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FIGURE 10.16 July Palmer drought indices for the Hudson Valley, New York, from 1694 to 1972 reconstructed from tree rings, (a) Unsmoothed estimates; (b) a lowpass filtered version of the unsmoothed series that emphasizes periods of > 10 yr (Cook and Jacoby, 1979).

techniques involve identifying the variance that is common to individual eigenvectors of the two different data sets and defining the relationship between them. The techniques are important in that they allow spatial arrays (maps) of tree-ring indices to be used to reconstruct maps of climatic variation through time (Fritts et al., 1971; Fritts, 1991; Fritts and Shao, 1992; Briffa et al., 1992b).

The most comprehensive work of this sort is that of Fritts (1991). Ring-width indices from 65 sites across western North America (i.e., 65 variables) were transformed into eigenvectors, where each one represented a spatial pattern of growth co-variance among the sites (Fig. 10.15). The first ten eigenvectors accounted for 58% of the joint space-time variance of growth anomaly over the site network. Eigenvectors were also derived for seasonal pressure data at grid points over an area extending from the eastern Pacific (100° E) to the eastern U.S. (80° W) and from 20 to 70° N; the first three eigenvectors of pressure accounted for -56% of variance in the data. Using amplitudes of all these eigenvectors for the years common to both data sets (1901-1962), canonical weights were computed for the growth eigenvectors to give maximum correlations with pressure anomalies. Amplitudes of these weighted eigenvectors were then used as predictors of normalized pressure departures at each point in the pressure grid network, by applying the canonical weights to the standardized ring-width data (the level Illb approach in Table 10.1). This resulted in estimates of pressure anomaly values at each point in the grid network, for each season, for each year of the ring-width network. Maps of mean pressure anomaly could thus be produced for any interval by simply averaging the individual anomaly values (Fritts and Shao, 1992). The same procedure was used for a network of grid-ded temperature and precipitation data across the United States. Figure 10.17 gives the mean pressure, temperature and precipitation anomalies for 1602-1900 for each gridded region compared to twentieth century means. This -300 yr interval spans much of what is commonly referred to as the "Little Ice Age" and it is interesting that the reconstruction suggests there was a stronger ridge over western North America, with higher pressure over Alaska during this time. This was associated with

Mean Pressure

Mean Temperature Total Precipitation

FIGURE 10.17 Anomalies (from 1901-1970 mean values) of mean sea-level pressure, temperature, and precipitation (in % of mean) for the period 1602-1900.Values were reconstructed from a 65-chronology network of tree-ring width data (see Fig. 10.15). Shaded areas on the temperature and precipitation maps are warm or dry anomalies, respectively (Fritts, 1991).

Mean Temperature Total Precipitation

FIGURE 10.17 Anomalies (from 1901-1970 mean values) of mean sea-level pressure, temperature, and precipitation (in % of mean) for the period 1602-1900.Values were reconstructed from a 65-chronology network of tree-ring width data (see Fig. 10.15). Shaded areas on the temperature and precipitation maps are warm or dry anomalies, respectively (Fritts, 1991).

Reconstructions 1602-1900 compared to instrumental record 1901-1970

Mean Pressure higher temperatures and lower precipitation over much of the western and southwestern United States, but cooler and wetter conditions in the east and northeast. Precipitation was also higher in the Pacific Northwest, presumably reflecting more frequent depressions affecting this area. In effect, the reconstruction points to an amplification of the Rossby wave pattern over North America, with an increase in cold airflow from central Canada into the central and eastern U.S. (Fritts, 1991; Fritts and Shao, 1992). Reconciling these reconstructions with evidence for extensive glacier advances in the Rockies and other mountain ranges of western North America during this period is clearly very difficult (Luckman, 1996).

Related procedures have been used by other workers. Briffa et al. (1988) for example, used orthogonal spatial regression to reconstruct April-September temperatures over Europe west of 30° E using densitometric information from conifers over Europe. In their procedure both the spatial array of temperature and the spatial array of densitometric data were first reduced to their principal components. Only significant components in each set were retained. Each retained PC of climate was then regressed in turn against the set of retained densitometric PCs. This procedure can be thought of as repeating the level lib approach (Table 10.1) m times, where m is the number of retained climate PCs. Having found all of the significant regression coefficients, the set of equations relating the climate PCs to the tree-growth PCs were then transformed back to original variable space, resulting in an equation for each temperature location in terms of all the densitometric chronologies. A similar approach was used by Schweingruber et al. (1991) and Briffa and Schweingruber (1992) to derive temperature reconstructions for Europe, and by Briffa et al. (1992b), who derived temperature anomaly maps for the western United States from a network of tree-ring density data.

Fig. 10.18 shows some examples of these reconstructions in comparison with instrumental data for the same years, providing a qualitative impression of how good the pre-instrumental reconstructions might be. In fact, verification statistics over an independent period are generally good, providing a more quantitative assessment that earlier reconstructions are likely to be reliable. Of particular interest is the reconstruction of temperatures in the early nineteenth century, around the time of the eruption of Tambora (Fig. 10.19). Tambora (8° S, 118° E) exploded in April 1815; it is considered to have been the largest eruption in the last thousand years if not the entire Holocene (Rampino and Self, 1982; Stothers, 1984). Contemporary accounts

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FIGURE 10.1 8 Observed April-September mean temperature anomalies in the summers of the early 1930s (expressed as departures from the 1951-1970 mean) compared with (bottom panel) the corresponding reconstruction based on a tree-ring density network made up of 37 chronologies distributed across the region. (Schweingruber et al., 1991).

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FIGURE 10.1 8 Observed April-September mean temperature anomalies in the summers of the early 1930s (expressed as departures from the 1951-1970 mean) compared with (bottom panel) the corresponding reconstruction based on a tree-ring density network made up of 37 chronologies distributed across the region. (Schweingruber et al., 1991).

FIGURE 10.19 Reconstructed summer (April-September) temperature anomalies (from 1951-1970 means) for western Europe and western North America for the early nineteenth century based on a 37 site tree-ring density network in Europe and a 53 site tree-ring density network in North America. Conditions were cold in both regions in the years following the eruption of Tambora, though 1816 itself was mostly warm in western North America (Schweingruber et al„ 1991).

FIGURE 10.19 Reconstructed summer (April-September) temperature anomalies (from 1951-1970 means) for western Europe and western North America for the early nineteenth century based on a 37 site tree-ring density network in Europe and a 53 site tree-ring density network in North America. Conditions were cold in both regions in the years following the eruption of Tambora, though 1816 itself was mostly warm in western North America (Schweingruber et al„ 1991).

document the severe climatic conditions that were experienced in western Europe and in the eastern United States in the following year, which became known as "the year without a summer" (Harington, 1992). The dendroclimatic reconstruction for summer temperatures (April-September) in western Europe indeed show extremely cold conditions in 1816 with cold summers also in 1817 and 1818 over most of western Europe (and northwestern Russia; Shiyatov, 1996) continuing into 1819 in southern Europe. Over most of the western United States and Alaska, 1816 was not cold, but the following four summers were uniformly cooler than the 1951-1970 reference period. The coldest summer in the last few centuries in the western United States (1601) was also associated with an eruption, probably Huaynaputina in Peru (Briffa et al., 1992b, 1994). Temperatures across the region averaged 2.2 °C below the 1881-1982 mean as a result of that event.

Before concluding this section on calibration, it is worth noting that tree-ring indices need not be calibrated only with climatic data. The ring-width variations contain a climatic signal and this may also be true of other natural phenomena that are in some way dependent on climate. It is thus possible to calibrate such data directly with tree rings and to use the long tree-ring records to reconstruct the other climate-related series. In this way, dendroclimatic analysis has been used to reconstruct runoff records (Stockton, 1975; Stockton and Boggess, 1980) and lake-level variations (Stockton and Fritts, 1973). Some of these applications are discussed in more detail in Section 10.3.3.

10.2.5 Verification of Climatic Reconstructions

An essential step in dendroclimatic analysis (indeed in all paleoclimatic studies) is to test or verify the paleoclimatic reconstruction in some way. The purpose of verification is to test if the transfer function model (derived from data in the calibration period) is stable over time, usually by comparing part of the reconstruction with independent data from a different period. Inevitably, when the prediction estimates are tested against an independent data set the amount of explained variance will almost always be less than in the calibration period. To quantify how good the reconstruction is, in comparison with independent data, various statistical tests are generally performed (Gordon, 1982; Fritts et al., 1990; Fritts, 1991, Appendix 1). These statistics then provide some level of confidence in the rest of the reconstruction; the performance of the transfer function over the verification period is the best guide to the likely quality of the reconstruction for periods when there are simply no instrumental data.

Two approaches to verification are generally adopted. First, when calibrating the tree-ring data, very long instrumental records for the area are sought. Only part of these records are then used in the calibration, leaving the remaining early instrumental data as an independent check on the dendroclimatic reconstruction. If the reconstruction is in the form of a map, several records from different areas may be used to verify the reconstruction, perhaps indicating geographical regions where the reconstructions appear to be most accurate (Briffa et al., 1992b). This approach is difficult in some areas where tree-ring studies have been carried out (e.g., the western United States and northern treelines) because these are areas with very few early instrumental records (Bradley, 1976). Dendroclimatic studies in western Europe (Serre-Bachet et al., 1992; Briffa and Schweingruber, 1992) can be more exhaustively tested because of the much longer instrumental records in that area. Indeed, it is sometimes possible to conduct two calibrations, with both tree-ring and climatic data from different time periods and to compare the resulting dendroclimatic reconstructions for earlier periods derived independently from the two data sets (Briffa et al., 1988). This provides a vivid illustration of the stability of the derived paleoclimatic reconstructions (Fig. 10.20).

A second approach is to use other proxy data as a means of verification. This may involve comparisons with historical records or with other climate-dependent phenomena such as glacier advances (LaMarche and Fritts, 1971b) or pollen variations in varved lake sediments (Fritts et al., 1979) etc. It may even be possible to use an independent tree-ring data set to compare observed growth anomalies with those expected from paleoclimatic reconstructions. Biasing and Fritts (1975), for exam-

FIGURE 10.20 Two reconstructions of northern Fennoscandinavian temperatures for July-August using the same transfer function model, but with calibration based on 1852-1925 in the upper diagram, and 1891-1964 in the lower diagram. Ordinate axis is in standard deviation units with one unit approximately equal to I "C.The two calibrations accounted for 69% and 56% of the variance of instrumental temperature over the same (calibration) interval, respectively. Both gave statistically significant statistics when verified against data from the other "independent" interval.Thus, both reconstructions could be viewed as statistically reliable. Although the two series are strongly correlated (r = 0.87) there are important differences between them, which warns against overinterpreting the reconstructions for individual years. For example, the lower diagram shows an extreme in 1783 that does not appear in the upper diagram, and even the lower frequency variations show important differences requiring careful examination of the regression weights used for each reconstruction (Briffa et al., 1988).

FIGURE 10.20 Two reconstructions of northern Fennoscandinavian temperatures for July-August using the same transfer function model, but with calibration based on 1852-1925 in the upper diagram, and 1891-1964 in the lower diagram. Ordinate axis is in standard deviation units with one unit approximately equal to I "C.The two calibrations accounted for 69% and 56% of the variance of instrumental temperature over the same (calibration) interval, respectively. Both gave statistically significant statistics when verified against data from the other "independent" interval.Thus, both reconstructions could be viewed as statistically reliable. Although the two series are strongly correlated (r = 0.87) there are important differences between them, which warns against overinterpreting the reconstructions for individual years. For example, the lower diagram shows an extreme in 1783 that does not appear in the upper diagram, and even the lower frequency variations show important differences requiring careful examination of the regression weights used for each reconstruction (Briffa et al., 1988).

pie, used a network of trees from an area between northern Mexico and southern British Columbia to reconstruct maps of sea-level pressure anomalies over the eastern Pacific and western North America. A separate temperature-sensitive data set from Alaska and the Northwest Territories of Canada was then used to test the reconstructions. Periods of anomalously low growth in the northern trees were associated with increased northerly airflow as predicted by the pressure reconstructions.

In all verification tests, one is inevitably faced with two questions:

(a) If the verification is poor, does the fault lie with the dendroclimatic reconstruction (and hence the model from which it was derived) or with the proxy or instrumental data used as a test (which may itself be of poor quality and subject to different interpretations)? In such cases, re-evaluation of the tree-ring data, the model, and the test data must be made before a definitive conclusion can be reached.

(b) Is the dendroclimatic reconstruction for the period when no independent checks are possible as reliable as for the period when verification checks can be made? This might seem an insoluble problem but it is particularly important when one considers the standardizing procedure employed in the derivation of tree-growth indices (Section 10.2.3). Errors are most likely to occur in the earliest part of the record, whereas tests using instrumental data are generally made near the end of the tree-growth record (where replication is generally highest and the slope of the standardization function is generally lowest) and least likely to involve the incorporation of large error. The optimum solution is for both instrumental and proxy data checks to be made on reconstructions at intervals throughout the record, thereby increasing confidence in the overall paleoclimatic estimates.

Dendroclimatologists have set the pace for other paleoclimatologists by developing methods for rigorously testing their reconstructions of climate. Many other fields would benefit by adopting similar procedures.

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