1. Introduction
A number of changes in the global climate system have been attributed to increasing global temperatures resulting from anthropogenically supplied greenhouse gases (Solomon et al. 2007). To appropriately attribute climate changes to global warming it is necessary to understand the primary modes of global climate variability and to separate climate trends from natural climate variability (Ghil and Vautard 1991; Mann and Park 1996).
Dai et al. (1997) examined the variability of global precipitation using a dataset of gridded (2.5° × 2.5°) monthly precipitation for the period 1900–88. In their study, the first empirical orthogonal function (EOF) of the precipitation data indicated an (El Niño–Southern Oscillation) (ENSO–related pattern and the second EOF reflected a linear trend in global precipitation. The trends in precipitation were primarily increases in North America, mid- to high-latitude Eurasia, Argentina, and Australia. Dai et al. (1997) reported that this pattern of trends in precipitation was consistent with precipitation changes projected by general circulation model (GCM) experiments of future climate changes in response to increasing atmospheric concentrations of carbon dioxide.
In another study, Dai et al. (2004) examined the variability of global annual Palmer drought severity index (PDSI) values using principal components analysis. Similar to the study of global precipitation, Dai et al. (2004) reported that the first two principal components of global annual PDSI are related to long-term trends and the ENSO. However, for the analysis of the PDSI data, the first principal component reflected long-term trends in PDSI and the second component reflected ENSO variability. Long-term trends in PDSI represented more of the variability in the PDSI data than in precipitation data likely because PDSI values also include the effects of long-term trends in temperature.
McCabe and Palecki (2006) used principal components analysis and singular value decomposition (SVD) to examine primary modes of global PDSI and sea surface temperature (SST) variability on decadal to multidecadal (D2M) time scales. Results indicated two principal modes of D2M variability. The first mode of D2M variability is related to the Pacific decadal oscillation (PDO), Indian Ocean SSTs, and an index of ENSO, while the second mode is related to the Atlantic multidecadal oscillation (AMO).
Mann and Park (1996) performed a frequency analysis of the joint variability of twentieth-century Northern Hemisphere surface temperature and sea level pressure (SLP). Mann and Park (1996) identified significant modes of climate variability at quasi-biennial (2.1–2.2 yr), ENSO (3–7 yr), quasi-decadal (10–11 yr), and interdecadal (16–18 yr) time scales. Mann and Park also identified a secular trend as a significant mode of climate variability.
In a number of studies, variability in global SSTs have been shown to be a significant driving force of hydro-climate variability (Fontaine and Janicot 1996; Enfield and Alfaro 1999; Rodwell et al. 1999; Enfield et al. 2001; Nicholson et al. 2001; Giannini et al. 2003; Gray et al. 2003; Sutton and Hodson 2003; Hidalgo 2004; McCabe et al. 2004; Shabbar and Skinner 2004; Schubert et al. 2004; Seager et al. 2005; Sutton and Hodson 2005; McCabe and Palecki 2006). Some of these studies have shown the large influence of tropical Pacific Ocean SSTs (i.e., El Niño and La Niña events) on hydro-climate across the globe. More recently, several of these studies have shown substantial associations between North Atlantic SSTs and global hydro-climate, particularly on D2M time scales (McCabe and Palecki 2006; Dong et al. 2006; Dima and Lohmann 2007).
In this study we examine the joint spatiotemporal variability between global annual PDSI values and global annual SSTs. The PDSI data were chosen to represent land-based climate variability and SSTs were chosen to represent the large-scale climate variability forcing at interannual and interdecadal time scales. We use a nonparametric spectral domain technique called the multitaper method–singular value decomposition (MTM–SVD) on this joint dataset (Mann and Park 1996). This method aims to identify dominant modes (i.e., primary patterns of temporal and spatial climate variability that are identified through frequency analysis) of variability that are jointly shared by the two fields and subsequently, spatial and temporal patterns of these identified frequencies are reconstructed. This method is data driven and is unaffected by trends and other aliasing problems that commonly constrain the traditional time and frequency domain techniques. The dominant patterns will provide increased understanding of the low-frequency modes of variability, in particular, of the land surface conditions that are important for long-term drought monitoring and mitigation efforts. In addition, because this study uses a frequency domain approach it will provide a useful confirmation of previous research findings that were obtained using different methods. A brief description of the data is provided, followed by the description of the MTM–SVD methodology. The identified space–time modes of variability will be described and discussed in the results section.
2. Data
PDSI is a well known representation of meteorological drought and is computed from measured monthly precipitation and temperature data (Palmer 1965). Although there are known short comings inherent in the PDSI (Alley 1984), it has simple data requirements compared to more complex soil-moisture models. PDSI is also widely used by the water-resources engineering and science community as an important practical indicator of basin soil moisture state (e.g., dry, normal, wet, etc.).
Dai et al. (2004) have developed a dataset of gridded 2.5° × 2.5° (2.5° latitude × 2.5° longitude) monthly PDSI values for the global land surface for the period 1870–2003. The needed precipitation data follows from the work of Chen et al. (2002) for the 1948–2003 period and Dai et al. (1997) for the 1870–1947 period. An adjustment was made to place the two datasets on a compatible scale. Dai et al. (2004) applied step-change homogenization corrections to a small percentage of the original precipitation time series prior to gridding the data. The required temperature data were gridded by Jones and Moberg (2003) at a coarser 5° × 5° resolution, and the station temperature time series used were subjected to a variety of homogenization techniques by their sources. The monthly PDSI data were averaged to compute annual PDSI values. For grid cells with missing monthly data within a year, the annual value was not computed and designated as missing. Only 2.5° × 2.5° grid cells with complete annual data for the 1925–2003 period (1341 grid cells, Fig. 1a) were used for the analysis in this paper. The time period chosen provided a reasonable compromise between length of record and completeness of spatial coverage.
SST variability is strongly related to global climate variability (Diaz and Markgraf 2000; Mantua and Hare 2002; Hoerling and Kumar 2003; McCabe et al. 2004). Previous research indicates that SSTs over large areas vary simultaneously under preferred spatial modes and time scales (Kawamura 1994; Enfield and Mestas-Nuñez 1999; Mestas-Nuñez and Enfield 1999). In some of these studies, global-scale signals were removed prior to variability analysis, including trends and ENSO signals. For the analysis in this paper, 5° × 5° resolution grid cell SST data with complete annual records for 1925–2003 (1207 cells, Fig. 1b) were extracted from the Kaplan-extended SST dataset of monthly SSTs (Kaplan et al. 1998). The annual values were computed as 12-month averages of the monthly SSTs.
3. Frequency domain MTM–SVD approach
Robust diagnosis of the key low-frequency modes of large-scale climate entails capturing the coherent space–time variations across multiple climate state variables. Traditional time-domain decomposition approaches for univariate and multivariate data provide useful details on the broadscale patterns of variability. However, these approaches lack the ability to isolate narrowband frequency domain structure (Mann and Park 1994, 1996; more information available online at http://www.meteo.psu.edu/~mann/Mann/tools/tools.html).
The LFV spectrum was used to identify significant frequencies, and temporal and spatial reconstructions were carried out to understand the global joint variability of SST and PDSI. The spatial reconstruction yields the spatial patterns associated with the given time scales, and their relative amplitude and phase relations.
Similar to standard EOF analysis where a space–time dataset is decomposed into two components (e.g., von Storch and Zwiers 1999) 1) a set of time coefficients–principal components or EOF coefficients, and 2) projected onto a set of fixed patterns that are orthogonal–eigenvectors. The uk spatial EOF or eigenvector corresponding to a specified frequency is a complex number. The spatial reconstruction (or vector plots) consists of the vector amplitudes (magnitude of the complex number) and direction (phase of the complex number). Spatial reconstruction plots (arrows representing the vectors) are plotted using these amplitude and phase values.
4. Results
As described earlier the premise here is that SST forcings influence the variability of PDSI. The SST forcings typically come from the tropics (e.g., ENSO) and to a lesser extent from the midlatitudes. First we identify the dominant frequencies of the SST forcings from these two sources and then investigate the spatial and temporal reconstructions of both SST and PDSI.
a. SST
The MTM–SVD analysis was first performed on the global SST and the LFV spectrum is shown in Fig. 2a. The significant peaks (the 90% confidence levels) are seen at approximately 0 cpy (a secular trend) and in the 0.2–0.3 cpy range; which is the ENSO band. These results are consistent with the findings of previous research (e.g., Mann and Park 1996).
The significance level of the peaks is computed through a bootstrap method. We generate bootstrap samples of the data in which the temporal dependence is destroyed. In other words, we randomly select an observation with replacement thus obtaining a bootstrap sample that has the temporal structure destroyed. The MTM–SVD method is applied to this sample and the LFV obtained. This is repeated for a large number (1000) of bootstrap samples thus, obtaining 1000 estimates of LFV at each frequency. The 50th, 90th, 95th, and 99th percentiles at each frequency are estimated and plotted; these are the horizontal lines in the figures. This method of significance is data driven and robust (Mann and Park 1996, 1999) and has been used in all the previous studies.
The decadal and multidecadal frequencies are not significant—this is due to the fact that the methodology isolates frequencies that are shared by much of the spatial domain and in this regard the ENSO forcing is dominant. Furthermore, the decadal forcings are mainly from the midlatitudes (Sutton and Hodson 2003, 2005). To demonstrate this we performed the analysis over the Northern Hemisphere (20°N and above) subdomain (Fig. 2b). Here the ENSO band and the secular trend are weaker but a multidecadal frequency 0.0549 cpy is above the 90% significance level. The frequency of the AMO (0.0149 cpy, Enfield et al. 2001; Gray et al. 2003, 2004) is evident albeit at less than 90% confidence level. A MTM–SVD analysis of only SSTs in the North Atlantic Ocean (not shown) indicates a significant peak (at a 90% confidence level) at 0.0149 cpy, and another significant peak at a multidecadal frequency is at 0.0334 cpy (significant at a 99% confidence level).
The MTM–SVD analysis of the global and Northern Hemisphere SST indicates that collectively the dominant frequencies are in the secular trend, ENSO, and multidecadal bands. Spatial reconstruction of the secular trend (zero frequency) and at one of the ENSO frequencies (0.1956 cpy; this frequency is common in both Figs. 2a,b) is shown in Fig. 3. The secular trend is strong in the Indian Ocean, South and North Atlantic, and North and South Pacific; all are regions known to have strong trends in the SST (Cane et al. 1997). Also note that the SST trends in the Indian Ocean and North Atlantic and North Pacific are predominantly opposite. That is, temperature increases in the Indian Ocean would correspond to cooling of the North Atlantic and North Pacific and vice versa. The ENSO reconstruction shows a strong signal in the tropical Pacific, North Pacific, and Indian Ocean regions. Notice that the arrows in the tropical Pacific are in antiphase with the North Pacific, yet in-phase with the Indian Ocean; this pattern of effects is consistent with the ENSO phenomenon. Spatial reconstruction of the multidecadal signal (0.0149 and 0.0334 cpy) shows (Fig. 4) a strong signature in the Atlantic and Pacific regions. In particular, the reconstruction at the AMO frequency (Fig. 4a) shows the signal to be dominated by the Atlantic (Sutton and Hodson 2003, 2005).
Another interesting feature of the spatial reconstruction at the AMO frequency is the difference in phase between the tropical and northern regions of the North Atlantic Ocean. These differences in phase suggest a lag of SSTs in the northern region behind those in the tropical region of the North Atlantic. This lag is possibly indicative of the movement of warm water from the tropics to the north in the North Atlantic Ocean related to the thermohaline circulation (Delworth and Mann 2000).
To demonstrate that the reconstructions also capture the temporal signal of the large-scale features we performed temporal reconstruction at selected locations and compare them to the standard indices. Temporal reconstruction of frequencies significant in the ENSO band (0.1956, 0.2280, 0.2654, 0.2783, and 0.2942 cpy, identified from Figs. 2a,b) at the location of 2.5°S and 132.5°W (a grid point in the tropical Pacific) were performed and summed up and compared to Niño-3.4 SST index (Fig. 5a). The Niño-3.4 SST index is the average of SSTs in the tropical Pacific Ocean between 5°S and 5°N and 170° and 120°W and represents the variability of ENSO (Trenberth 1997). Combined reconstructions at the significant frequencies in the multidecadal band (0.0334, 0.0549, and 0.0898 cpy, identified from Figs. 2a,b) at the location of 17.5°N and 127.5°W (a grid point in the North Pacific) compare very well with the PDO (Mantua and Hare 2002; Fig. 5b). The PDO is an index of the decadal variability of the North Pacific Ocean. Likewise, the reconstruction at the AMO frequency (0.0149 cpy) combined over the entire Northern Hemisphere Atlantic is compared to the AMO index (Fig. 5c). The AMO is an index of sea surface temperatures across the North Atlantic Ocean between the equator and 70°N latitude and exhibits a long-term, quasi-cyclic variation at time scales of 50–70 yr (Enfield et al. 2001). Recent modeling studies reveal that multidecadal variability in the North Atlantic Ocean is dominated by this single mode of sea surface temperature variability (Sutton and Hodson 2005, 2007). The temporal reconstructions capture the low-frequency variability of the indices of large-scale forcings well. In addition the correlations between the reconstructed and measured time series are all statistically significant at a 99% confidence level.
The MTM–SVD analysis of the SST and their spatial and temporal reconstructions isolate the important drivers of low-frequency climate variability. Consequently, we used these identified frequencies for the PDSI analysis.
b. PDSI
The LFV spectrum from a joint analysis of global SST and global PDSI is shown in Fig. 6. The significant frequencies are consistent (secular trend and ENSO) with those identified in the SST analysis (Fig. 2a). Notice that the low-frequency signal is subdued relative to what was seen in the Northern Hemisphere SST analysis (Fig. 2b). This is to be expected because, as mentioned earlier, the technique isolates significant frequencies that are shared by a majority of spatial locations in both the fields. Because the multidecadal frequencies are restricted to a smaller spatial region they are not statistically significant but it does not imply their absence. Based on the individual and joint analysis we can state that the frequencies of a secular trend, ENSO, and multidecadal variability are dominant and shared by both fields and also these can be viewed as drivers from the SST field of the PDSI. Spatial and temporal reconstructions in the rest of the paper will be based on these identified frequencies.
The secular trend in the PDSI is shown in Fig. 7a and the ENSO reconstruction (0.228 cpy, one of the significant frequencies, identified from Fig. 6) is shown in Fig. 7b. The trend reconstruction shows higher amplitudes over central Africa including the Sahel and are weaker elsewhere. The regions with strong ENSO amplitudes are the southwestern and northwestern United States, South Africa, northeastern Brazil, central Africa, the Indian subcontinent, and Australia. These are consistent with the typical ENSO teleconnections of global precipitation (Ropelewski and Halpert 1987). This pattern of PDSI variability is most likely forced by precipitation variability related with ENSO (Ropelewski and Halpert 1987; Dai and Wigley 2000; Trenberth and Caron 2000; Dai et al. 2004).
Figure 8 illustrates the PDSI reconstruction for 0.0149 cpy (this multidecadal frequency was significant from the MTM–SVD analysis of North Atlantic Ocean SSTs and appears to represent AMO variability). The pattern of reconstructed PDSI for 0.0149 cpy indicates a number of areas with coherent signals. Central North America is dominated by a common signal, as well as western Africa, South Africa, and Australia. This pattern is similar to the pattern of AMO effects on global PDSI (McCabe and Palecki 2006). There is a conspicuous dipole in Europe, with northern Europe indicating one signal and southern Europe indicating another. The dipole of signals is consistent with findings by Pohlmann et al. 2006 who found that a warm North Atlantic Ocean was associated with enhanced precipitation in northern Europe and decreased precipitation in southern Europe.
To demonstrate the ability of the technique to capture the low-frequency variability we performed temporal reconstructions at selected locations around the globe. The reconstructions are performed at several significant frequencies identified earlier, which are the secular trend (0 cpy), the ENSO band (0.1956, 0.2122, 0.2280, 0.2654, 0.2783, 0.2942 cpy), and the AMO (0.0149 cpy). The reconstructions are performed separately at each frequency and are summed up to result in a single combined temporal reconstruction. We selected 12 locations (the northwestern United States at 43.75°N, 123.75°W; the southwestern United States at 36.25°N, 13.75°W; the East Coast at 38.75°N, 76.25°W; northeastern Brazil at 8.75°S, 36.25°W; the Sahel at 11.25°N, 16.25°W; Eurasia at 68.75°N, 21.25°E; western Australia at 21.25°S, 113.75°E; eastern Australia at 28.75°S, 153.75°E; South Africa at 31.25°S, 28.75°E; western India at 16.25°N, 73.75°E; central India at 21.25°N, 78.75°E; and eastern India at 21.25°N, 86.25°E), and the reconstructions are shown in Figs. 9, 10, 11 and 12. All of the correlations between the reconstructed time series and the time series of measured data are statistically significant at a 99% confidence level. The reconstructions appear to be a smoothing of the PDSI time series at each specific location.
5. Summary
Using a robust spectral domain analysis technique, MTM–SVD, we identified joint modes of variability in global SST and PDSI. This technique isolates dominant frequencies that are shared spatially by both fields and it does not suffer from aliasing effects as the traditional time-domain techniques. We find the dominant signal to be in the secular trend and ENSO band and to a lesser extent in the interdecadal band. The ENSO and trend were robust in both fields independently and also jointly, while the interdecadal band was mostly in the Northern Hemisphere SST, which is consistent with other studies. The temporal reconstructions of SSTs at these significant frequencies reproduce very well the dominant forcings: ENSO, PDO, and AMO. Also, the combined temporal reconstructions of the PDSI at all the significant frequencies at a suite of locations around the globe capture the low-frequency variability very well. The difficulty of performing a global analysis is the issue of seasonality especially with respect to PDSI. While this is not likely to interfere with the low-frequency variability, it can on the high-frequency end (e.g., at the 2–3-yr periodicity). Regional analysis will help provide insights into variability over a specific area of interest. Regardless, the findings in this research provide potential for decadal prediction and simulation of PDSI that can be very useful for drought mitigation planning.
This study confirms results from previous analyses, which is a useful research contribution, and provides new insights because 1) this study provides a simultaneous analysis of land-based and ocean climate variability, 2) raw data are used in the analyses presented (without any preconditioning or smoothing) to identify important temporal and spatial modes of global climate variability, and 3) the phase–lag relationships identified provide increased understanding of temporal and spatial interrelationships between land-based and ocean climate for regions across the globe.
The modes of climate variability identified in this study refer to historical climate variability of the twentieth century. The long-term trend may or may not continue into the future, however, the variability related to ENSO and the AMO are likely to continue to be a part of future global climate variability. Through paleo-climate research both ENSO and AMO climate variability have been identified as important components of global climate variability for the past several centuries (Gray et al. 2003; Hidalgo 2004).
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Grids (gray) with complete (a) PDSI and (b) SST data for the period 1925–2003.
Citation: Journal of Climate 22, 23; 10.1175/2009JCLI2791.1
LFV spectrum from MTM–SVD analysis of (a) global SSTs and (b) Northern Hemisphere (20°N and above) SSTs. The horizontal lines are the various confidence levels.
Citation: Journal of Climate 22, 23; 10.1175/2009JCLI2791.1
Spatial reconstruction of SSTs at (a) the secular trend and (b) the ENSO frequency (0.1956 cpy). The length of the arrows represents the relative amplitude of the signal and the angle from the horizontal represents the phase lag. For easier interpretation the arrows are colored according to angle from the horizontal [1°–90° (black), 91°–180° (red), 181°–270° (blue), and 271°–360° (green)].
Citation: Journal of Climate 22, 23; 10.1175/2009JCLI2791.1
As in Fig. 3, but for the multidecadal signal (a) 0.0149 and (b) 0.0334 cpy.
Citation: Journal of Climate 22, 23; 10.1175/2009JCLI2791.1
Temporal reconstruction of (a) frequencies significant in the ENSO band (summed for 0.1956, 0.2280, 0.2654, 0.2783, and 0.2942 cpy) at 2.5°S, 132.5°W (a grid point in the tropical Pacific) and a time series of the Niño-3.4 SST index; (b) frequencies in the decadal band (0.0334, 0.0549 and 0.0898 cpy) at 17.5°N, 127.5°W (a grid point in the North Pacific) compared with a time series of the PDO; and (c) the multidecadal frequency, 0.0149 cpy, compared with the AMO index.
Citation: Journal of Climate 22, 23; 10.1175/2009JCLI2791.1
As in Fig. 2, but from a joint MTM–SVD analysis of global SSTs and global PDSI values.
Citation: Journal of Climate 22, 23; 10.1175/2009JCLI2791.1
Spatial reconstruction of the PDSI at (a) the secular trend and (b) ENSO frequency (0.228 cpy). The length of the arrows represents the amplitude of the signal and the angle from the horizontal represents the phase lag. For easier interpretation the arrows are colored according to angle from the horizontal [1°–90° (black), 91°–180° (red), 181°–270° (blue), and 271°–360° (green)].
Citation: Journal of Climate 22, 23; 10.1175/2009JCLI2791.1
Spatial reconstruction of the PDSI at 0.0149 cpy. The length of the arrows represents the amplitude of the signal and the angle from the horizontal represents the phase lag. For easier interpretation the arrows are colored according to angle from the horizontal [1°–90° (black), 91°–180° (red), 181°–270° (blue), and 271°–360° (green)].
Citation: Journal of Climate 22, 23; 10.1175/2009JCLI2791.1
Temporal reconstructions of the PDSI at a suite of significant frequencies, which are the secular trend (0 cpy), the ENSO band (0.1956, 0.2122, 0.2280, 0.2654, 0.2783, and 0.2942 cpy), and the AMO (0.0149 cpy) at locations in the (a) northwestern United States at 43.75°N, 123.75°W; (b) southwestern United States at 36.25°N, 113.75°W; and (c) the East Coast at 38.75°N, 76.25°W. The reconstructions are performed separately at each frequency and are summed to result in a single combined temporal reconstruction. The actual PDSI time series is also shown.
Citation: Journal of Climate 22, 23; 10.1175/2009JCLI2791.1
As in Fig. 8, but for (a) northeastern Brazil at 8.75°S, 36.25°W; (b) the Sahel at 11.25°N, 16.25°W; and (c) Eurasia at 68.75°N, 21.25°E.
Citation: Journal of Climate 22, 23; 10.1175/2009JCLI2791.1
As in Fig. 8, but for (a) western Australia at 21.25°S, 113.75°E; (b) eastern Australia at 28.75°S, 153.75°E; and (c) South Africa at 31.25°S, 28.75°E.
Citation: Journal of Climate 22, 23; 10.1175/2009JCLI2791.1
As in Fig. 8, but for (a) western India at 16.25°N, 73.75°E; (b) central India at 21.25°N, 78.75°E; and (c) eastern India at 21.25°N, 86.25°E.
Citation: Journal of Climate 22, 23; 10.1175/2009JCLI2791.1
