The tree-ring data
The tree-ring widths (TRW) and maximum densities (MXD) used in this study originates from the Lake Torneträsk area, northern Sweden (68.21–68.31°N, 19.45–19.80°E, and 350–450 m a.s.l.). The sample material is derived from living and subfossil Scots pine (Pinus sylvestris L.). The subfossil samples come from two sources: Dead wood found on dry ground, and submerged logs retrieved from small mountain lakes. All material is regarded as samples from the same population. A summary and temporal distribution of some raw data statistics are given in Table 1 and Fig. 1.
Table 1 Raw tree-ring data statistics
MXD data from Torneträsk were first published by Schweingruber et al. (1988). This original data set of 65 individual tree-series covered the time period ad 441–1980 and is hereafter denoted SEAL80 [WSL (Dendro Database, WSL, Switzerland. http://www.wsl.ch/dendro/dendrodb.html). Here, the MXD data is updated to ad 2004 using new samples from 35 relatively young trees. Thus, the new Torneträsk MXD data-base includes samples from a total of 100 trees and covers the period ad 441–2004. Dry dead wood covers the period ad 441–1789 and living trees cover the period ad 1336–2004. No subfossil lake material is included in the MXD data. In SEAL80, data for the most recent period originated entirely from old-aged trees and, as a result, tree rings from the twentieth century had a much higher average cambial age than the earlier part of the record. The new data have significantly reduced the average cambial age of the tree-ring data in the twentieth century (Fig. 1a).
The TRW data are part of a much larger data set than the one used for MXD (Grudd et al. 2002). The TRW data are updated to ad 2004 using the same 35 trees as for MXD and a total of 620 trees is now used to cover the period ad 500–2004 (Fig. 1b). The sources of these data are living trees, dead dry wood and subfossil logs that were recovered from small lakes.
X-ray densitometry
The new data were produced using an Itrax WoodScanner from Cox Analytical Systems (http://www.coxsys.se), while the original SEAL80 data were produced using the DENDRO2003 X-ray instrumentation from Walesch Electronic (http://www.walesch.ch). Both systems produce high-resolution radiographic (X-ray) images from thin laths that are cut from the samples. Before X-raying, the laths are treated with alcohol in a Soxhlet apparatus to extract resins and other movable compounds in the wood that are not related to the annual production of wood tissue (Schweingruber et al. 1978).
In the DENDRO2003 system, laths are placed on an X-ray film and exposed to X-rays (similar to the X-ray technique traditionally used in hospitals). Subsequently, light intensity (grey levels) in the film is analysed using a manually operated photo-sensor. The dimensions of the photo-sensor slit varies with the choice of magnifying lens, resulting in varying dimensions from 0.004 × 1 to 0.05 × 5 mm. Grey-level light intensity is calibrated to wood density using a standard calibration wedge which is X-rayed at the same time as the sample laths.
In the Itrax WoodScanner system, the sample laths are scanned in increment steps using a focused high-energy X-ray beam and an X-ray line camera that detects the amount of radiation that passes through the sample. The output from this system is a digital image with 65,536 grey levels (16 bit) with a maximum resolution of 0.01 mm (2,540 dpi). Resolution is user defined by the choice of increment step-length during the scanning procedure. The digital image is subsequently analysed using the commercial software WinDendro (http://www.regentinstruments.com) where density, as represented by the grey levels, is determined by means of a “virtual” slit scanning process (Guay et al. 1992). The width of the virtual slit is always 1 pixel and length is user defined. Grey-level light intensity is calibrated to wood density using the same type of standard calibration wedge as used in the DENDRO2003 system.
Hence, MXD in the new data was measured using a method which is comparable to the method used for the SEAL80 data. The sensor-slit dimensions, however, differ slightly which means that there could, potentially, be a difference in the definition of MXD between the two data sets. The new data were analysed using a sensor width of 0.01 mm and a sensor length of 1.0–2.0 mm. The SEAL80 data were analysed using a sensor width of 0.03 mm and a sensor length of 0.08–1.0 mm (Schweingruber 1988; and personal communication, Daniel Nievergelt at the WSL Laboratory). The difference in sensor width (the direction of tree-ring growth) will have a greater effect than the difference in length because the variation in intra-ring density is largest in this direction. For small rings, therefore, a smaller sensor width should provide more accurate MXD values.
To assess the difference between the two techniques, one sample from the original SEAL80 data was re-measured in the Itrax WoodScanner. The calibration results (Fig. 2) show that the average MXD is virtually identical in the two measurement series and that there is no significant relation between the residuals and the ring widths. However, the variability around the mean is different: The new measurement series has a significantly higher standard deviation (SD = 0.116) than the original measurement series (SD = 0.082). As it was not possible to re-measure all 65 series in the original SEAL80 data, 15 measurement series from each of the two data sets, and from a common time period, were used to construct two raw data chronologies which were analysed for differences in mean and variance (Fig. 3). The mean MXD in these two chronologies are equivalent. The standard deviation around the mean, however, is higher in the new data, consistent with the calibration results.
The higher variability introduced by the new data for the most recent period of the record will have significant implications for the climate reconstruction and will lead to an under-estimation of the climatic variability in the earlier part of the record. The variance in each individual measurement series of the new data was therefore reduced by 29% in accordance with the calibration results (Fig. 2).
Standardization
The annual growth of a tree, manifest as TRW or MXD, may in theory be attributed to a restricted number of different growth-controlling factors (Cook 1990). At Torneträsk, trees live close to their climatological limit of distribution and, hence, annual production of wood tissue is primarily controlled by the climate (Tranquillini 1979). A secondary factor that controls the annual ring width and maximum density of an individual tree is related to the age/size of the tree, and a third factor is the influence from non-climatic changes in the surrounding physical and ecological environments (Fritts 1976; Schweingruber 1988). Using this basic concept, the observed time series of annual wood tissue production in a tree may be defined as the cumulative result of three separate factors: Climate (C), tree age/size (A), and the (non-climatic) environment (E). Hence,
$$ G_t = C_t + A_t + E_t + \varepsilon _t $$
(1)
where G
t
is the observed growth, measured as TRW or MXD at calendar year t, and ε
t
results from random (error) growth processes not accounted for by these other processes (Cook 1990).
Tree-ring chronologies are constructed by averaging replicate data for each individual calendar year. However, when used for paleoclimate reconstruction, the non-climatic information (A
t
and E
t
in Eq. 1) first need to be removed from the individual raw data series (G
t
). This central concept in dendroclimatology is referred to as standardization (Fritts 1976; Cook et al. 1990) and the aim is to preserve as much of the climate-related information as possible while removing the un-wanted, non-climatic information. Inevitably, however, a varying proportion of the low-frequency climatic information is also lost in this process. The choice of standardization method depends on the character of the tree-ring data but, in general, more complex statistical methods are needed when the non-climatic environmental factors have a strong impact on tree growth (Cook et al. 1990). In this study, tree growth is assumed to be forced by two dominant factors: The summer climate and the age/size of individual trees. This assumption is based on the strong connection to temperature for Torneträsk TRW and MXD data (Briffa et al. 1990; Grudd et al. 2002). Non-climatic environmental factors will certainly have been important for individual trees at different times, but these factors are regarded as haphazard events with random distribution over space and time and, hence, they can be regarded as part of the random error variable (ε
t
) in the conceptual linear aggregate equation (Eq. 1). An index (I
t
) of the climate signal can then be extracted by simply subtracting the age/size-related trend (A
t
) from the observed growth (G
t
).
For MXD, the index (I
t
) is calculated by subtraction. For TRW, however, the amplitude of variation will change over the lifetime of individual trees and the index is therefore calculated by division (Fritts 1976; Schweingruber 1988):
$$ I_t = \frac{{G_t }} {{A_t }} + \varepsilon _t . $$
(2)
This approach simultaneously removes the age/size-related trend and stabilizes the variance such that the mean and variance no longer systematically change with time.
The age/size-related trend (A
t
) is commonly modelled with a deterministic approach, i.e. by fitting a negative exponential function or linear trend to the data, or by using more flexible functions such as a smoothing spline (Fritts 1976; Cook and Kairiukstis 1990). These deterministic methods effectively preserve the high-frequency variation in the data while removing much of the slowly evolving changes such as biological growth trends. However, they also remove a major part of the long-term climatic trends. In this analysis, therefore, the data is standardized using an empirical method denoted Regional Curve Standardization (RCS) which has demonstrated a particular ability to preserve long-timescale climate variability in long tree-ring chronologies while removing most of the age related variance (Esper et al. 2003; D’Arrigo et al. 2006). The basic concept of the RCS method was used already by Stellan Erlandsson in his pioneer studies at Torneträsk (Erlandsson 1936) and the method was later employed and developed by Keith Briffa et al. (1992) using a much larger set of tree-ring data from Torneträsk.
The RCS method has higher requirements on the data than other standardization methods: The method presumes that all trees in a population have a common age/size-related growth trend that can be empirically determined by aligning tree-ring samples according to their cambial age and calculating the average of rings 1; rings 2; etc. Hence, the cambial age of all tree rings must be known, i.e. samples should ideally include the pith (the centre of the tree). When the pith is absent, which often is the case in drilled core samples and subfossil wood, the pith offset (PO) has to be estimated. Here, PO was determined by first interpolating the distance to the geometric centre of the tree using the curvature of the innermost rings and then estimating the number of rings that would fill the missing segment. In the Torneträsk MXD data, the pith was present in 25 of the samples and PO was estimated in the remaining 75 samples. The 620 TRW samples were not adjusted for PO: Here, the first ring in the series is simply assumed to represent the ring of the first cambial year.
When averaging all individual tree-ring series according to their cambial age rather than their calendar year and calculating the average growth, it is also presumed that the influence from climate forcing will be levelled out. Therefore, when using the RCS method, it is critically important that there is a wide distribution of the data over time, i.e. the data lined up for each cambial year should ideally come from a wide range of climatic conditions. To avoid the bias introduced by an insufficient number of replicate samples, therefore, only data where the sample depth ≥25 were used to calculate the average curve (Fig. 4). A smoothed “Hugershoff” version (Warren 1980) of the average curves was then used for the RCS standardization.
After standardization, each individual series is re-aligned according to the calendar age and an arithmetic mean series is calculated. Figure 5 shows the RCS standardized index chronologies for MXD and TRW. The signal strength and confidence in these chronologies is assessed by calculating R-BAR and expressed population signal (EPS) statistics in a 50-year window moved in 25-year steps over the total length of the series (Wigley et al. 1984). The R-BAR statistic is a measure of the average inter-correlation of all overlapping series, while EPS denotes the percent common signal. EPS is related to R-BAR and to the number of replicate series, with EPS values above 0.85 generally regarded as satisfactory (Wigley et al. 1984). Figure 5 shows that although the R-BAR values for the TRW chronology are lower and more variable as compared to the MXD chronology, the confidence in the TRW signal is much higher, with EPS values typically above 0.95 as a result of the much higher sample replication in the TRW chronology. In the MXD chronology, EPS is on average 0.89, but with critically low values in some periods, particularly at ad 650, 1025, 1275 and 1425.
The significance of the century-timescale variation observed in the chronologies is assessed by, first, smoothing all individual index series with a 100-year spline filter, thus generating a new set of low-frequency series which are, then, averaged into a low-frequency chronology (Sheppard 1991). Using this approach, it is possible to calculate bootstrapped 95% confidence intervals for the century timescale variation and hence visualize sections of the chronologies where poor sample replication and/or low signal-to-noise ratio results in a weakening of the low-frequency signal. Figure 5 shows that there is a higher confidence in the low-frequency signal in the TRW chronology. It is also evident that the low-frequency signals are very similar in the two chronologies up to about ad 1800 where there is a clear diversion between the trends.
Tree-growth response to climate
Three different sets of instrumental monthly mean climate data (Fig. 6) were used in order to identify climatic signals in the MXD and TRW chronologies and to investigate the optimum season for a climate reconstruction: (1) Abisko, a local record (ad 1913–2004) provided by Abisko Scientific Research Station (http://www.ans.kiruna.se), which is located within the Torneträsk area (Andersson et al. 1996); (2) Tornedalen, a long composite record (ad 1802–2002) based on a combination of historical data and synoptic station data from Haparanda (65°49′N, 24°8′E) approx. 350 km south-east of Torneträsk (Klingbjer and Moberg 2003); and (3) Bottenviken, a regional record (ad 1860–2004) provided by the Swedish Meteorological and Hydrological Institute (SMHI) and based on data from six synoptic stations in northern Sweden (Alexandersson 2002). The Bottenviken record includes data from both Abisko and Haparanda.
Response function analyses (Fritts 1976) were carried out using the climate data and the RCS standardized TRW and MXD chronologies. This involves calculating principal components (PC’s) of monthly temperature and precipitation data and regressing the PC’s on the annual tree-ring indices over a common period. In response functions, however, normal significance levels of coefficients may be misleading because error estimates are underestimated (Cropper 1985). Hence, the method used here involves the technique of bootstrapped confidence intervals to estimate the significance of both correlation and response function coefficients (Biondi and Waikul 2004) which produces more robust results (Guiot 1990, 1991). The response function analysis gives an indication of the direction and relative strength of the climatic forcing and the results show that both MXD and TRW have a significant positive response to growing-season temperatures (Fig. 7). There is no significant response to monthly sums of precipitation.
Local (Abisko) summer temperatures have a positive effect on both MXD and TRW, but the significant response time-window is much broader for MXD. For TRW, forcing is dominated by July temperatures of the current year of growth while MXD has a significant positive response to June, July and August temperatures of the current growing season. When analysed with the regional (Bottenviken) record, the response window for MXD is even broader including spring temperatures (April and May).
TRW also show significant response values to May and June temperatures of the previous year which reflects the high auto-correlation usually found in TRW chronologies (Fritts 1976). Therefore, a lagged TRW-variable must be included in the linear regression model for summer temperature reconstruction:
$$ C_t = a\bar I_t^{{\text{MXD}}} + b\bar I_t^{{\text{TRW}}} + c\bar I_{t + 1}^{{\text{TRW}}} + d, $$
(3)
where C
t
is the reconstructed temperature in calendar year t;
\( \bar I_t^{{\text{MXD}}} \) is the MXD chronology index in year t; \( \bar I_t^{{\text{TRW}}} \) and \( \bar I_{t + 1}^{{\text{TRW}}} \) are the TRW chronology indices in years t and t + 1; a−d are the regression coefficients.
The fidelity of the reconstruction equation was then tested in a calibration/verification exercise (Fritts 1976; Cook and Kairiukstis 1990) where the Bottenviken mean summer (April–August) temperature was split into two independent 72-year periods. Equation (3) was fitted over one period using linear regression, and with the derived coefficients applied to the tree-ring data in the other period. This calibration/verification scheme produces independent estimates of temperature that can be compared to the instrumental temperature data. The procedure was applied using the TRW and MXD chronologies combined, and repeated for the TRW chronology and the MXD chronology individually (Fig. 8). The verification results were tested using the squared Pearson correlation (R
2), the reduction of error (RE), and the coefficient of efficiency (CE) (Table 2). The R
2 statistic, ranging from 0.0 to 1.0, is a measure of the proportion of variation “explained” by the regressors in the model. The RE and the CE statistics both range from −∞ to +1.0 with RE > CE and where values greater than 0 give confidence to the model performance (Fritts 1976; Briffa et al. 1988). Of these three statistics, CE is the most difficult to pass (Cook et al. 1994). The TRW chronology used alone give poor results (CE = 0.17; 0.27). When the TRW and MXD chronologies are used in a multiple regression the verification results improve significantly (CE = 0.37; 0.49). The best verification results are obtained with the MXD chronology alone (CE = 0.55; 0.54).
Table 2 Calibration and verification results
Hence, based on the verification results, a reconstruction using the MXD chronology alone should give the best results. However, the stronger low-frequency signal strength in the TRW chronology (Fig. 5) indicates that there is useful information to be gained by including also the TRW chronology in the reconstruction. The low frequency variation in these two chronologies is very similar for the first 1,300 years of the records. Around ad 1800, however, the trends in MXD and TRW start to diverge significantly with the largest diversion occurring in the early nineteenth century (Fig. 9). The diverging trends could, potentially, be caused by a change in the sensitivity to summer temperature of one, or both, of these growth parameters. To examine the nature of this “divergence problem” the 200-year long Tornedalen record of June–August mean temperature was divided in four 50-year segments and compared individually to the standardized TRW and MXD series (Fig. 10). The results show that the correlation between TRW and summer temperature is very low (R = 0.20) in the first 50-year period (ad 1802–1852) while it is significantly higher and relatively consistent in the following three periods (0.47; 0.58; 0.47). For MXD, the correlations are much higher (R = 0.70–0.81) and with no obvious inconsistency in the response to summer temperature between the four periods. Hence, the “divergence problem” seems to be isolated to TRW in the first half of the nineteenth century.
ad 500–2004 climate reconstruction
Two reconstructions of summer temperature were made using regression weights for the Bottenviken April–August mean temperature and the full 1860–2004 calibration period (Table. 2): A reconstruction based on MXD exclusively (Fig. 11a), and a “multi-proxy” reconstruction based on TRW and MXD (Fig. 11b). The reconstructions are expressed as temperature (°C) anomalies from the ad 1951–1970 baseline period which enables the new results to be directly compared with previously published reconstructions from Torneträsk (Briffa et al. 1992; Grudd et al. 2002).
The two new reconstructions show summer temperature variation over the last 1,500 years. The maximum amplitude is about 5°C with the warmest summers occurring around ad 1000 and the coldest summers occurring around ad 1900. Figure 11c shows that the two reconstructions are very similar on decadal-to-centennial timescales. On these timescales, notably cold periods occur around ad 650, 800, 1150, 1250, 1350, 1600 and 1900. Notably warm periods occur around ad 750, 1000, 1400, 1750 and 2000. The 200-year long warm period centred on ad 1000 is especially noticeable. With a 95% confidence interval applied to the low-frequency (century timescale) signal, this period is significantly warmer than the late twentieth century (Fig. 12).