INTERNATIONAL JOURNAL OF CLIMATOLOGY
Int. J. Climatol. 28: 421–433 (2008)
Published online 1 June 2007 in Wiley InterScience
(www.interscience.wiley.com) DOI: 10.1002/joc.1553
Freezing of lakes on the Swiss plateau in the period
1901–2006
H. J. Hendricks Franssena * and S. C. Scherrerb†
a
b
Institute for Environmental Engineering, ETH Zurich, HIL G33.3, 8093 Zurich, Switzerland
Climate Services, Federal Office of Meteorology and Climatology MeteoSwiss, Krählbühlstrasse 58, 8044 Zurich, Switzerland
ABSTRACT: Data of ice cover for deep Alpine lakes contain relevant climatological information since ice cover and
winter temperature are closely related. For the first time, ice cover data from 11 lakes on the Swiss plateau have been
collected and analysed for the period 1901–2006. The ice cover data used stem from systematic registration by individuals
or groups (fishermen, an ice club and lake security service) and from several national, regional and local newspapers. It
is found that in the past 40 years, and especially during the last two decades, ice cover on Swiss lakes was significantly
reduced. This is in good agreement with the observed increase in the winter temperature in this period. The trend of reduced
ice cover is more pronounced for lakes that freeze rarely than for the lakes that freeze more frequently. This agrees well
with the stronger relative decrease in the probability to exceed the sum of negative degree days (NDD) needed for freezing
the lakes that rarely freeze. The ice cover data are related with the temperature measurements such as the sum of NDD
of nearby official meteorological stations by means of binomial logistic regression. The derived relationships estimate the
probability of a complete ice cover on a lake as function of the sum of NDD. The sums of NDD needed are well related
to the average depth of the lake (rNDD – Depth = 0.85). Diagnosing lake ice cover on the basis of the sum of NDD is much
better than a prediction on the basis of a climatological freezing frequency. The variance of lake ice cover that cannot be
explained by the sum of NDD is important for judging the uncertainty associated with climate reconstruction on the basis
of data on lake ice cover. Copyright  2007 Royal Meteorological Society
KEY WORDS
ice cover; lakes; Alps; Swiss plateau; Switzerland; proxy data; climate change; trend analysis
Received 13 October 2006; Revised 21 March 2007; Accepted 25 March 2007
1.
Introduction
Time series of ice cover on a lake may contain important climatological information. The duration of ice cover,
the freezing and thawing up dates or the thickness of ice
cover have been used in climatological studies and show
mostly trends that are in agreement with an observed
local temperature increase (e.g. Palecki and Bary, 1986;
Gilbert, 1991; Wharton et al., 1992; Anderson et al.,
1996; Doran et al., 1996; Livingstone, 1997, 1999; Magnuson et al., 2000). In some cases, associated chemical (Koinig et al., 1998) and biological changes (Straile
et al., 2003) could also be explained. Since deep lakes
are important heat reservoirs, the freezing of pre-alpine
lakes is of special interest for many climatological applications. The appearance of ice cover is indicative of a
longer period with temperatures below 0 ° C. The deeper
the lake, the more cold is needed to cool down the lake
so that ice forms. Owing to the fact that at the lower altitudes in the Alpine region (between 300 and 600 m a.s.l.
in Switzerland) the average winter (DJF) temperature in
∗ Correspondence to: H. J. Hendricks Franssen.
E-mail: [email protected]
† Currently at: Climate and Global Dynamics Division, National Center
for Atmospheric Research, PO Box 3000, Boulder, CO 80307–3000,
USA.
Copyright  2007 Royal Meteorological Society
the 20th century was slightly above 0 ° C, many deeper
lakes tend to freeze in some winters, but do not freeze in
other winters. The information whether such a lake froze
or did not freeze in a given winter has therefore a relevant
discriminatory value. In addition, if we look at a larger
spectrum of lakes with different depths, the lakes will
need different amounts of cold to freeze. Ideally (if temperature and lake freezing are perfectly correlated), each
of the lakes acts as an indicator for a certain threshold
temperature: if the lake froze, the average winter temperature was below that threshold and if it did not freeze, the
temperature was above. In this ideal case, the combined
information on freezing from lakes that ‘sample’ different
temperature thresholds would allow a very good estimate
of the winter temperature. Pfister (1984) investigated the
freezing of some very deep pre-alpine Swiss lakes and
this investigation gave important information on changes
in the frequency of very cold and exceptionally cold winters since 1525. He did not collect systematic information
on the freezing of smaller and less deep lakes that freeze
more frequently. In this paper, for the first time, freezing
data of 11 such lakes on the Swiss plateau have been
collected and analysed for the period 1901–2006.
To get full benefit from ice cover information as
proxy data for air temperature, a probabilistic relationship
422
H. J. H. FRANSSEN AND S. C. SCHERRER
between ice cover and air temperature has to be established. From a statistical standpoint, it can be expected
that the estimated relationship between information on ice
cover and air temperature is better for long time series.
For very deep lakes, the reconstruction of such a probabilistic relationship was not possible since the number of
cases with a complete ice cover and recorded temperature data was limited. Pfister (1984) estimates an average
amount of cold needed for the complete freezing of Lake
Zurich and Lake Constance. This paper is concerned with
the estimation of probabilistic relationships for 11 deep
natural pre-alpine lakes that freeze more frequently. The
observed unexplained variance in the regression based
ice cover estimations can be used as an indicator of the
expected uncertainty for the very deep lakes like those
investigated by Pfister.
In Section 2, the definition of a freezing event is
defined and motivated in more detail. In Section 3, the
data collection is discussed and the data sources are
highlighted. Section 4 presents the statistical analysis of
the data. Section 5 discusses the results. Conclusions are
drawn in Section 6.
2.
Definition of lake freezing
In this paper, the freezing of a lake is defined as follows:
‘The lake is completely or almost completely covered
with ice during more than one day. The ice does not
necessarily have to be thick enough to carry persons.’
The ice cover needs to be present during more than
one day for several reasons:
• In order to avoid counting cases, where in clear,
very calm nights a very thin ice layer forms, which
disappears later in the morning. Such an ice layer forms
because of the outgoing long-wave radiation in clear
nights, in combination with no wind, so that a very
sharp temperature gradient develops in the upper few
centimetres of the lake. These ice layers are observed
frequently by fishermen around sunrise, and disappear
very fast due to the incoming short-wave radiation later
in the morning.
• These events are normally not reported by local or
regional newspapers.
• In case of lakes with a larger surface, it is difficult
to judge for an observer whether the complete lake is
frozen. In case ice disappears within one day, this was
normally not the case.
• On the other hand, if ice cover is present for more
than one day it does not matter whether it is present
2 or 90 days for this study. This strongly reduces
the data needed. In addition, since alpine lakes are
relatively deep and as such important heat reservoirs,
a considerable amount of cold is needed before a lake
can freeze. Hence, even ice cover that is present during
a short period of a few days is indicative of a preceding
period of considerable cold.
Copyright  2007 Royal Meteorological Society
The lake has to be covered completely or almost
completely with ice because:
• For smaller lakes, a partial cover of the lake with ice
is normally not reported by newspapers and observers.
• A partial cover of ice is always subject to the ice
eliminating effect of the wind. Wind is able to remove
ice even if temperatures remain below zero.
• However, frequently small parts of the lake remain free
of ice, even if all the lake is covered with thick ice.
The ice-free parts are associated with flows that enter
the lake, or, in recent times, devices that artificially
aerate the lake.
The ice does not have to be thick enough to carry
persons because:
• The ice growth is strongly influenced by the presence
of snow.
• No ice depth data are available, and the decision
whether a lake is accessible for persons is normally
taken by the lake police. The lake police has changed
the criteria during time, and in the first part of the 20th
century there was less control; people decided more
spontaneously to access the ice.
• The amount of weight ice can carry depends on the
quality of the ice. So-called black-ice (which is highly
transparent, very hard and smooth) can carry double
the amount of weight per squared meter as compared
to so-called snow-ice (white ice, which contains frozen
snow and is less hard).
3.
3.1.
Data sources
Selected lakes
Ice cover data from 11 Swiss lakes have been collected for the period 1901–2006. The 11 lakes have been
selected because they do not freeze in each winter. As a
consequence, the knowledge whether they freeze/do not
freeze in a certain winter, contains important climatological information. Excluded from the analysis are lakes
that freeze every year. In general, this holds for Swiss
lakes with an average depth of less than 10 m (most of
the small lakes, also Lake Lauerz). For these lakes, the
observation that the lake at some moment was completely
covered with ice, does not have any discriminatory value.
Also, for the same reason, Swiss mountain lakes, even
the deep mountain lakes, are excluded from the analysis. Additional data, like the freeze and thaw up dates
of lakes would be needed to gain valuable climatological
information. Magnuson et al. (2000) found and analysed
these kinds of data for some lakes, including the mountain
lakes in the Swiss region of the Oberengadin. Artificial
lakes are also excluded from the analysis, although some
of them freeze in some winters, and not in other winters
(e.g. Lake Waegital, Lake Schiffenen and Lake Gruyère).
Excluded as well are the lakes that never froze completely
according to historical records (Lake Geneva, Lake
Int. J. Climatol. 28: 421–433 (2008)
DOI: 10.1002/joc
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FREEZING OF SWISS PLATEAU LAKES DURING 1901–2006
Brienz, and Lake Walenstadt). Finally, also the lakes that
were already analysed by Pfister (1984, 1999): Lake Constance, Lake Lucerne, Lake Thun and Lake Neuchatel are
excluded. It was noted that these lakes freeze very rarely.
Lake Constance froze only once (1962/1963), the other
lakes never froze during the 20th century. Lake Zurich,
which also has been studied by Pfister, is considered in
this paper, because this lake has a relatively independent
basin, the Upper Lake Zurich, from which ice data are
collected. In addition, also a complete time series of partial ice cover data of Lake Zurich has been collected, but
these data are not analysed in this paper.
For some lakes the data from the beginning of the 20th
century were considered to be unreliable or incomplete.
Therefore, the time series starts in 1914 for Lake Aegeri
and Lake Biel and in 1922 for Lake Pfaeffikon. The
geographical setting of the 11 lakes in Switzerland is
shown in Figure 1. The lakes have surfaces ranging from
3 to 40 km2 and average depths between 18 and 49 m.
Table I gives additional information about the lakes.
3.2. Lake ice data
In Switzerland, there is no systematic registration of the
freezing of lakes. Therefore, data had to be gathered
from various sources. For the last decades, detailed
data could be found for many lakes from people who
systematically registered the appearance of ice on lakes.
For other years, data have been collected from the
local, regional and national newspapers. The winter
months (December–March) have been systematically
investigated in those newspapers in order to find data on
the freezing of the lakes. Information on a complete lake
ice cover (according to the definition given in Section
2) was sought, but in many cases also the first day with
a complete ice cover was registered or reported by the
sources. The quality of these data is discussed in Section
5. The situation for each of the lakes is given in Table II.
3.3. Temperature data
All temperature data used in this study are Swiss observational 2 m temperature data measured, quality checked
Table I. Hypsographic data of the 11 pre-alpine Swiss lakes considered in this study and the meteorological stations close to the
lake that have been used to establish the relationship between lake ice and surface air temperature.
Name Lake (english and local name)
Surface
Altitude (m) Average Maximum
depth (m) depth (m)
area (km2 )
Lake Biel (Bielersee)
Lake Murten (Lac de Morat)
Lake Sempach (Sempachersee)
Lake Hallwil (Hallwilersee)
Lake Baldegg (Baldeggersee)
Lake Sarnen (Sarnersee)
Lake Aegeri (Ägerisee)
Upper Lake Zurich (oberer Zürichsee)
(has connection to Lake Zurich)
Lake Greifensee (Greifensee)
Lake Pfaeffikon (Pfäffikersee)
Untersee (has small connection
to Lake Constance)
Meteorological
station and elevation (m a.s.l.)
39.8
23.0
15.0
10.3
5.2
7.1
7.3
429
429
504
449
463
469
724
31
26
43.6
28.7
33.1
33.5
48.5
74
46
85
48
66
51
81
Neuchatel (485)
Neuchatel (485)
Lucerne (456)
Lucerne (456)
Lucerne (456)
Lucerne (456)
Einsiedeln (910)/Zurich SMA (556)
20.3
8.5
3.2
406
435
537
23
17.8
18.6
48
32
36
Zurich SMA (556)
Zurich SMA (556)
Zurich SMA (556)
29.3
397
19.1
46
Kreuzlingen (445)/Guettingen (440)
Figure 1. The geographical setting of the 11 prealpine Swiss lakes from which ice cover information has been analysed. Also shown are the
meteorological stations of MeteoSwiss (grey dots) from which daily 2 m temperature measurement derivates have been used for the regressions.
Copyright  2007 Royal Meteorological Society
Int. J. Climatol. 28: 421–433 (2008)
DOI: 10.1002/joc
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H. J. H. FRANSSEN AND S. C. SCHERRER
Table II. Properties of the ice cover data for the 11 pre-alpine Swiss lakes considered in this study. NZZ = Neue Zürcher Zeitung.
The start and end year of the data considered are bold.
Lake name
Time period
Lake Biel
1914–1922
NZZ newspaper
1923–2006
Family of fishermen
1901–1970
Newspaper Murtenbieter
1971–2006
Fishermen
1901–1955
Newspaper Luzerner Zeitung
1956–2006
Fishermen
See Lake Sempach
1901–1954
Newspaper Luzerner Zeitung
1955–2006
Boot constructor
1901–2006
Newspaper Obwaldner Volksfreund
1947–1954
Personal diary
Scattered
Lake police, captain of a boat
Since 1971
Some particulars
1914–2006
Newspaper Zuger Zeitung
1914–1964
Hand-written chronic
After 1964
Livingstone (1988)
1981–2006
Lake police
Some years
Fisherman
1901–1948
Newspapers NZZ, Luzerner Zeitung,
Anzeiger von Uster
1949–1980
von Eugen and Örn (1982)
1963–2006
Lake security service
Before 1922
Incomplete data
1922–1948
Newspapers NZZ, Luzerner
1982–2006
Zeitung, Zürcher Oberländer
1942–1999
Anton Hiestand
1949–1980
von Eugen and Örn (1982)
1901–2006
Newspapers NZZ, Luzerner Zeitung,
Zürichseezeitung
1901–1955
Ice club Steckborn
1956–2006
Newspaper Bote vom Untersee and Rhein
Lake Murten
Lake Sempach
Lake Baldegg
Lake Hallwil
Lake Sarnen
Lake Aegeri
Lake Greifensee
Lake Pfaeffikon
Upper Lake Zurich
Untersee
Data source
Remarks
4
3
2
1
0
−1
−2
−3
1900
1920 1940 1960 1980 2000
year (1902 = winter 1901/1902)
–
Non-systematic registration
–
Systematic registration
–
–
Systematic registration
–
Systematic registration for 1981–1992
Non-systematic registration
–
–
Systematic registration
Data not considered
–
–
Systematic registration
–
–
Systematic registration
–
Sum neg. degree days
Neuchatel 1902–2006
sum of negative
degree days
temperature [°C]
Winter (DJF) temperature
Neuchatel 1902–2006
–
Systematic registration
–
Non-systematic registration
–
Systematic registration
400
350
300
250
200
150
100
50
0
1900
1920 1940 1960 1980 2000
year (1902 = winter 1901/1902)
Figure 2. Temperature time series in Neuchatel (1902–2006) for the averaged 2 m winter temperature (December–January–February, left panel)
and the sum of negative degree days for the winter half year (October–April, right panel). In both the panels, the corresponding linear trend
line is also plotted. Both trends are statistically significant on the 5% level.
and stored by the Swiss Federal Office of Meteorology
and Climatology MeteoSwiss. Table I lists the meteorological stations that have been used to relate temperatures
to the lake ice data. Some additional remarks have to
be made. Neuchatel is located relatively close to the
Lakes of Biel and Murten, and the weather station is also
located close to a lake. However, the Lake of Neuchatel
Copyright  2007 Royal Meteorological Society
is deeper and larger and therefore warmer than Lake Biel
and Lake Murten in winter. This may result in winter
temperatures that are slightly higher than those measured
at Lake Biel and Lake Murten. Figure 2 shows a graph
with the average winter temperature and the sum of negative degree days (NDD) for Neuchatel. The sum of NDD
is calculated over the period October–April and is the
Int. J. Climatol. 28: 421–433 (2008)
DOI: 10.1002/joc
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FREEZING OF SWISS PLATEAU LAKES DURING 1901–2006
sum of the daily temperature averages (Before 1971,
the daily mean is defined as (T6 : 30 UTC + T12 : 30 UTC +
2T20 : 30 UTC )/4. Beginning in 1971, the evening measurement was taken already at 18 : 30 UTC. To get similar daily means as before 1971 the daily mean computation has been changed to (n − k)(n − Tmin ), where
n = (T6 : 30 UTC + T12 : 30 UTC + T18 : 30 UTC )/3, Tmin is the
minimum temperature of the day and k is a fitting parameter which depends on the month of the year and station
location), counting only the contributions from the days
with a daily average below 0 ° C. Figure 2 shows a significant increase in temperature and a significant decrease
of the sum of NDD. The same holds for the temperature
time series used for other lakes (not shown, cf. Begert
et al., 2005).
The time series of Zurich is homogenized for an
altitude of 556 m a.s.l. (Begert et al., 2005), whereas
Lake Greifensee and the Upper Lake Zurich are located
at 435 and 406 m a.s.l. respectively. Hence, the average
temperature at these lakes is likely higher than the
ones used in this study. Furthermore, it is expected
that because of local effects the measured temperatures
at Lake Pfaeffikon are clearly lower than the ones
measured in Zurich, especially during clear, calm nights.
Unfortunately, no long time series are available to explore
this local effect in more detail.
For the lakes of Hallwil, Baldegg, Sempach, Sarnen and the Untersee, temperature data from the nearby
meteorological stations (Table I) are only available
since 1931. The temperatures from the missing years
(1901–1930) have been estimated from the temperature
measurements in Zurich. The winter temperatures at the
meteorological stations for 1901–1930 are estimated by
calculating the average difference in winter temperature
(DJF) with respect to Zurich for the years 1931–1950,
and applying the same difference to the years 1901–1930.
The sum of NDD for those stations (1901–1930) is
estimated from the sum of NDD measured in Zurich
(1901–1930). A simple linear regression is made between
the sum of NDD for the years 1931–1950 in Zurich on
the one hand and the corresponding meteorological station on the other hand.
The ice cover data of Lake Aegeri are correlated
with a roughly homogenized series of temperature measurements in Einsiedeln (1932–2006) and Zurich. Lake
Aegeri is situated lower than Einsiedeln, but in a nearby
valley that also has a north-south orientation. The estimated temperatures at the lake (724 m a.s.l.) are the result
of giving equal weights to the series measured in Zurich
(556 m a.s.l.) and Einsiedeln (910 m a.s.l.).
4.
Statistical analysis
4.1. Basic statistics
Figure 3 shows winters in which the 11 selected lakes
froze (crosses). Table III provides some sample statistics
with respect to the freezing frequency of each of the
lakes. It can be seen that the freezing frequency varies
strongly between the lakes (between 13 and 75% of the
winters for the observation periods).
Table III also shows that only for the last part of
the 20th century (after 1966, and especially after 1987)
the amount of freezing events was reduced. The last
part of the 20th century was also characterized by
a strong temperature increase (cf. e.g. Scherrer et al.,
2006 and Figure 2). Hence the data on the freezing
of lakes are in correspondence with air temperature
measurements. Especially for the lakes that freeze less
often, a decrease in freezing frequency with time is
observed. For instance, Lake Sempach froze 11 times
in the years 1901–1950 (22% of the winters), but did
not freeze completely after 1965, i.e. a record of 41
consecutive winters (1966–2006) without a complete ice
cover. Lake Hallwil has not frozen since 1986, while
for the period 1901–1985 the longest period without
complete freezing was 10 years (1971–1981). Also, Lake
Murten, Lake Biel, Lake Baldegg, Lake Sarnen, Upper
Lake Zurich and Untersee experienced long periods
without freezing in the last 40 years, which for all these
lakes were considerably longer than the longest periods
Table III. Some statistics (# = number (bold) and relative frequencies and tendencies: ↑(↓): larger (smaller) than frequency for
full time period) for the appearance of a complete ice cover on 11 prealpine Swiss lakes during the period 1901–2006.
Lake
name
Lake Biel
Lake Murten
Lake Sempach
Lake Hallwil
Lake Baldegg
Lake Sarnen
Lake Aegeri
Upper Lake Zurich
Lake Greifensee
Lake Pfaeffikon
Untersee
Time
period
# (overall freq)
1914–2006
1901–2006
1901–2006
1901–2006
1901–2006
1901–2006
1914–2006
1901–2006
1901–2006
1922–2006
1901–2006
Copyright  2007 Royal Meteorological Society
14
29
16
25
26
14
45
34
51
64
36
(0.15)
(0.27)
(0.15)
(0.24)
(0.25)
(0.13)
(0.48)
(0.32)
(0.48)
(0.75)
(0.34)
# (freq.)
1901–1925
# (freq.)
1926–1950
# (freq.)
1951–1975
# (freq.)
1976–2000
−(−)
(0.36) ↑
(0.16) ↑
(0.28) ↑
(0.28) ↑
(0.12) ↓
−(−)
11 (0.44) ↑
14 (0.56) ↑
−(−)
13 (0.52) ↑
7 (0.28) ↑
9 (0.36) ↑
7 (0.28) ↑
8 (0.32) ↑
8 (0.32) ↑
7 (0.28) ↑
14 (0.56) ↑
9 (0.36) ↑
13 (0.52) ↑
19 (0.76) ↑
9 (0.36) ↑
4 (0.16) ↑
8 (0.32) ↑
5 (0.20) ↑
7 (0.28) ↑
7 (0.28) ↑
3 (0.12) ↓
14 (0.56) ↑
10 (0.40) ↑
13 (0.52) ↑
19 (0.76) ↑
8 (0.32) ↓
0 (0.00) ↓
2 (0.08) ↓
0 (0.00) ↓
3 (0.12) ↓
3 (0.12) ↓
1 (0.04) ↓
9 (0.36) ↓
3 (0.12) ↓
8 (0.32) ↓
20 (0.80) ↑
5 (0.20) ↓
9
4
7
7
3
Int. J. Climatol. 28: 421–433 (2008)
DOI: 10.1002/joc
426
H. J. H. FRANSSEN AND S. C. SCHERRER
lake altitude [m a.s.l.]
730
720
+ ++ + ++++++++ ++++++ ++++++ +++++ +++
11
+++++++++++ +++++ +++++++++++++ +++++++++++ +++++++++++++++ +++++++++
10
500
450
400
9
++++++ ++ + ++++
+ + ++
+ +++
++
+
++
+++
+ + +
+ + +++ ++ ++ +
8
+ ++ +++ ++ ++ ++++ +
7 + +++ + ++
++
++
+
+
+
+
++ +++ ++ ++ ++++ +
6
+++ ++ ++++++ ++++ +++ +++++++ +++++ +
5 ++++++++ +
+ ++
+ ++ +++ + + + +
+
4
+ +++ +++ ++ ++++ +++ +
3 + ++++ + +++
2 ++ +++ + +++ ++ ++++ +++ ++ +++++ +++ ++
1 +++++++ + +++ ++ + +++ +++ ++ ++++ +++ +
+
+
+
++
+
++
++
+++ +
+
+
++ +++
+
+ ++
+ + +++
+
+
1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000
year
Figure 3. Freezing of 11 lakes on the Swiss plateau in the years 1901–2006 (abscissa) shown as a function of lake altitude (m a.s.l., ordinate).
Years with complete ice cover are indicated by crosses. The years of missing data are indicated with a black line. Lakes: 1, Untersee; 2, Upper
Lake Zurich; 3, Lake Murten (plotted 6 m lower than in Nature to distinguish it from Lake Biel which has the same altitude); 4, Lake Biel; 5,
Lake Greifensee; 6, Lake Hallwil; 7, Lake Baldegg; 8, Lake Sarnen; 9, Lake Sempach; 10, Lake Pfaeffikon; 11, Lake Aegeri.
without freezing that occurred before 1966. However,
such a generalized statement cannot be made for lakes
that freeze more often, like Lake Pfaeffikon, Lake Aegeri
and Lake Greifensee.
The data also show some peculiar trends. While
for the lakes that freeze more frequently (frequency
>0.30 over the complete observation period), the freezing
frequency was larger during the years 1901–1925 than
in the 25 years afterwards; the opposite behaviour was
observed for lakes that freeze less frequently (frequency
<0.20 over the complete observation period). There is
a link with the temperature observations. The period
1901–1925 had many below average winters (e.g. ten
winters with an average winter temperature below 0.5 ° C
in Neuchatel), but a few well below average winters
(e.g. three winters with an average winter temperature
below −0.5 ° C in Neuchatel). On the contrary, the period
1926–1950 had nine and six such winters in Neuchatel
respectively.
4.1.1. Trends
We tested whether the observed trends are statistically
significant. The time series of the ice cover data for each
of the lakes is stored in a vector y with NT entries
(NT being the length of the time series in years). Ice
cover is a binary variable that takes the value 1 if the
lake freezes during a winter and 0 if it does not freeze
or only partially freezes. Another vector x contains the
time in years from 1901 until 2006. For all lakes, a
binomial logistic regression was performed (e.g. Wilks,
2006) using the ice cover as a response variable (having
values of 0 or 1), and the year as an explanatory variable,
which takes the form of a probability P :
P =
1
1+e
−(a+bX)
,
where a and b are the regression coefficients such
that the estimation of the value for the outcome of
Copyright  2007 Royal Meteorological Society
the variable y is unbiased with minimum variance. P
gives the probability that the lake freezes as function
of time. Temporal autocorrelation is neglected. The
estimated regression coefficient b was smaller than 1 (i.e.
decreasing frequency) for all lakes. The Walk chi square
test has been applied to the fitted regression coefficients
b (for each lake separately) with the null hypothesis that
the lake freezing does not show a trend in time (b = 1)
and the alternative hypothesis that the frequency of lake
freezing decreases during the investigated period (b < 1).
Significant trends on the 5% level are found for Lake
Biel, Lake Murten, Lake Sempach, Untersee and Upper
Lake Zurich. Lake Hallwil, Lake Baldegg, Lake Sarnen
and Lake Greifensee show a clear, but not statistically
significant negative trend on the 5% level. For Lake
Aegeri and Lake Pfaeffikon, the negative trend is far
from significant (P -value 0.05). Table IV summarizes
the P -values of the test statistics. The significance is
very sensitive to a few observations only. However, what
makes it more remarkable is the fact that for most lakes
a clear trend towards less winters with complete freezing
can be observed. This tendency is especially pronounced
at the end of the 20th century. No separate tests for
shorter periods (e.g. for the last 50 years) have been
carried out as the significance of trends for such a short
period is even more sensitive to a few observations only.
The link between these trends and the sum of NDD is
discussed in detail below.
4.2.
Binomial logistic regression
Binomial logistic regression has also been used to estimate the probability of lake freezing as a function of
measures for winter temperature. The vector x now contains temperature information. For each of the entries the
average winter (DJF) temperature (T ), the sum of NDD
(V ) and the natural score transform of V have been
considered. The average winter temperature T seemed
normally distributed for all temperature stations (cf. also
Int. J. Climatol. 28: 421–433 (2008)
DOI: 10.1002/joc
FREEZING OF SWISS PLATEAU LAKES DURING 1901–2006
Table IV. P -statistics for testing on a temporal trend in the
freezing of 11 Swiss lakes during the period 1901–2006 (or
somewhat shorter for some of the lakes). The lakes where a
significant negative temporal trend (P < 0.05) is found are
shown bold.
Lake
name
Lake Biel
Lake Murten
Lake Sempach
Lake Hallwil
Lake Baldegg
Lake Sarnen
Lake Aegeri
Upper Lake Zurich
Lake Greifensee
Lake Pfaeffikon
Untersee
Time
period
P -statistics
1914–2006
1901–2006
1901–2006
1901–2006
1901–2006
1901–2006
1914–2006
1901–2006
1901–2006
1922–2006
1901–2006
0.005
0.02
0.04
0.053
0.13
0.11
0.68
0.01
0.09
0.98
0.01
Scherrer et al., 2006). The natural logarithm of V has
also been used as an explanatory variable in the analysis
since in contrast to V , ln(V ) is normally distributed, as
p –p and q –q plots suggest (not shown).
The probability P now is the probability that the lake
freezes as a function of T , V or ln V . Figure 4 shows
the fits for the different lakes (together with the data),
using ln V as an explanatory variable. The best results
were found using ln V as explanatory variable (see below
for further explanations). Table V gives some summary
statistics of the fitted regression lines, like the amount of
cold needed to reach a certain probability that the lake
freezes completely.
Table V. The sum of the negative degree days at a nearby
meteorological station for which the investigated lake freezes
with a probability of 10, 33, 50, 67 and 90%. The numbers
are based on a binomial logistic regression using data for the
period 1901–2006 (see text for details).
Ice
on:
Lake
Lake
Lake
Lake
Lake
Lake
Lake
Negative
degree
days in:
Biel
Murten
Sempach
Hallwil
Baldegg
Sarnen
Aegeri
Neuchatel
Neuchatel
Lucerne
Lucerne
Lucerne
Lucerne
Einsiedeln/
Zurich SMA
Zurich SMA
P0.10 P0.33 P0.50 P0.67 P0.90
122
91
144
134
131
160
137
155
118
190
160
159
200
192
172
132
216
174
174
222
224
192
148
246
188
191
247
262
244
191
325
225
232
309
366
Upper Lake
147
Zurich
Lake
Zurich SMA 101
Greifensee
Lake Pfaeffikon Zurich SMA 55
Untersee
Kreuzlingen/ 128
Guettingen
174
188
203
240
132
149
168
220
76
156
89
170
105
187
147
228
Copyright  2007 Royal Meteorological Society
427
The fitted regression lines illustrate the relationship
between low temperatures and the freezing of the lakes.
Visual inspection of Figure 4 shows that some lakes
exhibit a larger uncertainty than others (e.g. Lake Sempach and Lake Aegeri). There might not be a specific reason for this behaviour of Lake Sempach, as the regression
lines are prone to a considerable uncertainty. Especially
for lakes, which rarely freeze (like Lake Sempach), the
fit is based on a relatively limited amount of freezing
cases. Also for Lake Aegeri, the uncertainty is larger. In
the case of Lake Aegeri, this might be due to the fact that
the ice data were correlated with temperature stations that
are less representative for the lake (altitude differences)
or some inhomogeneity problems with the temperature
series in Einsiedeln. On the other hand, the uncertainty
is largest for the three lakes which need the most cold to
freeze (Lake Aegeri, Lake Sarnen and Lake Sempach).
This indicates that the uncertainty in the fit on the basis
of ln V is larger for deeper lakes (or the lakes that need
more cold to freeze). Note, that for the three deepest lakes
considered in this study P0.67 − P0.33 varied between 47
and 70 (Table V), while for less deep lakes P0.67 − P0.33
is smaller (between 28 and 37). This implies that also for
deeper lakes that rarely freeze (e.g. the lakes analysed by
Pfister (1984)) the estimation of the freezing probability
as function of the sum of NDD could be subjected to at
least a similar amount of uncertainty. For instance, if we
assume that for Lake Constance P0.67 − P0.33 = 60, the
statement that Lake Constance needs a sum of 400 NDD
to freeze (Pfister, 1984) would mean that in one-third of
the cases a sum of 430 NDD is not enough to let the lake
freeze (P0.67 > 430), while in another one-third of the
cases the lake already freezes with less than 370 NDD
(P0.33 < 370). In addition, notice that the estimated sum
of 400 NDD is associated with considerable uncertainty,
because only for a very few freezing cases the actual
temperatures have been measured accurately.
Finally, it is interesting to determine the relationship between the sum of NDD at which the probability
for freezing is 50% and the average depth of the lake
(Figure 5). The energy reservoir of the lake, which prevents the lake from freezing, is the temperature of the
water volume with dimension L3 . On the other side, the
lake loses energy in winter due to meteorological forcing,
which acts on a small top layer of the lake with dimension L2 . The complete water volume has to be cooled
down until the maximum density of water is reached;
in addition, a colder top layer at the lake surface may
develop. As a result, the average lake depth (dimension
L3 /L2 = L) is expected to be related with the sum of
NDD. The Upper Lake Zurich and Untersee are not suited
for this analysis. These lakes are not completely separated
from the bigger lakes they form part of (Lake Zurich
and Lake Constance respectively). Some exchange exists
with the main, deeper basin of these lakes and therefore
more cold is needed to freeze these lakes, than would be
expected from the average depths. Looking at the nine
remaining lakes, it is indeed found that the three deepest lakes (Sarnen, Sempach and Aegeri) need the largest
Int. J. Climatol. 28: 421–433 (2008)
DOI: 10.1002/joc
428
H. J. H. FRANSSEN AND S. C. SCHERRER
Untersee (Kreuzlingen/Guettingen)
1
0.8
0.6
0.4
0.2
0
| | | | | || | | | ||||| |
|| | ||
||
Lake Baldegg (Lucerne)
1
0.8
0.6
0.4
0.2
0
| |
| || || | || |||||||||||| ||||| |||||| |||| | | |
0
100
200
300
400
500
|| || | | | | || || | | | |
| || ||||||||||||||
||||| | ||||||||||||
||| || |
0
100
Lake Hallwil (Lucerne)
1
0.8
0.6
0.4
0.2
0
| || | | | ||| || | | | | |
| || ||||||||||||||
||||| | ||||||||||||
||| ||| |
0
100
|
300
1
0.8
0.6
0.4
0.2
0
|
|| |
| || | | |
| || ||||||||||||||
||||| | ||||||||||||
||| ||||| | ||| | ||
0
100
400
500
|
300
| || ||||||||||||||
||||| | ||||||||||||
||| ||| |
0
1
0.8
0.6
0.4
0.2
0
|
|
|| | | | | | || |
400
|
500
100
200
300
0
1
0.8
0.6
0.4
0.2
0
|
400
||| | | | || ||| ||| | | | | | | | ||
| | | | |||||||||||||||||||||
| |||| ||||||| |
0
100
200
500
100
||| | ||
|
|
| |
200
300
400
500
|
|
100
200
300
400
500
| | | | | | | |||| | |
|
|
0
| |||||| ||| | | ||| | | | | |
| ||| | |||||||||| | | |||| | || | | || | |
100
200
300
||
|| |
400
500
Lake Greifensee (Zurich)
|
|
|
300
500
| |||||||||||||||||||||| ||||
|||||||||||| || ||| |
Upper lake Zurich (Zurich)
1
0.8
0.6
0.4
0.2
0
400
Lake Aegeri (Einsiedeln/Zurich)
| |||||||||||||||||||| ||||
||||||||||| || | || | | | |
0
300
| | | | | || ||| | || |||| | || |
Lake Biel (Neuchatel)
1
0.8
0.6
0.4
0.2
0
200
Lake Murten (Neuchatel)
|
200
|| | |
| | | | | || | | | |
Lake Sarnen (Lucerne)
1
0.8
0.6
0.4
0.2
0
|
Lake Sempach (Lucerne)
| |
200
|
400
500
1
0.8
0.6
0.4
0.2
0
| | ||| ||||| | |||| || | || ||| | | | | | | | | | ||
| | | | |||||||||||| |||| || || | || | |
0
100
200
|
|
|
300
400
500
Lake Pfaeffikon (Zurich)
1
0.8
0.6
0.4
0.2
0
| | || ||||||||||||
| |||| |||| | || | | | | | || | | | | | ||
|
|
| | | | |||| |||| | | | |
0
100
200
300
400
500
Figure 4. The probability of freezing for 11 prealpine Swiss lakes as a function of the sum of negative degree days NDD (fit for ln V ) measured
at a nearby meteorological station (grey fit). Plotted are also the raw binary data (vertical dashes: 0, no freezing; 1, freezing of the lake) and the
sum of NDD for a 50% probability of freezing (vertical dashed line).
sums of NDD (P0.50 above 200). However, Lake Sarnen is only slightly deeper than the other lakes like Lake
Baldegg or Lake Biel, and needs considerably more cold
to freeze. The needed sum of NDD for Lake Biel might
be slightly underestimated because at the lake it might
be colder than measured in Neuchatel. The three other
lakes (Lake Hallwil, Lake Biel and Lake Baldegg) with
average depths of around 30 m need all a similar sum of
NDD to freeze completely (P0.50 around 170). The three
lakes, which have the smallest average depths, need less
Copyright  2007 Royal Meteorological Society
cold to freeze as compared to the other lakes, but the
correlation is not perfect. Lake Murten, nearly as deep
as Lake Hallwil, needs considerably less cold than Lake
Hallwil. Again, the station of Neuchatel might be somewhat ‘warm’ for Lake Murten (cf. Figure 5). For Lake
Greifensee and Lake Pfaeffikon, the weather station of
Zurich (556 m a.s.l.) is used. Lake Greifensee is situated clearly lower; hence, the amount of needed cold is
overestimated for this lake. On the other hand, at Lake
Pfaeffikon local conditions result in clearly lower night
Int. J. Climatol. 28: 421–433 (2008)
DOI: 10.1002/joc
429
FREEZING OF SWISS PLATEAU LAKES DURING 1901–2006
temperatures than measured in Zurich. Therefore, the sum
of needed cold for Lake Pfaeffikon is expected to be
underestimated (cf. Figure 5).
In summary, a clear relationship between lake depth
and the sum of NDD needed to freeze the lake (in terms of
P0.50 ) is found (ordinary least squares fit: NDD = 3.74 ×
depth + 55.6; r = 0.85, cf. Figure 5). Deviations, e.g. for
Lake Greifensee, Lake Pfaeffikon and Lake Murten can
be explained (among other things) by local temperatures,
which deviate somewhat from the chosen temperature
time series. The relatively large amount of cold that Lake
Sarnen needs to freeze is harder to explain. The distance
between the meteorological station of Lucerne and Lake
Sarnen is relatively large, considering the fact that the
topography is complex in this area. Unfortunately, no
long time series of temperature measurements close to
Lake Sarnen is available.
4.3. Classification and verification
The fitting can also be used to classify the winters
into winters for which freezing is expected (P > 0.50)
negative degree days (NDD) [°C*days]
225
NDD = 3.74*depth + 55.6
R2 = 0.723
and winters for which freezing is not expected (P <
0.50). The classification can then be compared with
the observation. It is correct when freezing is predicted
and also observed, or when freezing was not predicted
and the lake did not freeze indeed. Table VI gives the
percentage of correct classification and the calculated
average residuals for all the lakes and the different
explanatory variables (T , V and ln V ). Overall, the
number of correct classifications (average residuals) is
slightly larger (smaller) for V and ln V than for T . For
ln V , the misclassifications are more evenly distributed
(as compared with V and T ). For example, for Lake
Greifensee, classification with V yields 9 cases with
observed lake freezing, but not predicted lake freezing
and 4 cases with predicted, but not observed lake
freezing. Classification with ln V results in a more
symmetric distribution: 6 versus 5 cases, respectively.
Also for Lake Aegeri, Lake Pfaeffikon and Lake Baldegg,
more evenly distributed misclassifications are obtained
with ln V . For the other lakes, no differences between V
and ln V were observed. Therefore, ln V is considered
Lake Aegeri
Lake Sempach
Lake Sarnen
200
Lake Hallwil
175
Lake Baldegg
Lake Biel
Lake Greifensee
150
Lake Murten
125
100
Lake Pfaeffikon
75
15
20
25
30
35
40
45
50
average lake depth [m]
Figure 5. The sum of October–April negative degree days (NDD) needed to observe a complete lake freezing with a probability of 50% as a
function of the average lake depth (in m) for nine prealpine Swiss lakes. The least squares fit equation and multiple R 2 value are also shown.
Table VI. Binomial logistic regression: diagnosing the freezing of 11 Swiss lakes by means of T , V or ln V .
Lake name
Lake Biel
Lake Murten
Lake Sempach
Lake Hallwil
Lake Baldegg
Lake Sarnen
Lake Aegeri
Upper Lake Zurich
Lake Greifensee
Lake Pfaeffikon
Untersee
Time period
1914–2006
1901–2006
1901–2006
1901–2006
1901–2006
1901–2006
1914–2006
1901–2006
1901–2006
1922–2006
1901–2006
Copyright  2007 Royal Meteorological Society
Correct classification (%)
Average residual
ln V
V
T
ln V
V
T
93.5
88.5
87.5
93.3
91.4
91.4
71.7
91.4
82.9
81.2
91.4
93.5
88.5
87.5
93.3
90.4
91.4
68.5
94.3
81.0
82.4
91.4
90.2
92.3
88.5
89.4
91.4
91.4
76.1
87.6
83.8
77.7
88.5
0.095
0.153
0.144
0.107
0.121
0.113
0.318
0.142
0.232
0.217
0.138
0.099
0.150
0.147
0.112
0.123
0.111
0.315
0.138
0.236
0.212
0.136
0.107
0.148
0.141
0.167
0.143
0.121
0.318
0.204
0.266
0.245
0.202
Int. J. Climatol. 28: 421–433 (2008)
DOI: 10.1002/joc
430
H. J. H. FRANSSEN AND S. C. SCHERRER
the best of these three variables to predict the freezing of
the lakes.
For most lakes, the number of correct classifications
is around 90% (predictor: ln V ). For Lake Greifensee
(83%) and Lake Aegeri (72%), the number of correct
classifications is clearly lower. This can be explained by
the fact that these lakes froze in about half of the winters
in the 1901–2006 period. A correct classification is more
difficult than for a lake which freezes in 20% or 80% of
the winters. For a lake that freezes in 50% of the winters,
a prediction using only the climatological frequency of
the event would give a correct prediction in 50% of the
cases, whereas for a lake that freezes in 20% or 80%, the
hit rate (correct prediction) is expected to be 68%.
Since many lakes rarely freeze and hence the predictions are relatively easy (i.e. the hit rate is high even for
a climatological prediction), other verification measures
need to be considered. Table VII gives the threat score
(TS), the probability of detection (POD) and the falsealarm rate (FAR) for the 11 lakes (cf. Wilks, 2006). The
TS is the number of correct ‘freezing’ forecasts divided
by the total number of cases in which freezing of the lake
was forecasted and/or observed. The POD is the fraction
of occasions when the freezing event was forecast and
also occurred. The FAR is the proportion of forecasted
freezing events that failed to materialize. Note that the
year to be fitted is not omitted to determine the verification measures. Although omitting the year to be predicted
would be more rigorous, the differences to the numbers
determined using all the years as presented are negligible.
For most of the lakes, the TS using ln V as predictor
is above 60%, the POD is above 70% and the FAR
is below 20%. The three lakes that were found to
have the broadest probability distribution functions (cf.
Figure 4) have the worst scores. The improvements with
respect to a climatological estimate are also shown
in Table VII. The half-Brier score (Wilks, 2006) is
calculated, and this average squared residual is divided
by an average squared residual that would result from
Table VII. Accuracy measures for predicting the freezing of
lakes with ln V as explanatory variable. TS = threat score,
POD = probability of detection, FAR = false-alarm rate and
BSS = Brier skill score (see text for definitions of the score).
Lake
name
Lake Biel
Lake Murten
Lake Sempach
Lake Hallwil
Lake Baldegg
Lake Sarnen
Lake Aegeri
Upper Lake Zurich
Lake Greifensee
Lake Pfaeffikon
Untersee
Series
1914–2006
1901–2006
1901–2006
1901–2006
1901–2006
1901–2006
1914–2006
1901–2006
1901–2006
1922–2006
1901–2006
TS POD FAR BSS(%)
(%) (%) (%)
62.5
61.3
38.1
74.1
67.9
50.0
56.7
80.0
70.0
78.4
75.7
71.4
70.4
50.0
83.3
79.2
64.3
73.9
84.8
84.0
90.6
82.4
Copyright  2007 Royal Meteorological Society
16.7
17.4
38.5
13.0
17.4
30.8
29.2
6.7
19.2
14.7
9.7
63.3
59.9
41.5
70.1
65.9
49.4
36.3
67.8
53.2
40.3
66.1
using a climatological mean frequency in the estimation
procedure. The resulting score is subtracted from one to
give a Brier skill score (BSS). A BSS of zero means no
improvement over a climatological forecast, whereas one
is a perfect forecast. The table shows that considerable
improvement over a climatological forecast is obtained
with skill scores of at least 0.36 (Lake Aegeri) and in
about half of the cases scores are above 0.60.
There are several possible reasons for the low BSS
values for Lake Aegeri. The temperature at Lake Aegeri
is estimated from two stations (the higher Einsiedeln
and the far away, lower Zurich) that may be less
representative for the site than the stations for the
other lakes. In addition, the data of Einsiedeln was not
rigorously homogenized and may therefore not be totally
trustworthy.
5.
5.1.
Discussion
Temporal trends
The freezing frequency of lakes on the Swiss plateau
is declining in the investigated period. This decline is
most pronounced for the last 40 years, with the last
20 years showing the smallest freezing frequencies of
the considered period. Especially the deeper lakes, which
freeze more rarely, show a significant downward trend.
For the three lakes, viz Lake Aegeri, Lake Greifensee and
Lake Pfaeffikon that freeze more frequently, the freezing
frequencies reduced less in the period 1901–2006 and
the observed trends were also not judged as significant
(Section 4.1). For the freezing of a lake, a certain amount
of cold is needed and this is smaller for the lakes like
Lake Greifensee, Lake Pfaeffikon and Lake Aegeri that
freeze more frequently. The frequency of the winters that
produce the necessary cold to freeze these often freezing
lakes has not decreased strongly. The relative decrease
of the probability of exceedance for the sum of NDD
needed to freeze Lake Pfaeffikon (Lake Greifensee) with
a probability of 50% is −21%(−31%) at Zurich SMA
when comparing the 1966–2006 with the 1902–1965
period (Figure 6). On the other hand, the frequency of
winters that also produce enough cold to freeze deeper
lakes like Lake Sempach show a significantly declining
trend. For these lakes, the decrease of the probability of
exceedance needed for the sum of NDD is much larger
and highly significant (between −52 and −74% at nearby
stations, Figure 6 for details).
5.2.
Data reliability
An important issue is the reliability of the ice cover
data, especially, the data from newspapers. The data from
observers are not perfect, but of good quality. However,
data from newspapers could be of worse quality and
probably be biased due to the fact that not all the cases
are reported in the newspapers. It is especially this kind
of error that could modify our conclusions. Therefore, a
closer look has been taken on the homogeneity of the
data. Unfortunately, it is difficult to judge data quality.
Int. J. Climatol. 28: 421–433 (2008)
DOI: 10.1002/joc
431
FREEZING OF SWISS PLATEAU LAKES DURING 1901–2006
50
100
Lake Biel
150
200
250
300
-53%
-57%
0
0
50
100 150 200 250
negative degree days
100
150
200
250
300
Kreuzlingen/Guettingen
300
-56%
Untersee
Upper lake Zurich
-21%
-31%
50
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
-52%
Lake Greifensee
Lake Pfaeffikon
probability of exceedance
Zurich SMA
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
-53%
-57%
Lake Sempach
Lake Sarnen
-74%
-67%
0
Lucerne
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Lake Hallwil
Lake Baldegg
1902–1965
1966–2006
Lake Murten
probability of exceedance
Neuchatel
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0
50
100 150 200 250
negative degree days
300
Figure 6. The probabilities of exceedance for October–April sums of negative degree days NDD at the stations Neuchatel (top left), Lucerne
(top right), Zurich SMA (lower left) and Kreuzlingen/Guettingen (lower right) in the periods 1902–1965 (black) and 1966–2006 (grey). Also
shown are percentage decreases (1966–2006 vs 1902–1965) in the probability of exceedance for the NDD sum at which ten prealpine Swiss
lakes freeze with a probability of 50% in the 1902–2006 period (arrows and numbers).
For Lake Hallwil, Lake Baldegg and Lake Sempach,
data from observers since 1956 are available. In the case
of Lake Baldegg and Lake Sempach, these data were
systematically registered. For the period 1901–1955, data
have been obtained from newspapers. If the newspapers
under-report (or over-report) one would expect that the
residuals of the binomial logistic regression would show
a (possibly significant) difference for the period until
1955 and the period after 1955. The average residual
for the period 1901–1955 would be negative in case of
an underestimation. For the three lakes for the period
1901–1955, the average residuals are close to zero,
never significantly different from zero, and only for Lake
Baldegg slightly negative (−0.02). Considering the other
lakes, we see that Lake Biel has almost a complete
time series from observers, while the newspaper data
for Lake Greifensee and Upper Lake Zurich are of high
quality, with detailed reporting. For Lake Murten, Lake
Sarnen and Lake Aegeri, data are almost exclusively from
newspapers. The quality of these newspaper data could
not be investigated in more detail.
The newspapers also reported during war time without
restrictions on ice cover on the lakes. Some of the
newspapers did not appear daily (the ones used for Lake
Murten, Lake Sarnen and the Untersee), but in these local
newspapers the freezing of the lake was an important
event to be reported.
Copyright  2007 Royal Meteorological Society
5.3. Uncertainty associated with estimation
The estimated binomial logistic regression lines give an
estimation of the amount of cold (in terms of sum of
NDD) needed to freeze a lake. Such data may help to
make more precise temperature constructions with the
help of historical ice cover information. For instance,
Buisman (1995) reports data on the freezing of the
Untersee, which go back until the 13th century. It is also
of interest to know when a lake was completely covered
with ice. Although not shown in this paper, the date at
which a lake froze for the first time completely in a winter
is also strongly correlated with the sum of NDD until
that day, according to the experimental data we have.
Buisman (1995) reports a case in the 13th century where
the Untersee already froze in December. This indicates
that already so early in winter the necessary sum of
NDD was reached. Another example can be found in
the work of Pfister (1984). He reports that the Untersee
froze as early as the 9th of December in the winter of
1572/1573. In the 20th century the Untersee froze only in
two winters already in December. Probably old chronics
still contain a lot of valuable information on the freezing
of the smaller lakes that were analysed in this study,
for example, because fishery was not possible due to the
freezing or because of accidents on the ice.
Int. J. Climatol. 28: 421–433 (2008)
DOI: 10.1002/joc
432
5.4.
H. J. H. FRANSSEN AND S. C. SCHERRER
Physical explanation
The regression lines indicate that a significant uncertainty
is left in the prediction of the freezing of a lake
on the basis of temperature data only. The average
autumn temperature has also been used as an additional
explanatory variable in the binomial logistic regression.
This variable could determine how much heat the lake
already lost in the period preceding the winter, but results
show that the additional variable could explain hardly
anything of the unexplained variance. Looking at winters
in which the ice behaviour was substantially different
from what one might expect from temperatures; however,
suggests that the temporal distribution of NDD has some
effect on the development of lake ice. Given a certain
NDD-value for a winter, the probability of lake freezing
is somewhat larger in case this cold is concentrated
(especially if concentrated during the second half of the
winter) than in case it is scattered over the winter season.
Overall, this effect seems to be rather small.
Possibly, a combination of wind speed, actual temperature and cloud cover could explain a large amount of
the unexplained variance. If all the water in a lake is
cooled down sufficiently so that an inversion in the top
layer develops, low temperatures in combination with
a low wind speed (energy loss limited to a smaller
top layer of the lake), low relative humidity and little
clouds (increased outgoing long-wave radiation) favour
the development of an ice layer. Low temperatures in
combination with a clouded sky, an elevated relative
humidity and strong winds, on the contrary, only result
in a slow temperature decrease of the top layer of the
lake. A study with a numerical model would be necessary to compare e.g. the relative importance of wind
speed in comparison with the cloudiness of the sky.
However, solving numerically the 1D partial differential
equation that describes the lake temperature as a function
of time and depth (assuming perfect horizontal mixing)
would add little to the regression-type relationships that
we established between air temperature and ice cover.
Such a numerical model would need a large amount of
input parameters like data on:
1) measured global radiation (in order to determine shortwave radiation adsorbed by the lake)
2) air temperature (long-wave radiation adsorbed by
the lake, convective heat flux between lake and
atmosphere)
3) actual vapour pressure (latent heat flux between lake
and atmosphere)
4) wind speed (latent heat flux, convective heat flux,
turbulent diffusion in the lake)
5) amount of water inflow and outflow with water
temperature of these inflows
6) surface lake temperature (outgoing long-wave radiation, latent heat flux, convective heat flux); could be
avoided by numerical-iterative solutions
7) the geothermal heat flux
8) the initial system state
Copyright  2007 Royal Meteorological Society
In addition, at least for some of the considered lakes
the 1D representation is not adequate as during winter
systematic horizontal gradients of the water surface temperature are observed. Even for a 3D lake model that
is fed with the mentioned detailed input data, it is very
likely that it has to be calibrated, for example, owing
to wrong turbulent diffusion coefficients or a mismatch
between the ‘true’ meteorological forcing and the measured meteorological data at the site (e.g. differences in
wind speed and air temperature). In summary, a numerical model would only serve to gain insight into the
freezing process, but would not be useful for the purpose
of the presented study. Also for temperature reconstructions based on historical ice cover data, a model based
on temperature only is needed, since this variable is the
only one available in sufficient quality for a time period
of the order of 100 years.
6.
Conclusions
For the first time, ice cover data from 11 mid-sized
lakes on the Swiss plateau have been collected and
analysed for the period 1901–2006. It is shown that the
freezing frequency of the lakes declines in the observation
period, especially during the last 40 years. The decline of
lake ice is most pronounced for lakes that freeze more
rarely, and for most of these lakes a trend test showed
a significant decrease in freezing frequency. The three
lakes that have the highest mean freezing frequency (Lake
Pfaeffikon, Lake Greifensee and Lake Aegeri) show a
less pronounced and not significant decrease of freezing
events. This is in good agreement with the relative
changes in the sum of NDD at stations near the lakes.
When comparing data from the last forty years with the
1902–1965 period, the relative change in the probability
to exceed the sum of NDD needed for freezing is much
larger at the lakes that rarely freeze −52–(−74%) than
at the lakes that often freeze −21–(−31%). Binomial
logistic regression has been used to estimate the freezing
probability of the lake as a function of the natural
logarithmic transform of the sum of NDD. The regression
relationships explain a large part of the variance observed
in the freezing of the lakes. Using the logistic regression
approach to predict the probability of lake freezing shows
a skill significantly better than climatology. The sums
of NDD needed for lake freezing are well related to
the average depth of the lakes (rNDD – Depth = 0.85). The
probabilistic relationships that have been derived may
also be useful for estimating winter temperatures on the
basis of historical lake ice data.
Acknowledgements
Thanks are due to A. Martin, P. Schaer, U. Merz, A.
Hofer, T. Hofer, M. Ruf, von Moos, A. Hiestand and T.
Egli for providing historical observations on ice cover
on the Lakes Biel, Murten, Hallwil, Baldegg, Sempach,
Greifensee, Sarnen, Pfaeffikon and Untersee. Thanks are
Int. J. Climatol. 28: 421–433 (2008)
DOI: 10.1002/joc
FREEZING OF SWISS PLATEAU LAKES DURING 1901–2006
also due to M. Rubli and R. Morosoli for helping with
finding data in newspapers on the freezing of Lake
Murten and Lake Aegeri.
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