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Natural Climate Variability on Decade-to-Century Time Scales
sion was also reached by Ikeda (1990), who considered effects of runoff on sea ice in the Barents Sea.
CROSS-CORRELATION ANALYSIS OF SEA-ICE ANOMALIES IN THE WESTERN ARCTIC AND GREENLAND SEA
To verify that sea-ice anomalies produced in the Beaufort Sea are advected into the Greenland and Iceland seas in 2 to 3 years' time (as proposed in the feedback loop), we first grouped according to subregion the monthly sea-ice concentration data (Walsh and Johnson, 1979) that had been collected on a square 1° × 1° (latitude) grid for the period 1953-1988. Figure 4 depicts these subregions; B1 to B4 are in the Beaufort Sea and Canada Basin, and D1 to D3 are in the Greenland, Iceland, Irminger, and Labrador seas, the latter two seas being source regions of North Atlantic Deep Water. Then a monthly time series of the areal sea-ice anomalies was computed for each subregion (i.e., the concentration departure from the long-term mean for each month at a grid point in the subregion was multiplied by the grid area). The procedure is similar to that followed by M3, who studied the advection of Greenland Sea ice anomalies into the Labrador Sea via five subregions (see Figures 2 and 3 in M3). The monthly time series for each subregion was next low-pass filtered to eliminate high-frequency components, i.e., those periods shorter than 30 months. (A description of the filtering process can be found in Power and Mysak (1992).) An example of one such low-passed time series is shown in Figure 3c.
Note that the subregions B1 through B3 were chosen to follow the Beaufort gyre ice-drift pattern in the deep part of the Arctic Ocean, so that the anomaly advection would not be contaminated by smaller-scale ice motions on the Eurasian shelf. The lagged cross-correlation functions for the low-passed fluctuations in B1 versus those in the other subregions were computed and examined for asymmetries about zero lag (e.g., as seen in Figure 4 of M3). The maximum lagged correlation coefficients obtained from this analysis are given in Table 1. To find the 95 percent significance level for the correlations, the number of degrees of freedom (for simultaneously correlated data) was estimated to be 2N/30 = 29, where N = 432 (total number of points of data). Then from Table 13 in Pearson and Hartley (1966), we obtained, using a one-tailed test for normally distributed data, a 95 percent significance level of r = 0.3. For lagged cross-correlations, the estimated number of degrees of freedom decreases with lag; the 95 percent significance level for the correlation coefficient r, which is estimated to be 0.3 for simultaneously correlated data, slowly increases to 0.36 for a lag of 120 months.
The results in Table 1 show that the low-pass filtered sea-ice anomalies in B1 lead those in the Greenland Sea (subregion D1) by just over 2 years, and, moreover, that there appears to be a continuous advection of ice anomalies by the Beaufort gyre, the Transpolar Drift Stream, and the East Greenland Current all the way into the Labrador Sea. (Although the maximum cross-correlations for B1 versus D2 and D3 are not significant at the 95 percent level, the correlations between data from adjacent regions are significant (Mysak and Power, 1992) and support the above conclusion.) Chapman and Walsh (1991) found that (unfiltered) monthly Beaufort sea-ice anomalies also led those in the Greenland Sea (see their Figure 12); however, they did not estimate the time lag involved nor did they carry out an analysis of the sea-ice fluctuations between subregions B1 and D1. A detailed discussion of the sea-ice anomalies described here, and also of those in the other subregions shown (but not labeled) in Figure 4, is given in Mysak and Power (1992). The possible role of wind forcing in creating these anomalies is examined by Mysak and Power (1992) as well.
To estimate the average advection speed of the anomalies from the Beaufort Sea into the Greenland Sea and beyond, a cumulative lag plot was constructed (Figure 5). From the best linear fit to the data, we find an average advection speed of about 2000 km/yr, or roughly 5 km per day, which lies well within the range of typical drift speeds for sea ice, namely 1 to 10 km per day (Chapman and Walsh, 1991).
EVIDENCE FOR EARLIER GISAs
In M3 the ice-limit data of the Danish Meteorological Institute (DMI) for the period 1901-1956, which give the summer ice-edge positions in the Greenland, Iceland, Irminger, and Labrador seas, were analyzed for evidence of earlier GSA-like events. It was noted that in response to large North American runoff increases in 1931-1932 and 1945-1947 (see Figure 17 in M3), the sea-ice extent in the Greenland and Iceland seas increased noticeably a few years
TABLE 1 Maximum Lagged Correlation Coefficients (r) for Smoothed Areal Sea-Ice Anomalies in Subregion B1 (see Figure 4) Versus Those in Other Subregions, with the Lag at Each Maximum Correlation