Seasonal Ice Prediction

I have been interested in the seasonal prediction of sea ice conditions for some years and recently wrote a paper about using model estimates of the state of the ice and ocean conditions to estimate the ice extent up to a year in advance. The idea is that there might be a memory in the system that would allow such predictions. It uses past statistical correlations between the model fields of ice thickness, ice concentration, or ocean temperatures in an earlier month and the ice extent in September.

The method is based on a retrospective analysis of the state of the ice and ocean system created by a high resolution coupled ice/ocean model.  The model uses the observed air temperature, wind, clouds, and precipitation to estimate maps of the ice motion, ice thickness distribution, and ocean temperatures and currents for past years, up to and including the most recent month.  Statistical relationships between the model parameters in March (or any other month) and the ice extent in September are found from past years using a method developed by Dr. Drobot.  This relationship is then used with the current March model output to predict the September ice extent.  The method may be used to predict either the pan-Arctic ice extent or the extent in particular regions.  It depends fundamentally on a stable relationship between the various components of the system, such as ice thickness in March compared to the ice extent in September. 

It seemed to work fairly well using historical data. However the summer of 2007 showed a tremendous loss of sea ice and the predictions from this method were way too conservative. This has led me to think that the statistical relationships between the ice extent and the state of the ice and ocean are changing rapidly and the past relationships cannot be a reliable guide to the future.

Predicting ice conditions months in advance is a challenging problem for Arctic scientists.  The current condition of the ice pack can help some because we know old thick ice can often survive the summer melt season but new thin ice can't.  The exact thickness of the ice in spring that might survive depends on the location and on the air temperatures and cloud cover during the summer, both of which are not possible to predict more than a week or so into the future.  Also, the ice extent is strongly dependent on the winds as we saw in the summer of 2007.  It is not possible to accurately predict the strength and direction of the winds months in advance and, depending on the air pressure patterns, the winds may or may not herd the remaining ice to one side of the basin, thus reducing the extent.  What we do know is that the reduced ice thickness of recent years will lead to much more variability in the fall ice area and extent because the open water created during the summer is more sensitive to the initial ice conditions and the amount of melt.  We still have a lot to learn about seasonal ice prediction. 

However I'll continue to use the method outlined above as an excercise to see if we can learn more about how the system is changing and how we might be better able to predict the changes in the future.

• The paper:

Lindsay, R. W., J. Zhang, A. J. Schweiger, and M. A. Steele, 2008: Seasonal predictions of ice extent in the Arctic Ocean, J. Geophys. Res., 113, C02023, doi:10.1029/2007JC004259. pdf file 

 

• Poster from the 2007 Polar Meteororlogy and Oceanography Conference, St John's Newfoundland

 

 

My colleague Jinlun Zhang's Ensemble Predicition page which uses quite a different method

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Recap of the 2008 Prediction Season

Our method uses estimates of ice thickness from a coupled ice-ocean model as predictors for a statistical forecast of the minimum ice extent in September. Fields of ice thickness (H), ice concentration (IC), area with less than 0.66 m thick ice (G1), and area with less than 1.94 m thick ice (G2) 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 1987–2007. The performance of each predictor at each lead time is shown in Figure 1.

In retrospect the mean thickness H was the best predictor from almost all months but the error standard deviation of the prediction equation using H in past years was larger than for the G1 or G2 predictors. Ice concentration was a poor predictor in every month except August. The predictions from both G1 and G2 were correct to nearly within the error bars every month and one of the two was the best predictor each month. As might be expected, the area with less than 0.66 m of ice, G1, was the best predictor at shorter intervals, 1 to 3 months, while the area with less than 1.94 m of ice, G2, was better for longer intervals.

The main reason the ice extent was quite low in 2008 was that there were large areas of thin ice. Figure 2 shows the time series of each of the four predictors in March and August, along with the trend lines. There are two reasons why 2008 didn’t quite match the ice record low extent of 2007: 1) thin ice was more extensive in the spring of 2007 than in 2008 and 2) the unusually persistent winds from the Pacific side of the basin that blew much of the ice to the opposite side in 2007 were absent in 2008. Note that, relative to the trend line, the March H, IC, G1, and G2 values all fully recovered during the winter from the extreme 2007 values.

As discussed in Lindsay et al (2008b) the linear trend accounts for much more of the variance of the mean ice thickness than for the variance of either the mean ice concentration or ice extent. The mean ice thickness in 2008 was nearer the linear trend line (1987–2007) than in 2007. So while the thickness in 2008 was the thinnest in the record except for 2007, it was quite consistent with the downward trend in the mean ice thickness in the basin over the last 21 years. The fact that 2008 sea ice extent did not establish another record minimum is thus consistent with our understanding that the 2007 sea ice record anomaly was established by a combination of long-term thinning and unusual wind patterns (Maslanik et al., 2007; Lindsay et al., 2008b; Zhang et al, 2008)

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. Here the trend is our friend. It allows us to obtain some skill relative to climatology. The harder part is to predict the increasingly large deviations about the trend and to know when the trends are changing.

As the September ice extent and ice thickness decrease, they will be more subject to variable and unpredictable wind patterns earlier in the season, making the total ice extent more difficult to predict. More importantly, the summer ice extent in particular regions (where individuals can actually use the predictions for planning purposes) will be even harder to predict beyond what the trends suggest.

The 2008 observations reinforce our contention (Lindsay et al., 2008b) that the record minimum of 2007 was less just the damage left by a perfect storm of unusual winds, but more the result of a gradual erosion of the mean sea ice thickness over the past 20 years and the increasing abundance of thin young ice at the beginning of the melt season.

REFERENCES

Drobot, S. D., J. A. Maslanik, and C. F. Fowler (2006), A long-range forecast of Arctic summer sea-ice minimum extent, Geophys. Res. Lett., 33, L10501, doi:10.1029/2006GL026216

Lindsay, R. W., J. Zhang, A. J. Schweiger, and M. A. Steele, 2008a: Seasonal predictions of ice extent in the Arctic Ocean, J. Geophys. Res., 113, C02023, doi:10.1029/2007JC004259.

Lindsay, R. W., J. Zhang, A. J. Schweiger, and M. A. Steele, and H. Stern, 2008b: Arctic sea ice retreat in 2007 follows thinning trend. J. Clim., in press.

Maslanik, J., C. Fowler, J. Stroeve, S. Drobot, J. Zwally, D. Yi, and W. Emery, 2007: A younger, thinner Arctic ice cover: Increased potential for rapid, extensive sea-ice loss, Geophys. Res. Lett., 34, L24501, doi:10.1029/2007GL032043.

Zhang, J., R. Lindsay, M. Steele, A. Schweiger, 2008: What Drove the Dramatic Retreat of Arctic Sea Ice During Summer 2007? Geophys. Res. Lett., 35, L11505, doi:10.1029/2008GL034005.

Figure 1. The performance of each predictor in 2008 in predicting the September minimum ice extent (in million sq km) . 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 and G2 plots show which variable of the four had the minimum prediction uncertainty in each month and hence the value chosen for the prediction at the end of each month. The orange triangle and dotted line is the observed minimum September ice extent (4.52 million sq km) from the NSIDC web site.

Figure 2. The simulated mean ice thickness H, ice concentration IC, area with less than 0.66 m thick ice, G1, and area with less than 1.94 m ice, G2, for the Arctic Ocean in March and August. The trend lines are computed for 1987–2007 and the extension of the trend is shown in orange along with the estimates for 2008 as an orange cross.

 

*** Predictions from the model state at the end of July 2008

Our best estimate is 4.27 +/- 0.19 million sq km using the G1 predictor (the area fraction of ice and wayer less than 1 m thick). This is slightly lower than the prediction using May data and the error is smaller (as would be expected). The large area of open water currently in the eastern Beaufort Sea is not in a region that does well for predicting the September ice extent. There is a large area north of the Chukchi Sea that has more than normal thin ice and which is a better predictor for the September ice extent.

Using the area of ie less than 1 m thick, G1 :

Using the mean ice thikness, H:

Using the ice concentration, IC:

 

*** From the model state at the end of June 2008

Our best estimate is 4.44 +/- 0.21 million sq km using the G1 predictor (the area fraction of ice and wayer less than 1 m thick). This is slightly higher than the prediction using May data and the error is smaller (as would be expected). The large area of open water currently in the eastern Beaufort Sea is not in a region that does well for predicting the September ice extent. There is a large area north of the Chukchi Sea that has more than normal thin ice and which is a better predictor for the September ice extent.

Using G1 :

Using H (the mean ice thickness):

 

 

 

*** From the model state at the end of May 2008

Our best porediction is for 4.36 +/- 0.33 million sq km using the G2 predictor (area of ice and open water less than 2 m thick).

Using G2:

Using H:

 

 

 

*** From the model state at the end of April 2008

The model field in March that is best correlated with the pan-Arctic ice extent in September over the last 20 years is the area of ice and water less than 2 m thick (what we call the G2 field). The predicted ice extent is 4.5 +/- 0.3 million sq km This field is correlated at a level of R-squared=0.86. The field of G2 for 2008 would predict a very low ice extent in September but the prediction is not as low as the prediction for 2007 and is much above the observed extent for 2007. The simulated G2 field shows very little ice 2 m thick in the Chukchi Sea, but near normal conditions elsewhere.

A similar prediction is made using the mean ice thickness fields, although the correlation is smaller and the error bar is larger. Using the mean ice thickness, we predict the September ice extent to be 4.6 +/- 0.4 million sq km.

 

*** From the model state at the end of March 2008

The model field in March that is best correlated with the pan-Arctic ice extent in September over the last 20 years is the area of ice and water less than 2 m thick (what we call the G2 field). This field is correlated at a level of R-squared = 0.83. The field of G2 for 2008 would predict a very low ice extent in September but the prediction is not as low as the prediction for 2007 and is much above the observed extent for 2007.

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• Predictions for September 2007

From the end of July

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From the end of June

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