College of Engineering Department of Meteorology and Oceanography Technical Report An Attempt to Use Satellite Photography in Numerical Weather Prediction James H. S. Brdley Christopher M. Hayden Akiael C. Wiin"-Nielsen, Project Director Supported by: Environmental Science Services Administration Contract Cwb-11145 Washington, D. C.

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TABLE OF CONTENTS Page LIST OF TABLES LIST OF FIGURES Vii ABSTRACT i 1. INTRODUCTION 1.1 Purpose 1.2 Method 2 2. REANALYSIS PROCEDURES 2.1 Basic Maps 4 2.2 Radiosonde Data 4 2.3 Vorticity 2.4 Stream Function 7 2.5 Estimation of Vorticity and Wind 8 2.6 Energetics 9 3. VERIFICATION 3.1 Change Correlation Coefficient, RMS 10 Error, Error Maps, Forecast Improvement Chart 3.2 Zonal Harmonic Analysis 12 4. HINDCAST-REFORECAST TECHNIQUE 4.1 Removal of Mountains and Friction 14 4.2 Conclusions 15 4.3 Computational Instability 15 4,4 Negative Absolute Vorticities 17 5. CASE OF 5 NOVEMBER 1963 5.1 Nature of System 20 5.2 Origins and Energetics of Such Systems 21 5.3 Errors of the Forecast 21 5.4 Reanalysis 23 5.5 Verification 23 6. CASE OF 26 JANUARY 1964 6.1 Synoptic Situation,. 29

ABLE OF CONTENTS (concluded) Page 7. CONCLUSIONS 58 8 SUGGESTIONS FOR FUTURE WORK 8l. The Analysis Problem 8.2 Continuity and Winds 61 8.3 Thermal Radiation Data 61 8.4 Gandin's Method of Omitted Stations 61 APPENDIX A. Successive Point Over-Relaxation 63 B. Diagnostics for the NMC Barotropic Model 68 C. Mosaics of TIROS Photographs, 69 26 January 1964. BI BLIOGRAPHY 72

LIST OF TABLES Table Page 4.1 Illustrative Locations of Negative 18 Absolute Vorticities, 0000Z 6 January 1964. 5.1 Amplitudes and Phases of Zonal 27 Wavenumbers 0-12, 5 November 963 Case. 6.1 Verification Statistics for SINAP 45 tream Function, 0000Z 26 January 964 Case. 6.2 Amplitudes and Phases of Zonal 56 Wavenumbers 0 and 1, 26 January 964 Case.

LIST OF FIGURES Figure Page 5.1 Above: Reanalysis area (interior rectangle) 22 and verification subarea for case of 5 November 1963. Dashed line indicates coverage by TIROS 7 orbit 2046 for 1934GMT 4 November. Below: Laplacian change field for OOOOGMT 5 November 1963. Units are in tems of meters. 5.2 NMC numerical analysis (dashed lines) and SINAP 24 relaxed.stream field for case of 5 November 1963. Stream function I isopletchs are D values labeled in tens of meters. 5 3 Left: NWP forecast minus observed for 1200GMT 25 6 November 1963. Isopletchs are stream function 4 differences labeled in tens of meters. Right: Forecast improvement chart for SINAP reanalysis of 5 November case. Isopleths, -are stream function V improvements labeled in meters. 6.1 NMC numerical analysis for OOOOGMT 26 January 30 1964. Stream function p isopleths are D values in tens of meters. 6.2 NMC forecast minus observed for 1200GMT 2;7 31 January 1964. Isopleths of stream function 4 difference are labeled in hundreds of meters. The dashed rectangle is the verification subset. Roman numerals identify error regions referred' to in the text. 6.3 Subareas used in 26 January stream function re- 33 analyses and verification. Satellite coverage is indicated by the dashed curves. I is TIROS 7orbit 3262 for 0342GMT; II is orbit 3264 for 0521GMT 26 January 1964. Rectangle 1 was included in reanalyses 1-6. Rectange 2 was added for reanalysis 3, Rectange 3 was added for reanalyses 4-6~ The exterior rectange is the verification subareao vii

LIST OF FIGURES (concluded) Figure Page 6.4 NMC numerical analysis (dashed lines) and SINAP 38 reanalysis 4 (solid lines) for case of 26 January. Stream function V isopleths are D values labeled in tens of meters. 6.5 Above: Reanalysis area and Laplacian change 42 field for vorticity reanalysis 1 for case of 26 January. Units are in hundreds of meters. Below: Relaxed stream field changes. Units are in tens of meters. 6.6 Laplacian change field and relaxed stream change 43 field for vorticity reanalysis 2 for case of 26 January. Units as in fig. 6.5. 6.7 Subarea forecast improvement charts for (left 49 to right) SINAP stream function reanalyses 4, 5 and 6 for case of 26 January. Stream function difference isopleths are labeled in tens of meters. 6.8 Subarea forecast improvement charts for (left 53 to right) SINAP vorticity reanalyses 1 and 2 for case of 26 January. Units as in fig. 6.7 A.1 Amplification factor against eigenvalue for 67 different values of c in Aitken extrapolation. C.1 Mosaic of photographs taken by TIROS VII, 70 orbital pass 3263, 0342GMT 26 January 1964. C.2 Mosaic of photographs taken by TIROS VII, 71 orbital pass 3264, 0521GMT 26 January 1964. viii

ABSTRACT TIROS photographs were used for barotropic reanalysis in the Pacific, changes in the stream function or its Laplacian being advected into areas with verification data by the NMC barotropic model, following McClain, Ruzecki and Brodrick. No significant forecast improvement was obtained in cases of unusually bad forecasts, despite experiments in varying the intensity of the reanalyzed systems. No continuity and no radiation data were available: the estimation of winds and vorticities is difficult. Hindcastreforecast procedures indicated that the main causes of error in unusually bad forecasts are not susceptible to satellite correction, and that difficulties in the balance equation had caused the stream...field to contain many negative absolute vorticities not present in the geopotential analysis The methods used would be more promising in cases with smaller forecast errors.

1 o INTRODUCTION 1o 1 Purpose It has been recognized for several years that the problems of forecasting over and on the eastern sides of large oceans might be alleviated by using satellite photographs to improve the analysis by- means of inferences about the fields of horizontal and vertical motion, temperature and humidity. A large sample of such papers can be found in almost every issue of the Monthly Weather Reivew for several years past. Rapid electronic computers have long been in routine use for large scale hydrodynamic forecasting: (see Thompson ~(1961), and Kibel (1963)), The integration of satellite data into such hydrodynamic schemes appeared to us a promising line of inquiry, although at present, modifications have been made only to the output from an automatic machine analysis program We have studied selected cases in which according to the Meteorological Satellite Center operational barotropic and baroclinic models gave unusually bad forecasts, using the techniques of McClain, Ruzecki and Brodrick (1965) to infer the stream, vorticity and vorticity advection fields from TIROS photographs when significant differences from NMC analyses appeared to exist over the Pacific Ocean. -1

-21.2 Method Either the 500 mb stream field or the 500 mb Laplacian field was reanalyzed by the methods and using the programs of McClain,: Ruzecki and Brodrick (1965) Since the few available conventional data were preserved (and conventional data which arrived too late for the NMC analysis introduced), it was necessary to forecast by the NMC barotropic model for some period, chosen as 36 hours, in order to propagate the modifications into another region where at least some verification data exist.- Attention was directed to the, quantitative assessment of the effects of changes in the intensity of the reanalyzed system. Further attempts were made to hindcast by a barotropic model without mountains or friction in order to elucidate how far the analysis required for a correct forecast might be ascertainable from satellite data. The numerical analysis problems of weather analysis and forecast models were investigated only in so far as improvements to them appeared likely to remove complications which masked changes due to satellite reanalysis. The verification programs of McClain, Ruzecki and Brodrick (1965) were used, plus verification in terms of zonal harmonics of the stream function in order to examine

-3separately those scales of motion which can be modified by the application of satellite data.

2. REANALYSIS PROCEDURES 2.1 Basic maps Five basic maps were printed from the NMC data tape for use with the reanalyses. These were: 500 mb heights, 500 mb streams, -12 hr 500 mb streams, 1000-500 mb thickness and 650 mb vertical velocity. These maps, in conjunction with the radiosonde data, were used in investigating the structure of the thermal advection and vertical velocity fields in the original NMC analysis. These permit some subjective analysis of the probable cloud formations prior to modfying the stream field or the vorticity field to more closely comply with the satellite photographs. 2.2 Radiosonde Data A program was prepared to extract conventional and bogus data from the Automatic Data Processing file of the NMC input tapes over any given grid rectangle or latitudelongitude sector. Station names were added from a look-up table. Listings of temperature, potential temperature, dewpoint, observed wind, D-value (height minus standard atmosphere height) and temperature advection (from the thermal wind equation) are made for all mandatory and significant temperature levels, and P-T diagrams and -4

-5tephigrams with automatically interpolated lines prepared for all radiosonde observations with enough levels. One seriously defective observation incorporated in the NMC analysis was found for OOOOZ 26 January 1964; other spurious points found appeared to have been excluded. The Northern Hemisphere Data Tabulations were used to supplement the ADP file with late data. 2.3 Vorticity Vorticity maps referred. to here are grid:point calculations of the five point finite difference str.eam Laplacians, The relative vorticity and vorticity advection are then written as: 2 V2, _ q__ ~2 ^ 2 22 2 42 qd` 2 2 ~ m 2 V 4d4F- J(m J?/7?df I2( ) O 0 f where V is the stream function, ~= -- I, J is the g Jacobian, m.: = (1 + sin 60) (1 + sin )-1 is the map factor, f is the Coriolis parameter at latitude 450N, d is the 0 NWP grid distance of 381 km. Printed maps are given as. 47 4 and J(,472 4) in meters and meters squared- respectively. In the following, the terms ""vorticity "~ and "'Laplacian" are used interchangeable to refer to the field of 2 2^~

-6The philosophy underlying modification of the vorticity is fully discussed. by McClain etalo (1965)o In essence,' the cloud- patterns viewed in the satellite photographs are assumed to be allied with areas of positive vertical velocity. This in turn is related to the vertical variation of the vorticity advection and horizontal Laplacian of the thermal advection. Since the latter terms are frequently additive, rather than compensatory (Pfeffer, 1962), and since a barotropic forecast model has been used, it is the normal practice to modify the vertical velocity field by variations in the vorticity field. It is apparent that this cannot be executed without some difficulty. Modifications of the vorticity field alter the vorticity advection, but the effect is only apparent after the. new stream field is obtained by relaxation. A second complication with reanalyses of the vorticity field is that there is no way of preserving observational data in close proximity to the reanalysis as it is impossible to predict the final form of the relaxed stream field. The difficulty can be circumvented only by restricting the size of the reanalysis area. A further difficulty of the vorticity reanalysis is the requirement that the-total relative vorticity be conserved in any modification. Failure to comply with this

restriction results in a relaxation stream field which evidences changes far outside the limits of the reanalysis area. The same effect is observed- if the vorticity modifications are sufficiently severe, but it is minimized through the conservation principle. This restriction places a considerable restraint on the subjectivity of the reanalysis and is quite time-consuming in terms of operational SINAP modifications For this reason, and those mentioned above, the majority of the work done under this project concerned stream-line reanalysis. 2 4 Stream function Stream finklds are printed as V with the symbol defined as above. Consequently the field is in meters. Modifications of the stream field are more straightforward than those of the vorticity- as the analyst is able to apply directly his knowledge of cloudy regions as related to wave patterns in the atmosphere.~ The integrity of the stream function modifications in conforming with the vorticity field is easily checked, though care must be exercised that negative absolute vorticities are not introduced. This problem occurred repeatedly on this work but only because the magnitudes of the stream function alterations were very large0 It is unlikely that smaller changes

would have the same effect. 2.5 Estimation of Vorticity and Wind While the positioning of stream or vorticity field modifications has been investigated quite broadly in the literature, the magnitude of such changes has understandably received little attention~ The satellite photograph provides no information concerning the primary atmospheric variables, nor, beyond some subjective interpretations, is it possible to determine the heights of the systems revealed by cloud formations. In all probability future work with satellite radiation data will alleviate these difficulties, but the work under this project was carried out solely with the cloud photographs. In essence, the analyst is guided by the available conventional data in the region of satellite coverage, wind direction estimates from the cloud photographs (Widger etoal.), persistence of systems recently over data dense areas, and climatology of the region. Beyond these aids, the magnitude of modifications is completely subjective. In an attempt to introduce some objectivity into the reanalysis procedure, considerable effort has been expended in an empirical study of the effects which variations in

magnitude of the modifications have on the forecast stream field. The results from this study of a single case cannot be considered general, but they certainly give an indication of the sensitivity of the reanalysis procedure. 2.6 Energetics We have assumed that the systems present in our reanalysis waves are similar to those known in areas of dense observations, i.e. that the barotropic and baroclinic mechanisms discussed by McClain, Ruzecki and Brodrick (1965) are dominant. A scale analysis by the method of Kibel (Chapter 3) suggests that this is valid even for the system of 5 November 1963. In order to influence the forecast significantly the meteorologist is both justified and obliged to draw conclusions about larger structures and scales of motion than are directly visible on the isolated swaths we have used. This extension has been made according to accepted synoptic principles.

3. VERIFICATION 3.1 Change Correlation Coefficient, RMS Error, Error Maps, Forecast Improvement Chart Verification of the improvement introduced by modifications in the analyses can be at best only tentative. The procedure utilized here follows that of the Satellite Laboratories in running numerical forecasts from both the NMC and SINAP initial stream fields. The 36 hour forecast fields are then compared with the NMC analyzed field for that time. Two problems are immediately apparent. Firstly, since the forecast model is barotropic, no initial modifications can correct baroclinic development. This problem is obviated by choosing for study only those cases where we are told that error charts derived from NMC barotropic and baroclinic forecasts both show large discrepencies from the observed state, This suggests that the failure of both forecasts may be due to poor specification of the initial state rather than baroclinic development. Secondly, and more importantly, the procedure assumes inherently that the NMC analysis at the forecast time is itself accurate. Since the analysis is derived from a previous forecast modified by observation, the analysis in all likelihood is biased to the previous forecast, at least in areas of sparse data. The verification analysis itself is thus suspect, particularly for those -10

-11cases where SINAP modification produces forecast changes which are in sparse data regions. This problem is evidently dependent on the scales of the systems involved. Even if it were possible to delineate the smaller systems from the satellite coverage, it is doubtful that improvements could be recognized in the verification statistics. It may be concluded that the modifications must be applied to the larger systems. The statistical verification procedure used in the reanalysis program at the Satellite Laboratories was used without modification. Root mean square errors and correlation coefficients were calculated from the NMC and SINAP barotropic forecasts for the following fields: stream function, vector geostrophic wind, stream Laplacian and stream Jacobian. More specifically, difference fields were utilized. For example with the stream field, the parameters from which the statistics were computed were: NMC forecast minus NMC initial field; NMC verification minus NMC initial field; and SINAP forecast minus SINAP initial field. In addition to the verification statistics two difference charts were computed for the forecast stream fields. These were: NMC forecast minus verify; SINAP forecast minus verify. Finally a forecast improvement chart was obtained

-12by subtracting the absolute magnitudes of the difference charts at each grid point. These charts permit detailed analysis of the point by point changes effected by the SINAP modifications. Computations were made over both the entire NMC 2329 grid and a subgrid which was determined to include only the region significantly affected by the reanalysiso 302 Zonal Harmonic Analysis The idea of analysis in zonal harmonics or any other orthogonal functions is to examine certain scales of motion separately; in this case, the zonal wavenumbers of the order of 12 in which modifications are made by the analyst. The corresponding weakness of harmonic analysis is that it diverts attention away from the meteorological system (wavegroup) visible on maps; harmonic analysis is most useful when the waves used have some almost autonomous existence and motion over the. period studied, or when barotropic or baroclinic interactions are conveniently describable in terms of them. Zonal Fourier analyses of the stream field in terms of sines, cosines, amplitudes and phases of wavenumberts 0-15 were made at 5 degree latitude intervals from 20 N to the pole0 The effects detected were large enough to indicate

that no further significant information would be obtained for our restricted verification purposes0 by more refined analyses in terms of surface harmonics, Gram-Schmidt grid orthogonal functions, or eigenvectors of the relaxation matrix used in the barotropic forecast. Analysis of the zonal mean stream function directed attention to changes in the zonal mean wind profile, as well as to changes in the hemispheric mean stream function-.caused by the boundary condition of the balance equation. This cannot radically alter the evaluation of - forecasts when the wind verification is poor, but it should be allowed for in calculating the RMS errors and correlations of changes in the stream function.

4. HINDCAST - REFORECAST TECHNIQUE 4.1 Removal of Mountains and Friction It was decided to prepare hindcasts from the verification data Jto the initial time in order to elucidate how far errors of analysis might be correctable by satellite data. First attempts rapidly overflowed in the mountain and friction terms, so they were deleted. Reforecasts to the verification time were prepared in order to cast light on the truncation error of this process. Mean and maximum forecast improvements for 5 November and 26 January were 46 and 53, and 183 and 333 meters repectively; and maximum errors were 111 and 201 meters respectively. The NMC barotropic forecast program and balance equation make the following approximations 1. The initial stream field is equal to the geopotential around the edge. 2. The tendency at the edge is zero. 3. The mean tendency over the whole grid (equally weighted for each point) is subtracted from interior points onLy, 4. The smoother does change edge points slightly we applied the smoother at every twelvth time stepo 5o Negative absolute vorticities are set to zero but the associated stream fields are not changed. -14

-15Tables 5.1 and 6.2 give some Fourier coefficients from these processes. 4.2 Conclusions It is clear both from the Fourier coefficients and from the maps that a substantial part of the error cannot be significantly influenced by isolated swaths of satellite photographs: much of it cannot be error in the initial analysis. In particular, the profile of the zonal mean required (hindcast) and observed shows differences up to 63 meters, and the required profile shows a greater pole-to-equator gradient. Wavenumber 1 shows little resemblance, and wavenumbers 2-15 no resemblance for 26 January 1964. On the other hand, the reforecasts also leave a good deal to be desired. While the mean forecast improvement (as defined by McClain, Ruzecki and Brodrick (1965) is 46 meters for 5 November 1963 and 53 meters for 26 January 1964, errors remain of 111 meters and 201 meters respectively. Around the edges differences reach 7 and 18 meters respectively, due to the smoother. 4.3 Computational Instability The suspicion of non-linear computational instability

arose from a hindcast-reforecast from 120OZ 27 January 1964 to OOOOZ 26 January 1964 and back, which was by far the worst of all the forecasts produced. Errors attained 450 meters, and an intense zonal jet replaced the strong block over the west coast of North America. The linear stability criterion (Knighting0 1962) was met in all cases by a factor slightly less than two. The hindcast was repeated with the over-relaxation coefficient a pre-determined function of time0 and with a diagnostic record tape (Appendix B): the two hindcasts bore no resemblance to each other. The hindcast was again repeated with half-hour time steps, and with the smoother applied at every twelfth step: the over-relaxation coefficient was a pre-determined function of time. The change in the time step made comparatively iittle difference to the hindcast0 and the explanation of this fact is unknown. Forecasts with the over-relaxation a function of time, with a diagnostic tape, and with half time steps were run from OOOOZ on both'5 November 1963 and 26 January 1964 to 1200Z the following day. It was concluded that computational instability was not a large factor in either of these cases, in the classical sense that the solution goes to infinity; yet it is clear from the Fourier analyses of the hindcastreforecast results that truncation errors and the irreversible

effects of the smoother and the zeroing of negative absolute vorticities introduce significant approximations. 4 4 Negative Absolute Vorticities The diagnostic program (Appendix B) prints the I,J and latitude-longitude location of each negative absolute vorticity and its ratio to the local Coriolis parameter. Ninety-two negative absolute vorticities occur in the original NMC stream field for 0000 GMT 26 January, with the largest rato -.o747f at 42,7 or 19.8 N 124.o2E. Of these, 29 are south of 20 N and 44 between 20 N and 30 N. One lies at 32,43 or 35.6 N 76.40W on land near Cape Hatteras. At 0000 0 GMT 5 November 1963,- 18 of the 55 are south of 20 No 28 between 20 N and 30 N, and the largest ratio is -o.567f at 23,47 or 18.8 N 53.4 0W A diagonal pattern is well marked (Table 41) and some triple groups suggest erratic high points in the stream field as though much short wave noise were present. Knighting (1962) gives the criterion for ellipticity of the balance equation as approximately that the absolute vorticity must exceed f/2; hand examination of a dozen points in the original geopotential field which had negative absolute vorticities in the stream field suggests that about a third of these points

-18violate the criterion for ellipticityo. No- points of negative absolute vorticity were found in this sample of the geopotential field During the forecast points of, negative absolute vorticity usually.intensify and propagate downwind, sometimes attaining -2.5fo. There is no apparent relation to the persistent points of slowest convergence,~ The smoother weakens them alL and removes some. In Iview of the slight changes in the forecast caused by halving the time step (section 4.2), with the smoother applied at every twelfth step, it is unlikely that negative absolute vorticities as, such greatly influence the cases studied. The ridge and trough positions in the stream and geopotential fields largely coincide, but we have not computed the geostrophic vorticity and momentum transports.. I J "Ratio I J Ratio 26 3.144 27 4.082 28 5.258 29 6.181 2 7. 747 43 6.568 44 5.070 45 6.234 46 7.o125 47 8.498 48 9.535 49 10.509 50 11.422 51 12.272 51 17.284 50 18.441 49 19.109' 44 44.165 45 45.407 44 46.522 16 36.1351' 17 37.176 16 38.030 TABLE 4.o1 Illustrative Locations of Negative Absolute Vorticities and Ratios to the Local Coriolis Parameter. NMC Stream Field, 500 rmb, 0000Z 26 January 1964o

-19From the stream and geopotential fields given on the NMC tapes, the complete balance equation is not satisfied by amounts approaching 100% even at points where the terms are individually large; including points at which the stream field has negative absolute vorticityo While we do not know what smoother is used in the operational balance equation, in our opinion further clarification of this matter is advisable if further studies are made on cases of unusually bad forecastso Although the operational barotropic model sets negative absolute vorticities to zero while leaving the associated stream field unaltered, we calculated the implied str.eam field by the usual relaxation used in Laplacian reanalysiso All changes were negative, the hemispheric mean cyclonic vorticity having been increased; the form is a rough egg shape with a maximum change of 142 meters at 50 N 130 W for OOOOGMT 26 January 1964. For 0000 GMT 5 November 1963 two maxima appear, with no apparent' relation to forecast errors. While the hindcast-reforecast procedure indicates a stronger zonal wind as one feature of the analysis necessary for a correct forecast, and while the relaxation of negative absolute vorticities appears to move in the right direction, it is known that zero absolute vorticity is not the correct value.

5. CASE OF 5 NOVEMBER 1963 5.1 Nature of. the System The visible cloud mass (TIROS 7, orbit 2046) suggesting a departure from the.NMC analysis lay near ship 4YP, with a size of about 5 degrees (2 grid lengths; wavenumber 72) zonally and 10 degrees meridionallyo No indication of its presence was found in the radiosonde soundingg at 4YP, and it was concluded that the surface cyclone was probably small and incipiento It is, however, permissible to infer a larger structure similar to that commonly found in areas of minor cyclogensis. Consultation of all surrounding conventional reports did not suggest that any, reanalysis should exceed wavenumber 12, although it was considered that in view of the smoothing used in the barotropic model components at wavenumbers greater than about 15 had little prospect of significantly influencing the forecast. The lapse rate at 4YP is near dry adiabatic to 850. mb, and near wet adiabatic but far from saturated.to 500 mbo. The sounding at Cold Bay (55 N, 163 W) shows a definitely warmer airmass above 530 mb. (-31 C at 500 mbS. as against -360C at 4YP). The wind direction at 4YP is constant with height~ Thus the wave can be only minor, with no thermal support for strong baroclinic developmentD and not of a type specifically associated with substantial long wave motion. -20

-215.2 Origins and Energetics of Such Systems According to the scale analysis of Kibel (Chapter 3), for a system of 500 km size the inertial terms in the equations of motion are in the order of 20% of the Coriolis ~term. Nor is it likely that much will be known observationally of such small systems except from the frequent satellite coverage which has just become available. It was concluded that in practice one can do no better than follow the energetic assumptions of McClain, Ruzecki and Brodrick (1965). The small wave observed of 5 November 1963 may probably be treated as a stable barotropic wave in a region of approximately zonal flow. The question which may be asked is what larger scales of motion are implied by the occurrence of such a wave. 5.3 Errors of the Forecast The error chart for the JNWP forecast showed errors up to about 190 meters, and the pattern of positive and negative areas indicated substantial contributions from zonal wavenumbers five and six, which were documented by Fourier analysis in Table 5.1. e It was noted that these are the baroclinically active waves, but no use can: be made of this fact within the confines of a barotropic investigation. The reanalysis made

-22170oW O IE 80 W 40~ 500. DB 1600W 1500W 1400W 300 130~W Figure 5.1. Above: Reanalysis area (interior rectangle) and verification subarea for case of 5 November 1963. Dashed line indicates coverage by TIROS 7 orbit 2046 for 1934GMT 4 November. Below: Laplacian change field for 0000GMT 5 November 1963. Units are in tens of meters.

-23by the Meteorological Satellite Laboratories and rerun on our computer gave similar results, identical to those obtained on the NMC machine, with forecast improvement up to 80 meters but with just as large errors remaining. No significant change resulted from our reanalysis. 5.4 Reanalysis Three Laplacian reanalyses were made, the first two being rejected as showing meteorologically implausible systems. In the third (fig. 5;. l) maximum changes of -69 meters and +11l meters at 45 N and with a zonal separation of 100 gave a trough and ridge separated by 150 (zonal wavenumber 12 for a whole wave) in the stream function change map; (fig. 5.2) o The grid resolution is a limitation on reanalysis on this scale. Small changes were implied in longer waves~ The Coriolis parameter corresponds to a Laplacian of 130 meters. 5 ~5 Verification No significant change in correlation coefficients or RMS errors resulted from this reanalysiso The maximum forecast improvement attained 56 meters in an area of large errors over the western United States0 but errors of 190 meters remained (fig0 5~3) Although forecast deprovements reached only 20

130 -48 120 0 180 170 160 150 140 1 -36 12 24 0~~~~~~~~~~~~01 12~~~~~~~~~~~~~01 -12..000~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~.~ / \~~ 1 2i -24 h,~~~~~~~~~~~~~~~~~~~ 24 ~~ 3~00~.\ ~~,~ 3~~~~~~~~~~~~~3 36 36 36 Figure 5.2. NMC numerical analysis (dashed lines) and SINAP relaxed stream field for case of 5 November 1963. Stream function V isopleths are D values labeled in tens of meters.

10 10 0 0 200 1500 40 0 0 170E 600 I (I0 0 N.O 10 10 -10 -10 0 130W 0 Figure 5.3. Left: NWP forecast minus observed for 1200GMT 6 November 1963. Isopleths are stream function 4 differences labeled in tens of meters. Right: Forecast improvement chart for SINAP reanalysis of 5 November case. Isopleths are stream function 4 improvements labeled in meters. function VI improvements labeled in meters.

-26meters, it was not considered that the changes were distinguishable from chance.

0 1 2 3 4 5 6 00Z 5 JNWP 450N.64.44/47.05/214.28/157.61/112.54/196.88/109 300N 2.21.38/193.50/82.35/204.29/85.15/177.39/23 JNWP FCST 450N.66.27/80.26/335.73/143.52/133.27/110.71/169 300N 2.17.31/220.75/331.19/214.37/88.15/130.19/331 12Z 6 JNWP 450N,64.36/50.24/158.60/149.70/161.11/81.66/157 300N 2.25.48/171.45/52.17/21-4.56/82.25/254.67/68 HI NDCAST 450N.59.68/46.34/165.30/236.75/150.37/224 1..09/104 300NN; 2.16.53/177.26/69.33/229.23/86.22/286.70/77 REFORECAST 450N.57.46/43.30/125.57/164.63/167.13/76.62/157 300N 2.20.40/174..58/42.21/196.56/97.28/278.62/62 JHB3 ANAL 450N.65.44/40.13/182.22/143.58/120.50/189.81/109 300N 2.21.38/197.52/86.32/207.28/90.14/169.38/205, JHB3 FCST 450.47.18/166.48/25.49/175.64/122.20/126.60/168 300N 2.17.32/222.78/34.21/222.39/90.13/127.18/329 ZERO ABS VORT 450N.97.50/44.09/132.27/159.62/110.55/196.87/108 300N 1.96.32/189.57/80.36/204.30/88.13/178.38/23 TABLE 5.1 Amplitudes (Cm.*1E4) and Phases (deg.E) of Zonal Wavenunbers 0-1,2, 5 November 1963 Case.

7 8 9 10 11 12 OOZ 5 JNWP 45~N.33/209.52/77.15/356.32/223.12/311.09/294 30ON.26/129.12/187.09/312.11/131.11/74:12/109 JNWP FCST 45~N.20/22.46/199.29/102.14/147.12/137.15/119 30~N.13/316.10/165.17/134.08/144.06/147.15/149 12Z 6 JNWP 45~N.20/166.32/211.29/90.70/64.12/252.15/76 30~N.33/182.23/214.14/75.10/36.02/253.11/102 HINDCAST 45oN.26/252.51/63.24/316.02/221.11/340.03/40 30~N.17/204.10/156.24/344.09/183.04/123.07/79 REFORECAST 45ON.22/0.32/197.28/83.07/47.07/239.11/86 30~N ~300N.25/17.20/207.16/63.06/354.24/250.13/100 JHB3 ANAL 45~N.34/198.51/70.10/352.37/23.14/295.06/311 30~N.27/129.11/190.08/308.11/128.10/74.12/109 JHB3 FCST 45~N.24/354.42/193.35/95.23/137.17/163.23/129 30~N.13/319.11/170.18/130.06/151.08/153.14/142 ZERO ABS VORT 45~N.32/207.50/77.16/359.32/214.13/312.09/292 30ON.24/131.12/184.08/312.11/129.10/71.12/109 TABLE 5.1 (concluded) Amplitudes (Cm.*lE4) and Phases (deg.E) of Zonal Wavenumbers 0-12, 5 November 1963 Case.

6 0 26 JANUARY CASE 6.1 Synoptic Situation The synoptic pattern of 26 January 1964 appeared promising for two reasons: firstly, the satellite photographs over the western Pacific revealed the presence of a large scale powerful system which was not apparent in the original JNWP analysis; secondly, verification statistics showed that the JNWP forecast for this period was outstandingly bad indicating fertile ground for improvement. Reproductions of the original analysis and the verification error chart are included as figures (6. 1) and (6.2).o t is apparent from the error chart that the maximum absolute error in the numerical forecast differed from the verification in excess of 500 stream meters; and in the area of the satellite coverage the difference exceeded 200 meters. This may be compared to the case of 5 November 1963, where the maximum absolute error was less than 200 meters. The oustanding feature of the satellite photographs is the frontal cloud band which is clearly distinguishable in the second pass. This front was interpreted to be associated with a young cyclone nearing maturation or the occlusion stage. This was determined by the fact that the typical spiral nature of the mature cyclone is not in evidence, while the extreme clarity of the frontal band suggests the formative

-301000 E 24 80~W / 24 -48 1700 W 10OE 80~W Figure 6.1. NMC numerical analysis for 0000GMT 26 January 1964. Stream function 1 isopleths are D values in tens of meters.

-31100E 800W Figure 6.2. NMC forecast minus observed for 1200GMT 27 January 1964. Isopleths of stream function indifference are labeled in is the verification subset. Roman numerals identify error regions referred to in the text.

-32rather than the dissipative stage. The cyclone center was approximated to be 430N, 1740E. A number of empirical rules concerning the flow aloft have been formulated by other researchers, and several of these were applied. They will be discussed in connection with the relevant SINAP reanalyses. 6.2 Streamline Reanalyses I. The original reanalysis was carried out without knowledge of the verification nor the JNWP difference map. The reanalysis area was chosen to coincide with the satellite coverage (figure 6.3). Observations within this area were limited to Midway Island and two radiosonde ships, one of which was positioned only 500 km from the center of the satellite observed clouds. Because of the difficulties encountered in the 5 November case, a streamline reanalysis was chosen. According to the decision that the cyclone was not yet mature, a closed low was not analyzed on the 500 mb. surface (see Thompson, Cronin and Kerr (1964)). Further, since the major cloud areas visible in developing systems are almost certainly indicative of strong vertical velocities (rather than continuity), the trough line was accordingly positioned to the west of the major cloudy region. The actual magnitude of the displacement was necessarily

-33IO ~E 3.. -.4 1700W -: 2 MSG 800W * Regular Radiosonde Stations a Radiosonde only (No Winds) MSG Missing data Figure 6.3. Subareas used in 26 January stream function reanalyses and verification. Satellite coverage is indicated by the dashed curves. I is TIROS 7 orbit 3263 for 0342GMT; II is orbit 3264 for 0521GM1T 26 January 1964. Rectangle 1 was included in reanalyses 1-6. Rectangle 2 was added for reanalysis 3. Rectangle 3 was added for reanalyses 4-6. The exterior rectangle is the verification subarea.

-34somewhat arbitrary, as no prior maps were available and thus no estimate of the speed of the system could be calculated. To account for the baroclinicity, and the time difference between satellite observation and aalysis time, the trough line was established at 1650E. On the basis of the slight changes resulting in the SINAP forecast for the 5 November case where changes in the reanalyzed streams were at maximum 86 meters, it was felt that more drastic modifications could be permitted. Accordingly the stream height in the trough area was decreased by a maximum of 178 meters. Further decrease was restricted by the observed data from the ships. To provide additional contrast with the original analysis and a steeper gradient on the leading edge of the trough, ridging to a maximum change of 324 meters was introduced downstream from the satellite coverage0 Very modest ridging was also introduced upstream. The shaping of the trough, after the trough line was geographically positioned, was largely determined from the observed winds contained in the ship data, and the resulting scale of the system approximated wavenumber 12. Maximum changes in the vorticity introduced by the stream changes amounted to +305 meters0 IIo Wilth the identification of erroneous data from

-35the verification of the first reanalysis (section 6.4), a second reanalysis was made to measure stream curvature effect in a SINAP reanalysis, the streamlines in the reanalysis area were made as zonal as possible within the restrictions offered by continuity of the mean latitude of the zonal jet and the observed data within the area. This reanalysis was performed without consideration of the satellite data. The effect on the JNWP analysis was to fill the erroneous trough, slightly fill the central portion of the cyclone evidenced in the satellite photographs, and deepen the southern-central region of the reanalysis area. The changes nowhere exceeded 107 meters. The Laplacian calculated from the modified stream field also showed only moderate changes, nowhere exceeding 189 meters. The changes of the vorticity were almost exactly opposite to what is indicated by the satellite coverage, but as this reanalysis was intended to serve only as a standard of comparison, the reanalysis was not altered. III One reanalysis was made to incorporate empirical rules postulated by Thompson et.al. These investigators found that old polar fronts south of fresh polar outbreaks can frequently be distinguished in the Pacific by east-west bands south of 30 N, and this may reflect some regeneration of the old front. Though such a band is not clearly

distinguishable in the coverage of 26 January, there is slight indication of such a front in the first pass of the satelliteo Because the secondary front was so close to the limit of the satellite coverage, the reanalysis area was extended two gridpoints to the east. Furthermore "cold migratory surface highs with westerly flow aloft appear as distinct clear areas. With more northwest to northerly flow aloft, there is a tendency for cellular clouds in the area."3 Since the cellular clouds are clearly represented in the satellite photographs, it was decided to enhance the ridging behind the cyclone in order to induce a more northerly flow. The reanalysis was constructed by graphical addition of two wave systems which were intended to represent the old polar front and the fresh outbreak associated with the strong frontal band in the satellite-. photographs. As a result, a rather broad trough was introduced into the reanalysis area. Relative to the first reanalysis, the trough line was moved east to approximately coincide with the center of the crescent-shaped cloud pattern. The maximum deepening was also displaced slightly south — by the addition of the second system. Ridging ahead of the system was curtailed, while ridging to the rear was enhanced. Maximum deepening in the trough was 210 m., while maximum ridging behind the

-37system was 97 mo Maximum ridging downstream was reduced to 133 mo (largely due to the removal of the erroneous trough). The maximum positive relative vorticity change associated with the modified stream field was 276 m. IV, A fourth reanalysis was constructed to emphasize ridging both up and downstream from the main cloudy area. Since the system in the first reanalysis was felt to be somewhat too baroclinic, the trough line was repositioned approximately three degrees to the east (168 E). Troughing in the area of the cyclone was held to a minimum with stream modifications not exceeding -72 m. while maximum increases up and downstream were 226 and 231 m. respectivelyO Error charts for the first and third reanalyses proved difficult to correlate with modifications of the respective analyses. A major purpose of this reanalysis was consequently to elucidate the effects of the forecast of the upstream ridging (reanalysis three) and downstream ridging (reanalysis one). The primary effect on the vorticity field was to introduce broad areas of anticyclonic vorticity ahead and behind the cloudy region (-144 and -180 in) with a moderately small area of cyclonic vorticity increase in the area of the cyclone (+288 mo). The modified stream field is portrayed in figure (6.4)

-12 -24 -36 -48 -60 -60 _ -48 14,._~~~~~~~ Nb N -~ 92,L~ z4~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~a /~~~~~~~~~~r - ~-0! 24~~4~24.0e - _ 20" 300 1500 000 36 1600 1700 180 36 1700 160 Figure 6.4. NMC numerical analysis (dashed lines) and SINAP reanalysis 4 (solid lines) for case of 26 January. Stream function isopleths are D values labeled in tens of meters.

-39Vo The fifth and sixth reanalyses were modifications of the fourtho It was felt at this time that the forecast could not in this particular case be significantly improved even by immoderate reanalyseso Consequently, attention was turned to the quantitative effect of alterations in the horizontal shear or the stream function gradient. In these three reanalyses0 the curvature was held approximately fixed: within the constraints offered by continuity at the edges of the reanalyzed area. Intensity variations were not large-, and so the three reanalyses test the sensitivity of the forecast to moderate changes in the shear. In the fifth reanalysis, ridging both up and downstream from the cyclone was further enhanced to change maximum of 257 and 278 mO respectively. Depression in the trough region was not altered from reanalysis 40 Predictably, in view of the finite difference scheme employed in its computation, the general vorticity pattern was not significantly altered but the magnitudes were intensified. Maximum change values in the downstream ridge, the trough, and the upstream ridge were -180, 398, and -253 m. respectively. VI. In the sixth reanalysis, the downstream flow was not significantly altered while the trough was deepened to a change maxirmum of -108 mo and the upstream ridge was

-40reduced to a change maximum of 178 m. The asymetric change in the stream function also changed- the vorticity pattern such that the positive alterations in the trough area were considerably expanded. Maximum change magnitudes in the downstream ridge, the trough, and the upstream ridge were -234, 218, -278 mo respectively. 6.3 Vorticity Reanalyses For completeness, two vorticity reanalyses were also made for the case of 26 January0 The principia aim of the experiment was to achieve maximum simplicity in the reanalysis procedure. Consequently, the reanalysis region was reduced to a 9 x 6 gridpoint area. In both trials an area of very strong positive vorticity was introduced. The maximum changes were centered approximately 3 WNW of the center of the crescent shaped cloud pattern as suggested in the Meteorological Satellite.Laboratories "SINAP Procedures for 500-mb analysis modification." Negative vorticity modifications were introduced around the maximum, with a balancing region of negative vorticity in the approximate region of the upstream ridge. The magnitudes of the changes were made to conform approximately to those induced in stream function reanalyses 4-6. It should be noted that

-41changes of this size cause alterations in the stream function well beyond the limits of the reanalysis area. Consequently, changes which are not insignficiant (50 m.) do occur over relatively dense data areas in the UoS.S.R. However, the gradient of the change outside the-reanalysis area is not large and so the dynamic effect on the forecast can be expected to be small. This assumption is certainly justified for the case of 26 January where the forecast error is so large. More importantly, large vorticity changes in a reanalysis necessarily violate neighboring observations in the reanalysis area. As remarked.. previously, radiosonde data was available within 500 km. of the center of the cloudy region, and this data could not be conserved when large vorticity changes were introduced. I. In the first reanalysis the area of cyclonic vorticity change was chosen to be..nine (3 x 3) gridpoints. The maximum change introduced was 300 mwo The balancing region of anticyclonic vorticity was also nine gridpoints, but with a maximum intensity of only -12-0 m. Through an oversight the total relative vorticity in the reanalysis area was not conserved; however, the relaxed stream field changes were considered satisfactoary for a forecast. A comparison of the stream function changes for this reanalysis and the second

-42150 E 140 E 30N 160E 170 W 170 E 180 E C 40N 50N Figure 6.5. Above: Reanalysis area and Laplacian change field for vorticity reanalysis 1 for case of 26 January. Units are in hundreds of meters. Below: Relaxed stream field changes. Units are in tens of meters. 100 E 170 W m X _ 110 E I 80 _0 E

150~E 140 E 30N 160E 170 E 01234 40N 50N Figure 6.6. Laplacian change field and relaxed stream change field for vorticity reanalysis 2 for case of 26 January. Units as in fig. 6.5. 100 E 170 W 0 E 80 W

-44Laplacian reanalysis (which was more intense) shows the spreading effect when relative vorticity is not conserved (figures 6.5 and 6.6). IIo The pattern for the second Laplacian reanalysis was not altered, but the magnitude of the cyclonic maximum was increased to 400 m. Negative values surrounding the maximum of anticyclonic vorticity could not be increased without the introduction of negative absolute vorticities. This was avoided for reasons set forth in section 4. 6.4 Verif ication A partial list of verification statistics is given in Table 6 l.o It is apparent from these that the errors in the original JNWP forecast and all reanalysis forecasts are so large that the statistics have little meaning. In view of the original error, it would be unreasonable to expect significant improvement in the verification over the entire grid. The fact that none of the SINAP forecasts show any improvement is somewhat unsatisfactory. In an effort to investigate this a comprehensive point by point analysis of the differences and forecast improvement charts has been made~ This has permitted some insight into the effects of the individual reanalyses as will be discussed below, but

CORRELATION COEFFICIENTS Field JNWP SINAP 1 SINAP 3 SINAP 4 SINAP 5 SINAP 6 SINAP 7 Wind Grid.49.43.46.46 0.44.45.48 Wind Sub.49.40.34.41.33.37.38 Stream Grid.39.32.3.4.33.36.30.38 Stream Sub.59.38.38.36.47.28.60 Lap Grid.65.53.55.52.53.55.54'Lap Sub.67.40.39.32.39.46.42 R.M.S. ERROR Wind Grid 12 14 13 14 14 14 12 Wind Sub 10 17 13 16 15 16 11 Stream Grid 9481 10394 9934 10040 9954 10364 9387 Stream Sub 7913 11158 9528 100 5 2 9386 11538 6780 Lap Grid 3878 4748 4472 4737 4784 4649 4157 Lap Sub 4105 6826 6036 6804 6912 6284 5111 TABLE 6.1 Verification Statistics for SINAP Stream Function (1,3-6 and Laplacian (7) Reanalyses

-46has not suggested any manner of significantly improving the forecast. Several points should be noted concerning the verification stream field and the difference chart computed from the JNWP forecast and verification fields~ The verification streamlines over the Pacific exhibit a wave pattern approximating wavenumber nine. The JNWP forecast streamlines on the other hand show little wave pattern whatever, and consequently the difference map is composed of fairly well ordered error maxima (figure 6.2). These maxima, moreover, are rather well correlated with the Pacific observing stations. This is felt to be quite meaningful in view of the arguments presented in section 3.1. The scale chosen for the SINAP reanalyses on the basis of the satellite data was wavenumber twelve, which turns out to be a fair approximation for the observed discrepancies. However, in no instance did a SINAP forecast approximate the wave pattern of the verification. The two entities therefore appear to be unrelated. Completion of the first SINAP forecast revealed that both it and the JNWP forecast mistreated a blocking pattern in the eastern Pacific near the west coast of North America. In both forecasts the block was to some degree broken, while

-47the verification analysis showed it to have intensified'. In view of the dominant role played by a blocking pattern in the general circulation much of - -the''error in the numerical forecast may be attributable to this feature. An attempt was made to isolate the cause for the breaking of the block but although this uncovered an erroneous observation in the central Pacific (corroborated by the Satellite Laboratories) the removal of a trough induced by the faulty data did not affect the behavior of the block in the forecast. Similarly, none of the SINAP forecasts altered the original behavior as the satellite coverage was too far removed~ ~The major error regions in the verification subareas are labeled in figure (6.2) o They will be referred to by number in the following discussion. As expanded below, only error I appears to be significantly correlated with the satellite observed weather system. Errors II and I-IIo, while influenced in magnitude by the reanalyses could not be changed in pattern. The verification of each error region is discussed separately below in terms of the stream function and Laplacian reanalyses. In most of the stream function reanalyses, error I is the region into which the satellite observed system is moved by the forecast. It represents a region where the JNWP forecast exhibits too: little troughing. This error was, however,

-48intensified in all the stream function reanalyses except the third. On this basis it is tempting to ascribe the discrepancy to ridging introduced downstream from the satellite observed clouds. This is clearly the case with the first reanalysis as the development followed throughout the forecast period shows amplficiation of the downstream ridge with the low center consequently steered too far to the north. However, in reanalyses 4, 5 and 6, there is also an effect from the ridging introduced upstream. In these trials the downstream ridging did not develop significantly, and the additional upstream ridging was advected into the error region. The end result on the difference maps is the same in all cases, but for intricately different reasons. In all cases the major failure results from insufficient troughing in the reanalyses, as ridging effects were emphasized. For reanalyses 4, 5 and 6, which were carried out to investigate the effects of slight changes in the shear, slight modifications had significant influence on the error field (figure 6~7). However, it proved to be impossible to correlate the analysis and forecast changes because of the complex interdependence of the two ridges. For example, the error was extremely similar in reanalyses 4 and 6 although in the latter analysis the upstream ridge had been intensified

150E -5 130E-5 -5 -5 40 o 0 0 170oE o. I 50*WL~Gir.:~z ~. 17 200 130W 0 0, 0 Figure 6.7. Subarea forecast improvement charts for (left to right) SINAP stream function reanalyses 4, 5 and 6 for case of 26 January. Stream function difference isopleths are labeled in tens of meters.

-50while the downstream ridge was weakened. Inexplicably, the forecast of reanalysis 5 was significantly different from either o It is evident from the Laplacian reanalyses' forecasts that the influences on error II were largely derived from the positioning and intensity of the upstream ridge which governed the extent to which the trough penetrated southward in the forecasts. It is consequently apparent that if the satellite observed system is to have any effect on this error, it will be in the nature of additional troughing. Since the verifie cation chart requires additional ridging in this region, it is highly doubtful that the discrepancy is attributable to the system observed in the satellite photographs. The effect on error II of the upstream ridging was most clearly demonstrated in reanalyses 4, 5, and 6. In all cases erroneous troughing was forecast in this region. The change was especially pronounced (200 m o.) for reanalyses 4 and 5 where the anticyclonic gradient introduced upstream from the trough proved to be unstable and caused explosive deepening of the system. For reanalysis 6, with the ridge modified, the effect was less intense (100 m ). Error II was also intensified in the second reanalysis which was an attempt to remove all curvature effects. An

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-52analysis of the six hourly forecasts showed that this was caused by lowering the mean height just west of the erroneous trough. This particular adjustment was unconnected with the satellite observed cloud patterns suggesting that the error itself is unconnected with the observed system. Error III like Error I represents an area where the forecast failed to produce a trough. This error was neither significantly nor systematically altered in the stream function reanalyses' forecasts. The vorticity reanalyses proved to be slightly more encouraging than the stream function reanalyses, even though the initial stream field was extremely noisy. In both trials error I was slightly improved (figure 6.8). This may be attributed in part to the removal of the downstream ridge but is largely a consequence of the repositioning of the upstream ridge to the northwest and the broadening of the trough in the cloudy region. The figure also reveals the introduction of a fictitious low center to the north of error I. This represents a direct advection of the original low center in the reanalysis and indicates that the original center was both slightly malpositioned and too intense. Although the change of the position of maximum ridging upstream from the cloudy area was only 5, this was sufficient

200 130~E 0 400 5 IIE 00 0 Figure 6.8. subarea forecast improvement charts for (left to right)' 10 SINAP vorticity reanalyses 1 and 2 for case of 26 January. Units as; in fig. 6.7.

-54to almost entirely eliminate influence on error II. This gives further support to the hypothesis that that error is not associated with the satellite observed system. Both Laplacian reanalyses contributed some corrective troughing in error III, In both cases, however, the area of maximum error is undisturbed from the JNWP forecast since the SINAP forecasts, as measured above, failed to produce the wave pattern of the verification. To a large extent this improvement is the result of a general lowering of the height of the stream field, and analysis of the six hourly forecasts shows that this lowering is retained from the original field. This is consistent with the failure of the stream function reanalyses' forecasts to show any improvement in this region, as they in no case significantly lowered the initial heights. This improvement is thus considered to be to some degree fortuitous, and error III, as error II is not believed to be related to the satellite observed system. 6.5 Conclusions In some instances it has been possible to draw cause and effect relationships from the forecasts of the SINAP reanalyses. In general, however, the internal mechanics of the forecast are too complex to permit formulation of any

specific rules. The separate effects of shear and curvature on the forecast could not be distinguished. As a rule of thumb the magnitude of the forecast changes approximates the magnitude of the initial changes, but the direction of propagation is extremely sensitive to rather small differences. Analysis of the verification maps for this case points out the importance of the geographic positioning of a satellite observed weather system. In particular, the Laplacian reanalyses demonstrated that a shift of a few gridpoints in the upstream ridge influenced an entire region (error II) of the forecast. Although this problem was probably emphasized in this work by the immoderate size of the analysis changes, it is hardly doubtful that it would exist in all cases.

LAT. 20 30 40 45 50 60 70 80 OOZ 26 Jan 1.68.72 1.30 2.33 3.15 4.18 4.96 5.99 JNWP 1.30/219 1.61/236 1.32/276 1.22/299 1.25/366 1.13/330.90/262 1.42/259 12Z 27 Jan 2.34.56 1.42 2.54 3.38 4.30 4.86 5.99 JNWP.77/187 1.48/227 1.44/294 1.81/322 1.70/324.52/327.29/95.61/174 JNWP 2.10 1.11 1.00 2.28 3.41 4.64 5.06 6.06 FCST 1.26/184 1.28/199.57/301 1.08/332 1.33/333.59/334.43/224 1.01/259 CMH1 2.10 1.09'.76 2.09 3.36 4.60 5.04 6.01 FCST 1.22/182 1.18/194.51/254.72/322 1.14/337.60/329.56/225 1.05/257 CMH2 2.11 1.09.94 2.21 3.37 4.63 5.05 6.04 FCST 1.25/184 1.20/198.54/292.96/327 1.23/333.58/333.54/225 1.02/259 CMH3 2.11 1.10.70 2.04 3.37 4.62 5.04 6.04 FCST 1.20/184 1.12/192.54/251.72/320 1.10/339.57/339.52/223 1.01/259 CMH5 2.11 1.11.71 2.05 3.33 4.59 -5.02 6.04 FCST 1.17/179 1.10/191.37/245.68/332 1.15/341.55/338.52/221 1.01/259 CMH6 2.16 1.16.93 2.23 3.35 4.55 4.99 6.04 FCST 1.26/180 1.17/194.51/316 1.10/344 1.32/342.51/349.43/216.95/264 CMH6 2.34.78 1.31 2.42 3.28 4.13 4.91 5.95 ANAL 1.12/195 1.53/231 1.07/284 1.33/335 1.53/349 1.07/336.82/260 1.38/258 CMH7 2.11 1.08.98 2.36 3.52 4.66 5.10 6.13 FCST 1.24/184 1.17/201.64/306 1.27/339 1.53/341.62/345.44/227.97/265 CMH7 2.31.71 1.44 2.59 3.42 4.23 5.01 6.04 ANAL 1.08/196 1.50/236 1.20/292 1.59/335 1.72/347 1.18/336.85/265 1.39/260 TABLE 6.2 Amplitudes and Phases of Zonal Wavenumbers 0 and 1, 26 January 1964 Case

LAT. 20 30 40 45 50 60 70 80 CMH8 2.13 1.12.81 -2.12 3.40 4.61 5.03 6.04 FCST 1.25/181 1.18/194.43/268.81/326 1.25/339.59/336.54/223 1.03/258 HINDCAST 2.42.78 1.19 2.12 3.05 4.42 5.06 5.96 OMEGA=1.4 1.15/175 1.76/206 1.36/270 1.91/306 1.84/321 1.20/341 1.14/130.46/141 REFORECAST 2.32.99.97 1.94 2.99 4.69 5.28 5.99 1.34/162 1.74/184'.78/267 1.21/317 1.24/326".26/177 1.22/138.67/103. HINDCAST OMEGA=1.70 2.31.66 1.61 2.57 3.32 4.09:5.02 5.95 AND 1.30.45/198 1.31/251 1.68/313 1.68/329 1.56/339 1.22/344 1.37/290.73/168 1/2 HOUR 2.30.67 1.60 2.56 3.32 4.08 5.01 5.94 HINDCAST.44/199 1.28/251 1.68/314 1.67/329 1.55/339 1.22/344.14/290.71/168 1/2, HOUR 2.25.69 1.28 2.42 3.30 4.30 5.01 5.98 REFORECAST.61/188 1.10/226 1.34/307 1.79/328 1.63/329.53/322.29/153.58/188 TABLE 6.2 (concluded) Amplitudes and Phases of Zonal Wavenumbers 0:O and 1, 26 January 1964 Case

7. CONCLUSION As a result of this investigation is is believed that SINAP procedure could not significantly alter the numerical forecasts in the cases studied. It is felt that for the case of 5 November the scale of the satellite observed weather system is too small to be effective whereas for the case of 26 January the initial state is too poorly specified on an hemispheric scale to be improved even by the proper interpretation of a moderately large system in the satellite photographs The greatest difficulty in the SINAP procedure remains the proper interpretation of the satellite observed cloud forms. The various trials with the case of 26 January point out that some improvement could be achieved in a limited region, but that this requires a very specific analysis of the system evident in the cloud photographs, particularly with regard to geographical position. Verification of the SINAP procedure is obfuscated both by the scant data in the region of verification and by the complexity introduced by the numerical forecast. Under these handicaps it was found to be impossible to draw quantitative conclusions~ In particular, it was not possible to distinguish in the forecast the individual effects of alterations in the shear and curvature. The complexity of the dynamic interaction -58

precluded their separate recognition although the combined effect is to preserve the magnitude of original alterations in the analysis~ The investigators found no inherent advantage to choosing a stream function rather than a vorticity reanalysiso From an operational standpoint, the difficulty in restricting the relaxed stream field changes is compensated by the ease of avoiding negative absolute vorticities and by the reduction of the area which must be reanalyzed. Delineation of their relative merits would require a more selective verification procedure than that utilized in this work. Hindcast-reforecast procedures gave disappointing results due to the large truncation and other numerical problems found, but point to the conclusion that substantial baroclinic effects and errors not remediable by satellite data are present0 Discrepancies in the balance equation are unexplained0 Changes in the forecast for different zonal wavenunbers are comparable in magnitude to changes in the analysis: differences in the zonal mean profile observed and forecast or hindcast are prominent,

8. SUGGESTIONS FOR FUTURE WORK 8.1 The Analysis Problem The SINAP procedure was introduced to supplement observations over sparse data areas. Through the use of a numerical forecast, the resulting analysis may in principle be validated in a dense data area. However, in attempting to utilize the satellite photographs for reanalysis with forecast verification, this project has compounded the difficulties of weather system recognition with the purely mechanical problems of numerical prediction. Further, in practice the verification has also taken place over data sparse areas, and itself is thus suspect. It is felt that the chances for success in such a venture are rather limited. The results of this project suggest that the proper interpretation of the cloud photographs remain the primary problem, and there is every indication that the analysis problem must be-more fully investigated before adding the additional complexities of the numerical forecast. It is thus suggested that alhtough the prime purpose of a SINAP reanalysis is to supplement observations in a data sparse area, analysis techniques cannot be perfected over such areas, as they cannot be directly verified. Only when an analysis technique has been developed and tested over an area of fairly good conventional coverage can it be applied in data sparse areas, At this time verification =60

through forecast would be more feasible, especially as expanding satellite coverage might permit modification of the verification as well as the initial field. Several factors which were not considered in the present project might be incorporated into such an analysis study. Following is a partial list. 8.2 Continuity and Winds The isolated photographic swaths used in our studies did not allow any determination of wind speeds or directions from the displacements of identifiable features. Current coverage should allow the use of this method0 8.3 Thermal Radiation Data Despite possible data processing problems, the use of thermal radiation data would substantially assist in guessing the height and type of stratiform clouds, and deducing the motion field. 8.4 Gandin s Method of Omitted Stations In his comprehensive book on automatic analysis, Gandin (1963) omits some stations from a network in order to have comparison data for his analysis. This method would provide

-62a direct test of the ability of satellite data to improve the thermohydrodynamic analysis if used over the dense data areas of Europe and North America.

APPENDIX A Successive Point Over -Relaxation The theory of Accelerated Liebmann or Point Successive Over-Relaxation used in the NMC routine WPA13 is treated in many texts, e.g.o J. Todd (1962), L. Fox (1962), D. K. Fadeev and V. N. Fadeeva (1963). The authors have not, however, found a discussion of the combined jury-marching method used in most forecast models. The constant omega (COEF) of 1.40B2 used in WPA13 is close to the overall optimum value (least number of scans) found by L. Norton (U.S.W.Bo Fort Worth) in unpublished work on a 14*23 point 36 hour barotropic forecast during Uo.S.W.B. Refresher Courses at the University of Michigan in 1965. Re-examination of Norton s results showed, however, that the best values for 14*23 are about 1o70 at the initial step and 1.30 at all subsequent stepso Further, a trial of Aitken extrapolation (Fox, p. 287) was found to require the assumption that the error vector at all steps after the initial time was dominated by one or more eigenvectors corresponding to eigenvalues much smaller than the spectral radius of the matrixo Under these circumstances Aitken extrapolation is of little value. -63

-64It may be shown (Dr. C. Young, private communication) that the theoretical optimum omega (for a minimum spectral radius of the relaxation matrix) is near 1.70, which coincides with the least number of scans only on the assumption that the error vector is reduced to a multiple of the special eigenvector (corresponding to the absolutely largest eigenvalue or spectral radius) before the convergence criterion is met. In practical forecast procedures this requirements is met only at the initial step, when a first guess of zero is used for the tendency field: the error vector at convergence is then dominated by an eigenvector approximating to a hemispheric dome. At subsequent steps the tendency field from the previous time step is used as a guess, and the error vector at convergence is dominated by short wave motions represented by eigenvectors corresponding to eigenvalues far from the spectral radius; since there are many such eigenvalues, the problem of least-scan omega becomes statistical and in practice one can do no better than make omega a pre-determined function of time. For a single jury problem such as a Laplacian reanalysis 1.70 would probably be best, but we have not tested this except of a 14*23 model~

Consider an arbitrary relaxation matrix A of order n, having eigenvalues A1,?2 i5l 2 A and corresponding eigenvectors U1 U o o U D and let the eigenvalues be ordered so that I 11 h> i > >~ o ol In the iterative solution of the equation Ax = b let the kth approximation t6 the correct answer x be called Xk, and let the error vector e = x - xk~ Then (Fadeev and Fadeeva, Chapter V) e C= U + C U C U k+l lk+l 1 2,k+l 2 n,k+l n =l C U +?lC U + +.+7 C U = C,k1 + 2C2,k2 n+. + Ckn on the assumption that the expansion can be made. Then the error change vector Xk+1 - Xk = ek - ek+l =(1-?l)ClkU1 +... + (1 - k )C U I l, kln n n kn =(1-?)?\ kC U + (1-\ )? C U. 1 1 1,o 1 n n n n0o n It is usual to use the absolutely largest element (maximum modulus norm) of the error change vector as a convergence criterion. Evidently the problem of minimizing the number of scans in a jury problem can be reduced to the

-66problem of minimizing the spectral radius (absolutely largest eigenvalue) only if the special eigenvector comes to dominate the error vector at convergence; this is not so in jury-marching problemsro For any given eigenvector one may define an amplification factor by a =C C m m,k+l m,k which for the accelerated Liebmann process leads to a = m = l 2..o n. m m For an Aitken extrapolation by the formula k+2 = (Xk+ cx k) (1 - c) where C is some arbitrarily assigned constanta the amplification factor for the mth eigenvector is a \ (L - C) - C0 m m Since the best value of C for a 14*23 model was found to be between 0 and 0~25, it is clear that after the initial time step the error vector is dominated by components correspond-ing to eigenvalues less than 01. Figure Ao1 shows the amplification factor as a function of A for various values of C0

-671.00.75.50.25 U. C.5 \lc= / / ///=lC~ 0 0 z I-I 4 a-25.L50.75 -1.00 -1.25 1*50gQ -.75 -.50 -.215 0.25.50.75 1.00 LAMBDA Figure A.1. Amplification factor against eigenvalue for different values of c in Aitken extrapolation.

APPENDIX- B Diagnostics for the NMC Barotropic Model The following parameters are currently saved on tape A4 and later printed in I,J and latitude-longitude coordinates by a MAD-UMAP pr ogram: 1. The absolutely largest change in the WPA13 relaxation, its linear subscript and the forecast hour, at convergence. 2. #1 upon no convergence. 3. All negative absolute vorticities, their linear subscripts, and the local Coriolis parameter. 4. All on-line comments from WPK03. 5o In case'of a fatal error exit, the whole of core in four blocks. A tamper program allows a new master tape to be written waith 28 secs. execution time. SPRA l's are changed to SPRA 4 to suit the on-line printer belts used here.

Mosaics of TIROS Photographs, 26 January 1964 Following are the TIROS VII photographs used in reanalysis of the 26 January case. -69

70 170 E 50/1 180 501V /60,p 40 /V170 E 17OW De>TG: 0'342 z TIQ /?G 19G4 180~~~~\0 "?ie OR__ 326! 63 l_ 16~~~~~7!ss TeV~~~~... *o: ~ I 0 W _ DTG., 0342 Z ORB IT' 32,8/526 180 i70WN

71 4X ~0N~.~ ~45N 150 E'; J..V 26 1964. ORBIT: 326a/3264 6o_

-72BIBLI OGRAPHY Fadeev, D. L. and V. N. Fadeeva, 1963: Computational Methods of Linear Algebra. W. H. Freeman and Co. Fox, L., 1962: Numerical Solution of Ordinary and Partial - Differential Equations. Pergamon Press. Gandin, L. S., 1963: Obektivnii Analiz Meteorologicheskikh Polei. Gidrometeoizdat, Leningrad, Library of Congress Photoduplication Service 414676. Kibel, I. A., 1963: Hydrodynamic Methods of Short Period Weather Forecasting. Pergamon Press. Knighting, E., "Numerical Weather- Prediction, See reference 2 above, pp. 478-493. McClain, E. P., M. A. Ruzecki, and H. J. Brodrick, 1965: "Experimental Use of Satellite Pictures in Numerical Prediction." Monthly Weather Review, 93 (7), pp. 445-452. Pfeffer, R. L., 1962: "Results of Recent Research in Meteorology at the Lamont Geological Observatory." Proceedings of the International Symposium on Numerical Weather Prediction in Tokyo, pp. 249-263, The Meteorological Society of Japan, Thompson, P. D., 1961: Numerical Weather Analysis and Prediction. The Macmillan Co. Thompson, J. R., J. C. Cronin, and R. E. Kerr, Jr., 1964: Silent Area Analysis Using TIROS Data. Aerometric Research Inc., Final Report, Contrait No. N189(I88) 57542A. Todd,- J., 1962: Survey of Numerical Analysis. McGraw Hill. Widger, Wo K., Jr., P. E. Sherr, and C. W. C. Rogers, 19650 Practical Interpretation of Meteorological Satellite Data. ARACON Geophysics Co., Final Report, Contract No. AF19 (628)-2471.

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