Climatology of precipitation extremes in Estonia using the method of
moving precipitation totals
Tiina Tammets, Jaak Jaagus
Abstract
Kokkuvõte andmetest, metoodikast ja tulemustest.
1. Introduction
Precipitation is the climatic variable having the highest variability in space and time. Therefore,
precipitation extremes – continuing period with small or without precipitation, which leads to
droughts as well as heavy rainfall inducing flash floods – are related to the most severe damages
for human activity nearly at all regions of the world. It is the reason that the analysis of extreme
precipitation and drought events and their long-term trends has become an important topic in
climatological research.
Generally, an increase in extreme precipitation events is observed and proposed that it is
connected with possible climate warming in future (Groisman et al. 2005). Analysing changes in
climatic extremes during the second half of the 20th century, significant increases revealed in the
extreme amount of precipitation derived from wet spells and number of heavy rainfall events
(Frich et al. 2002). At the same time, a significant decreasing trend in global series of the annual
maximum of consecutive dry days (CDD) was noticed. 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). 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 detail overview on studies in the precipitation extremes, droughts and wet spells in the Baltic
Sea region is 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 revealed in Norway and Sweden (Førland 2000; Alexandersson 2002)
while a positive trend was detected in Germany for summer season (Klein Tank and Können
2003).
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 in German mountain stations and in western Norway (Heino et al. 1999).
Maximum number of consecutive wet days has increased in many stations over Scandinavia during
1961-2004 (Achberger and Chen 2006). Simple daily intensity index (SDII) increased significantly
in central and western Europe in winter 1921-1999 (Moberg and Jones 2005). All these studies did
not cover data from the territory of Estonia.
The previous results are approved by new investigations during recent years. Using ensembles
of simulations from a general circulation model (HadCM3), large changes in the frequency of 90th
percentile precipitation events over Europe in winter are found from changes in the NAO from
1960s to 1990s (Scaife et al. 2008). This would lead to increased occurrence of heavy precipitation
over northern Europe and decreased 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 when 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 of the total number of wet days.
Becoming longer, wet periods in Europe are now characterized by more abundant precipitation.
Heavy precipitation events during the last two decades have become much more frequently
associated with longer wet spells and intensified in comparison with 1950s and 1960s (Zolina
2011). An increasing trend in the 95 and 99 percentiles were detected in winter, spring and
autumn, and negative trend in summer in the northern Germany in 1950–2004 (Zolina et al. 2008).
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 revealed for
mean precipitation during a given spell (Wibig 2009). Positive as well as negative trends in indices
of precipitation extremes were detected at 48 synoptic stations in Poland during 1951–2006 but the
part of decreasing trends was prevailing (Łupikasza 2010). The highest number of decreasing
trends revealed in summer but the number of increasing trend was more pronounced in spring and
autumn.
Increasing trends in time series of number of days with heavy precipitation (above 10 mm) and
of 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 number of days with heavy
precipitation (≥10 mm) has been observed also 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 while a small decrease in dryness was observed (Valiukas 2011).
Although Estonia is characterised by a humid climate where annual precipitation exceeds
annual evaporation, drought periods are rather often during the warm half-year. They cause severe
damages for human activity – loss of agricultural production, water shortage, forest fires,
expanding of different diseases etc. Flash floods caused by heavy rainfall and continuing wet
periods make 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 transitions zone between the area of rather maritime climate on islands
and on the coast of the Baltic Sea in the west, and the area of much more continental climate in the
southeast and east. Precipitation regime is similar to that of the neighbouring regions with
maximum rainfall in summer and autumn, and with the minimum in winter and spring. The annual
mean amount of precipitation in Estonia varies between 550 mm in the coastal zone up to 750 mm
on the windward slopes of uplands (Jaagus and Tarand 1988).
Time series analysis has revealed an increasing trend 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 and precipitation
are the highest in winter and spring (Keevallik et al. 1999; Keevallik 2003; Jaagus 2006).
Dependence of precipitation pattern on local landscape characteristics in the three Baltic countries
are analysed using data mining tools (Jaagus et al. 2010; Remm et al. 2011).
Extreme precipitation events in Estonia were analysed in relation to types of large-scale
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 95 and 99 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
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 has been rained before that period. In
other words, for many purposes it is essential not to show how much rains in a day but to show
how much it has been rained till this day.
Following this ideology, the first author of the current article has proposed a methodology for
analysing precipitation extremes using moving precipitation totals (Tammets 2007; 2010). Using
it, 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 precipitation is at least 10 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. Minimal and maximal precipitation totals for
any time periods (number of following days, months or years using moving totals) in a station has
been calculated with the aid of moving averages in Jõgeva, Pärnu and Ristna (Tammets 2010).
This study is a continuation of the previous one. Its main objectives are: to analyse the usual
characteristics of precipitation extremes and detect long-term changes; to elaborate a method
characterising climatology of extreme precipitation totals for any time periods (number of
following days, months or years using moving totals); to detect the most severe wet and dry spells
in Estonia during last 50 years; to analyse trends in the frequency of precipitation extremes using
different methods 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 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 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
estimates of precipitation extremes. Therefore, the time series used are considered reliable.
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 have been made manually using Tretyakov gauges. Since 1966 a wetting correction
0.2 mm was added to every measurement if at least 0.1 mm was recorded. Some gaps in 2009 are
filled using data from automatic weather station MILOS 520, which are less reliable. The VRG
type automatic precipitation gauge was introduced in Kuressaare since 1 January 2008 and in
Heltermaa since 1 May 2009.
For many purposes it is essential not to know how much it has rained during a day but to show
how much has been rained till this day. A day is extreme day, if the amount of precipitation till 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 dry day is zero rainfall, and of wet day is the
day with precipitation threshold, depending on climate conditions of observed area.
Fig. 1. Location map of precipitation stations in Estonia used in this study
In our study we specify extremely wet and extremely dry conditions for a day by counting of
the moving total of daily precipitation data till this day. So, an extremely wet or dry day is a day
with too much or too few precipitation in a period, which lasts n days and ends in observed day.
Limits of the precipitation amount M and number of subsequent days n in observed period depends
on the study object, which could be agricultural field, river basin etc. In agrometeorological studies
these limits depend on the species of plant, state of vegetation, soil conditions, air temperature,
humidity etc. Counting of the moving total of precipitation goes through the whole observed time
without separating time to the month or the year. To point on the meteorological,
agrometeorological, hydrological or socioeconomical drought or flooding conditions described
indicators should be calculated for determined number of days n and thresholds M (Tammets 2007;
2010).
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: sj(n)=aj
(by moving averages sj(n)= 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 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). So, a wet or a dry day is a day with too much or too little precipitation till this
day (month) in a specified period for a specific object.
if there are no
precipitation on
a day and
previous n
days the day
has been
counted as a
droughtday
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
22
23
if the average of
precipitations on
a day and
previous n days
is M mm and
more the day has
been counted as
a
wetday
18
19
20
Fig. 2. Scheme for 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 drought days and n = 10
in case of wet days
In different studies and climate conditions instead of the daily time step monthly or even annual
time step could be used for calculation of moving totals of precipitation. Soil moisture conditions
respond to precipitation anomalies in a relatively short scale. Groundwater, stream flow and
reservoir storage reflect the longer-term precipitation anomalies. Extreme precipitation totals for a
year and longer period is one of the essential factors of the water balance in the region.
To find the extreme precipitation totals of any number of days in observed period has been built
graphs with the y-axis showing maximum and minimum of moving total of precipitation in
dependence on the number of days or months in the calculated period, showed on the x-axis (Fig. 3
and 4) (Tammets 2010). The maximum curve on the daily graph (Fig. 3) shows values of
maximum precipitation and the minimum curve minimum precipitation in dependence on n
(number of days) in observed period. These graphs have been calculated over 51 Estonian
meteorological stations during 1957–2009 and could use as one characteristics of precipitation
regime for Estonia.
To analyse the moisture conditions in a certain period, for example the vegetation period of a
crop), after calculating of moving totals in a precipitation time series we need to separate only the
days of this period or season. The precipitation totals of these days shows then, which has been
moisture conditions in this period.
In agrometeorological studies some limits for defining extreme weather conditions in Estonia
are given (Kivi 1998). Extremely wet conditions are observed when the mean daily precipitation
amount is equal to or more than 10 mm during consecutively 10 days ( n = 10). So we calculate the
sequences si (10) giving moving total for 10-day periods. If si >= 100 mm, the last day of the period
has been counted as a extremely wet day (EWD). Extremely dry conditions for field plants
emerges if there are no precipitation in duration of consecutively 20 days ( n = 20). If si = 0, the
last day of the period has been 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 EWD or the
number of EDD show intensity of a wet or a dry spell. In some years the number of wet or dry
spells is two or more.
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
4000
absolute minimum of stations
highest minimum of stations
3 years
3500
absolute maximum of stations
3000
2 years
lowest maximum of stations
2500
2000
1 year
precipiation total, mm
4 years
Fig. 3. Maximum and minimum totals of precipitation in Estonian meteorological stations in 19572009 in dependence of number of days in the period
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 in Estonian meteorological stations in 19572009 in dependence of number of months in the period
To estimate differences between the number of extremely dry days when the amount of
precipitation has been 0 mm and 1 mm (maximum error measurements with Tretyakov gauge for
the 20 days) we calculated also the number of extremely dry days when the precipitation amount in
consecutively 20 days ( n = 20) is only 1 mm (EDD1).
Annual and seasonal number of extremely dry and wet days (EDD, EDD1, EWD) was
calculated for every 51 station during the period 1957-2009. To analyse of inter-annual variability
of the average number of wet and dry days EDD and EWD together the relative number of dry and
wet days has been calculated dividing the number of in a year to the average of 1957-2009. Also
the relative number of extremely wet and dry days in every season: spring (MAM), summer (JJA),
autumn (SON) and winter (DJF) has been also calculated.
Annual, seasonal and monthly precipitation totals are used to characterise general precipitation
regime in Estonia. Numbers of extremely wet days (EWD) and extremely dry days (EDD) in 19572009 was compared with the 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;
RX5day – the highest 5-day precipitation amount;
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;
XCDD – maximum number of consecutive dry days R = 0 mm;
PDD – probability of a dry day following a dry day (mean dry-day persistence);
DSMEA1 - mean dry spell length with R < 1mm;
DSMEA0 – mean dry spell length with R = 0 mm.
These indices of precipitation extremes are calculated for every station by years and seasons.
Then their mean values are found. In addition, absolute maximum values of the indices with
corresponding year and station name are determined. Maps for the indices of precipitation
extremes are drawn to analyse spatial and seasonal distribution of extreme precipitation and
droughts in Estonia.
Precipitation data as well as many indices of precipitation extremes are not normally
distributed. Therefore, the Sen’s method and Mann-Kendall test (Salmi et al 2002) are used for
trend analysis. Trends are expressed in millimetres per decade. Trends are considered statistically
significant on the p<0.05 level.
3. Results
3.1. Mean precipitation regime in Estonia
Before the analysis of extreme precipitation it is reasonable to describe mean precipitation regime
based on the data used in this study. Spatio-temporal variability of precipitation is very high on the
territory of Estonia. Variability of indices of precipitation extremes is even higher. It is clearly
demonstrated in Table 1 where are presented mean values of the indices averaged over the 51
stations during 1957-2009 together with maximum values of single stations and of station means,
and year numbers of corresponding maxima. The right column in Table 1 contains changes by
trend.
Table 1. Mean values of precipitation totals and indices of precipitation extremes averaged by 51
stations in Estonia during 1957–2009, their maximum values by station means and by single
station (mm), year numbers of corresponding maxima and changes by trend (mm per decade).
Statistically significant changes at p<0.05 level are typed in bold
Year
Winter
Spring
Summer
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
Mean of
stations
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
Maximum
of
Year of
Year of
stations'
the
Absolute the
mean
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
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
Autumn
PREC
EWD
SDII
CWD
R10mm
R20mm
RX1day
RX5day
R95p
R99p
196
0.11
5.54
6.25
4.81
0.65
21.1
43.1
1.78
0.21
268
0.8
7.05
9.04
8.76
1.41
27.7
57.4
3.49
0.63
1978
1978
2001
1978
2001
2008
1997
1997
2001
2005
380
10
9.41
19
16
7
78.4
141
9
3
1974
1987
2001
5 years
2 years
1991
2000
1985
2 years
6 years
5.1
0.01
0.12
0.02
0.02
0.09
0.75
1.88
0.14
0.03
Mean spatial distribution of annual precipitation PREC in Estonia is presented on Fig. 5. It
varies between 535 mm (Kihnu Island) and 732 mm (Mauri, Haanja Upland in South-East Estonia)
(Fig.5). Generally, lower annual precipitation is typical for coastal stations, also for the coast of
Lakes Peipsi and Võrtsjärv. Higher precipitation revealed in continental Estonia on uplands and,
especially, in the meridional zone parallel to the western coast on the distance of 20-100 km from
the mean coastline. The rainiest seasons are summer and autumn while the driest is spring. There
are remarkable differences in annual curve of precipitation between the coastal regions and the
hinterland (Fig.6). The western Estonia is much drier in spring and in the first half of summer than
the central and eastern Estonia. But in the second half of summer and especially in autumn the
western Estonia receives much more precipitation. It can be explained by different thermal regimes
of sea and land surfaces. In spring, sea surface is cold causing stable air stratification upon it,
which prevents convective air uplift, formation of clouds and precipitation. Sea surface warms up
during summer inducing unstable air stratification, convective ascending of air, formation of
clouds and precipitation. Sea surface acts as a warmer surface throughout autumn and winter.
The maximum of annual precipitation PREC varies between 1120 mm (Tahkuse, South-West
Estonia in 1981) and 759 mm (Kihnu Island in 2001). Absolute maximum of the 12-month moving
precipitation total in Estonia (1957-2009) was 1146 mm (Fig. 4). The year with the maximum
precipitation amount over Estonia has been 2008 with the average of stations total 858 mm. More
than 800 mm is observed also in 1981, 1978 and 1990. The rainiest year numbers are repeating
many times in Table 1.
Absolute maximum of summer precipitation has been 507.9 mm (1978, Praaga, East Estonia).
The maximum of stations’ mean over 1953-2009 was 246.0 mm (Mauri) and the year with the
wettest summer 1998 – mean of stations 360.1 mm. Maximum totals of precipitation for winter,
spring, summer and autumn seasons were consequently 320.2 mm (1989/90; Kuusiku), 225.9 mm
(1994/95, Tudu), 507.9 mm (1978, Praaga) and 380.3 mm (1974, Uue-Lõve). Absolute maximum
of the 90-days precipitation calculated through the moving total over all days and stations in 53
years was 578.7 mm (Fig. 3).
Fig. 5. Mean annual precipitation in Estonia during 1957-2009 using data of 51 meteorological
stations
3.2. Indices of extremely high precipitation
Precipitation extremes of Estonia are characterised using the number of extremely wet days
(EWD). A day is estimated as extremely wet in case of the last day of a 10-day period when the
precipitation total has been 100 mm or higher. Such periods has been observed in Estonia only in
summer and autumn during 1957–2009, i.e. from June to November. The highest values are
recorded in July and August (Fig. 7). The mean EWD per year was 0.83 (Table 1) while its
monthly maximum 11 days was observed in south-eastern Estonia in July 1978 and in August
1987. Annual maximum of EWD (20 days) was observed at Praaga in 1978 with two wet periods –
one in 12-22 July and the second in 10-18 August. Spatial distribution of EWD shows that the
greatest danger for extremely wet periods is situated in south-eastern and northern Estonia (Fig. 8).
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, frequency of wet
spells varies many times on the territory of Estonia. Generally, the same pattern as in case of EWD
is typical also for the other indices of precipitation extremes.
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
1,2%
90
EWD
precipitation
80
1,0%
0,8%
60
50
0,6%
40
0,4%
30
precipitation, mm
relative number of days
70
20
0,2%
10
0,0%
0
01
02
03
04
05
06
07
08
09
10
11
12
Fig. 7. Monthly mean number of extremely wet days (EWD) and total precipitation (PREC) at the
Estonian meteorological stations in 1957–2009
Fig. 8. Annual mean number of extremely wet days (EWD)
Simple daily intensity index (SDII) indicates the mean precipitation amount per one wet day
(≥1 mm). Its annual mean value was 5.4 mm. Lower values were observed in winter and spring,
similar ones in autumn and much higher in summer (mean value 7.3 mm). SDII is spatially
variable with higher intensity in the western part of the continental Estonia (Fig. 9). The absolute
maximum 17.5 mm per wet day were recorded in Räpina in 1997. The year 1978 has been with the
highest intensity of precipitation when mean SDII of the stations reached 6.3 mm/wet day.
Fig. 9. Annual mean simple daily intensity index (SDII)
Maximum number of consecutive wet days (≥1 mm) (CWD) has the highest mean value not in
summer but in autumn, and the lowest in spring (Table 1). Annual maximum of CWD at stations
varies between 10 and 19 days while it is higher in the hinterland and lower at the sea coast.
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 approximately 15 and 3 during
the study period. Days with precipitation above 10 mm may occur in Estonia in every month. The
number of very heavy precipitation days R20mm may also happen in Estonia in every month, but
more often in July and August. The spatial pattern of R10mm is very representative to the patterns
of mean precipitation as well as of the other indices of precipitation extremes (Fig. 10).
Fig. 10. 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 stations were 34.2 mm and 59.3 m
(Table 1). The highest values of RX1day and RX5day have been observed in summer and lowest
ones in winter and spring. RX1day maximum in 1957-2009 varies between the stations from 53
mm to 131 mm. The highest values were measured in south-east Estonia. RX5day varies between
85 and 184 mm and its spatial pattern is similar to the previous index.
Numbers of days with the 95th and 99th percentile daily precipitation (R95p, R99p) are, of
course, not high. In that sense the last year of the study period 2009 was very specific. Record high
values were fixed 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 spatial patter of Estonia. Their maximum values are concentrated in the rainy zone of
the western Estonia.
3.3. Indices of drought in Estonia
Spatial distribution of annual minimum precipitation in Estonia on Fig. 11 is quite variable but
similar to the mean annual pattern (Fig. 5). The annual minimum is generally lower in the eastern
Estonia than in its western part except the coastal zone. Absolute minimum value of annual
precipitation – 335 mm – has been registered at Kunda, North Estonia, in 1964 (Table 2). Absolute
minimum of 12-month moving precipitation total in Estonia was even 278 mm (Fig. 4). The year
1964 has been the driest during 1957–2009 with the minimum of mean annual precipitation over
stations 453 mm. Minimum values of precipitation for winter, spring, summer and autumn seasons
were 36 mm (1963/64, Võru); 16 mm (1964, Sõrve); 44 mm (1992, Rohuküla) and 54 mm (1988,
Piigaste), consequently. Absolute minimum precipitation found from the moving 90-day totals of
precipitation during the study period was only 1.4 mm (Fig. 3).
Fig. 11. Minimum of annual precipitation in Estonia in 1957-2009
Table 2. Annual and seasonal mean minimum and absolute minimum precipitation and their trends
in Estonia during 1957–2009. Statistically significant changes at p<0.05 level are typed in bold
Year
Winter
Spring
Summer
Autumn
Mean of
stations
649
128
108
215
196
Minimum of
stations' mean
453
66
50
118
116
Year of the
maximum
1964
1964
1974
1983
1958
Absolute
minimum
335
36
16
44
54
Year of the
maximum
1964
1964
1964
1962
1988
Trend
18.1
5.50
0.06
5.83
3.80
Duration of extremely dry period in Estonia has been characterized through 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 any precipitation. These days have occurred in Estonia at all months (Fig. 12). The
period of maximum EDD is observed in August. A clear minimum in July is highly remarkable on
Fig. 12. Hereby, it should be taken into account that EDD describes a dry period in advance.
Therefore, the minimum in July implies on less frequent dry periods during midsummer between
the second half of June and the first half of July. This is an interesting feature, which is not yet
detected in other regions.
0,9%
90
precipitation, mm
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
relative number of days
EDD
0,8%
0
01
02
03
04
05
06
07
08
09
10
11
12
Fig. 12. Monthly mean relative number of extremely dry days (EDD divided by the total number
of days in the months) and average monthly precipitation of Estonian meteorological stations in
1957–2009
The annual mean number of EDD during the study period was 1.2. The largest drought risk, i.e.
the highest average number of EDD has been obtained for 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 has been calculated for Jõhvi and Tartu (0.38, Fig. 13). The highest annual maximum
of EDD was registered at Mauri in August and September 2002 – 30 days. The same year was
extremely dry with the mean EDD over stations 12.6 days (Table 3).
Fig. 13. Annual mean number of extremely dry days (EDD)
Table 3. Mean values of drought indices averaged by 51 stations in Estonia during 1957–2009,
their maximum values by station means and by single stations (mm), year numbers of the
corresponding maxima and changes by trend (mm per decade). The rends 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 of
stations
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'
mean
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
maximum
2002
2002
2002
1972
1959
1959
1959
1983, 1984
1986
1984
1972
1996
1993
1970
2006
1972
2006
1972
1974
1974
1974
2002
2002
2002
1992
1997
2002
1969
1961
2002
1997
2002
1993
2005
1961
Absolute
maximum
30
45
49
71
0.56
5.68
6.75
6
11
25
44
0.57
3.36
10.8
18
45
46
71
0.79
11.0
31.7
21
28
36
57
0.76
11.2
13.3
13
18
49
52
0.67
7
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 spatio-temporal distribution of EDD is characterised by the fact that its maximum value in
spring and summer have been observed in the coastal region of West Estonia but in autumn in the
eastern Estonia. Maximum EDD in summer 21 days has occurred twice –in 1997 (Valga) and in
2002 (Rohuküla). In spring and in autumn drought risk has been lower. Maximum EDD in spring
was 18 (Kuusiku in 1972 and Räpina in 2009) and in autumn 13 days, which was calculated for
different stations, mostly in East Estonia (Lüganuse, Tudu, Tudulinna, Mauri) in 2000 and 2002.
If we widened the limits of defining a dry day until the daily precipitation below 1 mm then, of
course, the number of extremely dry days EDD1 increased significantly (Table 3). The mean
annual EDD1 was 3.9 with the highest values in spring season. The maximum EDD 45 days was
measured in Sõrve during the period …..
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 similar to EDD definition, the maximum number of
consecutive dry days XCDD was also the highest in 2002 at Mauri station – 49 days (Table 3).
Maximum number of consecutive dry days CDD – 71 – was recorded at the coastal station
Heltermaa on Hiiumaa Island in February-April 1964. Average CDD have been 22 days with the
highest values in spring. It varies from 20.5 (Mauri) till 26.1 days (Heltermaa). 2002 is also the
year of highest average of CDD over stations. Annual variation (mean of stations) of CDD varies
from 14.6 in1977 till 39.6 in 1972.
The dry-day persistence PDD was 0.34 as a mean of 51 stations during 1957–2009. It means
that a dry day will occur after a dry day in one third of cases. The probability of dry day was
significantly higher in spring and lower in autumn (Table 3). Spatial differences are not large in
Estonia but PDD has been mostly higher in dry coastal zone. The absolute maximum 0.79 was
observed at Kasari in spring 1974.
Mean dry spell durations DSMEA1 and DSMEA0 were 4.2 and 3.0 days. They are 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. 14 is similar to the patterns of other indices of drought in Estonia. The driest regions are
located in the coastal zone (Vihterpalu, Kunda, Virtsu, Rohuküla, Sõrve, Kihnu).
Fig. 14. Annual mean duration of the dry period (DSMEA0).
3.4. Long-term changes in precipitation extremes
Trends are calculated using the Sen’s method and their significance is estimated by the MannKendall test. Trend values for spatial mean time series of the indices of precipitation extremes are
presented in the last columns of Tables 1, 2 and 3 while statistically significant trends are marked
in bold. Annual precipitation amount PREC has increased significantly in the majority of the
Estonian stations during 1957–2009. The mean trend value averaged by the 51 stations was 25.8
mm per decade. This increase is statistically significant also in winter season (Fig. 15). In other
seasons significant trends are observed only in some stations. The most remarkable increase in
precipitation was found in north-eastern Estonia. The trend was weaker at the coastal stations.
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. 15. Time series of annual and seasonal precipitation (mean of stations) in Estonia during
1957–2009 and their trend lines
Generally, the indices of wet conditions (excl. CWD) have an increasing trend during 1957–
2009. It means that heavy rainfall has become more frequent and more intense. The indices of
maximum precipitation have statistically significant increasing trends in all cases in winter but not
at all in spring. There are trends in some indices and no trends in other ones in summer and
autumn. Trends in both cases (summer and autumn) revealed for SDII and R95p, and no trends in
both cases for PREC and CWD (Table 1). At the same time there are no any significant trends in
indices of droughts (Table 2).
Extremely wet or extremely dry conditions have been one of the main factors, which limit the
agricultural production. They cause hydrological and socio-economical stress in Estonia. To find
the total value of extreme days in a year and to estimate its long time changes we calculated the
relative numbers of EWD and EDD in each year by dividing its mean value over stations to the
average of 1957-2009. 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.16). As a
rule, extremely wet days prevail 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 level
in 1978-1991. The wettest years were 1978 and 1987 when the mean of relative number of wet
days was by 4-6 times higher than 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.
Relative values of EDD and EWD separately for each season show the most extreme dry or wet
conditions in Estonia in 1957-2009 (Fig. 17). The highest number of extreme days has been
observed in spring and summer of 2002 when extra dry conditions predominated. Existing of
extremely wet and extremely dry conditions together in 1997, 1999, 2006 and 2008 show great
spatial differences of precipitation regime over Estonia.
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. 16. Relative number of annual number of extreme dry, extreme wet and extreme days in
Estonia 1957-2009, and the trend line of the number of extreme days.
35
EDDwinter
EDD spring
EDD summer
EDD autumn
EWDsummer
EWD autumn
30
25
20
15
10
5
Fig.17. Relative values of extreme dry and wet days in different seasons in 1957-2009.
4. Discussion and conclusions
Acknowledgements
2009
2007
2005
2003
2001
1999
1997
1995
1993
1991
1989
1987
1985
1983
1981
1979
1977
1975
1973
1971
1969
1967
1965
1963
1961
1959
1957
0
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.
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