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Temperature extremes and detection of heat and cold waves at three sites in Estonia/Ekstreemsete temperatuuride esinemistoenaosused ning kuuma- ja kulmalainete maaratlemine Eestis.


The climate of a certain region is characterized not only by the average (long-term, annual, seasonal, monthly, daily) values of the meteorological parameters, but also by their variability. To describe the variability of air temperature, several characteristics can be used on long-term, annual, seasonal, monthly, or daily basis: standard deviation, average maxima and minima, absolute maxima and minima. The main objective of the present paper is to describe the statistics of the maximum and minimum temperatures at three sites characteristic of different regions of Estonia.

In many aspects, however, various types of severe events such as temperature extremes and heat and cold waves are of great importance. There are no universal definitions of heat wave and cold wave as both depend on the background climatic conditions of the region under consideration (Robinson, 2001; Meehl and Tebaldi, 2004). One purpose of our paper is to better justify the determination of heat and cold waves in Estonian climatic conditions.

As daily temperature maxima in summer are connected with heat waves and minima in winter with cold waves, analysis of temperature extremes permits one to estimate the occurrence probability of various severe events. In this context, extreme values of meteorological parameters need precise definitions (e.g. Wong et al., 2011).

Analysis of daily temperature extremes is usually directed towards detection of climate change. For this purpose, different indices have been constructed. The simplest indices--monthly mean maximum and 4minimum temperatures--are used by Jaagus et al. (2014) together with the diurnal temperature range to calculate trends in the Baltic States during 1951-2010. They chose that time interval to involve as many stations with homogeneous time series as possible. Homogeneity of the time series was granted by means of using similar measurement devices and routines and leaving out stations that had been relocated. Statistically significant increasing trends in maximum and minimum temperatures (which were coherent with changes in the mean temperature) were detected for the annual averages and several months. No trend in the annual values of the diurnal temperature range was detected.

Regarding temperature, the following indicators are suggested for mid-latitude climates (Frich et al., 2002):

* total number of frost days during a year (minimum below 0[degrees]C);

* intra-annual extreme temperature range;

* growing season length;

* heat wave duration index: maximum period for the year of at least 5 consecutive days with [T.sub.max] at least 5[degrees]C above the 1961-1990 daily [T.sub.max] normal;

* per cent of time [T.sub.min] exceeding 90th percentile of daily climatological distribution of minimum temperature--a measure of the number of warm nights. These indicators have been used to clarify whether the frequency and/or severity of temperature extremes changed during the second half of the 20th century on a global scale. The changes demonstrated considerable coherence showing an increase in the number of warm summer nights, a decrease in the number of frost days, and a decrease in the intra-annual extreme temperature range. The most popular indices of extremes to detect climate change (e.g. Wong et al., 2011; Garcia-Cue-to et al., 2014) are given by the Expert Team on Climate Change Detection and Indices (ETCCDI) (Klein Tank et al., 2009). These indices can be used also for establishing suitable thresholds for heat and cold waves at any site (Unkasevic and Tosic, 2015) and are used in this study.


For the calculation of the probabilities of rare events the time series must be as long as possible (Van den Brink et al., 2005). As homogeneity is not of vital importance in this context, we use data from three Estonian meteorological stations with the longest data sets: Tallinn on the southern coast of the Gulf of Finland, Tartu representing inland Estonia, and Parnu on the northern coast of the Gulf of Riga (Fig. 1).

The instrumental observations in Tallinn date back to the end of the 18th century (Tarand, 2003), but the time series of daily minimum and maximum temperatures starts in January 1920. Recordings of daily minimum and maximum temperatures in Tartu are available since 1 January 1894 and in Parnu from 1 January 1878.

For different reasons, there are gaps in the time series of daily extreme temperatures. These gaps are shown in Table 1 where WWI and WWII denote the hectic times of the two world wars.

Even though the employed time series contain several (minor) inhomogeneities (Keevallik and Vint, 2012), they are not crucial from the viewpoint of our study. Several changes (relocation, new instruments, different observation times) have indeed affected the data sets at these stations. For instance, the relocation of Tallinn meteorological station in 1980 and Parnu meteorological station in 1990 caused an increase in the daily averages in the data sets from 1931-2010 and 1901-2010, respectively. Such an increase was also detected for Tartu in 1966 (in the context of the data set for 1881-2010) when the observation routine of 4 times a day was replaced by 8 times a day (Keevallik and Vint, 2012).

The absolute maximum temperature in Estonia (35.6[degrees]C) was recorded on 11 August 1992 and the absolute minimum of -43.5[degrees]C on 17 January 1940. According to the homepage of the Estonian Weather Service, the situation is labelled as (very) dangerous when the daily maximal temperature is above 30[degrees]C during at least (three) two consecutive days or the daily minimal temperature is below -30[degrees]C during at least (three) two consecutive days. The choice of these thresholds is not documented, but it seems to be related to the comfort temperature of the human beings in this climate zone. We use the same thresholds below in this study to identify the extreme events. In Estonia, daily maxima above 30[degrees]C may only occur from May to September, and daily minima below -30[degrees]C from December to February. Notice that as the temperatures are given in the data files with the accuracy to the first decimal place, actually the thresholds [+ or -] 29.5[degrees]C were used.

A simple estimate of the return period of an extreme event within a relatively long time series is calculated as the ratio of the number of years in the time series to the number of recorded occurrences during this time period. A more complicated method to calculate values for large return periods from short records is described by Van den Brink and Konnen (2011). The inverse value of the return period is the probability of the occurrence p of the event in any one year. The probability P of the occurrence of this event k times in n successive years is presented by the binomial distribution:

P = n! / k! (n - k)! [p.sup.k] [(1 - p).sup.n-k]


The probability that daily maximum temperature exceeds 30[degrees]C is the highest in July (Table 2). In Tartu such temperatures occur nearly every year and in Tallinn every third year. The probability that the daily minimum is below--30[degrees]C is the highest in January, being 31% for Tartu and only 7% for Tallinn. This is consistent with the well-known difference between weather conditions at the seaside and in the inland of Estonia (Jaagus et al., 2014). The climate of Tartu is evidently more continental than that of Tallinn. The conditions in Parnu are not as mild as in Tallinn and not as contrasting as in Tartu.

These probabilities can be used as a benchmark to estimate the skill of forecasts of various kinds, for example to check how much a certain complicated forecast is better than the climatological one (Hamill and Juras, 2006; Keevallik et al., 2014).

A more detailed description of temperature extremes can be given, for instance, as

* the probability that a specific extreme event takes place at least once in n successive years;

* the probability that a specific extreme event takes place exactly k times in n successive years.

We analyse these probabilities for the test time interval on decadal scale (n = 10 years) using Eq. (1).

The probabilities of the occurrence of extreme temperatures (Tables 3 and 4) indicate, not unexpectedly, that the temperature contrasts are the largest in Tartu, which is situated inland. Here in July the temperature exceeds 30[degrees]C nine times during ten successive years with the probability of 36%. In each ten-year period this temperature is reached at least five times. In Tallinn, where the maritime conditions prevail, the probability that the temperature rises above 30[degrees]C at least once during ten successive years is practically similar to that in Tartu, but the difference is in the most probable number of events: in Tartu the probability is the highest that it happens nine times, in Tallinn three times. In January, the temperature in Tartu falls below -30[degrees]C during ten successive years three times with the probability of 27%. In Tallinn, this probability is only 3%.

The cases of very dangerous heat (three consecutive days with daily maximum above 30[degrees]C) are generally rare (Table 5). Only four such events and only in July-August took place in Tallinn during 92 years and 13 (in June-July) in Parnu during 96 years. In contrast, in Tartu as many as 13 such events took place before the year 1920 and 19 after that year. Mostly such hot periods occurred in July and August, but sometimes also in June and in 1906 even in May. Heat is extremely dangerous when the night between hot days is too warm. The occurrence of such events is reflected as the number of tropical nights (daily minimum higher than 20[degrees]C) during dangerous hot periods (Table 5).

Interestingly, dangerous heat conditions usually did not occur simultaneously at all measurement sites. The most serious heat periods were at the end of July 2003 when a heat period was recorded at all three measurement sites. In Parnu the dangerous situation lasted for five days separated by five tropical nights. At that time (until the end of 2004) the measurement site in Parnu was in the middle of the town, but in July of 2010 when very hot periods were detected in all three sites again, the measurements in Parnu were performed already at the airport.

Very dangerous cold, when the daily minimum temperature falls below -30[degrees]C during at least three consecutive days, never occurred in Tallinn and was recorded only once in Parnu (9-12 January 1987). However, in Tartu nine cases were detected, the longest lasted for nine days: from 5 January to 13 January 1987.


As the events to which the Estonian Weather Service refers as very dangerous situations are very rare, we make an attempt to find a more suitable definition of the heat and cold waves. According to the practice recommended by the ETCCDI, we applied more flexible thresholds to determine (extremely) cold nights, warm days, and heat and cold waves (Klein Tank et al., 2009):

* cold night: temperature lower than 10th percentile of daily minimal temperatures calculated for a 5-day window centred on each calendar day in 1961-1990;

* warm day: temperature higher than 90th percentile of daily maximal temperatures calculated for a 5-day window centred on each calendar day in 1961-1990;

* cold wave: six consecutive cold nights;

* heat wave: six consecutive warm days;

* tropical night: daily minimum higher than 20[degrees]C.

For Tallinn (Fig. 2) as well as for the other two sites (not shown) these thresholds for the detection of warm days and cold nights do not appear to be well suited for practical detection of the warm and cold waves, especially for the cold wave in winter when day-to-day variability of the threshold is remarkable. It may happen that the same minimal temperature during several days of a certain year is labelled differently for two consecutive days. For instance, -21.5[degrees]C is below the threshold on 10 February (cold) and above it on 11 February (not cold enough).

To avoid such shortcomings, these percentile thresholds were approximated by means of Fourier series


where [theta] is threshold temperature and t is the Julian day of the year (incl. 29 February). The Fourier coefficients are shown in Table 6.

Approximation (2) was used to detect heat waves in summer (June, July, and August) and cold waves in winter (December, January, and February) according to the ETCCDI practice.

The use of the current practice (the fixed threshold of [+ or -] 30[degrees]C in three consecutive days) is clearly problematic in Estonia as the data in Table 7 suggest.

It is sensible to use a site-specific ETCCDI method that is much more flexible and, most importantly, is adaptable in the sense that it is able to detect also periods throughout the year that are warmer and/or colder than normal.


The probability that the daily minimum temperature is below -30[degrees]C is the highest in January. Such low temperatures occur almost surely at least once (and most probably three times) during ten successive years in Tartu and with the probability of 53% in Tallinn. The probability that the daily maximum is above 30[degrees]C is the highest in July when such temperatures almost surely occur at least once during each ten successive years at all three stations. In Tallinn the probability that such maxima occur exactly three times during ten successive years is 26%, but in Tartu they normally occur at least five times during any ten successive years. This knowledge could be regarded as a climatological prediction and could be used as a benchmark to estimate the skill of various forecasts.

The current standard description of very dangerous warm and cold situations in Estonia is associated with daily maximum temperatures above 30[degrees]C or daily minimum temperatures below--30[degrees]C during at least three consecutive days. Such events are rare, especially in Tallinn. An extremely dangerous cold event took place in January 1987 when the temperature was -30[degrees]C or lower during a 14-day period in Tartu and a 3-day period in Parnu. An extremely dangerous heat was recorded in July 2003 and in July 2010 at all three stations. Then the daily maxima exceeded 30[degrees]C and the days were separated by some warm nights when the temperature did not fall below 20[degrees]C.

The ETCCDI method is eventually more practical to establish site-specific and more flexible thresholds and to detect heat and cold waves. In particular, the ETCCDI thresholds approximated by means of Fourier series seem to be more suitable for practical application, as the large day-to-day differences are removed.

doi: 10.3176/proc.2015.4.02


The meteorological data were drawn from the archives of the Estonian Environment Agency. The research was supported by institutional research funding IUT 19-6 of the Estonian Ministry of Education and Research.


Estonian Weather Service. ilmatarkus/kasulik-teada/hoiatuste-kriteeriumid/ (accessed 08.04.2015).

Frich, P., Alexander, L. V., Della-Marta, P., Gleason, B., Haylock, M., Klein Tank, A. M. G., and Peterson, T. 2002. Observed coherent changes in climatic extremes during the second half of the twentieth century. Clim. Res., 19, 193-212.

Garcia-Cueto, O. R., Cavazos, M. T., de Grau, P., and Santillan-Soto, N. 2014 Analysis and modeling of extreme temperatures in several cities in northwestern Mexico under climate change conditions. Theor. Appl. Climatol., 116, 211-225.

Hamill, T. M. and Juras, J. 2006. Measuring forecast skill: Is it real skill or is it the varying climatology? Q. J. Roy. Meteor. Soc., 132, 2905-2923.

Jaagus, J., Briede, A., Rimkus, E., and Remm, K. 2014. Variability and trends in daily minimum and maximum temperatures and in the diurnal temperature range in Lithuania, Latvia and Estonia in 1951-2010. Theor. Appl. Climatol., 118, 57-68.

Keevallik, S. and Vint, K. 2012. Influence of changes in the station location and measurement routine on the homogeneity of the temperature, wind speed and precipitation time series. Estonian J. Eng., 18, 302-313.

Keevallik, S., Spirina, N., Sula, E.-M., and Vau, I. 2014. Statistics of different public forecast products of temperature and precipitation in Estonia. Proc. Estonian Acad. Sci, 63, 174-182.

Klein Tank, A. M. G., Zwiers, F. W., and Zhang, X. 2009. Guidelines on Analysis of Extremes in a Changing Climate in Support of Informed Decisions for Adaptation. WMO, Geneva (WCDMP No. 72--WMO/TD No. 1500).

Meehl, G. A. and Tebaldi, C. 2004. More intense, more frequent, and longer lasting heat waves in the 21st century. Science, 305, 994-997.

Robinson, P. J. 2001. On the definition of heat wave. J. Appl. Meteorol., 40, 762-775.

Tarand, A. 2003. Tallinnas moodetud ohutemperatuuri aegrida [Time series of observed air temperature in Tallinn]. Publ. Geophys. Univ. Tartu., 93, 25-36 (in Estonian).

Unkasevic, M. and Tosic, I. 2015. Seasonal analysis of cold and heat waves in Serbia during the period 19492012. Theor. Appl. Climatol., 120, 29-40.

Van den Brink, H. W. and Konnen, G. P. 2011. Estimating 10 000-year return values from short time series. Int. J. Climatol., 31, 115-126.

Van den Brink, H. W., Konnen, G. P., Opsteegh, J. D., Van Oldenborgh, G. J., and Burgers, G. 2005. Estimating return periods of extreme events from ECMWF seasonal forecast ensembles. Int. J. Climatol., 25, 1345-1354.

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Sirje Keevallik (a) * and Kairi Vint (b)

(a) Marine Systems Institute at Tallinn University of Technology, Akadeemia tee 15 a, 12618 Tallinn, Estonia (b) Estonian Environment Agency, Mustamae tee 33, 10616 Tallinn, Estonia

Received 7 January 2015, revised 7 May 2015, accepted 21 September 2015, available online 26 November 2015

* Corresponding author,

Table 1. Missing values in the series of daily maximum and minimum

Station           Missing maxima                 Missing minima

Tallinn   1-2 Aug 1938                      1 Jun-30 Sep 1941 (WWII)
          1 Jun-30 Sep 1941 (WWII)          1-30 Sep 1944 (WWII)
          1-30 Sep 1944 (WWII)              17 Sep 1945
          1-31 Mar 1946, 11 Apr 1946, 18    1 Feb-31 Jul 1946
            Apr 1946, 30 Apr 1946, 17 May
          1946, 21 May 1946, 24-26 May      1 Sep 2003
            1946, 28-31 Jul 1946
          1 Sep 2003                        26-27 Oct 2005
          26 Oct 2005, 27 Oct 2005

Tartu     1 Mar 1894, 15 Mar 1894, 28       1 Aug-31 Sep 1944 (WWII)
            Jan 1895, 5 Feb 1895
          8-10 Feb 1895, 13-14 Feb 1895,    1-31 May 1951
            17 Feb 1895, 23 Feb 1895
          1 Aug-30 Sep 1944 (WWII)          11-29 Feb 1952
          1-31 May 1951                     1 Sep 2003, 11 Oct 2003,
          1 Sep 2003, 11 Oct 2003,            17 Oct 2003
            17 Oct 2003

Parnu     1 Jan 1878-31 Dec 1914            1-19 Aug 1878
          20 Aug-31 Oct 1915 (WWI)          31 Aug 1880
          1 Jun 1917-31 Dec 1919 (WWI)      31 May 1882
          5-10 Feb 1924                     1 Jan 1883-31 Dec 1886
          1-31 Jan 1942 (WWII)              1 Jul-23 Aug 1893
          1 Sep-31 Dec 1944 (WWII)          1-30 Jun 1903
          1 Mar-31 May 1945 (WWII)          20 Aug-31 Oct 1915 (WWI)
          1-31 Jul 1945                     1 Jun 1917-31 Dec 1919
                                            1 Mar-31 May 1945 (WWII)
                                            1-31 Jul 1945

Table 2. Probability of the occurrence p (%) of daily maxima above
30 [degrees]C in summer and daily minima below -30[degrees]C in

            Summer, t > 30 [degrees]C

Month      Tallinn   Tartu   Parnu

June           4.3    28.9    17.5
July          33.3    86.0    43.7
August         6.4    32.5    13.4

Month       Winter, t < - 30[degrees]C

           Tallinn   Tartu   Parnu

December       1.0     5.0     1.6
January        7.4    31.4    10.7
February       4.2    20.0     7.6

Table 3. Probability (%) that daily maximum temperature is above
30[degrees]C in 10 successive years according to Table 2 and Eq. (1)

                      2       3       4       5       6        7
              Once   times   times   times   times   times   times

  June         29      6       1
  July          9     20      26      22      13       5       2
  August       35     11       2
  May           8
  June         13     25      27      19       9       3       1
  July                                         1       3      12
  August        9     20      26      22      13       5       1
  September     8
  May          32      8       1
  June         31     30      17       6       2
  July         2       9      18      24      23      15       7
  August       37     26      11       3       1

               8       9       10     At least
              times   times   times     once

  June                                 36
  July                                 98
  August                               48
  May                                   8
  June                                 97
  July         26      36      22     100
  August                               98
  September                             8
  May                                  41
  June                                 85
  July          2                     100
  August                               76

Table 4. Probability (%) that daily minimum temperature is below -
30[degrees]C in 10 successive years according to Table 2 and Eq. (1)

                      2       3       4       5       6       7
             Once   times   times   times   times   times   times

  December    10
  January     37     13       3
  February    29      6       1
  December    31      7       1
  January     11     22      27      21      12       4       1
  February    27     30      20       9       3       1
  December    13      1
  January     39     21       7       1
  February    37     14       3

             At least

  December      10
  January       53
  February      35
  December      40
  January       98
  February      89
  December      14
  January       68
  February      55

Table 5. Periods of dangerous heat (at least three consecutive days
with daily maximum above 30[degrees]C). The number of tropical
nights during these periods is shown in brackets. For better
comparison the data for Tartu are presented separately before and
after 1920

Tallinn          Tartu before 1920     Tartu since 1920

                 6-10 Jun 1896        3-5 Jul 1920 (1)
                 1-3 Aug 1896 (1)     25-28 Jul 1925
                 22-25 Aug 1900
                 13-18 Jul 1901       25-27 Jul 1932
                 26-31 Jul 1901       9-12 Jul 1933
                 26-28 Jun 1905       24-26 Jul 1935
                 17-19 May 1906
                 19-21 Jul 1908       14-16 Aug 1939
                 8-10 Aug 1912        24-26 Jun 1940
                 8-13 Jul 1914        10-15 Jul 1941 (4)
                 20-24 Jul 1914
                 19-22 Jun 1917 (2)
                 3-5 Jul 1918         24-26 Jul 1963
                                      5-7 Jul 1973

                                      13-16 Jul 1994
28-30 Jul 1994                        28-30 Jul 1994
26-28 Aug 1997                        13-15 Jul 1999 (1)
                                      15-18 Jul 2001
                                      30 Jul-1 Aug 2002

28-31 Jul                             28-30 Jul 2003 (1)
2003 (3)                              7-10 Jul 2006

12-15 Jul                             11-16 Jul 2010 (3)
2010 (2)                              25-28 Jul 2010 (3)

Tallinn                  Parnu

                 17-19 Jul 1927 (1)

                 17-19 Jun 1939

                 8-10 Jun 1956 (1)
                 25-27 Jul 1959
                 27-30 Jun 1972
                 5-7 Jul 1973
                 12-14 Jun 1977 (1)
                 9-11 Jul 1983

28-30 Jul 1994
26-28 Aug 1997   30 Jun-2 Jul 1997 (2)

                 30 Jul-1 Aug 2002
                 15-17 Jul 2003 (1)
28-31 Jul        28 Jul-1 Aug 2003 (5)
2003 (3)

12-15 Jul        12-15 Jul 2010 (1)
2010 (2)

Table 6. Fourier coefficients of the threshold temperatures

            Threshold for heat wave       Threshold for cold wave

            Tallinn   Tartu     Parnu     Tallinn   Tartu     Parnu

[P.sub.0]    13.764    14.493    13.553    -4.036    -6.118    -3.606
[P.sub.1]    -3.012    -2.811    -2.972    -5.756    -5.782    -5.954
[P.sub.2]   -11.828   -12.909   -12.479   -12.373   -13.634   -13.225
[P.sub.3]    -0.670    -0.715    -0.883    -1.447    -1.828    -1.492
[P.sub.4]     1.057     0.518     1.239    -0.234    -0.945    -0.412
[P.sub.5]     0.262     0.479     0.261     0.507     0.521     0.562
[P.sub.6]     -0.24    -0.380    -0.451     0.126    -0.047    -0.071

Table 7. Number of heat waves and cold waves according to
the method of the ETCCDI approximated by means of Fourier
series and the number of cases (in brackets) when the fixed
thresholds of [+ or -] 30[degrees]C were used

Site                Heat waves   Cold waves

Tallinn             20 (4)       21 (0)
Tartu before 1920   12 (12)       1 (0)
  since 1920        30 (19)      17 (9)
Parnu before 1920    0           10 (0)
  since 1920        37 (13)      19 (1)
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Title Annotation:CLIMATOLOGY
Author:Keevallik, Sirje; Vint, Kairi
Publication:Proceedings of the Estonian Academy of Sciences
Article Type:Report
Geographic Code:4EXES
Date:Dec 1, 2015
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