U. S. Geological Survey, Denver, Colorado, United States

(3)

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.

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 mid-latitudes. 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.

The MTM-SVD analysis was first performed on the global SST and the LFV spectrum is shown in Figure 2a. The significant frequencies above the 90% confidence levels are secular trend and in the 0.2-0.3 cycles/year range which is the ENSO band – consistent with earlier findings (e.g., Mann and Park, 1996). 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 mid-latitudes (Sutton and Hodson, 2003; 2005). To demonstrate this we performed the analysis over the northern hemisphere (20^oN and above) sub-domain (Figure 2b). Here the ENSO band and the secular trend are weaker but a multidecadal frequency 0.0549cycles/year is above the 90% significance level. The frequency of the Atlantic Multidecadal Oscillation (0.0149 cycles/year, Enfield et al., 2001; Gray et al., 2003) is evident albeit at less than 90% 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 multi-decacdal bands. Spatial reconstruction of the secular trend (zero frequency) and at one of the ENSO frequencies (0.1956 cycles/year; this frequency is common in both Figures 2(a) and 2(b)) is shown in Figure 3. The secular trend is strong in the Indian Ocean, Southern and Northern Atlantic, 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, Northern Pacific and Indian ocean regions. Notice that the arrows are completely out of phase between the tropical and northern Pacific and in phase with the Indian Ocean - consistent with the ENSO phenomenon. Spatial reconstruction of the multidecadal signal (0.0149 cycles/year and 0.0334 cycles/year) shows (Figure 4) a strong signature in the Atlantic and Pacific regions. Especially, the reconstruction at the AMO frequency (Figure 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 northern and southern regions of the North Atlantic Ocean. These differences in phase suggest a lag of SSTs in the northern region behind those in the southern region of the North Atlantic. This lag is possibly indicative of the movement of warm water from the south 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 cycles/year, identified from Figures 1a and 1b) at the location of 2.5^oS and 132.5^oW (a grid point in the tropical Pacific) were performed and summed up and compared to NINO3.4 SST index (Figure 5a). The NINO3.4 SST index is the average of SSTs in the tropical Pacific Ocean between 5^oS and 5^oN and 170^oW and 120^oW and represents variability of the ENSO (Trenberth, 1997). Combined reconstructions at the significant frequencies in the multidecadal band (0.0334, 0.0549, 0.0898 cycles/year, identified from Figures 1a and 1b) at the location of 17.5^oN and 127.5^oW (a grid point in the North Pacific) compare very well with the Pacific Decadal Oscillation (PDO) (Mantua and Hare, 2002) (Figure 5b). The PDO is an index of the decadal variability of the North Pacific Ocean. Likewise, the reconstruction at the AMO frequency (0.0149 cycles/year) combined over the entire Northern hemisphere Atlantic is compared to the AMO index (Figure 5c). 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.

The LFV spectrum from a joint analysis of global SST and global PDSI is shown in Figure 6. The significant frequencies are consistent (secular trend and ENSO) with those identified in the SST analysis (Figure 2a). Notice that the low-frequency signal is subdued relative to what was seen in the northern hemisphere SST analysis (Figure 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 Figure 7a and the ENSO reconstruction (0.228 cycles/year, one of the significant frequencies, identified from Figure 6) in Figure 7b. The trend reconstruction shows higher amplitudes over central Africa including Sahel and are weaker elsewhere. The regions with strong ENSO amplitudes are the southwestern and northwestern US, 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).

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 cycles/year); the ENSO band (0.1956, 0.2122, 0.2280, 0.2654, 0.2783, 0.2942 cycles/year), and the AMO (0.0149 cycles/year). The reconstructions are performed separately at each frequency and are summed up to result in a single combined temporal reconstruction. We selected 12 locations (northwestern US at 43.75N and 123.75W; southwestern US at 36.25N and 113.75W; East Coast at 38.75N and 76.25W; northeastern Brazil at 8.75S and 36.25W; Sahel at 11.25N and 16.25W; Eurasia at 68.75N and 21.25E; western Australia at 21.25S and 113.75E; eastern Australia at 28.75S and 153.75E; South Africa at 31.25S and 28.75E; western India at 16.25N and 73.75E; central India at 21.25N and 78.75E, and eastern India at 21.25N and 86.25E), and the reconstructions are shown in Figures 8, 9, 10 and 11. 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.

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 inter-decadal 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 – 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 year 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.

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