Regional Flood Frequency Analysis

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Regional Flood Frequency Analysis For
Selected Regions in the Philippines   Leonardo Q.
Liongson National Hydraulic Research
Center University of the Philippines Diliman,
Quezon City, Philippines 12th Regional
Steering Committee Meeting for Southeast Asia and
the Pacific UNESCO International Hydrology
Programme in conjunction with the International
Conference on Water Sensitive Urban Design
Cities as Catchments (WSUD2004) 22-26 November
2004 Hilton Hotel, Adelaide, Australia  
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• Objective
• 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.
• Outline
• 1. Introduction
• 2. Statistical Analysis of Annual Flood Data
• Flood Index Method
  Regional Growth Curves
• Regression Equations for
  Moment Estimates

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Above The track of Typhoon Imbudo across Luzon,
Philippines on July 22, 2003. Right A map of
the Philippines which shows the 20 major river
basins located in 12 water resources regions,
including Regions 1 and 2 which are considered
in this Study.
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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 countrys major river basins (RBs)
Laoag RB - 1353 km2, Abra RB 5125 km2, Abulog
3372 km2, and the countrys 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 two Philippine agencies
NWRC and DPWH. 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.
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Past regional flood frequency analyses in the
Philippines, using traditional method of moments
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. STATISTICA
L ANALYSIS OF ANNUAL FLOOD DATA   Method of
Moments The moments of annual flood data, Qk ,
k1,2, 3,n, are estimated as follows   Mean
Qmean (1/n) ? Qk   Standard
Deviation S 1/(n-1) ? (Qk - Qmean) 2
1/2   Coefficient of Variation Cv
S/Qmean   Skewness Coefficient
Gs n/(n-1)(n-2) ? (Qk - Qmean) 3 / S3
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Table 1. Summary of annual flood data and moments
for 15 stations in Region 1. Station A
n Qmean S Cv Gs Qmax km2 years cms cms
cms Laoag 1355 19 4849 3370 0.6950 0.0417 1134
5 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
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Table 2. Summary of annual flood data and
moments for 14 stations in Region 2. Station A
n Qmean S Cv Gs Qmax km2 years cms cms
cms 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 Pina
canauan 655 23 1000 638 0.6385 1.1851 2776 Cas
ile 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 Ma
gat 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
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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 FFx(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.
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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)/(n0.12),
corresponding to the jth-ranked annual flood
value, Qj , in increasing order.
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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)/Qmean
versus y 1 - (1-F)/Fk / k Generalized
Pareto (GPA) Q(T)/Qmean versus y 1 - (1-
F) k / k However, the value of the best-fitting
shape parameter, k, may vary from station
to station within a group, or else may
be constant in the group but the shift scale
parameters (u, a) will vary from station to
station. Hence, the straight curves are separate
non-parallel. A single regional growth curve
may be difficult to obtain.
Theoretical plots of reduced variate y(Q-u)/a
versus the CDFF(Q), for EV-I and GEV, which are
curved in linear scales of y and CDF.
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Bonga River (DA 534 sq.km.) Linear Fit for
GEV k-0.20 Q/Qmean 0.5380 1 - (- ln
F)k/k 0.5814 N 33 R2 0.9809
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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 R2 0.9867
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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
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
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 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.  
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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 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.
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Figure shows the graph of the 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
relations. (shown in next frame)
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Figure shows the graph of the 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 Cv K(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 Gs and Cv may 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 Cv K(T, Gs )
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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 rs) 109.81 0.82 0.8
2 Thailand (5 rivers) 70.97 0.26 0.65 This
study Philippines (29 rs) 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 Kore
a (9 rivers) 1.97 0.81 0.74 Laos (6 rivers)
13.05 0.46 0.72 New Zealand (4 rs)
16.28 0.47 0.81 Thailand (5 rivers)
0.57 0.68 0.62 This study Philippines (29
rs) 6.06 0.69 0.74
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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 provide a good fit to the data
samples (Hosking 4). The probability weighted
moments are computed from data , Qj , in
ascending order b0 (1/n) ? Qj
aa
jn
?
(j-1) (j-2) (j-r)
__________
Qj
br (1/n)
(n-1) (n-2) (n-r)
j1
j
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 The
L-moment ratios are defined by L-CV t2
L2/L1 L-Skewness t3 L3/ L2 L-Kurtosis t4
L4/ L2
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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 tend to group around the
curves of the distribution functions GEV
(generalized extreme-value), LN3 (log-normal), or
PE3 (Pearson Type 3).
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CONCLUSION This paper has described and
demonstrated the regional flood frequency
analysis for selected 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. Studies are
continuing for the parameter estimation and the
fitting of distributions in a regional context
in the two selected regions and as well as the
other regions in the Philippines.  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). Other
Sources World Catalogue of Maximum Observed
Floods, compiled by Reg Herschy, IAHS Publication
284, (2003). Gumtang, Reynold J., Effects of
Basin Parameters on the Streamflow Characterstics
of Region 1 Catchments, MS Thesis, L. Q.
Liongson (adviser), College of Engineering,
University of the Philippines, Diliman, Quezon
City ( 1990). Macabiog, Rafael B., Peak and Low
Flow Investigations of Benguet Mountainous River
Catchments, MS Thesis, L. Q. Liongson
(adviser), College of Engineering,
University of the Philippines, Diliman, Quezon
City ( 1995).