SEASONALITY MEASURES TO FIND CATCHMENT

SIMILARITY FOR REGIONAL FLOOD FREQUENCY

ANALYSIS OF CATCHMENTS IN SRI LANKA
by
Nimal P.D. Gamage

Abstract The first step in regional frequency analysis is

identification of homogeneous regions in order for the
Regional flood frequency analysis is used for the results of frequency analysis to be valid. A region, in
'estimation of floods at sites where little or no data are this context, has come to mean a collection of catchments,
available. It involves the identification of groups (or not necessarily geographically contiguous, that can be
regions) of hydrologically homogeneous catchments and considered to be sim ilar in term s of catchm ent
the application of a regional estimation method in the hydrologic response. The goal of the regionalization
identified homogeneous region. An understanding of process can thus be viewed as the identification of
the hydrologic characteristics of a catchment is essential grouping of catchments (regions) that are Sufficiently
in order to obtain a reliable estimate of the relationship similar to warrant the combination and transfer of
between extreme flood quantiles and the associated extreme flow information for sites within the region. The
return periods. regions defined should thus be able to be considered
hom ogeneous w ith respect to extrem e flow
Catchment similarity is expressed using seasonality characteristics.
measures derived from the mean date of occurrence of
the annual m axim um flood and its associated This Paper describes the regionalization process, in the
dispersion. A regionalization approach is applied within context of regional flood frequency analysis. This is
the region of influence (ROI) framework and has the followed by a description of seasonality measures that
advantage of reserving the use of information derived have been used to characterize the timing and regularity
from flood m agnitudes for the examination of the of flooding events for catchments. Seasonality measures
homogeneity of flood regions as opposed to first using are subsequently suggested as an appropriate basis for
this inform ation to form regions. Regionalization characterizing the similarity of the flooding response of
technique is applied to a catchment in Sri Lanka and is catchments. A regionalization strategy is then developed
demonstrated result in the identification of region that and demonstrated through application to a collection
is effective for the estimation of extreme quantiles. of catchments in Sri Lanka.

1.0 Introduction 2.0 Regionalization

When data at a given location are insufficient for a Traditionally, the delineation of regions relied on
reliable estimation of flood quantiles, recourse must be geographic, political, administrative, or physiographic
made to regional frequency analysis. Regional flood boundaries. The resulting regions were assumed to be
^frequency an aly sis m akes use of sim ilarities in homogeneous in terms of hydrologic response, but this
^characteristics of flood at different gauging stations cannot in general be guaranteed, particularly if the
Iwithin a region. Records from nearby stations are used spatial variability of the physiographic and hydrologic
jto substitute spatial to tem poral characteristics. A characteristics is large. The importance of regional
\difficulty associated with flood frequency analysis is the homogeneity has been demonstrated by, among others,
|lack of sufficient data. Consequently, it is difficult to Hosking et al. (1985), and Lettenmaier et al. (1987).
j identify the parent distribution from which a sample is
i drawn. Large standard errors of estimate result because
•of small sample sizes. Estimation of the magnitude of
Eng. (Dr.) N im al P D Gam age, BSc (Eng.) (Hons), MSc (Hons), PhD, AMIE(SL),
*floods greater than the length of the available record Postdoctoral Research Fellow, Department o f Environmental Science and Human
represents an extrapolation in which the standard error Engineering, Saitama University, japan.
of estimate increases rapidly with increasing return
'periods.

7
Hydrologists have often used a regional regression and meteorological characteristics. Such catchments can I
model to estimate flow characteristics at ungauged sites thus be considered as p o ten tial can d id ates for1
based on catchment characteristics. Many studies use membership in the same region for regional frequency j
residuals from an overall regression relationship for an analysis. Although it would be possible to augment the*
entire area, to create geographically contiguous regions seaso n ality m easu res w ith p h ysiog rap h ic and)
based on the sign and magnitude of the residuals meteorological characteristics, this is not done herein l
(Wandle, 1977). However, deriving regions using this since it is often difficult to attain reliable estimates fori
method requires a large amount of subjective input. such attributes. The use of additional measures ofl
similarity could be expected to enhance the results from)
A novel regionalization approach involves dispensing the catchment grouping process.
with fixed regions. This approach allows each site to
have a p o ten tially unique set of station s w hich Directional statistics (Mardia, 1972) fdfm the basis for
constitutes the region for that site. Thus, it is possible defining similarity measures using the timing of flood
for two neighbouring sites to have completely different events. Following Bayliss and Jon es,.(1993), we can
sets of stations that represent the region for each site. define the date of occurrence of a flood as directional!
This methodology, w hich involves the transfer of statistics by converting the Julian date of the flood:
extreme flow information from similar stations to the occurrence for flood event Y to an angular value using:;
site of interest, was first suggested by Acreman and
Wiltshire (1987) and Acreman (1987). This approach ( In'
requires the choice of a threshold value that functions 6j = ( JulianDate)
as a cu t-o ff point for the d issim ilarity m easure. 1365;
Regionalization approaches, such as cluster analysis or
the ROl approach, require the selection of variables that where 6j = angular value (in radian) for the flood event!
are used to d efine the p air-w ise sim ila rity (or Y. Each flood date can now be interpreted as a vector
dissimilarity) for the catchments. There are two general with a unit magnitude and a direction given by 9.. If wei
types of v ariab les used to d efine sim ila rity ; have a sample of 'n' flood events (representing 'n' years]
physiographic catchment characteristics (such as the of extrean flow data), then the 'x' and 'y' coordinates ofj
drainage area, catchment slope, etc.) and flood statistics the mean flood date can be determined from: 1
(such as the L-m om ent ratios, or other statistical
measures, estimated from the available flood series).
D ifficulties can occur when using physiographic
catchment characteristics as similarity variables since
similarity in physiographic catchment characteristic
space does not necessarily imply similarity in hydrologic (3)1
„
li
response. This discrepancy may arise from the complex
interaction of physiographic param eters that are
responsible for generating a hydrologic response from where x and y represent the x and y coordinates ofi
a given set of meteorological inputs (Zrinji and Burn, the mean flood date and lie within, or on, the unit circle.!
1994). The same difficulty does not generally occur when The mean direction of the flood dates is then obtained,
flood statistics are used as the similarity variables., from:
However, the problem with this latter option is that the -3 6 5
flood statistics are then often used both to form the
MD = e ------ (4 )
2 7T
regions and to subsequently evaluate the homogeneity
of the collection of catchments in the region. This often The mean direction, 9 can be converted back to a day of
results in regions that are hom ogeneous bu t not the year using:
necessarily effective for regional flood frequency
analysis. In addition, the use of flood statistics as the — 365
basis for a sim ila rity m easure p reclu d es d irect MD = e ------ (5)1
2n
consideration of ungauged catchments.
The variable MD thus represents a measure of thej
3.0 Seasonality Measures average time of occurrence of flood events for a given
catchm ent. In addition to the m ean date of flood!
The timing and regularity of flood events can be used occurrence, it is also possible to determine a measure o^
as a measure of similarity in catchment hydrologic the variability of the ‘n' flood occurrence about this mean
response. Similarities in the timing and the seasonality date. This can be determined by defining the mean
of the flood response for catchments might be expected resultant as:
to result from similarities in influential physiographic

8
 r = yjx2 + y 2 (6) be com p aratively few 'o u tlie r' sites w ithin the
homogeneous ROI as these could unduly influence the
where ' f ' provides a measure of the spread of the data. estimation of extreme flow quantiles. Finally, the site of
Values of close to unity indicate a catchment with a interest should, ideally, be close to the 'centre' of the
strongly seasonal flood response. Values close to zero collection of catchments as measured in an appropriate
indicate that there is a great deal of variability in the similarity space. This latter requirement is to ensure that
date of occurrence of flood events for the catchment. It the site of interest is hydrologically representative of the
is to be expected that catchments with similar values sites in its region.
for MD and r might also exhibit similarities in other
In defining an ROI, a threshold value is generally
important hydrologic characteristics.
selected to determine a cut-off point for including
The seasonilty measure presented above can now be stations in the ROI. A number of strategies are available
employed in the definition of the dissimilarity between for selecting the threshold value (Burn, 1990, Zrinji and
catchments. This requires a single numerical value that Bum, 1994). The approach taken herein was to establish
will be used to define the seperation of two catchments a target membership of 25 stations for each ROI. A target
in seasonility space. An appropriate measure can be of 25 stations was selected based on results from
obtained using the E u clid ean d istan ce betw een Hosking and Wallis, (1996), demonstrating diminishing
catchment in the space of the V - and 'y-' coordinates of returns associated with increasing numbers of stations
the mean flood date for the catchment. The distance in a region. A larger target value might have been
measure is thus defined as: selected if the primary interest was in the extreme tails
of the distribution. The resulting collection of catchments
is then evaluated using a homogeneity te^t, described
d'i = [(*,-X jJ - J,)2] /2 <7> below, and if the ROI cannot be considered to be
homogeneous, the membership in the ROI is revised.
Revisions to the ROI membership are accomplished by
where d'i is the dissimilarity between catchments i and sequentially deleting the catchment that is furthest from
/, and ‘x ‘ and ‘y‘ are the 'x-' and 'y-' coordinates of the the catchment of interest and then re-evaluating the
mean flood date for catchment i. The value of 'd'i' is homogeneity of the revised ROI. This process is repeated
invarient to the choice of the origin for the seasionality until the ROI can be considered to be homogeneous.
measure (i.e. the definition of the water year). This is
one of the main benefits of using circular statistics to
define the seasonality of the flood events (Mardia, 1972).
4.2 Homogeneity Test
The m easure defined in Equ ation 7 gives the The homogeneity test used in this study was proposed
dissimilarity between two catchments and thus small by Hosking and Wallis, (1993), and is based on various
values for ‘d'i ' indicate that the corresp on d in g orders of sample L-moments ratios calculated from the
catchments exhibit similar seasonality in flood response. magnitudes of the peak flows. The homogeneity test is
based on the idea that in a homogeneous collection of
4.0 Catchment Grouping Process catchm ents, all catchments should have the same
population L-moments. This is, however, not true for
4.1 Regionalization the sample L-moments due to the sampling variation.
The question arises as to whether differences in sample
The region of in flu en ce (RO I) approach to L-moments indicate different populations, or arise from
regionalization is employed as the basis for the proposed sampling error. Therefore, the level of sampling, or
catchment grouping process. In the region of influence random, error has to be determined. Simulations can be
approach, a potentially unique collection of catchments used to establish an acceptable variability level. The
is defined as forming the ROI for each catchment. A ROI homogeneity test has three different levels that are
for a catchment can be viewed as a site-specific region evaluated by the variation of L-moments of different
consisting of a collection of gauged catchments that are order. In this study, the homogeneity test based on the
useful for the transfer of extreme flow information for LCV is used. More information about L-moments are
the estimation of extreme flow quantiles at the site of given in Gamage, (2001). The test is based on a weighted
interest. There are several desired characteristics for a variance of LCV, V, such that the statistics calculated is:
•collection of catchments forming the ROI for a given
site. The co llectio n of catch m en ts should be
hydrologically homogeneous so that the transfer of
extrem e flow inform ation is from sites that are N
hydrologically similar to the site of interest. There should
/=!

9
where 'n' = record length at site N = number of sites Figure 2 displays the results from calculating the
in the region. It is necessary to determine the mean and seasonality statistics for the catchments wherein each
the standard deviation of V to calculate the homogeneity catchment is plotted in the space defined by x and y .
measure. This can be done through simulation where a For calculating the seasonality statistics, the time of
realization of the statistic, labled Vk, is calculated from occurrence of a flood event is taken as the day on which
the klh simulation. The mean and standard deviation of the peak flow occurs during the event with the largest
the simulated population of the Vk values are defined peak flow magnitude in each year. Figure 2 reveals that
as fiv and era respectively. The homogeneity measure is the flooding regime for the collection of catchments
then defined as: exhibits a high degree of seasonality in that there are
two comparatively small ranges in the values for mean
date of occurrence of floods. The mean date of flood
H = V
- ^ - (09)
occurrence of the two ranges fall between Day 316
(November 11) to Day 22 (January 22) and Day 165 (June
A’
Acording to Hosking and Wallis, (1993), a region can be 14) to Day 278 (October 05). The value o f'r ' range from
declared homogeneous if the value of H is less than 1, 0.193 to 0.94 with an average value of 0.578 and a median
possibly homogeneous if the value of H is greater than value of 0.525. The magnitude of r for a catchment can
or equal to 1 but less than 2, and d efin itiv ely be determined in Figure 2 from the closeness of the
heterogeneous if the value of H is greater than or equal plotted point to the edge of the unit circle with points
to 2. on the unit circle corresponding to r =1.

5.0 Application It should be noted that during the period of the available
data set, discharge of some of the catchments were
regulated by upstream reservoirs or by a large number
5.1 Description of Data Set of small tanks (Master Plan for the Electricity Supply of
Sri Lanka, 1987). In the selected data set only 46
The use of seasonality measures for regional flood
catchments were not regulated by upstream reservoirs
frequency analysis is illustrated using a collection of 68
or by sm all tanks and ind icated in Table 1. The
catchm ents located in Sri Lanka. The data of the
discordancy statistics of these catchments were analyzed
catchments were obtained from Master Plan for the
by Gamage, (2001).
Electricity Supply of Sri Lanka, (1987). A total of 127
catchments of Sri Lanka are listed in the Master Plan for
the Electricity Supply of Sri Lanka, (1987). Out of this
set of catchments, 68 passed the screening criteria of
having at least 10 years of observation. It should be noted
that the record length threshold selected (10 years) is
not intended to signify that reliable at-site flood
frequency analysis could be conducted for catchments
having a record length as short as the threshold value.

It is decided to use the annual maximum flood series

for the analysis of this study as the extraction of the
partial duration series of floods is less straightforward
because of occasional bunching of flood peaks. The
p o ssib ility that such peak m agn itu d es are not
statistically independent has led to a certain amount of
unease about the validity of statistical methods used
with this model.

Locations of the 68 sites selected after screening are

shown in Figure 1. The selected data set contains a total
of 1564 stream flow observations of the period 1940 to
1985. The range of record lengths at the gauging stations
are from 10 to 42 years of annual maximum daily flow
values with a mean record length of 23 years and a
median length of 22.5 years. The catchment drainage
areas range from 53 km2 to 9606 km2 with an average
value of 1005 km2and a median value of 415 km2. Other
information of the selected sites i s given in Table 1.

10
 Table 1 Calculated Seasonality Measures of the selected sites

S it e Nam e R iv e r E le v . A re a Num . of L a t(N ) L o n (E ) r - bar MD

N um ber (m ) ( k m 2) R e c o rd s ( D e g .) ( D e g .) (D e g .)
1 Glencourse Kelarii Ganga 18 1463 36 6.9750 80.1808 0.425 190 5
2
------- —,------ Metiyadola Kelani Ganga 20 606 34 7.0261 80.2739 0.405 215 1
3 Algoda Bridge Sitawaka Ganga 26 345 15 6.9486 80:2611 0.490 180 4
4 Deraniyagala Sitawaka Ganga 82 152 28
------- 71------- 6.9250 80.3375 0.514 185 4
5 Kitulgala Kelani Ganga 56 388 38 6.9917 80.4125 0.609 205 7
6 Mousakelle Maskeli Oya 1158 122 18 6.8375 80.5500 0.439 181 6
7* Imbulana Gurugoda Oya 26 329 26 7.0631 80.2611 0.391 203.4
8 Laxapana Maskeli Oya 854 168 26 6.8875 80.5111 0.480 238.9
9 Holambuwa Gurugoda Oya 53 155 15 7.1931 80.2625 0.363 189.4
10 Hanwella Kelani Ganga 16 1782 10 6.9097 80.0792 0.411 270.8
11’ Putupaula Kalu Ganga 2 2598 37 6.6111 80.0653 0.401 211.3
12’ Millakanda Kuda Ganga 17 769 28 6.6236 80.1736 0.262 228.2
13' Malwala Kalu Ganga 18 329 24 6.6875 80.4233 0.511 187.6
14’ Nambapana Kalu Ganga 13 629 22 6.6864 80.4181 0.497 207.5
15’ Ellagawa Kalu Ganga 4 1393 26 6.7311 80.2167 0.456 195.4
16’ Dela Wey Ganga 29 220 27 6.6222 80.4528 0.265 249.3
17’ Kekulegama Kukule Ganga 200 334 10 6.5556 80.3417 0.460 202.6
18' Agaliya Gin Ganga 10 696 38 6.1875 80.1958 0.350 232.7
19' Jesmin Dam Gin Ganga 27 361 10 6.3444 80.3333 0.318 208.2
20’ Bopagoda Nilwala Ganga 18 442 42 6.1556 80.4847 0.273 215.9
21’ Bingimahara Nilwala Ganga 26 333 12 6.2111 80.4778 0.350 184.0
22’ Julampitiya Urubokka Oya 62 141 ■ 14 6.1944 80.7444 0.636 335.6
23’ Embil ipitiya Walawe Ganga 31 1580 22 6.3444 80.8986 0.358 355.2
24’ Samanalawewa Walawe Ganga 364 353 16 6.6750 80.8014 0.193 242.8
25 Lunugamwehera Kirindi Oya 35 913 25 6.3528 81.2194 0.525 356.0
26’ Wellawaya Kirindi Oya 154 160 11 6.7319 81.1069 0.372 22.1
27' Kuda Oya Kuda Oya 81 291 17 6.5250 81.1236 0.561 352.9
28 Kataragama Menik Ganga 34 787 34 6.4194 81.3292 0.652 343.8
29' Nakkala Kumbukkan Oya 160 216 10 6.8917 81.2958 0.677 354.3
30* Siyambalanduwa Heda Oya 55 295 20 6.9056 81.5444 0.891 6.5
31 Thottama Pannela Oya 34 95 14 7.1083 81.6903 0.924 13.2
32’ Periya Aru Magalwatuwan 36 119 32 7.5000 81.4889 0.899 6.5
33’ Nilobe Rumbukkan Oya 44 159 24 7.5111 81.3778 0.908 7.6
34' Maha Oya Maha Oya 39 300 11 7.5333 81.3583 0.940 12.1
35 Welikanda Maduru Oya 29 1062 29 7.9361 81.2500 0.914 4.8
36 Manampitiya Mahaweli Ganga 32 7418 33 7.9111 81.0861 0.790 361.2
37 Galoya Junction Gal Oya 84 199 12 8.1403 80.8528 0.526 347.1
38 Angamedilla Amban Ganga 67 1363 20 7.8500 80.9028 0.913 362.3
39* " Peradcniya Mahaweli Ganga 463 1167 39 7.2583 80.5903 0.558 233.7
40' Gurudeniya Mahaweli Ganga 425 1418 33 7.2750 80.6750 0.488 223.6
41’ Nalanda Nalanda Oya 243 126 10 7.6708 80.6375 0.802 342.4
42 Weragantota Mahaweli Ganga 76 4092 39 7.3167 80.9861 0.623 360.4
43* Elehera Amban Ganga 133 774 38 7.6792 80.7569 0.861 361.3
44’ Morape Kolmale Oya 640 555 32 7.5111 80.6222 0.389 246.0
45' Teldeniya Hulu Ganga 41 1 160 23 7.2944 80.7667 0.597 362.8
•
On

Randenigala Mahaweli Ganga • 141 2365 25 7.2028 80.9361 0.279 329.9

47’ Kandaketiya Badulu Oya 126 387 17 7.1750 81.0056 0.743 362.3
0.649 224.9
oo

Watawala Mahaweli Ganga 829 65 18 6.9472 80.5361

49' Talawakelle Kotmale Oya 1200 297 28 6.9403 80.6625 0.474 219.2
50’ Talawakanda uma Oya 575 520 12 ■ 7.0083 80.9736 •0.562 347.9
51 Altai Kantali Mahaweli Ganga 8 9606 16 8.3167 81.1667 0.886 363.8
52' Holbrook Agra Oya 1346 121 18 6.8806 80.6944 0.625 234.1
53* Welimada Uma Oya 1070 179 17 6.9042 80.9083 0.717 358.3
54* Wellewela Kalu Ganga 140 194 12 7.6069 80.8333 0.916 14.3
55’ Moragahamulla Galmal Oya 427 73 16 7.2825 80.8072 0.716 347.3
56 Pangurugaswewa Yan Oya 21 1311 33 8.7486 80.8792 0.864 356.8
57 Horowpotana Yan Oya 44 942 31 8.5767 80.8783 0.826 352.5
Wahalkada Hamillawa Oya 31 91 18 8.7267 80.8514 0.865 347.4
58
59 Kapachchi Malwathu Oya 36 2117 35 8.5986 80.2722 0.773 351.9
Tekkam Aruvi Aru 18 3071 11 8.7486 80.1833 0.712 359.6
60
Nochchiyagama kala Oya 24 1948 24 8.1972 80.0972 0.758 350.1
61
35 595 29 7.9639 80.0689 0.502 345.3
62 Mahauswewa Mi oya
Mi oya 10 1078 17 8.0472 79.9181 0.429 332.5
63 Tabbowa
1 2611 19 7.6000 79.8161 0.747 316.4
64 Chi law Deduru Oya
Maha Oya 49 804 23 7.2917 80.2403 0.332 251.9
65' Alawwa
12 1360 30 7.3028 79.9806 0.375 277.7
66' Badalgama Maha Oya
27 1191 21 7.3250 80.1153 0.438 274.5
67' Giriulla Maha Oya
28 53 14 7.1125 80.1708 0.466 164.9
68’ Karasnagala Attanagalu Oya
* N o upstream intervention

11
 Figure 1 Location of streamflow gauging stations
(Base Map Source: Master Plan for the Electricity Supply of Sri Lanka, (1987)).

Figure 2 Representation of catchments in terms of Seasonality Measures

12
5.2 Results When the annual maximum floods are distributed
according to a specified frequency distribution with cdf
The regionalization approach based on the seasonality F, the T-year event can be calculated as:
measures was dem onstrated using the catchment
Kitulgala (Site 5). There was no specific reason for
XT=F (11)
selecting this catchment. Variations of the moving
averages of the flood record at Kitulgala are shown in
Figure 3. Table 2 shows the results for the catchments
Consider a homogeneous region with N sites, each site
for which the regionalization approach based on the
i having sample size n.and observed annual maximum
seasonality measure. The identified 25 catchments in the
series x , j = 1,..., n.. The annual maximum series from a
ROI shows a very high heterogeneity with H=8.2. The
homogeneous region are identically distributed except
membership in the ROI was revised by sequentially
for a site specific scaling factor, viz., the index-flood. At
deleting the catchm ents that is furthest from the
each site the annual maximum series is normalised using
K itu lgala. This m ethod was able to id en tify a
the index-flood as:
hom ogeneous ROI with 6 sites for Kitulgala. The
heterogeneity measure of the identified ROI was 0.6 and
the sites in the region are listed in Table 2. The location Z- (12)
of the sites are shown in Figure 4. Mi

Years
Figure 3 Variation of 10 years moving averages of the annual maximum floods at Kitulgala

Table 2 Heterogeneity measure for the selected regions where ju.is the mean annual flood at site z, which is often
used as the index-flood. The sample L-moment ratios
Sites in the region of influence of Kitulgala H are estimated at each site and the regional record length
3,4, 5, 6, 7, 9 ,1 1 ,1 2 ,1 3 ,1 4 ,1 5 ,1 6 ,1 7 ,1 8 ,1 9 , 20, 8.2 weighted average L-moment ratios are calculated as:
21,39,40,44, 48,49, 52, 65, 68 N

4, 5, 6, 7, 48, 68 . 0.6
----- . r= 1,2 (13)
5.2.1 Estimation of quantiles for the selected 2>.
(=i
homogenous ROI
where is the r"' order sample L-moment ratio at site
The T-year event XTis defined as the event exceeded on z, and i f is the rth order regional average sample L-
average once every T years and is given as moment ratio.

The parameters of a regional frequency distribution can

be estimated using the method of L-moments together
^ > * r l =y <10) with the regional average sample L-moment ratios, as
shown, by Stedinger et al, (1993) and Hosking and
Wallis, (1996). The calculated quantile values of the
regional distributions are given in Table 3. Finally, the
T-year event at site i can be estimated as

13
 The test described above has been applied to the selected i
homogeneous region. For the region the data was tested 1
where A is the mean annual flood at site /, and zT is the against the GLO, GEV, GNO, P3 and the GPAj
regional growth curve. The regional growth curve is the distributions, and the results are shown in Table 4. This^
(1 - l/T)-quantile of the regional distribution of the m ethod id en tifies the GLO, GEV, GNO, and P3j
normalised annual maximum series as defined through distributions as valid regional distributions and rejects
Equation (12). the GPA distribution. However, the statistic ZD,ST

Table 3 Quantiles of the regional distribution selected for Kitulgala

Q u a n tile s o f th e R e g io n a l D is tr ib u tio n
- ( 1 - 1 /T) G e n e r a l L o g is tic G e n e r a l E x tr e m e G e n e r a l N o r m a l P earso n G e n e r a l P a r e to W akeby
V a lu e T y p e III
/i
0.0 1 0 .2 6 3 0 :3 0 2 0 .3 3 5 0 .3 9 5 0 .4 2 8 0 .3 1 4
0 .0 2 0 .3 1 4 0 .3 4 5 0 .3 6 6 0 .4 0 8 0 .4 3 5 0 .3 3 8
0 .0 5 0 .4 0 1 0 .4 1 6 0 .4 2 5 0 .4 4 1 0 .4 5 5 0 .4 0 2
0.1 0 .4 8 8 0 .4 9 0 .4 8 9 0 .4 8 8 0 .4 9 0 .4 8 7
0.2 0 .6 0 6 0 .5 9 6 0 .5 8 9 0 .5 7 4 0 .5 6 5 0 .6 0 5
0.5 0 .8 8 0 .8 7 1 0 .8 6 7 0 .8 6 0 .8 5 4 0 .8 6 2
0 .9 1 .6 0 3 1 .6 4 3 1 .6 6 4 1 .6 9 7 1 .7 2 3 1 .6 7 3
0 .9 5 . 1 .9 6 9 2 .0 0 7 2 .0 2 2 2 .0 3 6 2 .0 4 7 2 .0 4 2
0 .9 9 3 .1 0 9 3 .0 0 8 2 .9 3 6 2 .8 0 6 2 .6 9 9 2 .9 4 7
0 .9 9 9 5 .9 1 3 4 .9 7 2 4 .5 0 2 3 .8 8 3 3 .4 2 9 4 .3 7 1
i

5.2.2 Search for a suitable distribution for the suggests that either GNO or GEV would be a better';
selected hom ogeneous RO I using G oodness-of- choice, as the statistic ZDIST is very low.
fit test
i
5.2.3 C om parison of distributions using Probability
The goodness-of-fit test described by Hosking and
plots |
Wallis, (1996) is based on a comparison between sample
L-kurtosis and population L-kurtosis for different As pointed out by Hosking et al, (1985), comparison of
distributions. The test statistic is termed ZDISTand given different regional frequency distributions against
as observed data cannot be used to discriminate between
. DIST
different distributions, as the observed data represents
z DIST (15) only one of an infinite number of realisations of the 'true'
underlying population. However, the probability plots
^4
may reveal tendencies such as systematic regional biasi
where DIST refers to a candidate distribution, r D,ST is in the estimation of the extreme events.
the population L-kurtosis of selected distribution, t Ris.
the regional average sample L-kurtosis, E^is the bias of Table 4 The test statistic ZDISTof regional distribution
regional average sample L-kurtosis, and cr4 is the based on L-kurtosis.
standard deviation of regional average sample L- D is tr ib u tio n Z -V a lu e Rank
kurtosis.
G e n e r a l L o g is tic (G L O ) 0 .5 9 * 3

A four parameter kappa distribution is fitted to the G e n e r a l E x tr e m e V a lu e (G E V ) -0 .0 7 * 2

regional average sample L-moment ratios. The kappa G e n e r a l N o r m a l (G N O ) -0 .0 5 * 1
distribution is used to simulate 500 regions similar to P e a r s o n T y p e III (P 3 ) -1 .2 3 * 4
the observed region, and from these simulations B4 and G e n e r a l P a r e to (G P A ) -1 .7 8 5
o 4 are estimated. Further details of the procedure are
* Accepted as regional distribution
described by Hosking and Wallis, (1996). Hosking and
Wallis, (1996), recommend that only distributions for
To assess how well the proposed regional frequency
which |zD/sr| < 1.64 should be considered as suitable
distributions fit to the observed annual maximum series
regional distributions for the particular region.
calculated using L-Moments for the selected site are
shown in Figures 5 to 9. The empirical exceedance
probabilities for the ordered observations X(i) were

14
calculated using the m edian probability plotting
position as described by Stedinger et al. (1993), and 9.H
shown in Equation 16.

/- 0 . 3
>x (16) l
n + 0.4
where i is the rank of the ordered observation and n is
£ *o-|
the total number of observations. i \
.svl
6.0 Discussion and Conclusion
. .. v/
Analysis of the seasonality measure clearly indicated ■-V y
the two seasons prevailing in Sri Lanka. However, it
should be noted that no unregulated flood data could \"n : -•••\vv£r\ •'
be found in the season falls between Day 316 (November \v .- ■■
11) to Day 22 (January 22). Even though it is possible to » •« 10.3 81 J) I i '. j f i.o

identify ROI's of the catchments fall in this season, it is t^«gi(u4<(De(.)

not possible to check the homogeneity of the regions Figure 4 Geographic display of the region of influence for
included with those catchments. However, the mean site 5, Kitulgala.
annual floods of the catchments in this seasonality space
is highly seasonal, compared to the catchment in the
other seasonality space, with rvalues of most of the
catchments close to unit circle (Figure 2).

Few catchments falling in to the ROI of Kitulgala

indicate high degree of heterogeneity between the
catchments in Sri Lanka. The identification of a suitable
regional distribution of the selected homogeneous ROI
with 6 sites was based on a Goodness-of-fit test and
evaluated using the probability plots. The goodness-of-
fit test statistic, however, suggest that region should
p referably use GNO or GEV d istrib u tio n s. The
probability plots of the selected site indicate marginal
variations of the estimates of all the distributions for
smaller return period floods of less than 10 years. GLO x Observed

Calculation of quantiles using the seasonality-based ROI

Figure 5 Probability plot for Kitulgala using General
can involve the weighting of the information from the Logistic distribution
stations in the ROI in accordance with the similarity of
each station with the site of interest. This was not done
in the p resen t w ork but form u latin g preferred
approaches to this task remains an avenue for further
investigation.

The regionalization approach presented herein is

directly applicable to sites that are gauged. The analysis
of ungauged sites might be achieved by estimating the
values for the seasonality statistics at an ungauged site
using available physiograp hic and m eteorologic
information. Alternatively, gauged sites that are similar
to an ungauged site could be identified and seasonality
sta tistics estim ated for the ungauged site as a
•combination of the values at the gauged sites that are Return period, T (Years)
similar to the ungauged site. This too remains an avenue — GEV x Observed
for further research.
Figure 6 Probability plot for Kitulgala using General
Extreme Value distribution

15
 7.0 REFERENCES
Acrem an, M .C.. 1987. R egional Flood Frequency'
Analysis in the UK: Recent Research-N ew Ideas.i
Institute of Hydrology, Wallingford. UK. *
i
Acreman, M.C.. Wiltshire. S.E., 1987. Identification ofi
regions for regional flood frequency analysis. EOS 681
(44), 1262 (abstract).

Baylis.s, A.C., Jones, R.C.. 1993. Peaks-Over-Threshold

Flood Database: Summary Statistics and Seasonality. IH
Report No, 121. Institute of Hydrology,-Wallingford, UK.
Bum, D.H., 1990. Evaluation of regional flood frequency
analysis with a region of influence approach, Water:
GNO x Observed
Resour. Res., 26(10), 2257-2265. !

Figure 7 Probability plot for Kitulgala using General Gamage, N.P.D., 2001. Analysis of regional homogeneityj
Extreme Value distribution of catchments in SriLanka by L - Moments. "Engineer",:
Journal of the Institution of Engineers, Sri Lanka. Vol:J
2500 xxxiv, No: 2, May 2001. pp: 78 -87. I

Hosking, J.R.M., Wallis, J.R., 1996. Regional Frequency

A n aly sis: An A pproach Based on L-m om ents.
Cambridge University Press.

Hosking, J.R.M., Wallis, JR.> 1993. Some statistics useful;

in regional frequency analysis. Water Resour. Res., 29,!
271-281. ;

Hosking, J.R.M ., Wallis, J.R., Wood, E.F., 1985. An!

appraisal of the regional flood frequency procedure in;
the UK "Flood Studies Report", Hydrol. Sd. J.. 30 (1),|
85-109. 1
I
Lettenmaier, D.P., Wallis, J.R., Wood, E.F., 1987. Effect of |
-------- P3 x Observed
regional heterogeneity on flood frequency estimation,
Figure 8 Probability plot for Kitulgala using Pearson Type Water Resour. Res., 23 (2), 3 13-323.
III distribution
M ardia, K.V., 1972. Statistics of D irectional Data.j
Academic Press, New York. NY.

Master Plan for the Electricity Supply of Sri Lanka, 1987:

Report Published by Ceylon Electricity Board. Volume
S -l, July 1987.

Reed, D.W., 1994. Plans for the Flood Estim ation

Handbook, Proceedings, MAFF Conference of River and
Coastal Engineers. Loughborough, UK. pp. 8.3.1-8.3.8.

Stedinger, J.R., Vogel, R.M., Foufoula-Georgiou, E., 1993.

Frequency analysis of extreme events. In: Maidment, DR.
(Ed.). Handbook of Hydrology. McGraw-Hill, New York.

Wandle, S.W., 1977. Estimating the magnitude andi

frequency of flood on natural streams in Massachusetts.
US Geological Survey Water Resources Investigations
GPA x Observed 77-39, 27 pp.

Figure 9 Probability plot for Kitulgala using General Zrinji. Z., Bum, D.H., 1994. Flood frequency analysis for1'
Pareto distribution ungauged sites using a region of influence approach, J. I
Hydrol,, 153.1-21 f

16