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Title: Influence of sampling and disturbance history on climatic sensitivity of temperature-limited conifers
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Authors:
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Miloš Rydvala,b, email: rydval@gmail.com, tel. (00420)735872634
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Daniel L. Druckenbrodc
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Miroslav Svobodaa
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Volodymyr Trotsiuka,d,e
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Pavel Jandaa
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Martin Mikoláša
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Vojtěch Čadaa
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Radek Bačea
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Marius Teodosiuf,g
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Rob Wilsonb
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a. Faculty of Forestry and Wood Sciences, Czech University of Life Sciences Prague,
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Kamýcká 129, Praha 6–Suchdol, Prague, 16521, Czech Republic
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b. School of Earth and Environmental Sciences, University of St Andrews, UK
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c. Department of Geological, Environmental, & Marine Sciences, Rider University,
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Lawrenceville, NJ, USA
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d. Swiss Federal Research Institute for Forest, Snow and Landscape Research (WSL), Birmensdorf,
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Switzerland.
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e. Institute of Agricultural Sciences, ETH Zurich, Switzerland
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f. “Marin Drăcea“ National Research and Development Institute in Forestry, Romania
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Voluntari, Romania
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g. Faculty of Forestry, Ştefan cel Mare University of Suceava, Romania
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ABSTRACT: Accurately capturing medium-to-low frequency trends in tree-ring data is vital to assessing
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climatic response and developing robust reconstructions of past climate. Non-climatic disturbance can
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affect growth trends in tree-ring width (RW) series and bias climate information obtained from such
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records. It is important to develop suitable strategies to ensure the development of chronologies that
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minimize these medium-to-low frequency biases. By performing high density sampling (760 trees) over a
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~40ha natural high elevation Norway spruce (Picea abies) stand in the Romanian Carpathians, this study
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assessed the suitability of several sampling strategies for developing chronologies with an optimal
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climate signal for dendroclimatic purposes. There was a roughly equal probability for chronologies (40
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samples each) to express a reasonable (r=0.3-0.5) to non-existent climate signal. While showing a strong
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high-frequency response, older/larger trees expressed the weakest overall temperature signal. Although
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random sampling yielded the most consistent climate signal in all sub-chronologies, the outcome was
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still sub-optimal. Alternative strategies to optimise the climate signal, including very high replication and
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principal component analysis, were also unable to minimize this disturbance bias and produce
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chronologies adequately representing climatic trends, indicating that larger scale disturbances can
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produce synchronous pervasive disturbance trends that affect a large part of a sampled population. The
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Curve Intervention Detection (CID) method, used to identify and reduce the influence of disturbance
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trends in the RW chronologies, considerably improved climate signal representation (from r=0.28 before
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correction to r=0.41 after correction for the full 760 sample chronology over 1909-2009) and represents
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a potentially important new approach for assessing disturbance impacts on RW chronologies. Blue
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intensity (BI) also shows promise as a climatically more sensitive variable which, unlike RW, does not
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appear significantly affected by disturbance. We recommend that studies utilizing RW chronologies to
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investigate medium to long-term climatic trends also assess disturbance impact on those series.
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KEYWORDS: disturbance detection; sampling bias; climatic signal; blue intensity; tree rings; Norway
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spruce; Romanian Carpathian Mountains
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INTRODUCTION
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The accurate representation of climatic variability in the growth trends contained in tree-ring
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records from climatically sensitive trees is central to assessing growth-climate response and the
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development of robust dendroclimatic reconstructions (e.g. Anchukaitis et al., 2017; Cook et al., 2015;
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Cook et al., 2016; D’Arrigo et al., 2006; Luterbacher et al., 2016; Wilson et al., 2016). The suitability of
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strategically sampled tree-ring chronologies for reconstructing a particular climatic variable is typically
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evaluated by examining the growth-climate response and the strength of this relationship. This process
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partly relies on the assumption that chronologies are developed from a finite number of samples that
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are representative of the population. In climatically sensitive stands (i.e. temperature sensitive trees at
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high latitude or elevation tree-line locations) it is usually assumed that when adequate measures are
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taken to avoid sampling trees likely affected by non-climatic influences, the common signal of the
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sample chronology represents the common climatic signal of the population (Hughes, 2011).
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Tree growth is the product of a range of environmental influences that are integrated into the
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annual growth increment (Cook, 1985; Vaganov et al., 2006). Natural disturbance is one key element of
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forest ecosystem development (Attiwill, 1994). The presence of non-climatic disturbance trends in tree
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ring width (RW) series complicates the development of climatically sensitive tree-ring based records
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(e.g. Briffa et al., 1996; Gunnarson et al., 2012; Rydval et al., 2016). Yet few, if any, studies explicitly
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assess the influence of disturbance as a part of dendroclimatic research. A common presumption is that
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the effects of disturbance are either negligible or asynchronous so that their influence is canceled out
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through the development of a mean chronology of detrended series, or they can be minimized by
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applying appropriate detrending techniques in cases when such trends occur systematically (Hughes,
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2011). It has been shown that larger scale intermediate and higher severity disturbances can result in
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synchrony of disturbance histories across the landscape on the stand level and regional spatial scales
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(e.g. D’Amato and Orwig, 2008; Kulakowski and Veblen, 2002; Zielonka et al., 2010). While flexible data-
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adaptive detrending approaches such as cubic smoothing splines (Cook and Peters, 1981) have been
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utilized to limit the influence of non-climatic (e.g. disturbance) trends in RW data, a detrimental side-
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effect of such techniques is the loss of lower frequency (i.e. multidecadal to multicentennial) climatic
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variability.
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Numerous studies have investigated dendrochronological biases and uncertainties related to
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various methodological aspects of tree-ring data development including detrending (e.g. Briffa and
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Melvin, 2011;Cook et al., 1995; Helama et al., 2004; Melvin and Briffa, 2008; Melvin et al., 2013), sample
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size and signal strength (e.g. Mérian et al., 2013; Osborn et al., 1997; Wigley et al., 1984), sampling
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design and microsite conditions (e.g. Cherubini et al., 1998; Düthorn et al., 2013, 2015; Nehrbass-Ahles
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et al., 2014), and tree age (e.g. Carrer and Urbinati, 2004; Esper et al., 2008; Fish et al., 2010). In an
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extensive assessment of sampling design strategies, Nehrbass-Ahles et al. (2014) highlighted that many
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common sampling approaches used for developing representations of forest response to environmental
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change can induce sampling related biases. However, relatively little is known about how disturbance
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related growth trends affect the climate signal in tree ring series.
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Time-series analysis with intervention detection (Box and Jenkins, 1970; Box and Tiao, 1975) is
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an evolving area for studying disturbance in RW data (Druckenbrod, 2005). A time-series based method
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called Curve Intervention Detection (CID) has been developed to characterize disturbance history and
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quantify the effects of disturbance trends on individual RW series and overall chronology structure
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(Druckenbrod, 2005; Druckenbrod et al., 2013). Chronology distortion and climate signal degradation,
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due to synchronous disturbance related growth releases as a result of systematic timber felling, was
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identified using the CID technique by Rydval et al. (2016) in Scots pine RW chronologies from Scotland.
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However, such a technique has not previously been applied to investigate trends resulting from natural
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sources of disturbance on the strength of the climate signal in tree-ring records.
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Building on the work of Rydval et al. (2016), in this study we applied the CID method to a new
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forest system and species by examining RW series from an unmanaged natural closed canopy Norway
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spruce (Picea abies) stand in Romania (shaped by a mixed-severity natural disturbance regime with
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partial landscape synchronization and unperturbed by human activities - Svoboda et al., 2014) to
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examine the extent to which natural disturbance can affect climate signal strength in RW data. We
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investigate (1) whether natural disturbance can produce widespread and synchronized trends, as those
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resulting from human activities, that would significantly impact the expression of the climate signal in
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tree-ring chronologies, and (2) which sampling or data processing approach best expresses the climate
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signal. To this end, we firstly evaluated a set of sampling strategies by subsampling a large dataset of RW
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data from a single stand according to a set of characteristics reflecting sampling strategies that are
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relevant in a dendroclimatic context. The application of additional data processing techniques (including
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disturbance trend detection and correction using the CID method, and isolation of the dominant signals
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through principal component analysis) were investigated in an attempt to optimize the climate signal.
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We applied the CID time-series analysis technique in order to characterize the disturbance history, its
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impact on overall chronology structure and subsequently to reduce the influence of disturbance-related
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trends on RW chronologies (Druckenbrod, 2005; Druckenbrod et al., 2013; Rydval et al.,2016). As an
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alternative to RW data, a subset of chronologies was developed from series of the blue intensity (BI)
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parameter (Björklund et al., 2014a; McCarroll et al., 2002; Rydval et al., 2014) to ascertain whether such
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data can be used to produce proxy climate records unbiased (or less biased) by the presence of
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disturbance trends.
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METHODS
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Sampling site
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Samples were collected and measured from 760 high-elevation Norway spruce (Picea abies)
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trees (cored at breast height) located in an approx. 40 ha natural Norway spruce dominant stand
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(47°06’53”N,25°15’26”E) in Călimani National Park (hereafter Calimani) in the Eastern Carpathians of
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northern Romania (Figure 1; see Svoboda et al. (2014) for details regarding sample collection). The
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selected sampling site is located within an elevational range of around 1500-1650 m a.s.l., ~100-250 m
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below the regional timberline (approx. 1780 m a.s.l.) and ~200-350 m below the treeline (approx. 1860
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m a.s.l.) (Popa and Kern, 2009) and with slope varying from around 10° to 25°. Podzols are the
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predominant soil type in the study region (Valtera et al., 2013). The area has a mean annual
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temperature of 2.1-3.1°C estimated from 0.5° gridded CRU TS3.23 temperatures (based on the period
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2005-2014 and adjusted for elevation). Over the same period, temperatures have increased by
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approximately 1.6°C relative to the first decade of the 20th century. Mean annual precipitation is about
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910 mm (2005-2014 mean).
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[insert Figure 1]
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Sample collection was performed in an area with no significant human activities in the past
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(including evidence from historical documentation) and subject only to natural stand dynamics and
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disturbance regimes (Svoboda et al., 2014). Considering the size of the sampled area and number of
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samples collected, this high density sampling strategy, similar to that of Nehrbass-Ahles (2014), was
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intended to provide a highly representative sample of the whole stand population by sampling a diverse
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range of tree size and age classes. This approach makes it possible to group samples and construct
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chronologies according to a range of characteristics.
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CHRON.
(SUBSET)
NR. OF
SERIES
MEAN
ELEVATION
CHRON.
LENGTH
EPS ≥ 0.85
CHRON.
(BY DBH)
DBH RANGE
(CM)
CHRON.
(BY AGE)
AGE
RANGE
PLOT-ALL
760
1578
1673-2009
1744-2009
110-925
31-337
PLOT-1
40
1523
1731-2009
1888-2009
DBH-1
110-235
AGE-1
31-82
PLOT-2
40
1585
1724-2009
1862-2009
DBH-2
235-265
AGE-2
82-85
PLOT-3
40
1602
1743-2009
1906-2009
DBH-3
265-280
AGE-3
85-87
PLOT-4
40
1616
1772-2009
1905-2009
DBH-4
280-300
AGE-4
87-89
PLOT-5
40
1588
1768-2009
1820-2009
DBH-5
300-320
AGE-5
89-92
PLOT-6
40
1626
1790-2009
1857-2009
DBH-6
320-340
AGE-6
92-97
PLOT-7
40
1633
1712-2009
1835-2009
DBH-7
340-360
AGE-7
97-111
PLOT-8
40
1516
1673-2009
1897-2009
DBH-8
360-380
AGE-8
112-118
PLOT-9
40
1514
1700-2009
1903-2009
DBH-9
380-400
AGE-9
118-122
PLOT-10
40
1606
1763-2009
1835-2009
DBH-10
400-415
AGE-10
122-127
PLOT-11
40
1565
1701-2009
1856-2009
DBH-11
415-430
AGE-11
127-134
PLOT-12
40
1587
1763-2009
1906-2009
DBH-12
430-450
AGE-12
134-142
PLOT-13
40
1590
1768-2009
1896-2009
DBH-13
450-480
AGE-13
142-148
PLOT-14
40
1552
1705-2009
1861-2009
DBH-14
480-500
AGE-14
148-156
PLOT-15
40
1551
1720-2009
1901-2009
DBH-15
500-520
AGE-15
156-162
PLOT-16
40
1541
1803-2009
1909-2009
DBH-16
520-550
AGE-16
163-176
PLOT-17
40
1511
1752-2009
1903-2009
DBH-17
550-590
AGE-17
176-201
PLOT-18
40
1552
1757-2009
1902-2009
DBH-18
590-650
AGE-18
201-234
PLOT-19
40
1572
1750-2009
1838-2009
DBH-19
651-925
AGE-19
235-337
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Table 1: Site and chronology descriptive information. PLOT represents chronologies developed
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according to sample location (i.e. plot-based), DBH chronologies are composed of samples
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grouped according to diameter at breast height, and AGE represents chronologies with samples
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grouped according to tree recruitment age. With the exception of the PLOT-ALL chronology, all
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other chronologies were developed using 40 samples. (EPS = expressed population signal,
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Wigley et al., 1984).
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Data analysis
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Sampled cores were mounted and glued on wooden mounts and subsequently surfaced with a
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blade to enhance the visibility of ring boundaries. To help determine tree recruitment age (i.e. the
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number of rings at coring height), pith-offset was estimated using an acetate sheet with concentric
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circles. However, the method of sample collection specifically focused on minimizing pith-offset and so
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the majority of samples included the pith. Ring width was then measured using a LINTAB traversing
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measuring stage coupled with TsapWin (RINNTECH, Germany) measuring software to a precision of 0.01
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mm. Sample crossdating was performed using standard dendrochronological approaches (Stokes and
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Smiley, 1968) and crossdating of measured series was checked with CDendro (Larsson, 2015).
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Disturbance detection and correction
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Curve Intervention Detection (CID) is a time-series intervention detection method based on the
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work of Druckenbrod (2005) and Druckenbrod et al. (2013). The method was used here to objectively
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identify and remove disturbance trends from individual RW series following the procedure described in
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Rydval et al. (2016), where it was used to identify and correct for growth release trends due to logging-
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related disturbance in Scottish Scots pine (Pinus sylvestris) samples. In this study, both growth release
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and growth suppression trends were detected and removed. Prior to the CID procedure, a constant of 1
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mm was added to all measurements to avoid the possibility of losing tree-ring information during the
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disturbance removal procedure (Rydval et al., 2016). As part of the CID procedure, RW measurement
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series were first power transformed (Cook and Peters, 1997) and then detrended by fitting a negative
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exponential or linear function. Disturbance trends were identified as outliers from 9-30 year running
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mean distributions based on the residual series of each detrended RW series and autoregressive model
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estimates. The identified release / suppression trend was removed by subtracting a curve (Warren,
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1980) fitted to the series from the point where the initiation of the disturbance-related trend was
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identified. The procedure was repeated until no further outliers were detected. The disturbance-
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corrected series were then re-expressed in the original (non-detrended) measurement format so that
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both the corrected and uncorrected series could then be detrended in the same way. For a detailed
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description of the method refer to Rydval et al. (2016). CID (ver. 1.05) was used in these analyses and is
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included in the supplemental materials as Matlab code files. A freely-available executable (ver. 1.07) is
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available using the Matlab compiler. Contact Daniel Druckenbrod (ddruckenbrod@rider.edu) as this
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version is dependent on operating system and Matlab release version. These time-series methods are a
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work in progress, but we also welcome other researchers to experiment with this tool to detect and
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isotlate disturbance events in ring-width series.
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RW chronology development
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Two sets of chronologies were developed with the first set composed of series prior to
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disturbance correction using the CID method (i.e. uncorrected for the influence of disturbance – pre-
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CID) and the second set using series after correcting for disturbance trends with CID (post-CID). Using
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ARSTAN (Cook and Krusic, 2005), both sets of RW series were power transformed to stabilize series
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variance (Cook and Peters, 1997) and detrended by subtracting negative exponential or negatively
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sloping linear functions. The mean chronology index was calculated using Tukey’s robust bi-weight mean
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to reduce the influence of outlier values (Cook and Kairiukstis, 1990). Variance stabilization of the mean
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chronology, due to changing replication, was then performed according to the procedure described in
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Osborn et al. (1997).
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In addition to developing an uncorrected (pre-CID) and disturbance corrected (post-CID) mean
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chronology from all 760 samples, the entire collection of series was also divided into 19 separate sub-
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plot chronologies (each including 40 series) compiled by grouping series according to 1) the plot location
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where the samples were collected (PLOT) (Figure 1); 2) random sample selection without replacement
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(RAN); 3) tree recruitment age (AGE), 4) and the diameter at breast height (DBH) (Table 1). All
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chronologies were truncated based on an expressed population signal (EPS – Wigley et al., 1984) cut-off
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of EPS ≥ 0.85.
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Principal Component (PC) analysis, with varimax rotation, was applied using the IBM SPSS
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(v.20.0) statistical package (SPSS, 2011) to both pre-CID and post-CID location-based (PLOT)
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chronologies to reduce the dimensionality of the RW predictor dataset in order to extract the dominant
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modes of variance. Based on the temporal span of the shortest chronology (Table 1), the period 1909-
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2009 was used in order to include all chronologies in the analysis. Only the lowest order PC scores with
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an eigenvalue >1 were retained.
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Blue Intensity chronology development
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Similar to maximum latewood density, blue intensity (BI) represents summer growing
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conditions usually reflecting a (late) summer response to temperature in conifers from temperature
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limited locations (e.g. Björklund et al., 2014b; McCarroll et al., 2013; Rydval et al., 2014; Wilson et al.,
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2014). BI measurements were developed for a subset of the samples (three chronologies – PLOT-3,
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PLOT-7 and PLOT-10; 40 samples each) following Rydval et al. (2014). Since, unlike other conifers such as
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pine, Norway spruce samples do not exhibit any apparent visual colour difference between the
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heartwood and sapwood that would affect BI measurements, chemical treatment involving sample resin
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extraction was not performed. Such an approach was also considered adequate in a study by Wilson et
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al. (2014) examining BI data from Engelmann spruce in British Columbia. Samples surfaced with sanding
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paper up to 1200 grit grade were scanned using an Epson Expression 10000 XL flatbed scanner
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combined with SilverFast Ai (v.6.6 - Laser Soft Imaging AG, Kiel, Germany) scanning software. Scanner
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calibration was performed with the SilverFast IT8 calibration procedure using a Fujicolor Crystal Archive
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IT8.7/2 calibration target. A resolution of 2400 dpi was used for scanning. During the scanning process,
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samples were covered with a black cloth to prevent biases due to ambient light.
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CooRecorder measurement software (Larsson, 2015) was used to measure BI from scanned
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images. The BI series were then inverted according to Rydval et al. (2014) to express a positive
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relationship with RW and instrumental temperatures and subsequently detrended by subtraction from
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fitted negatively sloping linear functions. The mean BI chronology was calculated and truncated (EPS =
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0.85) in the same way as the RW chronologies.
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Climate data
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For this study, in order to allow the assessment of the longest possible temporal span of the
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tree-ring data, we used mean temperature series from a meteorological station in Sibiu, Romania
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(hereafter SIBIU) covering the period 1851-2015 (data for 1918 were unavailable and were estimated
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from the relevant 0.5° CRU TS3.23 grid scaled to SIBIU) located approximately 170 km to the SSW of
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Calimani (Figure 1). An additional temperature record was composited using the longest Central and
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Eastern European instrumental records in order to assess the whole span of the full 760 sample Calimani
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chronology. This Central/East European (CEU) composite covers the period 1773-2014 and includes
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temperature series from Prague (Czech Republic), Vienna (Austria), Kraków (Poland), Budapest
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(Hungary), Lviv (Ukraine) and Kishinev (Moldova). The individual instrumental series were converted to
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anomalies relative to 1961-1989 and combined as a simple average. To adjust for variance changes due
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to the changing number of series in the composite through time, the variance of the mean series was
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adjusted according to Osborn et al. (1997). Climate data were used to assess the strength of the climatic
245
signal in tree ring chronologies using the Pearsons correlation coefficient (r).
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RESULTS
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Four sets of chronologies developed according to various sampling strategies are presented in
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Figure 2 with additional chronology information in Table 1. As the strongest significant chronology
250
response was observed with June-July mean temperatures (see supplementary Figure S1), RW
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chronologies were assessed using this seasonal window. This seasonal response agrees with Sidor et al.
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(2015) who also noted a significant June-July mean temperature signal in high-elevation spruce sites in
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the Romanian Carpathians including Calimani.
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The location-based ‘PLOT’ chronologies (Figure 2a – see Figure 1 for plot locations) displayed a
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large range of variability (especially before ~1960) which is also reflected in the wide range of variation
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in correlation between each chronology and June-July average instrumental temperatures (r = 0.07 to
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0.46; r = 0.26 – Table 2). The ‘RAN’ chronologies based on random selection of samples (without
258
replacement; Figure 2b) produced a more uniform range of variability which was also observed in the
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relationship between the chronologies and instrumental temperatures (r = 0.24 to 0.35; r = 0.26 – Table
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2). When compared with the PLOT chronologies, the correlation range of these ‘random sample’
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chronologies against instrumental temperatures was considerably narrower, although the mean
262
correlation was virtually the same and while the very low correlations were no longer observed, the
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higher correlations were also no longer present. When grouped according to stem size (i.e. DBH – Figure
264
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2c), chronologies displayed considerable variability particularly in the first half of the 20th century as well
265
as in the most recent period (i.e. after ~1990). Chronologies composed of series from broader-stemmed
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(higher DBH) trees tended to correlate more weakly with instrumental temperatures (r = - 0.06 to 0.28
267
for chronologies DBH-12 – DBH-19; see Table 3 for details), whereas trees with narrower stems (lower
268
DBH) appeared to exhibit higher correlations (r = 0.37 to 0.47 for chronologies DBH-1 – DBH-11
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excluding the weaker DBH-9 chronology; see Table 3). The chronologies grouped according to age
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showed a similar range of variability to the DBH-based chronologies (Figure 2d). Although not as clear,
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there was a tendency for younger chronologies to correlate more strongly than the oldest chronologies
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(Figure 2d; Table 3). However, when examining only the high frequency (inter-annual) relationship
273
between the chronologies and temperature (1st differenced results in Table 3), there was little
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difference between the young and old tree chronologies and larger trees actually displayed a stronger
275
signal than chronologies from smaller trees (r = 0.30 to 0.43, r = 0.38 for chronologies DBH-1 – DBH-11;
276
r = 0.42 to 0.51, r = 0.47 for chronologies DBH-12 – DBH-19). Unsurprisingly, a strong relationship (r =
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0.63) was observed between age and DBH (Figure S2), which indicates that older trees generally also
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tend to be larger (i.e. higher DBH) and vice-versa.
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[insert Figure 2]
280
281
SAMPLING TYPE
PRE-CID
POST-CID
1ST DIFFERENCED
LOCATION (PLOT)
(1909-2009)
r = 0.255 ± 0.124
rrange= 0.066 - 0.461
r = 0.383 ± 0.126
rrange = 0.079 - 0.540
r = 0.422 ± 0.044
rrange = 0.337 – 0.530
RANDOM
(1912-2009)
r = 0.265 ± 0.057
rrange = 0.183 - 0.381
r = 0.401± 0.049
rrange = 0.329 - 0.505
r = 0.441 ± 0.032
rrange = 0.387 – 0.503
DBH
(1917-2009)
r = 0.265 ± 0.174
rrange= -0.067 - 0.472
r = 0.379 ± 0.062
rrange= 0.263 - 0.489
r = 0.414 ± 0.059
rrange= 0.297 – 0.508
AGE
(1933-2009)
r = 0.309 ± 0.153
rrange = -0.067 - 0.483
r = 0.397 ± 0.081
rrange = 0.236 - 0.509
r = 0.377 ± 0.066
rrange = 0.255 – 0.485
Table 2: Average correlation and correlation range of chronologies before (pre-CID) and after (post-CID)
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disturbance correction and first differenced chronologies developed with different sampling
283
strategies, including samples grouped by location (PLOT), random sample selection (RAN),
284
grouping according to diameter at breast height (DBH), and sample age (AGE), against SIBIU
285
Jun-Jul mean instrumental temperatures. (r represents the mean correlation ± 1 standard
286
deviation, while rrange represents the full correlation range)
287
12
CHRON.
(RANDOM)
PRE-CID
CORR
POST-CID
CORR
1ST DIFF
CORR
CHRON.
(BY DBH)
PRE-CID
CORR
POST-CID
CORR
1ST DIFF
CORR
CHRON.
(BY AGE)
PRE-CID
CORR
POST-CID
CORR
1ST DIFF
CORR
RAN-1
0.318
0.505
0.471
DBH-1
0.473
0.453
0.297
AGE-1
0.374
0.339
0.294
RAN-2
0.239
0.436
0.503
DBH-2
0.373
0.311
0.331
AGE-2
0.483
0.451
0.421
RAN-3
0.279
0.473
0.471
DBH-3
0.393
0.418
0.351
AGE-3
0.414
0.440
0.353
RAN-4
0.218
0.406
0.480
DBH-4
0.402
0.396
0.369
AGE-4
0.473
0.452
0.431
RAN-5
0.246
0.380
0.475
DBH-5
0.402
0.389
0.389
AGE-5
0.446
0.509
0.449
RAN-6
0.248
0.381
0.415
DBH-6
0.397
0.358
0.390
AGE-6
0.470
0.489
0.414
RAN-7
0.300
0.329
0.451
DBH-7
0.406
0.368
0.344
AGE-7
0.362
0.433
0.309
RAN-8
0.381
0.406
0.417
DBH-8
0.471
0.489
0.426
AGE-8
0.370
0.323
0.321
RAN-9
0.241
0.407
0.471
DBH-9
0.196
0.327
0.387
AGE-9
0.348
0.267
0.338
RAN-10
0.228
0.405
0.397
DBH-10
0.403
0.390
0.433
AGE-10
0.237
0.310
0.352
RAN-11
0.301
0.379
0.441
DBH-11
0.357
0.409
0.429
AGE-11
0.258
0.309
0.307
RAN-12
0.334
0.434
0.439
DBH-12
0.135
0.353
0.418
AGE-12
0.227
0.334
0.255
RAN-13
0.183
0.349
0.387
DBH-13
0.275
0.353
0.451
AGE-13
0.356
0.390
0.338
RAN-14
0.359
0.487
0.414
DBH-14
0.182
0.464
0.507
AGE-14
0.414
0.489
0.381
RAN-15
0.187
0.360
0.436
DBH-15
0.054
0.394
0.454
AGE-15
0.348
0.430
0.401
RAN-16
0.247
0.334
0.429
DBH-16
0.145
0.457
0.496
AGE-16
0.034
0.470
0.485
RAN-17
0.238
0.368
0.415
DBH-17
-0.067
0.302
0.433
AGE-17
0.217
0.443
0.386
RAN-18
0.300
0.402
0.456
DBH-18
0.110
0.300
0.453
AGE-18
0.109
0.435
0.469
RAN-19
0.197
0.370
0.411
DBH-19
-0.064
0.263
0.508
AGE-19
-0.067
0.236
0.467
Table 3: Correlations of chronologies before (pre-CID) and after (post-CID) disturbance correction and
288
first differenced chronologies sampled using different sampling strategies, including random
289
sample selection (RAN), grouping according to diameter at breast height (DBH), and sample age
290
(AGE), against Jun-Jul mean instrumental temperatures from Sibiu (shading is used to aid
291
interpretation of the results with darker shades indicating higher correlations).
292
293
A summary of the general disturbance history at Calimani is provided in Figure 3a. The results
294
showed three major pulses or clusters of disturbance events, which affected a large proportion of the
295
stand, detected in the 1740s, the middle of the 19th century and the 1910s followed by growth releases
296
in the subsequent decades attributable to those disturbances. Disturbance suppression events were
297
detected in the mid/late 18th century, although the predominant release events were more prevalent
298
whereas suppression events did not appear to considerably affect the mean disturbance chronology.
299
The pre- and post- correction chronologies (Figure 3b and 3c respectively) indicated a wider spread in
300
individual pre-CID chronologies and greater deviation from the mean chronology compared to their
301
post-CID counterparts. This was also observed with the other sampling approaches (Table 2). The
302
disturbance growth chronology in Figure 3a identified periods of growth release pulses attributable to
303
disturbance which are evident in the Figure 3b mean chronology. After disturbance correction, the
304
spread of the individual chronologies was reduced as the growth release trends were removed and the
305
post-CID chronologies exhibited greater similarity to the mean chronology which did not contain the
306
growth release trends. The mean pre- and post-CID chronologies are displayed together with the SIBIU
307
13
instrumental temperature record (back to 1851) and the Central European (CEU) instrumental
308
temperature composite extending back to the 1770s (Figure 3d). The main differences between the
309
corrected and uncorrected chronologies become apparent with lower post-correction RW index values
310
in the first half of the 20th century and higher values from approximately 1770 until 1850. These results
311
also highlighted the improved agreement of the post-CID chronology with both the shorter SIBIU (rpre-CID
312
= 0.27; rpost-CID= 0.36) and longer CEU (rpre-CID = 0.14; rpost-CID= 0.26) instrumental temperature series.
313
[insert Figure 3]
314
315
The change in correlation between individual pre-CID and post-CID chronologies and the SIBIU
316
temperature series for the common 1909-2009 period (Figure 4a) showed overall improvement of the
317
mean chronology as well as all individual chronologies with the exception of PLOT-16. Similar results
318
were obtained when evaluating the full length of each chronology (Figure 4c). A comparison of the pre-
319
and post-CID root-mean-square error (RMSE) results for the common 1909-2009 period (Figure 4b) and
320
the full length of overlap (Figure 4d) between individual PLOT chronologies and SIBIU indicated a RMSE
321
decrease in nearly all post-CID chronologies. This RMSE pattern largely mirrored the correlation change
322
results and indicated chronology improvement in the sense that lower RMSE results were observed in
323
the post-correction chronologies. The results from Figure 4c were also represented spatially in Figure 1.
324
The greatest degree of post-CID chronology correlation increase with instrumental temperatures was
325
observed in chronologies from the southeastern slope, which predominantly contained growth release
326
trends in the first half of the 20th century. Chronologies showing intermediate improvement were
327
located farther north and included chronologies from the northwestern slope which predominantly
328
contained disturbance related trends in the second half of the 19th century. The least improvement was
329
observed in chronologies from the northwestern (PLOT-1) and northernmost (PLOT-18) investigated
330
locations as well as on the southern ridge (PLOT-6) and in the valley (PLOT-16), with the latter two
331
chronologies exhibiting no late 19th / early 20th century disturbance trends. Supplementary Figure S3
332
highlights in greater detail this broad spatial and temporal split in the pattern of disturbance of the
333
northwest / southeast groups and the very large percentage of trees in each group affected by these
334
two major disturbance events. Individual chronologies developed according to the other sampling
335
14
strategies showed an overall pattern of post-CID improvement similar to the location based (PLOT)
336
assessment (Table 3). The pre-CID and post-CID results from Table 3 along with their respective
337
chronologies are displayed graphically in supplementary Figure S4.
338
[insert Figure 4]
339
The principal component (PC) time-series scores of the dominant modes of variance of the pre-
340
CID dataset are presented in Figure 5a and include three PCs (loadings of the chronologies on each
341
eigenvector are presented in Table 4). PC3 showed the strongest correlation with SIBIU Jun-Jul
342
temperatures (r = 0.45) and PC1 correlated more weakly (r = 0.33), while PC2 was weakly negatively
343
correlated with temperatures (r = -0.24). When compared to the disturbance chronology in Figure 3a, a
344
strong correlation was observed with PC2 (r = 0.91). After CID correction, only two dominant PCs were
345
identified. Although the first PC was uncorrelated with temperatures, a stronger relationship was
346
observed between temperature and PC2 (r = 0.56) than was identified with any of the pre-CID PC scores.
347
Conversely, PC1 significantly correlated with the disturbance chronology (r = 0.50), whereas no
348
correlation was found with PC2.
349
350
[insert Figure 5]
351
352
CHRON.
(SUBSET)
PC1
(PRE-CID)
PC2
(PRE-CID)
PC3
(PRE-CID)
CHRON.
(SUBSET)
PC1
(POST-CID)
PC2
(POST-CID)
PLOT-10
0.911
0.163
0.275
PLOT-1
0.932
0.157
PLOT-5
0.907
0.216
0.168
PLOT-11
0.878
0.358
PLOT-19
0.885
0.302
0.265
PLOT-14
0.875
0.244
PLOT-2
0.826
0.350
0.301
PLOT-19
0.827
0.472
PLOT-1
0.813
0.528
-0.071
PLOT-6
0.791
0.508
PLOT-9
0.741
0.436
0.403
PLOT-10
0.791
0.478
PLOT-11
0.703
0.625
0.160
PLOT-2
0.777
0.530
PLOT-7
0.603
0.460
0.576
PLOT-8
0.772
0.374
PLOT-8
0.414
0.828
0.312
PLOT-5
0.721
0.402
PLOT-14
0.535
0.795
0.156
PLOT-7
0.718
0.601
PLOT-15
0.356
0.761
0.461
PLOT-9
0.714
0.585
PLOT-3
0.377
0.758
0.448
PLOT-16
0.112
0.876
PLOT-4
0.377
0.692
0.536
PLOT-4
0.337
0.858
PLOT-6
0.551
0.652
0.481
PLOT-13
0.367
0.858
PLOT-16
0.121
0.010
0.934
PLOT-17
0.438
0.815
PLOT-12
0.173
0.518
0.803
PLOT-12
0.539
0.788
PLOT-18
0.413
0.337
0.776
PLOT-15
0.523
0.780
PLOT-13
0.138
0.579
0.723
PLOT-3
0.529
0.772
PLOT-17
0.270
0.582
0.710
PLOT-18
0.587
0.635
353
Table 4: Principal Component (PC) Analysis loadings of location-based (PLOT) chronologies before (pre-
354
CID) and after (post-CID) disturbance correction on the dominant eigenvectors (results in bold
355
indicate the strongest loading of each chronology).
356
15
The restricted three site (PLOT3, 7 and 10) correlation response analysis assessing the
357
relationship between pre-CID, post-CID and BI data, with SIBIU temperatures (- Figure 6a) clearly shows
358
disturbance trends in the RW data with various degrees of post-CID improvement. In contrast to the
359
relatively narrow RW seasonal response, the BI chronology responded more strongly to a broader
360
seasonal window displaying highest correlations with mean July-September temperatures (r = 0.65). The
361
response of BI was stronger than post-CID RW with respect to the optimal season of each parameter.
362
Although improvement of the post-CID chronologies (Figures 6b, c and d) was apparent especially
363
before 1880 when the deviation of the pre-CID chronology from the instrumental record was reduced,
364
the degree of improvement was limited, particularly as periods of weaker agreement remained as
365
indicated by running correlations between the pre-/post-CID chronologies and SIBIU temperatures. In
366
contrast, the BI chronologies more closely matched the instrumental trends with running correlations
367
displaying a consistently strong relationship back into the 19th century.
368
[insert Figure 6]
369
370
DISCUSSION
371
Considering the relatively small area of the Calimani study area, it would be reasonable to
372
assume that chronologies developed from the plots would be similar in the absence of disturbance and
373
should therefore also express a very similar climate signal. However, despite the adequate replication of
374
the different chronologies, a range of chronology trends were observed (Figure 2a) expressing
375
substantial differences in correlation with temperature ranging from zero to ~0.5. The possibility of
376
developing a climatically sensitive chronology by randomly choosing and sampling all trees in a specific
377
plot would therefore depend on chance. An alternative approach, which randomly samples trees from
378
the whole stand (Figure 2b), produced a more consistent and uniform outcome, although generally
379
resulting in correlations of only ~0.3 with temperature.
380
A sampling strategy commonly applied for dendroclimatology favours the preferential selection
381
of larger / wider (i.e. higher DBH) and presumed older trees in order to extend a chronology as far back
382
in time as possible. The strong age / DBH relationship (Figure S2), would support this type of reasoning.
383
16
Forming chronologies by grouping series according to DBH, revealed that samples from the largest trees
384
expressed the weakest temperature signal (Figure 2c). Although less clear-cut than the DBH results,
385
there was also a tendency for chronologies composed of samples from old trees to produce a
386
climatically weaker signal. Yet the 1stdifferenced results indicate that there is no fundamental limitation
387
in the ability of older trees to record climatic information and that, at least at high frequencies, the
388
sensitivity of larger trees compared to smaller ones is actually greater. This observation demonstrates
389
that the overall response of trees does not simply weaken with age but is instead related to the
390
presence of disturbance related trends that bias the lower frequency expressed in the data after
391
detrending.
392
It would therefore be reasonable to conclude that the weaker performance of the older (and
393
generally larger) trees at decadal and longer timescales is at least, in part, related to the greater
394
likelihood that older trees will be affected by some disturbance event during their life than younger
395
trees. Although the Figure 2d results represent a common period of analysis in the 20th century,
396
disturbance trends in earlier parts of the older chronologies would still affect the chronology trends in
397
this recent period (i.e. by biasing the fit of the detrending functions). Therefore, without addressing
398
trend biases, sampling the largest (and perhaps oldest) trees will likely produce chronologies with poor
399
climatic sensitivity at decadal and longer timescales. This presents a problem as the oldest trees are also
400
the most valuable for studying longer-term climate. Furthermore, none of these strategies can
401
guarantee a good chronology response in terms of climate signal. We must therefore ask the question,
402
why is this the case, and does a reasonable approach exist for optimizing (maximizing) the climatic
403
potential of the population sample? If disturbance is an important factor influencing climate response,
404
then disturbance correction may be an appropriate strategy to improve calibration.
405
Previous studies have identified wind and windstorm damage as the dominant determinant of
406
large scale severe disturbance in the Romanian Carpathians and to a lesser extent insect outbreaks and
407
snow damage (e.g. Griffiths et al., 2014; Popa, 2008; Svoboda et al., 2014), which would account for the
408
observed synchronous and temporally clustered nature of disturbance (Figure 3a) and the imprinting of
409
disturbance trends in individual RW series on the mean chronologies (Figure 3b). There is also evidence
410
that large scale severe windstorm events can impact the majority of trees over relatively large areas, as
411
17
for example during the 2004 event in the Slovakian Tatra Mountains (Western Carpathians) which
412
affected 12,000 ha of montane forest stands (e.g. Holeksa et al., 2016; Zielonka et al., 2010). The
413
reduced range and more uniform trends expressed in individual PLOT chronologies, which more closely
414
matched the mean (all 760 series) chronology after CID correction in Figure 3c compared to the pre-
415
correction version in Figure 3b (particularly around the most prominent late 19th and early 20th century
416
periods of growth release), suggests that CID correction produced individual PLOT sub-chronologies that
417
more accurately approximate the larger-scale (regional population) chronology.
418
Compared to the lower mean correlation of the unfiltered pre-CID chronologies (Figure 3b, r =
419
0.28), correlations of the unfiltered post-CID chronologies (Figure 3c, r = 0.41) as well as the 1st
420
differenced pre-CID and post-CID chronology versions (r = 0.45 and 0.49 respectively) were all
421
considerably higher. This suggests that the high frequency climate signal in pre-CID chronologies was
422
unaffected by the presence of disturbance trends and that the weaker correlations of the unfiltered pre-
423
CID chronologies were related to the lower frequency trends, which was supported by the substantial
424
degree of unfiltered post-CID correlation improvement (Figure 3c). Furthermore, the long term trend of
425
the post-CID mean (all 760 series) chronology differed when compared to its pre-CID counterpart.
426
Specifically, the most apparent changes included a reduction of index values affected by growth release
427
in the first half of the 20th century and higher values before 1850 after correcting for non-climatic
428
growth suppression trends. Taken together, the above evidence suggests that a disturbance-free
429
chronology may not necessarily be achieved simply by collecting and averaging a very large number of
430
series.
431
The improvement in post-CID chronology running correlations (Figure 3e) against both SIBIU
432
and the longer CEU temperature series as well as the improved visual lower frequency trend agreement
433
with these instrumental records (Figure 3f) suggests that the CID-corrected chronology better
434
represented observed temperature trends. It should be pointed out that although CEU indicated
435
warmer temperature conditions before the mid-19th century than suggested even by the post-CID
436
chronology, early instrumental series (including those in central and eastern Europe) may contain a
437
positive warm bias as a result of measurement practices and the lack of screen use before the mid / late
438
18
19th century (Böhm et al., 2010; Moberg et al., 2003). Hence, it is unclear whether the post-CID
439
chronology indices were still too low or the instrumental record contained an early period warm bias.
440
The correlation and RMSE change results (Figure 4) indicate that, with one exception, all
441
chronologies showed some degree of improvement after CID correction. Specifically, nearly all
442
chronologies exhibited improved agreement (i.e. greater similarity) with the reference SIBIU
443
instrumental temperature series expressed by a correlation increase and reduced RMSE. However, CID
444
correction may not necessarily produce a substantial degree of improvement in all cases. In some
445
instances this may be a result of applying CID to chronologies that already expressed a strong climate
446
signal and did not exhibit any considerable degree of disturbance related trends (e.g. PLOT18 in Figure
447
4). In other cases, where only very limited improvement was observed in weakly correlating
448
chronologies with temperature (e.g. PLOT1 in Figure 4), other unidentified factors (not necessarily
449
related to disturbance) are likely responsible. In general, however, CID correction resulted in climate
450
signal improvement for RW data, which is true, not only for location-based sampling, but also the other
451
sampling strategies (Table 2 and 3). Spatially, it appears that a high severity disturbance event around
452
the 1840s and possibly others in the subsequent decades mainly affected the northern and western
453
slopes, whereas another event around the 1910s mostly affected the eastern slope. We hypothesize
454
that this distinct spatial pattern and segregation of areas affected by disturbance in these two cases may
455
point to windstorms as the most likely disturbance agent and that the spatial configuration of this
456
pattern may be indicative of the spatially distinctive impact of wind disturbance in these two instances.
457
The PC analysis (Figure 5) demonstrates that even extracting the dominant modes of variability
458
as PC scores, will not separate the climatic and non-climatic signals (i.e. this approach does not
459
guarantee best achievable results when the influence of disturbance is present). Though these are the
460
results of a local-scale analysis, it is conceivable that temporally common disturbance trends can be
461
present in chronologies even over a larger region (e.g. due to wind storms or large-scale insect
462
outbreaks). The inability to isolate the climate signal was expressed by the significant correlation of both
463
PC1 and PC3 with temperature, but to a lesser degree also through their correlation with the
464
disturbance chronology, which was mainly represented by PC2. After CID correction, a clearer
465
separation of the climatic and non-climatic signals was achieved with PC analysis as indicated by the
466
19
reduction from three dominant PCs to two and the increased correlation between PC2 and temperature.
467
Importantly, however, though weaker (compared to pre-CID), the influence of the disturbance signal
468
was reduced but not entirely removed by the CID procedure. This may be due to the relatively
469
conservative threshold (3.29 sigma) applied in the identification of release events in order to minimize
470
the likelihood of falsely identifying growth releases that are not disturbance related.
471
The parameter comparison for three sub-chronologies (PLOT 3, 7 and 10) in Figure 6 indicates
472
that BI is not only the strongest temperature proxy but could potentially serve as a disturbance-free
473
parameter, though further investigation in other locations and with additional species would be
474
required to assess whether the decreased susceptibility of this parameter to disturbance is observed
475
more generally. Kaczka and Czajka (2014) noted a similar (stronger than RW) summer temperature
476
response of Norway spruce BI from Babia Góra in southern Poland. The importance of BI (and by
477
extension maximum latewood density) to dendroclimatological research as a parameter that appears
478
generally unaffected (or less affected) by disturbance and with a stronger climate signal is clearly
479
emphasised by the evidence presented here. This may have implications for deriving chronologies free
480
of disturbance with a stronger climatic signal as one possible way to by-pass the undesirable impact of
481
disturbance on tree-ring data in dendroclimatic investigations. Furthermore, comparing RW and BI
482
chronologies may represent an additional approach to the identification of disturbance trends in RW
483
data.
484
A recent study by Rydval et al. (2016) demonstrated that disturbance related to anthropogenic
485
activities (i.e. extensive logging) can induce growth trend biases in RW chronologies. The evidence
486
presented herein demonstrates that natural disturbance can also potentially cause systematic
487
chronology biases within closed-canopy forests. This can occur even if care is taken to select seemingly
488
undisturbed sites as any evidence of disturbance occurring in the past (i.e. multiple decades or centuries
489
ago) may have been erased from the landscape and may therefore no longer be visible at the time of
490
sampling. By examining a very large number of samples, highly representative of the full stand
491
population in this study, it is clear that the strength of the climate signal expressed in a chronology from
492
a particular location can vary extensively and no sampling strategy can reliably ensure that the
493
chronology produced from any set of collected RW samples will contain a well expressed climatic signal
494
20
(i.e. the best achievable climate signal in RW data from a particular area). The development of
495
chronologies which express a sufficiently strong common population signal (i.e. assessed using the
496
widely applied EPS metric) can result in chronologies poorly correlated with climate even when the
497
relationship between climate and chronologies from other sets of samples from the same area is
498
considerably stronger. This can arise when non-climatic trends occur synchronously in those samples
499
that make up a chronology.
500
The presupposition that collecting a large number of samples and avoiding disturbance-affected
501
sampling locations can alleviate disturbance related biases in chronologies may be misleading because
502
large-scale disturbances can affect whole stands and presumably even many stands in a region (e.g. due
503
to wind disturbance or large-scale insect outbreaks). Nehrbass-Ahles (2014) performed an evaluation of
504
sampling strategies, although it mainly assessed chronologies based on various sampling techniques in
505
relation to the ‘full population’ and was also conducted in a managed stand that did not in fact display
506
much climatic sensitivity. Such an approach, however, implicitly assumes that the population itself is
507
unbiased in relation to its representation of the climate signal. Here we have demonstrated that the
508
assumption of an unbiased population may not be justified. Evaluating chronologies in relation to the
509
population (or rather a very large sample of the population) may therefore not represent a sound
510
strategy in some cases as the possible influence of disturbance should also be taken into account. This
511
finding provides some support for adopting strategies such as the careful selection (or screening) of
512
samples at the local site level, or chronologies on the multi-site network scale, by assessing their climatic
513
sensitivity in order to avoid including samples or chronologies significantly affected by disturbance in
514
dendroclimatic analyses. Such screening practices have already been commonly applied in the
515
development of reconstructions from large scale networks (e.g. Cook et al., 2013; Ljungqvist et al.,
516
2016). Nevertheless, the use of methods such as CID may be preferable as this can reduce the risk of
517
potential subjectivity and perhaps even expand the range of useable chronologies which may otherwise
518
be deemed unsuitable for dendroclimatic analysis.
519
Although this study demonstrates this issue only at a single location, there is potential for
520
systematic disturbance to affect RW chronologies in virtually any closed canopy forest ecosystem and
521
such a possibility cannot be dismissed a priori. The issues highlighted and discussed here may for
522
21
example directly affect calibration strength of reconstructions as well as the possibility of making
523
inaccurate inferences about past climatic conditions from RW-based reconstructions that may include
524
disturbance related biases. It is important to be able to perform some assessment of possible
525
disturbance effects on RW chronologies because assessing the fidelity of reconstructed climate
526
estimates before the instrumental period is difficult. We therefore recommend that all future
527
dendrochronological studies investigating medium to low frequency climatic trends should perform
528
some form of disturbance assessment and that the CID method (Druckenbrod et al., 2013; Rydval et al.,
529
2016) represents a reasonable approach.
530
531
CONCLUSION
532
In this study, we have demonstrated that natural disturbance events can act as agents which
533
significantly and systematically affect tree growth, subsequently biasing mid- to long-term RW
534
chronology trends. These disturbance trends cannot be removed using conventional detrending
535
approaches without also removing lower frequency climatic information. In closed canopy forests, the
536
oldest (and dendroclimatologically most valuable) trees are more likely to contain an embedded
537
disturbance response. It is not possible to ensure that this response can be factored out or minimized
538
simply by adopting a subjective sampling strategy or relying on a very large sample size (with respect to
539
both trees and sites). Furthermore, sampling trees across a landscape may produce a record with a
540
complex range of disturbance histories rather than reducing the disturbance signals. This important
541
finding highlights the need to develop site selection and sampling approaches for closed-canopy forests
542
that are very different from those developed by Fritts (1976) for open-canopy forests. More specifically,
543
it is imperative to develop better methods to disentangle disturbance and climate signals.
544
Disturbance detection techniques could be used, at a minimum, to identify and assess the
545
effects of disturbance on RW chronologies and (if replication permits) exclude subsets substantially
546
affected by such trends which would therefore represent a poorer expression of longer term climatic
547
variability. This also provides justification for the application of approaches such as data screening in
548
order to exclude subsets of larger datasets, which are weakly correlated with climate, from climatic
549
22
analyses. An alternative approach would include the utilization of some sort of disturbance correction
550
procedure (e.g. CID) to improve the expression of the climate signal in disturbance affected RW series.
551
Finally, other tree-ring parameters, such as BI (or maximum latewood density), which may be less prone
552
to the effects of disturbance and often express a stronger climate signal than RW (Wilson et al. 2016),
553
could also be developed.
554
The findings of this study are broadly applicable and of relevance to RW chronologies from
555
closed canopy stands. Additional larger scale investigations including various species from other
556
locations would be beneficial in assessing the relevance of our findings. Certainly, consideration should
557
be given to the possibility of disturbance related trends affecting medium to low frequency growth
558
trends in RW chronologies. We therefore recommend that some form of evaluation of this potential
559
effect should be performed as part of any dendrochronological research utilizing RW data to investigate
560
climatic trends as it may be possible to reduce this limitation and improve the expression of the climate
561
signal in such data.
562
563
564
ACKNOWLEDGEMENTS
565
The study was supported by the institutional project MSMT (CZ.02.1.01/0.0/0.0/16_019/0000803) and
566
the Czech Ministry of Education (Project INTER-COST no. LCT17055). We thank the Călimani National
567
Park authorities, especially E. Cenuşă and local foresters, for administrative support and assistance in
568
the field.
569
570
571
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572
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573
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713
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716
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717
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718
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719
31–42.
720
29
721
722
723
Figure 1: Site location and approximate distribution of sampling plots in Calimani National Park,
724
Romania. Red shading represents post-disturbance correction correlation increase* of plot-
725
based (PLOT) chronologies (see Table 1 for details) against June-July mean instrumental
726
temperatures for the full length of chronologies – same representation as Figure 4C. (*note
727
that chronology PLOT-16 shows a slight correlation decrease after disturbance correction).
728
729
730
731
732
733
734
735
736
737
738
739
740
741
30
742
743
744
745
746
747
748
749
Figure 2: Chronology plots and correlations with Jun-Jul mean temperatures from Sibiu for four
750
‘sampling’ methods including grouping according to (A) sample location (PLOT), (B) random
751
sample selection (RAN), (C) diameter at breast height (DBH) (D) and recruitment age (AGE) –
752
see Table 1 for additional details. Each chronology was truncated in the year where expressed
753
population signal dropped below 0.85. (pre-CID indicates that chronologies were developed
754
with series before correcting for disturbance trends using the Curve Intervention Detection
755
method)
756
31
757
Figure 3: (A) Summary of Calimani disturbance history from Curve Intervention Detection (CID) analysis;
758
(B) chronologies before disturbance correction (pre-CID) and (C) after disturbance correction
759
(post-CID) and (D) pre-CID/post-CID chronologies with Jun-Jul temperatures from Sibiu (SIBIU)
760
and the longer central/east Europe (CEU) Jun-Jul regional composite temperature series; (E)
761
51-year running correlations between instrumental and ring-width chronologies in (D); (F) as
762
in (D) except smoothed with a 20 year low-pass Gaussian filter.
763
32
764
765
Figure 4: Comparing the (A, C) change in correlation and (B, D) root-mean-square error change of
766
Calimani plot-based (PLOT) chronologies before disturbance correction (pre-CID) vs. after
767
disturbance correction (post-CID) in relation to instrumental temperature data from Sibiu for
768
the (A, B) 1909-2009 period and (C, D) full chronology length (max. back to 1851). (The green
769
colour in A and C indicates the size of the correlation increase after disturbance correction
770
whereas red colour (only PLOT16) indicates a correlation decrease.)
771
33
772
773
Figure 5: Amplitudes of the dominant principal components (PCs) from chronologies developed (A)
774
before disturbance correction (pre-CID) and (B) after disturbance correction (post-CID), and
775
their correlation with instrumental temperatures from Sibiu and the disturbance chronology
776
in Figure 3A. (Scatterplots of significant relationships (p < 0.01) between the PCs and the
777
disturbance chronology / Sibiu temperatures are represented in supplementary figure S5).
778
34
779
Figure 6: Comparison of the PLOT-3, PLOT-7 and PLOT-10 blue intensity (BI) and ring width (RW)
780
chronologies developed before (pre-CID) and after (post-CID) disturbance correction with
781
instrumental temperatures from Sibiu (SIBIU) over the 1851-2009 period showing (A) the
782
combined correlation response of the Calimani chronologies against SIBIU temperatures; and
783
the time-series of the RW and BI chronologies together with Jun-Jul and Apr-Sep SIBIU mean
784
temperature respectively for (B) PLOT-3, (C) PLOT-7 and (D) PLOT-10. (Highlighted periods
785
indicate where expressed population signal is < 0.85.)
786
35
Supplementary figures
787
788
789
790
Figure S1: Correlation response of chronologies composed of all 760 series from Calimani (PLOT-all)
791
before (pre-CID) and after (post-CID) disturbance correction against mean monthly and
792
seasonal temperatures from Sibiu for the 1851-2011 period.
793
794
795
796
797
798
799
Figure S2: Relationship between estimated tree age and diameter at breast height (DBH).
800
801
802
803
804
805
36
806
Figure S3: Summary of Calimani disturbance history from Curve Intervention Detection (CID) analysis (A)
807
using series from plots from the northwest part of the stand (Figure 1 - PLOT 1, 2 , 5, 6, 7,
808
10, 11, 18, 19) predominantly affected by disturbance in the mid-19th century and (B) from
809
the southeast part for the stand (Figure 1 – PLOT 3, 4, 8, 9, 12, 13, 14, 15, 16, 17)
810
predominantly affected by disturbance in the early 20th century. The before disturbance
811
correction (pre-CID) and after disturbance correction (post-CID) chronologies of these two
812
spatial groups are presented in (C) and (D) respectively.
813
37
814
815
816
817
818
819
Figure S4: Before disturbance correction (pre-CID) and after disturbance correction (post-CID)
820
chronology plots and correlations with Jun-Jul mean temperatures from Sibiu for four
821
‘sampling’ methods including grouping according to (A) sample location (PLOT), (B) random
822
sample selection (RAN), (C) diameter at breast height (DBH) (D) and recruitment age (AGE) –
823
see Table 1 for additional details. Each chronology was truncated in the year where
824
expressed population signal dropped below 0.85.
825
826
827
828
829
830
831
832
38
833
Figure S4 – continued
834
835
836
837
838
839
840
841
842
843
844
845
846
847
848
849
39
850
Figure S4 – continued
851
852
853
854
855
856
857
858
859
860
861
862
863
864
865
866
40
867
Figure S4 – continued
868
869
870
871
872
873
874
875
876
877
878
879
880
881
882
883
41
884
885
Figure S5: Scatterplots of significant relationships (p < 0.01) between the disturbance chronology in
886
Figure 3A / Jun-July average Sibiu temperatures and amplitudes of the dominant principal
887
components (PCs) from chronologies developed before disturbance correction (pre-CID) and
888
after disturbance correction (post-CID).
889
890
891
892
893
42
Curve Intervention Detection (CID) Matlab code
894
895
function [ymn,varyh,df,w,ybar,se]=bisqmean_CID(y)
896
%
897
% Biweight mean for a vector of numbers.
898
% Last revised 2011-7-09
899
% Revised by Daniel Druckenbrod 2012-1-11
900
%
901
% Source: Mosteller and Tukey (1977, p. 205, p 351-352)
902
% Cook and Kairiukstis (1990, p. 125-126)
903
%
904
%
905
%**************** INPUT *************************
906
%
907
% y (? x 1)r vector of data -- say, indices for ? cores in a year
908
%
909
%
910
%******************** OUTPUT ************************
911
%
912
% ymn (1 x 1)r biweight mean
913
% varyh (1 x 1)r asymptotic standard dev of biweight mean - p. 208,
914
% third eqn from top of page
915
% df (1x1)r degrees of freedom
916
% w (? x 1)r final weights on values in y
917
% ybar (1 x 1)r arithmetic mean corresponding to ymn
918
% se (1 x 1)r standard error of ybar
919
%
920
%******************** NOTES *********************
921
%
922
% ybar and se just included in debugging to double check
923
% on closeness of ybar to ymn, se to sqrt(varyh)
924
%
925
%*******************************************************************
926
927
928
sens = 0.001; % hard coded theshold of sensitivity for stopping
929
iterat
930
nits = 100; % max number of allowed iterations
931
932
[n,ny]=size(y);
933
if ny > 1;
934
error('y should be a vector')
935
end
936
937
if any(isnan(y));
938
error('y not permitted to have NaNs');
939
end;
940
941
if n<6; % if fewer than 6 sample size, use median
942
ymn = median(y);
943
w=[];
944
ybar=mean(y);
945
se= sqrt(var(y)/n); % standard error of mean
946
df=[];
947
varyh=NaN;
948
return;
949
end;
950
951
952
953
43
ww = 1/n; % weight for even average
954
ybar = mean(y); % arith mean
955
%ybar=median(y);
956
se= sqrt(var(y)/n); % standard error of mean
957
958
nz=0;
959
ymn = ybar; % initial biweight mean as arith mean
960
961
for i = 1: nits; % iterate max of nits times
962
ymnold = ymn; % store old value of mean
963
e = y-ymn; % deviations from mean
964
S = median(abs(e)); % median abs deviation
965
u = e / (6*S); % scaled deviations
966
967
w = (1 - u.^2).^2; % compute weights
968
L1 = abs(u)>=1; % flag huge errors
969
L1s = sum(L1);
970
if L1s>0
971
nz=0;
972
nz= nz(ones(L1s,1),:);
973
w(L1)=nz; % set weights on those obs to zero
974
end
975
w = w / sum(w); % adjust weights to sum to 1.0
976
977
ymn = sum(w .* y); % compute biweight mean
978
979
980
% Variance of estimate of biweight mean
981
ui= e / (9*S);
982
L2 = ui>1;
983
ui(L2)=[];
984
z =y(~L2);
985
nz = length(z);
986
nom1 = (z - ymn) .^2;
987
nom2 = (1-ui .^2) .^4;
988
nom = sum(nom1 .* nom2);
989
990
den1 = sum((1-ui .^2) .* (1-5*ui .^2));
991
992
varyh_hoaglin=(n^0.5)*(nom^0.5)/den1; % Dan: p. 417 3rd equation
993
den2 = -1 + sum ((1-ui .^2) .* (1-5*ui .^2));
994
% varyh = nom / (den1*den2); % variance of biweight mean
995
% last eqn, p. 208
996
997
varyh = n^.5*nom^.5 / ((den1*den2)^.5); % Dan: p.417 Kafadar
998
approach
999
1000
df = 0.7 * (nz -1); % degrees of freedom
1001
1002
1003
% if little change in mean, exit loop
1004
if abs (ymn - ymnold) < sens
1005
return
1006
end
1007
end
1008
1009
1010
1011
1012
44
% hugershoff.m
1013
% This function fits a tree ring time series to the growth trend
1014
equation
1015
% developed by Warren (1980) TRR.
1016
1017
% Function written Nov 12, 2013.
1018
% Function last revised Nov 12, 2013.
1019
1020
function qq = hugershoff(beta,x)
1021
1022
% Assign parameters from beta vector.
1023
a=beta(1);
1024
b=beta(2);
1025
c=beta(3);
1026
k=beta(4);
1027
qq=a*((x).^b).*exp(-c*(x))+k;
1028
% qq=a*((x+1).^b).*exp(-c*(x+1))+k;
1029
%q=log(a)+b*log(x)%-c*x;
1030
%qq=exp(
1031
1032
1033
1034
1035
1036
1037
1038
1039
1040
1041
1042
1043
1044
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1046
1047
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1058
1059
1060
1061
1062
1063
1064
1065
1066
1067
1068
1069
1070
45
% nonlinear_exp.m
1071
% This function fits a tree ring time series to the non-linear
1072
% equation used by Ed Cook in his ARSTAN program.
1073
1074
% Function written Jan 12, 2004.
1075
% Function last revised Jan 29, 2004.
1076
1077
function qq = nonlinear_exp(beta,x)
1078
1079
% Assign parameters from beta vector.
1080
a=beta(1);
1081
b=beta(2);
1082
d=beta(3);
1083
qq = a*exp(-b*x)+d;
1084
1085
1086
1087
1088
1089
1090
1091
1092
1093
1094
1095
1096
1097
1098
1099
1100
1101
1102
1103
1104
1105
1106
1107
1108
1109
1110
1111
1112
1113
1114
1115
1116
1117
1118
1119
1120
1121
1122
1123
1124
1125
1126
1127
46
% ringwidth_import_999.m
1128
% This function imports decadal format tree ring data for manipulation
1129
% as a matrix in Matlab. The number of header lines must be specified
1130
% as an input by the user. The end of each series must be flagged
1131
% with 999. Measurements are stored as one hundreth of a
1132
% millimeter. The filename can either be specified as an input or
1133
% found using a gui. The LAST LINE of the input text file must also
1134
% be blank!
1135
1136
% Function written Mar 4, 2004.
1137
% Function last revised May 24, 2012.
1138
1139
function [col_header,rings]=ringwidth_import_999(header,varagin)
1140
1141
if nargin==1
1142
[filename,path]=uigetfile('*.txt','Select ".txt" file');
1143
elseif nargin==2
1144
filename=varagin;
1145
else
1146
disp('Too many parameters entered (DLD).')
1147
end
1148
1149
% Read in header lines
1150
headers=textread(filename, '%q',10)';
1151
% disp([headers]) % Display 1st 10 words as screen output.
1152
[label yr y0 y1 y2 y3 y4 y5 y6 y7 y8 y9]=...
1153
textread(filename,...
1154
'%8s %4d %5d %5d %5d %5d %5d %5d %5d %5d %5d %5d',...
1155
'headerlines',header);
1156
% Place decadal format widths into one matrix
1157
widths=[y0 y1 y2 y3 y4 y5 y6 y7 y8 y9];
1158
1159
% Extract unique labels of each core.
1160
importedrows=length(label);
1161
a=1;b=1;
1162
while(a<=importedrows)
1163
core(b)=label(a);
1164
corestr(:,b)=strcmp(label(a),label);
1165
a=max(find(corestr(:,b)==1))+1;
1166
b=b+1;
1167
end
1168
1169
% Find range of years over all cores and set as col 1 in rings.
1170
% As it is difficult to know how many years are in the last row
1171
% of measurments for a core, assume that the last decade has 10
1172
% measurements.
1173
rings=(min(yr):(max(yr)+10))';
1174
1175
% Transfer widths into vectors by core
1176
for i=1:length(core)
1177
core_rows=find(corestr(:,i));
1178
core_yr=yr(core_rows);
1179
core_widths=widths(core_rows,:);
1180
% Find # of measurements in a row and assign to vector series.
1181
k=1;series=0;
1182
for j=1:length(core_rows)
1183
% Look for end of series flag
1184
flag=find(core_widths(j,:)==999);
1185
if flag>0
1186
msmts=flag-1;
1187
47
elseif (ceil(core_yr(j)/10)*10)-core_yr(j)==0
1188
msmts=10;
1189
else
1190
msmts=(ceil(core_yr(j)/10)*10)-core_yr(j);
1191
end
1192
series(k:(k+msmts-1))=core_widths(j,(1:msmts));
1193
k=msmts+k;
1194
1195
end
1196
% Determine start and end of series
1197
sos=find(rings(:,1)==min(core_yr));
1198
length(series)+sos-1;
1199
eos=length(series)+sos-1;
1200
% Assign series to output matrix and convert to 1/1000th of a mm
1201
rings(sos:eos,i+1)=(series./100)';
1202
1203
1204
% Remove 999 from end of series
1205
% for j=1:length(rings(1,:))
1206
% for k=1:length(rings(:,1))
1207
% if rings(k,j)==-99.99
1208
% rings(k,j)=0;
1209
% end
1210
% end
1211
% end
1212
1213
1214
end
1215
% Construct column headers
1216
col_header(2:(length(core)+1))=core;
1217
col_header(1)={'Year'};
1218
1219
1220
1221
1222
1223
1224
1225
1226
1227
1228
1229
1230
1231
1232
1233
1234
1235
1236
1237
1238
1239
1240
1241
1242
1243
1244
1245
48
% ringwidth_import_9999.m
1246
% This function imports decadal format tree ring data for manipulation
1247
% as a matrix in Matlab. The number of header lines must be specified
1248
% as an input by the user. The end of each series must be flagged
1249
% with -9999. Measurements are stored as one thousandth of a
1250
% millimeter. The filename can either be specified as an input or
1251
% found using a gui. The LAST LINE of the input text file must also
1252
% be blank!
1253
1254
% Function written Mar 4, 2004.
1255
% Function last revised May 24, 2012.
1256
1257
function [col_header,rings,flag]=ringwidth_import_9999(header,varagin)
1258
1259
if nargin==1
1260
[filename,path]=uigetfile('*.txt','Select ".txt" file');
1261
elseif nargin==2
1262
filename=varagin;
1263
else
1264
disp('Too many parameters entered (DLD).')
1265
end
1266
1267
% Read in header lines
1268
headers=textread(filename, '%q',10)';
1269
% disp([headers]) % Display 1st 10 words as screen output.
1270
[label yr y0 y1 y2 y3 y4 y5 y6 y7 y8 y9]=...
1271
textread(filename,...
1272
'%8s %4d %5d %5d %5d %5d %5d %5d %5d %5d %5d %5d',...
1273
'headerlines',header);
1274
% Place decadal format widths into one matrix
1275
widths=[y0 y1 y2 y3 y4 y5 y6 y7 y8 y9];
1276
1277
% Extract unique labels of each core.
1278
importedrows=length(label);
1279
a=1;b=1;
1280
while(a<=importedrows)
1281
core(b)=label(a);
1282
corestr(:,b)=strcmp(label(a),label);
1283
a=max(find(corestr(:,b)==1))+1;
1284
b=b+1;
1285
end
1286
1287
% Find range of years over all cores and set as col 1 in rings.
1288
% As it is difficult to know how many years are in the last row
1289
% of measurments for a core, assume that the last decade has 10
1290
% measurements.
1291
rings=(min(yr):(max(yr)+10))';
1292
1293
% Transfer widths into vectors by core
1294
for i=1:length(core)
1295
core_rows=find(corestr(:,i));
1296
core_yr=yr(core_rows);
1297
core_widths=widths(core_rows,:);
1298
% Find # of measurements in a row and assign to vector series.
1299
k=1;series=0;
1300
for j=1:length(core_rows)
1301
% Look for end of series flag
1302
flag=find(core_widths(j,:)==-9999);
1303
if flag>0
1304
msmts=flag-1;
1305
49
elseif (ceil(core_yr(j)/10)*10)-core_yr(j)==0
1306
msmts=10;
1307
else
1308
msmts=(ceil(core_yr(j)/10)*10)-core_yr(j);
1309
end
1310
series(k:(k+msmts-1))=core_widths(j,(1:msmts));
1311
k=msmts+k;
1312
end
1313
% Determine start and end of series
1314
sos=find(rings(:,1)==min(core_yr));
1315
length(series)+sos-1;
1316
eos=length(series)+sos-1;
1317
% Assign series to output matrix and convert to 1/1000th of a mm
1318
rings(sos:eos,i+1)=(series./1000)';
1319
end
1320
% Construct column headers
1321
col_header(2:(length(core)+1))=core;
1322
col_header(1)={'Year'};
1323
1324
1325
1326
1327
1328
1329
1330
1331
1332
1333
1334
1335
1336
1337
1338
1339
1340
1341
1342
1343
1344
1345
1346
1347
1348
1349
1350
1351
1352
1353
1354
1355
1356
1357
1358
1359
1360
1361
1362
1363
50
% v105pn.m
1364
% This function extracts a single tree-ring time series from
1365
% ringwidth_import.m and places it in a vector for time series
1366
analysis.
1367
% The ‘filename’ used to load tree-ring data for processing should
1368
refer to
1369
% the file containing data imported using the function
1370
ringwidth_import.m.
1371
% Following the approach used in ARSTAN (Ed Cook, Columbia
1372
University),
1373
% the function power transforms and removes the mean to create
1374
transformed
1375
% residuals. The function then detrends with an iterative neg.
1376
exponential
1377
% fit, or if that does not fit or fails to find a solution, then a
1378
linear
1379
% regression with either a positive or negative slope is fit to the
1380
data.
1381
% Using the maximum entropy model solution otherwise known as the Burg
1382
% method, the autoregressive model that is the best fit for the series
1383
is
1384
% determined. Using the best fit model, the function searches for
1385
% autoregressive outliers iteratively. These outliers may either be
1386
pulse
1387
% events (1 yr) or CSTs (> minimum no. of yrs). After the first pass,
1388
% the outliers are removed and the series is reconstituted. The best
1389
ar
1390
% order is then redetermined and the function searches for additional
1391
% outliers. The # of iterations is set by the user (8 should be
1392
enough).
1393
% This version uses a power transformation to minimize
1394
% the heteroscedastic nature of my time series. 'fig' is a flag that
1395
% specifies whether you want a figure (=1) or not (=0). Missing years
1396
are
1397
% set to the average of neighboring rings. The central limit theorem
1398
% is used to search the residuals for trend outliers. This version
1399
also
1400
% uses David Meko's (University of Arizona) biweight mean code and
1401
% currently runs with a window of 9 to 30 yrs. Estimated values for
1402
% missing rinngs are removed in the output series. This version uses
1403
a
1404
% modified Hugershoff curve with a potentially nonzero asymptote to
1405
% detrend + and - disturbance events. It also returns the transformed
1406
% standardized series.
1407
1408
% Function written Sep 10, 2002.
1409
% Function last revised Jun 6, 2014.
1410
1411
function [YEARS,transformed,detrended,St,Str,Dtr,Atr,age,outs]=...
1412
v105pn(core,fig,iter)
1413
global PARAM; PARAM=0; % vector of parameters for best order AR model.
1414
global ORDER; ORDER=0; % best order of AR model determined by AIC.
1415
global YEARS; YEARS=0; % calendar years of tree growth from datafile
1416
1417
% Load tree-ring data (returns vars *col_header* and *rings*)
1418
load filename.mat %Insert filename here
1419
1420
% Find pointer to start and end of series
1421
sos=find(rings(:,(core+1))>0, 1);
1422
eos=find(rings(:,(core+1))>0, 1, 'last');
1423
1424
51
% Assign years and raw widths to respective vectors.
1425
YEARS=rings(sos:eos,1);
1426
raw=rings(sos:eos,core+1);
1427
1428
disp(['Core: ' char(col_header(core+1))])
1429
nyrs=length(YEARS);
1430
disp(['Total no. of measured years: ' int2str(nyrs)])
1431
disp(['First year is ' num2str(YEARS(1))])
1432
disp(['Last year is ' num2str(YEARS(nyrs))])
1433
1434
% Estimate missing ring widths using mean of neighboring rings
1435
mss=NaN(length(raw),1);
1436
1437
if find(raw==0)
1438
m1=find(raw==0);
1439
disp(['Missing rings at years ' num2str([YEARS(m1)'])])
1440
for nm=1:length(m1)
1441
prior=mean(raw(find(raw(1:m1(nm)),1,'last')));
1442
subs=mean(raw(find(raw(m1(nm):length(raw)),1,'first')+m1(nm)-
1443
1));
1444
mss(m1(nm))=mean([prior subs]);
1445
end
1446
raw=nansum([raw mss],2);
1447
end
1448
1449
% Power transformation.
1450
fdiff=0;
1451
for x=1:(length(YEARS)-1) % Calculate 1st differences
1452
fdiff(x,1)=raw(x+1);
1453
fdiff(x,2)=abs(raw(x+1)-raw(x));
1454
end
1455
1456
s=1;
1457
for q=1:(length(YEARS)-1)
1458
if (fdiff(q,1)~=0) && (fdiff(q,2)~=0)
1459
nz_fdiff(s,:)=fdiff(q,1:2);% non-zero ring widths
1460
s=s+1;
1461
end
1462
end
1463
log_fdiff=[log(nz_fdiff(:,1)) log(nz_fdiff(:,2))];
1464
1465
X=[ones(length(log_fdiff(:,1)),1) log_fdiff(:,1)];
1466
bb = regress(log_fdiff(:,2), X);
1467
optimal_line = bb(2)*log_fdiff(:,1)+bb(1);
1468
1469
optimal_pwr = 1-bb(2);
1470
disp(['Optimal Power = ' num2str(optimal_pwr)])
1471
if optimal_pwr <= 0.05
1472
transformed=log10(raw);
1473
tzero=log10(0.001);
1474
disp('Series was log10 transformed')
1475
elseif optimal_pwr>1
1476
optimal_pwr=1;
1477
transformed=(raw.^(optimal_pwr));
1478
tzero=0.001.^(optimal_pwr);
1479
disp('Series was power transformed with power =1')
1480
else
1481
transformed=(raw.^(optimal_pwr));
1482
disp(['Series was power transformed with power = ' ...
1483
num2str(optimal_pwr)])
1484
52
tzero=0.001.^(optimal_pwr);
1485
end
1486
transm=mean(transformed);
1487
1488
% Nonlinear detrending option.
1489
% Function nlinfit employs nonlinear least squares data fitting by the
1490
% Gauss-Newton Method.
1491
crashed=zeros(nyrs,1);
1492
wlngth=zeros(nyrs,1);
1493
trendtype=0; % Neg exp = 1, neg linear reg = 2, or pos linear reg = 3
1494
minyr=30; % minimum # of yrs to fit to nlinfit
1495
if minyr>nyrs
1496
disp('Insufficient # of years to fit minimum nonlinear age
1497
trend.')
1498
end
1499
b=zeros(nyrs,3);
1500
mse=NaN(nyrs,1);
1501
warning off
1502
for i=minyr:nyrs
1503
try
1504
lastwarn('')
1505
beta = [.5 .1 1];
1506
xyrs = 1:i; % set years from 1 to length of series
1507
[b(i,1:3),~,~,~,mse(i)]=nlinfit(...
1508
xyrs(1:i),transformed(1:i)','nonlinear_exp',beta);
1509
crashed(i)=1;
1510
msgstr = lastwarn;
1511
wlngth(i)=length(msgstr);
1512
catch % Stops code from crashing because of problems fitting exp
1513
curve
1514
crashed(i)=2;
1515
end
1516
end
1517
warning on
1518
i_c=0;
1519
1520
% Dissallow curve to be concave up and make sure nlinfit
1521
% converges by making b(2) sufficiently large.
1522
% constant b(3) must be >=0 in original mm
1523
i_c=find(crashed==1 & b(:,1)>=0 & b(:,2)>0.001 & b(:,3)>=tzero &
1524
wlngth==0);% & b(:,2)<0.5);
1525
[mmse,imse]=min(mse(i_c));
1526
1527
if fig==1 % fig=1 if you want a figure as output
1528
figure('Position', [10 150 600 600])
1529
subplot(3,1,1)
1530
plot(YEARS,raw,'k','LineWidth',2)
1531
ylabel('\bf Ring width (mm)')
1532
fig1atext = {['Optimal power = ', num2str(optimal_pwr,4)]};
1533
text(range(YEARS)/3+YEARS(1), max(raw)/1.2,fig1atext)
1534
end
1535
1536
if i_c(imse)>0
1537
disp(['Lowest error from fit = ' num2str(mmse)])
1538
disp(['Best age trend fit from years ' num2str(YEARS(1)) ' to '
1539
...
1540
num2str(YEARS(i_c(imse)))])
1541
disp(['Best fit extends for ' num2str(i_c(imse)) ' years'])
1542
best=b(i_c(imse),:);
1543
1544
trendtype=1;
1545