Granger Causality of North Atlantic Ssts on the NAO

UBERN Report 9/02/2006

D11 – Assessment of time varying influence of SST and atmospheric circulation on European surface T and precipitation. (Author Chris Folland)

Granger causality of North Atlantic SSTs on the NAO

We used a Vector AutoRegression (VAR) model to examine the feedback process between north Atlantic Sea Surface Temperature (SST) and the first principle component (PC) of EMSLP on the monthly timescale. The first PC shows the well known dipole pattern referred to as the North Atlantic Oscillation (NAO), known to influence mainly winter temperature and precipitation patterns over northern and western Europe.

VAR is a linear statistical model incorporating the memory effects and feedback between multiple variables. A VAR model consisting of two variables X1 and X2 considering lagged values up to one time step before may be presented as:

The magnitude of the coefficients, 12 and 21 control the amount of feedback between the two variables whereas 11 and 22 indicate the amount of natural predictability there exists from persistence. This can be stated more concisely: A variable X1 is causal for another variable X2 if knowledge of the past history of X1 is useful for predicting the future state of X2 over and above knowledge of the past history of X2 itself (Mosedale et al. 2005; Granger 1969)

The coefficients, written:

If 12 is significantly different from zero then X2 is Granger causal of X1. Whereas if 21 is significantly different from zero then X1 is Granger causal of X2.

One way to test the significance of is with the Omega statistic which compares the full model given in the first equation and a restricted model with no feedback allowed.

Where RSSr and RSSu are the Residual Sum of Squares of the restricted and unrestricted model respectively. N is the number of time points and p the maximum lag value. The Omega statistic is F-distributed.

Figure 1 shows the Omega statistic p-value of North Atlantic SSTs influence on the NAO. Areas in red are highly significant indicating that SST in these areas influences the NAO up to 6 months prior to the current NAO. The pattern of significant influence reveals the well known north Atlantic tripole SST pattern. A possible advantage of the VAR approach over simple linear analysis is that the model removes the influence of intrinsic autocorrelation in each variable.

Figure 1. Lagged SST (up to six months) influence on the NAO calculated over all months. Shown is the p-value of the Omega statistic Granger causality test.

Figure 2 presents the areas where prior values of the NAO have a significant influence on north Atlantic SSTs.

Figure 2. Lagged NAO (up to six months) influence on SST calculated over all months. Shown is the p-value of the Omega statistic Granger causality test.

Granger causality of North Atlantic SSTs on the occurrence of temperature extremes

Here we use the same VAR model to investigate the influence of SSTs on the occurrence of the monthly frequency of temperatures above the long-term 90th percentile (index name; tx90) at two selected stations, Central England Temperature (CET) and Bern, Switzerland.

Figures 3 and 4 show the areas of lagged (up to thee months) SST which are statistically related to the occurrence of temperatures above the 90th percentile at CET and Bern, respectively. The results presented here represent the mean relationship over all months, no account for the seasonal variation has been made. For CET tx90 we see that a large area of SSTs surrounding the British Isles extending southward and westward into the Azores region are areas where we can expect some predictability (red in colour) of extreme temperatures.

Figure 3. Lagged SST (up to three months) influence on the CET tx90 series calculated over all months. Shown is the p-value of the Omega statistic Granger causality test.

The area of lagged SSTs that may provide some predictability for extreme temperatures in Bern, Switzerland is somewhat different from those for CET. For example, SSTs in the Mediterranean as
well as SSTs in the central north Atlantic west of the Iberian Peninsula (Figure 4, read and yellow areas) appear to have some influence on Bern extreme temperatures.

Figure 4. Lagged SST (up to three months) influence on the Bern tx90 series calculated over all months. Shown is the p-value of the Omega statistic Granger causality test.

Della-Marta et al. (2006) show that a similar pattern of both SST patterns shown in Figs. 3 and 4 is found in a CCA using SST to predict extreme summer temperatures at 54 locations in western Europe. The atmospheric pattern associated with these SSTs consists of higher SLP over the western European domain and lower SLP west of the Iberian Peninsula in a pattern which resembles a large scale Rossby wave pattern. Some researchers believe that this blocking activity is the result of tropical interactions with the summer mid-latitude climate however the correlations are weak and are not discussed further here (see Cassou et. al. 2005; Della-Marta et. al. 2006 and references therein).

The influence of the AMO on summer heatwaves (Della-Marta et al. 2006)

Many studies suggested that potential predictability of climate can be found in the decadal and longer cycles of SSTs (e.g. Rodwell et al., 1999). Here we find evidence supporting the analysis of Sutton and Hodson (2005) that the occurrence of warmer than average summer temperatures over Europe are related to long term changes in the Atlantic Multidecadal Oscillation (AMO) (Enfield et al., 2001). The AMO is believed to be caused by the North-Atlantic thermohaline circulation (Knight et al., 2005). The correlation between the LOESS smoothed (Cleveland and Devlin, 1988) first PC of summer heat wave variability (HWPC1) score series and the AMO (as defined by Sutton and Hodson, 2005) shown in figure 5a is 0.8. The significance is hard to determine since the effective number of degrees of freedom is around 2. Figure 5b, shows the loading pattern associated with HWPC1. According to this PC the western European domain is under the influence of anomalously high (periods with positive scores) or low (periods with negative scores) frequency of HWs. High occurrence of HWs between 1880-1905, 1925-1950 and 1990-2003 periods is coincident with anomalously high SSTs in the region defined by the AMO. Although this analysis does not provide a causal link between the long term variations in North Atlantic SSTs, it is interesting to compare them since for the first time such a long-term analysis of European HWs has been performed. It is tempting to extrapolate from figure 5a that there is a phase lag between the AMO series and the HWPC1 since the peaks (troughs) of the HWPC1 series tend to lag the AMO peaks (troughs) by approximately five years. Could the atmosphere retain and react to an ocean forcing from five years earlier? It is certainly an interesting question that could only be answered by many forced and unforced complex model simulations.

a) b)

Figure 5: A timeseries plot a), showing the smoothed Atlantic Multidecadal Oscillation (AMO, dashed line) index and the smoothed first PC of JJA HWs (HWPC1) from 1880 to 2003 and b) the loading patterns associated with the raw (unsmoothed) first PC. In b), the size of the crosses ('+') and the open circles ('o') denote the magnitude of the positive and negative PCA loadings according to the legend on the left side of the figure. The correlation between the two timeseries is 0.8, however it is hard to determine the statistical significance due to the limited number of degrees of freedom. The first PC of the HW index explains 37% of HW variability. The two timeseries have been smoothed using a LOESS smoother with a period set approximately to 25 years.

Multiple lagged predictors of heat waves (Della-Marta et al. 2006)

In this section we explore the use of a CCA model with lagged SSTs and lagged Mediterranean precipitation as predictors of summer HWs. We used DJF North Atlantic SSTs and JFMAM land based precipitation from the Mediterranean region (area 70°W - 50°E, 42°N - 46°N) as predictors of JJA HWs. The first CCA (Fig. 6a) shows a classic tripole pattern with anomalously cool SSTs east of Newfoundland, warm SSTs over most of central northern Atlantic and cool SSTs in the tropical north Atlantic. This is also associated with a dry northern Mediterranean region over the extended season JFMAM (Fig. 6b) and results in anomalously more HWs over most of the domain, especially in central western Europe and over the Iberian Peninsula. This predictive model has an overall hindcast correlation skill score (Fig. 6e) of 0.28 and in some cases reaches up to 0.5 indicating that between 10 and 25% of HW variance can be explained using the combination of these predictors.

a)

b)

c)

d)

e)

Figure 6: The first multiple predictor CCA between DJF averaged SSTAT, JFMAM PRECME and the JJA HW index which explains approximately 10.1% of JJA HW variability. The SSTNA canonical pattern a), b) the PRECWE canonical pattern, c) the HW canonical pattern and d) the canonical score series and e) the hindcast (1982-2003) Spearman rank correlation skill score. In c) and e) the size of the crosses ('+') and open circles ('o') show the canonical loadings expressed as a correlation coefficient and the Spearman rank correlation skill score respectively for each station. In d) the solid and dashed lines are the multiple predictor and HW canonical score series respectively with a canonical correlation of 0.56 (adapted from Della-Marta et al. 2006).

Discussion and Summary

VAR models show that extreme temperatures in different locations of Europe show different areas of potential predictability from north Atlantic SSTs. We have not investigated the use of these models in a strict cross-validated and hindcast framework, however the preliminary results indicate that different regions play important roles to explain the occurrence of extreme temperature events. Whether these areas represent true predictability and not only occur by chance is the goal of future research in this area. A strict caveat of this work is that Granger causality is not true causality, it is only based on statistical principles and therefore all the limitations associated with statistical analysis apply when drawing conclusions of the path of causality.

On the interannual timescale we have shown that winter North Atlantic SSTs and the extended season, JFMAM Mediterranean precipitation can be used to predict up to 15-25% of summer HW variability (Vautard etal., 2006; Colman, 1997), however other important predictors we have not explored such as the Eurasian snow cover extent (Qian and Saunders, 2003). A preceding dry winter and spring Mediterranean initiates a regional soil moisture feedback process (Schär etal., 1999) that is capable of amplifying the affects anomalous large scale circulation patterns such as those discussed earlier. The influence of winter and spring SSTs on European summer temperature has been discussed by Colman and Davey (1999). In this study it was suggested that the warm SSTs noticeable in JJA close to the European coast and extending in Azores region (same region as shown in Figure 3) are likely to be the result of air-to-sea interaction and the westward advection of latent heat. The excess latent heat was suggested to be gained by a sea-to-air interaction from previous (winter and spring) North Atlantic SSTs. We believe another plausible explanation for higher JJA SSTs associated with a higher number of HWs is due simply to the presumed increased insolation as a result of anomalously high pressure over the same region(s) also suggested by Xoplaki et al. 2003.

Della-Marta et al. (2006) shows in detail that north Atlantic SLP, SSTs and western Europe precipitation are not collinear, but increase the skill of the CCA model and hence represent a complex chain of regional and large-scale feedback processes. We have not investigated this complex chain of causality since it is beyond the scope of this paper. One way to tackle this problem would be to perform sensitivity experiments with a Regional Climate Model (RCM). Predictability at the decadal and interdecadal timescales appears to be modulated by the AMO. With a forecast of multidecadal weakening of the AMO in the next 50 years (Knight et al., 2005) the increase in HWs expected from anthropogenic influences (Schär et al., 2004; Stott et al., 2004) could be partially offset making the summer climate of Europe less extreme than it otherwise would be.

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