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Study of precipitation variability based on seasonality
and entropy over the Eastern Mediterranean
European Geosciences Union General Assembly 2015Vienna | Austria | 12 – 17 April 2015
Shifa MathboutClimatology Group
IntroductionMediterranean region has shown large climate shifts in the past
and it has been identified as one of the most prominent “Hot-Spots”
in future climate change projections.
CIMP5 multi-model mean results of projected average percent change in annual mean precipitation for (2081-2100) relative to (1986-2005).
Interannual variability of precipitation can
directly or indirectly affect many
hydrological, ecological and biogeochemical
processes that, in turn, influence climate.
The relative seasonality of rainfall represents
the degree of variability in monthly rainfall
throughout the year.
Entropy is a fundamental quantity in statistics and machine
learning. It evaluates the amount of information contained in
random signals and quantifies random signals based on their
occurrence probability. It provides a measure of dispersion,
uncertainty, disorder and diversity of precipitation intensity
and/or precipitation amount.
II-5
Prob
abili
ty
Normal DryWet ExtremeDry
More dryclimate
More dryclimate
More dryclimateMore wet
climate
AverageVariance
Average and Variance
RecentClimate
Future Climate
Precipitation change
Stations with daily and monthly precipitation data (70)
Stations with monthly precipitation data (34)
Log (o)
Lat (
o)104 series are considered for this study
Mean Annual Precipitation1961-2012
01002004006001,0001,400 mm
projections of future global precipitation changes from the 2007 IPCC
Observed change in wintertime precipitation
over the Mediterranean last century
(Hoerling et al,2012).
Trend in precipitation over the Eastern Mediterranean with altitude
508.8
399.3 391.8
456.6
361.6
-30
-25
-20
-15
-10
-5
0
5
0
100
200
300
400
500
<250 250500
500750
7501000
>1000
Cha
nge
mm
/dec
Mea
n A
nnua
l Pre
cipi
tatio
nm
m
Alt /MMean Annual Precipitation /mm Change mm/dec
1351 16Number of
Stations
14 24
Spatial distribution of mean
annual rainfall CVs values over
1961-2012.
R² = 0.4442
0%20%40%60%80%
100%
30 35 40 45
CV
%
Lat (o)
The Relationship between
latitude and CVs calculated
for each station.
Autumn Winter
Spring
Spatial distribution of mean seasonal variability index over Eastern Mediterranean
-0.64
-0.64
-0.50
-0.74
-0.80 -0.60 -0.40 -0.20 0.00
ANNUAL
AUTUMN
WINTER
SPRING The annual and
multiseasonal correlation
coefficients between rainfall
variability index and latitude
Scatterplots of latitude and
annual rainfall variability
index computed over 1961-
2012
R² = 0.4122
0.0
0.5
1.0
1.5
2.0
2.5
30 35 40 45Rai
nfal
l var
iabi
lity
Inde
x
Lat (o)
Relative seasonality of rainfall refers to the degree of variability
in monthly rainfall through the year. It assesses seasonal contrasts in
rainfall amounts rather than whether months are “dry” or “wet” in
absolute sense.
Seasonality index helps in identifying the rainfall regimes based
on the monthly distribution of rainfall. In order to define these
seasonal contrasts, the seasonality index 𝑆𝐼 and 𝑆𝐼𝑖 were computed to
quantify the annual rainfall regimes. These indices can show
differences in relative seasonality even in areas with 2 or 3 rainfall
peaks throughout the year.
Rainfall Seasonality Index
𝑆𝐼 in the whole stations over
1961-2012.
Mean 𝑆𝐼𝑖 values distribution
in whole stations over
1961-2012
R² = 0.7276
0.00.20.40.60.81.01.2
30 35 40 45Seas
onal
ity In
dex
SI
Lat (o)
Scatter diagram and linear regression line of
seasonality index 𝑆𝐼and latitude (ϕ)
0.30
0.50
0.70
0.90Min Mean Median Max
Box-whisker diagram of the ratio 𝑆𝐼 / 𝑆𝐼𝑖 in
all stations over1961-2012
About 60% of total stations have an 𝑆𝐼 increasing trend, which is
statistically significant in 10% of them. This increasing in 𝑆𝐼 trend
reveals that the rainfall distribution in these sites has become
asymmetric, accompanied with changes in rainfall characteristics such as
intensity and duration.
Positive trend (95%)
Nigative trend (95%)
Nigative trend
Positive trend
The Sum of Regime Shift Indices (RSI) calculated for each
of the 104 single stations resulted in highest cumulative values
in whole 1990s. It peaked in 1989, 1995 and 2005.
0.20
0.26 0.26
0.00
0.05
0.10
0.15
0.20
0.25
0.30
1961 1966 1971 1976 1981 1986 1991 1996 2001 2006 2011
Reg
ime
Shift
Inde
x R
SI Summary of all regime shift
index (RSIs) in mean
estimated by STARS for 103
stations during 1961–2012.
(α=0.05; cut-off length= 26;
Huber parameter = 1)
0.4
0.9
1.4
1.9
1961
1965
1969
1973
1977
1981
1985
1989
1993
1997
2001
2005
2009
H-4 Irwaished (Jordan)
0.4
0.9
1.4
1961
1965
1969
1973
1977
1981
1985
1989
1993
1997
2001
2005
2009
Kithira Airport (Greece)
0.4
0.9
1.4
1.9
1961
1965
1969
1973
1977
1981
1985
1989
1993
1997
2001
2005
2009
Ashdod (Israel)
Regime shifts in Mean Individual Seasonality Index from in selected stations 1961 to 2012 (α=0.05; cut-off length= 26; Huber parameter = 1)
0.00.51.01.52.0
1961
1965
1969
1973
1977
1981
1985
1989
1993
1997
2001
2005
2009
Palmyra (Syria)
A discrete form of entropy H(x) is given as
𝐻(𝑋) = 𝐻(𝑝1, 𝑝2, … . , 𝑝𝑛) = − 𝑖=1𝑛 𝑝𝑖𝑙𝑜𝑔𝑝𝑖
Where X is a discrete random variable, 𝑃𝑖 is the probability
that X assumes a value X =𝑥𝑖, and n is the number of values
(sample size) that X can take on this Equation defining
entropy in real time or space. Entropy is expressed in bits if
the base of the logarithm is assumed to be equal to 2.A corresponding R package “entropy” was deposited in the R archive CRAN and is
accessible at the URL:
http://cran.r-project.org/web/packages/entropy/ under the GNU General Public License.
Spatial distribution for the entropy of monthly (a) and daily (b) rainfall amounts
during 1961-2012 over the Eastern Mediterranean
“a”
“b”
R² = 0.7779
5.0
5.5
6.0
6.5
30 35 40 45Mon
thly
rain
fall
en
tropy
Lattitude
R² = 0.5985
0%
50%
100%
150%
200%
5.0 5.5 6.0 6.5
R² = 0.7053
0%
50%
100%
150%
5.0 5.5 6.0 6.5
AutumnSpring
Relationship between entropies and CVs in autumn and spring
Relationship of monthly
entropies, and latitude
over 1961-2012.
Thanks
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