The document discusses research on annual rainfall variability in Saudi Arabia, focusing on data from 1960 to 2011. A spreadsheet model was developed to analyze rainfall patterns, revealing significant cycles in the data and the necessity for continuous recording to ensure reliable analysis. Key findings include an average rainfall of 342 mm with variations indicating both wet and dry years.

1. 7/6/2016
Dept. of Hydrology and Water Resources Management
,Faculty of Meteorology, Environment & Arid Land
Agriculture, King Abdulaziz University , P.O. Box
80208 Jeddah 21589 Saudi Arabia
Elfeki, Al-Amri and Bahrawi (ICWRAE
2012)
Amro Elfeki, Nassir Al-Amri and Jarbou Bahrawi

2.  Research Objectives
 Typical Annual Rainfall Station Record
 Methodology and Model Development
 Results
 Conclusions
 Outlook
7/6/2016
Elfeki, Al-Amri and Bahrawi (ICWRAE
2012)

3.  Understanding the annual rainfall climate
variability in Saudi Arabia.
 Extraction of the modes of variations in the
annual rainfall record.
 Setting up an in-house tool (A spreadsheet
model) to perform analysis of the annual
rainfall variability and can be easily updated
once more data is available.
7/6/2016
Elfeki, Al-Amri and Bahrawi (ICWRAE
2012)

4. 7/6/2016
Elfeki, Al-Amri and Bahrawi (ICWRAE
2012)
-Investigated
the rainiest
part in the
Kingdom of
Saudi Arabia
(the south
western part).
-The stations
A121, B101
J102 , J113
SA104
SA110
SA111.
- Record
length (1960-
2011)= 51
years

5. 7/6/2016
Elfeki, Al-Amri and Bahrawi (ICWRAE
2012)
(411) YEAR LY SUMMARY OF RAINS FOR THE PE RIOD OF 19 65-1998 (DATED:14// )
========== ========== ========== ========== ========== ======= ============= ======
STATION: 00262 J212 /‫خليص‬ GEO_ AREA: 0020 8000‫محافظ‬ ‫خليـص‬ ‫ة‬ H YDRO_AREA: 6‫السادسـة‬
-------- ----------- --------- ------------ ---------- ---------- ---------- ---------- ------- ------------- ------ ---------- ---------- -----------
YEAR JAN FEB MAR APR MAY JUN JUL AUG SEP OCT NOV DEC TOTALS
-------- ----------- --------- ------------ ---------- ---------- ---------- ---------- ------- ------------- ------ ---------- ---------- -----------
1965 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
1966 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 7.2 16.2 0.4 23.8
1967 0.0 0.0 0.0 0.0 0.4 0.2 0.0 2.0 1.0 0.0 21.4 0.2 25.2
1968 0.4 0.2 0.4 72.2 2.0 1.0 0.0 0.0 0.6 0.0 32.6 25.6 135.0
1969 55.8 8.8 2.4 0.0 0.0 0.0 0.0 0.0 0.4 0.0 35.2 7.4 110.0
1970 56.8 0.4 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.7 30.6 1.8 90.3
1971 0.8 4.8 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.2 0.0 4.0 9.8
1972 18.2 0.0 0.0 0.0 0.0 0.0 0.2 0.2 0.0 15.6 11.4 7.4 53.0
1973 1.0 0.0 0.0 0.0 0.0 0.0 0.2 0.0 0.0 0.0 0.4 9.5 11.1
1974 77.7 0.0 2.8 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 80.5
1975 21.2 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.8 2.0 10.4 34.4
1976 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.6 2.0 10.4 13.0
1977 5.4 0.2 0.0 0.2 0.0 0.0 17.6 0.0 0.2 0.8 0.0 35.6 60.0
1978 14.0 15.0 0.2 0.0 0.2 0.0 4.0 0.0 0.0 0.0 0.0 0.4 33.8
1979 63.0 0.4 1.6 0.2 0.0 0.0 0.0 40.6 0.2 6.2 0.0 0.0 112.2
1980 0.0 0.0 1.2 0.0 0.0 0.0 0.0 0.0 0.0 0.0 43.4 0.0 44.6
1981 0.0 0.6 6.6 0.0 0.0 0.0 0.0 0.0 0.0 0.2 0.8 9.0 17.2
1982 3.4 0.2 0.0 0.0 1.6 0.0 0.0 0.0 0.0 0.2 0.0 0.0 5.4
1983 3.2 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.2 0.0 0.0 3.4
1984 0.4 0.0 0.0 0.0 0.0 0.0 0.0 0.0 6.6 0.0 7.2 0.0 14.2
1985 9.6 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 24.2 34.4 68.2
1986 0.0 0.2 0.0 3.2 0.0 0.0 0.0 0.0 0.0 3.6 0.0 0.0 7.0
1987 0.0 0.0 35.2 0.0 0.2 0.0 0.0 0.6 0.2 0.0 0.4 0.2 36.8
1988 1.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 1.8 0.0 60.2 63.0
1989 0.0 0.0 0.0 5.0 0.0 0.0 0.0 0.0 0.0 0.0 3.8 15.6 24.4
1990 0.6 0.0 0.2 9.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 9.8
1991 6.0 0.0 2.4 0.0 0.4 0.0 0.0 0.0 0.0 0.0 4.0 0.2 13.0
1992 39.6 0.0 0.0 0.0 0.0 0.0 0.0 11.0 0.0 0.0 0.0 0.0 50.6
1993 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
1994 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 4.4 2.4 1.2 1.4 9.4
1995 0.0 12.0 7.4 4.2 1.4 0.0 0.0 0.0 0.0 0.4 0.4 0.0 25.8
1996 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
1997 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 20.2 0.8 15.8 36.8
1998 51.0 10.2 0.0 0.0 0.0 0.0 0.0 3.0 0.0 0.0 0.0 0.0 64.2

6. 7/6/2016
Elfeki, Al-Amri and Bahrawi (ICWRAE
2012)
- Maximum = 729 mm occurred
on 1972 (wet year)
- Minimum =16 mm occurred on
1984 (dry year).
- Average = 342 mm
-Stander deviation = 144 mm
CV = 0.42

7.  Methodology: Use of the autocorrelation and the
spectral density functions to examine the
modes of variation in the annual rainfall data.
 Model Development: Develop a spreadsheet
model to estimate both the autocorrelation and
the spectral density functions from the annual
data and extraction of the modes of variations.
7/6/2016
Elfeki, Al-Amri and Bahrawi (ICWRAE
2012)

8. 7/6/2016
Elfeki, Al-Amri and Bahrawi (ICWRAE
2012)
 
2
( ), ( )
( )ZZ
z
Cov Z t Z t




ZZ
(0) 1
( ) 0
( ) = (- )
ZZ
ZZ
ZZ
=
=


  

Properties of stationary stochastic process maybe represented in a time domain which is
represented by the autocorrelation function of the lag τ. The autocorrelation function, , is
expressed as,
( )Z t ( )Z t 
2
z
 ( ), ( )Cov Z t Z t
is the variance of the stochastic process
are the stochastic process at two locations separated by a lag τ
is the covariance of the stochastic process at lag τ, which is given by,
( )
1
1
( ( ), ( )) ( ) - ( ) -
( )
n
j j
j
Cov Z t Z t Z Z Z Zt t
n

 
 
       + +

9. 7/6/2016
Elfeki, Al-Amri and Bahrawi (ICWRAE
2012)
2*1 1
( ) lim ( ). ( ) lim | ( ) |zz
L L
f z f z f z fS
L L 
   
where, L is the length of the signal in the
frequency domain,
the over bar means a sample time average, and
z(f) is Fourier transform of the process Z(t),
which is expressed as,
- 21
( ) ( )
2
i ft
z f Z t dte




 
and z*(f) is the conjugate of z(f) and f is the angular frequency.
Properties of the Auto-power spectrum are formulated as,
2
-
( ) 0
( )
( ) ( )
zz
zz z
zz zz
fS
f d fS
f fS S





 


10. 7/6/2016
Elfeki, Al-Amri and Bahrawi (ICWRAE
2012)
- 2
-
2
-
2
-
1
( ) ( )
2
( ) ( )
(0) ( )
i f
zz zz
i f
zz zz
zz zz Z
f dS C e
f d fC S e
f d fC S
 
 
 











 



The covariance functions and spectral density functions are Fourier
transform pairs. This can be expressed in mathematical forms using
Wiener-Khinchin relationships

11. 7/6/2016
Elfeki, Al-Amri and Bahrawi (ICWRAE
2012)
0
1
( ) ( )cos(2 )zz zzf C f dS    


 
1
1
ˆ ( ) (0) 2 ( )cos(2 ) ( )cos(2 )
2
m
zz zz zzzz
k
t
f C C k fk t C m fm tS  



  
     
 

,
max number of correlation lags=10%-25%(N)
/ ,
(Nyquist frequency) 1/ 2
0,1,2...,
n
n
where
m
f kf m
f t
k m


 


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Elfeki, Al-Amri and Bahrawi (ICWRAE
2012)

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Elfeki, Al-Amri and Bahrawi (ICWRAE
2012)

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2012)

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2012)

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2012)

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2012)

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2012)

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2012)

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Elfeki, Al-Amri and Bahrawi (ICWRAE
2012)

22.  Multiple temporal scales were obtained with
relatively significant variance and it is therefore
difficult to identify the organized structures in
the spectra except the 26 and 2 years cycles are
common for all stations.
 The significant cycles from all stations are 26,
13, 6.5, 3.5 and 2 years.
 Continuous recoding is a must to enable
reliable analysis.
7/6/2016
Elfeki, Al-Amri and Bahrawi (ICWRAE
2012)

23.  One of the applications of this study is to build
time series models from the available data. The
models are based on reconstruction of the
significant ‘signals’ from the data.
 Further analysis is needed to other stations in
the Kingdom.
7/6/2016
Elfeki, Al-Amri and Bahrawi (ICWRAE
2012)