Chinese National Report on Indensity- Frequency - Duration (IFD) for AP FRIEND Phase II
RAINFALL DURATION-FREQUENCIES AND FLOOD FREQUENCIES Kuala Lumpur, Malaysia, June 6, 2004
5. FINAL REMARKS
-83-When one is interested in estimating the flood frequency curve for an ungaged site in the northern part of the Philippines, the flood mean and standard deviation can be obtained in the above plots given the drainage area of the watershed,. Then, the skewness coefficient can be obtained as a function of coefficient of variation, being the ratio of the standard deviation and the mean. Then, a three-parameter flood distribution function such as the log-Pearson type III or general extreme value distribution can be adopted whereby the parameters of these distributions can be determined by method of moments given the mean, standard deviation and skewness coefficient obtained from the plots. With the fitted probability distribution, the flood frequency curve can be formed.
5. FINAL REMARKS
In the Philippines, rainfall and streamflow data are collected by government agencies and they are available to the public. Analyses of these data such as rainfall duration-frequency analysis and flood frequency analysis have been done for various water resources regions in the Philippines and have been published elsewhere. However, most of the analyses are done for data at specific sites or gaging stations. Regionalization of rainfall duration-frequency curves and flood frequency curves for purposes of data transposition or estimation at ungaged sites have only been done by certain independent researchers for specific projects.
Country Report (Presentation) –Phillipine Guillermo Q. Tabios III
University of the Philippines Diliman, Quezon City
Kuala Lumpur, Malaysia June 6, 2004
UNESCO APFRIEND MEETING
Intensity Frequency Duration and Flood Frequencies
Country Report: Philippines
Outline of Report
• Data Availability
• Rainfall Duration-Frequencies
• Flood Frequencies
Rainfall Data Availability to APFRIEND
• Rainfall data (and other meteorological data) are available mainly from the Philippine Atmospheric, Geophysical and Astronomic Services Administration (PAGASA).
• Rainfall in particular at 10 mins (about 38 stations), 15 mins, hourly and daily (over 50 stations) time intervals are available in digital (20%) and paper (80%)
• Minimal charges to procure electronic form of data
• Website: www.pagasa.dost.gov.ph
Streamflow Data Availability to APFRIEND
• Streamflow data (and other meteorological data) are available mainly from the Bureau of Research Standards (BRS) of the Dept of Public Works and Highways (DPWH).
• Streamflow data are available on hourly and daily time intervals and record lengths range from 15 years to 40 years.
• There are streamflow data available from other agencies such as MWSS (water supply), NAPOCOR (hydropower generation), NIA (irrigation), etc.
• Minimal charges imposed to procure data in electronic form
Rainfall Intensity Duration-Frequency (RIDF) Studies
• National Water Resources Council (NWRC, now NWRB) in 1977 through 1981 published the first comprehensive RIDF results for 12 regions in the Philippines.
• The RIDF analysis were only performed for individual rainfall stations.
• The gamma probability distribution was adopted in the analysis.
NWRC Reports – RIDF Studies
Country Report (Presentation) –Phillipine RIDF Studies (continuation)
• PAGASA in 1981 published RIDF curves for about 50 gaging stations in the Philippines.
• The RIDF analysis were also performed for individual rainfall stations only.
• The extreme-value Type 1 (EV-1 or Gumbel) probability distribution was adopted in the analysis.
• Report available: Rainfall intensity-duration-frequency data of the Philippines, Volume 1, National Flood Forecasting Office, PAGASA, Quezon City.
RIDF Studies (continuation)
• Flood Control and Sabo Engineering Center (FCSEC) of DPWH recently published RIDF analysis of 1-day rainfall of selected gaging stations in the Philippines.
• RIDF analysis performed for individual rainfall stations only.
• The EV-1 or gamma probability distribution were used in the analysis.
• Overall RIDF parametric curves were also fitted in the station RIDF curves.
• These manuals were specifically written to assist engineers at DPWH.
• Report available: (see next slide)
FCSEC Reports
Regional RIDF Study in Benguet Mountain Province, Philippines (Independent Study) 1. Fit probability model to estimate rainfall
quantiles at different durations of data at each gaged site referred to as the historical rainfall duration-frequency (RDF) curve.
2. Fit parametric functions to historical RDF curves to constitute the station-specific RDF curves.
3. Regionalize parameters of station-specific RDF curves as function of mean annual rainfall, elevation and spatial coordinates to constitute the regional RDF curve.
Station Name Elev (m) Longitude Latitude MAP* Records*
Baguio City 1482 120.6 16.4167 3810.2 1949-1997
Adaoay 1120 120.825 16.6428 2215.7 1982-1992
Ambuklao 735 120.7417 16.4611 2088.4 1950-1996
Atok 1500 120.6667 16.5 3271.7 1950-1981
Bauko 1290 120.8667 16.9936 2256.9 1964-1994
Cervantes 1370 120.67 16.9753 3693.5 1979-1995
Itogon 914 120.6833 16.3667 3345.9 1961-1996
Mt. Data 2340 120.8667 16.8667 3102.7 1970-1995
Tubao 100 120.4167 16.35 2520 1966-1997
La Trinidad 1400 120.5833 16.45 3755.4 1976-1995
Bakun 1500 120.6533 16.7864 ---
---Rainfall Data:
The data used are annual rainfall maxima representing maximum 1-day, 2-day and 3-day rainfalls for each year of record.
0 500 1000 1500 2000
1-Day Rainfall Amount (mm) 0.00
0.50 1.00
CDF (Prob < Rainfall)
Baguio City
0 500 1000 1500 2000
2-Day Rainfall Amount (mm) 0.00
0.50 1.00
CDF (Prob < Rainfall)
0 500 1000 1500 2000
3-Day Rainfall Amount (mm) 0.00
0.50 1.00
CDF (Prob < Rainfall)
0 500 1000 1500 2000
1-Day Rainfall Amount (mm) 0.00
0.50 1.00
CDF (Prob < Rainfall)
La Trinidad
0 500 1000 1500 2000
2-Day Rainfall Amount (mm) 0.00
0.50 1.00
CDF (Prob < Rainfall)
0 500 1000 1500 2000
3-Day Rainfall Amount (mm) 0.00
0.50 1.00
CDF (Prob < Rainfall)
Rainfall Probability Modeling: lognormal; Pearson Type III, log-Pearson Type III and general extreme value distributions.
Country Report (Presentation) –Phillipine Station-Specific Rainfall Duration-Frequency Curve
The parametric function fitted to constitute the station-specific RDF curve is given by:
]
where R is rainfall quantile at return period T and duration D; A1, A2and A3are model parameters and SDe is the standard error.
Station
Baguio City 453.817 0.163 0.3969 0.00088097 Adaoay 122.122 0.2424 0.4878 0.00214242 Ambuklao 225.674 0.1498 0.5151 0.00106491 Atok 239.324 0.1622 0.6201 0.00186144 Bauko 207.313 0.1931 0.3259 0.00270466 Cervantes 329.618 0.2032 0.7205 0.00858452 Itogon 364.425 0.1511 0.4798 0.00138807 Mt. Data 214.459 0.1656 0.4949 0.0014232 Tubao 169.893 0.0987 0.8973 0.00826536 La Trinidad 404.441 0.144 0.4046 0.00105857 MEAN 273.109 0.1673 0.5343 0.00880966
A1 A2 A3 Sde^2
Annual Rainfall Maxima (mm)
Baguio City
Annual Rainfall Maxima (mm)
Cervantes
Quantile Estimate
RDF Equation Prediction
Regional Rainfall Duration-Frequency Curve The parameters of the station-specific RDF curves are regionalized using the following equation:
where MAP is mean annual rainfall, EL is elevation;
[LONG,LAT] are station coordinates and
are model parameters. A similar function is fitted to the regional MAP as a function only of EL, LONG and LAT.
LAT
-5.29E+04 0.2035 -0.1021 450 -100 0.815
-1.84E-07 -1.24E-05 1.79E-05 -0.008258 0.07104 0.406 -1.05E-05 8.17E-05 -0.0002304 -0.02433 0.2113 0.337
MAP 5.38E+05 1.127 -4443 0.4996 --- 0.754
β0 β1 β2 β3 β4
Annual Rainfall Maxima (mm)
1-day 2-day 3-day Bakun
Regional RDF Curve for Bakun
Flood Frequency Studies
• The National Water Resources Council (NWRC, now NWRB) in 1977 through 1981 in also included in its publications flood frequency analysis of selected rivers for 12 regions in the Philippines.
• The analysis were performed for individual stations.
• The log-Pearson Type III probability distribution was adopted in the analysis.
NWRC Reports – Flood Studies
Country Report (Presentation) –Phillipine Flood Studies (continuation)
• Flood Control and Sabo Engineering Center (FCSEC) of DPWH it is recent publication also included flood frequency curves of selected streamflow stations in the Philippines.
• The log-Pearson type III probability distribution were used in the analysis.
• These manuals were specifically written to assist engineers at DPWH.
• Report available: (see next slide)
FCSEC Reports – Flood Study Report
Flood Studies in the Philippines (Independent Study)
Regional Flood Frequency Analysis For Selected Regions in the Philippines
Presented by Dr. Leonardo Q. Liongson at the 12thRegional Steering Committee Meeting for Southeast Asia and the Pacific UNESCO International Hydrology Programme , Adelaide, Australia (November 2004).
Statistical analysis procedures presented:
• Traditional Methods
• Flood Index Method: Regional Growth Curves
• Regional Regression Equations for Moment Estimates
Traditional Method
Regional flood frequency analyses based on moments of individual streamflow gaging stations. Then, regression analysis of moments versus basin properties (such as catchment, area, channel slope, soil type and land-use/cover factors).
Method of Moments
The moments of annual flood data, {Qk, k=1,2, 3,…n}, are estimated as follows:
Mean: Qmean= (1/n) ΣQk
Standard Deviation: S = [ 1/(n-1) Σ(Qk- Qmean)2] 1/2 Coefficient of Variation: Cv = S/Qmean
Skewness Coefficient: Gs= n/[(n-1)(n-2)] Σ(Qk- Qmean)3/ S3
Flood Index Method: Regional Growth Curves
The flood index method is applied wherein the scaled data of annual flood values divided by the sample mean annual flood, Q(T)/Qmean,
are plotted versus
the return period, T, or equivalently
the reduced variate, y = -ln(-ln(1-1/T)) = -ln(-ln F)) where F=Fx(Q) equals the cumulative distribution function or CDF of the annual maximum flood.
The curves obtained are also called “regional growth curves”, which may be lumped or averaged into a general form:
Q(T)/Qmean= f(T)
where the form of the regional function f(T) depends on the regionally fitted CDF.
For example, if the fitted CDF is extreme-value Type I (EVI or Gumbel), then f(T) is a straight-line function of the reduced variate,
y = -ln(-ln(1-1/T)), otherwise it is a curved function of y for other types of CDF.
Empirical plots of the regional growth curves for Regions 1 and 2 in the Philippines. The coordinates for the reduced variate, y = -ln(-ln F)), were calculated using the Gringorten plotting position, F = (j-0.44)/(n+0.12), corresponding to the jth-ranked annual flood value, Qj, in increasing order.
-2.0 -1.0 0.0 1.0 2.0 3.0 4.0 5.0 reduced variate, y = -ln (-ln F)
& return period, T (years):
0.0
Philippine Water Resources Region 1 Flood Index Method:
Growth Curves of Annual Flood Series:
Q/Qmean vs. reduced variate, y number of stations = 15
1.05 1.33 1.672.00 3.33 5.00 10.00 25.00 50.00 100.00
-2.0 -1.0 0.0 1.0 2.0 3.0 4.0 5.0 reduced variate, y = -ln (-ln F)
& return period, T (years):
0.0
Philippine Water Resources Region 2 Flood Index Method:
Growth Curves of Annual Flood Series:
Q/Qmean vs. reduced variate, y number of stations = 14
1.05 1.33 1.672.00 3.33 5.00 10.00 25.00 50.00 100.00
Country Report (Presentation) –Phillipine
In the quest for regional growth curves,alternative forms of the reduced variate, y(F), which require a sample estimate of the shape parameter k of the fitted distribution and are computed from the plotting position for CDF = F(Q), may yield theoretical straight growth curves:
Q(T) = u + a y(F), by definition Q(T)/Qmean= u/ Qmean+ (a / Qmean) y(F)
= linear function of y(F) Thus, the candidate linear fits may be as follows:
Generalized Extreme Value (GEV):
Q(T)/Qmean versus y = { (1- (- ln F)k }/ k Generalized Logistic (GLO):
Q(T)/Qmeanversus y = [1 - {(1-F)/F}k ] / k Generalized Pareto (GPA):
Q(T)/Qmeanversus y = {1 - (1- F)k} / k for GEV and EV-1
GEV: k=-1.0
Theoretical plots of reduced variate y=(Q-u)/a versus the CDF=F(Q), for EV-I and GEV, which are curved in linear scales of y and CDF. for GEV and EV-1
GEV: k=-0.50 GEV: k=-0.20 Linear Fit for GEV: k=-0.20 EV-1
GEV; k=+0.10 Linear Fit for GEV: k=-0.20:
Q/Qmean = 0.5380 * [1 - (- lnF)^k]/k + 0.5814 k = -0.20
N = 33 R^2 = 0.9809
Bonga River (DA = 534 sq.km.):
Linear Fit for GEV: k=-0.20 Q/Qmean = for GEV and EV-1 GEV: k=-0.50 GEV: k=-0.40 Linear Fit for GEV: k=-0.40 EV-1
GEV: k=+0.10 Linear Fit for GEV: k=-0.40 Q/Qmean = 0.4929 * [1 - (- ln F)^k]/k + 0.4627 N = 34
R^2 = 0.9867 Gasgas River (DA = 73 sq.km.):
Linear Fit for GEV: k=-0.40 Q/Qmean=
0.4929 * [1 - (- ln F)^k]/k + 0.4627 N = 34
R^2 = 0.9867
Regression Equations for Moment Estimates
Once a regional growth function, f(T), is fitted, then quantiles of Q or the T-year flood estimates, Q(T) , may be computed from the regional relation Q(T) = Qmean f(T) , provided that a regression relation between Qmeanand basin properties such as basin area, A, are developed.
In the present case, the following regression relations are developed:
Mean, Qmean= C Ab:
Skewness Coefficient vs. Coefficient of variation, Gs= a Cv+ b :
Region 1: Gs= 3.7310 * Cv- 1.7257 with R = 0.9084 and no. of stations = 15.
Region 2: Gs= 2.1910 * Cv- 0.5506 with R = 0.7434 and no. of stations = 14.
Regions 1 & 2: Gs= 2.8995 * Cv- 1.0418 with R = 0.8311 and no. of stations = 29.
Regression line and the scatter data for the mean flood, Qmean, versus drainage area, A for the combined Regions 1 and 2.
Also plotted in figure are the maximum recorded floods versus area (+) for comparison with the mean flood.
The regression function for the mean flood can be improved by
adding basin rainfall and basin & channel slopes as independent variables.
10 100 1,000 10,000
Drainage Area, A, km^2 2
Mean & Maximum Flood, m^3/s
Qmean = 5.90 A^0.7628 R^2 = 0.6502 Number of stations = 29 Philippine Water Resources Regions 1 & 2 Mean Annual Flood & Maximum Observed Flood
vs. Drainage Area Maximum Observed Flood, Qmax Mean Annual Flood, Qmean Regression: Qmean vs. Drainage Area
Regression line and the scatter data for the standard deviation flood, S, versus drainage area, A for the combined Regions 1 and 2.
Instead of the standard deviation, the coefficient of variation, Cv = S/Qmean may used in the regional elations.
10 100 1,000 10,000
Drainage Area, A, km^2 2
Standard Deviation of Annual Flood, S = 6.0622 A^0.6911 R^2 = 0.5402
Number of stations = 29 Philippine Water Resources Regions 1 & 2 Standard Deviation of Annual Flood Series
vs. Drainage Area Standard Daviation, S Regression: Standard Deviation vs. Drainage Area
Country Report (Presentation) –Phillipine
0.0 0.5 1.0 1.5
Coefficient of Variation, Cv -1
0 1 2 3 4
Skewness Coefficient, Gs
Regression:
Gs = 2.8995 * Cv - 1.0418 Number of stations = 29 Unweighted average Cv = 0.7207 Unweighted average Gs = 1.0479 R^2 = 0.6907
Philippine Water Resources Regions 1 & 2:
Coefficient of Variation vs. Skewness Coefficient Station data points: (Cv, Gs) Regression line: Cv vs. Gs
Regression line and the scatter data for the skewness coefficient, Gs, versus coefficient of variation, Cv. for the combined Regions 1 and 2.
In the context of the Flood Frequency Factor formula:
Q(T) = Qmean + S K(T, Gs)
= Qmean [1 + CvK(T, Gs) ] where K(T, Gs) = the flood frequency factor, which is a known function of T and Gs, the constant or averaged regional values of Gsand Cvmay be selected to make a single “regional flood frequency factor formula” with only one “variable”, Qmean. In effect, the regional growth curve may be Q/Qmean = 1 + CvK(T, Gs)
Thank you.