1474 MONTHLY WEATHER REVIEW VOLUM- 110Seasonal Snow Cover and Short-Term Climatic Fluctuations over the United StatesJOHN E. WALSH, DAVID R. TUCEK~ AND MIRIAM R. PETERSON2Department of Atmospheric Sciences, University of Illinois, Urbana 61801,(Manuscript received 16 March 1982, in final form 23 June 1982) ABSTRACT lnterannual fluctuations of snow cover in the United States are evaluated in the context of short-termclimatic variability. The analysis is based on 2.5 and 15.0 cm snow coverage digitized weekly for the wintersof 1949-50 through 1980-81. The winter of least snow (1980-81 ) and the winters of most snow (19?7-?8and 1978-79) have occurred in the most recent portion ofthe record. Considerable persistence of departuresfrom normal snow cover is evident in the monthly lagged autocorrelations, which range from 0.35 in thelee of the Rockies to 0.75 in the Far West. Fluctuations of surface temperature are most highly correlated with snow cover in a broad east-west bandwhich straddles the normal wintertime position of the snow edge. Snow anomalies in the eastern and westernUnited States are associated with opposite phases of a three-cell field of 700 mb height anomalies over theNorth Pacific Ocean and North America. A series of reg~ion analyses shows that a portion of the surfacetemperature variance unexplained by the large-scale (700 rob) circulation can be attributed to snow cover.In the marginal snow zone, this contribution is typically 10-20% of the variance of the concurrent monthlytemperature and 5-10% of the temperature variance of the following month. The effect of snow on surfacetemperature is largest during the late winter.1. Introduction On time scales of several days to several months,the largest changes in the earth's surface propertiesresult from variations in the extent of snow and ice.The extent of snow over land, for example, can varyby ---1000 km in response to individual cycloneevents. These surface changes are accompanied bysubstantial local changes in the surface heat budgetdue to the high albedo, high emissivity and low thermal conductivity of snow. Wagner (1973) and Dewey(1977) have demonstrated associations between snowcover and reduced surface temperature on the localscale, while Clapp (1967) derived empirical expressions for the frequency of snow cover as a functionofthe local temperature, precipitation and antecedentsnow cover. A quantitative evaluation of the role ofsnow cover in the larger-scale (synoptic and hemispheric) circulation is complicated by 1) inadequaciesin the quality, format or record lengths of existingsnow data sets, and 2) the likelihood that snow coverboth contributes and responds to large-scale changesin the atmospheric circulation. Nevertheless, Namias(1960, 1962) has shown that large-scale atmosphericchanges can, in selected cases, be interpreted in termsof the distribution of snow cover. Wagner (1979) hasfound that extremes of snow cover in the eastern ~ Present affiliation: U.5. Air Force Weather Training Center,Chanute Air Force Base, Rantoul, IL 61866. 2 Present affiliation: Statewide Air Pollution Research Center,University of California, Riverside 92521.002743644/82/101474-12507.00c 1982 American Meteorological SocietyUnited States are associated with rather strong 700mb height anomalies over much of the NorthernHemisphere. Namias (1978), Wiesnet and Matson(1979), Harnack (1980) and Kukla and Gavin (1980)have also noted that the extreme North Americanwinters of the late 1970's were associated with unusually extensive snow cover. Robock (1980) has usedzonally-averaged statistics to obtain relationships between l 1-year (1967-77) monthly means of snowcover and surface temperature. This work is an analysis of the interannual variability of snow cover over the United States in thecontext of short-term (weekly to seasonal) climaticfluctuations. The discussion will focus on the magnitudes and temporal and spatial scales of the fluctuations of snow cover and two associated climaticvariables: 700 mb height and surface temperature. Ofparticular interest here are: 1) the features of the largescale circulation associated with anomalies of snowcover over the United States; and 2) the contributionof snow anomalies to monthly temperature fluctuations over the United States. Since monthly fluctuations of snow cover, surface temperature and the700 mb circulation will be shown in Section 3 to beinterrelated, we will examine the surface temperaturefluctuations in terms oftheir association with the 700mb circulation and an "incremental" contributionattributable to snow cover. In this way, we will evaluate the diagnostic and predictive potential of snowcover in applications pertaining to short-term climatic variability.OCrOBER 1982 WALSH, TUCEK AND PETERSON 1475FIG. 1. Longitudes of digitized snow data (solid lines) and'surface temperature stations (circles).2. Data The analysis is based on weekly grids of snow coverand 700 mb height and on monthly grids of surfacetemperature for the months of December-March,beginning with the winter of 1949-50. The snow datawere available through 1980-81, the 700 mb datathrough 1978-79 and the surface temperature datathrough 1976-77. The snow data consist of the 2.5and 15.0 cm coverage at eleven longitudes in theUnited States: 70, 75, . . . , 120-W (Fig. 1). Thesnow data were digitized from the Weekly Weatherand Crop Bulletin (WWCB) published by the U.S.Department of Commerce (1949-81). The digitizedsnow data were linearly interpolated to 18 commondates extending from 4 December to 2 April at oneweek intervals. In cases where the snow cover wasbroken, so that several "patches" of 2.5 or 15.0 cmcoverage occurred at a particular longitude, the rangesof latitude covered by the different patches were simply summed. The data set, therefore, does not distinguish continuous from discontinuous snow coverage.Since only 8% of the digitized values correspond todiscontinuous snow cover, it was felt that this loss ofspatial information was more than offset by the advantage of the compactness of the one-dimensionalrepresentation of each map. The choice of the WWCB snow data was dictatedby the absence of any other digital snow data set covering a period comparable to that used to define climatological normals (~30 years). Satellite-deriveddata sets of hemispheric snow and ice coverage haverecently been described by Kukla and Gavin (1979)and Matson and Wiesnet ( 1981). While data sets such.as these are clearly desirable for studies of hemispheric snow/ice variability, the. necessary satellitedata have been routinely archived only since 1966.The record length of the satellite data is thereforeconsiderably shorter than that of the WWCB data. Several deficiencies of the WWCB snow data chartsare attributable to the nature of the raw data, whichare the reported snow depths from the network ofNational Weather Service (NWS) stations and selected cooperative stations. Since many of the NWSstations are located in urban areas, the snow depthsmay contain a slight negative bias. Moreover, becausesnow depths show a large amount of spatial variabilityin mountainous terrain, the representativeness of theWWCB snow areas and depths in the Rocky Mountains is limited (Kukla and Robinson, 1981). Consequently, the digitized version of the WWCB chartsused in this study does not include the 15.0 cm snowcoverage at the longitudes west of 105-W. Weekly and monthly values of 700 mb height werecompiled on a 98-point grid covering the midlatitudeportion of the' Western Hemisphere (20-80-N, 50180-W). The weekly and monthly grids were computed from the set of daily 5 x 5 o latitude-longitudegrids archived at the National Center for AtmosphericResearch (NCAR). As in the case of the snow data,a total of 540 weekly grids (30 winters, 18 weeks perwinter) were used in the analysis. Monthly temperatures for a network of 61 stations(Table 1; see also Fig. 1) were extracted from theWorld Monthly Station Climatology stored on magnetic tape at NEAR. With the exception of Montreal,all 61 'stations are in the contiguous United States.Since the temperature data set ended in December1977, only 28 winters (1949-50 through 1976-77) ofdata were incorporated into the computational analysis of the temperature associations (Sections 3b, 3d).All temperatures were converted to departures fromthe corresponding 28-year means.3. Results a. Fluctuations of snow cover As an illustration of the normal seasonal cycle of snow cover in the United States, Fig. 2 shows the 30TABLE 1. Stations used in analysis of monthly surface temperatures. Eastport, ME Hatteras, NC Abilene, TXBlue Hill, MA Asheville, NC Galveston, TXAlbany, NY Charleston, SC El Paso, TXOswego, NY Macon, GA Havre, MTMontreal, QUE Jacksonville, FL Helena, MTNew York, NY Pensacola, FL Sheridan, WYWashington, DC Key West, FL Denver, COLynchburg, VA New Orleans, LA Santa Fe, NMPittsburgh, PA Vicksburg, MS Boise, IDCincinnati, OH Little Rock, AR Salt Lake City, UTColumbus, OH St. Louis, MO Winnemucca, NV- Detroit, MI Des Moines, IA Phoenix, AZAlpena, MI Bismarck, ND Yuma, AZMarquette, M! Rapid City, SD Spokane, WAMadison, WI Huron, SD Walla-Walla, WADuluth, MN Omaha, NE Portland, ORMinneapolis, MN North Platte, NE Mr. Shasta, CAChicago, IL Topeka, KS Sacramento, CACairo, IL Dodge City, KS San Francisco, CANashville, TN Amarillo, TX Long Beach, CA San Diego, CA1476 MONTHLY WEATHER REVIEW VOLUME 11030-YEAR MEAN EXTENT OF SNOW~ ~- t /8765432 4 11 18 25'1 8 15 22 29 5 12 19 26 5 12 19 26 2 Decbmber January February March AprilFIG, 2. 30-year (1048-49 through 1978-70) mean latitudinal extent of' 2.$ cm snow cover averaged over all eleven longitudinal sectors.year mean (1949-50 through 1978-79) weekly extentof 2.5 cm snow cover averaged over all 11 longitudes.The maximum snow cover normally occurs in middleor late January. Aside from a small retreat in the thirdweek of January,-the normal snow coverage increasesmonotonically to its maximum and decreases monotonically thereafter. The rate of retreat in late winteris approximately equal to the rate of advance in earlywinter. While the small retreat of snow in the thirdweek of January coincides with the reputed "Januarythaw" (e.g., Wahl, 1952; Duquet, 1963), its appearance is not readily identifiable in the snow data forevery longitude. The mid-January retreat in Fig. 2 isapparent as a corresponding "dip" only at 110, 105,95, 90, 85 and 80-W. The interannual variability of snow cover is placedin a 30-year context in Fig. 3, which shows the winteraveraged coverage as percentage departures from the30-year "normal". The addition of data for the winters of 1979-80 and 1980-81 increases' the recordlength to 32 years. Interestingly, the winter of leastsnow (1980-81) and the two winters of the most snow(i977-78 and 1978-79) have occurred in the recentportion of the record. Fig. 3b shows that the wintersof 1977-78 and 1978-79 were characterized by approximately twice the normal coverage of heavy snow(15.0 cm or more). As shown in Fig. 3a, no otherwinter of the past 32 has even ~pproached 1980-81in terms of a nationwide snow "drought." The persistence of snow anomalies within a seasonis illustrated in Fig. 4, which shows autocorrelationsof the monthly departures from normal snow coverage. The plotted values are (left) averages of onemonth persistences from December, January andFebruary, and (right) averages of two-month persistences from December and January. (In.each case,the autocorrelation was computed from sums of the2.5 cm coverage and the 15.0 cm coverage; the useof snow variables derived from different weightingsof the 2.5 and 15.0 cm coverage did not change theresults appreciably.) The persistences in Fig. 4 tendto be strongest in the Pacific longitudes (115-120-W)and in the Midwest (90-100-W). Both the lag 1 andlag 2 plots show minima in the lee of the Rockies,where sudden and extreme weather Changes are associated with the onset of upslope or downslope(Chinook) winds. The 1 l-longitude mean persistences at one and two months are 0.58 and 0.34,which correspond to variance fractions of 0.34 and0.12. The one month persistences tend to increasethrough the winter: the 1 l-longitude mean persistences from December, January and February werefound to be 0.53, 0.57 and 0.63, respectively. Thesevalues indicate that the persistence of departures fromOCTOBER 1982 WALSH, TUCEK AND PETERSON 14770z0z40~- I I I I I I I I I (a) 2.5 cm COVERAGE3020-10-2O-30IIIIIII-401008060 4020 0-20-60(b) 15 cm COVERAGE~ -50 1950 52 54 56 58 60 62 64 66 68 70 72 74 76 78 80 1950 52 54 56 58 60 62 64 66 68 70 72 74 76 78 80 YEAR FIG. 3. Percentage departures from 30-year mean winter-averaged snow cover: (a) 2.5 cm coverage, (b) 15.0 cm coverage. Percentages are derived from sums of snow coverage in all 11 sectors.normal snow coverage tends to be greater than thecorresponding persistence of 700 mb height anomalies and less than the corresponding persistence of seasurface temperature anomalies (e.g., Namias, 1974,Fig. 1). The spatial distribution of the persistence of wintertime surface temperature anomalies over the UnitedStates has recently been evaluated by Klein (1982,Fig. 6). While the monthly temperatures generallyshow less persistence than does snow cover, the autocorrelations of monthly temperature range fromapproximately 0.0 in the central Great Plains (95105-W) to 0.4-0.5 along the West Coast and the Florida peninsula. A secondary maximum of 0.25-0.35is found in the upper Ohio Valley and the Great Lakesregion. The West Coast and Florida maxima are likelyattributable to the proximity of these regions to thermally persistent ocean surfaces. However, the patternof temperature persistence over the interior UnitedStates is quite consistent with the persistence of snowcover depicted in Fig. 2. Snow-temperature associations are described in more detail in the followingsubsections.b. Snow-temperature relationships The results discussed in this section are based onan analysis of monthly temperature at 61 stations,0,81'0f -0f9 . LAG 1 MONTH LAG 2 MONTHS120115110105100 95 90 85 80 75 70 120115110105100 95 90 85 80 75 70 LONGITUDE, -W FIG. 4. l-month (left) and 2-month (right) lag autocorrelations of departures from monthlynormal snow cover. Autocorrelations are means for all winter months. The 95% significance levelsare 0.21 for the one-month aut0correlations (N = 90) and 0.26 for the two-month autocorrelations(N = 60).1478 MONTHLY WEATHER REVIEW VOLUME 110and the corresponding monthly snow cover along themeridian (5- multiple) nearest to each station. "Snowcover" is again defined as the sum of the 2.5 and 15.0cm coverage. Fig. 5 shows the correlations between the departures from the monthly normal temperatures andsnow cover for the entire 112-month sample of available temperatures. The correlations are negative atevery station. The magnitudes exceed 0.6 in a broadeast-west band extending from the mid-Atlantic coastto western Nebraska. This band is characterized byhighly variable snow cover and might be describedas a wintertime "marginal snow zone." The correlations are comparable to those of Wagner (1973),whose snow data were monthly average snow depthsreported during eight winters at 15 stations in theUnited States. Plots corresponding to Fig. 5 for different calendar months show that the strongest correlations migrate from the East in December (r= -0.83 at Albany, -0.81 at Pittsburgh) to the Midwest in March (r = -0.88 at Minneapolis and Madison, -0.86 at Des Moines and Omaha, -0.81 at Topeka). The correlations can therefore correspond tovariance fractions of 0.65-0.74, although the correlations alone do not imply causality. Interestingly, the magnitudes of the correlations inFig. 5 exceed 0.5 as far south as Florida. Since snowcover is visually nonexistent in Florida, the correlations are evidently manifestations of a circulationregime which not only contributes to heavy snow inthe eastern United States but which also drives coldair sruth to Florida. Another contributing factor maybe the reduction of surface warming of southwardflowing air during winters with above-normal snowcover. Conversely, winters with little snow in the eastern United States are characterized by a circulationregime which also produces above-normal temperatures in Florida. -0.3 Correlation: Snow vs. Temperature FIG. 5. Correlations between departures from monthly normaltemperature and snow cover based on entire sample of I 12 months.Snow cover is obtained from 5- meridian nearest to station (seetext). Regions in which magnitudes of correlations exceed 0.5 areshaded. ~", k-~-' o ,, , t---q , ~.-~---~ '-.~ o,o. ........ ,o,..__,,, ,,>,/, ~ ~~3- j , ', ~o~ ..... ~ .... (c) AT (-C) : Dec - Mar 'FIG. 6. Composite differences between monthly temperatures(-C) during the three months of least snow and the three monthsof most snow at 5- me~dian nearest to each station. Contoured~elds are means of temperature di~crenccs for (a) Decembe~ and]anu~, (b) Febma~ and ~arch, (c) ~1 four months, Dccem~rMarch. Nodal (1949-79) positions of snow edge are shown bydashed lines. Fig. 6 shows the composite differences derivedfrom the monthly temperatures of the three years ofgreatest snow cover and the three years of least snowcover at the corresponding longitudes. The fields plotted in Fig. 6 are the means of the composite mapsfor (a) December and January, (b) February andMarch, and (c) all four months, December-March.Temperature differences exceeding 5-C are foundover distances of more than I000 km in both earlywinter (Fig. 6a) and late winter (Fig. 6b). As in theOCTOBER 1982 WALSH, TUCEK AND PETERSON 1479700 Ht. vs Snow (80-W): December FIG. 7. Correlations (X 100) between departure from normal 700 mb height and latitudinalextent of snow cover at 80-W (dashed line) for December (upper figure) and February (lowerfigure). Extent of snow is averaged over all weeks of appropriate month.case of snow-temperature correlations, the largestdifferences tend to migrate westward during the winter. One interpretation of this migration is that latewinter snow cover has a greater effect on temperaturein the continental interior where, in the absence ofsnow, the warming during late winter and early springis normally most rapid. Finally, Fig. 6c shows thatthe winter-averaged temperature differences are largest in an east-west band which straddles the normalposition of the snow edge.c. Snow-height relationships Prior to the incorporation of the snow and heightdata into a regression analysis, the relationships between monthly snow cover and 700 mb height wereevaluated in order to identify the pertinent circulationfeatures and their degree of association with snowcover. The circulation features were identified fromfields of the correlations between monthly 700 mbheight (30-70-N, 20-W-160-E) and 2.5 cm snowcover at single longitudes. Both concurrent and laggedcorrelations were evaluated. Since the correlationfields derived from snow at a particular longitude arequalitatively similar for adjacent longitudes and forconsecutive months, we present only a representativesample of the results. Fig. 7 shows the correlationsbetween snow at 80-W and the concurrent 700 mbheights during December and February. These correlation fields are very similar to those obtained byWagner (1979, Fig. l) in an analysis of the circulation1480MONTHLY WEATHER REVIEW700 Ht. (January) vs Snow120W (February)0' -20 .... 20 40 60700 Ht. (January) vs Snow120W (December) FIG. 8. Correlations (x 100) between departure from normal January 700 mb height andlatitudinal extent of snow cover at 120-W (dashed line). Extent of snow cover is obtained fromthe 4-week February average (upper figure) and from the final week of December (lower figure).VOLUME 110patterns associated with extremes of monthly snowfall in the eastern United States. While positive (negative) snow anomalies are clearly associated withbelow-normal (above-normal) heights locally, thefields for both months contain the three cells characteristic of the North Pacific-North Americanteleconnection pattern. This teleconnection patternhas been well documented in the literature (see Wallace and Gutzler, 1981, p. 788) and has been shownto be associated with winter .temperature fluctuationsover the United States (e.g., Dickson, 1977). The factthat snow cover in the eastern United States correlatesas strongly with North Pacific heights as with localheights is further support of the importance of thisteleconnection pattern in short-term climatic variability. As an illustration of the lagged relationships, Fig.8 shows the correlations derived from January 700mb data and the snow cover at 120-W during theprevious and subsequent months. The use of the endof-December snow cover in the case of lagging 700mb heights (as opposed to the February-averagedsnow cover in the case of leading 700 mb heights)was dictated by the fact that snow cover generallyincreases rapidly during December; the distributionof snow at the end of December represents the mostplausible physical linJ~ to the January circulation. Athree-cell pattern is again apparent, although theOCTOBER 1982 WALSH, TUCEK AND PETERSON 148-1FIG. 9. The first four EOFs of 700 mb height based on normalized departures from 30-year means for appropriate month and grid point.phase is opposite to that of Fig. 7. The signal implicitin Fig. 8 is stronger when snow lags 700 mb heightthan when snow leads 700 mb height. While theseresults do not constitute evidence of causality, theydo indicate that snow cover in the western UnitedStates is more closely associated with antecedent thanwith subsequent height anomalies. Monthly laggedcorrelations computed from snow extent at other longitudes contain a Similar temporal asymmetry.d. Regression analysis The fields of surface temperature and 700 mbheight frequently form the basis for diagnostic andpredictive studies of monthly climatic variability.Both these fields are significantly correlated with eachother, as well as with the distribution of snow cover.The potential utility of snow cover as a diagnostic/predictive variable is therefore largely dependent onthe incremental skill attributable to snow cover inconcurrent/lagged specifications of quantities such assurface temperature. In order to evaluate this potential utility, a series of regression analyses was performed with the monthly fields of surface temperature and snow cover over the United States and gridsof 700 mb height over the North American/NorthPacific region. For purposes of data reduction, empirical orthogonal functions (EOFs) of 700 mb height were constructed using a set of 98 grid points covering thedomain 20-80-N, 50-180-W. The EOFs were basedon the normalized departures from the monthlymean heights at each grid point. Fig. 9 shows the firstfour EOFs, H~-H4, of the total of 98 computed EOFs.H~-H4 depict large-scale features typical of the stationary (planetary-scale) waves. While each of thefirst four patterns contains three anomaly centers, thefirst pattern (H~) depicts primarily a north-south gradient in the height anomaly field. The flow patterncorresponding to a positive coefficient of H~ containsenhanced westerlies or a strengthened jet stream overthe northern United States and southern Canada. H2and H3 each contain three anomaly cells and aresuggestive of the North Pacific/North Americanteleconnection pattern discussed in Section 3c. Thethree-lobe pattern of H4 is phase-shifted by 20-30-longitude from the same teleconnection pattern.H~-H4 describe 63.5% of the total (98-point) variance.The regression analyses, described below, incorporatethe first eight patterns, Hi-Hs, which describe 80.3%of the variance. The EOF representation thereforeprovides an effective reduction of the number of statistically independent height variables, i.e., predictors.This data reduction minimizes the artificial skill(sampling error) when the sample size is not muchgreater than the number of predictors. Indeed, thedecision to retain eight patterns was a subjective compromise between the need to maximize the described1482 MONTHLY WEATHER REVIEW VOLUME ll0700 mb variance and the need to minimize the number of predictors. Since the EOFs were used solely forpurposes of data reduction, the patterns were not rotated.For each of the 61 stations listed in Table-l, amultilinear regression was performed in order to express the departure from the monthly normal temperature as a linear combination of the coefficientsor amplitudes of the first eight height patterns,H:-Hs. The sample-derived fraction o of the temperature variance described by the regression, wasthen reduced to an estimate of the corresponding fraction a0, appropriate to the population by an application of the Wherry formula for shrinkage correction: M P=Po+~(l-P), (1)where M is the number of predictors and N is thesample size. The derivatibn of (1) is outlined by Lorenz (1977), while an equivalent expression is presented by Kushner and De Maio (1980, p. 245). Theproblem of shrinkage is addressed here by using (1),rather than alternative expressions for the final prediction error (e.g., Akaike, 1969), because the linearcombinations employed here are not simple autoregressions. According to (1), the spurious or artificialcomponent, p - P0, of the described sample varianceclearly increases as the number of predictors is increased, and 'as the sample size is decreased. Whena sample-derived regression relation is applied to anindependent sample, the explained variance can beexpected to be less than po, by an amount equal tothe artificial component of the described variance.Since no screening procedure was employed in theregression of the monthly temperatures onto H:-Ha,M = 8 and N = 112. (The data values for adjacentmonths are weakly interdependent because of persistence; this lack of independence is neglected when Nis set .equal to 112.) Fig. 10a shows the distribution of p0 obtained fromthe regression of the 112 monthly temperatures ontothe concurrent values of the coefficients of H~-Hs.p0 exceeds 0.5 over most of the eastern half of thecountry, the Northern Rockies, and the Southwest.'The corresponding correlations between the specifiedand observed temperature anomalies exceed 0.7.Somewhat smaller values of p0 are found in thesouth-central states, the Pacific coastal states and theextreme Northeast. Fig. 10b shows the correspondingvalues of p, for the case in which snow cover is included as a ninth "predictor." For each station, thisninth predictor is the snow coverage (2.5 cm coverageplus 15.0 cm coverage) at the nearest 5- meridianaveraged over all weeks of the same month. The inclusion of snow increases p, to 0.7-0.8 in the vicinityof the Ohio Valley and the southern Great Lakes. Fig.10c, which is the difference between Figs. 10a and10b, can be interpreted as the contribution of snow0.4. - 0.6~5 * [ % g. ~ ~o - ~l I ~' __.~--~ ~ ' - ~ ..... ~ ...... ~ ~ i ~.-.-1 ..... ~ 0 ~ ~-~ 0.4 .... 0.4 0.5 '.~oZ~o0. 0.6 M FIG. 10. Fractions of monthly temperature variance describedby regression onto (a) coefficients of first eight patterns (H:-Ha)of 700 mb height during same month, and (b) H:-Ha and extentof snow S at nearest 5- meridian during same month. Increment/x, of described fraction of variance achieved by inclusion of snowis shown in (c). Variance fractions have been reduced by estimatedvalues of artificial skill and are based on data for all months, December-March.cover to the monthly temperature variance. This contribution, As, exceeds 0.10 in a broad east-west bandfrom the western Great Plains to the East Coast. Values in excess of 0.2 are found in Nebraska, SouthDakota, Iowa, Minnesota and Wisconsin. Little evidence of a contribution is found in the southernstates, which are generally far from the snow edge.There is also very little contribution from snow in theWest, where irregularities of the terrain undoubtedlylimit the usefulness of the snow data.OCTObEr1982 WALSH, TUCEK AND PETERSON 1483 mary and March described by the observed data of December, January and February, respectively. The plots of Fig. 12 are therefore based on 3 x 28 = 84 months of data. The predictors are (a) the surface temperature and the coefficients of H]-Hs, and (b) snow coverage at the end of the preceding month in addition to the same nine predictors in (a). The de scribed fractions of variance in Fig. 12a are clearly much smaller than those of the zero-lag case (Fig.,a) ~s:Dec x./ ~.fl--~ ~k~ 10a), despite the inclusion of persistence by the use t of the previous month's temperature as a predictor. -- q -~/ '~;-~,~) 5 ~~~ o~~_~;:.~/ X ~ ~ ~ .... ~ ~. " ~ I , , ~ ,/' X ~o W ' ' ~ ~ ~ ....... u _ t ~ ..... - ~ [ ....- .... ~' o ~ ' ;-~-~-~~~~-~~~~~~-~--d / ~ O I O ~ ~ O u.~ ~ . ~ t~ ,~~~~~ x~,,, / I ~ .... __I : ~ o ' t ' O -~ ~ .~-.~, ~. ~-, ~ ~ (b %: Mar ~ ~ 0.05 _ ,~ o:~o o ~* 0.~s ~ ~G. 11. As in Fig. 10c, but for individual months of ~~'~:5_d~_;o '~.'x ~~~ (a) Decem~r and (b)March. N - - -~---- ~,~: .10 The incrementals~llattdbutabletosnow(Fig.10c) shows a tendency to increase during the winter.../;_..~0.m._._ ,~In Fig. 11, the v~ues of ~ are presented separately ~ "~ ~--~~~----~ '--~~-~~~';~ ~~~-~) ' ~ o /-'~---X ~ ".for the months of December and M~ch. While A~ ' t ....... ---- , ' ~ois typic~ly 0.10-0.15 during December in the vicinity )~of the snow edge, values of 0.20-0.35 are found over ~20 ~ ~~~ (b) H~ a broader area during March. The Januau and Feb- H~, ~, ~. T ~ ~ ~20 ~ Smau values (not shown) are generally between the 0.05December and March values. This seasonal tendency ~ ' /~0.mimplies that snow has a ~eater effect on monthly ~. ~ ~ . ~ ~temperatures when incoming solar radiation is /- -/[ ~_!"- v > o ~ o ': / ,,, ~ o~eater. The tendency may, therefore, represent a sea- ~--~o~ "~-~-% ...... ---~:' -: ~- ~0~ ~0 "*--d_ I lo o ~____D o .... ~o t - J ~ .....[~ '~'~~~ ~-~'~:7 -"back. While the analysis was limited to monthly av- - x t o ; . -~ -_---~/y~eraged temperatures, it is reasonable to ~sume that [ x~ ~ o [ 'x '~*-< [; ~ N ' ~ ~ O~ ~ ~' ~-' .- X ~,~ ....d ....io ,: x~?~'~_.,~:: ...... $the larger spdngtime effect of snow is attdbutablc ~ ~,~-~ ..... ~ez: ....5.-0-~- ~.;9 ...... ~ / I o Io , I o /--I'-'V "~ 'primarily to a suppression of maximum temperatures ~)o_ ] o ]o~ ..... '~--~/~~'2~k/when the nodal m~ima cx~ed the freezing tern- --~ ;~~~~'-~ '~[~~ j 'r---~ o ~ ~ operature by more than several de~ees, Du~ng De- -- o ,, t_. ~,---z---cem~r and Janua~, on the other hand, the suppres- (c) as '~sion of maximum temperatures may be comparableto the enhanced radiational cooling effect on mini- F]o. 12. Fractions of monthly temperature variance describedmum temperatures in many areas, by regression onto (a) surface temperature T and coefficients ofFinally, Fig. 12 is a la~ed counte~a~ of Fig. 10, 700 mb heist patterns H~-H8 of preceding month, and onto (b)in the sense that the contoured values co~espond to T, H~-H8 and snow S at end of preceding month. Increment &~ of described fraction of variance achieved by inclusion of snow isthe temperatures of the month following the month shown in (c). Variance fractions have b~n reduced by estimatedof the independent (predictor) variables. The tern- values of a~ificial skill and am based on hindcasts for Januau,perature variance fractions are those of Januau, Feb- Febmau and March.1484MONTHLY WEATHER REVIEWVOLUME 1 10The fraction of variance described by' the nine predictors exceeds 0. i 0 0nly in the southern states andexceeds 0.15 at only three of the 61 stations. Theinclusion of snow increases p0 to 0.10-0.15 .in thenorth-central and northeastern states. Fig. 12c, thedifference between Figs. 12b and 12a, represents theincrement As of the forecast skill attributable to snow.An increment of 0.05 to 0.15 of the lagged temperature variance is found in the northern tier of statesfrom the Dakotas to Maine. As in the case of zerolag, the monthly plots of As for the lag relations showa general increase from the January "forecasts" to theMarch "forecasts." Interestingly, the signal (As) implicit in Fig. 12c was lost when the average snowcoverage of the previous month was used in place ofthe snow coverage at the end of the previous month.Since the predictive value of snow cover is thereforederived from its end-of-the-month distribution, it isquite likely that the effect of the snow distributionoccurs primarily in the early portions of the followingmonth.4. Summary and conclusions The results have shown that snow cover over theUnited States undergoes considerable interannualvariability which is associated with the variability ofsurface temperature and 700 mb height. Fluctuationsof surface temperature are most highly correlatedwith departures from normal snow cover in a broadeast-west band from the western Great' Plains to themid-Atlantic coast. This region, which straddles thenormal wintertime position of the snow edge, is a"marginal snow zone." Since the regions to the northand south are, respectively, snow-covered and snowfree during most of the winter months, the geographical dependence of the snow-temperature associationis quite plausible. Moreover, the longitudinal distribution of the monthly persistence of snow showssome qualitative similarity to Klein's (1982) distribution of wintertime temperature persistence in theUnited States. While fluctuations of both surface temperature andsnow cover can be viewed as consequences of a variable large-scale circulation, the results of Section 3dshow that a portion of the temperature variance,unexplained by the large-scale (700 mb) circulation,can be attributed to snow cover. In the marginal snowzone, this contribution is typically 10-20% of thevariance of the concurrent monthly temperature and5-10% of the temperature variance of the followingmonth. The predictability implicit in the lagged relationships is modest and is likely to be confined primarily to the first portion of the following month.Nevertheless, the state-of-the-art of monthly forecasting is such that the contribution of snow covermay be comparable to that of other predictors in themarginal snow zone during winter. The results inSection 3d suggest that the potential predictive valueof snow in the United States is greatest during thelatter part of the winter. Regarding the predictability of snow cover as adependent variable, two approaches can be distinguished. First, the monthly persistence of departuresfrom normal snow cover is considerable (0.35-0.75)at all longitudes of the United States. The fractionsof variance described by persistence alone are therefore 0.10-0.56. Second, the three-cell 700 mb teleconnection pattern (Figs. 7, 8) associated with fluctuations of snow cover may provide an indirectmeans to the prediction of snow cover. For example,there is evidence that this teleconnection pattern ispart of the Southern Oscillation (Horel and Wallace,1981; Hoskins and Karoly, 1981) which is a~ signalwith possible predictive potential for the NorthAmerican region during winter. If a substantial portion of the variance of large-scale snow fluctuationscan be shown to be associated ultimately with theSouthern Oscillation or any other planetary~scale signal, then it may be possible to supplement the persistence-derived predictability of snow cover. Acknowledgments. This work was supported by theClimate Analysis Center of the National Oceanic andAtmospheric Administration through Grant No.NA81AA-D-00022. Computing Facility support wasprovided by the National Center for AtmosphericResearch and by the University of Illinois ResearchBoard. We wish to thank Philip Clapp for his helpfulcomments 'during the course of the work, and twoanonymous reviewers whose suggestions helped toimprove the paper. 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