Six temperature proxies of Scots pine from the interior of northern Fennoscandia combined in three frequency ranges

Resea ch A icle Six Tempe a u e P oxies o Sco s Pine om he In e io o No he n Fennoscandia Combined in Th ee F equency Ranges Ma kus Lindholm,1Maxim G. Ogu so ,2Ris o Jalkanen,1 Bjö n E. Gunna son,3and Ta mo Aal o1 1Me la, Ro aniemi Resea ch Uni , P.O. Box 16, 96301 Ro aniemi, Finland 2A.F. Io e Physico-Technical Ins i u e, S . Pe e sbu g 194 021, Russia 3Bolin Cen e o Clima e Resea ch, Depa men o Physical Geog aphy and Qua e na y Geology, S ockholm Uni e si y, 106 91 S ockholm, Sweden Co espondence should be add essed o Ma kus Lindholm; ma kus.lindholm@me la. i Recei ed 20 Decembe 2013; Re ised 7 Ap il 2014; Accep ed 11 Ap il 2014; Published 6 May 2014 Academic Edi o : Sil io Gualdi Copy igh © 2014 Ma kus Lindholm e al. This is an open access a icle dis ibu ed unde he C ea i e Commons A ibu ion License, which pe mi s un es ic ed use, dis ibu ion, and ep oduc ion in any medium, p o ided he o iginal wo k is p ope ly ci ed. Six ch onologies based on he g ow h o Sco s pine om he inland o no he n Fennoscandia we e buil o sepa a ely enhance low, medium, and highe equencies in g ow h a iabili y in 1000–2002. Se e al pe iodici ies o g ow h we e ound in common in hese da a. Fi e o he low- equency se ies ha e a signi ican oscilla o y mode a 200–250 yea s o cycle leng h. Mos se ies also ha e s ong mul idecadal scale a iabili y and signi ican peaks a 33, 67, o 83–125 yea s. Recons uc ion models o mean July and June–Augus as well as h ee longe pe iod empe a u es we e buil and compa ed using s ingen e i ica ion s a is ics. We desc ibe main di e ences in model pe o mance (𝑅2= 0.53–0.62) be ween indi idual p oxies as well as hei a ious a e ages depending on p o enance and p oxy ype, leng h o a ge pe iod, and equency ange. A sepa a e medium- equency ch onology (a p oxy o June–Augus empe a u es) is p esen ed, which is closely simila in ampli ude and du a ion o he las wo cycles o he A lan ic mul idecadal oscilla ion (AMO). The good synch ony be ween hese wo se ies is only hampe ed by a 10-yea di e ence in iming. Recognizing a s ong medium- equency componen in Fennoscandian clima e p oxies helps o explain pa o he unce ain ies in hei 20 h cen u y ends. 1. In oduc ion Se e al ecen s udies ha e discussed he po en ial o high- esolu ion p oxies based on he g ow h o Sco s pine om no he n Fennoscandia o econs uc ion o summe em- pe a u es in pa icula a he low- equency scale o a iabil- i y [1–5]. The main conce n has gene ally been he in e es ing empe a u e di e ence be ween medie al imes, Li le Ice Age, and he mode n pe iod iewing ecen and p ojec ed wa ming wi hin he con ex o na u al a iabili y. Less a en- ionisusuallypaid o hes ongmul idecadalcomponen o empe a u e a iabili yin heobse a ionalaswellasp oxy eco ds, which may se iously hampe he iden i ica ion o an ampli ied wa ming signal in he las cen u y in he A c ic and su ounding egions [6]. Some in e nal clima e con ols mayha ein luenced egionalclima esimul aneouslywi h heca bondioxideinducedwa ming,andFennoscandian empe a u e p oxies may ha e eco ded bo h ypes o po en- ially coinciding, in e ac ing, o e en di e ging signals in he decadal- o-cen ennial scales o a iabili y. Mul idecadal a iabili y in Fennoscandian summe ime clima e may well be ela ed o he AMO (sea su ace empe a u es (SST)), which has a pe iod o abou 40–80 yea s, sugges ed o a ise om p edic able in e nal a iabili y o he ocean-a mosphe e sys em [7,8]. In addi ion A c ic ai empe a u e and p essu e ha e been shown o display s ong mul idecadal a iabili y on simila ime scales [9]. The goal he e is o s udy pe iodici y and ends in g ow h a iabili y o six ecen ly published and upda ed millennia leng h p oxies o Sco s pine om he no he n imbe line. I Hindawi Publishing Co po a ion Jou nal o Clima ology Volume 2014, A icle ID 578761, 13 pages h p://dx.doi.o g/10.1155/2014/578761 2Jou nal o Clima ology he six se ies show consis en and synch onous in e annual- o-decadal, decadal- o-mul idecadal, as well as cen ennial and longe ypes o a iabili y, h ee e sions o each se ies will be buil in o de o highligh he h ee equency bands sepa a ely in hese da a as well as in a ious combina ions o egional a e ages (no mixing equency classes). G ow h signals a e conside ed mo e o less equency dependen i hey all show simila and cohe en beha io in he sugges ed equency anges and may hus be use ully combined o egional high- equency (h- ), medium- equency (m- ), and low- equency (l- ) ch onologies. Cu en knowledge is ela i ely limi ed ega ding spec al de ails o he l- and m- ends and pe iodici ies in hese p oxies (excep o some olde e sions o indi idual p oxies o ela i ely na ow equency bands [10,11]). All he six se ies a e known p edominan ly as summe empe a u e p oxies [1,4,5,12,13]. This s udy will p o ide a synopsis o hei a he complex po en ial as p edic o s o high-summe (July), s anda d summe season (June– Augus ), and e en some longe wa m pe iod empe a u es in he h ee b oad equency anges. The esul s will se e as p ac ical guidelines o selec ing p ope p oxy ypes and choice o indexing me hods wi h espec o equi ed esponse pe iod as well as equency band. Such knowledge is c ucial in a ious mul ip oxy applica ions (see, e.g., [4]) whe e he ampli ude, du a ion, and iming o changes a e impo an . In pa icula , ou goal is o econs uc empe a u e a iabili y a he mul idecadal scale, which would be use ul in in e e- gional compa isons o meaning ul pe iodici y in land su ace empe a u es in he suba c ic egion as well as be ween land and sea su ace empe a u es o la ge ields in he sea ch o pe iodic pa e ns (bo h in insic and ex e nal o he clima e sys em). In o de o gain insigh in o his opic we will he e compa e he well-known cycles o annual AMO wi h m- pe iodici y in hese da a. Since G ay e al. [14] success ully econs uc ed he AMO using a la ge ne wo k o ee-g ow h ch onologies (including one ea ly e sion o ou da a se ies), i will be in e es ing o es an AMO model now wi h hese sixlonge andupda edse ies. Incalib a ionmodelpe o mancewillbee alua edin each case based on known s ingen e i ica ion es s. The aim is o p o ide easible models in h ee scales om h- o l- wi h inc easing p opo ion o low equency a iance (whe e h- necessa ily o e laps in m- and m- o e laps in l- ). The linea ela ionship be ween ee g ow h a he h ee equency anges and empe a u e o e he whole ange o a ge a ia ions (un il e ed) is analyzed. I would be easonable o expec model i gene ally o inc ease i meaning ul lowe equencies a e added o he pool o p edic o s ( om h- o l- ). Howe e he si ua ion is gene ally mo e complica ed as a ge s a e ela i ely sho se ies as compa ed o he p oxies, and he longes ends in ee g ow h can only ha eapa ialma chin empe a u e.Inanabou 100-yea empe a u e eco d (usual in calib a ions in his egion), he de ec ion o e i iable ends is es ic ed o a maximum o abou 50 yea s (in e pola ion). Howe e , i a good pa ial i o a longe end is ound, some ex apola ion is usually easonable. The esul s also aim o con ibu e o he la gely missing deba e on he unce ain ies and e en disag eemen o egional econs uc ions o p oxies as compa ed o he conside able a en ion o e he disc epancies in hemisphe ic econs uc ions [15]. 2. Ma e ials and Me hods The main in e es he e is in he inland egion, which is occupied by he Fennoscandian Shield and o ms a ela i ely homogeneous peneplane a he modes al i udes o abou 200 o500ma.s.l.wi hsha pclima icandgeobo anical bounda ies in he eas and wes [16–20]. Clima e in his in e- io egion is a guably mo e homogeneous and con inen al wi hou he mo e ma ine coas al egions. Gene al loca ion o all six da a se s is he no he n imbe line, be ween he Swedish Scandes and he Khibiny Low Moun ains egion. The da a include he ecen ly upda ed and bias-co ec ed ing wid h (SWR) and maximum densi y (SXD) om Sweden [5,21,22], ing wid h (FRW), heigh inc emen (FHI), and maximum densi y (FXD) om Finland [4,23], as well as ing wid h (RRW) om he Kola peninsula, Russia [4, 24]. The ing wid h (SRW and FRW) da a se s a e la ge, including da a om 650 and 536 ees, espec i ely. The o he s a e smalle , consis ing o samples om 167 (FHI) o 78 ees (FXD). Heigh da a (FHI) a e shi ed by one yea o making compa isons possible, because heigh g ow h e lec s condi ions in he p e ious yea [25,26]. Fou long, mon hly clima e eco ds ep esen he egional empe a u es o e hei common pe iod om 1908 o 2002 [17]. To nedalen (Sweden) composi e eco d is a ailable as con inuous be ween 1816 and 2002 [27], Ka asjok (No way) eco d since 1876, Ka esuando (Sweden) eco d since 1890, and Sodankyl¨ a (Finland) eco d since 1908. To nedalen and Ka esuando a e he closes o he wes e n (Swedish RW and XD) sampling si es, Ka asjok and Sodankyl¨ a o hecen al (FinnishRW,HI,andXD)si es,andSodankyl ¨ ais hecloses o he eas e n (Russian RW) si e. Ka asjok is he no h- e nmos and Sodankyl¨ a and To nedalen he sou he nmos clima e eco ds. Addi ional e i ica ion is ob ained om he Bo en iken compila ion se ies [28], which is based on he da a om six s a ions (Abisko, Ka esuando, K ikkjokk, Jokkmokk, Hapa anda, and Pi e˚ a, mainly om somewha mo e wes e n and sou he n loca ions han he ones used in calib a ions he e) in no he n Sweden. Mo eo e , annual AMO anomalies [29] a e used in mul idecadal compa isons. Regional cu e s anda diza ion (RCS; see [5,30–32]), 180-yea and 30-yea splines (see [33–35]) we e used in indexing. They a e well-known me hods in dend oclima ol- ogy and equen ly applied in a ge ing a ious equency- dependen esponses in p oxy-based econs uc ions [36, 37]. The RCS me hod is expec ed o p ese e any l- signal up o wa eleng hs exceeding he leng hs o he indi idual segmen s used in building he ch onologies. On he o he hand, he 180-yea splines will highligh m- signal by emo ing he lowe mos equencies, he mos mul icen u y- imescale a iance po en ially p esen in he da a. The 30- yea spline ex ac s he h- signal and will emo e in addi ion mucho hemul idecadalandalllonge scale a iances. The h ee equency anges co espond o in e annual- o- decadal, in e annual- o-mul idecadal, and cen ennial ypes Jou nal o Clima ology 3 o a iabili y in he ime domain. Fu he mo e, digi al low- pass il e s we e used o ex ac he ch onology a iance wi h a equencylowe han10yea s[38–40]. We used Fou ie analysis o de ine he spec al con en in he ch onologies, ha is, a spec al desc ip ion in e ms o cycles o a ying leng h, he ac ual equencies ha gene a e he o iginal se ies. The wa ele app oach has ad an ages o e he mo e adi ional me hods o analyzing po en ially nons a iona y signals, which ha e discon inui ies and non- pe iodic cha ac e is ics [41–43]. In he complex in e ac ions in clima e he e a e a numbe o componen s which end o damp ou he mo e apid luc ua ions. Thus clima e ime se ies wi h lowe equency/longe pe iod cycles ha e o con ain a g ea e p opo ion o he obse ed a iance o achie e he same signi icance as highe equency/sho e pe iod ea u es [44]. In he ime domain con idence in e als (c.i.) we e calcula ed sepa a ely o he l- and m- anges o g ow h a iabili y using nonpa ame ic boo s ap me hod (sampling wi h eplacemen ) [45,46]. A i hme ic a e ages (AA)andweigh eda e ages(WA)(see[47] and e e ences he ein) we e applied in combining egional ch onologies. Simple linea eg ession models ( ans e unc ions) [12, 48–50]we ede eloped o eacho he h ee e sionso he sixch onologiesand hei a e ages obeusedin u nas clima e p edic o s. Indi idual models we e hen es ed in spli pe iod calib a ion e i ica ion, whe e he o al calib a ion pe iod (1908–2002) was di ided in o wo equal 48-yea hal es: 1908–1955 and 1955–2002. These subpe iods, used o calib a ion du ing one pe iod and e i ica ion du ing he o he , a e e e ed o as ea ly calib a ion-la e e i ica ion and la e calib a ion-ea ly e i ica ion (EC-LV and LC-EV, esp.). Bo h subpe iods should p oduce posi i e alues o educ ion o e o (RE) [12,38,51] and coe icien o e iciency (CE) [12,51] s a is ics o he model in o de o pass he e i ica ion es s. RE and CE alues may a y om +1 o −∞,wi h0 indica ing ha he econs uc ion model pe o ms no be e as a p edic o han he calib a ion (RE) o e i ica ion (CE) pe iod mean alue. The models a e also compa ed using coe icien o de e mina ion (𝑅2) and explained a iance (𝑟2). 3. Resul s 3.1. Pe iodici y, T ends, and In e annual Shi s in G ow h. Fi e o he six l- se ies (RCS, no il e ing) sha e signi ican oscilla o ymodea 200–250yea so cycleleng h(Figu e 1) and SXD shows e en longe - e m ea u es (Figu e 1(b)). Mos se ies also ha e s ong mul idecadal scale a iabili y, iz. signi ican peaks a 67 yea s in SRW and SXD, as well as a 83–125yea sinFRW,FXD,andRRW.Al houghallse ies ha e cumula ed some concen a ion o a iance a m- scale, he wo wes e n se ies (SRW and SXD) ha e 67-yea peaks and bo h o he XD se ies ha e a (possibly ela ed) peak a 33 yea s. In addi ion he wo XD se ies di e e iden ly om he o he s wi h s ill dis inc ly highe equency con en a 0.1–0.3 cpa (Figu e 1).Basedon hese esul s hecommon spec al con en o hese da a is concen a ed p incipally on he ela i ely na ow equency anges om 0.005 cpa o 0.5 cpa; ha is, pe iodici ies a e om 200 o 2 yea s. Nex , he six l- ime se ies we e low-pass il e ed, no mal- ized, and hen a e aged (c.i. a ound he mean in Figu e 2(a), in 1006–1996, since six yea s a e los a bo h ends due o il e ing). Co ela ions be ween hese l- se ies a e all posi i e, anging om 0.81 (FRW-FHI) o 0.21 (FHI-RRW) wi h a mean alue o 0.52. Co ela ion declines in he h ee RW se ies wi h inc easing dis ance; he 𝑟- alue ( om wes o eas ) is 0.55 be ween SRW and FRW, 0.34 be ween SRW and RRW, and 0.49 be ween FRW and RRW. The wo densi y se ies (SXD and FXD) ha e high linea associa ion (𝑟 = 0.66). Howe e hei co ela ion is lowe han ha be ween ei he he wo wes e n o cen al RW and XD se ies (SRW-SXD, 𝑟 = 0.73 and FRW-FXD, 𝑟 = 0.77). The mean egional l- ch onology (Figu e 2(a))shows an o e all inc easing end ( eg ession o g ow h on ime in 1006–1996; 𝑦 = 0.0006𝑥), e lec ing he di e se long- e m a es o change in he o iginal se ies. P oducing a dis ibu ion o he mean alues and hen loca ing he lowe and uppe bounds o his dis ibu ion, i e signi ican (95% c.i.) pe iods o posi i e g ow h in he a e age se ies a e disce ned: 1083–1104, 1159–1178, 1428–1436, 1750–1769, and he longes om 1918 o 2002, sepa a ed by pe iods o poo g ow h o a ying leng hs and magni udes be ween hem. These pe iods a e de e mined in he egional g ow h signal wi hin he unce ain y limi ed by (sou ces o e o ) in e egional di e ences (e.g., wes e n, cen al, and eas e n p o enance) as well as di e ences due o p oxy ype (RW, XD. and HI). The highes alues in he second millennium a e clea ly eco ded in he las cen u y (Figu e 2(a)). The boo s apped con idence in e als a e nonsymme ic and pa icula ly wide in he i s and las cen u ies. The six m- ( il e ed) se ies a e mo e synch onous han he l- se ies as hei a e age has na owe c.i. and many mo e signi ican pe iods (Figu es 2(a) and 2(b)) in addi ion o ha ing a highe mean co ela ion (𝑟 = 0.58). Co ela ion is hehighes be weenFRWandFXD(𝑟 = 0.74)aswellas be ween FRW and FHI (𝑟 = 0.74) and he lowes be ween SXD and FHI (𝑟 = 0.39) as well as be ween SXD and RRW (𝑟 = 0.39). Twel e dis inc and signi ican (95% c.i.) pe iods o abo e a e age g ow h a e da ed (Figu e 1(b)): 1083–1101, 1157–1183, 1283–1289, 1411–1447, 1489–1498, 1535–1547, 1559– 1572, 1625–1634, 1653–1665, 1750–1767, 1850–1862, and he longes in 1920–1956. The con idence limi s indica e wide sp ead in he o iginal six se ies in he 13 h and 14 h cen u ies han in he es o he m- se ies. The a e age o he six h- (no il e ing) se ies ep esen s he h- a iabili y in his wo k (Figu e 2(c)). A e age co - ela ion be ween all he six se ies is 0.41. I is he highes be ween SRW and FRW (𝑟 = 0.68) and he lowes be ween SXD and FHI (𝑟 = 0.22). In he mean se ies g ow h was he lowes in 1601 (−2.6 s.d. uni s below he mean) and he highes in1826(2.4s.d.uni sabo e hemean).Theg ea es biennial shi s (di e ence be ween any wo consecu i e yea s) occu ed be ween 1600 and 1601 (3.8 s.d. om 1.2 o −2.6) as well as be ween 1640 and 1641 (3.8 s.d. om 1.8 o −2.0). In he 20 h cen u y, 1903 was unusually low and 1937 was high in he g ow h index. I is wo h no icing ha e en his h- se ies has e iden decadal luc ua ions. 4Jou nal o Clima ology 60 40 20 0 0 250 111 67 0.95 c.l. 0.1 0.2 F equency (y −1) Spec al powe densi y (𝜔) (a) 20 10 111 67 0.95 c.l. 500 0.1 0.2 F equency (y −1) Spec al powe densi y (𝜔) 0 0 (b) 40 20 0.95 c.l. 200–250 83 0.1 0.2 Spec al powe densi y (𝜔) F equency (y −1) 0 0 (c) 120 80 40 0.95 c.l. 200 0.1 0.2 F equency (y −1) Spec al powe densi y (𝜔) 0 0 (d) 30 20 10 0.95 c.l. 200 83–125 33 0.1 0.2 F equency (y −1) Spec al powe densi y (𝜔) 0 0 (e) 30 15 45 0.95 c.l. 200 100 0.1 0.2 F equency (y −1) Spec al powe densi y (𝜔) 0 0 ( ) Figu e 1: The Fou ie spec a o he six g ow h-based ch onologies (RCS indexing) o Sco s pine. Smoo h lines a e 0.95 con idence le els, calcula ed o ed noise wi h AR(1) coe icien s 𝛼:(a)SRW(𝛼 = 0.7), (b) SXD (𝛼 = 0.20), (c) FRW (𝛼 = 0.77), (d) FHI (𝛼 = 0.75), (e) FXD (𝛼 = 0.43), and ( ) RRW (𝛼 = 0.69). Cpa is cycles pe annum. 1000 1200 1400 1600 1800 2000 0 1 2 3 −2 −1 (a) 1000 1200 1400 1600 1800 2000 0 1 2 3 −2 −1 (b) 1000 1200 1400 1600 1800 2000 −4 −2 0 2 4 (c) Figu e 2: C.i. o he mean l- se ies (RCS, low-pass il e ing; (a)), o he m- se ies (low-pass il e ing o he six 180-yea spline indexed se ies; (b)) and he a e age o h- se ies (30-yea splines, wi hou low-pass il e ing; (c)). Jou nal o Clima ology 5 −2 0 To nedalen 2 1910 1930 1950 1970 1990 (a) −2 0 2 Ka asjok 1910 1930 1950 1970 1990 (b) −2 0 2 Ka esuando 1910 1930 1950 1970 1990 (c) −2 0 2 Sodankylä 1910 1930 1950 1970 1990 (d) −2 0 2 A e age 1910 1930 1950 1970 1990 (e) Figu e 3: Mean June–Augus empe a u es o he ou eco ds and hei a e age (z-sco es in 1908–2002). 3.2. Indi idual P oxies e sus July and June–Augus Tem- pe a u es. Ou clima ic a ge s a e a i hme ic a e ages o no malized mon hly da a. July empe a u es a e i s modeled using indi idual p oxies and hen June–Augus empe a u es using indi iduals as well as hei a ious combina ions. The s eng h o a ge ed egional signal is indica ed by co e- la ion o June–Augus mean empe a u es among he ou s a ions (Figu e 3), which a y be ween 0.88 (To nedalen- Ka asjok) and 0.94 (Ka esuando-Sodankyl¨ a), while he mean co ela ionis0.92.ThisJune–Augus meanhase enhighe co ela ion (𝑟 = 0.96,𝑟2= 0.93)wi h heJune–Augus mean o he Bo en iken egional empe a u e eco d exclusi ely om no he n Sweden [28], used in calib a ions in some p e- ious s udies [5,21]. All ou eco ds show, o example, cool condi ions in he ea ly 20 h cen u y un il a ound 1915, he ela i e wa m h o he 1930s, and a ecen wa ming since he la e 1980s. Summe empe a u e (June–Augus , no malized scale) a ies be ween −1.32and1.88,whichhe e o m he limi s o in e pola ion (Figu e 3). The mean empe a u e has a modes posi i e end (𝑦 = −0.07+0.0014𝑥)in1908–2002. When he six l- p oxies we e indi idually eg essed on mean July empe a u e (Table 1(A)), only FXD and RRW p oduced posi i e e i ica ion s a is ics. Al hough SXD has posi i e RE alues in bo h pe iods, he CEs a e ma ginally nega i e. Among he m- se ies (Table 1(B)), bo h o he wes e n se ies (SRW and SXD) clea ly pass he e i ica ion es s, while FRW and FHI do no . FXD and RRW se ies ha e imp o ed (highe han in l- ) posi i e RE and CE alues. In he highe equencies (Table 1(C)), in addi ion o all h ee RW se ies, also FHI passes bo h es s in bo h pe iods. Howe e ,bo hSXDandFXD alljus belowze o(−0.02) using he mo e sea ching CE s a is ic in he LC-EV pe iod. The same p oxies we e hen calib a ed agains mean June–Augus empe a u e. In he l- ange (Table 2(A)), SXD, FXD,andRRWpass he es s.NowSXDp oduces hehighes RE and CE alues in bo h pe iods. In he medium equencies (as p e iously in he case o July, Table 1(B)), he ou se ies (SRW, SXD, FXD, and RRW) show posi i e e i ica ion pe o mance. FRW and FHI again ha e nega i e RE and CE alues in he LC-EV pe iod. In he highe equencies (Table 2(C)), all six se ies pass he es s. The h ee RW se ies ha e gene ally lowe explained a iance (𝑟2≤0.21)aswellas lowe REandCE alues(≥0.18) han he wo o he ypes o p oxies (XD and HI), each o which has 𝑟2≥ 0.31 and bo h RE and CE ≥0.28. 3.3. June–Augus Tempe a u e Signal in l- , m- , and h- A e ages. All six se ies ( hei l- , m- , and h- a ian s) we ea e aged oasimplemean(AA)and oaweigh ed mean (WA) and es ed as combined p edic o s o June– Augus empe a u e (Table 3(A)–(C)). Simple mean (AA) p oduced posi i e e i ica ion esul s (bo h RE and CE du ing bo h pe iods) only in he highe equencies (Table 3(B), Figu e 2(c)). The ailu e o l- and m- models he e as well as in p e ious compa isons (Tables 1and 2)isdue oexcess g ow h a iabili y as compa ed o empe a u e in he LC- EV pe iod, which is mos p onounced in FRW and FHI. Howe e , he es alues o AAa eonlysligh lyweake han o WA. WA also had posi i e esul s in he lowe mos equencies (Table 3(A)). In he medium equencies, nei- he me hod (AA o WA) esul ed in an accep able model (Table 3(B)). In he nex s ep only hose se ies which indi idually passed RE and CE es s (in bo h ans e models o June– Augus empe a u es, Table 2) we e weigh ed and combined, namely, he h ee l- se ies (3RCS; 0.56 ∗SXD + 0.44 ∗FXD +0.14∗RRW) and ou m- se ies (4Spline; 0.22 ∗SRW + 0.54 ∗SXD + 0.41 ∗FXD + 0.16 ∗RRW). When hese we e calib a ed agains June–Augus empe a u e, bo h o hem passed he e i ica ion es s (Table 3(C)). I should be no ed 6Jou nal o Clima ology Table 1: Six p oxies e sus mean July empe a u es (a e age o he ou eco ds, no il e ing) in 1908–2002. Reduc ion o e o (RE), coe icien o e iciency (CE), and 𝑟2du ing EC-LV (ea ly calib a ion in 1908–1955 and la e e i ica ion in 1955–2002) and LC-EV (la e calib a ion in 1955–2002 and ea ly e i ica ion in 1908–1955). Only es esul s wi h RE and CE >0 a e included. EC-LV LC-EV RE CE 𝑟2RE CE 𝑟2 (A) RCS indexing FXD 0.29 0.21 0.35 0.10 0.02 0.14 RRW 0.25 0.17 0.19 0.21 0.14 0.16 (B) 180-yea spline indexing SRW 0.30 0.22 0.29 0.24 0.18 0.32 SXD 0.26 0.18 0.25 0.15 0.08 0.12 FXD 0.35 0.28 0.36 0.14 0.07 0.15 RRW 0.27 0.19 0.21 0.23 0.17 0.18 (C) 30-yea spline indexing SRW 0.27 0.19 0.30 0.4 0.34 0.43 FRW 0.29 0.21 0.39 0.13 0.05 0.24 FHI 0.52 0.47 0.57 0.23 0.17 0.23 RRW 0.18 0.09 0.25 0.27 0.20 0.33 Table 2: Six p oxies e sus mean June–Augus empe a u es in 1908–2002 (no il e ing). RE, CE, and 𝑟2du ing EC-LV (1908–1955 and 1955– 2002) and LC-EV (1955–2002 and 1908–1955). Only es esul s wi h RE and CE >0 a e included. EC-LV LC-EV RE CE 𝑟2RE CE 𝑟2 (A) RCS indexing SXD 0.53 0.53 0.56 0.53 0.53 0.56 FXD 0.43 0.42 0.44 0.42 0.42 0.44 RRW 0.1 0.1 0.11 0.15 0.15 0.17 (B) 180-yea spline indexing SRW 0.17 0.17 0.21 0.07 0.07 0.28 SXD 0.47 0.47 0.54 0.45 0.45 0.57 FXD 0.35 0.35 0.44 0.27 0.26 0.43 RRW 0.12 0.12 0.13 0.15 0.15 0.18 (C) 30-yea spline indexing SRW 0.18 0.17 0.21 0.14 0.13 0.20 SXD 0.49 0.49 0.50 0.41 0.41 0.42 FRW 0.14 0.14 0.16 0.11 0.10 0.15 FHI 0.46 0.46 0.48 0.28 0.28 0.31 FXD 0.39 0.39 0.40 0.37 0.37 0.38 RRW 0.16 0.16 0.17 0.14 0.14 0.15 ha since sample eplica ion is a leas i e in 1000–2002 in each o he six se ies i is hus >15 in 3RCS model, >20 in 4Spline model, >10 in he XD models, and >30 in models whe e all six se ies we e included. Because o he pe sis ence in he ime se ies o ee g ow h heya eusually il e ed oenhance hesignal obeanalyzed. I is o en ecommendable o also econs uc l- and h- a ia ions sepa a ely smoo hing he p oxy and ins umen al se ies p io o calib a ion [3,52]. In o de o u he s udy he co espondence be ween hese wo mean se ies (3RCS and 4Spline) and he a ge abo e decadal scales, he l- and m- p oxies as well as he June–Augus empe a u e we e low- pass il e ed (10-yea smoo hing; see [38–40]) and hen es ed again (using co espondingly sho e 42-yea calib a ion and e i ica ionpe iodsin1914–1996due o il e ing).The e i ica ions o hese models p oduced posi i e esul s o bo h;howe e ,he e hel- modelwassupe io o hem- model. The ou success ul mul ip oxy WA model combina ions o June–Augus empe a u e (Table 3)we e ecalib a ed using he ull 95-yea calib a ion pe iod (Figu e 4). The mean o all six RCS-indexed se ies (wi h he highes weigh onSXDand helowes onFRWandRRW)p oduceda sligh ly in e io model as compa ed o he 3RCS se ies (𝑅2= 0.57–0.59,3RCSinFigu e 4(c)). In he m- scale he only success ul combina ion (4Spline, Figu e 4(b))has Jou nal o Clima ology 7 Table 3: Simple mean (AA) and weigh ed mean (WA) o all six se ies e sus mean June–Augus empe a u es (no il e ing). The WA o RCS- based (A) and 30-yea spline indexed se ies (B) (see also Figu e 4(a)). Only es esul s wi h RE and CE >0 a e included. The WAs o hose h ee RCS-indexed se ies (3RCS; 0.56 ∗SXD + 0.44 ∗FXD + 0.14 ∗RRW) and ou 180-yea spline indexed se ies (4Spline; 0.22 ∗SRW + 0.54 ∗SXD + 0.41 ∗FXD + 0.16 ∗RRW) which indi idually passed RE and CE es s (see Table 2) e sus mean June–Augus empe a u es (C; he ull models shown in Figu es 4(b) and 4(c)). EC-LV LC-EV RE CE 𝑟2RE CE 𝑟2 (A) RCS WA 0.55 0.55 0.67 0.21 0.21 0.53 (B) 30-yea spline indexed AA 0.56 0.56 0.57 0.50 0.50 0.51 WA 0.65 0.65 0.65 0.58 0.57 0.58 (C) WAs o selec ed h ee RCS and ou 180-yea spline indexed se ies 3RCS 0.58 0.58 0.61 0.53 0.52 0.58 4Spline 0.46 0.46 0.60 0.28 0.28 0.60 in e media e alues be ween l- and h- scales. The WA o all six h- se ies (30-yea spline indexed, Figu e 4(a))shows he bes i wi h he a ge (𝑅2= 0.62). He e he modeled andobse ed aluesha epa icula lysynch onous(one-o wo-yea ) peaks in, o example, 1923, 1928–1929, 1949, 1962, and 1979–1980 (Figu e 4(c)). The l- model ep oduces, o example, he longe inc easing end om 1908 o 1937 as well as ha o he las i een yea s mo e consis en ly han he h- se ies (Figu es 4(a)–4(c)). Howe e , he ep oduc ion o he win peaks in 1969–1974 is no iceably poo e . The wo densi y se ies (SXD and FXD) we e u he combined (WA) in bo h he l- and m- anges and calib a ed agains longe wa m season pe iods (Table 4). Th ee di e en pe iods we e used, ou mon hs mean empe a u e om May oAugus (A), i emon hsmean omAp il oAugus (B), and six mon hs mean om Ap il o Sep embe (C). All hese six p oxy combina ions (bo h l- and m- ) pass he e i ica ion es s (RE and CE in bo h pe iods: EC-LV andLC-EV) o all h ee empe a u epe iods.Model i (𝑅2) ecalib a ed using all a ailable da a a ies om 0.48 o 0.58.Theweigh sinWAa e a he equal o SXDandFXD, anging om 0.51 o 0.34, bu sligh ly a o ing SXD. The bes empi icalmodels( o May–Augus empe a u es,Table 4) o he l- and m- bandwid hs o he wo XD-se ies we e de i ed by ecalib a ion in 1908–2002 wi h 𝑅2= 0.58 o hel- and 𝑅2= 0.53 o he m- model. 3.4. Building a P oxy o Subcen u y Scale Tempe a u e Va i- abili y. Acomposi em- summe empe a u ep oxywas p oduced using he 4Spline a ian (WA o SRW, SXD, FXD, and RRW) (Figu e 5(a), calib a ion in Table 3(C) and Figu e 4(b)). Se e al signi ican (abo e 0.99 c.l.) mul idecadal cha ac e is ics om pe iods o 33 and 67 yea s up o a peak exceeding a cen u y (111 yea s) a e highly signi ican in he Fou ie spec um (Figu e 5(c)).Thewa ele spec umshows ha he luc ua ions sp eading o e hese bandwid hs a e pa icula ly appa en in he 12 h and 17 h cen u ies. On he o he hand he e is a no iceable lack o signi ican ea u es esiding in he decadal o bidecadal anges (Figu es 5(b) and 5(c)). In his mul idecadal scale he 20 h cen u y does no s and ou as unusual in he pas millennium. In o de o assess he co espondence o ampli ude, du a- ion, and iming o ecen cycles be ween Fennoscandia and he No h A lan ic he m- p oxy (4Spline based) and AMO we e also isually compa ed (Figu e 6). Co ela ion be ween he wo se ies (in 1866–1992) is 0.27, ising o 0.49 using 10- yea mo ing a e ages (MA, Figu e 6(a)) and o 0.56 using 20- yea MA. P esuming Fennoscandian p oxy a iabili y is p e- ceding he AMO cycle (e iden in Figu e 6(a))andco ec ing o ( emo ing) his 10-yea ime shi he co ela ion ises o 0.34, 0.73, and 0.82, espec i ely. The 20-yea MA e ec i ely emo es all highe equencies and he ela ionship seems in ag eemen pa icula ly du ing ea ly o mid-20 h cen u y. This illus a es ha mul idecadal a iabili y in Fennoscandian and No h A lan ic clima es is closely simila in scale and leng h. To assess he po en ial o hese da a in modelling he AMO (e.g., ime s abili y o such s a is ical ela ionship), all sixm- p oxieswe ealsocompa ed oannualSSTanomalies. Sc eening he pool o candida e p edic o s i was also possible o build a ans e model o he AMO. The WA o h ee se ies (SRW, FXD, and RRW) was used wi h he same calib a ion (1922–1990) as well as e i ica ion (1856–1921) pe iods as in G ay e al. [14]. This model passed he e i ica ion ials (RE = 0.05 and CE = 0.05), bu model pe o mance is he lowes (𝑅2= 0.17)in hiswo k. 4. Discussion Fi e o he six se ies om di e en pa s o no he n Fennoscandia show e idence o a dominan 200–250 yea s o pe iodici y. Simila pe iodici y was ound signi ican in a ha monic decomposi ion o he a e age o six cen al Eu opean ins umen al as well as s alagmi e p oxy se ies om heAus ianAlpsin500–1935[53]. Howe e , he p onounced minimum du ing ecen cen u ies appea s in ou p oxies somewha la e (in he ea ly 20 h cen u y) as compa ed o he 1880s no ed by L¨ udecke e al. [53]. P e iously Helama e 8Jou nal o Clima ology 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000 0 1 2 −1 (a) High- equency model; all six 𝑅2=0.62 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000 0 1 2 −1 (b) Medium- equency model; 4Spline 𝑅2=0.56 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000 0 1 2 −1 (c) Low- equency model; 3RCS 𝑅2=0.59(all six model 𝑅2= 0.57) Figu e 4: Final linea eg ession models on June–Augus mean as a ge (do ed line) wi h a ious combina ions o p oxies ecalib a ed in 1908–2002 (solid line): (a) WA o all six h- (30-yea spline indexed) se ies, (b) WA o SRW, SXD, FXD, and RRW ( ou 180-yea spline indexed, 4Spline) m- se ies, and (c) WA o he SXD, FXD, and RRW (3RCS se ies). Table 4: Weigh ed a e ages o he Swedish and Finnish densi y se ies (SXD and FXD) buil using wo ypes o indexing (RCS and 180-yea splines, Sp) e sus a ou -mon h mean empe a u e (no il e ing) om May o Augus (A), a i e-mon h mean om Ap il o Augus (B), and a six-mon h mean om Ap il o Sep embe (C). Only es esul s wi h RE and CE >0 a e included. EC-LV LC-EV RE CE 𝑟2RE CE 𝑟2 RCS A 0.55 0.54 0.56 0.55 0.55 0.57 Sp A 0.33 0.33 0.55 0.29 0.28 0.58 RCS B 0.49 0.48 0.50 0.49 0.48 0.51 Sp B 0.26 0.25 0.47 0.25 0.25 0.50 RCS C 0.44 0.43 0.45 0.53 0.52 0.53 Sp C 0.24 0.24 0.41 0.32 0.32 0.52 Weigh s used in a e aging: 0.51 ∗SXD + 0.47 ∗FXD (RCS A); 0.47 ∗SXD + 0.42 ∗FXD (SP A); 0.47 ∗SXD + 0.41 ∗FXD (RCS B); 0.42 ∗SXD + 0.35 ∗ FXD (Sp B); 0.46 ∗SXD + 0.39 ∗FXD (RCS C); 0.41 ∗SXD + 0.34 ∗FXD (Sp C). al. [54] discussed cen ennial and mul idecadal empe a u e a iabili y o e No he n Fennoscandia ha bea s a po en ial link o oceanic o igins [8,55] and e iewed he paleoclima ic li e a u e ele an o he opic. Se e al indi idual Fennoscandian ee g ow h-based p oxies ha e indica ed p ominen spec al ea u es a abou 23, 30, and 90 yea s, 23–33 yea s, and 30.8–31.8 and 80.3–87.7 yea s in Finland [11,25,56] as well as ela i ely ime-s able peaks a 32–33 yea s and a ∼55–100 yea s in Sweden [10]. In an analysis o se en no he n hemisphe e empe a u e econs uc ions (including, e.g., [15,57–59]) Ogu so e al. [60] epo ed ha hey ha e an unambiguous 60–80-yea mul idecadal a iabili y in common (AD 1000–1930), which is close o he ange o a 67-yea cycle indica ed by ou da a. The 4Spline econs uc ion wi hou he mo e o less disc epan secula cha ac e is ics (see [17]) clea ly eco ds a bimodal s uc u e—c.a. 110-yea and 60–70-yea a ia ions— as well as a 33-yea clima ic cycle (simila o he B uckne cycle). Based on hese e idence he e exis s ob ious po en ial o analyses in subcen u y scales and a eal possibili y o gain insigh in o he ex en o gene al na u al a iabili y in he suba c ic egion. In he lowe equencies o hese da a (low-pass il e ing o he RCS and 180-yea spline indexed se ies) se e al g ow h su ges and oughs coincide in each g oup and hey we e also da ed in he a e ages in he ime domain (s a is ically signi ican luc ua ions; i einl- and12inm- ange).The la es , 37-yea pe iod (1920–1956) is he longes con inuous mul idecadal scale su ge and he 85-yea pe iod (1918–2002) is he longes l- su ge. The combined m- ch onology is e iden ly mo e consis en han he l- ch onology as he mo e di e ging l- ends a e le ou . O e all signal s eng h (mea- su ed as mean co ela ion) be ween he six se ies is highe in m- (𝑟 = 0.58) hanei he inl- (𝑟 = 0.52) o in h- se ies (𝑟 = 0.41).A leas pa o hel- disag eemen ispossiblydue o he (noisy) RCS me hod, which is usually ecommended o la geda ase so a iousageclasseso ees o each yea , ideally g own unde a ange o ep esen a i e ecological condi ions [10,21,61–64]. E en he ample da a bases o SRW and FRW may no ully mee hese equi emen s. Jou nal o Clima ology 9 1000 1200 1400 1600 1800 2000 Yea s Index 4 3 2 1 0 −1 −2 −3 (a) 1000 1200 1400 1600 1800 2000 296,3 195,5 129 85,1 56,1 37 24,4 16,1 10,6 7 4,6 Time scale (yea ) Yea s 6,500 6,000 5,000 5,500 4,500 4,000 3,500 3,000 2,500 2,000 1,500 1,000 0,500 0,000 (b) 20 15 10 5 0 0 0,05 0,10 0,15 0,20 F equency 𝜔(y −1) 67 y 33 y 111 y 0.999 c.l. 0.99 c.l. Spec al powe densi y (c) Figu e 5: The m- p oxy o summe empe a u es since AD 1000 ((a), un il e ed). Wa ele spec um (b) and Fou ie spec um (c) o his ime se ies. 1860 1880 1900 1920 1940 1960 1980 2000 −1.5 −0.5 0.5 10-yea unning means (a) 1860 1880 1900 1920 1940 1960 1980 2000 −1.5 −0.5 0.5 20-yea unning means (b) Figu e 6: Compa ison o annual AMO cycle (dash) and he Fennoscandian mul idecadal (m- ) summe empe a u e p oxy (solid) du ing common pe iod using 10-yea (a) and 20-yea (b) smoo hing. The ou ins umen al empe a u e eco ds used in cal- ib a ions show ema kable ag eemen jus i ying hei a e - aging o a egional mean. July is usually one o he mos impo an ac o s among mon hly empe a u es ela ed o a ious g ow h pa ame e s om di e en pa s o he egion [12,21,23,24,54]. When he six p oxies we e indi idually eg essedonmeanJuly empe a u e,onlyFXDandRRW passed he e i ica ion ials in he l- ange, SRW and SXD in he m- ange, and all bu he wo XD se ies in he h- ange. The g ow h esponse o June–Augus empe a u es has o enbeen ound imes ableand hispe iodhas ecen lybeen used in empe a u e econs uc ions in he egion [2–5,17]. A simple mean o all six p oxy se ies (AA) wo ks as a e i iable p edic o o mean June–Augus empe a u e only in he h- ange (30-yea spline indexing, Figu e 2(c))in heseda a. Al houghallse iespass he es s, heSXD,FHI,andFXDha e supe io indi idual calib a ion and e i ica ion pe o mance in his con ex . This is consis en wi h he esul s ob ained