.6 31.5 30.6 0.1 28.5 28.5 analysis minus 1970 NMC analysis 00Z 27 Mar 12.5 33.6 31.1 6.2 32.1 31.5 1971 12Z 15 Jun 7.5 45.6 44.9 2.0 49.0 49.0 1972 12Z 20 i ) ^ -^^^"^ — ' / ' / X /TWVr\ X ' ^^^o^ / X/ 7^ /^ jf"f, ( y "■"*— " ?v^vv/^ /"C^ -^f^^ *s/H-' \ ^»rP*\. \ T=^4— ">X\W\\ /\ \ . 'l^ > ^ir~^&r<\ /tC /\ X^^^^^^V IM-'AlS ^\j\^7^ Ig V/ \/ ^^ ■\\3^\!aV \'' *\y ' /N /x / >^ 7T7 / i r^ \ -A Figure 7. --The NMC 300-mb analysis for 18 January 1970, 0000 GMT. 3.4.2 Graphical comparison The NMC 300-mb analysis for 18 January 1970, a typical case, is shown in figure 7. The measured winds available for this case are plotted in figure la (section 2.4) and the corresponding edited winds, in figure lb. A con- spicuous gap in wind coverage is apparent in the Pacific south of Alaska. This gap coincides with an elongated trough and ridge system in the NMC analysis. The balanced height analysis with divergent winds (fig. 8a) completely fails to define this system, presumably because of the lack of data. Outwardly, figure 8a resembles the NMC analysis, but suffers from an overall loss of smaller scale detail. The difference field between the divergent -wind, balanced- height analysis and the NMC analysis is shown in figure 8b. Here, a pronounced negative bias is apparent, especially over Europe, Africa, Asia, and the western Pacific. Synoptic scale patterns in the difference field with values in the range +_ 200 meters are associated with a systematic and substantial erosion of wave amplitude in figure 8a. Figures 9a and 9b show similar results for the nondivergent wind case, but display a larger overall negative bias in mid and upper latitudes. 21 9700 9^00 a. Balanced height analysis b. Balanced height analysis minus the NMC analysis s/n. sSkY \ — n — i — c j | I | /■ ■ J j^ 9^ s(7y\ j^yMj" ^/C^kL- ■ % &*C* Wm^ ^2vv S ^/^Jyy\ TOt^^ - rnHqfg ■•'SMB 8# 9p8u£^ Ss)\ /\ / / f\ fsKS§l i 7 ■') / ■ / > X v* •vK/v >v- c. Final analysis d.' Final analysis minus the NMC analysis Figure 8. --ORAM analyses and their comparisons with the NMC analysis for 18 January 1970, 0000 GMT. Divergent wind case. 22 a. Balanced height analysis b. Balanced height analysis minus the NMC analysis Vi 50 c. Final analysis d. Final analysis minus the NMC analysis Figure 9. --CRAM analyses and their comparisons with the NMC analysis for 18 January 1970, 0000 GMT. Nondivergent wind case. 23 The divergent version of the final analysis for this date is given in fig- ure 8c. This map very closely resembles the NMC analysis. The difference field for the final analysis, shown in figure 8d, compared with that for the balanced height analysis has markedly lower values, generally in the range +_ 50 meters. One region of large difference values occurs near the North Pole where no observations of any kind are available. The remaining pattern of difference values is seen to be correlated with ridges and troughs as in the balanced height analysis, but the amplitudes are much lower. Figures 9c and 9d illustrate final analysis maps for the nondivergent wind case and are seen to be essentially identical to their counterparts in figures 8c and 8d. From these results we may conclude that the divergent property of the wind field is important , only in very large interpolation regions; for smaller interpolation regions normally found in the final analysis it is negligible. Of most importance here is the finding that the final CRAM analysis and the NMC analysis are virtually equivalent. No claim of superiority can be made for either technique. However, this study has made it possible to evaluate the accuracy of the final CRAM analysis and, equivalently the NMC analysis, in regions of interpolated heights influenced by wind reports. From the results of section 3.3, we may state that most of the time (80 to 85%) either analysis technique will provide reliable reference level height values in these interpolation regions. 4.0 SUMMARY AND CONCLUSIONS An accurate height analysis is required to provide a reference level for the recovery of height soundings from satellite measurements of radiance. To this end, an objective analysis technique for analyzing pressure height has been developed to make full use of winds through the wind law embodied in the balance equation. The technique was applied to data at the 300-mb level where many aircraft winds are normally available in otherwise data void regions along standard air routes over the oceans. Evaluation of the technique shows that the analysis accuracy is very dependent upon the size of the region within which height values are deter- mined solely from winds and peripheral observations of height. Over a hemisphere, the analysis is quite unacceptable. For regions the size of the United States or smaller, bounded by some height observations and con- taining winds at least of the quality of edited aircraft winds, the analysis accuracy is characterized by rms errors of 30 meters or less about 85% of the time. Regional analyses with these error characteristics are judged to be good to excellent. Analyses of this quality generally may be achieved over most of the North Atlantic Ocean because of the relatively dense network of radiosonde stations and numerous aircraft winds. Over the North Pacific Ocean, quality regional analyses are more difficult to achieve because of the sparse network of radiosonde stations and the distribution of aircraft winds with respect to those stations. In particular, there is a large region in the mid-Pacific south of Alaska of questionable quality because of the general lack of wind and height observations. Further evaluation shows that the best analyses using the balance equation and all available winds and radiosonde data are essentially identical to the 24 operational NMC analysis. It is impossible to state which type of analysis is superior. This study, however, has provided new estimates of the expected error of regional analyses. It is concluded that the 300 -mb height analysis, with the exceptions noted above, would provide a reliable reference level specification for the re- trieval of satellite -derived vertical height profiles. ACKNOWLEDGMENTS Special appreciation is extended to Dr. Christopher Hayden of the Meteorological Satellite Laboratory for his thorough and enlightening review of the manuscript and for his many useful suggestions offered throughout the course of this study. Mr. Fred Nagle, also of this laboratory, freely gave his time and talents to help apply his personally developed computer programs for producing graphical displays of the analyses. REFERENCES Arnason, C, Haltiner, G.T. and Frawley, M. J. , 1962: Higher-order Geostrophic Wind Approximations. Monthly Weather Review , 90, 175-185. Deutscher Wetterdienst , 1960: Part F, "Transformation of the Basic Equations of Dynamic Meteorology into Coordinates of Stereographic Projection for the Purpose of Numerical Weather Prediction." 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Alishouse, July 1972, 49 pp. (COM-72-50963) NESS 60 Satellite Measurements of Aerosol Backscattered Radiation From the Nimbus F Earth Radiation Budget Experiment. II. Jacobowitz, W. L. Smith, and A. J. Drummond, August 1972, 9 pp. (C0M-72- 51031) MESS 61 The Measurement of Atmospheric Transmittance From Sun and Sky With an Infrared Vertical Sounder. W. L. Smith and H. B. Howell, September 1972, 16 pp. (COM-73-50020) NESS 62 Proposed Calibration Target for the Visible Channel of a Satellite Radiometer. K. L. Coulson and H. Jacobowitz, October 1972, 27 pp. (COM-73-10143) NESS 63 Verification of Operational SIRS B Temperature Retrievals. Harold J. Brodrick and Christopher M. Hayden, December 1972, 26 pp. (COM-73-50279) NESS 64 Radiometric Techniques for Observing the Atmosphere From Aircraft. William L. Smith and Warren J. Jacob, January 1973, 12 pp. (COM-73-50376) NESS 65 Satellite Infrared Soundings From NOAA Spacecraft. L. M. McMillin, D. Q. Wark, J.M. Siomkajlo, P. G. Abel, A. Werbowetzki, L. A. Lauritson, J. A. Pritchard, D. S. Crosby, H. M. Woolf, R. C. Luebbe, M. P. Weinreb, H. E. Fleming, F. E. Bittner, and C. M. Hayden, September 1973, 112 pp. (COM-73-50936/6AS) NESS 66 Effects of Aerosols on the Determination of the Temperature of the Earth's Surface From Radi- ance Measurements at 11.2 urn. H. Jacobowitz and K. L. Coulson, September 1973, 18 pp. (COM- 74- 50013) NESS 67 Vertical Resolution of Temperature Profiles for High Resolution Infrared Radiation Sounder (HIRS). Y. M. Chen, H. M. Woolf, and W. L. Smith, January 1974, 14 pp. (COM-74-50230) NESS 68 Dependence of Antenna Temperature on the Polarization of Emitted Radiation for a Scanning Mi- crowave Radiometer. Norman C. Grody, January 1974, 11 pp. (COM-74-50431/AS) NESS 69 An Evaluation of May 1971 Satellite- Derived Sea Surface Temperatures for the Southern Hemisphere. P. Krishna Rao, April 1974, 13 pp. (COM-74-50643/AS) NESS 70 Compatibility of Low-Cloud Vectors and Rawins for Synoptic Scale Analysis. L. F. Hubert and L. F. Whitney, Jr., October 1974, 26 pp. (COM-75-50065/AS) NESS 71 An Intercomparison of Meteorological Parameters Derived From Radiosonde and Satellite Vertical Temperature Cross Sections. W. L. Smith and H. M. Woolf, November 1974, 13 pp. (COM- 7S-10432/AS) NESS 72 An Intercomparison of Radiosonde and Satellite-Derived Cross Sections During the AMTEX. W. C. Shen, W. L. Smith, and H. M. Woolf, February 1975, 18 pp. (COM-75-10439/AS) PENN STATE UNIVERSITY LIBRARIES 111 1 /; >6-l9l fe NOAA-S/T 76-1917