A statistical study of the relationship between the solar cycle length and tree-ring index values

\ PERGAMON

Journal of Atmospheric and Solar!Terrestrial Physics 59 "0887# 0600Ð0607

A statistical study of the relationship between the solar cycle length and tree!ring index values Keqian Zhoua\b\ C[J[ Butlerb\ a

Institute of Geo`raphy\ Henan Academy of Sciences\ Zhen`zhou\ 349941\ China b Arma`h Observatory\ Colle`e Hill\ Arma`h BT50 8DG\ N[ Ireland\ U[K[

Received 14 November 0886^ received in revised form 8 November 0887^ accepted 01 November 0887

Abstract We have determined the correlation coe.cient between tree!ring index values and the sunspot cycle length for 58 tree! ring data sets from around the world of greater than 483 years duration[ A matrix of correlation coe.cients is formed with varying delay and smoothing parameters[ Similar matrices\ formed from the same data\ but randomly scrambled\ provide a control against which we can draw conclusions about the in~uence of the solar cycle length on climate with a reasonable degree of con_dence[ We _nd that the data con_rm an association between the sunspot cycle length and climate with a negative maximum correlation coe.cient for 79) of the data sets considered[ This implies that wider tree!rings "i[e[ more optimum growth conditions# are associated with shorter sunspot cycles[ Secondly\ we _nd that the climatic e}ect of the solar cycle length is smoothed by several decades and the degree of smoothing is dependent on the elevation and the geographical location of the trees employed[ Thirdly\ we _nd evidence for a cyclic variation of ½199 years period in either solar cycle length or tree ring index[ Þ 0888 Elsevier Science Ltd[ All rights reserved[

0[ Introduction Friis!Christensen and Lassen "0880# found that the mean temperature of the northern hemisphere over the past 029 years closely parallelled the length of the sunspot cycle[ Their discovery suggested that\ of many indicators of solar activity\ the solar cycle length was the one most closely associated with climate change[ Currently\ most comparisons between the solar cycle length and climate have relied on instrumental climate measurements over the past 029Ð199 years "e[g[ Friis! Christensen and Lassen\ 0880^ Butler and Johnston\ 0885#[ Previous to this\ instrumental measures are less reliable and are geographically poorly distributed with almost all the available data gathered in either North America or Europe[ To extend this comparison in both time and geographical location\ composite temperature series\ which combine instrumental with proxy data\ have been used "Hameed and Gong\ 0883^ Lassen and Friis! Christensen\ 0884#[ In general these studies con_rm the

 Corresponding author[ Tel[] ¦33!0750!411817^ fax] ¦33! 0750!416063

behaviour found initially by Friis!Christensen and Lassen "0880# of higher temperatures occurring when the sunspot cycle was shorter and lower temperatures when sunspot cycles are longer[ In order to extend such com! parisons to even larger intervals we are forced to use proxy data alone\ e[g[ from ice!core or tree!ring analysis[ This study attempts to assess whether or not a long!term connection exists between the solar cycle length and tree! ring index values "widths# over the past two millennia[

1[ Solar cycle and tree!ring data Though sunspot number has frequently been used in the past to explore the connection between climate and solar activity\ it su}ers from the disadvantage that\ prior to the last two centuries or so\ monitoring has not been carried out in a consistent fashion[ Thus\ even though naked eye observations of sunspots were recorded by the Chinese from 670 BC\ the actual number of sunspots observed at any time depends on many factors[ There! fore\ a parameter that depends on the epoch of maximum activity\ such as the cycle length\ is preferable to one that depends on the level of activity\ such as the sunspot

0253Ð5715:88:, ! see front matter Þ 0888 Published by Elsevier Science Ltd[ All rights reserved PII] S 0 2 5 3 Ð 5 7 1 5 " 8 7 # 9 9 0 3 1 Ð 3

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Z[ Keqian\ C[J[ Butler:Journal of Atmospheric and Solar!Terrestrial Physics 59 "0887# 0600Ð0607

number[ This superiority becomes even more pronounced when the dates of occurrence of aurorae are included to determine the epochs of maximum activity[ There are many references to such aurorae in European annals\ as well as Chinese\ Korean and other oriental sources\ which can be used to bolster the relatively sparse information on solar activity levels that derive from naked eye obser! vations of sunspots[ It is therefore fortunate\ when we try to extend the comparison of solar activity and climate to the pre!instrumental era\ that we can use the solar cycle length\ rather than the sunspot number as our activity parameter[ However\ we may note that the solar cycle length is not at variance with other solar activity par! ameters^ both a cumulative sunspot number and a maximum sunspot number envelope follow similar trends with time over the period that sunspots have been regu! larly observed "c[0694Ðpresent#\ as is evidenced by the correlation coe.cients between cumulative sunspot num! ber and the solar cycle length "−9[63# and between the envelope of sunspot maximum and solar cycle length "−9[69#[ The solar cycle length can be de_ned as either the interval between two consecutive sunspot maxima or between two consecutive minima[ However\ as the mini! mum sunspot number is close to zero\ it is often more di.cult to identify than the maximum[ Therefore we prefer to use maxima rather than minima[ Schove "0844# compiled a list of the years of sunspot maxima from 537 BC to 0836 AD based on a variety of historical sources including observed sunspot numbers and the occurrence of aurorae[ The Ancient Sunspot Research Group at the Yunnan Observatory "0866# has made a similar com! pilation including many additional sunspot observations culled from early Chinese documents[ Ding You!ji et al[ "0872# have redetermined the epochs of peak sunspot number using these data and have compared their results with those of Schove "0844#[ In general\ the agreement between the two series is good with 47) of solar maxima in agreement to within one year and 79) in agreement to within two years\ for the period 32 BCÐ0480 AD[ Based on these results we conclude that Schove|s epochs of solar maximum from 173 BC are reasonably reliable but\ prior to that\ large gaps in the data leave considerable room for doubt[ Consequently\ we decided to adopt Schove|s values for the solar cycle length prior to 0699 AD[0 For the period since 0699 AD we have re!deter! mined this parameter using the annual total sunspot num! bers tabulated by the National Centre for Atmospheric Research\ Boulder\ Colorado[ The solar cycle length can be easily determined[ In every interval containing three sunspot maxima there are

0 Nevertheless\ we draw attention to the conclusion of Lassen and Friis!Christensen "0884# that a critical assessment and revision of the early "pre!0699 AD# sunspot data are needed[

two solar cycles[ From the average of the two cycle leng! ths\ we obtain the cycle length for the year of the second "middle# peak[ By interpolating between the peak years\ we obtain a nominal value for the solar cycle length for each year[ Several di}erent methods for the deter! mination of the length of the solar cycle have been proposed\ but we have chosen this as it is one of the simplest[ The behaviour of the solar cycle length with time is plotted in Fig[ 0[ A considerable quantity of tree!ring yearly index data has been deposited in the International Tree!Ring Data Bank "ITRDB# at the National Geophysical Data Centre\ Boulder\ Colorado\ and is made freely available via the Internet[ From a total of about 0299 data sets\ widely distributed over the world\ we have chosen the 58 sets which cover the longest time intervals "all greater than 483 years long#[ Out of this total number\ 34 sets cover more than 799 years and 13 sets more than a millennium[ In Table 0\ we list the location\ elevation\ period of cover! age\ species and origin of each of the chosen data sets[

2[ Comparison of tree!ring data and solar cycle length! methods It is evident that any given tree!ring data set will be in~uenced by only the local climate and that the degree of response to di}erent climatic factors will vary accord! ing to the species\ age and location of individual trees[ Therefore\ we expect any response to changes in the Sun to be similarly variable between data sets[ However\ in aggregate\ it is possible\ indeed likely\ that global climatic changes will be discernible if the data sets cover a su.ciently large geographical area[ The global climate does not necessarily respond quickly to changes in the solar input[ Close to large oceans\ the thermal inertia of the sea will prolong and postpone the e}ect of changes in the solar forcing*in other words\ the oceans both smooth and delay global climatic change[ The delay in the e}ect can be of the order of one or more decades depending on the size of the ocean and its latitude[ Thus individual trees will be subject to di}erent delays and smoothing functions according to their location[ For these reasons\ we have investigated both the delay "D# and the inte`ral "I# "i[e[ smoothing# e}ect in our comparison of each tree!ring data set with the solar cycle length[ To accomplish this\ we computed the correlation coe.cient between the nom! inal annual solar cycle length and the tree!ring index for the corresponding year\ with a range of values of D "from 9 to 139 years\ in steps of 4 years# and a range of values of I "from 0 to 090 years\ in steps of 4 years#[ Thus we built up a matrix of correlation coe.cients for each of the 58 sets of data[ It is important to realize that\ in these computations\ I is the number of years previous to the

Z[ Keqian\ C[J[ Butler:Journal of Atmospheric and Solar!Terrestrial Physics 59 "0887# 0600Ð0607

0602

Fig[ 0[ The solar cycle length as a function of time from 173 BC to 0889 AD[ See text for details[

year under consideration for which the solar cycle length has been integrated[ In Table 1\ we show an example of such a matrix of coe.cients for data set No[ 30\ a thousand year!old tree from Louisiana[ These matrices appear to have a number of common factors\ such as the tendency for the regions of highest correlation coe.cient to lie in diagonal bands across the matrix\ and the tendency for repeating patterns in these diagonal bands due to long!term oscillations in the solar cycle length such as the 79Ð89 year Gleissberg cycle[ This latter period is evident in both the sunspot cycle length and in the amplitude of the sunspot cycle[ In the example shown\ the maximum correlation coe.cient of −9[13 occurs with D  29 years and I  5 years "i[e[ the six years previous to Year 5 in the data set#[ We need to consider the location in the matrix of the maximum of the absolute value of the correlation coe.cient and to assess the statistical signi_cance of this coe.cient[ Because climate is likely to be a}ected by a number of factors\ which are probably unrelated in origin\ and because it is a complicated and probably non!linear system\ we should not expect to _nd high values of the correlation coe.cient in the matrices[ Nevertheless\ even relatively low correlation coe.cients can be meaningful if

they consistently exceed the coe.cients that are found for a random distribution[ In order to test the signi_cance of the correlation coe.cients we have used a Monte!Carlo test method[ We _rst re!arrange the tree!ring data set in a random way and then determine a correlation coe.cient matrix using the same range and step in the D and I parameters[ This process was repeated 099 times for each data set\ thereby yielding 099 randomised matrices for each data set[ If we de_ne Rmax as the maximum value of the correlation coe.cient in the matrix using the real\ unscrambled\ data and rmax as the maximum correlation coe.cient in each of the randomised data sets\ then we accept the value of Rmax as signi_cant if it exceeds rmax"n# for all n from 0 to 099[ That is\ we consider Rmax signi_cant if it exceeds all values of rmax in the 099 matrices using randomised data[ If any value of rmax in the 099 matrices using randomised data exceeds Rmax\ that particular data set is disregarded[ This procedure ensures a high level of signi_cance for any correlation coe.cient we use in our subsequent discussion[ Of the 58 data sets\ 48 "or about 75) of the total# have this very high con_dence level which indicates that there is a signi_cant connection between the solar cycle length and the tree!ring index[

0603

Z[ Keqian\ C[J[ Butler:Journal of Atmospheric and Solar!Terrestrial Physics 59 "0887# 0600Ð0607

Table 0 No

Site

CountryÐ State

Long[

Lat[

Elev[ m

Range years

Species

P[I[ File [crn

Rmax

D I MÐC years years Test

0 1 2 3 4 5 6 7 8 09 00 01 02 03 04 05 06 07 08 19 10 11 12 13 14 15 16 17 18 29 20 21 22 23 24 25 26 27 28 39 30 31 32 33 34 35 36 37 38 49 40 41 42

Sheep M[ Hager BR White M[ M[Eddy Flower L[ Cirque P[ Onion V[ Timber G[ Campito M[ Sheep M[ Jackson M[ Jarbidge C[ Hill 09713 Charlest[P[ Charlest[P[ Pearl P[ M[Wash[ Spruce M[ Hill 09731 Eagle Almagre M[ M[Evans Island L[ M[Goliath Windy R[ Almagre M[ Segelson P[ Frying PC Boulder Cr[ Granite M[ Scatter L[ Big Qui[R San Juan H[ Alt[R[ Eb[Cr[ Nine MC Wild Horse R[ S[Francis[Pe[ Gardiner It[Canyon Big Cypr[S[P[ Mayberry S[ Black R[ Blackw[R[ Lac Duparquet Seymour W[ Swan L[Alg[P Ardenmes A[ Liege A[ Meuse V[A[ Namur A[ Les Merv[ Les Merv[

USÐCA USÐCA USÐCA USÐCA USÐCA USÐCA USÐCA USÐCA USÐCA USÐCA USÐNV USÐNV USÐNV USÐNV USÐNV USÐNV USÐNV USÐNV USÐNV USÐCO USÐCO USÐCO USÐCO USÐCO USÐCO USÐCO USÐWA USÐWA USÐWA USÐWA USÐWA USÐWA USÐWA USÐGA USÐGA USÐUT USÐUT USÐAZ USÐMT USÐNM USÐLA USÐAR USÐNC USÐVA Canada Canada Canada Belgium Belgium Belgium Belgium France France

26>29?N 30>35?N 26>14?N 30>19?N 25>35?N 25>16?N 25>35?N 25>16?N 26>29?N 26>11?N 30>07?N 30>43?N 27>46?N 28>06?N 25>05?N 39>03?N 27>43?N 39>22?N 27>45?N 28>28?N 27>35?N 28>27?N 39>91?N 28>27?N 28>08?N 27>35?N 37>10?N 35>42?N 36>25?N 36>14?N 37>17?N 36>49?N 36>36?N 20>26?N 21>10?N 28>26?N 28>14?N 24>29?N 34>99?N 25>33?N 21>04?N 24>22?N 23>08?N 25>36?N 37>17?N 38>21?N 34>92?N 49>09?N 49>27?N 49>29?N 49>17?N 33>91?N 33>91?N

007>02?W 019>34?W 007>09?W 011>20?W 007>11?W 007>02?W 007>10?W 007>26?W 007>02?W 007>02?W 007>15?W 004>14?W 003>02?W 004>27?W 004>31?W 004>21?W 003>08?W 003>38?W 003>03?W 095>41?W 093>47?W 094>24?W 094>24?W 094>24?W 095>94?W 093>48?W 010>34?W 010>46?W 012>24?W 010>17?W 019>29?W 012>91?W 010>04?W 70>37?W 70>02?W 009>07?W 000>93?W 000>39?W 009>32?W 094>17?W 81>47?W 80>04?W 67>02?W 65>42?W 68>06?W 012>91?W 67>32?W 4>34?E 4>24?E 4>04?E 3>41?E 6>16?E 6>16?E

2491 0413 2002 1023 2180 2494 1754 2906 2399 2364 1986 0741 1815 2937 2314 2069 2304 2009 2949 0840 2424 2424 2199 2424 2469 2425 0079 0069 877 0429 1099 756 836 0599 4 0819 1794 2424 0565 1783 36 53 1 8 163 699 329 9 9 9 9 1054 1049

369Ð0869 0209Ð0879 799Ð0852 0277Ð0870 787Ð0876 806Ð0876 0916Ð0876 0949Ð0876 515Ð0872 −0Ð0889 0156Ð0873 0223Ð0873 0Ð0856 855Ð0853 799Ð0873 219Ð0874 714Ð0872 291Ð0874 −0Ð0873 0096Ð0853 459Ð0857 866Ð0857 0058Ð0878 414Ð0872 0949Ð0874 459Ð0872 0210Ð0865 0175Ð0868 0213Ð0879 0148Ð0868 0205Ð0879 0177Ð0876 0215Ð0876 0020Ð0864 889Ð0874 0190Ð0838 175Ð0874 437Ð0872 0074Ð0860 726Ð0876 886Ð0877 887Ð0889 254Ð0874 821Ð0874 0075Ð0876 0233Ð0882 871Ð0789 0007Ð0875 561Ð0503 561Ð0878 808Ð0527 0076Ð0863 877Ð0863

PILO JUOC PILO PIJE PIBA PIBE PIBA PIBA PILO PILO JUOC JUSC PILO PILO PILO PILO PILO PILO PILO PSME PIAR PIAR PIFL PIAR PIAR PIAR PSME PSME PSME TSME LALY PSME PSME TADI TADI PSME PILO PIAR PSME PIFL TADI TADI TADI TADI THOC THPL PIST QUSP QUSP QUSP QUSP LADE LADE

0 1 2 3 4 4 4 4 5 4 6 7 8 09 4 4 4 4 4 00 01 01 02 4 4 4 03 3 3 3 3 04 04 05 05 06 4 4 07 08 05 05 05 05 19 10 11 12 12 12 12 13 13

−9[24 −9[01 −9[01 9[11 −9[28 −9[22 −9[10 −9[05 −9[19 −9[14 9[00 −9[19 −9[96 9[19 −9[13 −9[14 −9[13 −9[11 9[09 −9[06 −9[16 −9[12 −9[03 −9[06 −9[28 −9[15 −9[14 −9[10 −9[05 −9[06 −9[10 −9[12 9[11 −9[01 9[03 −9[12 −9[06 −9[14 9[10 −9[01 −9[13 9[12 −9[96 −9[04 −9[10 −9[19 −9[01 −9[11 −9[14 −9[08 9[16 −9[02 −9[01

074 04 29 104 064 9 54 059 129 139 4 104 124 029 124 084 09 099 44 9 09 39 139 049 089 09 09 084 19 9 084 4 099 029 079 124 069 024 004 54 29 199 9 9 119 4 89 089 139 114 034 089 29

CA935 CA962 CA947 CA412 CA417 CA429 CA420 CA421 CA422 CA423 NV959 NV950 NV499 NV490 NV409 NV401 NV402 NV403 NV405 CO941 CO960 CO961 CO400 CO411 CO412 CO413 WA930 WA937 WA942 WA945 WA950 WA975 WA989 GA991 GA992 UT495 UT497 AZ409 MT995 NM459 LA990 AR941 NC997 VA910 CANA095 CANA009 CANA023 BELG990 BELG991 BELG992 BELG993 FRAN998 FRAN909

090 0 0 05 75 65 40 15 80 090 0 05 0 70 090 090 70 75 0 0 35 0 5 090 090 40 0 0 50 0 0 0 0 30 0 5 75 80 0 00 5 0 40 0 0 0 50 50 090 090 60 0 5

! x ! ! ! ! ! ! ! ! x ! x ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! x ! ! ! ! x ! ! ! ! ! x ! ! x ! ! ! ! ! ! ! ! x x

Continued next pa`e

0604

Z[ Keqian\ C[J[ Butler:Journal of Atmospheric and Solar!Terrestrial Physics 59 "0887# 0600Ð0607 Table 0[ Continued[ No

Site

CountryÐ State

Long[

Lat[

Elev[ m

Range years

Species

P[I[ File [crn

43 44 45 46 47 48 59 50 51 52 53 54 55 56 57 58

Bourgogne18 Franche C36 Bodensee Eskisehir Karhunpe E[Pomerania Chenque P[ Lonco Luan Primeros P[A[ Rio Cisne San Gabriel Piedra D[A[C[ Urewera Hauhung[ Mount Field Wulan

France France Germany Turkey Finland Poland Arg[ Arg[ Arg[ Arg[ Chile Chile N[Z[ N[Z[ Australia China

35>04?N 35>49?N 35>34?N 39>99?N 57>49?N 42>29?N 27>95?S 27>48?S 27>42?S 31>98?S 22>36?S 26>49?S 27>30?S 28>03?S 31>28?S 26>99?N

3>99?W 5>04?E 8>29?E 20>94?E 16>04?E 05>99?E 69>40?W 60>92?W 69>26?W 60>22?W 69>04?W 62>91?W 006>01?E 064>15?E 035>23?E 099>99?E

9 9 349 0199 199 19 0549 0009 0519 449 0599 0299 743 0999 0199 2599

570Ð0880 0183Ð0876 0164Ð0875 0182Ð0879 0287Ð0882 885Ð0874 0135Ð0863 0295Ð0863 0039Ð0863 330Ð0863 0020Ð0864 0131Ð0864 0039Ð0881 0102Ð0881 0917Ð0864 0052Ð0875

QUSP QUSP QUSP JUSP PISY QURO ARAR ARAR ARAR FICU AUCH ARAR LIBI LIBI ATCU JUSP

14 15 16 17 18 29 20 21 21 22 23 7 24 24 25 26

Rmax

FRAN918 9[19 FRAN929 −9[19 GERM921 −9[22 TURK990 9[08 FINL910 −9[17 POLA995 −9[97 ARGE995 −9[11 ARGE902 −9[16 ARGE904 9[16 ARGE929 9[04 CHIL996 −9[14 CHIL901 −9[08 NEWZ952 −9[12 NEWZ963 −9[10 AUSL995 −9[16 CHIN990A −9[19

D I MÐC years years Test 074 094 049 139 094 004 109 029 44 19 074 64 039 009 099 104

55 45 50 35 05 5 50 70 0 10 55 0 0 0 85 25

! ! ! ! ! x ! ! ! ! ! ! ! ! ! !

 Principal investigators] "0# Lamarche\ V[C[^ "1# Holmes\ R[L[ and Adams\ R[K[^ "2# Schulman\ E[ and Fritts\ H[C[^ "3# Graumlich\ L[^ "4# Graybill\ D[A[^ "5# Graybill\ D[A[ and Lamarche\ V[C[^ "6# Fritts\ H[C[^ "7# Holmes\ R[L[^ "8# Lamarche\ V[C[ and Ferguson\ C[W[^ "09# Ferguson\ C[W[^ "00# Stokes\ M[A[ and Harlan\ T[P[^ "01# Lamarche\ V[C[ and Harlan\ T[P[^ "02# Woodhouse\ C[^ "03# Brubaker\ L[B[^ "04# Earle\ C[J[\ Brubaker\ L[B[ and Segura\ G[^ "05# Stahle\ D[ W[\ Cleaveland\ M[K[ and John^ "06# Schulman\ E[^ "07# Ferguson\ C[W[ and Despain\ D[G[^ "08# Swetnam\ T[W[\ Caprio\ A[C[ and Lynch\ A[M[^ "19# Sylvain\ A[ and Yves\ B[^ "10# Dobry\ J[ and Klinka\ K[^ "11# Guyette\ R[ and Cole\ B[^ "12# Ho}summer\ P[^ "13# Serre\ F[^ "14# Lambert\ G[\ Lavier\ C[ and Trenard\ Y[^ "15# Lambert\ G[ and Lavier\ C[^ "16# Billamboz\ A[^ "17# Kuniholm\ I[^ "18# Lindholm\ M[ and Merilainen\ J[^ "29# Wazny\ T[^ "20# Lamarche\ V[\ Holmes\ R[\ Ambrose\ J[ and Bonin\ J[^ "21# Holmes\ R[ L[ and Ambrose\ J[ E[^ "22# Boninsegna^ "23# Lamarche\ V[\ Holmes\ R[\ Dunwiddie\ P[ and Gut\ J[^ "24# Xiong\ L[ and Palmer\ J[^ "25# Lamarche\ V[\ Ogden\ J[\ Campbell\ D[ and Dunwi\ P[^ "26# Local Met[Bur[ and Zu\ R[Z[

3[ Results We may note the following features of the statistical results[ "0# Most "36:48 ½ 79)# of the maximum correlation coe.cients Rmax are negative[ This implies that\ on average\ wider tree!rings are associated with a shorter sunspot cycle length[ "1# Many "34:48 ½ 65)# values of Rmax have a value of D in excess of 49 years and about half "17:48 ½ 36)# have a value for I in excess of 49 years[ The high value of I favours a relatively wide smoothing "i[e[ several decades# of the dependence of tree ring index on solar cycle length[ The distribution of the values of D is shown in Fig[ 1[ If there were no real correspondence between the solar cycle length and tree ring index we would expect a roughly ~at distribution in this diagram\ whereas in fact there is a preponderance of values close to zero and around 199 years[ The observed distribution could be explained if the true response time were short "i[e[ less than 19 years# and if either parameter "tree

ring index or solar cycle length# contained a sig! ni_cant cyclic component with a period ½199 years[ "2# There is a disproportionate amount of data in the ITRDB from North America*indeed 39 out of the total 48 data sets are from this region of the globe[ The North America data can be divided into two parts] part A "11 sets# for elevations above 1499 m\ and part B "07 sets# for elevations below 1499 m[ The values of D and I associated with Rmax are sig! ni_cantly di}erent for parts A and B\ i[e[ Rmax tends to occupy a di}erent region of the correlation coe.cient matrix for data sets in parts A and B "see Fig[ 2\ upper panel#[ There is also a di}erence between data sets in part B of the North America and Europe "see Fig[ 2#[ Such a comparison with the data from other continents is unfortunately not possible due to the sparsity of data[ However\ as the number of data sets in other parts of the world increases\ we should eventually be able to study this geographical e}ect further[ "3# The distribution of correlation coe.cients in the matrices appears to re~ect either a climatic oscillation

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Z[ Keqian\ C[J[ Butler:Journal of Atmospheric and Solar!Terrestrial Physics 59 "0887# 0600Ð0607

Table 1 Site Name] BIG CYPRESS STATE PARK STANDARD[ State:Country] LOUISIANA:U[S[A[ Location] 21>04?N 81>47?W[ Year Range] 886Ð0877[ Elevation] 36 m[ Species Code] TADI[ Common Name] BALDCYPRESS[ P[I[] DAVID W[ STAHLE\ MALCOLM K[ CLEAVELAND\ JOHN[ File Name] LA990[CRN[ Rmax  −13 Delay\ "D#  29\ Integral"I#  5 "correlation coe.cient×099# I:D 0 5 00 05 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 090 I:D 0 5 00 05 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 090

9 4 09 04 19 14 29 24 39 34 8 6 2 −0 −5 −04 −12 −10 −01 −1 6 3 −9 −3 −00 −10 −13 −07 −7 0 4 1 −2 −7 −06 −12 −11 −03 −3 3 2 −0 −5 −03 −19 −12 −08 −09 −0 4 0 −3 −00 −07 −11 −10 −04 −5 0 4 −1 −8 −05 −19 −10 −07 −01 −3 1 3 −5 −02 −07 −19 −08 −04 −8 −2 0 2 −00 −05 −07 −07 −05 −02 −7 −2 9 1 −03 −05 −06 −05 −03 −00 −6 −2 −9 0 −03 −05 −04 −03 −02 −00 −7 −3 −0 9 −03 −03 −03 −02 −01 −00 −7 −3 −1 −0 −01 −01 −02 −01 −01 −00 −7 −4 −7 −2 −00 −00 −01 −02 −02 −00 −8 −5 −3 −3 −09 −00 −01 −02 −02 −01 −09 −6 −5 −4 −09 −00 −01 −02 −02 −02 −00 −8 −6 −4 −09 −00 −01 −02 −03 −02 −01 −8 −5 −3 −09 −00 −01 −03 −03 −03 −01 −8 −4 −2 −09 −00 −02 −03 −04 −03 −01 −7 −3 −1 −09 −01 −03 −04 −04 −03 −09 −5 −2 −0 −00 −02 −03 −04 −03 −01 −8 −4 −1 −0 −00 −02 −03 −03 −02 −00 −7 −3 −1 −9 014 00 7 5 3 3 3 4 4 4 4 3 2 1 0 −9 −0 −1 −1 −0 −9 −9

029 8 4 3 2 2 2 2 2 1 1 0 9 −0 −1 −2 −2 −2 −1 −0 −0 −1

024 5 2 2 1 1 1 0 0 9 −0 −1 −2 −3 −3 −3 −2 −2 −1 −1 −1 −2

039 4 2 2 1 0 9 −0 −0 −1 −2 −3 −4 −4 −4 −3 −2 −1 −1 −2 −3 −4

034 5 3 2 1 −9 −1 −2 −3 −4 −4 −5 −6 −5 −4 −2 −1 −1 −2 −3 −4 −5

49 5 6 6 5 4 2 1 0 9 −0 −2 −3 −4 −4 −3 −1 −0 −0 −9 −9 9

44 8 6 5 4 2 0 9 −0 −1 −3 −4 −5 −5 −3 −2 −0 −0 −0 −9 −9 9

59 7 5 2 0 −9 −0 −1 −2 −4 −5 −6 −6 −4 −2 −1 −0 −0 −0 −9 −9 9

54 4 1 −0 −1 −1 −2 −3 −5 −7 −7 −7 −5 −3 −1 −0 −0 −9 −9 9 9 −9

69 0 −1 −2 −2 −3 −4 −6 −7 −8 −7 −5 −3 −1 −0 −9 9 0 0 0 0 −9

64 −1 −2 −2 −3 −4 −6 −7 −8 −7 −5 −3 −1 −9 0 0 1 1 1 1 0 9

79 −0 −1 −3 −4 −6 −7 −8 −7 −5 −3 −0 9 0 1 2 3 3 2 1 0 9

74 89 84 099 −1 −4 −7 −8 −3 −7 −09 −8 −5− 8 −09 −8 −7−09 −09 −6 −8−09 −7 −3 −8 −8 −5 −1 −8 −5 −2 −9 −5 −3 −0 1 −3 −0 0 2 −0 0 1 3 0 1 3 5 1 2 4 6 2 4 5 7 3 4 6 6 4 5 5 6 4 4 4 5 3 3 3 3 2 2 2 1 1 1 0 0 0 9 −9 −0 −9 −0 −0 −1

049 044 059 054 069 064 079 074 089 084 199 194 109 104 119 5 5 0 −2 −2 −5 −8 −7 −09 −09 −4 1 6 09 6 3 1 −2 −4 −5 −8 −09 −00 −01 −8 −3 2 6 6 1 1 −0 −4 −6 −8 −00 −01 −01 −01 −7 −0 3 5 2 −1 −0 −3 −6 −8 −00 −01 −02 −02 −00 −4 9 3 2 −9 −4 −1 −4 −8 −00 −01 −03 −03 −01 −7 −2 0 2 0 −2 −6 −3 −6 −09 −01 −02 −03 −02 −09 −5 −0 0 0 −0 −4 −7 −4 −7 −00 −02 −03 −02 −09 −6 −2 −0 9 −9 −2 −5 −8 −5 −8 −01 −02 −02 −00 −7 −4 −1 −0 −0 −1 −3 −5 −8 −6 −09 −01 −01 −00 −7 −4 −2 −1 −1 −1 −1 −3 −5 −8 −7 −09 −00 −09 −7 −5 −3 −2 −2 −2 −1 −2 −3 −5 −8 −7 −8 −8 −7 −5 −4 −3 −3 −3 −2 −2 −2 −3 −5 −7 −7 −7 −6 −5 −4 −3 −3 −3 −3 −2 −2 −2 −3 −5 −7 −5 −5 −4 −4 −3 −4 −4 −4 −3 −3 −2 −2 −3 −5 −6 −3 −3 −3 −3 −4 −5 −5 −4 −4 −3 −2 −2 −3 −4 −5 −2 −2 −3 −4 −5 −5 −5 −5 −4 −3 −2 −2 −2 −3 −4 −1 −3 −4 −5 −6 −6 −6 −5 −4 −4 −3 −2 −2 −3 −4 −2 −4 −6 −7 −7 −7 −7 −6 −5 −4 −3 −2 −2 −3 −4 −4 −5 −7 −8 −8 −8 −7 −7 −6 −5 −3 −2 −3 −4 −5 −5 −6 −8 −8 −8 −8 −8 −7 −6 −5 −3 −3 −3 −4 −5 −6 −7 −8 −09 −09 −09 −8 −7 −6 −5 −4 −3 −3 −4 −5 −6 −7 −8 −09 −09 −09 −8 −7 −6 −5 −4 −3 −3 −4 −5

094 −6 −6 −3 −1 9 1 2 3 4 5 7 7 7 7 6 4 3 1 9 −0 −0

009 004 019 −2 4 8 −0 4 7 1 5 6 2 5 5 3 5 4 3 4 4 4 5 4 4 6 5 6 7 6 7 7 6 8 8 6 8 7 5 7 7 4 7 5 3 5 4 2 4 2 0 2 1 −9 0 9 −0 −9 −0 −0 −0 −9 −9 −9 0 0

114 129 124 139 0 3 −6 −7 −2 −6 −8 −8 −6 −09 −09 −8 −8 −00 −00 −09 −09 −00 −00 −00 −00 −01 −01 −00 −00 −01 −01 −00 −09 −00 −00 −00 −09 −00 −00 −8 −09 −09 −8 −7 −09 −8 −7 −6 −7 −7 −6 −5 −6 −6 −5 −4 −5 −5 −4 −3 −4 −4 −3 −2 −4 −4 −3 −2 −4 −4 −3 −2 −5 −4 −4 −3 −5 −5 −4 −4 −5 −5 −5 −4 −5 −5 −4 −3

Z[ Keqian\ C[J[ Butler:Journal of Atmospheric and Solar!Terrestrial Physics 59 "0887# 0600Ð0607

0606

Fig[ 1[ A histogram of the number of data sets for which a given value of D gives the optimum correlation coe.cient "binned in 09! year intervals#[

Fig[ 2[ The values of the parameters I and D at which the correlation coe.cient between solar cycle length and tree!ring index reaches its maximum value Rmax[ Upper panel*North America] _lled squares*data from part A "elevation × 1\499 m#^ open squares*data from part B "elevation ³ 1499 m#^ Lower panel*Europe[

"possibly due to solar activity# or periodic changes in solar activity such as the Gleissberg cycle\ or both[

4[ Discussion The aforegoing statistical study of the correlation between solar cycle length and tree ring index values has

allowed us to probe the connection between climate and solar activity over time intervals in excess of previous similar studies[ In general\ we _nd a statistically sig! ni_cant correlation between tree ring indices and solar cycle length in the sense that more optimum growth con! ditions occur during short solar cycles[ Exactly which climatic factor the tree ring index is most sensitive to "i[e[ rainfall\ temperature\ humidity\ sunshine\ length of

0607

Z[ Keqian\ C[J[ Butler:Journal of Atmospheric and Solar!Terrestrial Physics 59 "0887# 0600Ð0607

growing season\ etc[# may depend on the location\ age and species of tree involved[ However\ the fact that shor! ter cycles have been shown to be associated with increased tropospheric temperatures would suggest that\ for the majority of trees used in this study\ temperature is an important constraint on growth[ With the proviso that our study involves a proxy climate indicator\ rather than instrumental measurements\ our conclusions support the contention that solar cycle length\ or something closely related to it\ has been associated with climate change for over a millennium[ For many samples\ our analysis has shown the highest correlation between the solar cycle length and tree ring index when the e}ect is integrated over periods of several decades[ This might be unexpected after one has seen the close correspondence between the solar cycle length and mean northern hemisphere temperature found by Friis! Christensen and Lassen "0880#[ However\ in fact it is compatible with their result\ as their index of solar cycle length has already been smoothed with a broad _lter of total width _ve cycles "½44 years#[ Thus both results imply that the solar e}ect on climate is cumulative over several decades[ The possibility of a delay in the response of tree ring widths to changes in the solar cycle length has been included in the statistical analysis by a variable value for D[ The results show a greater preponderance of very low "³19 year# and high "×069 year# values of D than expected from random behaviour[ The low values are consistent with a small delay in the e}ect on tree ring widths of changes in the solar cycle length[ However\ the group of higher values of D\ which concentrate in the range 069Ð139 years\ require a rather more elaborate explanation[ Supposing the correlation coe.cient to reach a peak at D  9\ then cyclic variation in either the tree ring index or the solar cycle length\ or in both\ will give rise to a second peak in the correlation coe.cient as the trial value of D becomes close to the period of the cycle[ In the present data this second maximum\ which can be larger than the _rst\ occurs for many trees at P ½ 199 years[ Evidence of an ½199!year cycle has been previously found in tree!ring index values "Sonett and Finney\ 0889#\ in C03 levels "Sonett and Finney\ 0889^ Murphy and Palmer\ 0881# and in Chinese sunspot rec! ords "Xu Zhantao\ 0889#[ Both the ½199 year periodicity

in C03 levels and a similar periodicity in auroral intensity found by Schove "0844# are believed to be related to an underlying ½199!year periodicity in solar activity levels[ The presence of the same periodicity in tree ring indices once again suggests\ but does not prove\ a link between solar activity and climate[

Acknowledgements We wish to acknowledge the support of a Royal Society Ex!Quota Travel Grant to enable one of us "ZH# to work in the U[K[ for a period of three months[ Research at Armagh Observatory is grant!aided by the Department of Education for Northern Ireland[

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