analysis of annual rainfall climate variability in saudi arabia by using spectral density function

05/02/2023 Elfeki, Al-Amri and Bahrawi (ICWRAE 2012)

ANALYSIS OF ANNUAL RAINFALL CLIMATE VARIABILITY IN SAUDI

ARABIA BY USING THE SPECTRAL DENSITY FUNCTION

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

Amro Elfeki, Nassir Al-Amri and Jarbou Bahrawi


Outline Research Objectives Typical Annual Rainfall Station Record Methodology and Model Development Results Conclusions Outlook


Research Objectives 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.


Stations Considered in the Study

-Investigated the rainiest part in the Kingdom of Saudi Arabia (the south western part). -The stations A121, B101 J102 , J113 SA104SA110SA111. - Record length (1960-2011)= 51 years


Typical Rainfall Record (Khules Station)

(411) YEAR LY SUMMARY OF RAINS FOR THE PE RIOD OF 19 65-1998 (DATED:14// )

========== ========== ========== ========== ========== ======= ============= ======

STATION: 00262 J212 خليص / GEO_ AREA: 0020 محافظ 8000 خليـص ة H YDRO_AREA: السادسـة 6-------- ----------- --------- ------------ ---------- ---------- ---------- ---------- ------- ------------- ------ ---------- ---------- -----------

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 0.01966 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 7.2 16.2 0.4 23.81967 0.0 0.0 0.0 0.0 0.4 0.2 0.0 2.0 1.0 0.0 21.4 0.2 25.21968 0.4 0.2 0.4 72.2 2.0 1.0 0.0 0.0 0.6 0.0 32.6 25.6 135.01969 55.8 8.8 2.4 0.0 0.0 0.0 0.0 0.0 0.4 0.0 35.2 7.4 110.01970 56.8 0.4 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.7 30.6 1.8 90.31971 0.8 4.8 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.2 0.0 4.0 9.81972 18.2 0.0 0.0 0.0 0.0 0.0 0.2 0.2 0.0 15.6 11.4 7.4 53.01973 1.0 0.0 0.0 0.0 0.0 0.0 0.2 0.0 0.0 0.0 0.4 9.5 11.11974 77.7 0.0 2.8 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 80.51975 21.2 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.8 2.0 10.4 34.41976 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.6 2.0 10.4 13.01977 5.4 0.2 0.0 0.2 0.0 0.0 17.6 0.0 0.2 0.8 0.0 35.6 60.01978 14.0 15.0 0.2 0.0 0.2 0.0 4.0 0.0 0.0 0.0 0.0 0.4 33.81979 63.0 0.4 1.6 0.2 0.0 0.0 0.0 40.6 0.2 6.2 0.0 0.0 112.21980 0.0 0.0 1.2 0.0 0.0 0.0 0.0 0.0 0.0 0.0 43.4 0.0 44.61981 0.0 0.6 6.6 0.0 0.0 0.0 0.0 0.0 0.0 0.2 0.8 9.0 17.21982 3.4 0.2 0.0 0.0 1.6 0.0 0.0 0.0 0.0 0.2 0.0 0.0 5.41983 3.2 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.2 0.0 0.0 3.41984 0.4 0.0 0.0 0.0 0.0 0.0 0.0 0.0 6.6 0.0 7.2 0.0 14.21985 9.6 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 24.2 34.4 68.21986 0.0 0.2 0.0 3.2 0.0 0.0 0.0 0.0 0.0 3.6 0.0 0.0 7.01987 0.0 0.0 35.2 0.0 0.2 0.0 0.0 0.6 0.2 0.0 0.4 0.2 36.81988 1.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 1.8 0.0 60.2 63.01989 0.0 0.0 0.0 5.0 0.0 0.0 0.0 0.0 0.0 0.0 3.8 15.6 24.41990 0.6 0.0 0.2 9.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 9.81991 6.0 0.0 2.4 0.0 0.4 0.0 0.0 0.0 0.0 0.0 4.0 0.2 13.01992 39.6 0.0 0.0 0.0 0.0 0.0 0.0 11.0 0.0 0.0 0.0 0.0 50.61993 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.01994 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 4.4 2.4 1.2 1.4 9.41995 0.0 12.0 7.4 4.2 1.4 0.0 0.0 0.0 0.0 0.4 0.4 0.0 25.81996 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.01997 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 20.2 0.8 15.8 36.81998 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


Visualization of Annual Rainfall Record (Station A121)

- 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


Methodology and Model Development

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.


Autocorrelation Function

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

2z

( ), ( )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 jj

Cov Z t Z t Z Z Z Zt tn

+ +


The Power Spectral Density Function (SDF)

2*1 1( ) lim ( ). ( ) lim | ( ) |zzL L

f z f z f z fSL 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 ftz f Z t d t e

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

f S

f d f S

f fS S


Wiener-Khinchin Relationships

- 2

-

2

-

2

-

1( ) ( )2

( ) ( )

(0) ( )

i fzz zz

i fzz zz

zz zz Z

f d S C e

f d fC S e

f d f C S

The covariance functions and spectral density functions are Fourier transform pairs. This can be expressed in mathematical forms using Wiener-Khinchin relationships


Estimation of The Auto-power Spectrum

0

1( ) ( )cos(2 )zz zzf C f dS

1

1

ˆ ( ) (0) 2 ( ) cos(2 ) ( )cos(2 )2

m

zz zz zzzzk

tf 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

wheremf kf mf tk m


Spreadsheet Model


Results (Makkah Al-Mukaramah)


Results (Jeddah)


Results (Al Baha)


Results (Abha)


Results (Jazan)


Results (Jazan) cont.


Statistical Parameters of The Stations


Summary


Conclusions 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.


Outlook 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.

analysis of annual rainfall climate variability in saudi arabia by using spectral density function

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