Elsevier

Dendrochronologia

Volume 48, April 2018, Pages 52-73
Dendrochronologia

A comparison of some simple methods used to detect unstable temperature responses in tree-ring chronologies

https://doi.org/10.1016/j.dendro.2018.02.002Get rights and content

Abstract

Temporal stability of the relationship between a potential proxy climate record and the climate record itself is the foundation of palaeoproxy reconstructions of past climate variability. Dendroclimatologists have spent considerable effort exploring the issue of temporal instability of temperature records at high-latitude and −altitude Northern Hemisphere sites. Much of this work has focused on the Divergence Problem in which the modern ends of tree-ring chronologies exhibit pronounced departures from the climate-proxy relationships of preceding decades. However, there has been little scrutiny of how different methods might influence determinations of temporal instability at either the local scale or across broader spatial domains. Here we use four sets of Southern Hemisphere (SH) chronologies and three sets of synthetic data with known interventions to compare four methodologies that have been widely used to assess the temporal stability of relationships between tree-ring series and climate. Our analyses demonstrate that a determination of temporal instability may be partially dependent on method used to examine data, that some methods are more sensitive to standardisation choice than others, and that all methods are better at detecting high- rather than low-frequency instability. In all cases, the relatively modest strength of the relationships between the selected SH ring-width chronologies and temperature is likely to be an issue, especially if changes in trends are of interest. We recommend that robust assessment of temporal instability between tree-ring chronologies and observational climate data should use a range of methods and that unstable temporal relationships across space be carefully considered in the context of large climate field reconstructions.

Introduction

Uniformitarianism is one of the bedrock principles of palaeoclimatology. It states that relationships between the climate and climate-recording proxies are stable over time. Temporal instability in proxy-climate relationships would undermine long-term extrapolation of climate from proxy records to pre-observation periods. This applies not only to the proxy-climate relationships at the local level, but also to broader regional reconstructions. It is, therefore, a concern that in recent years a number of tree-ring studies have reported temporal instability in the relationship between tree growth and temperature. Some of this reported instability has been short-lived and occurred early in the 20th Century (e.g., Schneider et al., 2014). However, the overwhelming majority of these studies indicate an apparent divergence between climate records and tree-ring chronologies in recent decades at high-altitude or high-latitude locations. This ‘modern-end’ phenomenon has largely become encapsulated in the “Divergence Problem” (DP) debate (e.g., Jacoby and D’Arrigo, 1995; Briffa et al., 2004; Wilson and Luckman, 2002; Carrer and Urbinati, 2006; Frank et al., 2007; Wilson et al., 2007; D’Arrigo et al., 2008; Esper and Frank, 2009; Esper et al., 2010; Büntgen et al., 2012). In particular, these studies have commonly shown that observed temperatures appear to be increasing faster than changes in measured tree-ring parameters (i.e., ring width or density). Two types of divergence have been described in the literature. A sufficiently large and significant divergence in trend (i.e., low frequency divergence) in the calibration period can result in a reconstruction model that either under- or over-estimates the relationship between the climate target and the climate proxy outside the calibration period. Less discussed in the literature is divergence at the interannual scale (i.e., high-frequency divergence), which may prevent verification of a calibrated model (D’Arrigo et al., 2008). Many studies of the DP do not explicitly identify whether any observed occurrence of divergence is low or high frequency in nature, although low-frequency is often implied (Appendix A).

Decoupling between a chronology and climate was first discussed in relation to forest decline in North America in the 1970s and 80 s (Visser, 1986; Cook et al., 1987, Downing and McLaughlin, 1987; Cook and Johnson, 1989; Van Deusen, 1990). However, subsequent concerns about its impact on temperature reconstructions initiated extensive interrogation of key millennial-length tree-ring chronologies in the Northern Hemisphere (NH) with strong temperature signals (often based on maximum density rather than ring-width chronologies) for its occurrence (e.g., Briffa et al., 2004; Wilson et al., 2007; Esper et al., 2010; Anchukaitis et al., 2013). Discussions of the potential drivers of temporal instability have focussed on the modern end phenomenon. Proposed explanations have included inappropriate standardisation, global dimming, changes in growth-limiting factors, differential responses to maximum and minimum temperature when mean temperature is the target, local pollution, and changes in ozone concentration (D’Arrigo et al., 2008 and references therein). Changes in limiting factors (e.g., from temperature to precipitation or drought stress) or threshold effects have been widely suggested as the primary reason for recent divergence (Appendix A). Another possibility, and one that is not necessarily limited to the modern end of series, lies with problems in the climate data such as sparse coverage, fewer stations and poorer quality data back in time, or station inhomogeneities (Büntgen et al., 2006a, ; Allen et al., 2014).

Numerous studies have also pointed to the role of inappropriate standardisation of tree-ring chronologies as an important contributing factor to the DP (Esper and Frank, 2009; Esper et al., 2010; Büntgen et al., 2008; Linderholm et al., 2010; Andreu-Hayles et al., 2011a; Anchukaitis et al., 2013; Briffa et al., 2013). While a variety of standardisation approaches have been used in studies that identified divergence as an issue, few have explored the role of the standardisation choice on the presence divergence (Appendix A). Of these studies, three have specifically undertaken rigorous examination of how different standardisation methods may bias chronologies. Anchukaitis et al. (2013) implemented different standardisation choices on a set of pseudo-proxy data and both Briffa and Melvin (2011) and Briffa et al. (2013) examined the impact of different applications of regional curve standardisation on resultant chronologies. All three studies found important differences in resultant chronologies due to standardisation. Despite the attention given to standardisation choice, both Frank et al. (2007) and Esper et al. (2010) remarked that this alone could not fully account for the presence of the DP. Other methodological choices such as different standardisation of sample subgroups (Esper and Frank 2009, Briffa et al., 2013), the influence of using pith offset (or not), or power transformation of residuals together with standardisation methodology have also been considered (e.g., Büntgen et al., 2012). Signal-free standardisation methodology has further reduced end-effects that can occur with more traditional standardisation approaches (see Melvin et al., 2007; Melvin and Briffa, 2008; Briffa et al., 2013; Melvin et al., 2013), although it may also introduce some biases into chronologies (Anchukaitis et al., 2013).

Detection of divergence has entailed a variety of approaches, although many studies have used a single approach (some important recent exceptions include Àlvarez et al., 2015; Galvàn et al., 2015; Lavergne et al., 2015; see also Appendix A). Commonly used methods include: 1) visual comparison of tree-ring chronologies and climate target on the same plot (e.g., Jacoby and D’Arrigo, 1995; D’Arrigo et al., 2009; Appendix A); 2) comparison of response/correlation functions for two or more separate periods (e.g., Leal et al., 2008; D’Arrigo et al., 2009; Andreu-Hayles et al., 2011a); 3) moving correlations (e.g., Büntgen et al., 2006a,b; Naulier et al., 2015; Lavergne et al., 2015); 4) process-based modelling of tree-ring growth (e.g., the Vaganov-Shashkin-Lite model; Tolwinski-Ward et al., 2011; Lavergne et al., 2015; Sànchez-Salguero Camarero et al., 2017; Tumajer et al., 2017); and 5) application of the Kalman Filter (KF) to estimate regression models with time-varying coefficients (Visser and Molenaar, 1988; Jacoby and D’Arrigo, 1995; Wilson et al., 2013; Cook et al., 2013). Different approaches, however, may impact conclusions regarding the presence or absence of divergence (or temporal instability more generally) and each will have its own strengths and weaknesses. They may also be differentially sensitive to standardisation method used and some may be more suitable than others for the detection of low or high frequency instability—neither of these issues has previously been examined.

To date, there has also been a greater emphasis on checking chronology-climate relationships for stability using single climate records nearest the field site or composites of local records, rather than across a gridded data set (e.g., Büntgen et al., 2008; Tardif et al., 2003; Wilson et al., 2007; Grudd, 2008; Zhang et al., 2009; Allen et al., 2014). However, climate field reconstructions (CFR) implicitly assume that relationships across an often pre-defined spatial field are sufficiently stable over time, as do reconstructions relying on broadscale composites of temperature. With a growing interest in spatial field reconstructions of Southern Hemisphere (SH) temperature and precipitation using gridded climate data (e.g., Neukom et al., 2011; Neukom et al., 2013), and a rapidly increasing pool of available predictors, it will be increasingly important to scrutinise temporal stability of relationships across various spatial scales and domains. Although the underlying causes for temporal instability at broad scales may differ from those operating on local site reconstructions, instability in relationships across broad scales may have ramifications for our understanding of regional and global temperature dynamics.

In this study, we compare several simple and commonly used pre-reconstruction techniques to examine data series for temporal instability at both the local and broader regional levels in four long SH tree-ring chronologies. Our primary question is whether any of these techniques are more effective than others in detecting temporal instability. A secondary question is whether some methodologies for detecting divergence appear more sensitive to standardisation choice than others. We also extend two of the methods to examine temporal stability over broader spatial domains. Critically, three of the four SH chronologies used here, like many of the SH ring-width chronologies thus far developed, contain only a moderately strong relationship with temperature (typically ∼ 0.35 < |r| < 0.5; e.g., Villalba, 1990; Allen et al., 2011; Anon (2014); Lavergne et al., 2015; Lavergne et al., in press) which is likely to make detection of an actual change in the relationship with climate more challenging (Esper and Frank, 2009). These weaker relationships may in turn have implications for the effectiveness of different methods used to detect instability at both local and regional scales. Due to the scarcity of highly resolved multi-century proxies in the SH (e.g., Fig. 1a PAGES2k Consortium, 2017), exclusion of SH ring-width chronologies with only moderate correlations with climate from multi-proxy reconstructions would effectively prohibit inclusion of a large number of SH tree-ring chronologies.

This study is not intended as an exhaustive review of the SH chronologies for temporally unstable relationships with temperature. Although we do briefly consider impacts of different standardisation methodologies on the results, our focus is on the methods used for detecting temporal instability, particularly in situations where the relationship between chronologies and climate is of moderate strength only. We also examine the relationships between synthetic temperature and tree-ring series that have had known interventions. In what follows, we use the term temporal instability to refer to a separation in trend or to dissonance in the interannual relationship between two series that is sufficiently strong – or exists for a sufficiently long period of time – to be identifiable by a particular method. We do not, therefore, apply a lower threshold on the amount of time any stability must exist. Also, to be consistent with the DP literature, we use the term ‘divergence’ to describe modern end decoupling.

Section snippets

Data and methods

We use several common methods to check for temporal instability in two sets of data. The first of these is the selected tree-ring chronologies and relevant climate data described in Sections 2.1–2.3, and the second includes synthetic ring width and climate series, as described in Section 2.4. In Section 2.5 we outline the methods used to check for temporal instability at the local and broader spatial scales.

Results

Below, we firstly report the results for the synthetic data (Fig. 2, Fig. 3, Fig. 4) and then the results for the different sites (Fig. 5, Fig. 6, Fig. 7, Fig. 8, Fig. 9, Fig. 10, Fig. 11). For the site results, a single figure is used to present results based on a particular technique across all sites. The information presented in each figure is as follows: Fig. 5, the smoothed chronologies standardised in different ways; Fig. 6, a visual comparison of the chronology sets against mean

Is there a ‘best’ method to detect temporal instability?

Ideally, any method used to test temporal stability of the relationship between two series would identify known issues between two series. Additionally, given overwhelming evidence (e.g., Büntgen et al., 2008; Esper et al., 2010) that standardisation is a critical aspect of temporal instability at the modern ends of series (i.e., the DP), any method used should be sensitive to standardisation method. A summary of the results for each method by site (Table 3) illustrates that no one method is

Conclusions

Our review of methods commonly used to detect temporal instability in relationships between climate and tree-ring chronologies is certainly not exhaustive and is, to some degree, conditional on the particular data being examined. Our analyses identify the relative difficulty in identifying changing relationships in trends between series that are modestly associated with one another—as is typical of many of the multicentennial SH tree-ring chronologies. They also highlight that commonly used

Acknowledgements

Australian tree-ring data for this study were obtained under permits issues by Parks Tasmania. Rob Evans and Michael Goddard were instrumental in obtaining the cell wall thickness data from Silviscan3. This research was funded by Australian Research Council grants DP120104320 to PJB, ERC, and JGP and FT 12010715 to PJB. David Drew received funding from the Herman-Slade Foundation (HS 09/5). Lamont-Doherty contribution no. XXXX. Data for the four sites examined here are, or will become available

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