DUL. C 55.13: NESDIS-6 BOOKSTACKS DOCUMEMTS NOAA Technical Report NESDIS 6 .•^^ ^^''°'ca c 7 " \ s5 ^^ Spatial and Temporal Distribution of Northern Hemisphere Snow Cover Washington, D.C. October 1983 WITHDRAWN University of Illinois Library atU;Uina-Clnfi-^.aicjn U.S. DEPARTMENT OF COMMERCE National Oceanic and Atmospheric Administration National Environmental Satellite, Data, and Information Service NOAA TECHNICAL REPORTS National Environmental Satellite, Data, and Information Service The National Environmental Satellite, Data, and Information Service (NESDIS) manages the Nation's civil operational Earth-observing satellite systems, as well as global national data bases for meteo- rology, oceanography, geophysics, and solar-terrestrial sciences. From these sources, it develops and disseminates environmental data and information products critical to the protection of life and property, national defense, the national economy, energy development and distribution, global food supplies, and the development of natural resources. Publication in the NOAA Technical Report series does not preclude later publication in scientific journals in expanded or nedified form. The NESDIS series of NOAA Technical Reports is a continuation of the former NESS and EDIS series of NOAA Technical Reports and the NESC and EDS series of Environmental Science Services Administration (ESSA) Technical Reports. These reports are available from the National Technical Information Service (NTIS), U.S. Department of Commerce, Sills Bldg. , 5285 Port Royal Road, Springfield, VA 22161. Prices on request for paper copies or microfiche. A more complete listing of these reports, by title and NTIS accession number, is available from the Assessment and Information Services Center, National Oceanic and Atmospheric Administration, Code E/AI13, Page Bldg. 2, 3300 Whitehaven Street, N.W. , Washington, DC 20235. A partial listing of more recent repwrts appears below: NESS Series EDIS Series NESS 89 A Statistical Approach to Rain- fall Estimation Using Satellite and Conventional Data. Linwood F. Whitney, Jr. April 1982. (PB82 215435) NESS 90 Total Precipltable Water and Rain- fall Determinations From the SEASAT Scanning Multichannel Microwave Ra- diometer (SMMR). John C. Alishouse, May 1982. (PB83 138263) NESS 91 Numerical Smoothing and Differenti- ation by Finite Differences. Henry E. Fleming and Lawrence J. Crone, May 1982. (PB82-258385) NESS 92 Satellite Infrared Observations of Oceanic Long Waves in the Eastern Equatorial Pacific 1975 to 1981. Richard Legeckis, November 1982. (PB83 161133) NESS 93 A Method for Improving the Estima- tion of Conditional Instability from Satellite Retrievals. W.E. Togstad, J.M. Lewis, and H.M. Woolf, November 1982. (PB83 169938) EDS 29 GATE Convection Subprogram Data Center: Final Report on Rawinsonde Data Validation. Robert W. Reeves, March 1978. (PB-281-861) EDS 30 Gamma Distribution Bias and Confi- dence Limits. Harold L. Crutcher and Raymond L. Joiner, September 1978. (PB-289-721) EDIS 31 Calibration and Intercomparison of the GATE C-Band Radars. M. Hudlow, R. Arkell, V. Patterson, P. Pytlowany, F. Richards, and S. Geotis (MIT), November 1979. (PB81 120305) EDIS 32 Distribution of Radiosonde Errors. Harold L. Crutcher, May 1979. (PB-297-383) EDIS 33 Accurate Least-Squares Techniques Using the Orthogonal Function Ap- proach. Jerry Sullivan, March 1980. (PB80 223241) EDIS 34 An Application of Stochastic Fore- casting to Monthly Averaged 700 mb Heights. Albert Koscielny, June 1982. (PB82 244625) NESDIS Series NESDIS 1 Satellite Observations on Variations in Southern Hemisphere Snow Cover. Kenneth F. Dewey and Richard Helm, Jr., June 1983. (PB83 252908) NESDIS 2 NODC 1 An Environmental Guide to Ocean Thermal Energy Conversion (OTEC) Operations in the Gulf of Mexico. National Oceanographic Data Center (DOC/NOAA Interagency Agreement Number EX-76-A-29-1041), June 1,983. NESDIS 3 Determination of the Planetary Radiation Budget From TIROS-N Satellites. Arnold Gruber, Irwin Ruff, and Charles Earnest, August 1983. (PB84 100916) NESDIS 4 Some Applications of Satellite Radiation Observations to Climate Studies. T. S. Chen, George Ohring, and Halm Ganot, September 1983. NESDIS 5 A Statistical Technique for Forecasting Severe Weather From Vertical Soundings by Satellite and Radiosonde. David L. Keller and William L. Smith, June 1983. UM,VER3ITY OF ILLINOIS LiBRAhY AT iH B/\NA-CHAfv;PAIGN •STACKS ^^^PJJMO^^^^ ^''^'Went of ^°^ N( 'I'lic person oharg-iiif^ this material is re- sponsible for its return to the library from which it was withdrawn on or before the Latest Date stamped below. Theft, mutilation, and underlining off books ore reasons for disciplinary action and may result In dismissal from the University. To renew call Telephone Center, 333-8400 UNIVERSITY OF ILLINOIS LIBRARY AT URBANA-CHAMPAIGN DIS 6 0i)Z im S JUN 12 11184 H Bui Naj Dal Ch Nal We Oc Doral )rthern N Cover L161— O-1096 U.S. DEPARTMENT OF COMMERCE Malcolm Baldrige, Secretary National Oceanic and Atmospheric Administration John V. Byrne, Administrator National Environmental Satellite, Data, and Information Service John H. McElroy, Assistant Administrator NOAA TECHNICAL REPORTS National Environmental Satellite, Data, and Information Service The National Environmental Satellite, Data, and Information Service (NESDIS) manages the Nation's civil operational Earth-observing satellite systems, as well as global national data bases for meteo- rology, oceanography, geophysics, and solar-terrestrial sciences. From these sources, it develops and disseminates environmental data and information products critical to the protection of life and property, national defense, the national economy, energy development and distribution, global food supplies, and the development of natural resources. Publication in the NOAA Technical Report series does not preclude later publication in scientific journals in expanded or modified form. The NESDIS series of NOAA Technical Reports is a continuation of the former NESS and EDIS series of NOAA Technical Reports and the NESC and EDS series of Environmental Science Services Administration (ESSA) Technical Reports. These reports are available from the National Technical Information Service (NTIS), U.S. Department of Commerce, Sills Bldg. , 5285 Port Royal Road, Springfield, VA 22161. Prices on request for paper copies or microfiche. A more complete listing of these reports, by title and NTIS accession number, is available from the Assessment and Information Services Center, National Oceanic and Atmospheric Administration, Code E/AI13, Page Bldg. 2, 3300 Whitehaven Street, N.W. , Washington, DC 20235. A partial listing of more recent reports appears below: NESS Series EDIS Series NESS 89 A Statistical Approach to Rain- fall Estimation Using Satellite and Conventional Data. Linwood F. Whitney, Jr. April 1982. (PB82 215435) NESS 90 Total Precipitable Water and Rain- fall Determinations From the SEASAT Scanning Multichannel Microwave Ra- diometer (SMMR). John C. Alishouse, May 1982. (PB83 138263) NESS 91 Numerical Smoothing and Differenti- ation by Finite Differences. Henry E. Fleming and Lawrence J. Crone, May 1982. (PB82-258385) NESS 92 Satellite Infrared Observations of Oceanic Long Waves in the Eastern Equatorial Pacific 1975 to 1981. Richard Legeckis, November 1982. (PB83 161133) NESS 93 A Method for Improving the Estima- tion of Conditional Instability from Satellite Retrievals. W.E. Togstad, J.M. Lewis, and H.M. Woolf, November 1982. (PB83 169938) EDS 29 GATE Convection Subprogram Data Center: Final Report on Rawinsonde Data Validation. Robert W. Reeves, March 1978. (PB-281-861) EDS 30 Gamma Distribution Bias and Confi- dence Limits. Harold L. Crutcher and Raymond L. Joiner, September 1978. (PB-289-721) EDIS 31 Calibration and Intercomparison of the GATE C-Band Radars . M. Hudlow, R. Arkell, V. Patterson, P. Pytlowany, F. Richards, and S. Geotis (MIT), November 1979. (PB81 120305) EDIS 32 Distribution of Radiosonde Errors. Harold L. Crutcher, May 1979. (PB-297-383) EDIS 33 Accurate Least-Squares Techniques Using the Orthogonal Function Ap- proach. Jerry Sullivan, March 1980. (PB80 223241) EDIS 34 An Application of Stochastic Fore- casting to Monthly Averaged 700 mb Heights. Albert Koscielny, June 1982. (PB82 244625) NESDIS Series Hemisphere Snow Cover. Kenneth F. Dewey Operations in the Agreement Number NESDIS 1 Satellite Observations on Variations in Southern and Richard Helm, Jr., June 1983. (PB83 252908) NESDIS 2 NODC 1 An Environmental Guide to Ocean Thermal Energy Conversion (OTEC) Gulf of Mexico. National Oceanographic Data Center (DOC/NOAA Interagency EX-76-A-29-1041), June 1.983. NESDIS 3 Determination of the Planetary Radiation Budget From TIROS-N Satellites. Irwin Ruff, and Charles Earnest, August 1983. (PB84 100916) NESDIS 4 Some Applications of Satellite Radiation Observations to Climate Studies George Ohring, and Halm Ganot , September 1983. NESDIS 5 A Statistical Technique for Forecasting Severe Weather From Vertical Soundings by Satellite and Radiosonde. David L. Keller and William L. Smith, June 1983. Arnold Gruber, S. Chen, T. UNiVERSITY OF ILLINOIS LIBRARY AT ^iJBANA CHAMPAIGN •^■fACKS ^MMOS^,, "''•.tlToft"" NOAA Technical Report NESDIS 6 Spatial and Temporal Distribution of Northern Hemisphere Snow Cover Burt J. Morse, National Environmental Satellite, Data, and Information Service Chester F. Ropelewski, National Weather Service Washington, D.C. October 1 983 / U.S. DEPARTMENT OF COMMERCE Malcolm Baldrlge, Secretary National Oceanic and Atmospheric Administration John v. Byrne, Administrator National Environmental Satellite, Data, and Information Service John H. McElroy, Assistant Administrator Digitized by the Internet Archive in 2013 http://archive.org/details/spatialtemporaldOOmors 'tSV>[£-U CONTENTS Abstract I. Introduction -----------------------------1 II. Snow transition zones and snow cover frequency charts -------- 2 III. Asymptotic singular decomposition ------------------ 3 IV. Analysis of the ASD patterns ---------------------4 V. Conclusions and suggestions for further research -----------6 Acknowledgments ------------------------------7 References ---------------------------------7 111 Spatial and Temporal Distribution of Northern Hemisphere Snow Cover Burt J. Morse, National Environmental Satellite, Data, and Information Service, NOAA and Chester F. Ropelewski, National Weather Service, NOAA Washington, D.C. 20233 ABSTRACT. The archive of weekly Northern Hemisphere snow cover maintained by the National Environmental Satellite, Data, and Information Service since 1966 has been analyzed using asymptotic singular decomposition. The results are shown on charts covering the months of November through April and the winter season. These suggest that anomalies in snow cover over northwestern North America, the Baltic area, the Caspian Sea and Caucasus, the Tibetan Plateau, and Mongolia and Korea may occur synchronously. In addition, charts of Northern Hemisphere snow cover frequencies and snow transition zones have been included. They cover the winter season and the months of September through May. Comparison of these charts with similar ones derived from surface observations shows quite good agreement. I. INTRODUCTION The National Environmental Satellite, Data, and Information Service has main- tained a continuous archive of weekly Northern Hemisphere snow cover since November 1966 (Matson and Wiesnet, 1981). It is digitized onto uniform 89x89 grids which overlay a polar stereographic map of the area (Dewey and Heim, 1982). One such grid is generated for each week and consists of ones and zeros repre- senting, respectively, greater or less than 50 percent satellite-measured snow cover per grid box region. The archive is of considerable importance in numerous climatological applications including albedo studies, investigations of the connections between snow cover and various parameters of the synoptic scale circulation, the provision of boundary and initial conditions for global climate and forecast models, studies of cyclical or feedback phenomena dependent on snow cover, and the investigation of possible correlations or teleconnections in global patterns of the snow cover itself. For these and other applications, a statistical summary of the data is a necessary first step. In this paper, such a summary has been supplied by means of asymptotic singular decomposition (ASD). This technique is related to empirical orthogonal functions and factor analysis, and a description is provided by Jalickee and Ropelewski (1979). ASD is quite an effective technique for consolidating the mass of snow cover data contained in the archive. Indeed, for the periods we discuss - the months of November through April and the winter season, here defined as December through February - the first two ASD vectors explain 88 to 95 percent of the total variance. These analyses are provisional because only 15 to 15 years of data have been accumulated at this time. However, tests indicate that the patterns are statistically stable, and comparisons with independent data suggest that the major features of hemispheric snow cover for this period are correctly portrayed. In addition to the ASD charts, combined charts showing snow cover frequencies and snow transition zones ( STZ ' s ) are included. The STZ described by Kukla (1981) is the zone between the regions with and 100 percent frequency of snow cover for the given time period. Hence it comprises the region which was sometimes but not always snow covered. All of the ASD analyses are confined to the areas of the corresponding STZ's. This restricts the calculation to the dynamic areas of the snow record and effects both numerical economy and a more accurate analysis . II. SNOW TRANSITION ZONES AND SNOW COVER FREQUENCY CHARTS The STZ and snow cover frequency charts for winter and the months of September through May are shown in figures 1 through 10, respectively. The symbols "+" and "-" on these charts, respectively, fill the regions always or never snow covered during the periods of record. The zones between these symbols are thus the STZ's. The latter are covered with the numbers 0, 1,...., 9, and the letter T. These denote increasing frequencies of snow cover. Specifically, "0" denotes cover greater than but less than or equal to 5 percent of the number of archived weeks during the period of record; "1" denotes greater than 5 but less than or equal to 15 percent; "2" denotes greater than 15 but less than or equal to 25 percent and so forth up to and including "9". Finally, "T" denotes greater than 95 percent but less than 100 percent. At the time of this work, the archive contained 15 winter periods starting in December 1956 and ending in February 1981. These comprised a total of 189 weeks of data from which the winter charts are derived. The remaining monthly charts are derived from data in the interval November 1966 to December 1981 and are based on from 60 to 67 weeks of data depending on the month. The boundaries of the various STZ's are the outlines of record periods of snow cover that occurred during the time span of the archive. Indeed the northern boundaries are the imprints of extreme sparse periods and the southern boundaries of record abundant periods of snow cover. They appproximately correspond to the extreme positions of the storm track over the period of the archive, and, as more and more data accumulate, they are likely to expand. It is interesting to compare the frequency data on these charts with earlier maps of global snow cover that antedate the use of satellites. An example of the latter was prepared by Dickson and Posey (1967). They used data extending from pre-1915 into the early 1960 's. In spite of the differences in base periods, the general agreement between the two sets of charts is quite good except in the Tibetan Plateau area where we show higher frequencies of cover. This may be due to problems with the archived data over the Himalayas in the earlier years. The advantages of satellite data are particularly evident in filling in remote or data sparse areas and in regard to increased spatial resolution. Examples are Central Asia, Iceland (where formerly no data were available), and in the accurate delineation of the cover in movintainous areas such as the Alps and the California coast range. III. ASYMPTOTIC SINGULAR DECOMPOSITION ASD is one of several, closely related methods for consolidating large data sets. A mathematical description is given in Golub and Reinsch (1970). The outline presented here follows the development given by Jalickee and Ropelewski, (1979). Factor analysis and empirical orthogonal functions (EOF's) are in the same family and indeed the singular vectors shown in figures 11 through to 24 are the same as would result from an EOF analysis. The advantages of ASD are its numerical stability, particularly for large order systems as here, and the fact that the spatial and temporal aspects of the problems are treated symmetri- cally. Thus we not only obtain a spatial summary but a chronological one as well. The ASD method is based on the fact that any NxM matrix A=[Aj^ ^] may be represented in the form ''io k=l (1) (k ) (k ) where X. . , „ and Y. . , .. are known as the kth left and 1 1=1, . . .N 3 D=l/ • • . /M right singular vectors, respectively, and the A^ are called singular values. If the summation (1) is truncated at any point L, where 1 < L < N, we obtain the approximation. (L) A. . Z. A- ■ = y^ ^T^- (k)y (k) J k=l (2) (L) The essential requirement in ASD is that, for all L, A^ a is the best approxi- mation in the following sense: N M (L) ^ _] = minimum i=l j=l '^ (3) Zv^ (L) (L) with respect to all choices of L vectors |x,Y,A[. Thus Aj^ j is best in terms of the amount of variance explained. The requirement (3) implies the following properties. The X's are monotonically decreasing, so that , > , >...>, > 0. Ai - X2 - - X^ - (4) The two sets of singular vectors are mutually orthonormal. Hence Z(k) a) V^ (k) (£) ' ^ i=l j=l (l' k=£ Finally (5) substituted in (3) yields a convenient formula for calculating the amount of total variance explained: N M N M L (L) 2 „_^ ,-^ ^ „_^ ^ (6) i=1 j=1 i=1 j=1 k=1 2 k .^ In this application, the columns of the matrix A above consisted of snow cover frequencies for the month or season in question for a single year with successive columns containing consecutive years. In each case, the area of the analysis was restricted to that of the corresponding STZ. This eliminated superfluous regions, such as oceans and areas always or never covered by snow during the period, and substantially reduced the space dimension N of A. Typically N was about 1300 and M, the number of years of data, equaled 15 or 16. In applying equation (2), the truncation was chosen at L equals 2. The resulting singular vectors x' ' and X^^ are shown in figures 11 through 24. IV. ANALYSIS OF THE ASD PATTERNS The patterns of the ASD first-components X^^, shown in figures 11 through 17 for each month and the winter season as a whole, are typical of the mean snow patterns. This may be seen by observing the similarity of the largest amplitudes on each of these ASD patterns to the patterns described by the 50 percent and greater contour on the snow cover frequency maps for the corresponding season/month shown in figures 1 and 4 through 9. Calculations using (5) show that X^^' accounts for between 85 and 90 percent of the total variance in each of the months analyzed. The patterns of the ASD second-components X^ ' for each month appear in figures 18 through 24. These may be viewed as the principal anomaly patterns and typically account for less than 5 percent of the total variance. In these figures, using the same uniform increment measured from 0, the numbers 1,2,3,... represent increasingly positive amplitudes and the letters A,B,C,... increasingly negative amplitudes. The components X^ / X^ ', and x'^ were also computed but are not shown here because there is a real concern that they may not represent physical patterns. Indeed, since the analyses were performed on only 15 or 16 independent samples, the validity of the X^^^ components is also open to question. This uncertainty is twofold. First there are concerns about the quality of the archived data. As previously mentioned there may be a problem with the Himalayan data generated during the intial years, 1966-1974, which resulted from a lack of analysis. The satellite data is also known to be quite poor during extended periods of cloud cover. Snow cover may be either over- or under- estimated during these periods. These erroneous readings introduce noise into the data which will show in the ASD components. Since our monthly snow frequency charts are in close agreement with snow cover probability charts derived from surface data (Dickson and Posey, 1967) we believe the cloud cover problem is not serious in defining the mean fields and the ASD first-component patterns X^ "• ^ . However, the effect of this problem on x'^' cannot be estimated simply. The future utility of these data would be greatly enhanced and potential noise problems eliminated if the weekly satellite snow cover charts were systematically compared with charts derived from surface observations. Such comparisons would be the basis for correcting the data set. This comparison is beyond the scope of our study. The second uncertainty in the interpretation of the ASD patterns, due to the short period of the record, concerns the stability of the ASD components themselves. There is a danger that the addition or subtraction of one sample from the 15 or 16 analyzed could result in entirely different patterns for the higher order components. In a recent paper. North et al. (1982) present a rule of thumb for estimating when an EOF, or in this case an ASD component, may be subject to sampling errors of this type. In the context of the ASD analysis, this rule of thumb amounts to computing 2 2 _ (Xk -A ]^+i)/ A^(2/S)^/^ , (7) where: the X's are defined in (1), ^ is the mean of the successive ^'s, and S is the number of independent samples. If the ratio in (7) is less than one, then the ASD component x'**^^ associated with A, is suspect. All of the ASD first-components X in this analysis pass the test. However, all higher order components fail. Because we cannot now increase the sample size for the monthly data, there is no way to increase the confidence levels in the components X^^^, for k >^2 , until more data accumulate in the archive. This should be kept in mind during the discussion of the monthly patterns below. The stability of the seasonal (winter) patterns was checked by dropping one year and forming a 14-year time series of three months each (Dec, Jan., Feb.) to produce a sample size of 42. The first and second ASD patterns were virtually the same as those produced from the analysis of the 15 winter fre- quency charts. The 42-month sample easily passed the test of North et al. (1982) for both X^"") and X^^), rpj^^ f^^t that the 14-year (42 month) analysis passed the stability test and produced the same patterns as the 15-year frequency analysis gives us some confidence in the ASD patterns for the winter months. The ASD first-component pattern for winter resembles the mean frequency chart for winter given in figure 1. Since this pattern represents three months of data, it includes part of the annual cycle. This accounts for the strong north- south gradient, except in mountainous regions, in this pattern. The ASD second-component pattern for winter shows five areas of principal variations in snow cover. These areas are: (1) northwestern North America, (2) the Baltic Area, (3) the Caspian Sea and Caucasus, (4) the Tibetan Plateau, and (5) Mongolia and Korea. Areas 1 and 2 have the same sign and are opposite in sign to areas 3, 4, and 5. This implies that positive anomalies of snow cover in western North America tend to occur in the same years as positive anomalies in the Baltic. A further implication is that these positive anomalies are mirrored by negative anomalies in the remaining three areas. Two points of caution are required. First, this "anomaly pattern", i.e. x'^^, accounts for only 2 percent of the total variance of the frequency chart or 4 percent of the total variance of the 42-month, 14-season analysis. Thus these patterns are only slight variations about the mean. A second caveat is that data in the Tibetan Plateau, region 4, may be erroneous due to problems in the early part of the record (1956-1974). With all these reservations, this ASD pattern points to four or five regions which may prove to be worthwhile for future research. The ASD second-component patterns for the individual winter months, December, January, and February (figures 20 through 22) are consistent with the winter analysis. The December patterns, show the largest difference probably because December is a "transition" month for snow cover. Indeed, x''^^ for this month appears to have retained part of the annual cycle. The right singular vectors Y^'' and y'^^ (figure 25) represent a time series of the relative strength of the patterns from year to year. The time series of y'^ corresponding to the ASD first-component pattern shows little year to year variation. This reflects the fact that the annual march of the snow cover follows essentially the same pattern each year. On the other hand, the time series of y^^' shows considerable year to year variability, indicating that the pattern represented by the ASD second-component is stronger in some years than in others. However the poor Himalayan data may account for the apparent trend in y(2) f^-oni 1966-1974. V. CONCLUSIONS AND SUGGESTIONS FOR FURTHER RESEARCH In this paper, we have exhibited snow cover frequency and snow transition zone charts and charts of the ASD first- and second-component vectors for the Northern Hemisphere. These are based on weekly satellite snow cover charts covering the period from November 1, 1966, to December 31, 1981. As this time span is rather small, we recommend that the calculations be repeated, some years hence, when more data have accumulated. This will test the stability of the patterns found here, particularly in the Tibetan Plateau area where the initial years of the satellite data are not of consistent quality. Even with the length of the record already available, our snow cover frequency maps compare favorably with those of Dickson and Posey (1967) based on surface observations. It is recommended that, as a check, similar compari- sons between satellite and conventional snow cover data be continued. The ASD analysis indicated that the first-components resembled the mean frequency charts. Thus the second-components may be regarded as variations about the mean. The first-components typically explained 85 to 95 percent of the variance, whereas the second explained less than 4 percent and hence represent only small variations. Given this caution, these second components indicated five areas of principal variation in winter snow cover: (1) northwestern North America, (2) the Baltic Area, (3) the Caspian Sea and Caucasus, (4) the Tibetan Plateau, and (5) Mongolia and Korea. Furthermore, the charts indicate that positive or negative anomalies in these areas may occur synchronously. The testing of these points should prove worthwhile for future research. ACKNOWLEDGMENTS The authors would like to thank Olivia Smith, Emily Tidmore and Regina Woodard for yeoman efforts in preparing the typescript and Robert Ryan for help with the graphs . REFERENCES Dewey, K.F. and R. Heim, Jr. (1982): "A digital archive of northern hemisphere snow cover, November 1966 through December 1980." Bull. Amer. Met. Soc , Vol. 63, No. 10, 1132-1141. Dickson, R.R. and J. Posey (1967): "Maps of snow-cover probability for the Northern Hemisphere." Monthly Weather Review , Vol. 95, No. 6, pp. 347-353. Golub, G.H. and C. Reinsch (1970): "Singular value decomposition and least squares solutions." Num. Math ., Vol. 14, pp. 403-420. Jalickee, J.B. and C.F. Ropelewski (1979): "An objective analysis of the boundary-layer thermodynamic structure during Gate. Part I: Method." Monthly Weather Review , Vol. 107, No. 1, pp. 68-76. Kukla, G. (1981): "Snow covers and climate," in Snow Watch 1980 , Kukla, G. , Hecht, A., and Wiesnet, D. eds. Glaciological Data, Report GD-11 , pp. 27-39. Matson, M. and D. Wiesnet (1981): "New data base for climate studies." Nature, 289, No. 5797, pp. 451-456. North, F.R., T.L. Bell, R.F. Cahalan and F.J. Moeng (1982): "Sampling errors in the estimation of empirical orthogonal functions." Monthly Weather Review, Vol. 110, No. 7, pp. 699-706. Figure 1. — Snow transition zone and snow cover frequency chart for winter, 1966-81 ("5" contour shown). Percent of time area was snow covered + : 100% T >95 to < 100% 9 >85 to < 95% 8 >75 to < 85% 7 >65 to < 75% 6 . >55 to < 65% 5 >A5 to < 55% 4 >35 to <4 5% 3 : >25 to < 3 5% 2 >15 to < 25% 1 > 5 to < 15% > to < 5% - 0% Figure 2. --Snow transition zone and snow cover frequency chart for September, 1966-81. Percent of time area was $now covered + 100% T >95 to <100% 9 >85 to < 95% 8 >75 to < 8 5% 7 >65 to < 7 5% 6 >55 to < 65% 5 >45 to < 55% 4 >35 to <45% 3 >25 to <35% 2 >15 to <25% 1 > 5 to <15% > to < 5% - 0% Figure 3.— Snow transition zone and snow cover frequency chart for October, 1966-81 ("5" contour shown). Percent of time area was snow covered + : 100% T >95 to 100% 9 : >85 to <95% 8 : >75 to <8 5% 7 : >65 to <75% 6 >55 to <65% 5 >45 to <55% 4 >35 to <45% 3 >25 to <35% 2 >15 to 25% 1 > 5 to . rcy > to < D% 0% 10 Figure 4. — Snow transition zone and snow cover frequency chart for November, 1966-81 ("5" contour shown). Percent of time area was now covered + 100% T. >95 to <100% 9 >85 to < 95% 8 : >75 to < 85% 7 : >65 to < 7 5% 6 : >55 to < 65% 5 : >45 to < 55% 0% >35 to <_45% >25 to 05% >15 to ^25% > 5 to <^15% > to "5% 11 Figure 5. — Snow transition zone and snow cover frequency chart for December, 1966-81 ("5" contour shown). Percent of time area was snow covered + : 100% T >95 to <100% 9. -85 to < 95% 8 >75 to < 85% 7 -65 to < 7 5% 6 : >55 to < 65% 5 : >45 to < 55% 4: >35 to <45% 3: >25 to <3 5% 2: >15 to <25% 1: > 5 to <15% 0: > to < 5% - : 0% 12 Figure 6. — Snow transition zone and snow cover frequency chart for January, 1966-81 ("5" contour shown) . Percent of time area was snow covered + 100% T: >95 to 100% 9 : >85 to <95% 8 : >75 to <85% 7 : >65 to <7 5% 6 >55 to <65% 5 : >45 to <55% A: >35 to <4 5% 3: >25 to <35% 2: >15 to <25% 1: > 5 to <15% 0: > to < 5% -:0% 13 Figure 7.— Snow transition zone and snow cover frequency chart for February, 1966-81 ("5" contour shown). Percent of time area was snow covered + : 100% T: >95 to <100% 9 >85 to <95% 8: >75 to <8 5% 7 >65 to <7 5% 6 >55 to <65% 5 : >45 to <55% 4: >35 to 25 to 135% 2: >15 to 125% 1: > 5 to 115% 0: > to 1 5% - : 0% 14 Figure 8. — Snow transition zone and snow cover frequency chart for March, 1966-81 ("5" contour shown). Percent of time area was snow covered + 100% T >95 to < 1 00% 9 >8 5 to < 95% 8 >7 5 to ± 85% 7 >65 to < 7 5% 6 >55 to < 65% 5 >45 to < 55% 4 >35 to <45% 3 >25 to £35% 2 >15 to £25% 1 > 5 to £15% : > to £ 5% 0% 15 Figure 9. — Snow transition zone and snow cover frequency chart for April, 1966-81 ("5" contour shown). Percent of time area was snow covered + : 100% T >95 to <100% 9 >85 tol 95% 8 >75 to < 8 5% 7 : >65 to < 75% 6 : >55 to < 65% 5 : >45 to < 55% >35 >25 >15 > 5 > 0% to <45% to <3 5% to <25% to <15% to < 5% 16 Fig. 10. — Snow transition zone and snow cover frequency chart for May, 1966-81 ("5" contour shovm) . Percent of time area was snow covered + : >100% T: > 95 to <100% 9: > 85 to 1 95% 8: > 75 to 1 85% 7: > 65 to < 75% 6: > 55 to < 65% 5: > 45 to < 55% 4 >35 to 145% 3 >25 to 135% 2 >15 to 125% 1 > 5 to 115% > to 1 5% 0% 17 Fig. 11. — ASD left singular vector x ("2.5" contour shown). (1) for winter, 1966-81 Kez *: Always snow covered during winter, -: Never snow covered during winter. Digits "0", "1", "2", etc., indicate increasingly positive amplitudes of x in uniform increments. (1) 18 Fig. 12.-- ASD left singular vector x shown) . (1) for November, 1966-81 ("2.5" contour Ke^ Always snow covered during winter, Never snow covered during winter. Digits "0", "1", "2", etc in uniform increments. indicate increasingly positive amplitudes of x (1) 19 Figure 13. — ASD left singular vector x shown) . (1) for December, 1966-81 ("2.5" contour Key *: Always snow covered during winter. -: Never snow covered during winter. Digits "0", "1", "2", etc., indicate increasingly positive amplitudes of x in uniform increments. (1) 20 Figure 14. — ASD left singular vector x contour shown) . (1) for January, 1966-81 ("2.5" Key ": Always snow covered during winter. -: Never snow covered during winter. Digits "0", "1", "2", etc., indicate increasingly positive amplitudes of x in uniform increments. (1) t 21 Figure 15, — ASD left singular vector x^ '^for February, 1966-81 ("2.5" contour shown) , Key * : Always snow covered during winter. -: Never snow covered during winter. Digits "0", "1", "2", etc., indicate increasingly positive amplitudes of x in uniform increments. (1) 22 Figure 16. — ASD left singular vector (1) for March ("2.5" contour shown) Key *: Always snow covered during winter. -: Never snow covered during winter. Digits "0", "1", "2", etc., indicate increasingly positive amplitudes of x in uniform increments. (1) 23 Figure 17. — ASD left singular vector x for April, 1966-81 ("2.5" contour shovm) Key '-: Always snow covered during winter. -: Never snow covered durine winter. Digits "0", "!', "2", etc., indicate increasingly positive amplitudes of x in uniform increments. (1) 24 (2) Figure 18. — ASD left singular vector x^ for winter, 1966-81. (The five areas of maximum variation referred to in the text are enclosed in contours) . Key *: Always snow covered during winter. -: Never snow covered during winter. Numbers " l" , "2", "3", etc. represent increasingly positive amplitudes and the letters "A", "B", "C", etc., represent increasingly negative amplitudes, all measured in uniform increments from "0". 25 Figure 19. — ASD left singular vector x^^for November, 1966-81. Kez '': Always snow covered during winter. -: Never snow covered during winter. Numbers "1", "2", "3", etc. represent increasingly positive amplitudes and the letters "A", "B", "C", etc., represent increasingly negative amplitudes, all measured in uniform increments from "0". 26 Figure 20.— ASD left singular vector (2) for December, 1966-81. Key ": Always snow covered furing winter. -: Never snow covered during winter. Numbers '^" ' ^^'2" ,^^"3" , etc. represent increasingly positive amplitudes and the letters "A", "B" , "c", etc., represent increasingly negative amplitudes, all measured in uniform increments from ''0". 27 (2) Figure 21. — ASD left singular vector x for January, 1966-81. Kez *: Always snow covered during winter. -: Never snow covered during winter. Numbers "1", "2'', "3", etc. represent increasingly positive amplitudes and the letters "A", "B", "C" , etc., represent increasingly negative amplitudes all measured in uniform increments from "0". 28 ( ?) Figure 22. — ASD left singular vector x^^for February, 1966-81. Key ": Always snow covered during winter. -: Never snow covered during winter. Numbers "1", "2", "3", etc. represent increasingly positive amplitudes and the letters "A", "B", "C", etc., represent increasingly negative amplitudes, all measured in uniform increments from "0". 29 Figure 23. — ASD left singular vector x^^-'for March, 1966-81. '': Always snow covered during winter. -: Never snow covered during winter. Numbers "1", "2", "3", etc. represent increasingly positive amplitudes and the letters "A", "B", "C", etc., represent increasingly negative amplitudes, all measured in uniform increments from "0". 30 Figure 24.--ASD left singular vector (2) for April, 1966-81. Key *: Always snow covered during winter. -: Never snow covered during winter. Numbers "1", "2", "3", etc. represent increasingly positive amplitudes and the letters "A", "B", "C", etc., represent increasingly negative amplitudes, all measured in uniform increments from "0". 31 MAG. X 100 60 1 40 20 -20 -40 /\ / \ / \ I \ I \ I \ I \ I \ I \ _ / / / / / -60 Yd) \ I \ I \ / J L J I \ L Y(2) J I L 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 YEAR Figure 25. — ASD right singular vectors Y^ ^and Y ^^ for winter, 1966-8( 32 UNIVERSITY OF ILLINOIS-UHBANA 3 0112 101860135 NOAA SCIENTIFIC AND TECHNICAL PUBLICATIONS The S'ational Oceanic and Atmospheric Administration was established as part of the Department of Commerce on October 3. 1970. The mission responsibilities of NOAA are to assess the socioeconomic impact of natural and technological chanjres in the environment and to monitor and predict the state of the solid Earth, the oceans and their living resources, the atmosphere, and the space environment of the Earth. The major components of NOAA regularly produce various types of scientific and technical informa- tion in the following kinds of publications: PROFESSIONAL PAPERS— Important defini- tive research results, major techniques, and special investigations. 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