These authors contributed equally to this work.
The detection and attribution (D&A) of paleoclimatic change to external radiative forcing relies on regression of statistical reconstructions on simulations. However, this procedure may be biased by assumptions of stationarity and univariate linear response of the underlying paleoclimatic observations. Here we perform a D&A study, modeling paleoclimate data observations as a function of paleoclimatic data simulations. Specifically, we detect and attribute tree-ring width (TRW) observations as a linear function of TRW simulations, which are themselves a nonlinear and multivariate TRW simulation driven with singly forced and cumulatively forced climate simulations for the period 1401–2000 CE. Temperature- and moisture-sensitive TRW simulations detect distinct patterns in time and space. Temperature-sensitive TRW observations and simulations are significantly correlated for Northern Hemisphere averages, and their variation is attributed to volcanic forcing. In decadally smoothed temporal fingerprints, we find the observed responses to be significantly larger and/or more persistent than the simulated responses. The pattern of simulated TRW of moisture-limited trees is consistent with the observed anomalies in the 2 years following major volcanic eruptions. We can for the first time attribute this spatiotemporal fingerprint in moisture-limited tree-ring records to volcanic forcing. These results suggest that the use of nonlinear and multivariate proxy system models in paleoclimatic detection and attribution studies may permit more realistic, spatially resolved and multivariate fingerprint detection studies and evaluation of the climate sensitivity to external radiative forcing than has previously been possible.
One of the crucial questions in climate change research is to determine how external radiative forcings bring about climate variation and change and if the forced response may be distinguished from the internal, unforced variability. To address this question, so-called “detection and attribution” (D&A) methods have been developed (Hegerl and Zwiers, 2011; Gillett et al., 2021). Generally speaking, D&A studies match observed changes with patterns derived from climate model simulations driven by single and multiple external forcings, including solar variability, volcanic aerosols, the well-mixed greenhouse gases, orbital variations and land use change. This idea was initiated in early work by Hasselmann (1979). After methodological refinements and advances in climate modeling in the early 1990s (e.g., Hasselmann, 1993; Santer et al., 1993) there was growing evidence that the external greenhouse gas signal may be differentiated from climate variability generated within Earth's climate system (Hegerl et al., 1996). Detection and attribution studies have been an important part of the Assessment Reports of Working Group I of the Intergovernmental Panel on Climate Change, from the calling for better detection of the role of human activities in climate forcing in the First Assessment Report (1990), to formal detection and attribution studies comparing observed and simulated climate change in all assessment reports since, with increasingly confident assessments of the detection of human influences and estimates of the human contribution derived from attribution results.
Typically, D&A analyses have been limited to periods when instrumental observations of physically measurable variables and derived diagnostics are available, with global observation networks becoming dense enough for such studies about 100 to 150 years before present. This period allowed for attribution of trends in many thermodynamic and dynamic characteristics of the climate system, including global and regional temperature, temperature extremes, ocean heat content, tropopause height, specific humidity, zonal mean precipitation, and air pressure fields to potential forcings (e.g., Hegerl et al., 1996; Santer, 2003; Polson et al., 2013a; Bindoff et al., 2014; Eyring et al., 2021; Gillett et al., 2021). While 19th and 20th century instrumental observations cover a major increase in greenhouse gases and other human influences, studying the climate system response to non-anthropogenic external radiative forcings, such as solar variability or volcanic eruptions, benefits from studying longer periods over which more realizations and/or longer-term processes are evident and where the anthropogenic influence is less dominant. For instance, very few climatically important volcanic eruptions occurred in the past 150 years, but more than a dozen occurred over the past 600 years (Sigl et al., 2015) at nonuniform frequency in time, possibly creating long-term forcing of the climate system (McGregor et al., 2015; PAGES 2k Consortium, 2019; Brönnimann et al., 2019). Such longer-term studies would integrate longer-term responses of the climate system to external radiative forcing, enabling a more complete picture of the equilibrium and transient response and ultimately of the climate sensitivity to external radiative forcing.
Paleoclimatology allows for extension of the observational record into the past using indirect measurements of climatic conditions, which can be used to reconstruct past climate. Previous studies have detected a role of external forcing in the climate of the last millennium using annual mean surface temperature anomaly reconstructions on both a hemispheric scale (Hegerl et al., 2003; Schurer et al., 2013, 2014) and regionally (PAGES 2k-PMIP3 group, 2015). These analyses have found that volcanic forcing is detected with a smaller contribution from greenhouse gases that is detectable by 1900, and a contribution from solar forcing that was not detectable against climate variability. However, the reconstruction process itself introduces additional assumptions into detection and attribution studies that arise from the nature of the reconstructions but which may not be justified. Many of these are demonstrated in pseudo-proxy experiments (Smerdon et al., 2011) and through study of the extensive network of tree-ring width observations. These include assumed univariate, normally distributed, and linear responses of the paleoclimatic indicators to the target reconstruction variable (Evans et al., 2014; Wang et al., 2014); stationarity of patterns of regional- and global-scale climate variability (Wilson et al., 2010); seasonal and spatial representation (St. George, 2014; Smerdon et al., 2011); and auto-regression characteristics in observations and target variables (Cook et al., 1999). Limited adherence to assumptions in observations and statistical modeling has been found to introduce biases into reconstructed variables, even in large-scale averages (PAGES2k Consortium, 2017) and may lead to the underestimation of errors in D&A studies that are necessary to separate the forced and unforced responses (Neukom et al., 2019). In particular, autocorrelation due to memory in tree-ring width (TRW) affects the response to volcanism which, if not accounted for, biases D&A results (Lücke et al., 2019).
Progress in process understanding of paleoclimatic observations has led to
the development of proxy system models (Evans et
al., 2013), which may be used to identify systematic uncertainties and
evaluate the extent of biases introduced by the reconstruction process into
the D&A problem. One recent example is the Vaganov–Shashkin Lite (VSL)
sensor model, which simulates standardized tree-ring width (TRW) chronology
variations based on monthly mean temperature, precipitation and latitude.
These inputs are used to estimate nondimensional growth arising from
temperature and soil moisture conditions (
Here we leverage VSL, historical gridded climate data products (Harris et al., 2014), singly and multiply forced climate simulations for the period 1401 to 2000 CE (Schurer et al., 2013), and the nearly 3000 consistently detrended TRW observations (B14, Breitenmoser et al., 2014) to perform an extratropical Northern Hemisphere D&A exercise directly using observed and simulated TRW data (Fig. 1, Eq. 1):
Schematic overview of the performed analysis. General steps are indicated in bold, and study-specific procedures are shown in roman text. B14 refers to the Breitenmoser et al. (2014) dataset,
The remainder of this paper is organized as follows. First, we estimate and
evaluate parameters for VSL, using gridded instrumental temperature (
The inputs into and process of this detection and attribution study are illustrated in Fig. 1 and described below.
We use the tree-ring width (TRW) collection described by and employed in Breitenmoser et al. (2014), now referred to as B14, as the observational basis for the development and validation of VSL parameters and as the D&A predictand (Eq. 1). B14 consists of 2918 uniformly detrended and standardized tree-ring width chronologies from six continents and 163 species that had been uploaded to the International Tree-Ring Data Bank (ITRDB, Zhao et al., 2019) up to 2014. These series have been quality controlled for metadata errors, repetitive measurements, incorrect units, decimal point errors and misplaced positions (Table S1 in Breitenmoser et al., 2014). Detrending for biological age trends and stand dynamics and standardization to dimensionless growth indices was done in a hierarchical approach. If possible, negative exponential curves and linear regression curves of any slope were fitted. In case both methods failed, “a smoothing spline was fit with a 50 % cut-off frequency at 75 % of each series length” (ARSTAN, Cook, 1985; Breitenmoser et al., 2014). Multiple measurements at the same site have been combined into robust means (Cook and Kairiukstis, 1990), which are variance adjusted for changing sample size through time (Osborn et al., 1997). For every point in time, which is explicitly resolved as one value per growing season each year, a chronology is based on at least eight samples. We use the auto-regressive standardized (Osborn et al., 1997; Frank et al., 2007) version of the available chronologies from B14. We require that the chronologies have at least 40 years observed within the period 1901–1970 (see Sect. 2.2 below).
We restrict subsequent analysis of simulations and the D&A exercise to the extratropical Northern Hemisphere continental areas, where the vast majority of TRW observations are located, with high concentrations in North America, Europe and northern Asia (Fig. 2). Record length varies from 100–600 years (Fig. 2). Series availability is generally greatest between the mid-19th century and the late 20th century (Fig. 3), and the longest records are equally distributed in longitude across the Northern Hemisphere boreal terrestrial latitudes (Fig. 2).
Limitations determined for all TRW chronologies with valid parameter sets, separated into temperature-sensitive values
For the purpose of VSL parameter estimation, we use the global, gridded
instrumental temperature and precipitation datasets CRU TS 3.23 (Harris et al., 2014), regridded to 64 longitude
Temperature and precipitation input data for VSL are derived from climate
model simulations. We use the set of simulations described in Schurer et al. (2014), which have been conducted with HADCM3 and interpolated to the same
All-forcing and single-forcing HADCM3 simulations and control runs used in this study (“V” stands for volcanic, “S” stands for solar, “G” greenhouse gases, “L” stands for land use, and “A” stands for tropospheric aerosols).
To solve for the D&A coefficients in Eq. (1), we use the total least-squares (TLS) D&A technique to account for errors in both dependent and
independent variables within the regression procedure (Allen and Stott, 2003) to account for internal variability in both observations and model simulations. We follow the analysis used in Allen and Stott (2003), Polson et
al. (2013a), and Schurer et al. (2013), which estimates a best-fit regression
coefficient (
A total of 1664 of 2761 TRW chronologies in the B14 compilation were climate sensitive and therefore successfully simulated and retained for further analysis. With small differences between climate simulations, we found that 21 % of the successfully simulated chronologies are temperature sensitive, ca. 57 % are moisture sensitive, ca. 11 % are both moisture and temperature sensitive, and ca. 11 % are not climate sensitive, i.e., neither moisture nor temperature sensitive (Fig. 2). Distributions of temperature, moisture, both temperature and moisture, and neither temperature nor moisture sensitivity overlap in space. There are many moisture-sensitive TRW chronologies found in North America, the Mediterranean and other arid regions (Fig. 2b). However, there are also temperature-sensitive chronologies (Fig. 2a) and mixed responders (Fig. 2c) that are co-located in arid regions (Fig. 2a). Chronologies found to be neither temperature nor moisture sensitive (Fig. 2d) tend to be found at the highest latitudes, but this is not exclusively the case.
We found that bootstrapped VSL parameter estimates were in many cases distinctly non-normal in distribution for some or all of the four parameters and for some TRW simulations. Distributions were sometimes uniformly distributed across the prior expected parameter ranges, unimodal non-normal and even bimodal. Because there were not necessarily well-defined means or medians across parameter sets and simulations, we used all valid parameter sets to produce TRW simulations. Hence, we propagate uncertainty arising from stochastic variation in the climate simulations through parameter and structural uncertainty in the ring width sensor model.
Because the fingerprint of external radiative forcing may or may not be
distinct and unique in temperature and moisture, we use the fit of VSL
diagnostic variables
TRW simulations (Sect. 2.2, 2.3) are developed for all locations where TRW observations exist and the parameter estimation has been successful, i.e., for most of the extratropical Northern Hemisphere (Fig. 3). We exclude the Southern Hemisphere in this because only five temperature-sensitive chronologies and one moisture-sensitive chronology are located there. The record length of the simulations is constrained by TRW observations (see Sect. 2.1 and Fig. 3). The longest records are equally distributed in longitude across the Northern Hemisphere boreal terrestrial latitudes (Fig. 3). Thus, statistics assessed across the simulations and observations are best described as representing the Northern Hemisphere temperate and subpolar terrestrial regions.
Furthermore, we note that the locations of temperature- and moisture-sensitive chronologies overlap (Fig. 2) but are generally not coincident (Fig. 3): for either the observed or simulated sets, only about one-third are both coincident in space and significantly correlated with each other (Fig. 2). Hence, for the remainder of the analysis presented here, we develop and discuss the temperature- and moisture-sensitive results separately.
Numbers of years (color scale) available for comparison between
gridded, observed and climate-sensor-simulated TRW chronologies, within the
period 1401–2000.
Figure 4 shows the growth functions
Simulated intra-year partial growth response functions
To detect an external-forcing signal in noisy, local observations, the signal-to-noise ratio has to be enhanced. This is commonly achieved by averaging in space and/or time (Sects. 1, 2.4). We begin with analysis of global mean TRW variability at all locations where tree growth is either temperature or moisture limited, for comparisons between TRW observations and climate-sensor simulations driven with all forcings (Table 1). The variance of the average over all grid boxes increases back in time because of the decreasing numbers of records (Fig. 5), likely reflecting increasing uncertainty; the variance in the beginning of the 15th century is twice as large as that observed at the end of the 20th century. To reduce the sensitivity of the detection and attribution analysis to observational uncertainty, we homogenize the variance through time by multiplication of a time-dependent factor that is estimated by linear regression of the observed variance on the variance of TRW climate-sensor simulations from the control simulations.
Results suggest limited but significant correlation between global mean
observed and simulated TRW temperature-sensitive simulations for both
annual and decadally filtered series (Fig. 5). Nonsignificant correlations
are found for moisture-sensitive observations vs. simulations at both annual
and decadal timescales (Fig. 5). We find similar results for correlations
between volcanically forced simulations and temperature-sensitive (
Based on these results, we test for detection of patterns in the TRW
following volcanic eruptions in temperature- and moisture-sensitive TRW
chronologies using a composite analysis across the seven largest (above 95th
quantile) volcanic forcing responses for events between 1670 and 1970 (Fig. 6). We show the composite for observations based on two forcings,
stratospheric atmospheric optical depth (AOD) reconstructed by Crowley and
Unterman (2013) that was used to force the climate simulations (Fig. 1; Table 2) and the more recent and probably more realistic inferred global volcanic aerosol forcing (GVF, in W m
Largest volcanic eruptions used in the composite analysis based on atmospheric optical depth (years CE).
For our moisture-sensitive comparison, we do not find a global volcanic response of the same sign but rather regions with uniform responses (Fig. 6, bottom row). The simulated event composite based on Crowley and Unterman (2013) (Fig. 6f) produces positive growth anomalies around the Mediterranean and in western North America and negative anomalies in Eurasia and eastern North America, with more prominent composite positive regions than negative regions. The observed composite based on the Toohey and Sigl (2017) chronology produces no negative composite response in eastern North America and a small positive response in southwestern North America, the latter of which is consistent with simulations (Fig. 6e and f).
Composite average ring width anomaly (standardized units) in temperature-sensitive TRW chronologies in the first 2 years after volcanic
eruptions in observations and volcanic-forcing simulations
We detect and attribute a response to volcanic forcing in both the spatial
mean temperature time series and the spatiotemporal pattern of moisture-limited tree-ring records. As large volcanic eruptions disturb the climate
system for a few years, we show results 3-year and 11-year moving averages.
For the 3-year smoothed temperature-sensitive TRW averaged over all grid
boxes, we find a significantly detectable scaling factor
As described above, moisture-sensitive trees show positive growth anomalies in some regions and negative anomalies in other regions. We define a two-region spatiotemporal pattern identified in the moisture-sensitive TRW simulations (Fig. 6f). Scaling factors that are not significantly different from one for both all-forcing and volcanic-forcing simulations (Fig. 7c) again allow us to attribute moisture changes in response to volcanism.
Detection and attribution studies using paleoclimatic data have previously focused on regression of reconstructed climate variables on realistically forced climate simulations (PAGES 2k Consortium, 2019; Schurer et al., 2014). In this study, we have attached a validated, realistically multivariate and nonlinear, intermediate-complexity proxy-sensor model (Evans et al., 2013; Tolwinski-Ward et al., 2013, 2015) to enable the D&A framework within the space of the paleoclimatic observation – in this study, tree-ring width chronologies. Because this particular sensor model is a scaled and time-integrated transformation of temperature and precipitation variations into a single diagnostic that is commonly observed across the terrestrial landscape, the potential for fingerprinting either distinct univariate or integrated plant-stress-like signatures of the different radiative forcings becomes possible. The approach also substitutes structural and parametric uncertainty in the sensor model for the uncertainty arising from inversion of multivariate paleoclimatic observations for univariate climatic reconstruction, and it thus provides a complementary assessment of the uncertainty that propagates into the D&A results.
We find that the global mean forced response in temperature-sensitive TRW chronologies is consistent with observations within the 1401–2000 period, a result that supports the prior work using global mean surface temperature reconstructions as a predictand (Hegerl et al., 2006, and references therein) and implicitly the use of temperature-sensitive TRW chronologies for producing those results. However, we also find that moisture- and temperature-sensitive chronologies (Fig. 3) form distinct subgroups in space (Fig. 2) and in temporal averages (Fig. 4). The fingerprint of climate forcing, as determined by comparison between all-series-averaged temperature- and moisture-sensitive observations and simulations is statistically significant in temperature (but not in moisture) for both all-forcing and volcanic-forcing simulations (Fig. 7).
For the attribution analysis targeting volcanic forcing (Figs. 6, 7), we find disagreement in the amplitude of the temperature-sensitive forcing as a function of timescale, with the observed annual, 3-year, and decadal timescale variance being smaller than, equal to, and greater than the simulated variance, respectively (Fig. 7a and b). One explanation would be that the simulated peak temperature response to volcanic forcing is unrealistically large. This has been observed for the HadCM3 climate model simulation in a previous study (Schurer et al., 2013). Volcanic forcings used to produce the climate simulations may also be oversimplified in time and/or space relative to actual forcing (Stevenson et al., 2017), or its timing may be incorrect (yielding suppressed amplitude in reconstructions). For many eruptions with an unknown date, the eruption was set to 1 January, and the AOD is entered into the model in four equal latitude bands only, proportional to the amount of sulfur in the Antarctic and Greenland ice cores (Crowley and Unterman, 2013). Because TRW simulations are a simplified representation of actual TRW variation, they neglect the observational uncertainty and the potential for superimposed and competing influences, such that the simulated TRW response to forcing may be relatively large. This is indeed the case; for either volcanic forcing or all forcing, simulated variance is about one-third larger than observed variance (results not shown).
A further explanation could be that autocorrelations in observed and simulated TRW are different. We find observed mean TRW autocorrelation to be about two-thirds larger than that of volcanic-forced simulations (results not shown). Consequently, we find the observed TRW variance at decadal resolution to be significantly greater than simulated TRW variance. This result suggests that (i) the observed response contains decadal timescale non-climatic variation not adequately removed by observational signal processing (Cook and Kairiukstis, 1990); (ii) mechanisms represented in the climate simulations are inadequate to represent slower response timescales of volcanic forcing (Miller et al., 2012); and (iii) mechanisms of forest response to volcanic forcing via soil moisture, air temperature, or insolation variations as represented in VSL, or a combination of all three factors, are insufficient to represent the observed lower-frequency response (Esper et al., 2015; Lücke et al., 2019)Ṗrevious studies found scaling factors to increase as more smoothing is applied (Schurer et al., 2013). However, they did not reach the point of a significantly larger response in observations than simulations.
Previous studies based on historical observations found that volcanic eruptions produced positive precipitation and streamflow anomalies in the Mediterranean and the southwestern United States, whereas negative anomalies were observed at high latitudes and in western North America, the Indian and the Southeast Asian region, and the tropics (Iles et al., 2013; Iles and Hegerl, 2015). This is in agreement with the CMIP5-simulated precipitation response (Fig. 1a in Iles and Hegerl, 2015), although the pattern in observed precipitation was very noisy and not clearly observed. In contrast, the response was identifiable in observed streamflow data, which cover a longer period and integrate the precipitation response. Reasons that the precipitation response could not be detected are likely to include the small number of eruptions in the instrumental period over which a composite was formed, combined with low signal-to-noise ratio for precipitation (Fig. 1a in Iles and Hegerl, 2015), and the complex precipitation response pattern with regions of increases and decreases, which is more difficult to detect (see also Polson et al., 2013b). We would obtain similarly non-detection and non-attribution levels were we to define regions manually (e.g., northern Europe vs. Mediterranean or western vs. eastern North America) or for a smaller integration over the years following an eruption. This finding is in agreement with Rao et al. (2017), who see the effect in tree-ring reconstructed drought severity index only in a very small region of northwestern Europe, southern Spain and northern Morocco, and with Fischer et al. (2007), who found increased precipitation in the Mediterranean and Scandinavia and decreased precipitation in northwestern and central Europe following volcanic eruptions, although not to a level that is statistically significant in many locations and which is accompanied by high uncertainty in the reconstructed precipitation response. For such small-scale regions, our TRW network is too sparse, our simulation grid too coarse and the time span of the TRW series is too limited to calculate robust composites. The present study respects some of these challenges by extending the analysis several centuries into the past (Table 1), integrating the forced response over time and space (Fig. 7), and forming the attribution model using the native observed variable rather than a reconstructed climatic variable (Sect. 1; Fig. 1). We find a similar pattern in moisture-sensitive TRW (Fig. 6). Simulations are most consistent with the expected pattern if the composite is based on the same forcing chronology as that used to drive the underlying HadCM3 simulations (Crowley and Unterman, 2013). The pattern in TRW observations agrees better with the more recent volcanic forcing chronology of Sigl et al. (2015). This suggests the latter forcing series reconstruction may be more consistent with the response as observed in TRW. However, the two forcing chronologies are similar enough that the two-region detection and attribution analysis (Fig. 7, right panel) produces the significant detection of both the all-forcing and volcanic-forcing TRW signals, within uncertainty of unity, lending support to the conclusions of Iles and Hegerl (2015).
We have estimated the contribution by all forcing and volcanic forcing to tree-ring data, based on a detection and attribution study using observed and modeled tree-ring width data directly for the exercise. We found that temperature- and moisture-sensitive TRW data contain different signatures of the forced climate response over the past 6 centuries. Specifically, we find that the signature of the all-forcing and volcanic-forcing response is most evident across the mean of all temperature-sensitive chronologies but not across the mean of all moisture-sensitive chronologies. The amplitude of the temperature-sensitive forced response is larger than expected from the model simulations in decadally filtered results, suggesting inaccuracies in the representation of forcing and/or responses on those timescales in observations, simulations or both sources of information. Additionally, we detect and attribute a previously identified spatial pattern in moisture-sensitive response to volcanic forcing at annual timescales, with a dipole drying and moistening pattern similar to the one previously identified by others within the historical time period and with direct moisture observations. In this study we demonstrate for the first time that climate change D&A can be conducted directly on paleoclimatic observations and their multivariate, nonlinear proxy system simulations, allowing for a much more reliable model evaluation than possible if using reconstructed climate variables. The results may realistically diverge from those obtained by D&A studies using univariate surface temperatures reconstructed from similar datasets because the underlying observations may in reality be multivariate nonlinear responders. Further studies could improve upon this proof of concept by incorporating stable isotopic observations in combination with isotope-enabled climate model simulations and by accessing a longer time interval for developing composite analyses, additional data types and a larger ensemble of realistically forced climate simulations.
The HADCM3 simulations are available at the Center for Environmental Data Analysis:
JF and MNE designed the study with contributions from GCH. JF prepared the inputs for the TRW simulations, which were conducted by MNE. JF performed the D&A analysis with the support of AS. JF and MNE wrote the paper with the help of AS and GCH.
The contact author has declared that none of the authors has any competing interests.
Publisher's note: Copernicus Publications remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
We thank the British Atmospheric Data Centre (BADC) for access to the HadCM3 climate simulation (
This research has been supported by the European Research Council, H2020 European Research Council (PALAEO-RA; grant no. 787574) and the Schweizerischer Nationalfonds zur Förderung der Wissenschaftlichen Forschung (SNSF; grant no. 162668). This study originated during a sabbatical stay of Michael N. Evans at the University of Bern supported by the Oeschger Center for Climate Change, the Sigrist Foundation and the University of Bern, Department of Geography. Andrew Schurer and Gabriele C. Hegerl were funded by the UK Natural Environmental Research Council (via the Vol-Clim (grant no. NE/S000887/1) and GloSAT (grant no. NE/S015698/1)) and under the Belmont forum, PacMedy Grant (NE/P006752/1).
This paper was edited by Nerilie Abram and reviewed by Kevin Anchukaitis and one anonymous referee.