Climatology of precipitation extremes in Estonia using the method of
moving precipitation totals
Tiina Tammets
Estonian Meteorological and Hydrological Institute
Jaak Jaagus *
Department of Geography, Institute of Ecology and Earth Sciences, University of Tartu
Abstract
A method of moving precipitation totals is described and applied for the analysis of precipitation
extremes in Estonia. Numbers of extremely wet and extremely dry days other indices of
precipitation extremes were calculated using the daily precipitation data measured at 51 stations
over Estonia during 1957–2009. Mean regularities of spatial and seasonal distribution were
determined. Long-term changes were detected using Sen’s method and Mann-Kendall test. The
highest risk of heavy precipitation is in the regions of higher mean precipitation on the uplands,
and on the belt of higher precipitation in the western part of continental Estonia. Wet spells have
their sharp maxima in July and August. The highest risk of droughts is observed in the coastal
regions of West Estonia. In the coastal area, droughts appear mostly in the first half of summer
while in the eastern Estonia, they are usually observed during the second half of summer.
Statistically significant increasing trends were, first of all, found in the time series of the indices of
extreme precipitation all in winter. In summer and autumn, trends existed in some indices but in
spring there were no trends at all. Consequently, extreme precipitation events have become more
frequent and intense. There were no trends in time series of dryness indices in Estonia in 1957–
2009.
* - corresponding author, jaak.jaagus@ut.ee, tel. +3727375824, fax +3727375825
1
1. Introduction
Precipitation is the climatic variable that has the highest variability in space and time. Therefore,
precipitation extremes – continuing periods with little or without any precipitation leading to
droughts, or heavy rainfall-induced flash floods – are related to the severest damages to human
activities in nearly all regions of the world. That is why the analysis of extreme precipitation and
drought events and their long-term trends has become an important topic in climatological
research.
An increase in the number of extreme precipitation events has been noticed, and proposed to be
generally connected with possible climate warming in the future (Groisman et al. 2005). Analyses
of changes in climatic extremes during the second half of the 20th century revealed a significant
increase in the amount of precipitation derived from wet spells and numerous heavy rainfall events
(Frich et al. 2002). At the same time, a significant decreasing trend was noticed in global series of
the annual maximum of consecutive dry days (CDD). Similar trends have been detected by many
local studies (Karl and Knight 1998; Stone et al. 2000; Osborn et al. 2000; Zhang et al. 2001; Frei
and Schär 2001; Alpert et al. 2002; Kiktev et al. 2003; Sen Roy and Balling 2004; Schmidli and
Frei 2005). An increasing frequency of droughts is also evident in different regions of the world
(Dai et al. 2004; Zou et al. 2005; Groisman et al. 2007; Balling and Goodrich 2010).
A detailed overview of studies in the precipitation extremes, droughts and wet spells in the
Baltic Sea region has been presented by the BACC Author Team (2008). The CDD trends are
mostly insignificant in this region (Frich et al. 2002; Haylock and Goodess 2004). A slightly
decreasing insignificant trend of CDD was revealed in Norway and Sweden (Førland 2000;
Alexandersson 2002), while a positive trend was detected in Germany for the summer season
(Klein Tank and Können 2003). A comprehensive overview of trends in temperature and
precipitation extremes were given within the EU project EMULATE (Chen et al. 2006).
Different indices of heavy rainfall events indicate positive tendencies, but also no changes, in
the Baltic Sea region during the second half of the 20th century. The number of days with
precipitation ≥10 mm has increased at German mountain stations and in western Norway (Heino et
al. 1999). The maximum number of consecutive wet days has increased at many stations over the
Scandinavian Peninsula during 1961-2004 (Achberger and Chen 2006). The simple daily intensity
index (SDII) increased significantly in central and western Europe in winter in 1921-1999 (Moberg
and Jones 2005). However, none of these studies used data from the territory of Estonia.
Previous results have been confirmed by recent new investigations. Based on changes in the
NAO from the 1960s to 1990s, and using simulation groups from a general circulation model
(HadCM3), large changes were found in the frequency of the 90th percentile precipitation events
over Europe in winter (Scaife et al. 2008). This would lead to growing occurrence of heavy
precipitation over northern Europe and lessening occurrence over southern Europe during high
NAO periods.
Zolina et al. (2009) obtained mostly positive trends of daily precipitation and precipitation totals
at 116 stations in different regions of Europe, including the Baltic Sea region, during 1950–2000.
The positive trends were characteristic for winter and spring while the negative trends occurred
mostly in summer and, in some cases, in autumn. Wet periods with the daily precipitation R>1 mm
have become longer over most of Europe by about 15-20% during 1950–2008 (Zolina et al. 2010).
The lengthening of wet periods was not caused by an increase in the annual total number of wet
days. Becoming longer, wet periods in Europe are now characterised by more abundant
precipitation. Heavy precipitation events during the last two decades have much more frequently
become associated with longer wet spells and intensified in comparison with the 1950s and 1960s
(Zolina 2011). An increasing trend was detected in the 95th and 99th percentiles in winter, spring
and autumn, and a negative trend in summer in northern Germany in 1950–2004 (Zolina et al.
2008).
2
Positive trends were detected for the number of wet spells and days with precipitation at five
stations in Poland during the second half of the 20th century, while negative trends were revealed
for mean precipitation during a given spell (Wibig 2009). Positive as well as negative trends in the
indices of precipitation extremes were detected at 48 synoptic stations in Poland during 1951–
2006; however, the decreasing trends were prevailing (Łupikasza 2010). The highest number of
decreasing trends was revealed in summer, while the number of increasing trends was more
pronounced in spring and autumn.
Increasing trends in time series of the number of days with heavy precipitation (above 10 mm)
and of the percentage of heavy precipitation in the total annual amount were detected in Lithuania
during 1961-2008 (Rimkus et al. 2011). This tendency is especially clear in summer months when
an increase in precipitation extremity can be observed on the background of neutral or negative
tendencies in the total summer precipitation. A significant increase in the number of days with
heavy precipitation (≥10 mm) was also observed in Latvia during 1924-2008 (Avotniece et al
2010). Statistically significant trends in two drought indices were not detected for Vilnius,
Lithuania, in 1891–2010; however, a small decrease in dryness was still observed (Valiukas 2011).
Although Estonia is characterised by a humid climate where annual precipitation exceeds
annual evaporation, dry periods occur rather often during the warm half-year. They cause severe
damages to human activities – loss of agricultural production, water shortage, forest fires,
expanding of different diseases, etc. Flash floods caused by heavy rainfall and continuing wet
periods pose serious problems for agriculture, transport and everyday life of local residents.
Estonia is located on the eastern coast of the Baltic Sea between 57.5 and 59.5 degrees north.
Climatically, it lies in the transition zone between the area of rather maritime climate on the islands
and the coast of the Baltic Sea in the west, and the area of much more continental climate in the
south-east and east. Precipitation regime is similar to that of the neighbouring regions with
maximum rainfall in summer and autumn and minimum in winter and spring. The annual mean
amount of precipitation in Estonia varies between 550 mm in the coastal zone and up to 750 mm
on the windward slopes of the uplands (Jaagus and Tarand 1988).
Time series analysis has revealed an increasing trend of precipitation in winter and autumn
(Jaagus 1996). Clear periodical fluctuations of 50-60, 25-30 and 6-7 years have been detected for
annual precipitation in Estonia since 1866 (Jaagus 1992). Relationships between atmospheric
circulation indices and precipitation totals are the strongest in winter and spring (Keevallik et al.
1999; Keevallik 2003; Jaagus 2006). The dependence of precipitation pattern on local landscape
characteristics in the three Baltic countries is analysed using data mining tools (Jaagus et al. 2010;
Remm et al. 2011).
Extreme precipitation events in Estonia were analysed in relation to different types of largescale atmospheric circulation (Grosswetterlagen) (Merilain and Post 2006) and cyclones of
different trajectories (Mätlik and Post 2008). It was found that more than 25% of all heavy rainfall
events (at least 50 mm per 24 hours) in Estonia have been caused by the southern cyclones
originated in the region of the Black and Mediterranean Seas. The frequency of the 95th and 99th
percentile daily precipitation events at 40 stations in Estonia has increased significantly during
1961–2008 (Päädam and Post 2011).
The main disadvantage of the studies on extreme precipitation and extreme dry spells is the
calculation of characteristics of extremes in discrete time intervals (seasons, months, ten-day
periods, days etc.). To estimate water content in the soil, it is not so important to know how much
it has rained during the observed period but how much it had rained before that period. In other
words, for many purposes it is essential not to show how much it rains in a day but to show how
much it has rained till this day. Following this ideology, the first author of the current article has
proposed a methodology for analysing precipitation extremes by using moving precipitation totals
(Tammets 2007; 2010). Using this method, wet and dry days have been defined and their numbers
are analysed for Estonia. A day is considered as extremely wet when the moving total of
3
precipitation is at least 100 mm on ten successive days leading up to this day and as extremely dry
when there was no precipitation during the successive twenty days till the observed day. An
increase in the number of extreme (wet and dry) days was distinguished during 1957-2006.
To present the minimum and maximum of precipitation totals in long time series of a station in
any time period, which has been measured by days, months or years, special relationships were
built (Tammets 2010).
This study is the continuation of a previous one. Its main objectives are to compare the usual
characteristics of precipitation extremes with the number of extremely dry and wet days; to
develop a method for characterising the climatology of extreme precipitation totals for any time
periods (the number of following days, months or years using moving totals); to detect the most
severe wet and dry spells in Estonia during the last 50 years; to analyse trends in the frequency of
extremely wet and dry periods using different indices and to compare the results.
2. Data and method
Daily precipitation data at 51 stations (25 meteorological stations and 26 precipitation stations)
over Estonia (Figure 1) during 53 years (1957-2009) was used as the initial data in this study. The
stations were selected according to the quality and continuity of time series. There were only very
few gaps in the data series, which were filled by measured data from a neighbouring station
located in the similar landscape conditions and having the highest correlation. There have been
relocations of the measuring sites at the Tallinn, Tartu, Narva and Pärnu stations, which may cause
inhomogeneities in the data series. It is difficult to detect the influence of data inhomogeneity on
the estimates of precipitation extremes. Therefore, the time series used are considered reliable.
Fig. 1. Location map of precipitation stations in Estonia used in this study
4
All the daily precipitation totals are registered at 06 p.m. GMT. The only exception was the
period from 11 February 2005 until 30 April 2009 when the measurements in the meteorological
stations were made in the morning of the next day at 06 a.m. GMT. The precipitation
measurements were made manually using Tretyakov gauges. Since 1966, wetting corrections of
0.2 mm for liquid and 0.1 mm for solid precipitation were added if at least 0.1 mm had been
measured. Some gaps in 2009 were filled with the data from an automatic weather station MILOS
520, which are less reliable. The VRG type automatic precipitation gauge was applied in
Kuressaare since 1 January 2008 and in Heltermaa since 1 May 2009.
Following the method of moving totals, a day is an extreme day if the amount of precipitation
up to this day has been too small or too large. The preliminary task, when looking at dry or wet
spells, is to define a dry and a wet day. The simplest definition of a dry day is zero rainfall, and a
wet day is the day with a precipitation threshold, depending on climate conditions of observed
area.
An extremely wet or a dry day is a day with too much or too few precipitation in a period,
which lasts n days and ends on the observed day. Limits of the precipitation amount M and the
number of subsequent days n in the observed period depend on the study object, which could be an
agricultural field, a river basin, etc. In agro-meteorological studies, these limits depend on the plant
species, the state of vegetation, soil conditions, air temperature, humidity, etc. Counting of the
moving totals of precipitation continues throughout the whole observation period without
separating time into months or years. To point out the meteorological, agro-meteorological,
hydrological or socio-economical drought or flooding conditions, indicators should be calculated
for the specified numbers of days n and thresholds M (Tammets 2007; 2010). A similar idea for
describing drought conditions was applied to work out the concept of effective precipitation (Byun
and Wilhite 1998; Kim and Byun 2009).
Mathematically, the sequence of moving totals (averages){sj(n),1 £ j £ N-n+1} is derived from
a sequence {ai, 1 £ i £ N} obtained by taking the totals (averages) of the subsequent n terms:
i+n− 1
sj(n)= ∑
j=i
aj (by moving averages sj(n)=
1
n
i+n− 1
∑
j=i
aj), , where N is the total number of days in
the precipitation time series and n the number of days through which the moving average is
calculated. We find extremely dry and extremely wet days after calculating sj(n) with the time
period n for each day i in precipitation time series choosing the days with values of sj(n) that are
smaller or larger than the given threshold M (Fig. 2).
In different studies and climate conditions, instead of the daily time step, a monthly or even an
annual time step could be used for calculating the moving totals of precipitation. Soil moisture
conditions respond to precipitation anomalies in a relatively short time. Groundwater, stream flow
and reservoir storage reflect the longer-term precipitation anomalies. Extreme precipitation totals
for a year and a longer period are one of the essential factors of the water balance in the region.
To find the extreme precipitation totals for any number of days or months in the observed
period, graphs were built with the y-axis showing the maximum and minimum of the moving total
of precipitation in dependence on the number of days or months in the calculated period, shown on
the x-axis (Fig. 3 and 4) (Tammets 2010). The highest curve on the daily graph (Fig. 3) shows
values of the highest maximum, the second high curve – of the lowest maximum precipitation of
all studied stations; the lowest curve shows values of the lowest minimum and the second curve
above it – of the highest minimum of precipitation in dependence on n (number of days) in the
observed period. These graphs were calculated over 51 Estonian meteorological stations during
1957–2009 and they can be used as one of the characteristics of the precipitation regime for
Estonia. This method allows to analyse the precipitation conditions in any period. After calculating
of moving totals through the time series, the period under observation should be separated and
statistically analysed.
5
if there are no
precipitation
on a day and
previous n
days the day
has been
counted as a
extremely dry
day (EDD)
days
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
days
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
17
21
21
22
23
if the total of
precipitation on a
day and previous
n days is M mm
and more the day
has been counted
as a extremely
wet day (EWD)
18
19
20
22
23
Fig. 2. The scheme for the calculation of extremely dry days and extremely wet days using a
moving precipitation total of the preceding days. In this example, n = 20 in case of dry days and n
= 10 in case of wet days
Some limits for defining extreme weather conditions in Estonia have been given in agrometeorological studies (Kivi 1998). Extremely wet conditions are observed when the mean daily
precipitation amount is equal to or larger than 10 mm during 10 consecutive days (n = 10). We
calculate the sequences si (10) giving the moving total for 10-day periods. If si >= 100 mm, the last
day of the period is counted as an extremely wet day (EWD). Extremely dry conditions for field
plants emerge if there are no precipitation in the duration of 20 consecutive days ( n = 20). If si
(20) = 0, then the last day of the period is counted as an extremely dry day (EDD). Extremely wet
days and also extremely dry days frequently follow each other. In such case, the number of EWDs
or the number of EDDs show the intensity of a wet or a dry spell.
To estimate differences between the number of extremely dry days with the amount of
precipitation of 0 mm and 1 mm (maximum error measurements with Tretyakov gauge for 20
days) we also calculated the number of extremely dry days with the precipitation amount of only 1
mm (EDD1) in 20 consecutive days ( n = 20).
Annual and seasonal numbers of extremely dry and wet days (EDD, EDD1, EWD) were
calculated for each of the 51 stations during the period 1957-2009. To analyse the inter-annual
variability of the average number of wet and dry days EDD and EWD together, the relative
numbers of dry and wet days were calculated by dividing the number of EDDs and EWDs in a
year by their average in 1957-2009. We also calculated the relative numbers of extremely wet and
dry days for every season: spring (MAM), summer (JJA), autumn (SON) and winter (DJF).
6
total precipitation, mm
1000
absolute maximum of stations
900
lowest maximum of stations
800
absolute minimum of stations
700
highest minimum of stations
600
500
400
300
200
100
0
0
20
40
60
80
100
120
140
160
180
200
220
number of days
4 years
Fig. 3. Maximum and minimum totals of precipitation at Estonian meteorological stations in 19572009 in dependence on the number of days in the period
4000
absolute minimum of stations
absolute maximum of stations
3000
2 years
lowest maximum of stations
2500
2000
1 year
precipiation total, mm
3 years
highest minimum of stations
3500
1500
1000
500
0
0
3
6
9
12
15
18
21
24
27
30
33
36
39
42
45
48
51
number of months
Fig. 4. Maximum and minimum totals of precipitation at Estonian meteorological stations in 19572009 in dependence on the number of months in the period
7
Annual, seasonal and monthly precipitation totals are used to characterise the general
precipitation regime in Estonia. Numbers of extremely wet days (EWD) and extremely dry days
(EDD) in 1957-2009 were compared with other more frequently used indices of precipitation
extremes. In this study we used the following indices:
Wet conditions
SDII – simple daily intensity index: annual total precipitation divided by the number of days with
R ≥ 1 mm (mm/wet day);
CWD – maximum number of consecutive wet days R ≥ 1 mm (days);
R10mm – number of heavy precipitation days R ≥ 10 mm (days);
R20mm – number of heavy precipitation days R ≥ 20 mm (days);
RX1day – the highest 1-day precipitation amount (mm);
RX5day – the highest 5-day precipitation amount (mm);
R95p – days with RR> 95th percentile daily amount (R ≥ 1 mm);
R99p – days with RR> 99th percentile daily amount (R ≥ 1 mm).
Dry conditions
CDD – maximum number of consecutive dry days R < 1 mm (days);
XCDD – maximum number of consecutive dry days R = 0 mm (days);
PDD – probability of a dry day following a dry day (mean dry-day persistence);
DSMEA1 - mean dry spell length with R < 1mm (days);
DSMEA0 – mean dry spell length with R = 0 mm (days).
These indices of precipitation extremes were calculated for every station by years and seasons,
and their mean values for 1957-2009 were found. The absolute maximum and minimum values of
the indices with the corresponding year and station name were determined. The maximum and
minimum for years (mean of stations) and maximum and minimum for separate stations were
calculated as well (Tables 1, 2, 3). Seasonal values of R99p and R95p were calculated using annual
limits (Table 1). Maps for the indices of precipitation extremes were drawn to analyse the spatial
and annual distribution of extreme wet and dry periods in Estonia.
Precipitation totals, as well as many indices of precipitation extremes are not normally
distributed. Therefore, Sen’s method and Mann-Kendall test (Salmi et al 2002) were used for trend
analysis. Trends are expressed in millimetres per decade. Trend time series of the indices of
precipitation extremes are presented in Tables 1, 2 and 3, where statistically significant trends are
marked in bold.
3. Results
3.1. Mean precipitation regime in Estonia
Before analysing the precipitation extremes we describe the mean precipitation regime based on
the data of 51 stations in 1957–2009, used in this study (Table 1). The spatio-temporal variability
of precipitation is very high on the territory of Estonia (Fig. 5a). Variability of the indices of
precipitation extremes is even higher. This is clearly demonstrated in Table 1, where mean indices
of the 51 stations over years 1957–2009, the annual maxima of the stations’ mean values, their
changes by trend, and the absolute maxima at single stations with the years of the corresponding
maxima are presented.
8
Table 1. Mean values of precipitation totals and mean indices of extremely wet conditions at 51
stations in Estonia during 1957–2009, their maximum values and the absolute maxima of the
station data (mm), years of the corresponding maxima and trends (per decade) of the stations’
mean values. Statistically significant changes at p<0.05 level are typed in bold
Year
Winter
Spring
Summer
Autumn
Index
PREC
EWD
SDII
CWD
R10mm
R20mm
RX1day
RX5day
R95p
R99p
PREC
SDII
CWD
R10mm
R20mm
RX1day
RX5day
R95p
R99p
PREC
SDII
CWD
R10mm
R20mm
RX1day
RX5day
R95p
R99p
PREC
EWD
SDII
CWD
R10mm
R20mm
RX1day
RX5day
R95p
R99p
PREC
EWD
SDII
CWD
Mean
649
0.83
5.42
7.53
14.8
2.85
34.2
59.3
6.24
1.23
128
4.03
5.53
1.55
0.07
12.7
26.9
0.34
0.01
108
4.72
4.26
1.97
0.26
16.0
29.1
0.68
0.09
215
0.72
7.33
5.07
6.47
1.87
31.6
54.2
3.44
0.91
196
0.11
5.54
6.25
Maximum Year of
Year of
of stations
the
Absolute
the
means
maximum maximum maximum
858
2008
1120
1981
4.7
1978
20
1978
6.28
1978
7.72
1997
9.82
1984
19
5 years
21.5
2001
35
2003
5.49
2008
12
1991
52.5
1987
131
1988
85.6
1987
184
1997
10.6
2008
19
2009
2.55
2008
7
2009
206
1999
320
1990
5.12
1993
7.32
1993
8.20
2007
16
3 years
4.55
1999
11
2 years
0.41
1990
4
2003
18.1
1989
41.3
1978
38.9
2003
80.4
1990
1.27
1999
6
2003
0.08
2004
1
16 years
176
1995
226
1995
6.56
1969
12.2
2005
6.24
1990
12
1986
4.31
1969
9
1983
1.04
1995
4
2 years
29.8
1995
65.4
1998
40.1
1996
88
1999
1.94
1969
5
1977
0.57
1995
3
1983
360
1998
508
1978
3.86
1978
20
1978
8.69
1986
17.5
1997
7.57
2005
15
2 years
11.4
1998
18
1981
3.94
1998
10
1998
49.0
1987
131
1988
81.3
1978
184
1997
6.59
1998
12
2 years
2.12
2008
6
3 years
268
1978
380
1974
0.8
1978
10
1987
7.05
2001
9.41
2001
9.04
1978
19
5 years
9
Trend
25.8
0.13
0.11
0.15
0.93
0.32
0.89
1.53
0.58
0.11
5.8
0.07
0.28
0.15
0.02
0.54
1.6
0.05
0.03
1.1
0.03
0.04
0.02
0.00
0.14
0.54
0.02
0.00
10.2
0.11
0.19
0.12
0.47
0.15
0.86
1.71
0.28
0.06
5.1
0.01
0.12
0.02
R10mm
R20mm
RX1day
RX5day
R95p
R99p
4.81
0.65
21.1
43.1
1.78
0.21
8.76
1.41
27.7
57.4
3.49
0.63
2001
2008
1997
1997
2001
2005
16
7
78.4
141
9
3
2 years
1991
2000
1985
2 years
6 years
0.02
0.09
0.75
1.88
0.14
0.03
Mean spatial distribution of annual precipitation PREC (Fig. 5a) varies between 535 mm
(Kihnu Island) and 732 mm (Mauri, Haanja Upland in South-East Estonia). Lower annual
precipitation is generally typical for coastal stations, and for the coast of Lakes Peipsi and
Võrtsjärv. Higher precipitation can be seen in continental Estonia on the uplands and, especially,
on the meridional zone parallel to the western coast at the distance of 20-100 km from the mean
coastline. The rainiest seasons are summer and autumn while spring is the driest (Table 1). There
are remarkable differences between the coastal regions and the hinterland in the annual curve of
monthly precipitation totals (Fig. 6). Western Estonia is much drier in spring and the first half of
summer than central and eastern Estonia. In the second half of summer and especially in autumn,
western Estonia receives much more precipitation. This can be explained by different thermal
regimes of sea and land surfaces. In spring, sea surface is cold causing a stable air stratification
upon it, which prevents convective air uplift, the formation of clouds and precipitation. Sea surface
warms up during summer, inducing unstable air stratification, convective ascending of the air, and
the formation of clouds and precipitation. Sea surface acts as a warmer surface throughout autumn
and winter.
The highest mean seasonal precipitation of 246 mm was observed in summer in Mauri (Haanja
Upland) while the lowest summer mean values are typical for the coastal stations (155 mm in
Vilsandi). The corresponding mean precipitation amounts in autumn were recorded in Uue-Lõve
(243 mm) and in Praaga (158 mm).
a)
b)
Fig. 5. Mean (a) and maximum (b) annual precipitation in Estonia during 1957-2009 using the data
of 51 meteorological stations
10
90
VÕRU
VILSANDI
80
precipitation, mm
70
60
50
40
30
20
10
0
I
II
III
IV
V
VI
VII
VIII
IX
X
XI
XII
months
Fig. 6. Monthly mean precipitation in Vilsandi and Võru during 1957–2009
3.2. Extremely wet conditions
The highest annual precipitation PREC in Estonia varies between 1120 mm (Tahkuse, 1981) and
759 mm (Kihnu Island, 2001) (Fig. 5b). Absolute maximum of the 12-month moving precipitation
total was 1146 mm in Tahkuse (December 1980 till November 1981) (Fig. 4). 2008 has been the
year with the maximum precipitation amount over Estonia with the average value of 858 mm.
More than 800 mm was observed also in 1981, 1978 and 1990 when many maximum values of
extreme precipitation indices were recorded (Table 1). The highest mean seasonal precipitation
amount was registered in summer 1998 (360 mm).
The absolute maximum totals of precipitation for the winter, spring, summer and autumn
seasons were consequently 320.2 mm (Kuusiku, 1989/1990), 225.9 mm (Tudu, 1995), 507.9 mm
(Praaga, 1978) and 380.3 mm (Uue-Lõve, 1974). The absolute maximum of the 90-days
precipitation, calculated through the moving total over all days and stations during 53 years was
578.7 mm (Fig. 3) in Tõrva from 25 June till 22 September 1978.
Precipitation extremes of Estonia are characterised using the number of extremely wet days
(EWD). A day is estimated as extremely wet if it is the last day of a 10-day period with the
precipitation total of 100 mm or more. In Estonia, such days have been observed only in summer
and autumn during 1957–2009, i.e. from June to November. The highest number of such days was
recorded in July and August (Fig. 7). The mean EWD per year was 0.83 (Table 1) while its annual
maximum (20 days) was observed at Praaga in 1978, calculated in two wet periods – one in 12-22
July and the second one in 10-18 August. In autumn, the maximum number of EWD was twice
lower – 10 in 1987. Spatial distribution of EWD shows that the greatest danger for extremely wet
periods appears in south-eastern and northern Estonia (Fig. 8a). Annual mean EWD varies highly
at different stations. Its maximum was found in northern Estonia (Vanaküla, 1.79) and minimum in
western Estonia (Sõrve, 0.13). Consequently, the frequency of wet spells varies by many times
over the Estonian territory. Annual maximum of EWDs is rather randomly distributed over the
territory (Fig. 8b). Generally, the same pattern as in case of EWDs is also typical for other indices
of precipitation extremes.
11
1.2%
90
EWD
precipitation
80
70
0.8%
60
50
0.6%
40
0.4%
30
precipitation, mm
relative number of days
1.0%
20
0.2%
10
0.0%
0
01
02
03
04
05
06
07
08
09
10
11
12
months
Fig. 7. Monthly mean relative number of extremely wet days (EWDs divided by the total number
of days in the months) and average monthly precipitation (PREC) at the Estonian meteorological
stations in 1957–2009
a)
b)
Fig. 8. Annual mean (a) and maximum (b) number of extremely wet days (EWD)
A simple daily intensity index (SDII) indicates the mean precipitation amount per one wet day
(≥1 mm). Its annual mean value was 5.4 mm/wet day. Lower values were observed in winter and
spring, slightly higher in autumn, and much higher in summer (mean value 7.3 mm/wet day). SDII
is spatially variable with higher values in the western part of the continental Estonia. The absolute
maximum of 17.5 mm per wet day was recorded in Räpina in 1997 during the summer season. The
highest intensity of precipitation was calculated for 1978, when mean SDII of the stations reached
to 6.3 mm/wet day.
The maximum number of consecutive wet days (≥1 mm) (CWD) has the highest mean value not
in summer but in autumn (especially in October), and the lowest in spring (Table 1). The annual
maximum of CWDs at stations varies between 10 and 19 days while it is higher in the hinterland
and lower at the sea coast.
12
The number of wet days is usually described by the number of heavy precipitation days R10mm
(R≥10 mm) and R20mm (R≥20 mm). Their mean numbers were correspondingly 15 and 3 during
the study period. Days with precipitation above 10 mm may occur in Estonia in every month. Very
heavy precipitation days R20mm may also happen in every month, but more often in July and
August. The spatial pattern of R10mm is in a good accord with the patterns of mean precipitation,
as well as of other indices of precipitation extremes (Fig. 9).
Fig. 9. Annual mean number of days with heavy precipitation (R10mm)
The absolute maximum of daily precipitation (RX1day) during the study period (130.8 mm)
was measured in Võru on 3 July 1988, and of 5-day precipitation (RX5day) – 183.5 mm – in
Räpina on 15-19 July 1997. The corresponding mean values of the stations were 34.2 mm and 59.3
m (Table 1). The highest values of RX1day and RX5day were observed in summer and lowest
ones in winter and spring. RX1day maximum in 1957-2009 varied between the stations from 53
mm to 131 mm. The highest values were measured in south-eastern Estonia. The RX5day varied
between 85 and 184 mm and its spatial pattern is similar to the RX1day.
The last year of the study period, 2009, was very specific for the 95th and 99th percentile daily
precipitation (R95p, R99p). Record high values were documented at many stations. The mean
R95p for all stations and all years was 6.24 days and the mean R99p – 1.23 days. The spatial
pattern of these indices was in a good concordance with mean territorial distribution of
precipitation in Estonia. Their maximum values were concentrated in the rainy zone of the western
Estonia.
3.3. Extremely dry conditions
Spatial distribution of annual minimum precipitation in Estonia (Fig. 10) is quite variable but
similar to the mean annual pattern (Fig. 5a). The annual minimum is generally lower in eastern
Estonia than in its western part except the coastal zone. The absolute minimum value of annual
precipitation – 335 mm – was registered in Kunda, North Estonia, in 1964 (Table 2). The absolute
minimum of 12-month moving precipitation total in Estonia was 278 mm (Fig. 4), again in Kunda,
from September 2005 till August 2006. The year 1964 was the driest in the period of 1957–2009
with the minimum of mean annual precipitation of 453 mm over the stations. Minimum values of
precipitation for the winter, spring, summer and autumn seasons were 36 mm (Võru, 1963/1964),
16 mm (Sõrve, 1964), 44 mm (Rohuküla, 1992) and 54 mm (Piigaste, 1988), consequently. The
absolute minimum precipitation found from the moving 90-day totals of precipitation during the
13
study period was only 10 mm (Fig. 3), in Väike-Maarja from 28 December 1971 to 26 March
1972.
Fig. 10. Minimum of annual precipitation in Estonia in 1957-2009
Table 2. Mean values of precipitation and mean minimum precipitation (the stations mean),
absolute minima of the station data (mm), years of the corresponding minima and trends of the
minimum values of the station data (mm per decade) in Estonia during 1957–2009. Statistically
significant changes at p<0.05 level are typed in bold
Year
Winter
Spring
Summer
Autumn
Mean
649
128
108
215
196
Minimum of
stations means
453
66
50
118
116
Year of the
minimum
1964
1964
1974
1983
1958
Absolute
minimum
335
36
16
44
54
Year of the
minimum
1964
1964
1964
1962
1988
Trend
18.1
5.50
0.06
5.83
3.80
Duration of an extremely dry period in Estonia has been characterised by the number of
extremely dry days (EDD). A day is estimated as extremely dry if it is the last day of a 20-day
period without precipitation. These days have occurred in Estonia in all months (Fig. 11). The
maximum number of EDD days is observed in August. A clear minimum in July is highly
remarkable (Fig. 11). Hereby, it should be taken into account that EDD describes a dry day that
follows a 19-day dry period. Therefore, the minimum of EDDs in July implies on less frequent dry
periods during midsummer. This is an interesting feature, which has not yet been detected in other
regions.
The annual mean number of EDDs during the study period was 1.2. The largest dryness risk, i.e.
the highest average number of EDDs was obtained in the north-western part of Estonian mainland
with the mean value above 2 days (maximum 3.2 days in Rohuküla). The least number of dry days
was calculated for Jõhvi and Tartu (0.38, Fig. 12). The highest annual maximum of EDDs was
registered in Mauri in 2002, showing 30 extremely dry days from August and September. The
same year was extremely dry over the whole of Estonia – the mean number of EDDs over all
stations was 12.6 days (Table 3).
14
0.9%
90
relative number of days
0.8%
precipitation
80
0.7%
70
0.6%
60
0.5%
50
0.4%
40
0.3%
30
0.2%
20
0.1%
10
0.0%
precipitation, mm
EDD
0
01
02
03
04
05
06
07
08
09
10
11
12
Fig. 11. Monthly mean relative number of extremely dry days (EDD divided by the total number
of days in the months) and average monthly precipitation totals at Estonian meteorological stations
in 1957–2009
a)
b)
Fig. 12. Annual mean and maximum number of extremely dry days (EDD)
The spatio-temporal distribution of EDD is characterised by the fact that its maximum values in
spring and summer were observed in the coastal region of West Estonia but in autumn in eastern
Estonia. The maximum number of EDD in summer (21 days) occurred twice – in 1997 (Valga) and
in 2002 (Rohuküla). In spring and in autumn, the drought risk has been lower – the maximum
number of EDD in spring was 18 (Kuusiku in 1972 and Räpina in 2009) and in autumn 13 days,
calculated for different stations, mostly in East Estonia (Lüganuse, Tudu, Tudulinna, Mauri) in
2000 and 2002.
If the daily precipitation limits of a dry day are higher – up to 1 mm, the number of extremely
dry days EDD1 increases significantly (Table 3). In this case the mean annual number of EDD1
was 3.9 with the maximum in the spring season – 1.9. The maximum EDD1 of 45 days was
measured at Sõrve in spring 1964.
15
Table 3. Mean indices of extremely dry conditions at 51 stations in Estonia during 1957–2009,
their maximum values and absolute maxima of the station data (mm), years of the corresponding
maxima and trends (per decade) of the stations mean values. The trends are insignificant
Year
Winter
Spring
Summer
Autumn
Index
EDD
EDD1
XCDD
CDD
PDD
DSMEA0
DSMEA1
EDD
EDD1
XCDD
CDD
PDD
DSMEA0
DSMEA1
EDD
EDD1
XCDD
CDD
PDD
DSMEA0
DSMEA1
EDD
EDD1
XCDD
CDD
PDD
DSMEA0
DSMEA1
EDD
EDD1
XCDD
CDD
PDD
DSMEA0
DSMEA1
Mean
1.20
3.92
16.6
22.0
0.34
2.99
4.16
0.02
0.30
7.92
13.6
0.25
2.40
3.84
0.42
1.86
13.4
19.0
0.45
3.70
5.60
0.48
1.18
11.9
15.2
0.40
3.44
4.51
0.28
0.73
10.1
14.3
0.28
2.76
3.73
Maximum of
stations means
12.6
22.3
29.9
39.6
0.46
4.19
5.40
0.20
1.04
14.3
24.9
0.37
3.36
6.11
3.31
13.3
20.5
39.5
0.65
6.93
13.1
10.1
13.9
23.47
24.4
0.61
6.45
7.82
3.31
7.24
20.5
34.6
0.51
4.18
6.17
Year of the Absolute
maximum maximum
2002
30
2002
45
2002
49
1972
71
1959
0.56
1959
5.68
1959
6.75
1983, 1984
6
1986
11
1984
25
1972
44
1996
0.57
1993
3.36
1970
10.8
2006
18
1972
45
2006
46
1972
71
1974
0.79
1974
11.0
1974
31.7
21
2002
2002
28
2002
36
1992
57
1997
0.76
2002
11.2
1969
13.3
1961
13
2002
18
1997
49
2002
52
1993
0.67
2005
7
1961
8.5
Year of the
maximum
2002
1964
2002
1964
1959
1959
1996
1993
1993
1993
1987
1993
1993
1993
1972
1964
1964
1964
1974
1974
1974
2002
1994
2002
2008
1997
1959
1994
2002
1961,2000
2002
2002
1993
1993,1998
1998
Trend
0.09
0.19
0.17
0.22
0.00
0.03
-0.06
0.00
0.00
0.12
0.11
0.00
0.02
-0.07
0.00
0.00
-0.21
-0.19
0.00
0.01
-0.10
0.00
0.00
0.07
-0.19
0.00
0.01
0.01
0.00
0.00
0.28
-0.11
0.00
0.03
0.01
The numbers of consecutive dry days XCDD (R=0 mm) and CDD (R<1 mm) also describe a
deficit of precipitation. Their mean values were 16.6 and 23.0 days, correspondingly. Average
XCDD varied between 13.5 (Jõhvi) and 19.2 (Rohuküla). Among seasons, their highest values are
typical for spring and the lowest for winter. Due to their similar to EDD definition, the maximum
number of consecutive dry days XCDD was also the highest in 2002 at the Mauri station – 49 days
(Table 3). The maximum number of consecutive dry days CDD – 71 – was recorded at the coastal
station of Heltermaa on Hiiumaa Island in February-April 1964. Average CDD was 22 days with
16
the highest values in spring. It varies from 20.5 (Mauri) to 26.1 days (Heltermaa). 2002 was also
the year of the highest average of CDD over the stations. Annual variation (mean of stations) of
CDD varies from 14.6 in 1977 to 39.6 in 1972.
The 51 stations-mean of the dry-day persistence PDD was 0.34 during 1957–2009. This means
that a dry day will occur after a dry day in one third of the cases. The probability of a dry day was
significantly higher in spring and lower in autumn (Table 3). Spatial differences are not large in
Estonia but PDD was higher mostly in the dry coastal zone. The absolute maximum of 0.79 was
observed at Kasari in spring 1974.
Mean dry spell durations DSMEA1 and DSMEA0 were 4.2 and 3.0 days, correspondingly.
They were shorter than the average in autumn and winter, and longer in spring and summer. The
absolute maximum DSMEA1 was registered at Heltermaa in 1976. The spatial pattern of mean dry
spell duration on Fig. 13 is similar to the patterns of other dryness indices in Estonia. The driest
regions are located in the coastal zone (Vihterpalu, Kunda, Virtsu, Rohuküla, Sõrve, Kihnu).
Fig. 13. Annual mean duration of the dry period (DSMEA0).
3.4. Changes in precipitation extremes
Annual precipitation amount PREC has significantly increased at the majority of the Estonian
stations during 1957–2009. The mean trend value averaged by the 51 stations was 25.8 mm per
decade (Table 1). This increase is statistically significant also in the winter season (Fig. 14). In
other seasons, significant trends were observed only at some stations. The most remarkable
increase in precipitation was found in north-eastern Estonia. The trend was weaker at the coastal
stations.
17
1000
900
summer
winter
annual
Linear (annual )
Linear (summer )
Linear (winter )
precipitation, mm
800
700
600
500
400
300
200
100
2008
2005
2002
1999
1996
1993
1990
1987
1984
1981
1978
1975
1972
1969
1966
1963
1960
1957
0
Fig. 14. Time series of annual and seasonal precipitation (mean of the stations) in Estonia during
1957–2009 and their trend lines
The relative number of extreme days, i.e. the sum of relative EWD and EDD has significantly
increased (MK statistic 5.9) in Estonia during 1957–2009 (Fig.15). As a rule, extremely wet days
prevailed in some years and extremely dry days in other years. Extremely dry days dominated in
1957-1977 while the number of extremely wet days was on the highest in 1978-1991. The wettest
years were 1978 and 1987 when the mean relative number of wet days was by 4-6 times higher
than the average of the study period. The number of dry days has substantially risen from the end
of 20th century. The severest drought in 2002 with mean relative number of EDD (10 days) was
observed in August and September.
12
EDD
EWD
10
extreme days /EWD+EDD)
relative number of days
Linear (extreme days /EWD+EDD) )
8
6
4
2
2008
2005
2002
1999
1996
1993
1990
1987
1984
1981
1978
1975
1972
1969
1966
1963
1960
1957
0
Fig. 15. Relative annual number of extreme dry, extreme wet and extreme days in Estonia during
1957-2009, and the trend line of the number of extreme days.
18
Relative values of EDD and EWD separately for each season show the most extreme dry or wet
conditions in Estonia in 1957-2009 (Fig. 16). The highest number of extreme days was observed in
spring and summer of 2002 when extra dry conditions predominated. The presence of extremely
wet and extremely dry conditions together in 1997, 1999, 2006 and 2008 shows great spatial
differences in the precipitation regime over Estonia.
Generally, the indices of wet conditions (excl. CWD) had an increasing trend during 1957–
2009. It means that heavy rainfalls have become more frequent and more intense. The indices of
extreme precipitation had statistically significant increasing trends in all cases in winter, but not at
all in spring. In summer and autumn, some indices had trends, and some had no trends. In both
cases (summer and autumn), trends were seen for SDII and R95p, and no trends for PREC and
CWD (Table 1). At the same time there were no significant trends in the indices of extreme dry
conditions (Table 3).
EDD winter
EDD autumn
35
EDD spring
EWD summer
EDD summer
EWD autumn
30
25
20
15
10
5
2008
2005
2002
1999
1996
1993
1990
1987
1984
1981
1978
1975
1972
1969
1966
1963
1960
1957
0
Fig.16. Relative values of extremely dry and wet days in different seasons in 1957-2009.
4. Discussion and conclusions
Using daily precipitation data measured at 51 stations in Estonia during 1957–2009, the numbers
of extremely dry and extremely wet days were calculated together with other indices of
precipitation extremes. Their spatial and seasonal distribution and long-term trends were analysed.
The main results of these analyses are presented and discussed here.
4.1. Data quality
Generally, the quality of precipitation data is not high. Data inhomogeneity has been discussed
in many works, for example by Heino (1994). Precipitation inhomogeneities in the former USSR
were thoroughly discussed by Groisman et al. (1991). During the time period involved in this
article, the main change in the methodology of precipitation measurement occurred in 1966; since
that time, a wetting correction was added to every measured amount of precipitation. It caused an
upward shift in the time series of precipitation totals. We can assume that the increasing trend in
annual and seasonal precipitation could partly be induced by the wetting correction.
The role of the wetting correction in the extreme precipitation totals is negligible. Therefore, we
consider these time series as homogeneous and not affected by wetting corrections. At the same
19
time, these corrections may significantly increase minimum precipitation and influence the indices
of dryness. As these time series have no trends, we consider the effect of the wetting correction on
the parameters of dry conditions also as not substantial.
Relocations of some stations could have disturbed the homogeneity of data series. We assume
that due to the relocation of the stations, an upward shift in precipitation was possible in Tallinn,
Tartu and Pärnu, and a downward shift in Narva. But we have not noticed any influence on the
time series of precipitation extremes. The possible inhomogeneities have no influence on the
results of data analysis.
4.2. Mean precipitation
The mean pattern of annual precipitation in Estonia for the period 1957–2009 coincides with the
results of the previous studies, for example Jaagus et al. (2010). The western part of continental
Estonia receives significantly more precipitation than the other regions. It could be explained with
the coastal effect. It means that a large part of air moisture moving from the sea to the land area
falls down in a moderate distance from the coast (20–80 km), forming a zone of higher
precipitation parallel to the coastline. The influence of the Baltic Sea appears also in the annual
curve of precipitation. Its clear maximum in continental Estonia is observed in July and August but
on the western coast in October and November. This is caused by the thermal inertia of sea
surface.
4.3. Method of moving totals
The proposed method of moving totals of precipitation was successfully applied for the study of
precipitation extremes. Weather conditions in the previous days are taken into account in defining
extremely wet and extremely dry days. There might be different criteria for the extremes. We used
a ten-day precipitation total of 100 mm for describing extremely wet days and a 20-day period
without precipitation for describing extremely dry days.
The extremely wet days were observed only in summer and autumn. August and July are the
months most affected by the risk of wet spells in Estonia. This lies in a good concordance with the
maximum of precipitation in these months.
Surprisingly, the annual curve of the numbers of extremely dry days in Estonia has two clearly
expressed maxima and a period with less frequent droughts between them around the midsummer
day, i.e. the second half of June and the first half of July. The two-peaked distribution of dry
periods has not been mentioned in literature. We explain it with two main factors that cause
droughts in Estonia. The late spring and early summer droughts are probably related to the coastal
regions. Comparatively cool sea surface prevents the formation of convective rainfall and induces
long dry periods. The droughts in the second half of summer are usually related to the extensive
areas of high pressure over the East European Plain that have influence, first of all, on the eastern
parts of Estonia.
4.4. Comparing results
Comparing the indices of extreme precipitation in Estonia with the same variables in other
regions we can conclude that the intensity of rainfall is slightly lower in Estonia. The mean number
of days with precipitation above 10 mm was about 15 in Estonia, but in Latvia (Avotniece et al.
2010) and Lithuania it has been higher, between 12 and 22 (Rimkus et al. 2011). Comparing the
mean indices of precipitation extremes in Estonia and Europe (Klein Tank and Können 2003), we
can see that the latter are remarkably higher. The corresponding values are the following: R10mm
15 in Estonia (21 in Europe), R20mm 3 (7), R1day 34 (44), R5day 59 (77). We suggest that higher
20
latitude, lower temperature and a shorter warm period are the main reasons for lower precipitation
extremes in Estonia.
4.5. Trends
Time series of the indices of extreme precipitation have statistically significant increasing
trends in Estonia during 1957–2009. The frequency and intensity of heavy precipitation has
increased; this is assumed to be a consequence of global climate warming. This change has been
determined also in many other regions of the world (Karl and Knight 1998; Frich et al. 2002;
Groisman et al. 2005) and in Europe (Klein Tank and Können 2003; Haylock and Goodess 2004;
Moberg and Jones 2005; Zolina et al. 2009; 2010; Zolina 2011). An increase in total precipitation
and extreme precipitation was detected in Fennoscandia in 1951–2002 and in the western part of
the former USSR in 1936–1997 (Groisman et al. 2005).
This increase in extremely wet conditions is seasonally different. All indices of extreme
precipitation have increased annually (except CWD) and, first of all in the winter season. Some
indices have significant trends also in summer and autumn but no trends at all in spring. We
assume that the most remarkable change in winter is directly related to temperature change that has
also been the highest in winter. The intensification of cyclone activity over northern Europe in
winter during the last decades has caused the temperature increase, higher storminess, precipitation
and precipitation extremes. All these changes are governed by the North Atlantic Oscillation
(Scaife et al. 2008).
No trends were detected for the indices of dry extremes. It means that the frequency of droughts
has not changed during the study period, although two extremely dry years were observed in the
end of the time series (2002, 2006). This result lies in a good concordance with analogous studies
from the neighbouring regions (Haylock and Goodess 2004).
Acknowledgements
This study has been supported by the grant No. 7510 of the Estonian Science Foundation and by
the target financed project SF0180049s09 of the Ministry of Education and Science of the
Republic of Estonia. The authors thank their colleagues Raivo Aunap and Andres Luhamaa for the
assistance in preparing cartographic images.
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