Abrupt temperature changes during the last 1500 ...

Abrupt temperature changes during the last 1,500 years

István Matyasovszky & Fredrik Charpentier Ljungqvist

Theoretical and Applied Climatology ISSN 0177-798X Volume 112 Combined 1-2 Theor Appl Climatol (2013) 112:215-225 DOI 10.1007/s00704-012-0725-8

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Author's personal copy Theor Appl Climatol (2013) 112:215–225 DOI 10.1007/s00704-012-0725-8

ORIGINAL PAPER

Abrupt temperature changes during the last 1,500 years István Matyasovszky & Fredrik Charpentier Ljungqvist

Received: 22 February 2012 / Accepted: 9 July 2012 / Published online: 31 July 2012 # Springer-Verlag 2012

Abstract We investigate the occurrence of abrupt changes in a total of 35 different proxy records from the extra-tropical Northern Hemisphere for the last ~1,500 years. The proxy records include ice-core δ18O, speleothem, tree ring width/density, marine sediment and lake sediment records with annual, sub-decadal or decadal resolutions. The aim is to explore the spatio–temporal distribution of abrupt climate changes using a kink point analysis technique. A clustering of warm kink points (the kink points with the highest temperatures) around AD 1000 appears corresponding to the Medieval Warm Period and indicates a geographically widespread temperature peak at that time. Kink points around AD 1000 are somewhat more numerous on higher latitudes than on lower latitudes. There are some tendencies for the coldest kink points (the kink points with the lowest temperatures) to be clustered in the ninetenth century, but they are generally more unevenly spaced in time than the warm peaks around AD 1000. The relative lack of kink points detected during the 1500 s–1700 s, likely the coldest part of the Little Ice Age, implies that this cold period was relatively stable and without abrupt events. A possible cluster of kink points on lower latitudes in the early ninth century is also found. No clear difference in the timing of kink points between the different proxy types can be observed.

I. Matyasovszky (*) Department of Meteorology, Eötvös Loránd University, Pázmány Péter sétány 1/A, Budapest 1117, Hungary e-mail: [email protected] F. C. Ljungqvist Department of History, Stockholm University, 106 91 Stockholm, Sweden e-mail: [email protected]

1 Introduction The general overall evolution of the large-scale climate changes during the last one to two millennia is rather well known. A warmer climate regime persisted c. AD 800–1300 and a colder climate regime persisted c. AD 1300–1900. The earlier warm period is usually referred to as the Medieval Warm Period (MWP) or Medieval Climate Anomaly (Bradley et al. 2003; Broecker 2001; Diaz et al. 2011; Esper and Frank 2009; Goosse et al. 2012; Klimenko 2001; Ljungqvist et al. 2012), whereas the later colder period is referred to as the Little Ice Age (LIA) (Grove 1988; Lamb 1977; Matthews and Briffa 2005; Wanner et al. 2008). Making use of proxy data sensitive to temperature variations—such as fossil pollen, δ18O ice-cores, lake and marine sediments, speleothems and tree ring width and density— extensive efforts have been made since the late 1990s to reconstruct global or, more often, Northern Hemispheric temperatures for the past 1,000 to 2,000 years in order to place the amplitude of the modern warming in a long-term perspective (e.g. Ammann and Wahl 2007; Briffa 2000; Christiansen and Ljungqvist 2011, 2012; Cook et al. 2004; Crowley and Lowery 2000; D’Arrigo et al. 2006; Esper et al. 2002; Hegerl et al. 2007; Jones et al. 1998; Juckes et al. 2007; Ljungqvist 2010; Ljungqvist et al. 2012; Loehle 2007; Mann et al. 1999, 2008, 2009; Moberg et al. 2005; Osborn and Briffa 2006). Less focus has been placed on the question of abrupt trend breaks in the temperature history of the last one to two millennia despite the fact that the occurrence of such abrupt trend breaks can be of key importance for understanding the relative role of natural climate variability and anthropogenic forcing in the ongoing global warming. One reason for the lack of such studies can probably be attributed to the fact that the field of palaeoclimatology has in the last decade to large extent moved from traditional descriptive climatology to physical climatology, focusing on questions

Author's personal copy 216

concerning the dynamics of the climate changes. To a certain extent, this change of focus has come at the expensive of the descriptive palaeoclimatology that is still needed in order to increase our knowledge of how the climate actually was during different periods of the past. In this article, we will employ the novel kink point analysis technique presented by Matyasovszky (2011) for detecting significant abrupt temperature changes during the last ~1,500 years in 35 individual proxy records. Matyasovszky (2011) demonstrated that a kink point analysis can be a very useful tool for detecting abrupt changes in the instrumental temperature record and he also applied it on a multi-proxy temperature reconstruction with promising result. By detecting the significant abrupt temperature changes in individual proxy records, we hope to: (1) investigate if the twentieth century climate shift (e.g. warming) is the most abrupt trend break in the last ~1,500 years, (2) see if the MWP and the LIA can be better constrained in time, (3) assess the spatio–temporal pattern and the timing of abrupt temperature changes and (4) see if the timing of abrupt temperature changes differs between different kinds of proxy records.

2 Data The peer-reviewed literature was systematically searched for proxy records spanning the last ~1,500 years and considered by their authors to be primarily a quantitative measure of local and/or regional temperature variability. Only records with decadal or higher resolution were considered. The data were obtained digitally either from public databases or, in a few cases, by direct request from their authors. The criteria that all proxy records must extend back to the sixth century excludes many potentially useful records but guarantee that trend breaks in the beginning of the MWP are not missed. A total of 35 different proxy records from around the Northern Hemisphere used in the present study are listed in Table 1 with information about (1) name of the record, (2) longitude and latitude, (3) type of proxy, (4) seasonality of signal and (5) reference to the original publication. Geographical distribution of these records can be seen in Fig. 1. For more detailed information about a specific data set, the reader is referred to the references given. In cases where different versions of the same proxy record have been published, reference is consistently given to the latest publication. Our proxy collection includes eight high-latitude ice-core δ18O records originating from Greenland and the Canadian Arctic Archipelago and two mid-latitude ice-core δ18O records originating from the Tibetan Plateau. The Agassiz Ice Cap record (Vinther et al. 2008) on Ellesmere Island has

I. Matyasovszky, F.C. Ljungqvist

annual sampling but in reality possesses sub-decadal resolution and is interpreted to reflect annual mean temperature. The Devon Ice Cap record (Fisher et al. 1983) on eastern Devon Island and the Prince of Wales Ice Cap record (Kinnard et al. 2011) on Ellesmere Island have subdecadal resolution and are, like Agassiz Ice Cap, interpreted to reflect the annual mean temperature. The NorthGRIP record (NGRIP members 2004) from the north–central part of the Greenland inland ice sheet has annual resolution and reflects the annual mean temperature with a possible bias towards winter temperature. Both the GRIP and the Crête records (Vinther et al. 2010) originate from the summit of the Greenland inland ice sheet and are seasonally resolved winter (November to April) δ18O records, thus reflecting changes in cold season temperature. The Dye-3 record (Vinther et al. 2010) is similar to GRIP and Crête but is drilled further south on the Greenland inland ice. The Renland δ18O record (Vinther et al. 2008) is drilled in a coastal glacier on the east coast of Greenland that is not part of the inland ice sheet and reflects the annual mean temperature primarily over the sea outside east Greenland. The Dunde and Guliya records (Thompson et al. 2006) from the Tibetan Plateau have been interpreted as temperature records but probably do not contain a pure temperature signal due to, among other things, changes in the seasonality of the precipitation in monsoon climates. Our proxy collection includes four high-latitude tree ring width records from locations close to the Arctic latitudinal tree line and four mid-latitude tree ring width records from locations close to the altitudinal tree line. The Avam–Taimyr record (Briffa et al. 2008) is a regional composite from larch (Larix gmelinii Rupr.) of the Taimyr tree ring width chronology (Naurzbaev et al. 2002) and the Bol’shoi Avam tree ring width chronology (Sidorova et al. 2007) from the northernmost forest in the world on the Taimyr Peninsula in northern Siberia. Due to the extremely short growing season in this area, the record primarily reflects July temperatures. The Indigirka record (Moberg et al. 2006) is based on larch (L. gmelinii Rupr.) from the tree line area of the Indigirka River Valley in north-eastern Siberia. The Finnish Lapland record (Helama et al. 2010) derives from living and subfossil wood of Scots pine (Pinus sylvestris L.) trees from the northern tree line in Finland and reflects the mean summer temperature. The Yamal record (Briffa 2000) is derived from remains of subfossil and living Siberian larch (Larix sibirica) trees from the Yamal Peninsula in northwestern Siberia and reflects the mean June and July temperatures. The regional composite tree ring width chronology from the Alps of Central Europe (Büntgen et al. 2011) reflects the mean summer temperature near the altitudinal tree line in the Alps. The Solongotyn Davaa record (D’Arrigo et al. 2001) from Mongolia consists of Siberian pine (Pinus sibirica)

Author's personal copy Abrupt temperature changes during the last 1,500 years

217

Table 1 List of proxy records used in the study #

Site

Longitude Latitude Proxy type

1 2 3

Lower Murray Lake −69.32 Agassiz Ice Cap −73.10 Prince of Wales Ice Cap –80.40

81.21 80.70 78.40

4

Devon Ice Cap

–82.50

75.33

5 6 7 8 9 10 11 12

NorthGRIP GRIP Renland Crête Indigirka Avam-Taimyr Finnish Lapland Torneträsk

–42.32 –37.38 –26.70 –37.32 148.15 93.00 25.00 19.80

13 Vøring Plateau

Resolution

Season Reference

Correlation

July Cook et al. (2009) Annual Vinther et al. (2008) Annual Kinnard et al. (2011)

0.78 0.13a –

Annual Fisher et al. (1983)

0.58a

75.10 72.35 71.30 71.12 70.53 70.00 69.00 68.31

Laminated lake sediment Annual Annual Ice-core δ18O Ice-core δ18O Subdecadal SubIce-core δ18O decadal Ice-core δ18O Annual Ice-core δ18O Annual Ice-core δ18O Annual Ice-core δ18O Annual Tree ring width Annual Tree ring width Annual Tree ring width Annual Tree ring density Annual

Annual N–A Annual N–A JJA July JJA A–A

NGRIP members (2004) Vinther et al. (2010) Vinther et al. (2008) Vinther et al. (2010) Moberg et al. (2006) Briffa et al. (2008) Helama et al. (2010) Grudd (2008)

0.15a 0.53 0.39a 0.45 0.31a 0.36 0.64 0.79

7.64

66.97

Marine sediment

A

Berner et al. (2011)

0.31a

14 Yamal 15 North Iceland Shelf

69.17 –19.30

66.92 66.30

JJ JJA

Briffa (2000) Sicre et al. (2011)

0.56 –

16 Dye-3 17 Haukadalsvatn

–43.49 –21.37

65.11 65.03

N–A AM

Vinther et al. (2010) Geirsdóttir et al. (2009)

0.57 –

18 Storegga Slide 19 Hallet Lake

5.26 146.20

63.76 61.50

JJA JJA

Sejrup et al. (2011) McKay et al. (2008)

0.24a 0.41a

20 Iceberg Lake 21 Gardar Drift

–142.95 –21.97

60.78 57.45

MJ JJA

Loso (2009) Sicre et al. (2011)

0.23 –

22 23 24 25

Russian Plains Teletskoe Lake Sol Dav Spannagel Cave

45.00 87.61 98.93 11.40

55.00 51.76 48.30 47.05

Annual Annual A–O Annual

Sleptsov and Klimenko (2003) Kalugin et al. (2009) D’Arrigo et al. (2001) Mangini et al. (2005)

0.86a 0.31a 0.58 –

26 The Alps 27 Northern Spain 28 Gulf of Taranto

8.00 –3.50 17.89

46.30 42.90 39.76

JJA J–D SON

Büntgen et al. (2011) Martín-Chivelet et al. (2011) Taricco et al. (2009)

0.69 0.53a 0.68a

29 30 31 32 33

ShiHua Cave Chesapeake Bay Dunde Dulan Guliya

116.23 –76.40 96.40 98.00 81.48

39.54 39.00 38.10 36.00 35.28

Subdecadal Tree ring width Annual Marine sediment Subdecadal Ice-core δ18O Annual Lake sediment Subdecadal Marine sediment Decadal Lake sediment Subdecadal Laminated lake sediment Annual Marine sediment Subdecadal Multi-proxy Decadal Laminated lake sediment Annual Tree ring width Annual Speleothem δ18O Subdecadal Tree ring width Annual Speleothem δ13C Decadal Marine sediment Subdecadal Speleothem Annual Marine sediment Decadal Ice-core δ18O Decadal Tree ring width Decadal Ice-core δ18O Decadal

M–A Warmb Annual Annual Annual

Tan et al. (2003) Cronin et al. (2010) Thompson et al. (2006) Zhang et al. (2003) Thompson et al. (2006)

0.65 0.18a – 0.44a –

34 S. Colorado Plateau 35 China composite

–111.40 105.00

35.20 35.00

Tree ring width Multi-proxy

Annual Decadal

Maxc Salzer and Kipfmueller (2005) 0.68 Annual Yang et al. (2002) 0.72a

Correlation stands for the Pearson correlation coefficients between proxy and instrumental temperature in by the original author, when available a

Correlation values calculated by us

b

The exact months are not specified

c

The temperature signal is interpreted to reflect annual mean maximum temperature

and is originally calibrated to local April to October temperatures. The Southern Colorado Plateau record (Salzer and Kipfmueller 2005) from Arizona, southwestern USA

reflects the annual maximum temperature, but given that it comes from a semiarid region, it may periodically have been affected by drought stress and thus show a nonlinear



Fig. 1 Map showing the geographical distribution of the proxy records

response to warming if summer temperatures also reduce the water availability. The Dulan tree ring width record (Zhang et al. 2003) of Qilian juniper (Sabina przewalskii Kom.) from the northeastern Qinghai–Tibetan Plateau likely contains a mixed temperature and precipitation/drought signal but has previously been used as a temperature proxy by Yang et al. (2002), Ljungqvist (2010), Christiansen and Ljungqvist (2011, 2012) and Ljungqvist et al. (2012). We have also one tree ring maximum latewood density record. Tree ring maximum latewood density chronologies generally have a stronger correlation with temperature than tree ring width records and reflect the conditions over a longer period of the growing season than tree ring width records (Briffa et al. 2002; D’Arrigo et al. 2009). The Torneträsk (Grudd 2008) record of Scots pine (P. sylvestris L.) from Lapland, close to both the altitudinal and latitudinal tree line in northern Sweden, is originally calibrated to April to August mean temperature. We have three speleothem records. The ShiHua Cave speleothem micro-layer thickness record (Tan et al. 2003) from outside of Beijing, China is the only millennia-long stalagmite temperature record that possesses absolute annual resolution. It has been interpreted to reflect changes in May to August temperatures in the region around ShiHua Cave. The speleothem δ18O record from Spannagel Cave in the Central Alps of Austria (Mangini et al. 2005) has a subdecadal resolution and is interpreted to reflect annual mean temperature but with a bias towards winter temperature. It

has also been proved to clearly correlate with climate changes in the larger North Atlantic region (Mangini et al. 2007). The speleothem δ13C record from Northern Spain (Martín-Chivelet et al. 2011) has decadal resolution and comes from Cueva del Cobra in the Cantabrian Range. It is interpreted to reflect changes in summer temperature. We have three annual laminated lake sediment records among our proxies. The Lower Murray Lake record (Cook et al. 2009) is a laminated sediment record from Ellesmere Island, Nunavut, Canada in the extreme High Arctic that has a very short snow and ice-free season. Calculated annual mass accumulation rate from the lake sediment core has been used to estimate July temperature. The Iceberg Lake record (Loso 2009) in southern Alaska is based on several sediment cores that have been spliced to each other (with some missing years), and the temperature estimates have been calculated from the modern relationship between varve thickness and late spring/early summer temperature. The Teletskoe Lake record (Kalugin et al. 2009) from the Altai Region of southern Siberia reflects annual mean temperature. It has sub-annual sampling and thus the highest resolution for any long lake sediment record. The temperature is calculated from multiple indicators: the X-ray density of the sediment, the Sr/Rb ratio as well as the contents of Ti and Br. We have two non-laminated lake sediment records in our proxy collection. The Haukadalsvatn record (Geirsdóttir et al. 2009) from northwestern Iceland has sub-decadal


resolution and is based on information from biogenic silica data in two sediment cores. Although it could not be quantitatively calibrated to instrumental temperature, it is interpreted to reflect changes in spring temperatures in the lakes catchment's area. The Hallet Lake record (McKay et al. 2008) from south–central Alaska has sub-decadal resolution and is based on biogenic silica concentrations preserved in the lacustrine sediments. It has been quantitatively calibrated to local summer air temperature. We also have six marine sediment records. The alkenone paleothermometry marine sediment record from the North Iceland Shelf (Sicre et al. 2011) has sub-decadal resolution and reflects late summer temperature variability just north of Iceland where temperate Atlantic water meets ice-filled Arctic water masses. The Vøring Plateau marine sediment record (Berner et al. 2011) comes from the eastern Norwegian Sea and has approximately decadal resolution and infers summer sea surface temperatures from diatoms. The Storegga Slide marine sediment record (Sejrup et al. 2011) has sub-decal resolution and comes from the southwestern Norwegian continental margin. It is based on δ18O values from planktonic foram that is interpreted to reflect surface water summer temperature. The marine sediment record from Gardar Drift (Sicre et al. 2011) south of Iceland has sub-decadal resolution and is an alkenoneinferred warm season sea surface temperature record. The δ18O marine sediment record from the Gulf of Taranto (Taricco et al. 2009) in the Ionian Sea in the eastern Mediterranean has a sub-decadal resolution and reflects fall sea surface temperatures but is also influenced by changes in salinity. The relative influence of temperature on the one hand and salinity on the other hand has not been stable over time. The Chesapeake Bay marine sediment record (Cronin et al. 2010) comes from the mid-Atlantic region of the eastern USA and infers early warm season temperatures at a sub-decadal resolution using Mg/Ca ratios from ostracodes and oxygen isotopes from benthic foraminifera. We have chosen to include two regional multi-proxy temperature reconstructions with decadal resolution in our proxy collection. It is the Russian Plain record (Sleptsov and Klimenko 2003) of Eastern Europe showing regional annual mean temperatures and the China composite of Yang et al. (2002) with a reconstruction of annual mean temperature over the whole of China. Both records have decadal resolution and are based on a large number of high- and low-resolution proxies from different archives within each region.

3 Methodology A time series yt, t 0 1, …, T can be written in the form yt ¼ mðtÞ þ rt , where m(t) is a deterministic function called the trend function, and rt is a noise (residual)

219

term with an expected value of zero. The existing techniques of jump detection are based on stepwise constant approximations to trend functions such that they are constant over different time intervals and have jumps at boundaries of the intervals (Fraedrich et al. 1997; Smadi 2006; Zhao et al. 2007). A review of these methodologies can be found in Feng et al. (2010). The concept of these applications may be criticised for both physical and mathematical reasons. Instantaneous climate changes implied by the stepwise constant approximation are rather questionable. Take, for simplicity, annual data values. Having a constant climate during a time interval ending in a year and having another constant climate from this year is completely unrealistic. Furthermore, a smooth trend function can evidently be approximated by a stepwise function with jumps, which are, however, not physically meaningful jumps. Therefore, there is a need for a methodology, which does not require the trend to be stepwise constant, but allows rather complex forms satisfying some mild smoothness conditions. It should be mentioned that Mudelsee (2000) introduced a ramp function that has no jumps but involves linear transitions between the stepwise constant stages of the trend function. The concept, however, may be regarded as a profoundly simplified version of the procedure used in this paper. Fundamental aspect of our methodology (Matyasovszky 2011) is that abrupt changes are identified with discontinuities of the first derivative of the trend function. The concept is evidently a compromise because a jump in the trend itself has no rationale (see the above paragraph), while big changes only in the second or higher derivatives provide trends that are too smooth to be considered abrupt. Without making any assumptions about the mathematical form of m(t), the trend can be estimated non-parametrically by local linear smoothers. There are several versions of b ðtÞ. The weighted local regression nonparametric estimates m (WLR) has several advantageous properties (Fan 1992, 1993; Fan and Gijbels 1992) and can be applied to any data set satisfying some mild smoothness and statistical dependence conditions for the trend and the residuals, respectively. The locality called bandwidth plays a crucial role in the accuracy of the procedure. Large bandwidths that allow large amounts of data smoothing produce small variances with possibly large biases, while small bandwidths provide large variances with small biases. Thus, an optimal bandwidth that recognises the trade-off between the bias and variance has to be estimated. For further details see, for instance, Fan and Yao (2005). The trend function, however, does not satisfy the above-mentioned smoothness conditions when its derivative has jumps at certain points. It is written, therefore, as


mðtÞ ¼ μðtÞ þ

I. Matyasovszky, F.C. Ljungqvist K X k¼1

ck 8 k ðtÞ with 8 k ðtÞ ¼

0; t < t k ; t; t t k

where ck, k 0 1, …, K are the jumps in the derivative m ′(t) (kink sizes) at t 1 t 2 :::t K. Knowing the kink points τ1, …, τK and the number of these points K, μ(t) and ck, k 0 1, …, K (and so m(t)) can be estimated by combining the nonparametric and parametric estimation principles (Cline et al. 1995). The task is to find K, select τ1, …, τK and decide whether an estimate bck differs significantly from zero. Our procedure will be the following. As nonparametric regressions are able to estimate not just smooth trend functions but their derivatives b 00 ðtÞ is created. An estimate from as well, an estimate m noisy data of the second derivative of the trend is evidently finite but large at kink points because the true second derivative is infinite at these points. The kinks bc1 ; :::; bcK are significant when estimate of the trend function with kink points fits the data better than the estimate without kinks. The goodness of fit is measured by the generalised cross-validation representing an estimate of the residual variance penalised by coefficients of the local linear smoother (e.g. Fan and Yao 2005). The model with (without) kink points has lower (higher) residual variance but with higher (lower) penalising term; thus, the decision on these models is based on a trade-off between the magnitudes of residual variances and statistical uncertainties due to the model complexity (number of kink points). The only remaining crucial question is the bandwidth choice. An important recognition is that when exploring kink points the emphasis is on small biases (Wishart 2009) and selection of relatively small bandwidths is preferred. A reason is that a bandwidth smaller (or larger) than the optimal bandwidth overestimates the residual variance. Additionally, the penalising term mentioned above is higher under a smaller bandwidth. These two effects thus produce a decreased chance for overfitting the model when using relatively small bandwidths (Overfitting means detection of too many kink points). Knowing the properties of bandwidth selection procedures, it can be concluded that a bandwidth optimal for estimating a smooth trend will not be smaller than a bandwidth optimal for estimating the trend function having kinks. Therefore, regardless of smoothness, the bandwidth can be estimated by traditional techniques as outlined in the Appendix. Evidently, the resulting bandwidth depends on smoothness of the trend and autocovariances of the data. Four typical examples can be seen in Fig. 2. A high bandwidth (320 years) for Agassiz Ice Cap is due to a relatively smooth trend, while Torneträsk requiring a small bandwidth (150 years) exhibits a highly complex trend. Alps and Teletskoe Lake data represent intermediate cases with 240-year- and 210-year bandwidth, respectively.

4 Results The spatio–temporal distribution of the kink points detected in the proxy records is shown in Fig. 3. Of the analysed 35 records, 21 exhibit well-shaped peaks of warm periods before the modern era. Seventeen of these 21 peaks are characterised by kink points. Twelve peaks (11 kinks and 1 peak with smooth trend) appear around AD 1000. Four kink points are detected around AD 800. One further kink point is around AD 1100 (perhaps it can be considered as an additional kink point around AD 1000) and a late kink point is around AD 1350. Warming related to our modern era (approximately the period after AD 1800) is clearly detected in 18 records. Ten of them are identified as kink points. Four additional kink points indicate a much earlier start of the present warming trend, namely, the warming period that

Fig. 2 Smooth trend (dashed) and trend with kink points (solid) in four of the proxy records used in this study


221

Fig. 3 Spatio–temporal distribution of the kink points detected in the proxy records: ice-cores, lake sediments, marine sediments, multiproxy, speleothems, and tree rings

Fig. 2 (continued)

begins slightly before AD 1500 in one record, around AD 1500 in one record and around AD 1650 in two other records. Concerning the LIA, six patterns can be seen: (1) almost no change during the entire period (11 records), (2) decreasing temperatures during the entire period (3 records), (3) smooth cooling after a warm period lasting to around AD 1800 (8 records), (4) one cold kink point (6 records), (5) multiple cold peaks (3 records) and (6) multiple cold–warm peaks (4 records). Our analysis shows that the start of the modern global warming in the nineteenth century is not the most abrupt trend break in the last ~1,500 years according to most of the proxy records. Actually, it is difficult to observe any overall spatio–temporal pattern, and the timing of abrupt temperature changes and, especially, the timing of the strongest trend break seem to differ from record to record (Table 2). We find, as shown in Fig. 4, a significant cluster of the

warmest (e.g. the kink points with the highest temperatures) kink points around AD 1000. This likely corresponds to the MWP and indicates that a geographically widespread temperature peak indeed occurred at that time. There is some tendency for the “coldest” kink points (e.g. the kink points with the lowest temperatures) to be clustered in the nineteenth century but they are generally more evenly distributed than the peak of the MWP around AD 1000 (Fig. 4). What is noteworthy is the relative lack of kink points during the 1500 s–1700 s, likely the coldest part of the LIA, indicating that this cold period was relatively stable and without abrupt events. More proxy records show kink points marking the start of the modern warming in the nineteenth century in lower latitudes than in higher latitudes. On the other hand, kink points around AD 1000 are slightly more numerous on higher latitudes. We have not been able to discern any difference in the timing of abrupt temperature changes between different kinds of proxy records, although we acknowledge that the different proxy categories are not evenly distributed across the Northern Hemisphere.

5 Discussion and conclusions We have in this article demonstrated that the kink point analysis technique by Matyasovszky (2011) is a useful tool to analyse high-resolution temperature proxies for detecting abrupt changes. Investigating the spatio–temporal distribution of abrupt climate changes in the 35 proxy records that we analyse, we find a major clustering of warm kink points (the kink points with the highest temperatures) near AD 1000. This cluster of kink points most likely represents the peak of the MWP, and the warm peak seems to have been somewhat more distinct or more widespread on higher latitudes than on lower latitudes. A possible, albeit smaller, cluster of kink points is also found on lower latitudes in the early nineteenth century. The relative lack of kink points

Author's personal copy 222 Table 2 List over the dates when kink points have been detected in the different proxy records

The dates are listed in order of the magnitude of the kink points. Thus, column 1 represents the kink point with the largest magnitude and column 6 represents the kink point with the smallest magnitude. More than six kink points have not been detected in any record


Proxy record

1

2

Lower Murray Lake Agassiz Ice Cap Prince of Wales Ice Cap GRIP Devon Ice Cap NorthGRIP Renland Crête Indigirka Avam-Taimyr Finnish Lapland Torneträsk Vøring Plateau Yamal

1796 1695 No kink No kink No kink No kink No kink No kink 933 1848 No kink 1620 1485 1848

1435 1594

North Iceland Shelf Dye-3 Haukadalsvatn Storegga Slide Hallet Lake Iceberg Lake Gardar Drift Russian Plains Teletskoe Lake Sol Dav Spannagel Cave The Alps Northern Spain Gulf of Taranto ShiHua Cave Chesapeake Bay Dunde Dulan

1025 No kink 1530 1190 1885 701 No kink 1120 1880 1853 1030 1842 No kink No kink 827 No kink No kink 738

Guliya S. Colorado Plateau China composite

845 1870 855

Fig. 4 Spatio–temporal distribution of the warmest and coldest kink points (kink points with the highest and lowest temperatures) detected in the proxy records

3

4

5

6

839

1064

740

points detected points detected points detected points detected points detected points detected 1016 1263

1292 1014

674 865 997

1753

points detected

911

645 points detected 1440 750 1020

909

1796

830 1792 1767 747 1406

740 665 853 1453 1314

970 838 1425 1888 1020

1190 1189 781

948

1396

1501

743

894

1261

1180 1424

1735

1221

points detected

points detected points detected points detected points detected 1008 1270 1650 1655

detected during the 1500 s–1700 s, a period that likely was the coldest part of the Little Ice Age, is interesting since it implies that this cold period was quite stable and was lacking abrupt climate events. The start of the modern warming trend, occurring during the still cold period of the midnineteenth century, seems to have been a rather abrupt and geographically quite coherent event and is clearly detected by the kink point analysis. No apparent difference in the timing of kink points between the different proxy record types has been observed. However, one major conclusion is that most high-latitude icecore δ18O records do not produce any kink points and thus possess no abrupt events. It seems that not all types of proxy


records preserve the signal of abrupt temperature changes equally well. The fact that high-latitude ice-core δ18O records do not seem to preserve the signal from abrupt temperature changes during the last ~1,500 years is of significant interest considering that such records are often used in large-scale multi-proxy temperature reconstructions. The reasons for their inability to preserve the signal from abrupt temperature changes are not entirely clear. It is, however, well known that the temperature signal on centennial and longer time scales in ice-core δ18O records can be affected by ice flow movements and layer compaction (e.g. Reeh et al. 1985), but this can hardly be the only explanation. It is obvious that separation of data into terms of trend and residual is crucially affected by bandwidths. The optimal bandwidth depends on the shape of the trend and the residual variance. Temporal density of data is also important; sparser temporal resolutions require larger bandwidths resulting in smoother trends. Additionally, changing temporal data resolution needs changing bandwidths. Finally, positive autocorrelations of residuals enlarge the optimal bandwidths compared to uncorrelated residuals. The bandwidth estimation procedure of Fernandez and Fernandez (2004) cares about these questions when residuals do not come from a long-memory process. A stationary longmemory process can exhibit data taking long excursions around their mean and these excursions can appear as trend. A study of Rea et al. (2011) is therefore important in this respect. They analysed six records (three of them are used in our work) and found no long memory but identified nonstationarity characterised by several breaks in the mean. Some of these breaks are detected as kinks in our paper, while others are not. This is because trend is not allowed to be smooth but assumed to be stepwise constant in Rea et al. (2011). Kink point analysis of the kind conducted in this study could be a potentially useful tool for detecting abrupt climate changes in the often noisy low-resolution pollen and marine sediment records that cover the whole of the Holocene or even the Pleistocene. It would also be of interest in the future to try to detect significant abrupt changes in drought and precipitation proxy records covering the last one to two millennia. The result from such an analysis could preferably be compared with the spatio–temporal pattern of kink points detected in the temperature proxies in the present article in order to gain a better understanding of the relationship between abrupt changes in temperature and abrupt changes in precipitation patterns. Acknowledgments This work was supported by the European Union and co-financed by the European Social Fund (grant agreement no. TAMOP 4.2.1./B-09/KMR-2010-0003). We wish to express our gratitude to several scholars that provided us with proxy data that are not available from public databases: Thomas M. Cronin, National Center US Geological Survey; Ivan A. Kalugin, Siberian Branch of the Russian

223 Academy of Sciences; Vladimir V. Klimenko, Global Energy Problems Laboratory, Moscow Energy Institute and Carla Taricco, Dipartimento di Fisica, Generale dell' Università.

Appendix: Bandwidth estimation According to Fernandez and Fernandez (2004), the quantity TSCVðhÞ ¼ 1=ðn pÞ

n X

ðyt byt Þ2

t¼pþ1

is minimised with respect to h, where h is the bandwidth and byt is an estimate with an auto-regression of order p as byt ¼ m e ðtÞ þ

p P

j¼1

b e ðt jÞÞ . Coefficients a1, …, ap are aj ðytj m

e ðt jÞ is estimated by the least squares technique, while m a WLR estimate of m(t-j), j 0 0, …, p with bandwidth h that uses only y1, y2, …, yt-p. Since TSCV uses only the data to the left of a time point t and the aim is to estimate the trend using data on either side of time t, the bandwidth selected by TSCV has to be corrected by a factor found, e.g. in Müller (1991). The order p of auto-regression is chosen such that partial autocorrelations estimated from y1, y2, …, yn for lags larger than p are not significantly different from zero.

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