University of Thessaly
"Severity-Duration-Frequency
relationships of heatwaves in Greece"
Nicolas R. Dalezios
Professor of Agrometeorology
University of Thessaly, Greece.
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University of Thessaly
Map of Greece with 13 Stations Used in the Analysis
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University of Thessaly
Data Base
Stations Used for
period 1955 – 2000
Stations Used for
period 1963 – 1982
1.
2.
3.
6.
7.
8.
9.
10.
11.
12.
13.
4.
5.
Larissa
Irakleio
Athens
(Helleniko)
Ierapetra
Rhodos
Agrinio
Arta
Korinthos
Ioannina
Kalamata
Chania
Patra
Tripoli
Daily Maximum Temperatures above 35oC were used
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Description of Methodology
Step 1: Probability Tables.
The episodes for each station are identified (when maximum temperature for successive
days exceeds 35oC). The cumulative value of temperature (above 35oC) for each episode is
used. In this way multiple events for the whole period are calculated for several durations.
In the Table produced column 1 shows the ranking numbers, column 2 shows the
cumulative temperature values in ascending order, column 3 the corresponding probability
(P) of occurrence using the Weibull plotting position equation , where m is the current
ranking number and n is the total number of data points, column 4 shows the
corresponding return period T duration using the equation , where P was previously
defined.
Step 2: Fitting Gumbel Distribution.
For each episode the identified cumulative temperatures are plotted versus the
corresponding return period and a statistical distribution is fitted to the plotted data points.
Specifically, the extreme value law is used by fitting the EVI distribution (Gumbel, 1958),
which has the following Cumulative Distribution Function, : F(x)  exp exp( A  (x  U))
where A, U are the fitted parameters, which are computed for each duration from the data.
The procedure of fitting EVI distribution is applied to all the identified episodes for each
station. As expected, each curve is plotted on top of the previous, since it corresponds to
ascending cumulative duration.
Step 3: Severity - Duration - Frequency (SDF) Curves.
Using the Gumber distribution, cumulative heatwave periods are computed, which
correspond to return periods of 2, 5, 10, 25, 50 and 100 years, respectively, for each
identified heatwave duration.
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Example: The Station of Larissa
RANK
CUM
TEMP
PROBAB
P
RETURN
PERIOD
T
1
30.6
0.058824
17
2
26.2
0.117647
8.5
3
25.8
0.176471
5.67
4
24.2
0.235294
4.25
5
21.2
0.294118
3.4
6
18.6
0.352941
2.83
7
16.2
0.411765
2.43
8
13.2
0.470588
2.13
9
12.0
0.529412
1.89
10
11.8
0.588235
1.7
11
11.6
0.647059
1.55
12
10.3
0.705882
1.42
13
8.2
0.764706
1.31
14
6.4
0.823529
1.21
15
5.0
0.882353
1.13
16
5.0
0.941176
1.06
Step 1:
Probability Table
For 6 successive days duration of
maximum daily temperature
above 35oC.
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Step 2: Fitting Gumbel Distribution
CUM. TEMPERATURE(>35οC)
GUMBEL DISTRIBUTION
100
GUMBEL1
GUMBEL2
80
GUMBEL3
60
GUMBEL4
40
GUMBEL5
GUMBEL6
20
GUMBEL7
0
-20
GUMBEL8
0
20
40
60
80
100
120
GUMBEL9
RETURN PERIOD
Gumbel Distribution for:
(1-Day):GUMBEL 1
up to (9-day): GUMBEL 9
total number of episodes for Larissa station.
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Step 3: Severity – Duration – Frequency (SDF) Curves
CUM.
TEMPERATURE(>35οC)
SEVERITY - DURATION - FREQUENCY
100
2 YEARS
5 YEARS
10 YEARS
25 YEARS
50 YEARS
100 YEARS
80
60
40
20
0
0
2
4
6
10
8
HEATWAVE DURATION (IN DAYS)
Example: the Station of Larissa
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SDF Curves for the Station of Agrinio
CUM. TEMPERATURE
(>35οC)
Severity - Duration - Frequency
80
70
60
50
40
30
20
10
0
2 YEARS
5 YEARS
10 YEARS
25 YEARS
50 YEARS
100 YEARS
0
2
4
6
8
10
HEATWAVE DURATION (IN DAYS)
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University of Thessaly
SDF Curves for the Station of Hellenikon (Athens)
CUM. TEMPERATURE
(>35οC)
Severity - Duration - Frequency
25
2 YEARS
20
5 YEARS
15
10 YEARS
10
25 YEARS
50 YEARS
5
100 YEARS
0
0
2
4
6
HEATWAVE DURATION (IN DAYS)
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University of Thessaly
SDF Curves for the Station of Ierapetra
CUM.
TEMPERATURE(>35οC)
Severity - Duration - Frequency
35
30
2 YEARS
25
5 YEARS
20
15
10 YEARS
10
50 YEARS
5
100 YEARS
25 YEARS
0
0
2
4
6
HEATWAVE DURATION (IN DAYS)
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Cumulative Temperature Values for all stations:
Return Period 100 years, 4-day duration
25.0
20.0
15.0
10.0
24.3
21.6 21.2 21.1
17.4
15.1 14.9
12.7
12.0
8.4
5.0
0.0
0.0 0.0 0.0
TR
IP
LA O L
I
RI
IE
S
R A SA
PE
TR
A
AT
HE
NS
IO
AN
NI
N
PA A
T
RH RA
O
DO
AG S
KA RIN
IO
LA
M
AT
A
KO AR
R I TA
NT
HO
CH S
A
IR NIA
AK
LE
IO
Cum. Temperature
30.0
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13 Stations That were Used in the Analysis
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University of Thessaly
Conclusion
Severity – Duration – Frequency (SDF) Curves are produced for
13 stations in Greece when daily maximum temperature for
successive days exceeds 35oC.
Results indicate that continental stations (Larissa, Agrinio,
Tripoli) are more vulnerable to heatwaves that coastal stations
(Ierapetra, Chania, Irakleio and Rhodes).
Results can be used for producing isoseverity maps for Greece
and for agroclimatic design and planning.
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