 |
 |
 |
 |
 |
 |
Penentuan Taburan Terbaik daripada Hujan Maksimum Bagi Tempoh Ribut (Storm) yang Panjang Melebihi 48 Jam (MR) dan Hujan Maksimum Tahunan (MT) (The
Best Fitting Distribution of Maximum Storm Rainfall with Long Duration
with
More than 48 H (MR) and Maximum Rainfall Annualy (MT))
R. YENDRA1*, A.A. JEMAIN2 & W.Z. WAN ZIN3
1Department
of Mathematics, Faculty of Science and Mathematics
Universitas
Islam Negeri Sultan Syarif Kasim Riau, 28293, Pekanbaru, Riau
Indonesia
2School
of Mathematical Sciences, Faculty of Science and Technology
Universiti
Kebangsaan Malaysia, 43600, Bangi, Selangor, Malaysia
3School
of Mathematical Sciences, Faculty of Science and Technology
Universiti
Kebangsaan Malaysia, 43600, Bangi, Selangor, Malaysia
Diserahkan:
2 April 2013/Diterima: 2 Januari 2014
ABSTRAK
Kajian ini tertumpu
kepada penentuan taburan terbaik untuk memodelkan siri data maksimum tahunan (MT) dan siri maksimum
hujan dalam tempoh ribut yang melebihi 48 jam (MR). Data hujan setiap jam dari
tahun 1970 hingga 2008 dari 4 stesen hujan di Semenanjung Malaysia telah
digunakan dalam kajian ini. Kedua jenis data maksimum ini mempunyai kegunaan
yang sangat baik bagi mengesan banjir di kawasan bandar terutama yang
disebabkan oleh kegagalan sistem perparitan dalam menampung hujan lebat semasa
tempoh ribut yang panjang, manakala kajian yang boleh meramalkan ketahanan
empangan dalam masa 50 atau 100 tahun kehadapan sangat bergantung kepada
penentuan taburan hujan maksimum tahunan. Pelbagai taburan yang sering
digunakan bagi kajian pemodelan ekstrim digunakan untuk mendapatkan taburan
yang terbaik bagi menerangkan taburan kedua jenis data hujan maksimum tersebut.
Dua ujian kebagusan model telah digunakan iaitu kaedah bergraf dan kaedah PRKD. Hasil menunjukkan
bahawa taburan Pearson Jenis 3 adalah yang terbaik untuk menerangkan taburan
hujan maksimum tahunan pada kesemua stesen hujan yang digunakan pada kajian
ini. Taburan Pareto dan Gama adalah taburan yang terbaik bagi menerangkan
taburan hujan maksimum yang berlaku pada tempoh ribut yang panjang. Hasil
kajian penentuan taburan terbaik bagi hujan maksimum tahunan di atas juga telah
berjaya dalam meramalkan hujan maksimum yang akan berlaku untuk masa 50 dan 100
tahun yang akan datang.
Kata kunci: Gama;
hujan ribut; maksimum tahunan; Pareto; Pearson jenis 3; RMSE
ABSTRACT
The focus of this
study was to determine the best distribution to represent the annual series of
maximum hourly rainfall and the maximum series rainfall from the storm
exceeding 48 h. Data from 1970 to 2008 for 4 rain gauge stations in Peninsular
Malaysia is used. Both types of maximum data series used in the detection of
flood at urban areas, especially those caused by the failure of the drainage
system to, while the study to predict the resistance of dam over 50 or 100
years’ time is very dependent on the determination of the best fitting
distribution for annual maximum rainfall. Various distributions which are often
used for modeling extreme events are used to obtain the best distribution for
two types of data. The goodness of fit test performed are the graphical and RMSE methods have
identified Pearson Type 3 distribution is the best model to explain the annual
maximum rainfall at all stations used in this study. On the other hand Pareto
and Gamma distribution are the best distribution to describe the maximum
rainfall occurring during storm period. The study is successful in predicting
the maximum rainfall at 50 and 100 years from now.
Keywords: Annual maximum; gamma; pareto; Pearson type 3; RMSE;
storm rainfall
RUJUKAN
Adams,
B.J. & Howard, C.D.D. 1986. Design storm pathology. Canadian Water
Resources Journal 11(3): 49-55.
Adams,
B.J. & Papa, F. 2000. Urban Stormwater Management with Analytical
Probabilistic Models. Toronto, Ontario: John Wiley and Sons Inc.
Adamowski,
K. & Bougadis, J. 2003. Detection of trends in annual extreme rainfall. Hydrol.
Proc. 17: 3547-3560.
Aronica,
G., Cannarozzo, M. & Noto, L. 2002. Investigating the changes in extreme
rainfall series recorded in urbanized area. Water Sci. Technol. 45:
49-54.
Bacchi,
B., Becciu, G. & Kottegoda, N.T. 1994. Bivariate exponential model applied
to intensities and durations of extreme rainfall. Journal of Hydrology 155:
225-236.
Crisci,
A., Gozzini, B., Meneguzzo, F., Pagliara, S. & Maracchi, G. 2002. Extreme
rainfall in a changing climate: Regional analysis and hydrological implications
in Tuscany. Hydrol. Proc. 16: 1261-1274.
Deni,
S.M., Jemain, A.A. & Ibrahim, K. 2010. The best probability models for dry
and wet spells in Peninsular Malaysia during moonson seasons. International
Journal of Climatology 30: 1194-1205.
Eagleson,
P.S. 1972. Dynamics of flood frequency. Water Resources Research 8(4):
878-897.
Goel,
N.K., Kurothe, R.S., Mathur, B.S. & Vogel, R.M. 2000. A derived flood
frequency distribution for correlated rainfall intensity and duration. Journal
of Hydrology 228: 56-67.
Guo,
C.Y.J. 2002. Overflow risk analysis for stormwater quality control basins. Journal
of Hydrology Engineering 7(6): 428-434.
Guo,
Y. & Adams, B.J. 1998a. Hydrologic analysis of urban cacthments with
event-based probabilistics model 1. Runoff volume. Water Resources Research 34(12):
3427-3431.
Guo,
Y. & Adams, B.J. 1998b. Hydrologic analysis of urban catchments with
event-based probabilistics model 2. Peak discharge rate. Water Resources
Research 34(12): 3433-3443.
Hosking,
J.R.M. 1990. L-moments: Analysis and estimation of distributions using linear
combinations of order statistics. J. R. Stat. Soc. Ser. B 52(1):
105-124.
Koutsoyiannis,
D. & Baloutsos, G. 2000. Analysis of a long record of annual maximum
rainfall in Athens, Greece, and design rainfall inferences. Nat. Haz. 22(1):
31-51.
Nadarajah,
S. & Choi, D. 2007. Maximum daily rainfall in South Korea. J. Earth Sci. 116(4): 311-320.
Nguyen,
V.T.V., Nguyen, T.D. & Ashkar, F. 2002. Regional frequency analysis of
extreme rainfall. Water Sci. Technol. 45: 75-81.
Noratiqah,
M.A. & Jemain, A.A. 2012. Comparisons between the window-based and
storm-event analysis. Sains Malaysiana 41(11): 1377-1387.
Parida,
B.P. 1999. Modeling of Indian summer monsoon rainfall using a four-parameter
Kappa distribution. Int. J. Climatol. 19: 1389-1398.
Rakhecha,
P.R. & Soman, M.K. 1994. Trends in the annual extreme rainfall events of 1
to 3 days duration over India. Theor. Appl. Climatol. 48: 227-237.
Salvadori,
G. & De Michele, C. 2004. Frequency analysis via copulas: Theoretical
aspects and application to hydrological events. Water Resources Research 40(12):
W12511.
Singh,
K. & Singh, V.P. 1991. Derivation of bivariate probability density function
with exponential marginals. Journal of Stochastic Hydrology and Hydraulics 5:
55-68.
Suhaila,
J. & Jemain, A.A. 2007. Fitting daily rainfall amount in Peninsular
Malaysia using several Types of exponential distributions. Journal of
Applied Sciences Research 3(10): 1027-1036.
Wan
Zin, W.Z. & Jemain, A.A. 2010. Statistical distributions of extreme dry
spell in Peninsular Malaysia. Theoretical & Applied Climatology 102(3-4):
253-264.
Wan
Zin, W.Z., Jemain, A.A., Ibrahim, K., Suhaila, J. & Deni, S.M. 2009. A
comparative study of extreme rainfall in Peninsular Malaysia: With reference to
partial duration and annual extreme series. Sains Malaysiana 38(5):
751-760.
Yen,
B.C. & Chow, V.T. 1980. Design hyetographs for small drainage structures. J.
Hydraul. Eng. ASCE 106(HY6): 1055-1076.
Zhang,
l. & Singh, V.P. 2007. Bivariate rainfall frequency distributions using
Archimedian Copulas. Journal of Hydrology 332: 93-109.
*Pengarang untuk surat menyurat; email: yendra_75@yahoo. com.sg
|
|||
|
