Paper Template for HIC2004 s1

Regional Flood Frequency Analysis

for Philippine Rivers

LEONARDO Q. LIONGSON

National Hydraulic Research Center and Department of Civil Engineering

University of the Philippines, Diliman, Quezon City, Philippines

Regional flood frequency analysis has long been recognized as useful in providing statistical relationships for the transfer of flood frequency information from one river basin to another within the same homogeneous region, in order to augment data and improve estimates of annual flood magnitudes in the latter basin. This paper describes the regional study made on the annual maximum flood series of selected Philippine rivers situated in two water resources regions in northern Luzon, the largest island of the Philippines. Rivers with sufficiently long flow records were selected, and their sample means and higher moments were computed. Within each region, 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)). Regression equations are developed to relate the mean annual flood, Qmean, and other statistical moments to the basin properties such as basin area, A. The regional equations obtained for the Philippine rivers are also compared with similar equations developed in other countries of the Asia-Pacific region. Computations of probability weighted moments (PWMs) yield graphs of L-moment ratios which give indications of distribution functions such as generalized extreme-value distribution (GEV) which are expected to give a good fit to the data samples.

INTRODUCTION

Water Resources Regions 1 and 2 in northern Luzon are here selected for the study for three main reasons: first, the two regions are located in the intense-rainfall and flood-prone areas with one of the highest frequencies of tropical cyclone passage (45-70 times in the period 1948-2000); second, the regions include four of the country’s major river basins (RBs): Laoag RB - 1353 km2, Abra RB – 5125 km2, Abulog – 3372 km2, and the country’s largest, Cagayan RB – 25,649 km2 ; and third, post-WWII streamflow records exist for 29 river stations inside the regions with sufficient lengths (15 to 40 years) over a wide range of catchment areas (36 to 4800 km2). The annual flood series data are taken from NWRC [1] and DPWH [2]. In addition, the World Catalogue of Maximum Observed Floods (IAHS Publication 284) includes Cagayan River (A = 4,244 km2) with a maximum flood record of 17,550 m3/s.

Figure 1 shows a Philippine map with 20 major river basins located in the 12 water resources regions, including Regions 1 and 2 considered in this study.

Figure 1. 20 major river basins and 12 water resources regions of the Philippines

Past regional flood frequency analyses in the Philippines, using traditional method of moments and regression analysis of moments versus basin properties (such as catchment, area, channel slope, soil type and land-use/cover factors) were done by researchers and consultants in several regions of the Philippines. Lack of space in this paper prevents a detailed survey and discussion of these past studies.

STATISTICAL ANALYSIS OF ANNUAL FLOOD DATA

Method of Moments

The moments of annual flood data, {Qk , k=1,2, 3,…n}, are estimated as follows:

Mean: Qmean = (1/n) S Qk (1)

Standard Deviation: S = [ 1/(n-1) S (Qk - Qmean) 2 ] 1/2 (2)

Coefficient of Variation: Cv = S/Qmean (3)

Skewness Coefficient: Gs = n/[(n-1)(n-2)] S (Qk - Qmean) 3 / S3 (4)

Tables 1 and 2 show the summary of moment computations for 15 river stations and 14 river stations in Regions 1 and 2, respectively.

Table 1. Summary of annual flood data and moments for 15 stations in Region 1

Station / A, km2 / n / Qmean / S / Cv / Gs / Qmax
Laoag / 1355 / 19 / 4849 / 3370 / 0.6950 / 0.0417 / 11345
Bonga / 534 / 33 / 1162 / 1012 / 0.8712 / 1.4819 / 4392
Gasgas / 73 / 34 / 194 / 220 / 1.1355 / 2.2210 / 1041
Abra / 4813 / 20 / 4477 / 2772 / 0.6192 / 1.0217 / 10846
Tineg / 664 / 21 / 1317 / 882 / 0.6697 / 1.3190 / 3951
Abra-2 / 2575 / 19 / 2976 / 1245 / 0.4183 / -0.7503 / 4542
Sinalang / 120 / 19 / 496 / 417 / 0.8420 / 1.5274 / 1151
Sta.Maria-1 / 67 / 18 / 43 / 60 / 1.3920 / 3.3382 / 261
Sta.Maria-2 / 123 / 18 / 75 / 74 / 0.9821 / 2.3422 / 316
Bucong / 49 / 27 / 158 / 130 / 0.8216 / 0.9360 / 476
Buaya / 195 / 35 / 543 / 464 / 0.8539 / 1.5592 / 1950
Maragayap / 36 / 40 / 288 / 130 / 0.4529 / -0.3652 / 496
Baroro / 129 / 17 / 395 / 323 / 0.8180 / 1.3756 / 1321
Naguilian / 304 / 34 / 1160 / 718 / 0.6194 / 1.3004 / 3632
Aringay / 273 / 35 / 478 / 297 / 0.6209 / 0.8350 / 1082

Table 2. Summary of annual flood data and moments for 14 stations in Region 2

Station / A, km2 / n / Qmean / S / CV / Gs / Qmax
Baua / 103 / 19 / 280 / 167 / 0.5957 / 1.4340 / 777
Banurbor / 112 / 24 / 61 / 15 / 0.2382 / -0.9215 / 83
Abulog / 1432 / 18 / 2815 / 1258 / 0.4469 / 0.5102 / 5120
Sinundungan / 189 / 16 / 432 / 264 / 0.6096 / 0.6028 / 961
Matalag / 655 / 15 / 382 / 314 / 0.8220 / 1.5155 / 1195
Pangul / 312 / 21 / 824 / 1164 / 1.4122 / 1.6807 / 4014
Pinacanauan / 655 / 23 / 1000 / 638 / 0.6385 / 1.1851 / 2776
Casile / 195 / 24 / 131 / 65 / 0.4967 / 0.0693 / 241
Mallig / 563 / 24 / 426 / 247 / 0.5799 / 0.5679 / 1000
Siffu / 686 / 22 / 423 / 223 / 0.5257 / 0.8948 / 997
Magat / 4150 / 24 / 2688 / 1596 / 0.5937 / 0.7232 / 6795
Magat / 1784 / 18 / 674 / 425 / 0.6302 / 0.4307 / 1541
Matuno / 558 / 22 / 436 / 244 / 0.5593 / 1.0598 / 638
Diadi / 196 / 23 / 153 / 144 / 0.9402 / 2.4532 / 663

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) (5)

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 for other types of CDF.

Figure 2 provides the empirical plots of the regional growth curves for Regions 1 and 2. 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 annual flood value, Qj , in increasing order.

Figure 2. Empirical plots of the regional growth curves, Q(T)/Qmean = f(T), as a function of the reduced variate, y , or else return period, T, for Region 1 (left) and Region 2 (right)

Alternative forms of the reduced variate, y, which require the estimate of the shape parameter k of the fitted distributions, also yield theoretical straight growth curves:

Generalized Extreme Value (GEV): Q(T)/Qmean versus y = { (1- (- ln F)k }/ k

Generalized Logistic (GLO): Q(T)/Qmean versus y = [1 - {(1-F)/F}k ] / k

Generalized Pareto (GPA): Q(T)/Qmean versus y = {1 - (1- F) k} / k (6)

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 Qmean and basin properties such as basin area, A, are developed. In the present case, the following regression relations are developed:

Mean, Qmean = C Ab : (7)

Region 1: Qmean = 5.29 A0.8388 with R = 0.8729 and no. of stations = 15.

Region 2: Qmean = 3.37 A0.7987 with R = 0.8105 and no. of stations = 14.

Regions 1 and 2: Qmean = 5.90 A0.7628 with R = 0.8063 and no. of stations = 29.

Standard Deviaton, S = C Ab : (8)

Region 1: S = 6.92 A0.7392 with R = 0.8835 and no. of stations = 15.

Region 2: S = 1.65 A0.8326 with R = 0.7259 and no. of stations = 14.

Regions 1 and 2: S = 6.06 A0.6911 with R = 0.7350 and no. of stations = 29.

Skewness Coefficient vs. Coefficient of variation, Gs = a Cv + b : (9)

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 and 2: Gs = 2.8995 * Cv - 1.0418 with R = 0.8311 and no. of stations = 29.

Figure 3 shows the graph of the 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 3 are the maximum recorded floods versus area for comparison with the mean.

Figure 3. Regression line and scatter data for the mean flood, Qmean , versus drainage area, A. for the combined Regions 1 and 2, including plots of maximum recorded flood.

COMPARISON WITH OTHER ASIA-PACIFIC RIVERS

The present results for the regression of mean annual flood and standard deviation versus catchment area in Regions 1 and 2 in the Philippines are compared in Tables 3 and 4 with the results for the other Asia-Pacific rivers, obtained by Loebis [3]. The great differences in the values of the coefficients between countries may be explained by possible large variations in basin and channel slopes, effective rainfall, and other basin properties which also affect maximum flood magnitudes but are ignored in the regression functions of drainage area alone.

Table 3. Mean annual flood versus drainage area in the Asia-Pacific region

For Qmean = C Ab
Countries / C / b / R
Loebis [3]:
Australia (6 rivers) / 1.58 / 0.81 / 0.94
China (9 rivers) / 0.92 / 0.85 / 0.75
Indonesia (8 rivers) / 30.12 / 0.40 / 0.52
Japan (9 rivers) / 50.05 / 0.50 / 0.53
Korea (9 rivers) / 2.50 / 0.80 / 0.80
Laos (6 rivers) / 10.53 / 0.56 / 0.74
New Zealand (4 rivers) / 109.81 / 0.82 / 0.82
Thailand (5 rivers) / 70.97 / 0.26 / 0.65
This study:
Philippines (29 rivers) / 5.90 / 0.76 / 0.81

Table 4. Standard deviation versus drainage area in the Asia-Pacific region

For S = C Ab
Countries / C / b / R
Loebis [3]:
Australia (6 rivers) / 1.21 / 0.83 / 0.93
China (9 rivers) / 4.40 / 0.61 / 0.68
Indonesia (8 rivers) / 205.38 / -0.04 / 0.04
Japan (9 rivers) / 89.26 / 0.36 / 0.53
Korea (9 rivers) / 1.97 / 0.81 / 0.74
Laos (6 rivers) / 13.05 / 0.46 / 0.72
New Zealand (4 rivers) / 16.28 / 0.47 / 0.81
Thailand (5 rivers) / 0.57 / 0.68 / 0.62
This study:
Philippines (29 rivers) / 6.06 / 0.69 / 0.74

APPLICATION OF L-MOMENTS

Computations of probability weighted moments (PWMs) yield graphs of L-moment ratios which give indication of distribution functions such as generalized extreme-value distribution (GEV) which are expected to have a good fit to the data samples (Hosking [4]). Figure 4 is an example of a L-moment ratio diagram applied to the flood data of 29 river stations of Regions 1 and 2 in the Philippines. The scatter of data tends to group around the curves of the distribution functions GEV (generalized extreme-value), LN3 (log-normal), or PE3 (Pearson Type 3).

Figure 4. An L-moment ratio diagram for annual flood series of 29 river stations in Regions 1 and 2 of the Philippines. Legend of theoretical moment-ratio curves: GEV (generalized extreme-value), LN3 (log-normal), PE3 (Pearson Type 3).

The probability weighted moments are computed from data , Qj , in ascending order:

b0 = (1/n) S Qj ; br = (1/n) S (j-1) (j-2) … (j-r) Qj / [(n-1) (n-2) … (n-r)] (10)

Afterwards, the first L-moments are obtained from the equations

L1 = b0 L3 = 6 b2 – 6 b1 + b0

L2 = 2 b1 – b0 L4 = 20 b3 – 30 b2 + 12 b1 – b0 (11)

The L-moment ratios are defined by

L-CV: t2 = L2/L1

L-Skewness: t3 = L3/ L2

L-Kurtosis: t4 = L4/ L2 (12)

CONCLUSION

This paper has described and demonstrated the regional flood frequency analysis for Philippines rivers, using ordinary moments, flood index method, regional regression relations for moments and drainage areas, and L-moment ratios for identifying regional distribution functions.

REFERENCES

[1] NWRC, Philippine Water Resources Summary Data, Vol. 1 (1980).

[2] DPWH-BRS, Philippine Water Resources Summary Data, Vol. 2 (1991).

[3] Loebis, J., “Frequency analysis models for long hydrological time series in Southeast Asia and the Pacific region”, FRIEND 2002 - Regional Hydrology: Bridging the gap between Research and Practice, IAHS Publ. No. 274, (2002), pp 213-219.

[4] Hosking, J.R.M., Fortran routines for use with the method of L-moments, Version 3.03, IBM Research Report, RC 20525 (90933), (2000).