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