The likelihood of holding outdoor skating marathons in the Netherlands as a policy-relevant indicator of climate change
A. C. Petersen
When I was born - in 1956 - the chance of realizing a Frisian Eleven City Ice Skating Marathon in Netherlands was 1 in 4. When my daughter was born - in 1999 - this chance had diminished to 1 in 10. An enormous change in one generation! This quote was taken from a speech by J. P. Balkenende, prime minister of the Netherlands. It illustrates how a seemingly odd indicator of climate change, the chance of organizing large-scale outdoor ice-skating marathons, can play a role in the public and political debate on climate change. Outdoor skating has a very strong public appeal in the Netherlands, and the diminishing chances of holding such events provide an additional Dutch motive for introducing climatepolicy measures. Here, ice skating marathons are approached from three angles: (1) the societal/political angle as described above, (2) the more technical angle, of how to derive annual chances for holding large-scale marathons such as the Eleven City Marathon ('Elfstedentocht'), and (3) the role of (communicating) uncertainties. Since the statistical approach was developed in response to communicational needs, both statistical and communicative aspects are reported on in this article.
deforestation will continue for many years to come. We all know the pictures of
melting glaciers on Greenland and satellite images of the hole in the ozone layer.
An example closer to home: when I was born in 1956 the chance of realizing
a Frisian Eleven City Ice Skating Marathon taking place was 1 in 4. When
my daughter was born in 1999 this chance had diminished to 1 in 10. An
enormous change in one generation!
(From a speech of J.P. Balkenende, prime minister of the Netherlands,
June 6, 2005)
Climatic change is abound with uncertainty. Not only are uncertainties intrinsic in
the science; societal actors also have different opinions on what aspects of climatic
change constitute a problem and why. When analysts search for indicators to analyze
and communicate information about climatic change, they therefore have to address
both scientific and societal uncertainties. In this article, we report on the development
and communication of a new indicator of climatic change for the Netherlands.
The indicator is innovative in two regards. First, the Dutch public was informed
about a dimension of climatic change that directly appeals to them and that had not
been clearly communicated before. Second, a new statistical approach was developed
in order to be able to communicate robust messages about changes in this indicator.
Since the statistical approach was developed in response to communicational needs,
both statistical and communicative aspects of the new indicator are reported on
in this article. Both aspects or storylines meet in the Dutch prime ministers
Outdoor skating is an extremely popular sport in the Netherlands, with a large
number of skating tours being organized throughout the country in the coldest winter
periods. The tour of all tours is the Elfstedentocht, the Eleven City Ice Skating
Marathon, held in the province of Friesland. Here we will explore from several
angles the likelihood (the annual chance) of an Elfstedentocht being organized.
This likelihood is considered to be a complex indicator of climate change, with many
uncertainties attached to it, but with a very strong public appeal too, providing an
additional Dutch motive for setting climate-policy measures.
Climate warming has influenced the conditions necessary for holding this outdoor
skating marathon since the beginning of the twentieth century. In this article, the
focus is on the evolution of the chance of holding an annual Elfstedentocht in the
period from 1901 to 2008.
For several reasons, estimating this chance indicator is more complex than
evaluating other climate indicators such as annual averaged temperatures, annual
total precipitation and drought frequencies. The chance of holding a marathon is
maximal ice thicknesses that are not measured routinely.
the amount of open water due to drainage or flowing under bridges.
organizational factors delaying the decision about whether to hold a marathon,
e.g. creating kluning (walking on skates) facilities, and mobilizing competitive
and non-competitive skaters.
Our approach here is to find an indicator calculated from standard meteorological
data from the beginning of twentieth century, and related to maximal ice thickness
in the province of Friesland. Clearly, this indicator should be homogeneous (i.e.
corrected for changes in instruments, location of instruments, changes to the instrument
by environment etc.). Finally, the annual chance for organizing the Elfstedentocht
is deduced from the chance of the ice-thickness indicator crossing a threshold.
Uncertainties play an important role in the evaluation of change in chances for
a skating marathon. These uncertainties need to be assessed and communicated. To
express uncertainty in statistical terms, we need to apply a trend model from the class
of structural time-series models in combination with the Kalman filter. The rationale
for choosing this particular model is not that it necessarily yields the best trend, but
that it offers uncertainties for flexible trends and for any trend differences of interest
(Visser 2004a, 2005).
The Elfstedentocht indicator has appeared to be a good indicator for
communicating climate change aspects in the Netherlands. The indicator, included by the
Netherlands Environmental Assessment Agency in its Environmental Balance of
May 2005, was subsequently taken up by the media and politicians (as can be seen, for
instance, in the quote of the prime minister cited above). When the Agency started
its research on climate impact indicators the goal was to explain impacts of climate
change to policy makers and the general public in the Netherlands, while searching
for simple but convincing examples.
Our hypothesis was that such examples differ from country to country. For France,
examples could relate to the annual number of elderly people dying during heat
waves; for the Alps, it could be the melting of snow and glaciers, and the
corresponding loss of ski tourism; for the USA it could be an increase in droughts, coupled
with agricultural losses; changes in temperature (extremes) will affect tourist flows
in many countries (Gssling and Hall 2006). For the Netherlands we chose, from
amongst the indicators, the changing chances of holding large outdoor skating events.
This article will start with the history of the Elfstedentocht (Section 2), followed
in Section 3 by showing how the chance for organizing the marathon is derived in
three steps formulated as questions:
what is a simple annual indicator for maximal ice thickness, and how is this
indicator coupled to the decision of organizing the marathon? (Section 3.1),
how did the trend in ice-thickness indicator evolve over the 19012008 period
and what are the corresponding uncertainties? (Section 3.2),
what is the chance of an Elfstedentocht being organized in the 19012008 period
and what are the corresponding uncertainties? (Section 3.3).
Section 4 will wind up with a discussion on the role this rather odd Elfstedentocht
indicator has played in the public and political debate on climate change issues.
For a long time the Eleven city marathon, or Elfstedentocht in Dutch, has been
considered in the Netherlands as an attractive opportunity to skate along eleven
Frisian cities on the ice-covered waterways in 1 day, covering a distance of almost
200 km (Fig. 1). The names of dozens of successful skaters from the last century
Fig. 1 The Elfstedentocht covers a course of almost 200 km, proceeding from town to town,
over lakes and ditches, between fields and under bridges. Hundreds of thousands of spectators
cheer the skaters along the route. Leeuwarden, the capital of Friesland, has always been the start
and finish. The marathon takes the participants from Leeuwarden (Ljouwert) to Sneek (Snits),
IJlst (Drylts), Sloten (Sleat), Stavoren (Starum), Hindeloopen (Hynljippen), Workum (Warkum),
Bolsward (Boalsert), Harlingen (Harns), Franeker (Frentsjer), Dokkum and back to Leeuwarden.
At registration, every participant gets a card which has to be stamped in each town and at a number
of checkpoints located in concealed places along the route. Source: http://www.elfstedentocht.nl
are still familiar, their stories being proudly passed on within their family circles
from generation to generation. The Elfstedentocht offers both competitive and
noncompetitive marathons for the same route on the same day. This event has taken
place 15 times since 1909 (although tours were organized along the eleven cities long
before this, the first description of a tour dates from 1749).
The marathon is highly dependent on specific weather conditions. For the
marathon to actually take place, the ice needs to be at least 15 cm thick along virtually
the whole route. During prolonged freezing, the regional organizing committee goes
out every day at least once to measure the thickness of the ice. Sometimes ice is
transplanted to places where the natural ice layer is thin. Once the marathon committee
has given the green light, klunen (skate-walking) facilities are constructed along
the vulnerable parts of the route. More information about the tour can be found at:
http://www.elfstedentocht.nl (choose English).
A winner of the Elfstedentocht becomes a hero whose name is remembered for
generations. These winners are summarized by year and final time in Table 1 for
all 15 tours organized since 1909. The extremely cold conditions in 1963 make that
years tour famous as national story of perseverance, solidarity and lonely fighting.
Of the more than 10,000 starters only 136 skaters made it to the finish. Weather
conditions during the tour were extremely grim, with a lot of snow falling during the
tour. The 1963 tour has taken on almost mythical proportions in peoples memories
Table 1 Winners of the Elfstedentocht since 1909 in which final times were reduced from
13 h 50 min in 1909 to 6 h 47 min in 1985
(a contributing factor was the 22 year period between 1963 and the next marathon
3 Derivation of the Elfstedentocht indicator
3.1 Two-stage procedure
In principle, the marathon is organized if ice thicknesses exceed 15 cm, as stipulated
by an Elfstedentocht committee. For this reason it would seem logical to derive
an ice-thickness indicator and determine a threshold for maximal ice thicknesses so
that conditions will be declared optimal for organizing the Elfstedentocht. Finding
this indicator and the corresponding threshold will be briefly described here. Other
factors such as the amount of open water due to drainage or occurring under bridges
are accounted for in our choice of a threshold.
Brandsma (2001) used averaged winter temperatures as an indicator for maximal
ice thickness. He compared the winter temperatures with calculated maximal annual
ice thicknesses for the province of Friesland over the 19012000 period, and found
a reasonable linear relation. Maximal ice thicknesses were calculated by an
icegrow model developed at the Royal Netherlands Meteorological Institute (KNMI)
(de Bruin and Wessels 1988, 1990).
Here, we followed the approach of Brandsma except that we correlated computed
ice thicknesses with a number of simple meteorological indicators based on
homogeneous temperature records at De Bilt. De Bilt is the location of the main observatory
of KNMI and data can be downloaded from the Internet website http://eca.knmi.nl.
For a discussion on the homogeneity of this series the reader is referred to Brandsma
et al. (2002).
The indicator It the average temperature of the coldest period of 15 consecutive
days in winter (C) was found to perform best (in terms of the highest correlation,
namely 0.86). Here, winter is defined by the months DJF and the indicator value falls
by definition in the year of JF.
A scatterplot between maximal ice thicknesses and It is shown in Fig. 2. Green
bullets denote years in which a marathon was organized (15 times) or a year with
a potential marathon (4 years). These potential years are years in which the
marathon could have been organized (ice thicknesses of more than 30 cm). Potential
years are 1939, 1979, 1987 and 1996.
The vertical orange line in Fig. 2 shows the optimal threshold, based on calculated
ice thicknesses, for making a positive decision to organize a marathon. The optimal
threshold appears to be 20 cm. The horizontal orange line shows the corresponding
optimal threshold for It: 4.2C. We applied the latter threshold in the following
decision criterion: It below the limit value 4.2C implies a marathon, and It above
the limit implies no marathon.
The performance of this simple criterion is as follows. In the 81 years in which
no marathon was organized (black bullets in Fig. 2) only 4 years came out below
the threshold of 4.2C (thus yielding faulty predictions in 5% of the cases). In the
19 years with a (potential) marathon (green bullets in Fig. 2) only 3 years came out
above the threshold (yielding faulty predictions in 16% of the cases). In fact, the
indicator is almost as good as the model-based ice-thickness predictions: four faulty
Year with no marathon
Year with (potential) marathon
10 20 30 40 50
Maximal ice thickness in the province of Friesland (cm)
Fig. 2 Scatterplot between maximal ice thicknesses and the indicator selected. Green dots represent
years for a (potential) marathon (19 for 19012000)
predictions for 81 years with no marathon (5%), and 2 faulty predictions for 19 years
with (potential) marathons (11%). We note here that it is reasonable (from historical
notes) to assume that plans for organizing the marathon started around the year 1901.
3.2 Time-series approach
To find the annual chance for organizing an Elfstedentocht we should evaluate the
trend evolution of It over the period of 1901 to 2008 along with uncertainties. There
are a large number of methods to calculate a trend in a series of measurements. And
generally speaking, there is no best trend model. The most appropriate model will
depend on ones goals or wishes. Here, we are looking for a trend model, t, that
is to a certain extent flexible. Furthermore, we want to have significance intervals
for t, with 1901 t 2008, and the corresponding differences 2008 t, with
t < 2008. The latter difference is of importance because we want to make inferences
on whether the Elfstedentocht indicator is significantly increasing/decreasing over
an arbitrary time interval [t, 2008], as we will point out in the next section.
The Integrated Random Walk (IRW) model (a submodel from the class of
structural time series models) in combination with the Kalman filter appears to satisfy
our wishes. The IRW model reads as
with t and t normally and independently distributed noise processes.
Statistical details are beyond the scope of this article. For the theoretical
considerations, we refer to Harvey (1989) and Durbin and Koopman (2001), and for
applications in the field of climatic change research to Visser and Molenaar (1995),
Allen et al. (1999), Stern and Kaufmann (2000), Lenten and Moosa (2003), and
Visser (2004a). Applications of the IRW model are given by Kitagawa (1981),
Young et al. (1991), van den Brakel and Visser (1996) and Visser (2005). Tests
for choosing the proper time-series model are given by Visser (2004a, Appendix B
therein). Trends have been estimated with the TrendSpotter software (Visser 2004b),
a software package that allows one to estimate a variety of structural time-series
models. TrendSpotter is available, without charge, from the first author.
An IRW trend model has been estimated for the indicator described in the
preceding section. Because the residuals of the estimated trend model turn out to
be skewed, the annual indicator values are transformed by taking logarithms:
with t and t normally and independently distributed noise processes.1 The constant
10.0 was found by trial and error and the threshold of 4.2C transforms to 2.65.
Figure 3 shows the IRW estimation results for model (2).2 The upper panel shows
the estimated trend t. The narrow bounds (t 2 ,t, green dashed lines) are
95% confidence limits for t, while the wider bounds t 2 2,t + 2 , red dashed
lines) are 95% confidence limits for a predicted value of yt. The upper panel shows a
slightly increasing indicator series up to 1950 and a decreasing trend thereafter. The
lower panel shows that trend differences 2008 t are statistically significant for any
year within the 19051997 period ( = 0.05 and a two-sided test of significance).
3.3 Chance of organizing an Elfstedentocht
Given the transformed indicator trend estimates t, its standard deviation ,t and
the standard deviation of the residuals we can calculate for each year, t, the
probability of an Elfstedentocht being organized (the ln-transformed indicator yt
is normally distributed with mean t and variance 2,t + 2). More formally, if we
denote the annual chance for organizing an Elfstedentocht with Et, we have:
Et = P (It < 4.2C) = P (ln (10.0 It) > 2.65) = P (yt > 2.65)
with yt N t, 2,t + 2 , and 1901 t 2008.
1Because we are modeling a cold extreme, i.e. the coldest 15-day period, we might expect the
residuals to follow a generalized extreme value (GEV) distribution. Please see http://www.isse.ucar.
edu/extremevalues/extreme.html and references therein. To quote the statistician J. Tukey: As I am
sure almost every geophysicist knows, distributions of actual errors and fluctuations have much more
straggling extreme values than would correspond to the magic bell-shaped distribution of Gauss and
Laplace. However, our experience with many long-term climate series in the Netherlands is that
residuals (or innovations in Kalman filter terms) do follow that magic bell-shaped curve (Visser
2004a, 2005). We only had to apply a logarithmic transformation of the form yt = log (constant - It)
to correct for skewed innovations. A probability plot of the innovation series showed that the data
are in good approximation normally distributed.
2We have applied the filter equations of the discrete Kalman filter, using a diffuse prior for the state
vector. For calculation of the maximum-likelihood estimate of the unknown noise variance 2 we
have omitted the residuals over the period 19011920 (the start-up period of the filter). Afterwards,
trend estimates have been smoothed by the fixed-interval smoother. The rationale is that we can
improve a trend estimate t by using not only all the data before and up to time t, but also data
after time t. As a consequence, the start up behavior of the filtered estimates is not seen anymore
in the smoothed estimates for the first 20 years. For a condensed formulation of the Kalman filter
equations, we refer to Harvey (1984).
log-transformed marathon indicator
95% confidence limits predictions
95% confidence limits trend
decision criterion (= 2.65)
Fig. 3 Transformed Elfstedentocht indicator yt (black line), the estimated trend t (green line) and
the corresponding 95% confidence limits (dashed green lines). The dashed red lines represent 95%
confidence limits for the yt predictions. Note that the original indicator It has been transformed to
yt = ln(10.0It) to account for the skewness of minimum temperature data. The lower panel shows
the trend differences 2008 t with corresponding 95% confidence limits
We illustrate this by showing the probability density functions of I1901 (orange
line), I1950 (green line) and I2008 (red line) in Fig. 4 (based on the estimates from
Fig. 3). The densities follow a log-normal distribution with the long tail to the left
due to the log transformation. The chances E1901, E1950 and E2008 equal the surface
of the density functions tail to the left of the vertical decision line at 4.2C (yellow
areas). For 1901 this is E1901 = 0.19, for 1950, E1950 = 0.27 and for 2008, E2008 = 0.055.
'Elfstedentocht' is organized
'Elfstedentocht' not organized
'Elfsteden' indicator It (C)
Fig. 4 Probability density functions (Pdfs) for the Elfstedentocht indicator I1901 (orange line), I1950
(green line) and I2008 (red line). Vertical lines are the geometric mean values: 1.6C in 1901, 2.3C
in 1950 and +0.22C in 2008. The probability functions are shifted log-normal with long tails to the
left (due to the transformation yt = ln (10.0It). The surface of the yellow area for each curve equals
the chance for holding a marathon
The chances, Et, are shown in Fig. 5 for all years in the 19012008 period. Since
yt is normally distributed and its variance 2,t + 2 is almost constant 2 2,t , we
can state that:
Annual chance for an 'Elfstedentocht'
95% confidence limits (approx.)
Fig. 5 Annual chance of organizing an Elfstedentocht Et. The right y-axis shows the corresponding
return periods Rt, which are simply the inverse of the annual chances
with = 2,t + 2 0.22 (cf. red dashed lines in upper panel of Fig. 3). Now, the
95% confidence limits for Et follow in good approximation from:
with f defined in (4). These confidence limits from are also shown in Fig. 5.
Has the chance of organizing an Elfstedentocht E2008 been significantly reduced
since 1999, 1956 or any other year? To answer this question, we have to make an
approximation explained in Appendix. The difference t E2008Et can be shown
to be approximated by (first-order Taylor expansion):
Now, t will simply be statistically significant if the same holds for the difference
2008 t (the exponential term on the right-hand side is always positive). Therefore,
the significance periods of marathon chances follow in first approximation from
the significance of 2008 t, as shown in the lower panel of Fig. 3. Thus, if we
choose = 0.05 and a two-sided test on significance,3 we find that the chance of
an Elfstedentocht taking place in 2008 is (statistically) significantly smaller than all
the chances within the 19051997 period.
The chances Et can also be expressed in terms of average return periods Rt (right
axis of Fig. 5). A return period is simply the inverse of the annual chance Et:
Rt = 1/Et, so that R1901 = 5.3 [2.713.0] years, R1950 = 3.7 [2.75.6] years and R2008 =
18.2 [6.864] years. The results found here are consistent with the prime ministers
quote at the beginning of this article (a chance of 1 to 4 in 1956 and 1 to 10 in
1999): R1956 = 3.8 [2.75.7] years and R1999 = 11.3 [5.924] years.
4 Communication of uncertain but policy-relevant indicators
An initial question in communicating chances or uncertainties to policy makers
and/or the public is: do they understand what the chance expression means?
Gigerenzer et al. (2005) used a survey to find out if the statement there is a 30%
chance of rain tomorrow would invoke contradictory interpretations. According
to their findings, if the class of events that the chance expression is referring to is
not specified, the chance will be multi-interpretable. Most European respondents
thought that chance meant it will rain 30% of the time, followed by it will rain in
30% of the area. Only respondents in the city of New York supplied in majority the
standard meteorological interpretation, namely that when the weather conditions
are like today, in 3 out of 10 cases there will be (at least a trace of) rain the next day.
Wardekker et al. (2008) discuss problems concerning verbal probability expressions.
The use of such expressions as is done for instance by the IPCC is problematic,
since differences in interpretation are large and context-dependent.
3Without giving details we note here that tests on significance have not gone unquestioned in
literature. For discussion, please refer to Sterne and Smith (2001) and references included in the
In our case the class of events is unambiguous. The location of the Eleven City
marathon is known to everybody and the specific day is of no importance. The only
factor that counts is the gono-go decision of the Elfsteden committee.
How was the Elfstedentocht indicator communicated? In the report the
significance of climate change in the Netherlands (Visser 2005), the conclusion concerning
the Elfstedentocht indicator was presented as follows:
Over the course of the twentieth century the chance of an Elfstedentocht has
decreased from once every 5 years (in 1901) to once every 10 years (in 2004).
Even though this change is not yet statistically significant, it resides on the edge
of significance: within a few years more evidence may become available to firmly
establish the diminishing likelihood of outdoor skating in the Netherlands.
Three months later, the Environmental Balance (MNP 2005) displayed a graph to
illustrate this indicator (Fig. 5 in this article, without confidence limits and the period
19012004) accompanied by the following conclusion:
It is likely that the chance of an Elfstedentocht has decreased from once every
4 years in 1950 to once every 10 years in 2004.
This statement about the second half of the twentieth century was alluded to by
the prime minister of the Netherlands in his speech (see quote cited above). The
term likely is used in the same way as in WG I of the Intergovernmental Panel on
Climate Change, i.e. as a 6690% chance.
The great amount of attention that we have paid to determine and communicate
the uncertainties in the Elfstedentocht indicator have not prevented this indicator
from being taken up rapidly as an icon of climate change in the Netherlands. We
were careful about making overly strong claims, since we feel responsible for being
just as rigorous and transparent in our treatment of uncertainty as in assessing climate
change and communicating the risks to a wider audience.
There is an historical reason for being extra careful. In 1999, the environmental
assessment division (later: Netherlands Environmental Assessment Agency, MNP and
since May 2008: PBL) of the Dutch National Institute for Public Health and the
Environment (RIVM) made news in the Netherlands for having failed to communicate
properly about uncertainties (van Asselt 2000; van der Sluijs 2002; Petersen 2006).
This led to the development of the RIVM/MNP Guidance for Uncertainty Assessment
and Communication (MNP/UU 2003), designed to help environmental assessors to
deal with uncertainty and the framing of policy problems in a more appropriate and
systematic way. It was produced by RIVM/MNP, together with Utrecht University
and an international team of uncertainty experts (see Janssen et al. 2005; Refsgaard
et al. 2007; van der Sluijs et al. 2008 see also http://www.nusap.net/guidance).
The Guidance documents offer assistance to PBL employees in mapping and
communicating uncertainties in environmental assessments and have been evaluated
as good means for facilitating scientists in dealing with uncertainties throughout
the whole environmental assessment process. It was not to be limited to applying
ready-made tools for uncertainty analysis and communication, since in all aspects of
environmental assessments choices are made which influence the way uncertainties
are dealt with. Especially the way perspectives of other scientists and stakeholders
are treated is crucial in assessing policy problems that are relatively unstructured
(see also Petersen 2006; van der Sluijs 2007).
The Guidance identifies six parts of environmental assessments which have an
impact on the way uncertainties are dealt with:
1. problem framing;
2. involvement of stakeholders (that is, all those involved in or affected by a policy
3. selection of indicators representing the policy problem;
4. appraisal of the knowledge base;
5. mapping and assessing relevant uncertainties and
6. reporting the uncertainty information.
Parts 5 and 6 usually reveal a focused effort to analyze and communicate
uncertainty. However, the choices and assessments made in the other four parts are also
of great importance in dealing with uncertainty.
In the case presented in this article, the Elfstedentocht indicator, we have
addressed all six parts. First, by focusing on the example of the ice-skating
marathon, climate change is framed at the level of collective cultural experience. The
Elfstedentocht is largely a cultural phenomenon, deeply rooted in Dutch culture.
Second, although we did not invite stakeholders to sit at the table while developing
the indicator, we decided to take the viewpoints of the Dutch population into
account in the development of a set of climate change impact indicators. Third, we
have provided adequate scientific backing for these indicators and discussed their
limitations. Fourth, we have determined the bottlenecks in the available knowledge
and methods, and their impact on the results, and fifth, we have done a statistical
uncertainty analysis for indicator It.4 Our final effort was to ensure that all relevant
uncertainty information would be published with the indicator.
The Elfstedentocht indicator was one of many other interesting indicators
published by Visser (2005). Examples of other changes over the twentieth century
were the number of extremely wet days (increased from 19 3 to 26 3 days) and
the length of the growing season (increased by nearly a month). Globally averaged
temperatures are obviously much less appealing to the public than indicators more
related to local conditions. Apparently, the peculiar ice-skating marathon indicator
hit a nerve in Dutch society and has therefore received wide publicity. We reckon
that more such peculiar measures of climate-change impacts can be found for many
countries and urge scientists to look for the indicators that really appeal to a larger
The statistical approach in this article only offers the possibility to detect changes
in climate change impact indicators, but does not provide for the possibility to
attribute these changes to, e.g., anthropogenic influences. A separate argument is
needed and can be given to make the results policy-relevant. As van Oldenborgh
and van Ulden (2003) have shown, the seasonally averaged temperature in De Bilt
over the twentieth century is described well by (1) a warming, independent of wind
direction, proportional to the globally averaged temperature; (2) an increase in
4The uncertainty analysis holds for the second stage of the analysis, the trend analyses. The
uncertainty in the 4.2C criterion, the first stage of our analysis, is difficult to give. It is based
on 19 (potential) marathons in the period 19012000. However, since the criterion is directly coupled
to ice-thickness calculations, shown in Fig. 2, yielding faulty predictions in only 5% and 16% of the
cases, we judge the criterion to be reasonably robust.
southwesterly circulation in FebruaryApril after 1950; and (3) almost white noise
due to other variations in wind directions and other effects. Since the first term
explains most of the observed trend over the twentieth century, we can say that the
changes observed in the Elfstedentocht indicator are consistent with what we would
expect from anthropogenic climate change. Visser (2005) also shows extrapolations
of this indicator to 2020, on the basis of both statistical extrapolation and GCM
results (which give consistent values).
Scientists bear a responsibility for addressing the concerns of their societies, but
also need to remain diligent and communicate uncertainties in a consistent and
transparent fashion. We endeavored in this article to provide an example of a
policyrelevant indicator for climate-change impacts with large uncertainties associated with
it. Communicating these uncertainties as part of the message to policy makers will not
prevent them from getting the message that the climate is changing, as is illustrated
by the quote of the Dutch prime minister at the beginning of the introduction. Still,
policy makers and politicians also have a responsibility to make uncertainties explicit
and defend their decisions in the context of uncertainty.
Acknowledgements The authors wish to thank Theo Brandsma (KNMI) for supplying model
calculated ice-thickness data for the Province of Friesland (19012000). Anton van der Giessen,
Peter Janssen, both from Netherlands Environmental Assessment Agency, and three reviewers are
thanked for their thorough comments on the manuscript.
From Eq. 4 we have:
Now, if two trend values t and s are near, or in other words the difference
(t s) is small, we may apply the following Taylor series expansion:
Et = Es + (t s) f (s) + 0.5 (t s)2 f (s) + .....
Now, if we combine (A.1) and (A.2) we find in first approximation:
Et Es = (t s) ds E (s) + higher order terms
The last expression in (A.3) equals Eq. 6 if we set year t to 2008.
The chance of holding a large
outdoor skating marathon
such as the Elfstedentocht,
has decreased from once
every five years in 1901 to
once every 18 years in 2008.
Photo: H. Visser