Review of Data and Methods
Details about the data and methods used are provided by MBH98 (and Mann et al, 1999). The most important aspects of the data and methods used in that study are summarized here for the benefit of the reader. In Figure 1 we show the distribution of
proxy and long instrumental data that comprise the "multiproxy" network used by MBH98.
Figure 1:
Distribution of annual resolution proxy indicators used in this study. Dendroclimatic reconstructions are indicated by "tree" symbols, ice core/ice melt proxies by "star" symbols, coral records by "C" symbols. Long historical records and instrumental "gridpoints" series are shown by squares (temperature), or diamonds (precipitation). Groups of "+" symbols indicate principal components of dense tree ring sub-networks, with the number of such symbols indicating the number of retained principal components. Sites are shown dating back to at least 1820 (red), 1800 (blue-green), 1750 (green), 1600 (blue), and 1400 (black). Certain sites (e.g., the Quelccaya ice core) consist of multiple proxy indicators (e.g., multiple cores, and both oxygen isotope and accumulation measurements). [Reprinted with permission from Mann et al (1998). Nature (London), 392, 779-787. Copyright (C)1998 Macmillan Journals Limited.]
These data were calibrated(see details in MBH98) by the instrumental surface temperature data (Figure 2) available during the 20th century, based on a multivariate regression of the proxy data network against the primary eigenvectors of the monthly global instrumental temperature data (Figure 3) to yield a statistical relationship that would allow the projection of temperature patterns on a year-by-year basis, preceeding the 20th century (1902-1980) period of widespread instrumental data. The spatial temperature patterns were determined by summing over the reconstructed histories of the retained eigenvectors (the reconstructed Principal Components or "RPC"s). The reader is referred to MBH98 for details regarding the calibration process. In the present study, the entire procedure has been repeated for two distinct half-year seasons: the Boreal Warm season/Austral Cold season (Apr-Sep) and the Boreal Cold season/Austral Warm season (Oct-Mar) [NOTE: It is our convention to reference the Boreal cold season reconstructions to the year corresponding to Jan-Mar rather than Oct-Dec. This differs by one year from certain other conventions (e.g,. the typical convention for referring to winter mean SOI) and should be kept in mind in making comparisons with other winter climate indices]. The results of the temperature pattern calibrations for both the annual mean reconstructions of MBH98 and the more recent seasonal (boreal cold and warm half-year) reconstructions are provided for the reader.
Figure 2:
Distribution of the (1082) nearly continuous available monthly land air/sea surface temperature gridpoint data available from 1902 onward indicated by shading. The squares indicate the subset of 219 gridpoints with nearly continuous records extending back to 1854 that are used for verification. Northern Hemisphere (NH) and global (GLB) mean temperature are estimated as areally-weighted (ie, cosine latitude) averages over the Northern hemisphere and global domains respectively. The large rectangle indicates the tropical Pacific SST sub-domain discussed in the text. The small rectangle in the eastern tropical Pacific shows the traditional NINO3 region. These data are described in more detail by Jones (1994 [Initial comparisons using an updated version of this dataset (e.g., Jones et al, 1999) showed no significant differences in the large-scale structure of the 20th century surface temperature dataset, although some specific differences are notable, particularly during the WWII years (e.g., the mid 1940s). Future updates of these reconstructions will employ this latter instrumental surface temperature dataset.] [Reprinted with permission from Mann et al (1998). Nature (London), 392, 779-787. Copyright (C)1998 Macmillan Journals Limited.]
For Mann et al(1998) Temperature: Reconstructed Data(1730-1980), Raw Instrumental Data-Verification(1854-1901), Calibration(1902-1993), and Eigenvector Filtered Raw Data(1902-1993)
click here:
Figure 3:
Empirical orthogonal functions (EOFs) for the five leading eigenvectors of the monthly global temperature data from 1902-1993. CLICK on a EOF graph to see larger viewing image as well as the time history ("Principle Component": these are shown for both annual and seasonal means of the monthly data) of the associated pattern from 1902-1993. [Reprinted with permission from Mann et al (1998). Nature (London), 392, 779-787. Copyright (C)1998 Macmillan Journals Limited.]
View Annual, Warm and Cold Season Principle Component 1
View Annual, Warm and Cold Season Principle Component 2
View Annual, Warm and Cold Season Principle Component 3
View Annual and Cold Season Principle Component 4
View Annual and Cold Season Principle Component 5
The validity of the annual-mean reconstructions was demonstrated based on a series of statistical cross-validation or "verification" experiments. In these experiments, the reconstructions based on the calibration of 20th century instrumental data were compared against withheld instrumental data, including those available on a large-scale basis during the latter half of the 19th century (see Figure 4), and sparser data available in certain regions (e.g., Europe and North America) several centuries back in time. The reader is referred to MBH98 for details of these experiments. We provide here the actual statistical results from the verification experiments for
annual mean, cold-season and warm-season. The reconstructions have been demonstrated to be unbiased back in time, as the uncalibrated variance during the 20th century calibration period was shown to be consistent with a normal distribution (Figure 5) and with a white noise spectrum. Unbiased self-consistent estimates of the uncertainties in the reconstructions were consequently available based on the residual variance uncalibrated by increasingly sparse multiproxy networks back in time [this was shown to hold up for reconstructions back to about 1600. For reconstructions farther back in time, Mann et al (1999) show that the spectrum of the calibration residuals is somewhat more "red", and more care needs to be taken in estimating the considerably-expanded uncertainties farther back in time].These various internal consistency checks and verification experiments, together, indicate that skillful and unbiased reconstructions are possible several centuries back in time, both for the annual-mean and separate cold- and warm- season. However, the reader will note that a considerably smaller fraction of the instrumental variance is calibrated in the seasonal reconstructions (particularly the warm-season) than in the annual-mean reconstructions. We attribute this to the diverse seasonal information in the widespread network of proxy data used, which allows more effective reconstruction of annual mean conditions than particular seasonal conditions. The uncertainties are thus considerably greater for the seasonal reconstructions. Moreover, the annual mean reconstructions are not equivalent to the sum of the cold-season and warm-season reconstructions since the substantially greater uncertainties in the latter add in quadrature, rather than canceling, in a numerical average. For example, the amplitude of the NH series variations in past centuries is similarly underestimated for both warm and cold-season, and the average of the two is a considerable underestimate of the annual-mean reconstruction. For these reasons, the quantitative details of these latter reconstructions should be interpreted quite cautiously, although the qualitative insights afforded by the seasonally-resolved versions of the reconstructions are useful.
Figure 4:
Spatial patterns of (top) calibration beta and verification beta (middle) and r-squared (bottom) statistics for annual-mean reconstructions. The calibration statistics are based on the 1902-1980 data, while the verification statistics are based on the sparser 1854-1901 instrumental data (see Figure 2) withheld from calibration. For the beta statistic, values that are insignificant at the 99% level are shown in gray, while negative, but 99% significant values are shown in yellow, and significant positive values are shown in two shades of red. For the r-squared statistic, statistically insignificant values (or any gridpoints with unphysical negative values of correlation) are indicated in gray. The color scale indicates values significant at the 90% (yellow), 99% (light red), and 99.9% (dark red) levels (these significance levels are slightly higher for the calibration statistics which are based on a longer period of time). More details regarding significance level estimation are provided in MBH98. [Reprinted with permission from Mann et al (1998). Nature (London), 392, 779-787. Copyright (C)1998 Macmillan Journals Limited.]
For larger calibration image click here or on image.
Figure 5:
Histogram of calibration residuals for annual-mean NH series.
A Gaussian parent distribution is shown for comparison, along with the +/- 2 standard error bars for the frequencies of each bin. The distribution is consistent with a Gaussian distribution at a high (95%) level of confidence. The distribution of residuals for the NINO3 index (not shown) is consistent with a Gaussian distribution at a 99% level of confidence. For larger viewing image of figure 5 please click here or on image.
Owing to the decreased number of
spatial degrees of freedom in the earliest reconstructions (associated with significantly decreased calibrated variance before e.g. 1730 for annual-mean and cold-season, and about 1750 for warm-season pattern reconstructions) regional inferences are most meaningful in the mid 18th century and later, while the largest-scale averages are useful further back in time. For example, the NH annual mean temperature series appears to exhibit skill back to at least AD 1400 (and has now been extended back to AD 1000 by Mann et al (1999), albeit with expanded uncertainty estimates). We have also verified that possible low-frequency bias due to non-climatic influences on dendroclimatic (tree-ring) indicators is not problematic in our temperature reconstructions.A NINO3 SST index, describing El Nino-related variability, can be calculated in the eastern tropical Pacific directly from these reconstructions (i.e., by averaging the global reconstructions over the NINO3 rectangular region defined in Figure 2). The NINO3 reconstructions are also discussed in more detail in the next section.
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Temperature Reconstructions