Ron Lindsay's Web Pages 

Polar Science Center, Applied Physics Laboratory 


Predictions of the Total Ice Extent in September Recap: Our method uses estimates of ice thickness from the PIOMAS coupled iceocean model as predictors for a statistical forecast of the Sea Ice Index mean ice extent in September. Fields of ice thickness (H), ice concentration (IC), area with less than 0.40 m thick ice (G0.4m), and area with less than 1.00 m thick ice (G1.0m) are the predictors considered in this forecast. The method is described in Lindsay et al (2008a). The model fields are collapsed to scalar time series by weighting each field with its correlation to the September ice extent (Drobot, 2006). A statistical model is then fit for the years 1988–2009. The performance of each predictor at each lead time from February through August is shown in Figure 1. In retrospect the mean thickness H was the best predictor from almost all months, particularly early in the season, but the error standard deviation of the prediction equation using H in past years was larger than that for the G1.0m predictor. The G1.0m predictor was the best in terms of the minimum prediction error in the months of February through May and G0.4 was best in June, July, and August. This makes sense, since simplistically one might expect all the ice less than 1 m thick at the beginning of the season to melt out and only ice less than 0.4 m to melt out late in the season. The region with the greatest influence in determining the value of these two variables, that is where the correlation with the September ice extent is high and where there was a significant anomaly in the G1.0m or G0.4m parameter is in the Beaufort Sea. This region had both high values of the parameter and high correlations for it with the September ice extent. As shown in Figure 1, the observed September mean ice extent, 4.90 million sq km, was within the error bars of the predictions only for February, March, and April. The method worked poorly this year. One reason may be that the ice was very loose at the end of September. Figure 2 shows the compactness of the ice, which is the ratio area / extent, for the last 30 years. This September was a record low compactness in the modern era of very low ice extents. In the early 1980s the September compactness was also low, but the extent was high. When the pack is loose, the total extent is very dependent on the prevailing winds, which this year did not herd the ice to one side of the basin.
References
Figure 1. The performance of each predictor in 2010 in predicting the September minimum ice extent (in million sq km) using data through the end of each predictor month. The orange triangle and dotted line is the observed mean September ice extent (4.90 million sq km) from the NSIDC Sea Ice Index web site. The black lines show the prediction based on each of the four variables for each predictor month back to February. The dashed lines are the prediction uncertainties…the error standard deviations of the linear regression fit. The blue squares in the G1.0m and G0.4m plots show which variable of the four had the minimum prediction uncertainty in each month and hence was the basis of the value chosen for the prediction at the end of each month.
Figure 2. The ice compactness in September. The compactness is the ratio of the m,ean ice area to the mean ice extent.
End of July: Our prediction using model retrospective simulations from the month of July gives a forecast similar to last month's: the best predictor is G0.4 (area with less than 0.4 m of ice) and the predicted extent is 3.7 +/ 0.3 million square kilometers. The R2 value for this predictor is still 0.84. Here is the diagnostic plot for this month: End of June: According to our model retrospective simulations, the ice in the Arctic has continued to thin at a remarkable rate. The statistical method based on the PIOMAS model analysis now is projecting a new record low ice extent. The best predictors are G1.0 (area withless than 1.0 m of ice) and G0.4 (area with less than 0.4 m of ice) which give nearly identical results. Using the same one as last month (G1.0) the predicted extent is 3.96 +/ 0.34 million square kilometers. The R2 value for this predictor is 0.84. which now indicates a high degree of skill in the forecast. Here is the diagnostic plot for this month:
End of May 2010: Our prediction is made with model data from the end of May 2010. We are using May data for the 22 years 1988 through 2009 to fit the regression model and then the ice conditions for May 2010 to make the predictions. The best single predictor is the fraction of the area with open water or ice less than 1.0 m thick, G1.0. This predictor explains 79% of the variance. The predicted extent in September is 4.44 +/ 0.39 million square kilometers. This is much lower than what was observed last September, however the error bars are still quite large, though smaller than that of the trend line prediction over the same years (5.15 +/ 0.57 milion sq km). The onestandarddeviation error bar includes the record low of 2007. The regions most influential in making the prediction are in the Beaufort Sea, the Barents Sea, and the Kara Sea (right map in the figure). All of these regions have greater than normal fractions of thin ice (middle map) and the G1.0 variable in these regions have a significant correlation with the September ice extent (left map). The figure shows the time series of the observed September ice extent (solid line), the predictions of the model for past years (cyan diamonds), and the prediction for this year (orange star and error bars). The error bars are the standard deviation of the error in the fit of the regression. The trend line (dashed) and the prediction of the trend line (black star) are also shown. The mean ice thickness predicts more ice but the error is larger, 4.76 +/ 0.51 m sq km (R2 = 0.63). The region most influential in the prediction is the thin ice in the Beaufort Sea and along the Canadian Archipelego to Fram Strait. The ice concentration is a poor predictor this time of year. The prediction using ice concentartion is lower than that from the G1.0 predictor and gives 4.37 +/ 0.47 m sq km (R2 = 0.69) and the regions most influential are small places in the Kara and Barents Seas. End of April 2010: Our prediction using model data from the end of April is for 5.12 +/ 0.42 million sq km of ice in September, a little higher than what we said last month. Again the most important predictor is the area with less than 1 m of ice. End of March 2010: Our first prediction is made with model data from the end of March 2010. The best single predictor is the fraction of the area with open water or ice less than 1.0 m thick, G1.0. This predictor explains 72% of the variance. The predicted extent in September is 5.05 +/ 0.45 million square kilometers. This is a little lower than what was observed last September, however the error bars are still quite large, but smaller than that of the trend line prediction (5.15 +/ 0.57 milion sq km). The regions most influential in making the prediction are in the Beaufort Sea, near the pole, in the Barents Sea, and in the Kara Sea (right map in the figure). All of these regions have greater than normal fractions of thin ice and the G1.0 variable in these regions have a significant correlation with the September ice extent (left map). The figure shows the time series of the observed September ice extent (solid line), the predictions of the model for past years (cyan diamonds), and the prediction for this year (orange star and error bars). The error bars are the standard deviation of the error in the fit of the regression. The trend line (dashed) and the prediction of the trend line (black star) are also shown. The mean ice thickness predicts less ice but the error is larger, 4.95 +/ 0.52 m sq km (R2 = 0.62). The region most influential in the prediction is the thin ice in the Beaufort Sea and along the Canadian Archipelego to Fram Strait. The ice concentration is a very poor predictor this time of year. The prediction using ice concentartion is 5.93 +/ 0.56 m sq km (R2 = 0.55) and the regions most influential small places in the Greenland Sea and in the Kara and Barents Seas. The NSIDC preliminary estimate of the total Arctic sea ice extent in September 2009 is 5.36 million sq km, very near the linear trend line since 1979.
In retrospect the mean thickness H was the best predictor from almost all months, particularly early in the season, but the error standard deviation of the prediction equation using H in past years was larger than that for the G1.0m predictor. Unlike last year, the G1.0m predictor was the best every month in terms of the minimum prediction error. This variable measures the fractional area of both open water and thin ice less than 1.0 m thick. The region with the greatest influence in determining the value of this variable, that is where the correlation with the September ice extent is high and where there is a significant anomaly in the G1.0m parameter is in the Beaufort Sea. This region had both high values of the G1.0m parameter and high correlations for it with the September ice extent. As shown in Figure 1, the observed September mean ice extent, 5.36 million sq km, was within the error bars of the predictions except for the short lead times, July and August.
To improve predictions using a statistical approach such as the one we used would require a longer and more accurate record of the seasonal changes in the ice thickness distribution. Unfortunately that is only obtainable through models. New observations can’t help much except for driving improvements in the models because they can’t give a consistent record of the past behavior of the system. Perhaps a more problematic issue is that the statistical relationships between elements of the system are changing rapidly. Until a new stable regime is established and we can get an adequate number of sample years of this new regime, statistical methods of prediction will be limited in their accuracy. With nonstationary statistics the standard error of the fit over past years is not a good measure of the uncertainty in the prediction. Figure 1. The performance of each predictor in 2009 in predicting the September minimum ice extent (in million sq km) using data through the end of each predictor month. The orange triangle and dotted line is the observed mean September ice extent (5.35 million sq km) from the NSIDC Sea Ice Index web site. The black lines show the prediction based on each of the four variables for each predictor month back to February. The dashed lines are the prediction uncertainties…the error standard deviations of the linear regression fit. The blue squares in the G1.0m plot show that this variable of the four had the minimum prediction uncertainty in each month and hence was he basis of the value chosen for the prediction at the end of each month

