Foto: Nationaal Archief/Joop van Bilsen
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# Probability of an Elfstedentocht in a changing climate

The Elfstedentocht (Eleven Cities Tour) is a famous ice skating event in  the Netherlands. A century ago the probability that it was cold enough to organise an Elfstedentocht was about 20% each year. This has already decreased to 8% per year now.

The Elfstedentocht (Eleven Cities Tour) is a famous ice skating event in  the Netherlands. Because of its rareness, the 200 kilometer tour along the eleven traditional cities of in the northern province Friesland has a special status. Since 1909 only fifteen tours have been skated, less than once every seven years. The last fifty years only three tours could be organised. The question to what extent the probability of having thick enough ice for an Elfstedentocht is influenced by global warming is asked every year. In this article we compute this probability for past, current and future climates.

A century ago the probability that it was cold enough to organise an Elfstedentocht was about 20% each year. This has already decreased to 8% per year now (with an uncertainty range of 5% to 19%). This only considers an indicator for extreme cold. Howver, even when it is cold enough other factors can ruin the ice, like a layer of snow in 2012. However, with modern weather forecasts and technical possibilities to improve the ice locally, most opportunities can be used nowadays.

The future evolution of the probability depends on the magnitude  of global warming and on the circulation response, which is still uncertain. If we manage to keep the earth's temperature below 2ºC above the late 19th-century value the probability stays at about 5% per year, depending on how strong the circulation response is. However, if we let the earth warm further the probabilities decrease quickly and after one or two Tours from now it will be become very unlikely that it gets cold enough.

## Elfstedentocht and the weather

Due to the large number of participants, about 30 thousand, the Elfstedentocht can only be organised when the ice is at least 15 cm thick on almost all of the route. Short pieces of thinner ice can be circumvented by walking on skates (klunen in West Frisian). We could use an ice growth model for the whole 200 km route. However, Visser and Petersen (2009) showed that the temperature of the lowest 15-day mean daily mean temperature of the winter (TG15n) predicts well whether an Elfstedentocht could be organised in the past. If that temperature is lower than −4.2 ºC in the homogenised series from the KNMI headquarters in De Bilt, the ice in Friesland was almost always thick enough. This criterion works just as well as a one-point ice growth model forced with the local weather in Friesland and is much simpler to use.

This lowest 15-day averaged temperature in De Bilt is shown in Figure 1, together with the organised Elfstedentochten (arrows). There are a few years when it was cold enough, but no Tour was organised. In the past the organisation only started when the ice was thick enough and took three days. For instance, in 1984 the decision to go ahead was no longer possible at that time because a thaw was forecast. By using the forecast ice thickness rather than the observed one, and by reducing the time needed to organise a Tour to two days, almost all opportunities can be realised nowadays.

That leaves unfortunate coincidences like in 2012, when it was cold enough but snow fell when the ice was still very thin, reducing further growth (de Vries et al, 2013). Therefore, the Elfstedentocht prediction using the -4.2 degrees Celsius criterion will occasionally be too optimistic.

## Present climate

It is not easy to determine trends in winter extremes, simply because the variability is so large. A mild winter can be five degrees warmer than a harsh one, much larger than the trend up to now of 1.5 to 2 degrees Celsius. The differences for extremes are even larger. This can be seen by the erratic nature of the observed values of the coldest 15-day spell of the year, the blue line in Figure 1. It also shows that the distribution is very skewed: cold deviations are much larger than warm ones. That is because the Arctic or Siberian air that causes the cold extremes is much more different from the mean than the mild air from the Atlantic Ocean that dominates the rest of the winters.

By eye it looks as if there is a decrease of cold extremes since the 1970s, and a corresponding decrease in Elfstedentochten. We use two statistical methods to compute how large the probability is now, based on these observations. This probability can be expressed in two ways: a percentage per year or a return time. Those mean exactly the same a return time of 12 years means a probability each year of 100%/12 ≈ 8% each year, not that it happens once every 12 years.

The first method is based on Visser and Petersen (2009). We first transform the lowest 15-day mean temperature, TG15n, to a more symmetric distribution by considering log(10-TG15n). This series is fitted to an Integrated Random Walk (IRW) statistical model. This model assumes the variability is constant over time. The fit follows the increase of extremely cold winters from the beginning of the century to the md-century and decreases more strongly after that (figure 2).

This computation is sensitive to the last few years. When we did the calculation in 2008, the probability of a potential Elfstedentocht was 5.5% (1 in 18 years, with a 95% uncertainty margin of 1 in 64 to 1 in 7 years). After the relatively cold winters of 2009–2013 the same method gave a probability of 10% (CLO 2014) , 1 in 10 with a margin of 1 in 5 to 1 in 25 years. This year, after a few mild winters, the probability is back at 7% (1 in 15 years with a margin of 1 in 6 to 1 in 41 years), as can be read off from Fig. 2. Within the uncertainty margins all the numbers are equal. However, the decrease in probability from mid-century to now is statistically significant.

The second method is a fit with an extreme value function, in this case the Generalised Extreme Value (GEV) distribution. Mathematical theory tells us that the highest or lowest value of a large number of identically distributed independent quantities should be described by this distribution. The number of 15-day means per winter is not that large, but we find that the distribution still fits the observations well. We incorporate the global warming by following van Oldenborgh et al (2015) and assume that it shifts the whole distribution to higher temperatures proportional to the (smoothed) global mean temperature but without changing the shape.

This method also gives a significant trend in the coldest 15 days of the year, TG15n, 1.7 (0.2 to 2.8) times the global mean temperature rise over 1902–2017. This trend seems somewhat higher than the winter mean trend of 1.4±0.9 times the global mean temperature. This is expected, as the Arctic warms much faster than the rest of the globe, and hence the Arctic air that often causes the cold period warms more  quickly than the mild oceanic air that determines the temperature on mild winter days (Screen 2014, van Oldenborgh et al 2015).

This method gives a probability of a potential Elfstedentocht in the current climate of 9% (1 in 11 years), with an uncertainty margin of 5% to 19% (1 in 5 to 1 in 21 years). This agrees well with the values from the IRW model. A difference is that this statistical model is not as sensitive to the last few years: in 2008 we would have obtained 13% (7% to 21%), in 2014 11% (6% to 20%).

## Other predictors

There are ideas that the probability of an Elfstedentocht varies with the sunspot cycle. Indeed, more tours have been skated in winters with a low sunspot number, but the temperature of the coldest 15 days show no relation (Fig 4). This is in agreement with the lack of correlation between sunspots and circulation or cold winters that van Oldenborgh et al (2013) already found. Other anecdotal predictors have also been found to have no skill.

## Future climate

The next question is how the probability will develop in the future. We use the KNMI'14 scenarios. These provide transformed temperature series for De Bilt, in which the quantiles Q01, Q05, Q50, Q95 en Q99 of the observations over 1981–2010 are transformed such that the distribution agrees with the four scenarios (Bakker and Bessembinder, 2012). Accidentally this period is representative for the whole twentieth century, with a probability of a potential Elfstedentocht of 15% per year. We fit each 30-yr series with a stationary GEV.

These fits show that the variability of cold extremes decreases: the coldest extremes warm more quickly than the mean TG15n (also found by de Vries et al, 2012), partly because of the rapid warming of the Arctic. We can therefore not use the methods that we used for the climate up to now, as these both assume a constant variability. The change up to now was so small that we could neglect it, but this in the future this is no longer the case. We therefore quote results from stationary fits over the 30-yr transformed series.

 scenario \ time 2050 2085 GL 6% 4% GH 2% 1,5% WL 2% 0,2% WH 0,5% <0,2%

Table 1 gives the probabilities for a potential Elfstedentocht for the four different KNMI scenarios. These probabilities depend strongly on the two axes of these scenarios (van den Hurk et al, 2014): the global mean temperature rise (moderate, G, or Warm) and the shift to more westerly circulation types in winter (Low or High). If the temperature rise in 2100 is high (4ºC above 1981–2010 in 2100) and the westerly circulation gets stronger (WH), the probability of a period cold enough for an Elfstedentocht is only 0.5% in 2050 and negligible in 2085 (<0.2%). If the warming is moderate (2ºC above 1981–2010) and the circulation shift on the low end simulated by models there is still a chance to skate the Tour at the end of the century (4%).

These values agree well with an analysis of raw model output of 30-year periods of the 16 runs of the regional climate model RACMO that were used to construct these scenarios: 1.3% to 3.8% in 2050 and 0.02% to 0.5% in 2085 in the warm IPCC RCP8.5 scenario. This climate model also shows a significant decrease in variability.

If we manage to keep the warming to below 2ºC above late nineteenth century levels, as agreed in Paris, the temperature rise is below the lowest KNMI'14 scenarios. Even the moderate G scenarios have a temperature rise of 2.6ºC at the end of the century, an increase from now that is 50% larger than a 2ºC scenario. We estimate the probability of a potential Elfstedentocht by interpolating the current probability with the G scenarios to obtain about 5%.

We can also estimate from Table 1 the number of Elfstedentochten that can be skated this century. The best estimate is one or two in the WH scenario to about five in the GL scenario. These are best estimates: due to the variability of the weather the number may well be somewhat higher or lower.

## Conclusions

In the current climate, the probability of weather cold enough to have a layer of 15 cm ice—as needed for an Elfstedentocht—has decreased due to global warming. A 15-day averaged temperature below −4.2 ºC, which is usually enough to organise a Tour, occurred in about 20% of the years in the middle of the twentieth century. Two independent statistical analyses show that this probability has now decreased to about 8%, with an uncertainty margin of 5% to 19%. Winters in Friesland are erratic, hence the large uncertainty. The fact that there has not been an Elfstedentocht for 22 years now does not change the probability: every year is independent of the previous ones, except for the common trend. Not every cold period gives an Elfstedentocht, so the true probability is a bit lower still.

The probability decreases further in the KNMI'14 scenarios for the twenty-first century. By how much depends strongly on the global warming and circulation changes. If we keep the temperature below 2ºC warmer than the end of the 19th century, as agreed in Paris, the chances stay reasonable at about 5% per year, once every 20 years. However, if we let the earth heat to 4 degrees  above 1981–2010 the probabilities quickly drop and only one or two Tours will be possible in the foreseeable future.

### References

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