1. Introduction

Understanding interannual to interdecadal variations in continental drought is important for improved water resource planning and management. The 1988 drought and accompanying heat waves over the midwestern United States caused around $39 billion in damages and contributed to increased heat-related mortality rates (Riebsame et al. 1991; Trenberth and Branstator 1992). Water rights allocations and reservoir operating rules are predicated on long-term assessments of drought frequency, and seasonal to interannual forecasts of seasonal drought are of interest for crop insurance, reservoir operation, and disaster planning.

Associations of North American hydrologic drought with the El Niño–Southern Oscillation (ENSO) have been identified in previous studies (Piechota and Dracup 1996; Trenberth and Branstator 1992; Cole and Cook 1998). Other researchers (Ropelewski and Halpert 1986, 1989; Halpert and Ropelewski 1992; Kiladis and Diaz 1989) have also identified strong relationships between ENSO and seasonal mean anomalies in U.S. temperatures and precipitation, which are key factors in the initiation of drought. ENSO is understood as an interannual, quasiperiodic, coupled mode of the tropical ocean–atmosphere system, with worldwide hydroclimatic teleconnections (Battisti and Sarachik 1995). The strength, duration, and frequency of the El Niño and La Niña events, which comprise the two phases of ENSO, have varied significantly over the current century (Trenberth and Hoar 1996, 1997; Rajagopalan et al. 1997; Kestin et al. 1998). Indeed, significant variations in ENSO are noted in a 10 000-yr integration of the Cane–Zebiak ENSO model (Cane et al. 1995) under a stationary climate scenario. Corresponding changes in the nonlinear response of the tropical and extratropical atmosphere (Hoerling et al. 1997) and in the North American climate (Hoerling and Kumar 1997) have also been noted from analyses of data obtained from both observational and climate model studies.

Decadal variations in ENSO teleconnections to continental temperature, precipitation, stream flow, and drought indices around the globe have also been noted by many. In particular, Power et al. (1999) noted decadal variability in ENSO teleconnections to Australian climate and suggested that it might be due to interdecadal Pacific oscillation; Krishna Kumar et al. (1999a,b) noted decadal changes in the Indian summer monsoon–ENSO association; Rodo et al. (1997) saw changes in ENSO and North Atlantic Oscillation (NAO) teleconnections to southern Europe precipitation; and Price et al. (1998) found an increasing association of northern Israel precipitation to ENSO in the recent decades. Temporal variations in ENSO teleconnections to U.S. climate have also been reported; McCabe and Dettinger (1998), Dettinger et al. (1995, 1998), and Cayan et al. (1998) found decadal variability in ENSO teleconnections to western U.S. precipitation, and Cole and Cook (1998) noted changes in the spatiotemporal variability in U.S. summer Palmer Drought Severity Index (PDSI), while Dai et al. (1998) found decadal variations in the areas of severe drought over the globe during the twentieth century. They also found that the recent variations in the drought area closely relate to changes in ENSO frequency. Interannual variability of the summer precipitation regime over the United States, through modulation of the North American monsoon system, has been shown (Higgins et al. 1998, 1997) to be linked to the SSTs in the eastern Pacific and cold tongue regions, via anomalous Hadley circulation.

ENSO influence on wintertime intraseasonal extreme precipitation and temperature over the United States has been documented by Gershunov (1998) and Gershunov and Barnett (1998a). They find that the ENSO-based predictability of extreme rainfall and temperature is sensitive to the ENSO phase and is spatially variable. Furthermore, there is an asymmetric response of precipitation and temperature with respect to El Niño and La Niña phases. Model reproduction of these general features has been reported by Gershunov and Barnett (1998a). These observational and model findings have useful implications for long-range predictability.

It is not clear whether these changes are due to 1) variations in ENSO strength and frequency and the nonlinearity of the teleconnection; 2) extratropical decadal ocean–atmosphere variability, for example, the NAO (Hurrell and van Loon 1997; Kushnir 1994; Mann and Park 1996) and interdecadal variability, for example, the North Pacific Oscillation/Pacific Decadal Oscillation (PDO; Mantua et al. 1997; Gershunov and Barnett 1998b; Gershunov et al. 1999) modulating the ENSO response; or 3) secular changes related to century-scale global warming that may have changed the planetary climate dynamics. Relationships between decadal variations in ENSO, and the state of the PDO or NAO are also unclear at this point. Weaver (1999), Gu and Philander (1997), and Trenberth and Hurrell (1993) suggest that internal ENSO modulation and subsequent teleconnection to the North Pacific can explain the PDO. Latif and Barnett (1994) explain the interdecadal variability in the North Pacific through subtropical gyre mechanisms. In two recent papers, Barnett et al. (1999a,b) provide evidence of an ocean–atmosphere coupled mode in the Pacific midlatitude as the origin of decadal variability. They also suggest that decadal changes over the North Pacific can cause modulations of ENSO.

In the Atlantic, the nature of decadal variability of NAO is far from conclusive. Two hypotheses compete to explain this variability: coupled ocean–atmosphere and uncoupled modes of variability. In the coupled mode hypothesis, pronounced decadal changes in the SST and sea level pressure (SLP) in the subpolar and subtropic Atlantic gyres have been observed from data (Kushnir 1994; Deser and Blackmon 1993; Tourre et al. 1999), suggesting coupled ocean–atmosphere interactions. This is largely viewed as a low-frequency response of the ocean to atmospheric forcing (e.g., NAO), and its feedback on the atmosphere, resulting in oscillatory behavior. The uncoupled mode of variability is viewed as a passive response of the atmosphere to internally generated oceanic variations (Delworth et al. 1993; Barnett 1985; Grotzner et al. 1998), or as due to stratospheric cyclonic vortex (Kodera et al. 1996). Causes for variability on decadal to interdecadal timescales are areas of active research.

Droughts can have variable spatial scale depending on their severity and duration. Regional drought likely reflects a consistent response to large-scale climate patterns. There is considerable interest in the use of ENSO forecasts and teleconnections for seasonal to interannual forecasts of North American climate and, in particular, of regional summer droughts. In this context, it is necessary to develop a diagnostic understanding of how the preceding winter (and earlier) ENSO and, more generally, global SST states affect the spatial structure of summer drought. Given the ENSO perspective above, the variation in the relationship between winter ENSO or global SSTs and summer drought indices at interannual to interdecadal timescales is of particular interest. Should ENSO be considered as an episodic behavior of the climate system, with a typical episode life cycle of 12–18 months, or as a continuous phenomenon with a continuous hydrologic response? Is the information needed to predict continental drought response contained in measures of ENSO, or does one need extratropical SST information to properly resolve the winter climate–summer drought association? Insights into these issues are useful for selecting proper statistical prediction methods, as well as for making decisions concerning the specification of dynamic coupled ocean–atmosphere models used for seasonal to interannual drought forecasting.

In this paper, we explore these issues using century-long historical instrumental data on SST fields and the PDSI. The spatial and temporal variations in the teleconnection response of summer drought over the continental United States and the associated variations in winter SST fields are analyzed for three nonoverlapping, approximately 30-yr epochs of the twentieth century that have different ENSO, PDO and NAO attributes. The Niño-3 index is used for ENSO, and standard indices are used for the PDO and NAO, as described in the next section. Specifically, we assess, for the full record and for each of the three epochs, 1) the correlations between the PDSI and Niño-3, PDO and NAO indices; 2) the partial correlations between PDSI and one of the indices, given one of the other two indices;3) the correlation between PDSI and Niño-3 for El Niño and La Niña years only; and 4) a singular valve decomposition (SVD) of the joint correlation structure of the continental PDSI and the global SST fields. These analyses are used to describe the space–time variation in the respective teleconnections, with a primary focus on ENSO, and for inferences on whether 1) the interdecadal changes in the teleconnections can be attributed directly to variations in ENSO, 2) the PDO and NAO contribute any linear information beyond that provided by Niño-3, and 3) the leading components of mutual correlation structure across the spatially distributed global winter SST and summer PDSI fields have coherent and consistent structure across the three epochs.

2. Data

The following data were used in our study:

1. global SST anomalies on a 5° × 5° grid from a“reduced space” optimal smoother algorithm applied to 131 years (1865–1995) of global SST monthly anomalies obtained from the U.K. Hadley Centre archives (Bottomley et al. 1990; Kaplan et al. 1998);

2. PDSI data on a 2° latitude × 3° longitude grid obtained from a nearest neighbor gridding procedure of Cook et al. (1999), applied to the Climate Division PDSIs from the National Climate Data Center for the period 1895–1995;

3. Niño-3 index, a widely used index of ENSO activity, obtained by averaging the SST anomalies [from the Kaplan et al. (1998) dataset] in the region comprising 5°S–5°N and 150°–90°W;

4. NAO index, defined as the difference in normalized SLP anomalies between Ponta Delgada (Azores) and Reykjavik (Iceland); and

5. PDO index, defined in Mantua et al. (1997).

The PDSI, a measure of moisture deficit, takes into account both temperature and precipitation and also contains information from previous seasons (Palmer 1965). The PDSI is a standardized index that has comparable meaning at all locations. Negative values of the index imply droughtlike (or moisture deficit) conditions, and vice versa. Variants of the PDSI, such as the modified PDSI, and the hydrologic drought index emphasize different aspects of drought persistence. We do not discuss the merits of different indices here, and use only the PDSI, which is the most commonly cited index. The summer PDSI reflects a memory of the precipitation and temperature experienced at each location in, approximately, the previous 12-month period.

Winter SSTs are defined as the October–March averages of SST at each grid point. Summer PDSIs are the average of the June–August PDSI values. The Kaplan et al. (1998) SST dataset used by us reconstructs gridded SST values back to 1856, using ship track records and an optimal estimation procedure that relies on an empirical orthogonal function decomposition of the recent high quality records. From the estimated data covariance patterns, the method fills gaps, corrects sampling errors, and produces spatially and temporally coherent datasets. Cross-validated tests of their algorithm showed a high fidelity of the large-scale patterns inferred from sparse samples (similar to the pre-1930 data locations) to the observed patterns.

3. PDSI–Niño-3 teleconnections and extratropical factors

For simplicity, we chose to divide the period of record into three roughly equal epochs (1895–1928, 1929–62, and 1963–95) for analysis of time variations in the teleconnections. Moving window and wavelet analyses reveal changes in the frequency and amplitude of the key climate oscillations. Kestin et al. (1998) note that the dominant frequencies of ENSO do not seem to be constrained to a fixed frequency band, and that ENSO has been more active in approximately the 1960–99 and 1895–1920 periods than in the intervening period. Correspondingly, a number of continental hydrologic time series show a U-shaped trend over the twentieth century (Baldwin and Lall 1999; Lall and Mann 1995). The exact years at which trends in different indices change sign are not always consistent. Cole and Cook (1998) used 15-yr blocks to look at the correlation structure of the Southern Oscillation index with instrumental and tree-ring reconstructed PDSI. Their results are generally consistent with our analysis using Niño-3.

Figure 1 maps the correlations between the summer PDSI at each grid point over the United States and the preceding winter (December–January–February) Niño-3 value for the three epochs. Only correlations significant at the 95% level are shown. Since autocorrelation of Niño-3 is not significant, the standard significance test for the correlation of two series was used. We also checked the field significance, as suggested in Livezey and Chen (1983), and found that the correlations pass this test, as well, at a 99% significance level (p < 10⁻⁸). Large regions of the United States exhibit spatially coherent correlations with Niño-3. However, the location and strength of these teleconnections varies by epoch. At the beginning of the century (Fig. 1a), a striking feature of the teleconnection is the strong positive correlation between PDSI and ENSO covering southeastern Texas, with weaker extensions into the Midwest, all the way to the Great Lakes region. There is also an area of negative correlation west of the Rockies. During the second epoch (Fig. 1b), the strong positive correlations have moved westward, covering southwestern Texas, as well as southern New Mexico and Arizona. The positive correlations in the Midwest that were observed in the first epoch are now absent. The Great Lakes and the east central regions are now negatively correlated. In the most recent epoch, 1963–95, the positive correlations are somewhat weaker and cover a more diffuse westward region, that is, southern California, Nevada, and Arizona, with extensions into the Midwest. Similar epochal variations in the ENSO teleconnections have been reported by Cole and Cook (1998) from instrumental and tree-ring reconstructed PDSI.

It is known that a few strong ENSO episodes can contribute to the observed correlations in the teleconnection response, and that the response can depend on the ENSO indicator. Could the change in the relative frequency and strength of El Niño/La Niña events be a leading factor in the explanation of the different spatial correlation structure for the three epochs? Conditional correlations between PDSI and Niño-3 for ENSO and non-ENSO events in each epoch were computed to address this question. ENSO events were classified as those having an absolute value of the winter Niño-3 index larger than 0.75 (this is roughly the 1σ level). The ENSO years in each epoch are identified in Table 1. The PDSI correlations with ENSO events are shown in Fig. 2. Again, only correlations significant at the 95% level are shown, accounting for the unequal sample sizes for each computation. In the first and third epochs, the correlation patterns for ENSO years (Figs. 2a,c) and all years in the epoch (Figs. 1a,c) are very similar. Note that the significance levels for correlation are substantially higher in Fig. 2, given the reduced sample sizes. The 1929–62 period shows no significant regions for correlations in ENSO years (Fig. 2b). An examination of all the correlations (not just the significant ones) shows that the spatial pattern of correlation is similar to that in Fig. 1b. The small sample size of ENSO years in this epoch and the associated higher significance levels lead to the apparently anomalous conclusion. Correlation patterns for non-ENSO years show no significant correlation in any of the epochs. This indicates that the teleconnection response in the summer PDSI is largely due to ENSO. We also computed correlations between PDSI and Niño-3 for years in which 1) Niño-3 > 1.25 (14 yr), 2) 1.25 > Niño-3 > 0.75 (12 yr), and 3) Niño-3 < −0.75 (13 yr). The statistically significant spatial correlation patterns for PDSI in each of these sets were essentially identical. We also did a t test for differences in the means of the PDSI responses for 26 El Niño (positive response) and 13 La Niña events (negative response). By changing the sign of the La Niña response, we are able to test for asymmetry in the El Niño–La Niña response. The t test was done allowing for unequal population for the two samples. The number of significant differences in conditional PDSI means at the 5% and 10% levels was consistent with what would be expected by chance. These results suggest that 1) the summer PDSI response to Niño-3 is essentially linear, 2) changing relative frequencies of ENSO events in an epoch can change the apparent correlation with PDSI, and 3) the spatial structure of the teleconnection does vary by epoch, due to either modulation by another variable or to changing ENSO strength and persistence. The first observation is at odds with the observed response of winter precipitation and temperature to ENSO (see, for instance, Gershunov et al. 1999). Here, the difference is likely due to the time integrated nature of PDSI and potential changes in the season-by-season teleconnections to ENSO. It is also possible that the ENSO–PDSI relationship is nonlinear, but we are unable to detect it with the tools used. The second observation suggests that an approach that models ENSO as an episodic process (e.g., a marked nonhomogenous point process), or through a time–frequency decomposition (e.g., using wavelet methods), and models the PDSI teleconnection response through a nonlinear regression or transformation function may be useful. From a dynamical modeling perspective, the dynamical model would need to be able to generate the richness in ENSO variations seen in nature at interannual and interdecadal timescales, as well as the subsequent modulation of the teleconnections. The third observation deserves further attention. Gershunov et al. (1999) and Gershunov and Barnett (1998b) argue for the influence of the North Pacific variability in modulating ENSO–winter precipitation teleconnections. We explore the possibility of modulation of the ENSO–PDSI teleconnection by extratropical climate state through a partial correlation analysis with respect to the NAO and the PDO indices, which have a decadal to interdecadal character and may hence be relevant for explaining the interdecadal shifts in the teleconnection.

4. Partial correlation analyses

The NAO and the PDO indices are correlated with the Niño-3 index, so partial correlations for these variables are more useful than a direct comparison of correlation maps for each indicator. We looked at partial correlation maps of PDSI–Niño-3/NAO, PDSI–Niño-3/PDO, PDSI–PDO/Niño-3, and PDSI–NAO/Niño-3, for each epoch. The partial correlations are computed in the following manner. Consider the case of PDSI–Niño-3/NAO. We first perform a linear regression of PDSI on Niño-3. Residuals from the regression are then correlated with NAO (cf. Cole and Cook 1998, their Figs. 3b,c). Interestingly, the partial correlation maps for Niño-3, given either PDO or NAO, are essentially identical to Fig. 1, in which the direct Niño-3 correlation was computed. This suggests that knowledge of the extratropical indices does not change the ENSO teleconnection to PDSI. Next we consider the partial correlation of PDSI to PDO or NAO, given Niño-3. For the first two epochs, no significant correlations for large contiguous regions were found. Results for the third epoch are shown in Fig. 3. The spatial partial correlation pattern in Fig. 3 suggests that a large region, from eastern Texas to New England, and to the Great Lakes and the midwestern United States, is positively correlated with the NAO/Niño-3. This pattern is consistent with those found by Hartley and Robinson (1999) and Higgins et al. (1999) in their studies of variability of wintertime temperature and precipitation over the United States. A similar but more localized negative partial correlation pattern in the southeast United States is noted for PDSI–PDO/Niño-3. Our analysis of the PDO role on PDSI–Niño-3 connections is at odds with the PDO–Niño-3 winter precipitation results of Gershunov et al. (1999). This could be due to differences in the methods used and also to the nature of the target variables.

5. SST–PDSI connections

Having identified the epochal nature of the spatial teleconnection pattern of PDSI to ENSO and the two extratropical indices, we now investigate which regions of the global oceans participated in the PDSI teleconnection over the three epochs. The climate indices used are typically developed using limited areas of the ocean, and multivariate information about the joint state of the ocean evolution can be lost or confused in the process. It is also of interest to directly identify coherent spatial response regions for PDSI that relate to specific SST patterns. If this can be done reliably, a more parsimonious prediction scheme can be devised. To explore this issue, we perform a joint SVD of the winter SSTs and summer PDSIs at each grid point. The SVD analysis decomposes the covariance matrix of these two fields into orthogonal pairs of spatial patterns that maximize the squared temporal covariance between the two variables (Bretherton et al. 1992). The theory of SVD is discussed and compared with other multivariate techniques in Bretherton et al. (1992) and Wallace et al. (1992). The SVD of the covariance matrix of the PDSI and SST fields results in two matrices of singular vectors and one set of singular values. Each singular vector pair describes spatial patterns for each field, which have overall covariance given by the corresponding singular value. This is similar to canonical correlation analysis (CCA), in that both methods try to optimize joint patterns between the two fields. For in-depth analysis of CCA and its relation with SVD we refer the reader to Barnston and Smith (1996).

From the singular vector pairs, a so-called temporal expansion series (similar to a principal component series in EOF analysis) for each field can be obtained by projecting the data onto their corresponding singular vectors (Bretherton et al. 1992). The correlations between the values of each grid point of one field and the temporal expansion values of the other field result in heterogeneous correlation maps. In our application, the patterns shown by heterogeneous correlation maps for the kth SVD expansion mode indicate the strength of PDSI (SST) relative to the kth expansion coefficient of SST (PDSI). The different heterogeneous maps of each field are mutually orthogonal in the space domain.

Wallace et al. (1993) define a normalized squared covariance (NSC) value associated with each pair of spatial patterns, which indicates the strength of the relationship between the two fields. We use the NSC in the present study to compare the variability in SST and PDSI fields using a common scale.

We perform SVD analysis on the PDSI and SST data separately for the three epochs. The first two modes capture about 40%–50% of the joint variance in all three periods. The resulting heterogeneous correlation maps are shown in Figs. 4, 5, and 6.

6. Conclusions and future directions

We have explored the relationships between low-frequency winter climate indicators and summer drought in the continental United States, with a view to developing a statistical forecasting scheme. Relatively robust teleconnections between ENSO and drought indices in the southwestern United States were established. However, the strength and spatial signature of the correlation fields was found to vary over time. The analysis suggests that the Niño-3–PDSI relationships are likely to be nonlinear and are determined primarily by ENSO events that exceed some Niño-3 threshold. Thus, a composite, categorical probability forecast may be more useful than a linear regression approach for one-season-ahead forecasting, and a more complex approach may be necessary for analyzing longer run structure. The need to better understand the spatial structure of the tropical Pacific and the global SST fields in predicting PDSI was highlighted. Details of both fields and their timescales of evolution are likely to be important for successful forecasting schemes.

The epochal variations in the teleconnections and the PDSI predictors suggest that naïve statistical forecasting algorithms that use the full record may have limited predictability in practice. A Bayesian time series approach (West and Harrison 1997) that deals explicitly with nonstationarity, in the framework of dynamic linear models, may be more useful. Approaches based on wavelet decompositions may also be useful for such data. We plan to explore both methods in our future work. However, a more important problem concerns developing an understanding of why the nonstationarity occurs in the first place. Is it part of the nonlinear dynamics of the coupled system, or are we observing weakly coupled modes of the climate system that randomly evolve or are forced (e.g., by CO₂ changes) to a particular state? Empirical and conceptual approaches for insights into such questions need to be developed.

The PDSI and related variables are interesting in their own right when correlations with climatic predictors are sought. Like stream flow and lake volumes, the PDSI can reflect a relatively long-term memory modulated by seasonal factors. The frequency structure of such variables is a linearly or nonlinearly modulated version of the climatic forcing. The time integration associated with such a process can integrate over interseasonal climate structure, such as the negative correlation between winter snow and summer rainfall in the southwestern United States noted by Gutzler and Preston (1997). It is not always clear whether such seasonal averaging enhances or destroys predictability. We plan to explore the role of ENSO and the annual cycle in lending predictability to summer PDSI, as a function of the operative hydroclimatic mechanisms in different regions of the country. Both empirical analyses and conceptual modeling will be necessary to explore this multiscale interaction problem.