Hong-Kee Jee, Woon-Ki Yeo, Joong-Hoon Kim and Soontak Lee
8.1 Introduction
The FARD (Frequency Analysis of Rainfall Data) program which was developed by NIDP (National Institute for Disaster Prevention) of MOGAHA (Ministry of Government Administration and Home Affairs) in Korea is used in frequency analysis of rainfall for the estimation of design rainfalls in Korea.
This program consists of test of randomness, parameter estimation of probability distribution functions, goodness of fit tests and finally estimation of probable rainfall.
In this chapter, frequency analysis was carried out using FARD program for rainfall data of Daegu, Busan and Andong station in Korea as well as 40 stations of AP FRIEND regions in 8 countries.
8.2 Methodology
The process of FARD program is shown as Figure 8.1 for frequency analysis. First of all, FARD program computes basic statistics such as the mean, standard deviation, coefficient of variation and coefficient of skewness from collected annual maximum series. It tests randomness of rainfall data to make sure that the data are random variables. After preliminary test, FARD program is applied to analyze probability distributions in order of parameter estimation, validity check and goodness of fit test. Then best fit distribution is finally selected from which probable rainfalls are estimated.
Figure 8.1 Process of Frequency Analysis of Rainfall Data by FARD program
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8.3 Data supplied
Annual maximum rainfall series were supplied by participating countries attending the APFRIEND Workshop in Kuala Lumpur, Malaysia in June 2005. Countries supplied extreme rainfall data were as follows;
Australia 10 sites
People’s Republic of China 3 sites
Indonesia 5 sites
Republic of Korea 3 sites
Malaysia 3 sites
New Zealand 3 manual sites & 3 co-located automatic sites
Philippines 8 sites
Vietnam 3 sites
Japan 5 sites
Additional 1 more site was supplemented to already supplied 2 sites of Republic of Korea. The maximum series of rainfall data from 10 minutes to 72 hours were used in analyses for 3 sites of Daegu, Busan and Andong in Korea.
8.4 Results of Analysis
As results of frequency analysis, Gumbel distribution was selected as the best fit probability distribution with estimation of parameters by the method of probability weighted moments for every stations in Korea(Republic of) with return period of 10, 20, 30, 50, 80, 100 and 200 years.
Gumbel for Sydney and Log-Normal for Melbourne In Australia, Gamma for Yongcuan and Gumbel for Changzhou in China, GEV for Bandung and Gumbel for Bogor in Indonesia, Log-Normal for Nagoya and Ohkusa in Japan, Gamma for Empangan genting kelang and JPS ampang in Malaysia, Log-Normal for Wellington, Kelburn and Kaitoke in New Zealand, Log-Log-Normal for Naia and Gamma for Baler in Philippines and Gumbel for Ha noi and An Nhon in Vietnam were selected as the best fit probability distributions with estimation of parameters by method of probability weighted moments for every stations with return period of 10, 20, 30, 50, 80, 100 and 200 years.
The equation (1) below, is generally used in Korea to determine rainfall IDF (intensity-duration-frequency) relationship.
n x
t k T t T
I ( , ) =
(1)Results for the best fit distributions obtained by FARD program are shown in Figure 8.2(a)~(c) from Korean rainfall analyses and in Figures 8.3~8.10 from other APFRIEND region’s rainfall data.
1.0
(a) IDF Curve for Daegu by Gumbel
1.0 Figure 8.2 The IDF Curves for Korea
1.0
Figure 8.3 The IDF Curves for Australia
605
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1.0 Figure 8.5 The IDF Curves for Indonesia
1.0 Figure 8.6 The IDF Curves for Japan
684
1.0
Figure 8.7 The IDF Curves for Malaysia
1.0
Figure 8.8 The IDF Curves for New Zealand
1.0
Figure 8.9 The IDF Curves for Philippines
762
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1.0 10.0 100.0 1000.0
1 10 100 1000 10000
Duration(min)
Intensity(mm/h)
T=10yr T=20yr T=30yr T=50yr T=80yr T=100yr T=200yr
1.0 10.0 100.0 1000.0
1 10 100 1000 10000
Duration(min)
Intensity(mm/h)
T=10yr T=20yr T=30yr T=50yr T=80yr T=100yr T=200yr
(a) IDF Curve for Ha noi by Gumbel (b) IDF Curve for An Nhon by Gumbel Figure 8.10 The IDF Curves for Vietnam
8.5 Acknowledgments
The support of KMA (Korea Meteorological Administration), Nakdong River Flood Control Office of MOCT (Ministry of Construction and Transportation) and NIDP of MOGAHA is acknowledged through their commitment in providing rainfall data and FARD program.
8.6 References
Korea Meteorological Administration (1916~2006), Annual Climatological Report, Seoul, Korea
Ministry of Construction and Transportation (1962~2006), Annual Hydrological Report on Korea, Seoul, Korea
Korea Water Resources Association (2004), Statistical Analysis of Rainfall by FARD9(Frequency Analysis of Rainfall Data), 12th Hydro-Engineering Workshop Report, Seoul, Korea
National Institute for Disaster Prevention(NIDP) of Ministry of Government Administration and Home Affairs (MOGAHA) (1998), Development of Program for Frequency Analysis of Rainfall Data(FARD), Research Report NIDP-97-09, Seoul, Korea.
643 . 0
145 . 0
84 . 763 t
I= T 385.48 00.554.143
t I= T
D
This report illustrates how the various countries involved in this project perform their rainfall intensity-frequency-duration (RIDF) analysis. In the Philippines, the National Water Resources Board (formerly National Water Resources Council) published in 1977 through 1981 the first comprehensive RIDF analysis for 12 regions in the Philippines. The RIDF analysis were performed for individual rainfall stations and the 3-parameter gamma (also called Pearson type III) probability distribution was used in the analysis. In 1981, the Philippine Atmospheric, Geophysical and Astronomic Services Administration (PAGASA) published RIDF curves for about 50 gaging stations in the Philippines using the extreme value Type 1 (EV-1, also called Gumbel) probability distribution. The latest RIDF analysis of Philippines rainfall data was published by the Flood Control and Sabo Engineering Center (FCSEC) of the Department of Public Works and Highways (DPWH) in 2003 for 1-day rainfall of selected gaging stations in the Philippines using either the EV-1 or 3-parameter gamma probability distribution. These manuals were specifically written to assist engineers at DPWH. This chapter illustrates RIDF analysis using the 3-parameter gamma or Pearson Type III probability distribution and the fitting of a parametric function to smoothen the RIDF curves. The gamma distribution being a 3-parameter distribution is more versatile model than the EV-1 or Gumbel distribution being only 2-parameter distributions.
9.2 Methodology
For a given rainfall station, the RIDF analysis involves two steps. First is to fit the 3-parameter gamma or Pearson type III probability distribution function to the annual maxima series for a particular duration (e.g., 10 min, 30 min or 1 hour duration) to estimate the rainfall quantiles at different frequencies or return periods. The estimated rainfall quantiles constitute the historical RIDF curve. Second is to fit a parametric function to these historical RIDF curves at different frequencies and durations to constitute the smoothen or station-specific RIDF curves.
The gamma or Pearson type III probability distribution function is given by:
where
x
0 is the location parameter,α
is the scale parameter andλ
is the shape parameter and Γ(λ
) is the gamma function ofλ
. The parameters of the distribution are estimated by maximum likelihood methodThe parametric function fitted to the historical RIDF curves is given by:
where
i
T ,D is the calculated rainfall intensity (in mm per hour) at return periodT
(in recurrence interval in years) and durationD
(in hours);[ a
1, a
2, a
3]
are model coefficients; and, SDe is the standard deviation of the model residuals (model error term). The equation as written above is to corrected for bias (underestimation of predicted value) due to the use of logarithmic transformation in the nonlinear least squares parameter estimation.⎥⎦⎤