Changing response of the North Atlantic/European winter climate to the 11 year solar cycle

In this study, the Hadley Centre Sea Level Pressure (HadSLP2) dataset for the period 1851–2004, and HadSLP2r for the period 2005–2012 are employed (Allan and Ansell 2006), these two data sets can be found at www.metoffice.gov.uk/hadobs/. The NCEP/NCAR reanalysis is also used to extend the mslp data to 2016. Monthly sunspot numbers (SSN) are used to quantify the 11 year solar cycle (http://www.esrl.noaa.gov/psd/gcos_wgsp/Timeseries/SUNSPOT/). The NAO index (NAOI) is defined as the mslp difference between Gibraltar and Iceland (Jones et al 1997). Our analysis focuses primarily on Northern Hemisphere winter, defined as the average of December, January and February (DJF).

The DJF mean stratospheric aerosol optical depth (AOD) averaged over the Northern Hemisphere is employed to represent volcanic influences (Sato et al 1993). We use the DJF mean SST over the region 5°N–5°S and 180–90°W to represent El Niño and Southern Oscillation (ENSO), which is derived from the Hadley Centre Sea Ice and Sea Surface Temperature (HadISST) data set (Rayner et al 2003). For the analysis extending back to 1751 the reconstructed NAO (Luterbacher et al 1999), Niño 3.4 (Wilson et al 2010), and stratospheric AOD (Crowley and Unterman 2013) indices are used to fill the gap between 1751 and the HadSLP2/HadISST period. A reconstructed monthly averaged gridded mslp data (Luterbacher et al 2002) confined to the region (30°W–40°E; 30°N–70°N) is also used. This data set covers the period 1659–1999 (http://www.ncdc.noaa.gov/paleo/paleo.html). To ensure homogeneity, these data sets were adjusted to have the same mean and standard deviation values with the observations for the overlap period. The anthropogenic index for this extended analysis is represented by a linear trend, because the anthropogenic radiative forcing data is not available before 1850.

The multiple linear regression (MLR) method is frequently used to separate the influences of the SC from other sources of variability and has been widely applied to various climate data sets (Lean and Rind 2008, Frame and Gray 2010, Roy and Haigh 2010, Brugnara et al 2013). Following Gray et al (2013), a lead/lag multiple linear regression (L-MLR) method is used here to isolate the SC influences at different lead and lag times. We obtain the response of a climate variable over location x (a vector) in year t at l years leading/lagging the SC using the following equation:

$$\begin{equation} \begin{array}{l@{}l@{}l@{}} {T(x,t)} \hfill & = \hfill & {C_{\rm SSN} (x) \cdot {\rm SSN}(t - l) + C_{\rm VOLC} (x) \cdot {\rm VOLC}} \hfill \\ {} \hfill & {} \hfill & { + C_{\rm ENSO} (x) \cdot {\rm ENSO}(t)} \hfill \\ {} \hfill & {} \hfill & { + C_{\rm TREND} (x) \cdot {\rm TREND}(t) + \varepsilon (x,t)} \hfill \\ \end{array} \end{equation} \tag{ 1 }$$

The four indices employed in the L-MLR equation (1) are: (1) SSN: the DJF mean SSN at l year lag (note that time-variations greater than 15 years were subtracted from the SSN time series by applying a low-pass filter technique, to ensure that we only extract the quasi-11 year SC signal); (2) VOLC: the DJF mean stratospheric AOD averaged over the Northern Hemisphere to represent volcanic influences; (3) ENSO: the DJF mean SST over the region 5°N–5°S and 180–90°W to represent ENSO; and (4) TREND: a linear trend term.

To deal with autocorrelation in the residual term ε a pre-whitening procedure is employed in the MLR analysis (details are described in the appendix of Chen et al 2015). The procedure is repeated three times until most grids satisfy the Durbin–Watson test to ensure the residuals are whitened (Durbin and Watson 1971). After this, a1000-trial bootstrap re-sampling test is employed to measure the statistical significance level of the regression coefficients. In each trial, all the indices employed in the L-MLR equations were resampled (with replacement) to estimate the uncertainty in the solar signal. The climate responses to the SC are denoted by the regression coefficients of SSN, scaled to represent the atmospheric differences between S_max and solar minimum (S_min) years for the selected time intervals.

In order to examine the temporal evolution of the SC signal, a 44 year sliding L-MLR analysis with different leads/lags between 0–5 years is performed for the extended period 1751–2016. A sliding window length of 44 years contains roughly four sunspot cycles. This length of the sliding window was selected to be a compromise between being sufficiently long to maximize the chance of achieving statistical significance while being short enough to resolve time-periods with different SC responses. Assigning the regression coefficients to the center of the time window (centered on the 23rd year) yields the time varying solar signals for the time period 1773–1995.

When the separate Azores/Icelandic regions are examined, these are based on (latitudinally-weighted) area-averages in a rectangular box bounded by 30°W–15°W and 30°N–40°N for the Azores and bounded by30°W–15°E and 60°N–70°N for Iceland. Results were insensitive to the precise definition of these boundaries.

Firstly, we examine the 11 year SC signals in mslp at 0–5 year lags for 1851–2016 (left panel of figure 1). This time-period is selected so that the results can be compared with those of Gray et al (2013). At 0–1 year lags, the signals are generally weak and insignificant over the entire region. A statistically significant (p < 0.05) positive signal emerges subsequently around the Azores at 2–4 year lags, with a negative but statistically insignificant signal around the Iceland at the same time. This result confirms the 2–4 year lagged response first reported by Gray et al (2013), although the estimated lag between SSN and the Azores mslp anomaly is slightly shorter than theirs, primarily because Gray et al (2013) used the annual mean SSN to quantify the 11 year SC, while the present study employs the DJF-averaged SSN instead. Although the mslp response pattern bears some resemblance to the positive (negative) phase of the NAO 2–4 years following S_max (S_min), there are also notable differences. In particular the pattern is weighted more towards the Azores region. The maximum amplitude of DJF mslp response over the Azores is ∼3 hPa, while the standard deviation (STD) of the DJF mslp around the Azores is 2–3 hPa, therefore the SC effects contribute a substantial fraction of year-to-year variations for this region. There is a maximum negative mslp anomaly of less than 2 hPa in the northern part of the NAO (i.e. Iceland), only equivalent to ∼0.5 STDs of the wintertime Iceland mslp variability, which is not sufficiently strong to be distinguished from the background variability.

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Notably, when the data sets of the recent decades were employed, numerous previous studies had suggested a significant NAO response synchronized with the SC (i.e. zero-lag), including significant negative Iceland mslp anomalies (e.g. Woollings et al 2010, Ineson et al 2011, Chen et al 2015, Kodera et al 2016 and Lu et al 2017a). This synchronized response since ∼1970s is also confirmed by examining the spatial pattern of the DJF regression analysis over the recent period 1979–2016 shown in figure 1 (right panel), the period has been chosen to match as closely as possible the periods examined by earlier studies (e.g. Kodera et al 2016 and Lu et al 2017a). It is clear that the estimated SC signals over the recent period are quite different from those over the period 1851–2016, suggesting a changing nature of the SC signals. Therefore, it is necessary to further explore the nature and causes of time variations in the SC signals, including the possible reasons for the significant synchronized response since ∼1970s.

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Figure 2(a) shows the DJF-averaged SC response from a series of 44 year sliding window regression analyses of the NAOI over the period 1751–2016 in which the solar index is employed at different lead/lag times between 0–5 years. The year (x-axis) is labeled according to the central year of the 44 year window and the y-axis shows the lead/lag time employed. The shading shows the amplitude of the SC response from each of the individual regression analyses and solid black (white) dots denote that the regression coefficients are statistically significant at the p < 0.1 (p < 0.05) level after pre-whitening and a 1000-trial bootstrap resampling test. Although there are coherent periods showing a positive anomaly at ∼3 year lag e.g. 1780–1860 and 1930–1980, overall the signal shows very little statistical significance and is sporadic in nature so that an MLR analysis performed using the whole period (not shown) shows no statistically significant response in the NAOI, which is consistent with Gray et al 2013.

Notably, as figure 1 demonstrates, the dominant DJF SC response is found over the Azores region, so we examine the two components of the NAO separately; figure 2(b) shows the corresponding 44 year sliding window regression analysis over the Azores region. The lagged nature of the Azores mslp SC response is evident for most of the time intervals during 1751–2016 with positive (negative) responses predominantly evident at several years lagging (leading) the SC, although statistical significance is only achieved over limited time intervals because of the relatively short time window employed. This lagged nature of the response is insensitive to the choice of the sliding window length, as tests obtain nearly identical results with sliding window lengths of 33, 37 and 41 years (see figure S1 available at stacks.iop.org/ERL/13/034007/mmedia).

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Although the lagged nature of the Azores mslp response is relatively consistent throughout the historical record, its robustness and statistical significance exhibit substantial long-term variations. The stronger and significant Azores mslp responses (p < 0.1 at 2–4 years lag and 2–4 years lead) are mainly detected before ∼1810 and after ∼1930, while weak responses can be found during 1860–1930. An intriguing hint is that there seems to be a connection between the strength of solar variability and significance of the Azores responses, as the period when the Azores response is most significant is also the period when solar variability is strongest (in the mid-20th Century). To demonstrate this further, figure 2(d) shows the 44 year sliding average of SSN standard deviation and also the corresponding time-series of the statistical confidence of the Azores mslp response (averaged over all lags i.e. from lag −5 year to lag +5 year). A higher value of the averaged confidence level shows that the SC signal can be distinguished more clearly from the background noise and/or other external forcing during that time period. The correlation between the two time series is 0.614 (p = 0.02) for the whole time period (1773–1995), and it is even higher for the period 1873–1995 (r = 0.893, p < 0.01). However, in earlier times the weaker periods of solar variability do not correspond to the weakest responses, and the correlation is even opposite in sign and less significant for the period 1773–1829 (r = −0.349,p > 0.1), possibly because the earlier reconstructed data before 1850 is of poorer quality. (The p values of these above correlations are obtained by a 10000-trialbootstrap resampling test, in each trial the sequence of all the years using for analysis are resampled before performing the time-sliding L-MLR analysis and the corresponding correlation analysis). A possible explanation is that the larger amplitude of solar forcing is favorable for the SC responses to be distinguished from the confounding noise. On the other hand, the variation in significance may also result from reinforcement/cancellation between early and late winter responses, as will be discussed later in this section.

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The corresponding DJF regression analysis over the Icelandic region (figure 2(c)) shows an opposite structure to the Azores response at some time periods and at some lags. For example, the negative (positive) response at 3 year lags (2 year leads) in the period 1780–1810 corresponds well with the Azores signals, but with opposite sign. There is a similar correspondence in the period 1860–1930, with a particularly weak SC response over Iceland as well as the Azores. But overall the Icelandic response is sporadic in time and shows differences in the timing when compared with the Azores during certain periods, e.g. the positive SC signals maximize at 2–4 year lag (2–4 year lead) over the Azores in the period from ∼1970, while the negative SC signals over Iceland maximize at zero-lag. This mismatch in the lag of the response after ∼1970 will be examined in more detail later.

In summary, figure 2 suggests that a DJF-averaged SC response is present over both the Azores and Iceland during certain periods but with differences in timing that mean their combination into a single NAOI obscures the true nature of SC signal. The same is true of averaging over all winter months, since taking a DJF-average can result in the partial cancellation of SC signals in the individual months. Gray et al (2016) showed that the ∼2–4 year lagged response was primarily seen in the early winter months (December and January) while the February response was more clearly seen at lag-zero i.e. synchronized with the SC.

Figure 3(a–c) show the 44 year sliding window regression analysis of the Azores SC signal from each individual winter month. The December and January responses are similar and both consistently show lagged signals, with mainly positive anomalies at 2–5 year lag throughout the entire period. The statistical significance of the December response is generally greater than in January. In some periods (e.g. ∼1800–1860, ∼1900–1930) the maximum (positive) response is seen at relatively large lags so that there are significant negative anomalies at zero-lag. In February, on the other hand, the signal is rather variable, sometimes with a maximum (positive) response at zero lag (around 1840, 1890–1930, 1980-present) and sometimes with a 2–4 year lag, mainly in the intervening periods. In some periods (e.g. 1820–1860, 1890–1930) this results in patterns of anomalies in February at lag zero that are opposite to those in December/January and hence there is substantial cancellation in the DJF-mean, whilst in other periods (e.g. 1930–1960) the responses in all three months are of the same sign and reinforce each other. This underlines the importance of analyzing the response in terms of early winter/late winter months.

In figure 3(d–f) the corresponding 44 year sliding window regression is shown for the Icelandic region. As already noted, there is very little statistical significance because of the larger intrinsic variability, and overall the responses show less consistency than those of the Azores. Nevertheless, the pattern of response is similar to the Azores in most time periods, but with mainly negative lagged anomalies (and positive zero-lag anomalies) in December and January. February is again more variable, with some similarities to the Azores structure (but of opposite sign).

The above analysis of each individual winter month suggests a lagged response in early winter (December–January) which is relatively stable, as well as a variable response in late winter (February). In addition to the sliding window analysis, these findings can be further confirmed by time-averaged responses in separate periods. In figure 4 the epoch 1851–2016 (when HadSLP2 is available) is divided into four subperiods, i.e. 1851–1890, 1891–1930, 1931–1978 and 1979–2016, among them 1891–1930 and 1979-present have an evident synchronized behavior in late winter, while1851–1890 and 1931–1978 are periods that do not.

During early winter (see figure 4(a)), the zero-lag response for 1851–2016 is rather weak, with inconsistent response patterns in each subperiods. At 3 year lag, the response pattern is NAO-like with more statistical significance over the Azores region, very similar to the DJF mean response in figure 1. This is consistent with the analysis of Gray et al 2016 that suggested the lagged response signal in DJF comes primarily from early winter months, associated with ocean feedbacks that involve reinforcement by anomalies from the previous winter. Note this pattern is present not only in the whole period but also in three out of the four subperiods (except for 1931–1978), confirming the stable nature of the early winter responses shown in figure 3, although there is more statistical significance in 1851–1890 and 1891–1930 than in 1979-present.

The late winter (see figure 4(b)) response at zero-lag for 1851–2016 exhibits a NAO-like pattern, with statistical significance detected at Iceland and the southern Europe. According to G2016 this pattern reflects an immediate top-down solar forcing from the stratosphere. But the response pattern is very inconsistent among subperiods, possibly due to more dynamical variability resulting from the effect of sudden stratospheric warmings (SSWs) during late winter. In addition, a significant Azores response at 3 years lag is also found in late winter of 1851–2016, primarily arising from a strong and significant lagged response during 1930–1980. Again, this response is inconsistent among sub periods. This might suggest that a lagged solar influence associated with reemergent ocean signals is also present in late winter, but that the high dynamical noise masks the response to a degree. Another possibility is that the February response is influenced by both the direct stratospheric forcing and indirect ocean feedbacks, so the presence or absence of a lag in the mslp response in February may depend on which effect is more dominant.

There is a significant NAO-like response pattern synchronized with the SC (i.e. zero-lag) during 1979–2016, including significant negative Iceland mslp anomalies (see right panel of figure 1). But the sliding window analysis in figure 2 shows this significant synchronized DJF response is isolated in the historical record, i.e. it never appears in any other time intervals before 1970s. This leaves two possibilities that the recent synchronized relationship is a result of changes in physical mechanisms or just a result of chance fluctuation.

The early/late winter analysis in figure 4 shows that, the significant synchronized Iceland/NAO response in the DJF average during 1979–2016 arises primarily from late winter (i.e. February). The response amplitude during February exceeds −6 hPa around the Iceland region (figure 4(b)), with a large area of statistical significance, while the amplitude of the early winter (figure 4(a)) response is much weaker by contrast. It increases the chance that the derived synchronized signal is caused by aliasing with internal noise. In addition, the 3 year lagged response over the Azores region is still presentin early winter during 1979–2016 (figure 4(a)), suggesting the previously proposed ocean feedback mechanism also operates in this period, although the 3 year lagged response becomes less evident in the DJF average due to a cancellation between early and late winter.