1. Introduction

Drought occurrence remains a serious concern in the United States (U.S.). In 1996, the most severe drought of the past 20 years struck the Southwest. Such events place huge demands on rural and urban water resources and quality, and place huge burdens on agricultural and energy production. The 1996 drought was preceded by a severe drought in the late 1980s in California (Roos 1994; Haston and Michaelsen 1997), in 1986 in the Southeast (Bergman et al. 1986; Cook et al. 1988), in 1976–77 in the West (Namias 1978; Matthai 1979), in the 1960s in the Northeast (Namias 1966; Cook and Jacoby 1977), in the 1950s in Texas (Namias 1955; Stahle and Cleaveland 1988), and in the 1930s in the northern Great Plains (Warrick 1980; Stockton and Meko 1983). Clearly, drought is a common occurrence in the U.S. and can occur anywhere. Understanding the causes of drought, especially the severe multiyear events, is necessary if reliable methods of forecasting are to be developed. A major difficulty in using the available meteorological records to model drought in the U.S. is the limited time span covered by such records. There are often too few realizations of proposed forcing mechanisms of drought in the short instrumental records to test any of them in a statistically rigorous way. We hope to alleviate this problem through the use of centuries-long, annual tree-ring chronologies.

In this paper we describe the development of a gridded network of drought reconstructions covering the continental U.S. that is derived from a large collection of climatically sensitive tree-ring chronologies. The reconstructions cover the period 1700–1978 and are based on the Palmer Drought Severity Index (PDSI; Palmer 1965), a well-known and widely used measure of drought and wetness. Previous efforts in reconstructing drought from tree rings in the U.S. have been highly successful (e.g., Blasing and Duvick 1984; Cook and Jacoby 1977; Cook et al. 1988; Cook et al. 1992; Graumlich 1993; Haston and Michaelsen 1994, 1997; Meko 1992; Mitchell et al. 1979; Stahle and Cleaveland 1988; Stahle et al. 1985, 1988; Stockton and Meko 1975, 1983; Woodhouse and Meko 1997). However, most of these efforts have only involved reconstructing local or regional drought histories. Earlier efforts by Fritts (1976, 1991) to reconstruct seasonal temperature and precipitation across the U.S. met with limited success because the tree-ring data used were restricted to western North America. Since that pioneering work, the coverage of tree-ring chronologies across the U.S. has increased enormously. Consequently, an effort to expand these drought reconstructions in a homogeneous way to the entire continental U.S. was initiated by Meko et al. (1993) and developed further by Cook et al. (1996).

We will describe in considerable detail the method used to develop the continent-wide grid of drought reconstructions and provide a number of results that document the generally high fidelity of the tree-ring estimates. This has been done in an effort to make the reconstructions as useful as possible to climatologists and modelers who might want to use these data for studying past temporal and spatial patterns of drought and their association with hypothesized forcing functions. To this end, the drought reconstructions have already been used with considerable success to reevaluate the putative connection between a bidecadal drought area rhythm in the western U.S. and solar/lunar tidal forcing (Mitchell et al. 1979; Cook et al. 1997). In addition, they are presently being used to study and better understand the teleconnection between drought/wetness and the El Niño–Southern Oscillation in the U.S. (Ropelewski and Halpert 1986; Cook et al. 1999; Cole and Cook 1998).

Much of what we have produced is, in a sense, an extension of the work done by Karl and Koscielny (1982; referred to hereafter as KK) in their study of drought in the U.S. The research of KK was based on a 60-point grid of instrumental PDSI data covering the period 1895–1981. In so doing, they described some important temporal and spatial features of drought in the U.S. As will be shown, our tree-ring reconstructions faithfully capture most of the properties of drought described by KK. In the process, the drought database for the U.S. has been extended back in time by a factor of 3 on a much denser 154-point grid, which allows for more detailed temporal and spatial analyses.

2. The PDSI grid

The PDSI grid used in this study is 2° lat × 3° long and is patterned after a study of runoff and drought across the United States by Langbein and Slack (1982). This grid is shown in Fig. 1. It is based on 1036 single-station monthly PDSI records estimated from the Historical Climatology Network (Karl et al. 1990) and modified according to Guttman (1991). However, the Death Valley, California, record was deleted prior to gridding because of anomalously high (e.g., >20) monthly PDSI values in 1958. All stations used begin no later than 1925 and end no earlier than 1989.

The choice of the gridding dimension was a trade-off between spatial resolution and the desire to reduce the size of the PDSI network. A 2° × 3° grid reduces the PDSI network to about 15% of its original size. Yet, the spatial definition of the grid should still be high enough to capture mesoscale patterns of wetness and dryness and to resolve regional drought patterns found by KK using a coarser 60-point PDSI grid.

Following Meko et al. (1993) and Cook et al. (1996), the single-station records were interpolated to the 155 grid points using inverse-distance weighting of the form

View Expanded

where m is the number of stations within a given search radius of grid point k, PDSI_j is the jth PDSI station record, and d_j is the distance of station j from grid point k. The first 3 yr of data were deleted from each station record to eliminate starting-value transience in computing the monthly PDSIs (N. Guttman 1994, personal communication). Then, a 150-km search radius was used to locate stations local to each grid point. All stations found within that radius were used. If at least five stations were not found within 150 km, then the five closest stations were used. A minimum distance of 30 km was used in 1/d to avoid excessively weighting stations very close to the grid points. As stations dropped out prior to 1928, the weights of the remaining series were renormalized for interpolation to gridpoint k. This enabled the preservation of pre-1928 PDSI data for regression model validation.

Because the individual stations used in the grid have varying starting years, the first year of data available at each grid point varies over space. All of the grid points have data back to 1913. Prior to 1913, the number of grid points with data declines to 143 by 1903, 97 by 1895, 38 by 1890, and 10 by 1874 due to the changing beginning years of the instrumental PDSI data over the grid. The quality of the grid also varies over space, with the weakest areas located in the northern Great Basin and Rocky Mountains regions (Cook et al. 1996).

The PDSI data were gridded on a monthly basis. Yet, past experience indicates that summer (i.e., June–August) PDSI relates better to tree rings on average than to any single month when comparisons are made over large geographic areas. Cook et al. (1992) found that the peak correlation between PDSIs and tree rings shifted from June for chronologies south of Virginia, to July in the Virginia–New York region, and even to August for some chronologies in northern New England and Canada. This shift was attributed to regional differences in phenology (i.e., the timing of tree growth) associated with the northward march of the growing season in spring and to the time required for evapotranspiration demand to significantly draw down the soil moisture supply. Consequently, we also used summer PDSI here as the best drought index to reconstruct across the United States.

3. The tree-ring network

The tree-ring chronologies used here to reconstruct past drought across the continental U.S. number 425 now, an increase of 177 over those used by Meko et al. (1993) in their examinations of spatial patterns of tree growth. Many of the new chronologies were developed after the start of that study. Others were not included for a variety of reasons. We have chosen to include virtually all available chronologies that begin no later than 1700 and end no earlier than 1979, a criterion previously established by Meko et al. (1993). Figure 2 shows the distribution of sites across the United States. The distribution is highly patchy due, in part, to the uneven distribution of forested land. In addition, the distribution of tree species in the network is highly regional due to the natural distribution of forest communities and species range limits in the U.S. See Cook et al. (1996) for more details. Not all of these chronologies will be useful predictors of drought. However, the screening process described and tested below for retaining candidate tree-ring predictors of PDSI will guard against including those chronologies not statistically related to drought.

Prior to regression analysis, the tree-ring chronologies were put through a process of variance stabilization described in Meko et al. (1993). Variance stabilization was done to reduce the effects of changing sample size on the variance of the tree-ring chronology, especially in the early portions of chronologies below, say, six individual measurement series. This removed a potential artifact from the data that is unlikely to be related to changing climatic variability.

4. Calibration/verification results

The method used to reconstruct the PDSI grid from tree rings is point-by-point regression (PPR). As implemented here, PPR is simply the sequential, automated fitting of single-point principal components regression models of tree rings to a grid of climate variables. The sequential nature of PPR differentiates it from joint space–time methods used to simultaneously relate two fields of variables, such as canonical regression (Glahn 1968; Fritts et al. 1971), orthogonal spatial regression (Briffa et al. 1986; Cook et al. 1994), and singular value decomposition (Bretherton et al. 1992). Mathematical details of the PPR method and tests of its implementation are described in the appendixes at the end of the paper.

The PPR method is based on the premise that only those tree-ring chronologies proximal to a given PDSI grid point are likely to be true predictors of drought at that location, where “true” implies a causal relationship between tree rings and drought that is stable through time. The rationale behind this premise is our understanding of drought in the U.S. as a regional- or mesoscale phenomenon (see KK for mapped regions). Consequently, synoptic-scale teleconnections between tree rings and drought, while statistically significant during any given calibration period, may not be stable through time. This “local control” over the reconstruction of each gridpoint PDSI is not possible with the joint space–time reconstruction methods mentioned above.

In the PPR method, a fixed search radius around each grid point defines the zone of local control exercised by the method in selecting candidate tree-ring predictors of PDSI. A second level of control is also applied in the form of a screening probability, which eliminates tree-ring chronologies from the candidate pool that are poorly correlated with drought. Here we examine the statistical fidelity of the PDSI reconstructions based a 450-km search radius and a screening probability α = 0.10, selected after the extensive testing described in appendix B. The statistics used for this purpose are the same as those described for those tests: the explained variance (R²_c) over the 1928–78 calibration period, the squared Pearson correlation (R²_υ) over the pre-1928 verification period, the reduction of error (RE) in the verification period, and the coefficient of efficiency (CE) over the verification period. See appendix B for the mathematical definitions of these statistics. All four tests are measures of fractional variance in common between actual and reconstructed PDSI. In this sense, they are comparable. However, they differ markedly in their relative performances. As will be seen, the calibration period R²_c always overestimates the true fidelity of the tree-ring estimates of drought, while in the verification period, R²_υ usually indicates better fidelity in the estimates than RE and CE. Among the verification statistics used here, the CE is the most rigorous (Cook et al. 1994).

A PDSI grid point passed the R²_c test if it was successfully calibrated by tree rings following the procedures outlined in appendix A; it passed the R²_υ test if the Pearson correlation between actual and estimated PDSI in the verification period was significant at the 95% one-tailed confidence level; and it passed the RE or CE if either was >0. See appendixes A and B for details. For the R²_c test, 154 of 155 grid points were successfully calibrated. The only grid point not calibrated was the one in southern, subtropical Florida, where there are no tree-ring chronologies. For the R²_υ test, 147 grid points of the remaining 154 were successfully verified. In contrast, the number of RE and CE tests that passed dropped from 147 to 133 and 124 grid points, respectively. So, the verification test results indicate that the tree-ring reconstructions of drought are significantly related to actual PDSI over most of the grid. The median R²_c, R²_υ, RE, and CE fractional variances are 0.55, 0.36, 0.31, and 0.22, respectively. The decreasing trend in these test statistics follows exactly the expected level of rigor of the regression model calibration and validation tests.

As good as these verification results are, they are probably understating the true skill of the tree-ring reconstructions at some grid points. The instrumental PDSI data in the verification period are not likely to be as homogeneous as those in the calibration period due to widely variable station record lengths and fewer station observations per year. In addition, some of the single station records used in the grid may be inhomogenous. Consider, for example, two stations used in the PDSI grid in Nevada: Battle Mountain Airport (40°37′N, 116°52′W, elevation 1381 m) and Elko Federal Aviation Administration (FAA) Airport (40°50′N, 115°47′W, elevation 1548 m). These stations are only 53 and 63 km from the grid point in north-central Nevada (see Fig. 1) and are weighted most heavily in this five-station gridpoint average. Over the 1928–78 calibration period, the summer average PDSIs of these nearby stations have a correlation of 0.67. However, in the 1894–1927 precalibration period common to both stations, their correlation drops catastrophically to 0.05. Most of the loss of fidelity is in the pre-1910 data. If the comparison is made over the 1910–27 period only, the correlation improves somewhat to 0.27, but in either case the correlations are not statistically significant (p < 0.05). With regard to the tree-ring estimates of PDSI, the calibration R²_c is 0.69, while the verification period RE and CE are −0.67 and −0.95, respectively. In this case, there is little doubt that the poor quality of the pre-1928 instrumental PDSI data is contributing strongly to the negative tree-ring verification. Given the extremely high quality and drought sensitivity of the tree-ring chronologies in the Great Basin, it is almost certain that the trees are doing a better job at estimating regional drought and wetness than are the meteorological stations in northern Nevada prior to 1928. It is likely that similar instrumental data problems exist elsewhere in the grid, but we have not yet quantified the impact of this source of error on the verification statistics.

5. Spatial patterns of calibration and verification

The calibration/verification results provided above were summaries for the entire drought grid. We now take a detailed look at the spatial patterns of the fractional variance statistics to see how homogeneous the results are across space.

Figure 3 shows the contoured maps of these statistics. The R²_c map indicates that the regression models for large areas of the U.S. explain 50%–70% of the gridpoint PDSI variance. The weakest calibration areas are in the upper Midwest and in northern New England. The R²_υ map indicates that the drought estimates over virtually all of the United States covary significantly with the actual PDSI data in the verification period. That is, any R²_υ value in excess of 0.10 (i.e., a simple r > 0.32) is statistically significant using a one-tailed test and α = 0.05. The RE and CE maps reveal more clearly some weak areas in the reconstruction grid. Specifically, there are some regions (e.g., the Great Basin, the upper Midwest, and the central Great Plains) with RE and CE both <0. Since these regions verified reasonably well in the R²_υ map, the loss of fidelity is probably due mainly to differences in mean level between the actual and estimated PDSIs over the verification period. This suspicion was largely verified by a series of equality-of-means tests of the verification data. Figure 4 shows maps of the mean differences between the actual and estimated PDSIs (upper map) and the corresponding t-test probabilities for those differences (lower map). Most of the differences fall in the range of ±0.50 PDSI units, which are rarely significant even for α = 0.20. The largest region of significant differences (p < 0.10) is located in the Great Basin and Wyoming–Montana areas where the RE and CE statistics are conspicuously negative.

Similar verification problems in the RE and CE maps around the Great Basin were also found by Cook et al. (1996) in their earlier tests of the PPR method. Their analyses of the gridded instrumental PDSI data indicated that the regions of weak verification in Fig. 3 could be due in part to decreasing quality of the instrumental data, the Great Basin being the most likely case in point (Cook et al. 1996). However, it is also true that the quality and coverage of tree-ring data is somewhat poor in the other areas that do not verify well. Therefore, the gridpoint reconstructions in these regions should be used with more caution than those where the verification tests are all significant. The quality of these reconstructions should improve if new tree-ring chronologies can be developed in areas of poor coverage.

Finally, we examined the degree to which the reconstructions preserved the pattern of PDSI variability across the U.S. For example, it is known that drought variability is generally greater in the western half of the U.S. However, there is no guarantee that the reconstructions have preserved the spatial pattern of drought variability because of variance lost by regression. Yet, such information is important to retain if one is to make meaningful comparisons of drought variability over different time periods in the reconstructions. Figure 5 shows the contoured maps of gridpoint standard deviations for the actual and estimated PDSIs over the calibration period. There appears to be a high degree of similarity between the two maps, even down to the local level of detail. Indeed, the maps have a correlation of 0.91. The preservation of the standard deviation pattern is due to the reasonably homogeneous pattern of calibrated variance shown in the R²_c map. Thus, the reconstructions ought to be quite useful for studying changing patterns of drought variability across the U.S. over the past three centuries.

6. Additional spatial comparisons

The calibration/verification results for the PPR method indicate that the PDSI reconstructions are generally valid expressions of drought over the United States. However, the PPR method does not contain any explicit spatial component other than that related to the search radius. The spatial relationships of drought in the United States (sensu KK) extend over regions that are generally larger than the 450-km search radius used here. Thus, while the individual gridpoint reconstructions are reasonably accurate in a temporal sense, they are not necessarily guaranteed to be valid in a spatial sense beyond the scale of the search radius used here. For this reason, we will describe here a number of analyses that collectively indicate that the spatial patterns of drought have also been well reconstructed by the PPR method.

a. Mean field, correlation, and congruence analyses of yearly PDSI maps

First, we will describe the degree to which the yearly maps (or spatial patterns) of reconstructed PDSI agree with those based on the gridded instrumental data. For this purpose, we will compare (a) the mean PDSI fields over time, (b) the relative spatial patterns using the Pearson correlation coefficient, and (c) the absolute spatial patterns using the congruence coefficient. The reconstructed patterns will be compared to two gridded instrumental PDSI datasets: the original one used for calibration purposes and a new one based on climate division PDSI data not directly used for calibration purposes. Comparisons using the former will be made over the 1874–1981 time period for which there are at least 10 grid points of actual and reconstructed PDSI data, while the latter has data for all grid points back to 1895 only. The rationale for using the gridded climate division data for additional tests is discussed next.

As described earlier, the single-station instrumental PDSI records used in the grid vary in length over space. Thus, some grid points have much longer records than others. The ending years of the tree-ring chronologies also constrain the end year of analysis. This is revealed in Fig. 6a, which shows the number of grid points with actual and reconstructed PDSI data as a function of time. The maximum number (154) covers the period 1913–78. After 1978, the number of reconstructed grid points declines precipitously to 10 by 1981 due to the ending years of the tree-ring chronologies used. Prior to 1913, the number of grid points declines to 143 by 1903, 97 by 1895, 38 by 1890, and 10 by 1874, all due to the changing beginning years of the instrumental PDSI data over the grid. The quality of the instrumental PDSI grid declines back in time as well because the number of single-station records used to estimate the gridpoint values for each year decreases as shorter records drop out of the gridding process. For these reasons, some degradation in the map comparisons ought to be expected, which is unrelated to the true fidelity of the tree-ring estimates.

In contrast, the gridded climate division data are available for all 154 grid points back to 1895 (Fig. 7a), and the number of single-station records represented in the climatic division summaries is generally greater than that available from the Historical Climate Network alone. Consequently, the map comparisons (especially before 1928) ought to be more robust using the gridded climatic division data. Finally, the relationships between the actual and reconstructed data over the 1928–78 calibration period have been optimized in a least squares sense only for the single-station grid. The gridded climate division data, while highly related to the single-station grid, do not suffer from this constraint. Therefore, these additional spatial comparisons should provide a less biased evaluation of the true fidelity of the reconstructed PDSI maps.

1) Mean field comparisons

A simple first-order comparison of the actual and reconstructed PDSI maps can be made by simply comparing the mean fields over time. That is, for each year all of the available gridpoint values are averaged together, separately for the actual and reconstructed data. The resulting grand mean time series are shown in Figs. 6b and 7b for the single-station and climate division grids, respectively. Although the single-station data go back to 1874, correlations between the mean actual and reconstructed series have only been calculated back to 1895 for comparison with the climatic division grid results.

There is a high degree of similarity between the mean series in each case. First, for the single-station grid, the correlation between actual and reconstructed PDSI is 0.944 over the 1928–78 calibration period. The correlation then drops to 0.896 in the 1895–1927 precalibration (i.e., verification) period, but is still highly significant. And over the entire 1895–1981 period, the correlation is 0.889. For the climate division grid, the correlations are comparable: 0.932 for the 1928–78 calibration period, 0.829 for the 1895–1927 precalibration period, and 0.881 overall. Clearly, the mean PDSI fields are well estimated by tree rings back to 1895 at least and even where the number of grid points drops to 10 in the 1874–94 period (see Fig. 6b). The similarity of the calibration period correlations based on the different grids indicates that, at this spatial scale of comparison, there is no significant least squares fitting bias in the reconstructions. These results are highly encouraging. However, this analysis does not reveal how well the spatial patterns that make up the mean fields have been replicated each year by the tree rings. To determine this, we will use map correlation and congruence analyses.

2) Map correlation

To test the relative agreement between actual and reconstructed PDSI maps, we used the Pearson product-moment correlation coefficient. First, we normalized each gridpoint reconstruction using its calibration period mean and standard deviation. This was done to avoid any regional bias in the map correlations due to spatial variations in the PDSI standard deviation (see Fig. 5). Then, for each year i of the n-yr overlap period between actual and reconstructed PDSI, we calculated

View Expanded

where the summation extends over the k = 154 PDSI grid points, p_k and q_k are the actual and reconstructed PDSI values at grid point k, respectively, and p and q are the mean fields for each year i, for example, those shown in Fig. 6b. Because the mean fields are subtracted from the gridpoint values, the information contained in them, which is a real component of drought over the coterminous United States, does not contribute to the estimate of r_pq.

Figure 6c shows the time series of map correlations (solid line) for the single-station grid. Also included is the one-tailed 99% confidence level (dashed line) estimated by randomizing the reconstructed PDSIs and calculating the correlation of this randomized field with the actual data. This was done 5000 times for each year. The resulting significance levels are very close to that which would have been obtained by the standard t test of the correlation coefficient. Note that back to 1889, where the number of grid points exceeds 30, the map correlations all exceed the 99% level. On average, the highest correlations occur during the 1928–78 calibration period (r = 0.652), a result that is probably related to the least squares optimization. Prior to 1928, the correlations decline systematically (e.g., r = 0.475 over the 1895–1927 precalibration period), a result that is consistent with the difference in the pointwise calibration/verification statistics reported earlier. Prior to 1889, the map correlations are mostly nonsignificant, in some cases catastrophically so. This result is probably a combination of a number of things that are at least partly unrelated to the overall quality of the PDSI reconstructions. Some of the longest (i.e., pre-1889) instrumental PDSI records come from the eastern U.S., where the calibration/verification statistics are relatively weak. So, a decline in spatial correlation is not too surprising when that restricted area contributes the most to the correlation analyses. And it is also likely that the quality of the actual gridded data declines back in time as the number of individual station records used in the grid declines.

The map correlations based on the climate division grid are shown in Fig. 7c. Except for 1979, when the number of grid points is small, all correlations exceed the 99% significance level. The average map correlation over the 1928–78 calibration period (r = 0.604) is somewhat weaker than that based on the single-station grid (r = 0.652), a result that is probably related to the lack of prior least squares fitting bias here. However, there is less evidence of the systematic decay in the map correlations prior to 1928 in this case, and the average correlation over the 1895–1927 period (r = 0.503) actually exceeds that based on the single-station grid (r = 0.475).

3) Map congruence

The map correlations are very useful for describing how well the spatial patterns of drought covary in a relative sense. However, because the mean fields are a true component of drought variability over time (see Figs. 6b and 7b), it is desirable to include this information in the spatial analyses as well. To do this, we have used the congruence coefficient, which was originally developed as a measure of the similarity between two factor patterns in multivariate research (Richman 1986; Broadbrooks and Elmore 1987). The congruence coefficient is computed for each year of the overlap period as

View Expanded

where p_k and q_k are the actual and reconstructed PDSI values at grid point k. Note that the only difference between c_pq and r_pq is the lack of p and q here. Thus, the means are not removed in computing c_pq, leading some earlier studies to describe the congruence coefficient as an unadjusted correlation coefficient (Broadbrooks and Elmore 1987). The theoretical range that c_pq may take is the same as r_pq. However, the presence of p and q in the calculation of congruence means that c_pq tends to be biased toward 1.0 relative to r_pq (Richman 1986). There is no theoretical sampling distribution for testing the significance of c_pq because of its partial dependence on p and q, which are random variables in their own right. Several studies have used Monte Carlo methods to generate empirical limits for c_pq (e.g., Broadbrooks and Elmore 1987). Here, we have generated our own significance levels using the randomization procedure described for the correlation coefficient.

Figure 6d shows the map congruence coefficients over time for the single-station grid, along with the empirical 99% confidence levels. The results are qualitatively similar to that found by correlation alone. The highest average congruence occurs in the 1928–78 calibration period (c = 0.694), followed by declining but still significant congruence from 1895 to 1927 (c = 0.563). Prior to 1895, congruence remains significant back to 1889 and then becomes very poor. A close comparison of the correlation and congruence plots reveals that, as expected, there is a small positive bias in the estimates of the latter (e.g., r = 0.581 and c = 0.639, respectively, over the 1895–1981 period). Perhaps the greatest difference in the two analyses is in the estimates of the confidence levels. The dependence of c_pq on p and q has resulted in a highly variable and erratic series of confidence levels that are clearly related to the variability between the mean fields shown in Fig. 6b.

The map congruences based on the climate division grid are shown in Fig. 7d. These results are again qualitatively similar to the correlation results. As before, there is greater long-term stability in map congruence using this grid for comparison with the reconstructed maps, and, except for 1979, all congruences exceed the 99% confidence level. All other details concerning the map correlations above are similar here; for example, the average map congruence for the 1928–78 calibration period (c = 0.655) is weaker than that based on the single-station grid (c = 0.694), but the average congruence over the 1895–1927 period (c = 0.571) actually exceeds that based on the single-station grid (c = 0.563). None of these results indicate any serious deficiency in the annual PDSI maps produced by the tree-ring estimates.

4) Discussion

The analyses shown in Figs. 6 and 7 indicate that the spatial patterns of PDSI in the reconstructions have captured those in the actual data with high (p < 0.01) statistical fidelity. Prior to 1895 some of the differences between the actual and reconstructed PDSI clearly arise from the deterioration of the instrumental PDSI coverage in time and space. The mean fields of the reconstructions have been estimated extremely well back as far as it is possible to test them, while the more detailed reconstructed annual maps are significantly related to the actual PDSI fields back to 1895 at least. The correlations between the actual and reconstructed mean fields are higher than the mean calibration and verification results of the individual grid points using PPR. This result indicates that the gridpoint reconstructions contain more “local noise” than do larger-scale averages of PDSI, with the mean fields studied here being the limiting case of averaging over all grid points (i.e., a continental-scale average). Averaging gridded climate reconstructions spatially to improve the signal-to-noise ratio has been used with considerable success (e.g., Fritts 1991; Mann et al. 1998) and is clearly justified if the main interest is in climate variability at spatial scales larger than that initially reconstructed. However, how one averages the reconstructions spatially to preserve insights into the physical climate system needs to be carefully considered. One approach to this problem is to use rotated principal component analysis (Richman 1986) to objectively define the natural regional drought climatologies in the United States (sensu KK). In the next section, we will use rotated principal component analysis to demonstrate that the regional drought patterns found by KK in their instrumental data can be reproduced well in most cases by our PDSI reconstructions.

7. Concluding remarks

The U.S. drought reconstruction grid produced here is a significant new application of dendroclimatic techniques to reconstruct past climate. The quality of the gridpoint reconstructions is generally quite good and spatially homogeneous. As noted earlier, the automated nature of the PPR method virtually guarantees that the gridpoint reconstructions produced here will not necessarily be the best possible at any given grid point. However, the PPR method does guarantee that each gridpoint model is developed in a consistent manner. Its specific implementation here also guarantees a near-global optimum in terms of model verification.

There is little doubt that the joint space–time methods of climate reconstruction (e.g., canonical regression or singular value decomposition) would have resulted in better calibration statistics here (e.g., a higher global R²_c). These techniques are constrained to find the optimal linear association between two fields of variables. However, they would almost certainly lead to poorer verification results (see the verification surfaces shown in Appendix B, Fig. B1) because they would allow long-range, temporally unstable, tree-ring teleconnections to influence the estimation of the gridpoint PDSIs. The joint space–time methods would also be mathematically ill-conditioned if the original data were used directly here because the number of grid points (155) greatly exceeds the number of years (51) used for calibration. This problem can be ameliorated by reducing the dimensions of the problem through principal component analysis of the predictor and/or predictand fields prior to regression (Fritts 1976; Cook et al. 1994; Mann et al. 1998) but at the loss of higher-order dimensionality in the resulting field of reconstructions. The reconstructions produced by PPR do not have this limitation.

These reconstructions are freely available from the National Geophysical Data Center (NGDC), World Data Center-A for Paleoclimatology, in Boulder, Colorado. (The Web site addresses for these data are http://www.ngdc.noaa.gov/paleo/pdsiyear.html for the annual PDSI maps and http://www.ngdc.noaa.gov/paleo/usclient2.html for the summer PDSI time series.) We hope that future analyses of these reconstructions will lead to an improved understanding of drought variability in the U.S., especially on the interdecadal timescale (e.g., Karl and Riebsame 1984), which is very difficult to investigate with instrumental climate data alone.

We expect to improve the drought reconstructions for the United States in the future through the use of improved statistical methods and, more importantly, the development of new tree-ring chronologies in areas that are now weakly modeled. In addition, efforts are now under way to extend the reconstructions back in time to enable analyses of drought variability at longer timescales. Consequently, the PDSI reconstructions on the National Oceanic and Atmospheric Administration Web sites will be updated periodically as these improvements are made.