1965 M A R K D. S H U L M A N A N D R E I D A. B R Y S O N 107A Statistical Study of Dendroclimatic Relationships in South Central Wisconsin MARK I). SHULMAN~ AND REIn A. BRYSONThe University of W~scons~n, Madison, W~s.(Manuscript received 13 August 1963, in revised form 14 September 1964)ABSTRACTStepwise multiple regression analysis applied to annual radial growth increments of mid-latitude hardwoodsamples indicates that satisfactorily high levels of reduction of the growth variahce can be achieved only byutilizing a number of climatic and temporal parameters, both simple and compound. A large part of thevariance, as might be expected, is associated with the secular trend of the growth rate. Of the climaticparameters, July precipitation and July evaporative stress were found to be most significant. In particular,since these parameters occurred in the combination precipitation minus evaporative stress, a strong dependence of growth rate on water availability was found.1. Introduction The growth of trees is affected to a great extent bythe environmental conditions under which they live.The most variable part of a tree's physical environmentconsists of the various climatic parameters, and thesesame variables influence the amount and rate of growthof individual specimens in which genetic and otheredaphic factors are nearly constant. If the exact relationships between growth and the climate can beascertained, it is theoretically possible to establish themagnitude of such climatic variables by studying thepast growth record of trees. The purpose of this paperis to examine the statistical relationships betweenclimate and the annual radial growth variance, or yearto year variation in growth of early, late, and totalwood from trees obtained from a mid-latitude hardwoodstand. This will be investigated by means of stepwisemultiple regression techniques as applied to speciesmean growth values. Before proceeding with this study a brief review ofthe results reported in the literature is in order. Mostdendroclimatological studies hold that, in general, onlytwo climatic variables, temperature and precipitation,are important in influencing and limiting tree growth.Results of research performed in arid regions of thesouthwestern United States have stressed the importance of precipitation as a limiting factor to treegrowth (Schulman, 1956; Douglass, 1928; etc.). Holmesgaard (Eklund, 1956) feels that temperature in winterand early spring are of great importance to the growthincrement of Alder, Scotch pine, and Douglas fir. Hare(1950) similarly holds the view that northern forests ~ Now at the Department of Meteorology, Rutgers University,New Brunswick, N. J.are governed in their growth by temperature, and thatprecipitation is everywhere adequate to supply the needsof growth under such cool conditions. Miller (1950)states that the Arctic timberline can easily be shownto have nothing to do with precipitation except wheremuskeg and anaerobic conditions deter growth. Siren(1961) again indicates that the mean temperature ofthe period Jmle through August is the most significantclimatic determinant of tree growth. While it may be true that temperature and precipitation are of singular importance to tree growth underthe rigorous conditions of the desert or the Arctic,growth-climate relations become considerably morecomplex as one leaves such regions. Giddings (1943)showed some insight into the complexity of the problemby stating that, irrespective of species, the ring recordloses its pure temperature significance as one retreatsfrom the timberline and becomes a mixed record oftemperature, growing season, and unknown factors. With few exceptions little research has been carriedout in the field of mid-latitude hardwood dendroclimatology. One exception is that of Fritts (1962),working in the Charleston, Illinois, area. Fritts utilizedstepwise multiple regression techniques in relatingannual radial tree growth of ten mature white oaks toseveral statistically selected climatic factors. His studyindicates that, considering only climatic variables, asignificant portion of the growth variance of late woodmay be explained by mean June temperature, and theproduct of July evapotranspiration deficit and Junetemperature. As has been inferred, tree growth in mid-latitudes isa complex function of several interacting environmentalfactors. Acknowledging the general complexity of theproblem we proceed with the present analysis.108 JOURNAL OF APPLIED METEOROLOGY VOLUME4 Fro. 1. Stand subdivided into 40 foot squares, with contourlines in feet. Heavy outline in section 1E/1F indicates a locallandmark.2. The materials for present study A. Biotic. When a portion of Bascom Woods, on theUniversity of Wisconsin campus (lat 43-08~ N Long.,89o20' W), was cut in March of 1961, it was possibleto secure a cross section of each tree felled. The standsite consisted of a fairly uniform slope to the northnorthwest of approximately 18 per cent, ranging inaltitude from 942 down to 890 ft above sea level. Thelowest part of the stand was approximately 40 ft abovenearby Lake Mendota (Fig. 1). The site was welldrained a~nd possessed a Gray-Brown Podzolic soilassociation, the dominant type of which is Dodge siltloam, glacial outwash substratum phase (F. D. Hole,personal communication). Eighty-two samples were obtained in all and included: Burr, Red, White and Black Oak, Elm, Ash,Larch, Locust, and Hackberry (Table 1). The size of the annual growth rings is very dependentupon the age of the tree. In general a sapling will puton much larger annual rings than an older tree, regardless of climatic conditions. This is probably due to thefact that as a young tree matures, the ability to carryout photosynthesis, as determined by leaf surface, andthe carbohydrate production decrease in proportion tothe total mass of the tree (Kramer, 1960). Furthermore,in a stand of relatively uniform age, as was the BascomWoods stand, the saplings are relatively free of competition, allowing for rapid growth. As maturation takesplace, increased competition reinforces the physiologicaltrend toward slower growth rates. The ring thicknesses were measured on a Gaertnerspecially adapted 1949 model traversing microscopewith a 8X Wetzler ocular and a 16 mm Zeiss objectivecommensurable to the nearest ten thousandth o- aninch. Both early wood and late wood growth weremeasured, differentiating on the basis of relative cellwall thickness and sununed to give an annual or totalwood value. Two radii (of one diameter) were measuredin tiffs manner and averaged to give a more representative composite value. The data were then punched onIBM cards. B. Climatic. In selecting the climatic variables usedin this study, an attempt was made to include as manyas could possibly be significantly related to the varianceof the growth time series. Monthly values of the"standard" variables, mean temperature and total precipitation, were chosen. Their importance to radialgrowth has been adequately suggested elsewhere(Kramer, 1960; Schulman, 1956; Hustich, 1949; etc.).Winter averages of these variables were also used because they expressed the integrated effect of the individual parameters during the non-growh~g season, aperiod in which monthly values would have littlemeaning. It was hoped that these variables might indicate whether winter moisture storage or severity asreflected by means of temperatures during the dormantseason, could be related to the annual growth variance. The other two variables used were monthly valuesof total hours of bright sunshine and mean values ofevaporative stress (which will be defined below).Sunshine, while not necessarily limiting, is importantin its microclimatic thermal and evaporative effects.Evaporative stress is a complex variable which considers the combined effects of temperature, humidity,and wind speed. It expresses the conditions for physiological drought through the process of desiccation.TABLE i. Number of samples and range of tree ages, according to species. Number of AgeSpecies samples rangeBurr Oak 5 78-139Red Oak 25 75-109White Oak 13 71-107Black Oak 7 80-108Elm 13 48-70Ash13 10-56Larch 1 76Locust 3 14--33Itackberry 1 55FEBRUARY 1965 M A R K D. S H U L M A N A N D R E I D A. B R Y S O N 109Winter mean values of sunshine and evaporative stresswere not included since there was no reason to believethat such variables could explain any part of the annualradial growth variance. The meteorological variables used in this study (Table2) were measured at the U. S. Department of Commerce Weather Bureau office at Madison,2 locatedless than a tenth of a mile from the stand site. Thus theoften faced problem of using inadequate data, or datarequiring major adjustments for location was notpresent. Winter mean values for temperature and precipitation were obtained by averaging the monthly meanvalues from October through March of the prior andcurrent year. That is, the average of six mean monthlyvalues preceding the April value for the year in question.All the climatic variables used in the present study weredirectly measured except the monthly mean values ofevaporative stress, which were calculated using theformula E~= eaXw where ed is the monthly mean vaporpressure deficit and w the monthly mean wind speed.Values of ea were determined from the expression ea= (iO0--RH)e8where RH is the relative humidity and e, the saturationvapor pressure at the monthly mean temperature. Sincethe units of ea are inches of mercury and those of w,MPH, mean evaporative stress was determined in unitsof miles per hourXinches of Hg.3. Statistical techniques: Stepwise multiple regression--and application Let us now consider which of the many climaticparameters are most significantly related to the yearto year variance of the tree growth series. If the climaticvariables considered were completely independent ofeach other, the simplest way to obtain our results wouldbe by means of a straightforward correlation matrix.Such a technique would yield the simple productmoment correlations between each variable and everyother one without regard to their possible interdependence. A slightly more sophisticated analysis, thesimple multiple regression, would compute the partialcorrelations between the independent variables andthe dependent one, but would still only partially takeinto account the interaction between the independentvariables. These interactions are considerable. For instanceconsider evaporative stress and temperature. Evaporative stress is computed from relative humidity andsaturation vapor pressure, both highly related to temperature. Similarly, total hours of bright sunshine arerelated, in varying amounts, to precipitation, evaporative stress, and temperature. 2 The only exception being sunshine which was recorded at thecity office uhtil 1 January 1947, after which it was obtained at theairport office, located 5- miles to the northeast. Thus a statistical technique is required that, in.determinh~g the tree growth variance explained by theclimatic variables, considers the important interactionsbetween the independent variables themselves. Forthis purpose it was decided to use a stepwise multipleregression technique? With such a technique one teststhe significance of the relationship between the indi~vidual independent variables (climatic factors) andthe dependent variable (early, late, and total woodgrowth), without neglecting the varying interdependence among climatic variables. The following is a basicdescription of the stepwise multiple regression process. The simple regression equation may be expressed asY = A-kA ~X~q-A ~X2q-. - - q-A ,~X,~ where the dependentvariable is Y, A. - - A ~ are the coefficients, and X~. - - X~are preselected independent variables. In the stepwisemultiple regression analysis the "stepping" process considers the amount of variance contributed by the independent variables and eliminates those which are notsignificant according to predetermined criteria. Thesecriteria will be described below. This is done by calculating the standard errors of each coefficient as well asthe residual errors. The number of equations possiblewith n total independent variables and r independentvariables appearing in the final equation is given by thebinomial or r!(n--r)~-----]' Of these equations the oneselected according to our statistical specifications willgive the greatest reduction in variance. The procedure for deleting and selecting variables inthe stepwise regression equations is given elsewhere(Fritts, 1962). In the analysis of variance performed inthe development of the final equations, F tests areapplied after each variable is added to determine thereduction in variance by the addition of the particularvariable. This is required because the importance of avariable may be altered after it is placed in the regressionequation due to its interaction with the other variables. Similarly within the regressionanalysis, Student'st tests were applied and only those variables with regression coefficients determined significant to the 0.99 levelwere selected. Table 3 presents the final regression equations, asdetermined by the above analysis of the total woodgrowth of the various species. The terms on the rightside of the equations consist of the regression coefficientstimes the subscripted independent variable (seeTable 2). These and other variables were initiallyselected as significant by the program according to theabove mentioned criteria. As a final step all variablesfound to explain less than 5 per cent of the variance ofthe independent variable were deleted, resulting in theequations presented in Table 3. The independent a Malone, T. F., 1958: Studies in statistical weather prediction.Final Report AF19(604)-1590, Trax,elers Weather ResearchCenter, Hartford, Conn.110 JOURNAL OF APPLIED METEOROLOGY VOLUME4 T~Lg 2. Identifier numbers* of independent variables**.Description of Prior year Current yearelement Apr. May Jun. Jul. Aug. Sep. Winter Apr. May Jun. Jul. Aug. Sep.Mean temperature (-F) -- I1 12 13 14 15 10 4 5 6 7 8 9Evaporative stress 22 23 24 25 26 27 -- 16 17 18 19 20 21(MPHXinches of Hg)Total hours bright -- 33 34 35 36 37 -- -- 28 29 30 31 32sunshine (hours)Total precipitation 45 46 47 48 49 50 44 38 39 40 41 42 43(inches) * Number 1 is year number; number 2 is year number squared; number 3 is year number cubed. ** Standard U. S. Weather Bureau instruments used in obtaining the data included the mercury thermometer, wet and dry bulbthermometers, Marvin sunshine recorder, eight inch rain gage, Epply pyrheliometer, 4 cup anemometer to the mid 1930's, and a 3 cupanemometer from the mid 1930's to the present. TA~LF. 3. Regression equations with mean total wood growth as the dependent variable and climatic and temporal factors as independent variables. The equations are truncated so as to include only those independent variables which reduce at least 5% of thedependent variance. Asterisks refer to prior year variables.Red OakBlack OakI-IackberryBurr OakWhite OakElmLarchAshY=--0.01967278xxs +0.00315112x4~ +0.00260555xas --0.00110200xn*q-0.01199449x~x*Y=--0.00008561x~ +0.00000138x~ --0.01119473x~Y= --0.04240462xaa*+0.00485715xt0 --0.00312798x~Y= 0.00151306xdt --0.00902201x~ +O.O0879209x~a*--O.OOO91872xta*q-O.OO123843xds*F=--0.00012157x~ -t-0.00000434x~ --0.00000004x~ +0.00163831x~xY=--0.01937974x~s--0.00127702xta*+0.01938341xt0--0.00000732x~ +0.01756032x~*Y=--0.00010106xl +0.00000168x.* +O.O0025981xa**--O.OO225099xia*/z= 0.00315403x~ +O.O0527618xss q-0.00292561xa~ q-0.00252929xds*variables in these equations are presented in the order ofselection which corresponded to the amount of variancereduced. Examination of these equations makes it apparentthat the temporal variables, year number and yearnumber squared in particular, are important. Indeedthe greatest reduction in variance can be shown to bedue to variables x~ and X.>. This is a result of naturalphysiological trend evident in tree growth. The mostsignificant climatic variables in terms of reduction oftotal radial growth variance were July precipitation andJuly evaporative stress. The fact tl~at the regressioncoefficients for these two variables are of opposite signs,as would be expected, positive for July precipitationand negative for July evaporative stress, indicates astrong dependence of the radial growth rate on water~vMl~bility. This is of p~rticular interest in thatMadison is located in a vegetational transition or tension zone between the prairie, to the south and west,and the forest, to the north and east. If one were toplace tke isoline indicating equal annual precipitationand potential evapotranspiration on a map of the northcentral states, this line would coincide fairly well withthe prairie-forest border (Lindsay, 1953), which is notfar from Madison. The importance of the relationshipof evaporation or evaporative stress 'and precipitationto tree growth in this transitional zone is indicated bythe present results. Other climatic -ariables appearing in the equationsand given in order of the amount of growth variancethey reduce include the following: Evaporative stressof April for the prior year, May precipitation, Aprilprecipitation. June evaporative stress, temperature ofJune for the prior year, and precipitation of August forthe prior year. The surprising importance of several"prior year" climatic variables may indicate a dependence of annual radial tree growth on favorablegrowth conditions the year before.4. Conclusion Most prior dendroclimatic studies have consideredthe relationship between a single climatic variable andtree growth. The choice of the climatic factor used wasdependent on the geographic area studied. It has beenshown here, by means of stepwise multiple regressiontechniques, that the growth variance of mid-latitudehardwood samples can be satisfactorily explained onlyby numerous factors, climatic as well as temporal(Table 3). The greatest part of the cumulative growthvariance was explained by the time terms, indicatingthe importance of long-term trends in the growth series.Considering only the climatic factors, the two explaining the largest growth variance were July precipitationand July evaporative stress. In particular, since theseparameters occurred in the combination precipitationminus evaporative stress, a strong dependence of growthrate on water availability was found.Fl~Bau~ta-1965 MARK D. SHULMAN AND REID A. BRYSON 111 Acknowledgments. The authors wish to thank Mr.Donald Johnson for his assistance in statistical techniques, Mr. Charles Hutchins and Mr. Paul Sampsonfor their aid in computer programming, and Mr. MarvinBurley for his aid in climatic data accumulation. This research was supported by the AtmosphericSciences Division, National Science Foundation grantgp-444. REFERENCESDouglas, A. E., 1928: Climatic cycles and tree growth, a study of the annual rings of trees in rdatlon to climate and solar activity. Vol. IL Carnegie Institute of Washington, 166 pp.Eklund, B., 1956: Variations in the annual rings in pine and spruce due to climatic conditions in North Sweden, during the years, 1900-1944. Tree-Ring Bulletin, 21, Nos. 1-4, 1-35.Fritts, H. C., 1962: An approach to dendroclimatology: screening by means of multiple regression techniques, or. Geophys. Res., 67, 1413-1420.Gliddings, G. L., 1943: Some climatic aspects of tree growth inAlaska. Tree-Ring Bulletin, 9, 26-32.Hare, K. E., 1952: Some climatological problems of the arctic and subarctic. Compendium of Meteorology, Boston, Mass., Amer. Meteor. Soc., 952-966.Hustich, I., 1949: On the correlation between growth and the recent climatic fluctuation. Geographlca Annaler, Vol. 31, 90--105.Kramer, P. J., and T. L. Kozlowski, 1960: ~Physidogy of Trees. New York, McGraw-Hill Inc., 642 pp.Lindsay, D. R., 1953: Climate as a factor influencing the mass ranges of weeds. Ecology, 34, 308-321.Miller, A., 1950: Climatic requirements of some major vegeta tional formations. The Advancement of Science, 7, 90-94.Schulman, E., 1956: Dendroclimatic Changes in Semi-arid A merica. Tucson, Ariz., University o- Arizona Press, 142 pp.Siren, G., 1961: Skogsgranstallen sore indikator for klimatfluk tuationerna i Norra Fennoskandien under historisk tid. Metsantutkimuslaitoksen Julkaisuja 54.2, Communieationes Instltuti Forestalis Fenniae, 54.2, Helsingfors, 66 pp.

## Abstract

Stepwise multiple regression analysis applied to annual radial growth increments of mid-latitude hardwood samples indicates that satisfactorily high levels of reduction of the growth variance can he achieved only by utilizing a number of climatic and temporal parameters, both simple and compound. A large part of the variance, as might be expected, is associated with the secular trend of the growth rate. Of the climatic parameters, July precipitation and July evaporative stress were found to be most significant. In particular, since these parameters occurred in the combination precipitation minus evaporative stress, a strong dependence of growth rate on water availability was found.