Fig 1.
The four longest ice-on time series (left panels) and the four longest ice-off time series (right panels). Red lines are trendlines generated using least-squares linear regressions. Note that the axes differ between panels. Note also that the longest ice-on timeseries and the longest ice-off time series do not always occur at the same locations.
Fig 2.
Time series of sunspot number (top panel) and the Fourier transform of the same data (bottom panel). Note that both show a very clear 11-year cycle and a weaker 90-year cycle. Note also that while Fourier transforms are normally displayed as functions of frequency, we have used period as the horizontal axis here. The vertical axis on the second panel has been normalized so that the area under the curve would be 1 if it was plotted on a linear horizontal axis.
Fig 3.
Correlations between sunspot number averaged over the NDJ season and ice-on date.
Red and blue dots indicate positive and negative correlations, respectively, and the size of the dot indicates the absolute value of the correlation. The black dots in the upper-left corner represent correlations of 1 and 0.1, for scale. Note that statistical significance is not represented on this figure but is instead noted in the text.
Fig 4.
As in Fig 2, but for correlations between sunspot number averaged over the MAM season and ice-off date.
Fig 5.
Power spectra (generated using fast Fourier transforms) of ice-on data (top) and ice-off data (bottom). Thin blue lines represent individual locations, and bold red lines represent the average. The spectra are calculated at all locations with at least 60 years of data. To allow easier comparison with the 11-year cycle we are looking for, we have transformed the curves so that the horizontal axis represents period, rather than the more standard frequency. The vertical axes have been normalized so that the area under each curve would be 1 if it was plotted on a linear horizontal axis.
Fig 6.
The Moran’s I statistic represents the spatial autocorrelation of the individual correlations.
Shown here are the p-values of the I statistic, estimated using a bootstrapping method described in the text. Values below the red line are statistically significant at the 0.05 level.