Strengthening North Pacific Influences on United States Temperature Variability

Changes in the frequency of occurrence of atmospheric circulation patterns under a changing climate system has important implications for regional climate variability. While many studies have focused on understanding the trends in the atmospheric pattern amplitudes and probabilities of occurrence, little attention has been given to how the linkages between climate variables and the large-scale patterns have been changing. Here we first document the strengthening relationship between an important North Pacific teleconnection - the East Pacific/North Pacific (EP/NP) pattern – and United States (US) temperature variability since the 1950s. The EP/NP pattern is linked to tropical convection, and consistently the coherence between US temperature anomalies and tropical convection anomalies has also been increasing during the same time period. This upward trend in convection-temperature alignment is most notable during autumn and winter and is absent during the summer. The relationship strengths and trends further suggest that the EP/NP pattern should be incorporated into monthly and seasonal outlooks that are of broad importance to agriculture, industry, and fisheries.

Evidence for a tropical connection to the EP/NP pattern was supported by correlating the EP/NP index with precipitation from two separate data products. The correlation analysis using the CMAP precipitation data set revealed statistically significant relationships between precipitation and the EP/NP index across the western and central Pacific (see Supplementary Figure S12). Using the same precipitation product, many US climate divisional temperature time series were found to be related with precipitation across the central Pacific and, to a lesser extent, across the western Pacific ( Figure S12).
Trends in coherence between US temperature and precipitation was also computed (see Supplementary Figure S18). No significant trends in coherence were found from 1950 to 2015 across the central equatorial Pacific. That lack of significant coherence trends with tropical convection suggests that increasing coherence with the EP/NP index is related to another process. However, it is uncertain if the rather noisy results are related to the quality of the reanalysis data set, especially prior to 1979. Examining the 1980-2015 period in isolation, the region of significant upward trend is collocated with the region in which the EP/NP index is correlated with tropical convection and the region in which the majority of US climate division are related to convective precipitation. The coherence trends calculated using the CMAP data set (see Supplementary Figure  S18) produced even more robust trends across the central and western Pacific and the colocation of the statistically significant EP/NP-precipitation relationships and the significant upward trends was even clearer. The results imply that not only has US temperature anomalies become more coherent with changes in the EP/NP pattern but also the tropical convection that excites the EP/NP pattern.
A major assumption of the wavelet analysis is that the data are equally spaced and continuous. Therefore, missing EP/NP index data in December were filled by correlating the index with 300-hPa streamfunction anomalies and linearly regressing the index with a 300-hPa streamfunction anomaly time series calculated by averaging streamfunction in the region enclosed by a magenta contour shown in Figure 4a. The exact method by which the filling is done is not important because scale-averaged coherence at a point time is a weighted quantity based on data points surrounding the point of interest (see Methods). The simplest and most straightforward approach was thus adopted. Although the pattern is said not to be dominant one in December, there appears to be a large number of climate divisions whose December temperature time series is related to an upper-tropospheric circulation pattern (see Supplementary Figure S2) strongly resembling the EP/NP pattern (Figure 1). The result suggests that while the pattern may not be a dominant one from the perspective of an EOF analysis, the pattern seems to be a physically relevant one for the US.
Trends in time series can produce spuriously large correlation coefficients. We show that the same holds for scale-averaged coherence. To do so, two realizations, 1 and 2 , of a Gaussian white noise process were generated. A synthetic trend was then added to the time series resulting in two new time series 1 ( ) = 1 ( ) + 0.1 (Eq. S1) and 2 ( ) = 2 ( ) + 0.1 . (Eq. S2) The scaled-averaged coherence was computed between 1 and 2 , between 1 and 2 , and between 1 and 2 after detrending was performed. The results are presented in Supplementary Figure S21. The scale-averaged coherence between 1 and 2 (black line) is spuriously large at the edges of the time series and decreases toward the center of the time series. In contrast, the scaleaveraged coherence between 1 and 2 (magenta line) does not exhibit the high coherence at the edges and, in fact, if one detrends both 1 and 2 and then calculates the scale-averaged coherence (dotted line) one can remove the spuriously large coherence at the edges. It was found that the influence of the trend depends on how large the trends are in the input time series and the length of the time series (not shown). Shorter time series were found to need larger trends to produce the trend-induced edge effects. It is noted that the synthetic trend generated in the above experiment was quite exaggerated so that application of the coherence analysis to real data will generally produce considerably more subtle edge effects, perhaps too small to detect.
It is known that there are edge effects in wavelet analysis due to the finite length of the time series. The region in which edge effects are important is called the cone of influence (COI; 52). While effects are important in making inferences about wavelet power and cross-power spectra, they do not seem to interfere with the interpretation of scale-averaged coherence results. The lack of edge effects for scale-averaged coherence was demonstrated empirically using a simple experiment. In the experiment, two sinusoids of identical period (arbitrary units), length, and amplitude were generated. The scale-averaged cross-power and coherence was computed between them. Theoretically, the scale-averaged coherence should be unity at all times and the cross-power should be independent of time because the sinusoids are stationary and the proprieties of them are identical at all times. The experiment was computed for different periods of the sinusoids. The results are presented in Supplementary Figure S22. As expected for the scale-averaged crosspower, the cross-power is reduced near the edges. The reduction in power is largest for the pair of sinusoids with period of 62. The result is consistent with how the COI becomes larger at higher periods. In contrast, for the scale-averaged coherence, no time dependence was found, with the scale-averaged coherence being unity at all times. Moreover, the results were not dependent on the period of the sinusoids used to calculate the scale-averaged coherence. The result implies that the scale-averaged coherence results near the edges of the time series can be meaningfully interpreted so that trends calculated are not artifacts of the edge effects. Figure S1. The locations of the 344 US climate divisions. The map was generated using MATLAB's geoshow routine (MATLAB 2015a, http://www.mathworks.com/products/matlab/). Figure S2. Fraction of US climate divisions for which detrended December temperature anomalies are significantly correlated at the 5% level with detrended 300-hPa streamfunction anomalies. Red contours enclose regions where the mean correlation coefficient was greater than 1.0 and the blue contours enclose regions where the mean correlation coefficient was less than -1.0. Only US climate divisions that were negatively correlated with the EP/NP index were used to compute the mean correlation coefficients. The map was generated using MATLAB's geoshow routine (MATLAB 2015a, http://www.mathworks.com/products/matlab/). Figure S3. (a) Correlation between winter EP/NP index and Winter US climate divisional temperature. (b) Same as (a) but for the winter AO index. (c) Difference between the magnitude of the correlation coefficients in (a) and those in (b). Crosses denote those results that are statistically significant at the 5% level. The map was generated using MATLAB's geoshow routine (MATLAB 2015a, http://www.mathworks.com/products/matlab/). Figure S4. (a) Correlation between Spring EP/NP index and Spring US climate divisional temperature. (b) Same as (a) but for the winter AO index. (c) Difference between the magnitude of the correlation coefficients in (a) and those in (b). Crosses denote those results that are statistically significant at the 5% level. The map was generated using MATLAB's geoshow routine (MATLAB 2015a, http://www.mathworks.com/products/matlab/). Figure S5. (a) Correlation between Summer EP/NP index and Summer US climate divisional temperature. (b) Same as (a) but for the summer AO index. (c) Difference between the magnitude of the correlation coefficients in (a) and those in (b). Crosses denote those results that are statistically significant at the 5% level. The map was generated using MATLAB's geoshow routine (MATLAB 2015a, http://www.mathworks.com/products/matlab/).     Only climate divisions whose temperature time series was negatively correlated with the EP/NP index with at least 5% statistical significance were used in the computation of the means. The map was generated using MATLAB's geoshow routine (MATLAB 2015a, http://www.mathworks.com/products/matlab/). Figure S11. The fraction of statistically significant correlation coefficients calculated between CMAP precipitation and mean monthly temperature anomalies for the 344 US climate divisions from 1980 to 2015. Red contours enclose regions where the mean correlation coefficient exceeds 0.1 and the blue contours enclose regions where the mean correlation coefficient falls below -0.1. Only climate divisions whose temperature time series was negatively correlated with the EP/NP index with at least 5% statistical significance were used in the computation of the means. The map was generated using MATLAB's geoshow routine (MATLAB 2015a, http://www.mathworks.com/products/matlab/). Figure S12. Correlation between precipitation and the EP/NP index from 1980 to 2015. Contours enclose regions of 5% statistical significance. The map was generated using MATLAB's geoshow routine (MATLAB 2015a, http://www.mathworks.com/products/matlab/).        Contours enclose regions where the means are significantly different (at the 5% significance level) from zero, the statistical significance assessed using the student's t-test. Arrows indicate the wave activity flux ( 2 2 ), which have been scaled relative to the maximum wave activity flux vector length each panel. (c) The difference between the composite means shown in (b) and (a). Wave activity vector lengths are scaled relative to the largest wave activity vector length difference. The map was generated using MATLAB's geoshow routine (MATLAB 2015a, http://www.mathworks.com/products/matlab/) Figure S21. Wavelet scaled coherence between two realizations of a white noise process and between the same realizations with an added linear trend (black curve). The magenta line shows the scale-averaged coherence computed between the white noise realizations before the addition of the trend. The dotted shows the coherence for when the white noise realizations are detrended. Figure S22. The wavelet cross power between sine waves of length 200 and equal amplitude for three difference cases. In the first case both the sinusoids have period 15.5 and in the second and third cases the sinusoids both have, respectively, periods 31 and 62. Time units are arbitrary. The dotted line is the scale-averaged coherence corresponding to the three cases.