Climatology of precipitation extremes in Estonia using the method of
moving precipitation totals
Tiina Tammets, Jaak Jaagus
Abstract
A method of moving precipitation totals is described and applied for the analysis of precipitation
extremes in Estonia. Numbers of extremely wet days and of extremely dry days as well as a
number of indices of precipitation extremes have been calculated using daily precipitation data
measured at 51 stations over Estonia during 1957–2009. Mean regularities of spatial and seasonal
distribution of the indices are determined. Long-term changes are detected using the Sen’s method
and the Mann-Kendall test. It is natural that the highest risk of heavy precipitation is in regions of
higher mean precipitation on uplands and in the belt of higher precipitation in the western part of
continental Estonia parallel to the coast line. Wet spells have their sharp maximum in July and
August. The highest risk of droughts is observed in the coastal regions of West Estonia. In the
coastal area the highest risk of droughts appears in spring and in the first half of summer while in
the eastern Estonia it is usually during the second half of summer. There have been statistically
significant increasing trends in time series of indices of extreme precipitations, first of all in
winter. In summer and autumn there are trends 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 drought indices in Estonia in 1957–2009.
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). A comprehensive overview on trends in temperature and precipitation exremes 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 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 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 indiecies and precipitation totals are strongest 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.
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, has been built special
reltionships (Tammets 2010).
This study is a continuation of the previous one. Its main objectives are: to compare the usual
characteristics of precipitation extremes with the number of extremely dry and wet days; 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 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 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 for liquid and 0.1 mm for solid precipitation was added if at least 0.1 mm was recorded
and 0.1 mm for liquid precipitation was added if at least 0.1 mm was recorded to every
measurement. 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.
Following the method of moving totals 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
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). 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: 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).
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
22
23
if the average 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
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 dry 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 highest curve on the daily graph (Fig. 3) shows values of highest
maximum, the second high curve lowest maximum precipitation of all studied stations; the lowest
curve shows values of lowest minimum and the second curve above it the highest minimum of
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. This method allows to analyse the precipitation
conditions in any period. After calculating of moving totals through the time series interested
period should be separated and statistically studied.
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
Fig. 3. Maximum and minimum totals of precipitation in Estonian meteorological stations in 19572009 in dependence of number of days in the period
4 years
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 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 EDD and EWD in a year to their average in
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. Absolute maximum values of the indices with corresponding
year and station name are determined. Also, the maximum of years (mean of stations) and
maximum of stations separately has been calculated (Tables 1, 2, 3). Seasonal values of R99p and
R95p has been calculated using annual limits (Table 1). Maps for the indices of precipitation
extremes are drawn to analyse spatial and annual distribution of extreme precipitation and dry
periods in Estonia.
Precipitation totals 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. 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.
3. Results
3.1. Mean precipitation regime in Estonia
Before the analysis of extreme precipitation it is reasonable to describe the mean of precipitation
regime based on the 51 stations data in 1957-2009 used in this study (Table 1). Spatio-temporal
variability of precipitation is very high on the territory of Estonia (Fig. 5A). Variability of indices
of precipitation extremes is even higher (Fig 5 B). It is clearly demonstrated in Table 1 where
mean indices of the 51 stations, annual maximum of stations mean values and absolute maximum
in single stations with their year numbers of corresponding maxima are presented. The right
column in Table 1 contains changes by trend.
Table 1. Mean values of precipitation totals and mean indices of precipitation extremes of the 51
stations in Estonia in 1957–2009, their annual maximum values and absolute maximum at a 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
Index
PREC
EWD
SDII
CWD
R10mm
R20mm
RX1day
RX5day
R95p
R99p
PREC
Mean
649
0.83
5.42
7.53
14.8
2.85
34.2
59.3
6.24
1.23
128
Annual
maximum 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
Trend
25.8
0.13
0.11
0.15
0.93
0.32
0.89
1.53
0.58
0.11
5.8
Spring
Summer
Autumn
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
R10mm
R20mm
RX1day
RX5day
R95p
R99p
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
4.81
0.65
21.1
43.1
1.78
0.21
5.12
8.20
4.55
0.41
18.1
38.9
1.27
0.08
176
6.56
6.24
4.31
1.04
29.8
40.1
1.94
0.57
360
3.86
8.69
7.57
11.4
3.94
49.0
81.3
6.59
2.12
268
0.8
7.05
9.04
8.76
1.41
27.7
57.4
3.49
0.63
1993
2007
1999
1990
1989
2003
1999
2004
1995
1969
1990
1969
1995
1995
1996
1969
1995
1998
1978
1986
2005
1998
1998
1987
1978
1998
2008
1978
1978
2001
1978
2001
2008
1997
1997
2001
2005
7.32
16
11
4
41.3
80.4
6
1
226
12.2
12
9
4
65.4
88
5
3
508
20
17.5
15
18
10
131
184
12
6
380
10
9.41
19
16
7
78.4
141
9
3
1993
3 years
2 years
2003
1978
1990
2003
16 years
1995
2005
1986
1983
2 years
1998
1999
1977
1983
1978
1978
1997
2 years
1981
1998
1988
1997
2 years
3 years
1974
1987
2001
5 years
2 years
1991
2000
1985
2 years
6 years
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
0.02
0.09
0.75
1.88
0.14
0.03
Mean spatial distribution of annual precipitation PREC (Fig.5) varies between 535 mm (Kihnu
Island) and 732 mm (Mauri, Haanja Upland in South-East Estonia). 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 (Table 1). 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 highest mean seasonal precipitation 246 mm was observed in summer in Mauri (Haanja
Upland) while the lowest summer mean values are typical for the coastal stations ( mm in ). The
corresponding mean precipitation amounts in autumn were recorded in (… mm) and in (…
mm).
A
B
Fig. 5. Mean (A) and maximum (B) annual precipitation in Estonia during 1957-2009 using data of
51 meteorological stations
3.2. Extremely high precipitation
The highest annual precipitation PREC in Estonia varies between 1120 mm (Tahkuse, 1981) and
759 mm (Kihnu Island, 2001) (Fig. 5 B). Absolute maximum of the 12-month moving
precipitation total was 1146 mm in Tahkuse (December 1980 till November 1981) (Fig. 4). The
year with the maximum precipitation amount over Estonia has been 2008 with the average value
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).
Absolute maximum totals of precipitation for 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). 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
precipitation total 100 mm or more. Such days has been observed in Estonia only in summer and
autumn during 1957–2009, i.e. from June to November. Their highest numbers are 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 in 10-18 August. Consequently maximum number of EWD in summer is also 20. In
autumn the maximum number of EWD is twice lower – 10in 1987. Spatial distribution of EWD
shows that the greatest danger for extremely wet periods appears 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
months
Fig. 6. Monthly mean precipitation in Vilsandi and Võru during 1957–2009
XI
XII
1.2%
90
EWD
precipitation
80
1.0%
0.8%
60
50
0.6%
40
0.4%
30
precipitation, mm
number of days
70
20
0.2%
10
0.0%
0
01
02
03
04
05
06
07
08
09
10
11
12
months
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 and maximum 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/wet day. Lower values were observed in winter and
spring, some 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 (Fig. 9). The
absolute maximum 17.5 mm per wet day were recorded in Räpina in 1997 during the summer
season. Highest intensity of precipitation was calculated for 1978, when mean SDII of the stations
reached to 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 (especially in October), 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 correspondingly 15 and 3 during
the study period. Days with precipitation above 10 mm may occure 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 RX1day.
The last year of the study period 2009 was very specific for 95th and 99th percentile daily
precipitation (R95p, R99p). 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 territorial distribution of precipitation in Estonia.
Their maximum values are concentrated in the rainy zone of the western Estonia.
3.3. Dry periods
Spatial distribution of annual minimum precipitation in Estonia (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 in Kunda (North
Estonia) from September 2005 till August 2006 (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 (Võru,
1963/1964), 16 mm (Sõrve, 1964), 44 mm (Rohuküla, 1992) and 54 mm (Piigaste, 1988),
consequently. Absolute minimum precipitation found from the moving 90-day totals of
precipitation during the study period was only 10 mm (Fig. 3) in Väike-Maarja from 28 December
1971 to 26 March 1972.
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
649
128
108
215
196
Annual
minimum
(stations mean)
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 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
without precipitation period. These days have occurred in Estonia in all months (Fig. 12).
Maximum number of EDD days is observed in August. A clear minimum in July is highly
remarkable (Fig. 12). Hereby, it should be taken into account that EDD describes a dry day,
following to the 19-day dry period. Therefore, the minimum of EDD number 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
relative number of days
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
0.8%
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 drieness risk, i.e.
the highest average number of EDD has been 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 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 and maximum number of extremely dry days (EDD)
Table 3. Mean values of extrme dry conditions indices of 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 trends are insignificant
Year
Winter
Spring
Summer
Autumn
Index
EDD
EDD1
XCDD
CDD
PDD
DSMEA0
DSMEA1
Mean
1.20
3.92
16.6
22.0
0.34
2.99
4.16
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
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
Annual
Year of
minimum
the
(stations mean) minimum
12.6
2002
22.3
2002
29.9
2002
39.6
1972
0.46
1959
4.19
1959
5.40
1959
1983,
0.20
1984
1.04
1986
14.3
1984
24.9
1972
0.37
1996
3.36
1993
6.11
1970
3.31
2006
13.3
1972
20.5
2006
39.5
1972
0.65
1974
6.93
1974
13.1
1974
10.1
2002
13.9
2002
23.47
2002
24.4
1992
0.61
1997
6.45
2002
7.82
1969
3.31
1961
7.24
2002
20.5
1997
34.6
2002
0.51
1993
4.18
2005
6.17
1961
Absolute
minimum
30
45
49
71
0.56
5.68
6.75
Year of the
minimum
2002
1964
2002
1964
1959
1959
1996
Trend
0.09
0.19
0.17
0.22
0.00
0.03
-0.06
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
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
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 number of 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
number of 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 the daily precipitation limits of a dry day are higher – till 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 spring season – 1.9. The maximum EDD1 45 days was measured at
Sõrve in spring 1964.
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, correspondingly.
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 dryness 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. Changes in precipitation extremes
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 (Table 1). 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
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.
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.17. Relative values of extreme dry and wet days in different seasons in 1957-2009.
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 3).
4. Discussion and conclusions
Using daily precipitation data measured at 51 stations in Estonia during 1957–2009 numbers of
extremely dry and extremely wet days have been calculated together with other indices of
precipitation extremes. Their spatial and seasonal distribution and long-term trends have been
analysed. The main results of these analyses are presented and discussed here.
The mean pattern of annual precipitation in Estonia for the period 1957–2009 coincides with the
results of the previous studies, for example with Jaagus et al. (2010). The western part of the
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 the continental Estonia is observed in July and
August but in the western coast in October and November. This is caused by the thermal inertia of
sea surface.
The proposed method of moving sums 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
ten-day precipitation total 100 mm for describing extremely wet days and 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.
Comparing the indices of extreme precipitation in Estonia with the same variables in the other
regions we can conclude that intensity of rainfall in Estonia is a bit lower. The mean number of
days with precipitation above 10 mm in Estonia was ca 15, but in Latvia (Avotniece et al. 2010)
and Lithuania it has been higher, between 12 and 22 (Rimkus et al. 2011). Comparing mean
indices of precipitation extremes in Estonia and Europe (Klein Tank and Können 2003) we can see
that the last ones 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
latitude, lower temperature and shorter warm period are the main reasons for lower precipitation
extremes in Estonia.
Surprisingly, the annual curve of the number of extremely dry days in Estonia has two clearly
expressed maxima and a period with less frequent droughts between them nearly in midsummer
time, 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 causing 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 influence, first of all, on the eastern parts of
Estonia.
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 that 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). 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 winter season. Some
indices have significant trends also in summer and autumn but not 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 the 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 there were observed two extremely dry years 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).
At last about the reliability of the daily precipitation data. Generally, the quality of precipitation
data is not high. There are many sources of data inhomogeneity discussed, for example by Heino
(1994). Precipitation inhomogeneities in the former USSR were thoroughly discussed by Groisman
et al. (1991). During the study period of the current study the main change in methodology of
precipitation measurement occurred since 1966 when a wetting correction was added to every
measured amount of precipitation. It caused an upward shift in time series of precipitation totals.
We can assume that the increasing trend in annual and seasonal precipitation could be partly
induced by the wetting correction.
The part of the wetting correction in extreme precipitation totals is negligible. Therefore we
consider these time series as homogeneous and not affected by wetting corrections. At the same
time these corrections may significantly increase minimum precipitation and influence on the
indices of drought. As these time series don’t have any trends we consider the effect of wetting
correction on parameters of dry conditions also as not substantial.
Relocations of some stations might disturb homogeneity of data series. We assume that an
upward shift in precipitation was possible due to relocation of the station in Tallinn, Tartu and
Pärnu, and a downward shift in Narva. But we haven’t noticed that they have influenced on time
series of precipitation extremes. The possible inhomogeneities have not influence on the results on
data analysis
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.
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