Comparative Assessment of Different Methods in Generating Design Storm Hyetographs for the Philippines

Abstract

Design storm hyetographs are synthetic temporal rainfall patterns used as input for flood modeling studies, drainage design and hydrodynamic modeling. In practice, the Philippines adopts the alternating block (AB) method to derive hyetographs using PAGASA-synthesized rainfall intensity-duration-frequency (RIDF) curves. In this study, six other methods-AB from actual RIDF curve, actual normalized 24-hour storms and four different patterns derived by Huff (1967)-were tested using the tipping-bucket raingauge records of a local weather station. Nonparametric statistical tests were employed to determine the significant difference between and among distributions. Moreover, Chi-squared goodness-of-fit test was used to compare the hyetographs with data from actual storms. The PAGASA AB hyetographs, while accurate in some instances, do not always represent actual storms well. Furthermore, other methods may have better fits for other storms. This study recommends further research in establishing design hyetographs in the Philippines.

Full text

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Journal of Environmental Science and Management 21-1: 82-89 (December 2017) ISSN 0119-1144
Maurice A. Duka1*
Jonathan David D. Lasco2
Celso D.Veyra, Jr.1
Alexis B. Aralar1
1 Land and Water Resources Division
Institute of Agricultural Engineering
College of Engineering and Agro-
Industrial Technology University of
the Philippines Los Baños (CEAT-
UPLB), College, Los Baños, Laguna,
4031, Philippines
2 Department of Civil, Architectural,
and Environmental Engineering,
University of Texas at Austin, TX,
USA 78712
*Corresponding author:
mauriceduka@gmail.com
ABSTRACT
Design storm hyetographs are synthetic temporal rainfall patterns used as input
for ood modeling studies, drainage design and hydrodynamic modeling. In practice,
the Philippines adopts the alternating block (AB) method to derive hyetographs using
PAGASA-synthesized rainfall intensity-duration-frequency (RIDF) curves. In this study,
six other methods- AB from actual RIDF curve, actual normalized 24-hour storms and
four different patterns derived by Huff (1967)- were tested using the tipping-bucket
raingauge records of a local weather station. Nonparametric statistical tests were
employed to determine the signicant difference between and among distributions.
Moreover, Chi-squared goodness-of-t test was used to compare the hyetographs
with data from actual storms. The PAGASA AB hyetographs, while accurate in some
instances, do not always represent actual storms well. Furthermore, other methods
may have better ts for other storms. This study recommends further research in
establishing design hyetographs in the Philippines.
Key words: design storm hyetograph; alternating block; Huff; RIDF curve
INTRODUCTION
The apparent increase in storm intensity
and frequency over the recent years has made the
Philippines one of the most ood-prone countries in
the world. From 2004 to 2013, there had been over 60
reported major reported oods in the country (Badilla
et al. 2014), including those events brought about by
Typhoon Ketsana (Ondoy) on September 2009 and the
heavy Southwest Monsoon (Habagat) on August 2012.
According to Israel and Briones (2012), the World Bank
has stated that climate change may worsen the incidence
of ooding in already high risk areas and may make
other areas historically not ood-prone be eventually
vulnerable. This has prompted the Department of
Public Works and Highways (DPWH) to push for a
number of ood-mitigating projects and the Philippine
Atmospheric Geophysical and Astronomical Services
Administration (PAGASA) to carry out studies about
impacts of climate change on oods (Badilla et al. 2014).
Highly essential to ood modeling studies, drainage
design, hydrodynamic modeling and to engineering
Comparative Assessment of Different Methods in
Generating Design Storm Hyetographs for the
Philippines
hydrology in general (Palynchuk and Guo 2011) is the
development of reliable storm hyetographs. Hyetographs
depict the relationship of rainfall depth over a certain
duration and return period. Preference is given to the
use of actual storm distributions and its derivatives for
simulating ood events in existing drainage systems
(Santra and Das 2013), while synthetic hyetographs are
favored for designing stormwater facilities. Additionally,
the most appropriate hyetographs are necessary ow
modeling of watercourses as well as the hydrodynamic
analyses of the functioning of surface water runoff
systems. In the Philippines, actual hyetographs are
generally unavailable and research studies about
hyetograph development specic to a location and
climatic type have been scarcely, if not at all, established.
As a result, ood modelers and drainage designers resort
to extensively using the technique called “alternating
block” as recommended by DPWH-JICA (2003).
Alternating Block (AB) is a simple procedure of
generating synthetic storm patterns (Chow et al. 1988)
JESAM

83
and is heavily dependent heavily dependent on
Rainfall-Intensity-Duration-Frequency (RIDF) curves
(Ghazimezade et al. 2011). RIDF curves are derived from
statistical analysis of rainfall events, either on annual
maxima series or partial duration series, over a period of
time and used to capture important characteristics of point
rainfall for shorter durations (Bougadis and Adamowski
2006). In the Philippines, PAGASA generates the RIDF
curves and makes them commercially available for
hydrologists and drainage designers at a certain price.
Being the country with practically one of longest
and most complete rainfall records in the world, the
United States has actively pioneered to produce standard
methods for generating synthetic design storm proles.
To name a few, Pochwat et al. (2017) enumerated the SCS
(1986) Types I, IA, II and III, Huff (1967) Types I, II, III
and IV and Triangular Storms by Yen and Chow (1980).
Prodanovic and Simonovic (2004) likewise mentioned
the RIDF-based methods of USACE (2000) and Keifer
and Chu (1957), which exhibit extreme peaking patterns
similar to SCS and AB. Hyetograph research is so
advanced and established in the US that their existing
hyetographs are just continuously being improved.
Other countries have likewise explored developing
novel methods of hyetograph generation and in most
cases, adopted and modied the existing methods to suit
a particular location. These include the double triangular
hyetographs (Lee and Ho 2008) and regionalized design
storms (Yeh et al. 2013) in Taiwan, storm proles for the
arid mountainous and coastal regions of Jordan (Al-Rawas
and Valeo 2009) and design storms from multi-parameter
probability distribution modeling in Brazil (Beskow et
al. 2015). Modication of the Huff curves has also been
particularly popular especially for the three climatic
types in Slovenia (Dolsak et al. 2016), for design storms
and ood simulations in Guangzhou, China (Pan et al.
2017) and for Peninsular Malaysia (Azli and Rao 2010).
Research on establishing design storm hyetographs
in the Philippines is still at its infancy. This is due to the
fact that the pertinent data for this undertaking is either
limited or inaccessible. The AB method may ll in for this
gap for now but Guo and Hargadin (2009) emphasized
that SCS and RIDF-based design storms like those derived
from AB method, represent the “worst time distribution
to form a severe storm”. The imprudent use of these
methods may result to overdesign of drainage facilities.
Likewise, while the current practice of developing
design storms may take into account the factor of climate
change, it is but necessary to evaluate rst how well these
synthetic storm patterns represent the actual storms.
This study therefore aims to provide options in
generating design storm hyetographs in the context of
the Philippines. This has preliminarily tested the readily
available tipping bucket rainfall records from the UPLB-
PAGASA-National Agrometeorological Station (NAS).
Comparative assessment was done among the design
storms derived using the AB method and those from six
other selected methods namely, AB from actual RIDF
curve, actual normalized 24-hour storms and four patterns
developed by Huff (1967). Lastly, the reliability of each
method to represent the actual storms was investigated.
MATERIALS AND METHODS
Data Collection and Processing
The rainfall charts from the tipping-bucket recording
raingauge of the UPLB-PAGASA-NAS were used
to extract the maximum rainfall intensities at 0.5,
1-, 1.5-, 2-, 3-, 4-, 5-, 6-, 7-, 8-, 9-, 12-, and 24-hour
durations. Data from 1998 to 2014 was considered,
which corresponds to the same 17-year period used by
PAGASA to derive its own RIDF for that station. This
study particularly tested the readily available data from
that weather station in Los Baños, Laguna and as such,
this paper recognizes the limitation that the area only
represents one of the four climatic types in the country.
While the PAGASA RIDF (PAGASA 2014) is
available, it was imperative to create the study’s own
actual RIDF that is tailor-t to the actual rainfall data.
Gumbel method was used in the frequency analysis
of the rainfall values, which is the same method that
PAGASA uses in generating its RIDF. The actual RIDF
curve typically exhibits an exponential decrease of
rainfall intensity with duration (Figure 1). Storms with
shorter duration tend to have greater intensity for a given
return period. The RIDF was established only for 2-,
10-, 50- and 100-year return periods, noting that these
return periods are the most commonly used in drainage
evaluation and design (DPWH-JICA 2003).
Development of Different Hyetographs
Design storm hyetographs were generated from
RIDF and actual rainfall patterns from the same rainfall
charts of UPLB-PAGASA-NAS. The 24-hour rainfall
distribution was highly considered as this is the typical
synthetic storm temporal pattern used by PAGASA in
their ood risk assessments (Badilla et al. 2014) and
by DPWH in drainage design (DPWH-JICA 2003). The
study in runoff modeling of Levy and McCuen (1999)
likewise reinforces that 24 hours is a reasonable storm-
Journal of Environmental Science and Management Vol. 21 No. 1 (June 2018)

Generating Hyetographs in the Philippine Context
84
length specically for watersheds with sizes from 3.2
to 80.5 km2. Small catchments are sensitive to rainfall
events of short duration, while large catchments should
consider events longer than 30 minutes, to reasonably
account for the travel time of ood. The selected storms
must be sufciently long (in common cases, 24 hours) so
that the entire watershed is contributing to runoff at the
concentration point (Placer County Flood Control and
Water Conservation District 1999).
Hyetographs by Alternating Block Method
The alternating block method (Chow et al. 1988) is
a procedure used to generate synthetic storm patterns,
as recommended from the Manual on Flood Control
Planning (DPWH-JICA 2003). The rainfall intensity at a
certain return period for each of the duration is obtained
from the RIDF curve. The increments, or blocks, are
recorded into a time sequence with the maximum intensity
occurring at the center of the required duration and the
blocks are arranged in descending order alternately to
the right and left of the central block to form the storm
plots. The method was employed for both the PAGASA-
generated RIDF and the actual RIDF.
Normalized 24-hour Hyetographs
From the same rainfall charts, the extreme 24-hour
rainfall events were selected for the months of July to
November for the same 17-year period. Numerous
rainfall proles were produced and the values per prole
were rearranged to peak on the 12th hour using alternating
block method. The values per duration were averaged
and then individually divided by the maximum 24-hour
rainfall magnitude to produce a single normalized 24-
hour rainfall pattern. The hyetographs at specied return
periods were obtained by multiplying the ordinates of
the normalized 24-hour storm with the corresponding
24-hour rainfall depth obtained from Gumbel analysis.
Hyetographs by Huff (1967) Method
The four storm patterns by Huff method were
developed by considering the observed 24-hour storms
in the months of July to November. The storms, a total
of 70, were classied according to the quartiles in which
the rainfall is heaviest. The quartiles describe the time
of peak intensity occurred in a given storm. The storms
were grouped and analyzed into four distributions with
the following time of peak: Type I (0 to 6 hours); Type
II (6 to 12 hours); Type III (12 to 18 hours); and Type IV
(18 to 24 hours).
Nomenclature
For purposes of brevity throughout the study, each
distribution method has been given denotations (Table 1).
Statistical Analysis
Test for signicant difference
To prove signicant difference among the
Figure 1. Actual Generated RIDF Curve from UPLB-PAGASA-NAS.

hyetographs, nonparametric tests were employed.
Nonparametric tests are more advantageous than
parametric tests when the distribution is not normal
(Chalmer 1987). They usually involve ranking of
observations and deducing similarity from the ranks. In
this study, the method developed by Kruskal and Wallis
(1952), henceforth referred to as Kruskal-Wallis test
was employed to see if at least one of the distributions
are signicantly different (the alternative hypothesis).
Moreover, rank-sum test– which may be used in
comparing two independent datasets such as rainfall
data– was employed to see how each of the distribution
compare to what PAGASA is using and how the values
are overestimated or underestimated.
Goodness-of-t test for each hyetograph with actual
data
To accomplish the main objective of this work, i.e. to
see what distributions represent actual rainfall events well,
chi-squared goodness-of-t test was employed among
the distributions and selected storms from 1998-2014.
This test employs comparing observed and expected data
sets. The test statistic is obtained as follows:
where Oi is the ith value of the observed data set and
Ei is the ith value of the actual data set. Microsoft
Excel has a function (syntax: =CHISQ.TEST(actual_
range,expected_range)) to immediately compute the
p-value for sets of expected and observed data sets. In
the analysis, cumulative 24-hour rainfall hyetographs of
the seven distributions were deemed as expected values
and the 24-hour cumulative storm depths derived from
actual data provided by PAGASA were denoted to be the
observed or actual values. The cumulative hyetographs
were normalized by the total value so that the range of
values will be from 0 to 1. In determining the return
periods of the storms, RIDF curves were used. Since
it would be tedious to construct hyetographs for each
return period, the closest of the 2, 10, 50, and 100-year
return periods were selected. For example, if a value of
0.015 was obtained as the annual probability of non-
exceedance for a storm (corresponding to a 67 year
return period), the return period was rounded off to 50
years. Such assumption is not erroneous because the
distributions were normalized – in fact for the HUFF
distributions, the normalized distributions for each return
period are the same.
In selecting the type of intervals, one can opt to
select by equal probabilities or by equal intervals. The
latter was followed in this paper. In selecting the number
of intervals, one must avoid intervals that yield very low
expected values because the test statistic may blow up
(tend to innity) when expected values are near zero.
RESULTS AND DISCUSSION
Comparison of Generated Hyetographs
There were 24-hour cumulative hyetographs
generated from the different distribution methods at
different return periods (Figure 2). It can be observed
that not all curves are the same. Furthermore, AB-A
generally provides the largest values of rainfall and the
steepest slope. On the other hand, HUFF2 has consistently
produced the smallest curves. Moreover, HUFF4 has the
mildest slope.
The observation that there is variety among the seven
hyetographs was statistically proven using Kruskal-
Wallis test (Table 2) as applied to the 100-year storms.
At six degrees of freedom and 1% level of signicance,
the critical value is 16.8 while at 5% level of signicance
the critical value is 12.6. The value obtained is 21.45,
which indicates that there is at least one distribution that
is signicantly different from the rest.
It can be also hypothesized if there is signicant
85
Journal of Environmental Science and Management Vol. 21 No. 1 (June 2018)
Table 1. Nomenclature of the distributions.
Distribution Denotation
Alternating block method using RIDF from
PAGASA
Alternating block method using RIDF from
actual data
Normalized
Type 1 of HUFF method
Type 2 of HUFF method
Type 3 of HUFF method
Type 4 of HUFF method
AB-P
AB-A
NORM
HUFF1
HUFF2
HUFF3
HUFF4
Table 2. Summary of Kruskal-Wallis test parameters as
tested for 100-year storm patterns.
Distribution Average rank KW
AB-P
AB-A
NORM
HUFF1
HUFF2
HUFF3
HUFF4
118.146
153.500
196.125
188.740
184.740
172.167
166.083
21.45

86
difference between AB-P and each of the six other
distributions (Figure 2). To test this hypothesis, rank-sum
test was performed. At 5% signicance level, there is a
signicant difference between each of the six distributions
and AB-P (Table 3) at 5% signicance level; however at
1% signicance level, only NORM, HUFF1, and HUFF2
are supported by statistical evidence to have dissimilar
distributions with AB-P. Furthermore, the distributions
are overestimating the values with respect to AB-P based
from their rank sums with NORM overestimating the
most at 62.83%.
Validation of Hyetographs with Actual Data
To see how well the hyetographs represent the pattern
of actual data, the cumulative hyetographs normalized
by the total were compared. The best distribution varies
for each storm. For example, AB-P looks the best t for
the 2010 Typhoon (TY) Conson (Figure 3). However,
for the 1999 Tropical Storm (TS) Eve, HUFF4 seems
the best t with the other distributions seem to t poorly.
Furthermore, there is not one distribution that ts the
2008 TY Fengshen well.
To put numbers to the observations, chi-squared
goodness-of-t test was applied between each
distribution and each of the selected tropical cyclones
from 1998 to 2014. For a signicance level of 5%, a
p-value greater than 0.05 means that there is not enough
evidence to reject the null hypothesis that the distribution
Figure 2. Cumulative 24-hour hyetographs at different return periods.
Table 3. Parameters of rank sum test (N=96, n = 48, m=48, µ=2328, σ= 136.47).
Parameters Storm Hyetographs
AB-A NORM HUFF1 HUFF2 HUFF3 HUFF4
Rank sum
Rank sum (AB-P)
% difference
Z
Zα = 1%
Zα = 5%
2640
2016
30.95
2.28
2.58
1.96
2884.5
1771.5
62.83
4.07
2.58
1.96
2771
1885
47.00
3.24
2.58
1.96
2761
1895
45.70
3.17
2.58
1.96
2659
1997
33.15
2.42
2.58
1.96
2668
1988
34.21
2.49
2.58
1.96
Generating Hyetographs in the Philippine Context

87
of the hyetograph conforms to the distribution of the
selected storm (Table 4). For example, in comparing
AB with the 1998 TY Faith the p-value was 0.0000,
which means that the hyetograph from PAGASA is not
representative of the TY Faith, as are AB-A, HUFF1, and
HUFF4. However, NORM, HUFF2, and HUFF3 have
p-values greater than 0.05; therefore, they represent the
TY Faith well. For TY Faith, HUFF3 – with the largest
p-value – is the best t.
Several observations were observed in the chi-squared
test p-values (Table 4). First, there is not one distribution
that best represents each storm– one distribution may
be a better t for a certain storm than others. Second,
only TY Conson is best represented by AB-P compared
to the other distributions. Third, the distributions that
follow the alternating block method have storms that t
them reasonably but in some cases, there are better ts;
moreover, in some storms the family of alternating block
1
Figure 3. Cumulative hyetographs of the seven distributions and rainfall data from TY Conson, TS
Eve, and TY Fengshen.
Journal of Environmental Science and Management Vol. 21 No. 1 (June 2018)
Table 4. Chi squared test p-values (four signicant gures); values in bold numbers are the highest p-values for each
row, corresponding to the best distribution.
Storm Year AB-P AB-A NORM HUFF1 HUFF2 HUFF3 HUFF4
Faith
Eve
Lingling
13W
Nepartak
Xangsane
Durian
Mitag
Fengshen
Ketsana
Conson
Noul
Haikui
Son-Tinh
Trami
Hagupit
Rammasun
1998
1999
2001
2002
2003
2006
2006
2007
2008
2009
2010
2011
2012
2012
2013
2014
2014
0.0000
0.0001
0.0000
0.0000
0.1347
0.2494
0.0000
0.0727
0.0000
0.0000
0.8149
0.0727
0.0000
0.0000
0.0000
0.0000
0.0000
0.0019
0.0044
0.0000
0.0001
0.8300
0.3887
0.0001
0.5254
0.0000
0.0001
0.6260
0.5254
0.0003
0.0010
0.0017
0.0012
0.0026
0.2190
0.0673
0.2259
0.1611
0.7003
0.2752
0.4079
0.3680
0.0000
0.1472
0.1384
0.3680
0.0857
0.4152
0.1870
0.4636
0.0369
0.0065
0.0000
0.0174
0.0000
0.0002
0.0193
0.0221
0.0000
0.0000
0.0001
0.0006
0.0000
0.2322
0.2998
0.0000
0.0633
0.0000
0.1544
0.0113
0.0897
0.0417
0.5789
0.3783
0.1831
0.1678
0.0000
0.0367
0.1880
0.1678
0.1148
0.4247
0.0592
0.3217
0.0088
0.2524
0.3027
0.0334
0.0540
0.8332
0.3045
0.1279
0.7368
0.0000
0.2407
0.2022
0.7368
0.0323
0.0206
0.4217
0.3067
0.0478
0.0029
0.9467
0.0258
0.1320
0.0410
0.0017
0.0543
0.3186
0.0000
0.1831
0.0007
0.3186
0.0000
0.0009
0.1676
0.0092
0.0225

88
method fails miserably. Fourth, TY Fengshen has a
distribution that does not t any of the seven methods.
These observations can be summed up in one statement:
that the storms have varied distribution in time. Such
observation is not surprising. According to Wright et al.
(2013), extreme rainfall can vary greatly temporally and
spatially. Such variation has far-reaching implications in
the reliability of the current method used by PAGASA
and DPWH.
One implication based from these observations is to
avoid using exclusively one hyetograph to model all the
storms. In the Philippine context, where PAGASA and
DPWH use alternating block method, Table 2 revealed
that while in some cases the method can best represent
a storm, in other cases it does poorly. Moreover, even
if the method is reasonable in some storm events, there
are better methods. Furthermore, while HUFF3 seems to
represent storms better than alternating block method in
this analysis, the study does not intend to suggest that the
former should be adopted rather than the latter. In fact,
Koutsoyiannis (1994) has pointed out the advantages
of the alternating block method over the Huff methods
and while he also discussed the limitations of the latter,
he stated that alternating block method “remains a
powerful engineering tool that results in reliable design
values”. However, if in the case that the two agencies’
method misrepresents a storm, the method being an
underestimation (Table 3) of the other methods will
produce underestimated design ood values, which will
lead to the construction of ood-weak infrastructures.
The warning, therefore, is not to rely on only one
encompassing hyetograph for all the storms, rather to
be open-minded to pursue research on other methods of
generating rainfall hyetographs.
CONCLUSIONS AND RECOMMENDATIONS
In this study, design storm hyetographs using
alternating block and other methods were generated and
the reliability of each method to the represent the actual
storms was investigated with validation from the tipping
bucket rainfall records from 1998-2014 for the weather
station in Los Baños, Laguna. The design hyetographs for
2-, 10-, 50- and 100-year return periods were established
using alternating block method based on PAGASA’s
RIDF, actual generated RIDF and normalized 24-hour
storm, and four distributions of Huff. Nonparametric
statistical methods were employed to see how the current
method of PAGASA compares with other methods.
Goodness-of-t test was applied in each of the methods
tested to see if PAGASA represents each storm well
and which method best represents each storm. From the
results of the analysis, the following are concluded:
1. There are many ways of representing storms by
generating hyetographs and these methods are
signicantly different. Thus, if some methods represent
a storm well, other methods may perform poorly.
2. There is not one hyetograph that best represents every
storm. As a corollary, the alternating block method,
which is the method used by PAGASA and DPWH, is
not the best representation of any storm.
3. One distribution may be better than others in some
instances but worse in other instances. Therefore,
even though HUFF3 best represented most storms
in this paper, it still cannot be concluded that it is the
best method of generating hyetographs and while
alternating block only performed the best in one
storm, it does not follow that it is the worst method of
generating hyetographs.
4. In some storms, and considering the methods of
generating hyetographs discussed, all the available
methods may not be sufcient, such as in TY Fengshen.
Thus, having several models of representing rainfall
patterns is not a guarantee of the accuracy of the
representation.
There is not one best representation of storm and
that one distribution may be better than others in some
instances but worse in other instances. In conclusion,
variability of the performance of alternating block
method- the method used by PAGASA and DPWH in
designing hyetographs- should prompt the government
and the hydrologic community in the Philippines to put
more effort in storm hyetograph research in the country.
This study likewise recommends to test data from other
weather stations representing other climatic types.
REFERENCES
Al-Rawas, G. A. and Valeo, C. 2009. “Characteristic of
rainstorm temporal distribution in arid and mountainous
coastal region”. Journal of Hydrology 376:318-326.
Azli, M. and Rao, A. R. 2010. “Development of Huff curves for
Peninsular Malaysia”. Journal of Hydrology 388:77-84.
Badilla, R. A., Barde, R. M., Davies, G., Duran, A. C,
Felizardo, J. C., Hernandez, and Umali, R. S. 2014.
Enhancing risk analysis capacities for ood, tropical
cyclone severe wind and earthquake for the greater Metro
Manila area. Retrieved December 13, 2015 from http://
ndrrmc.gov.ph/attachments/article/1509/Component_3_
Flood_Risk_ TechnicaL_Report_-_Final_Draft_by_GA_
and_PAGASA.pdf
Generating Hyetographs in the Philippine Context

89
Journal of Environmental Science and Management Vol. 21 No. 1 (June 2018)
Beskow, S., Caldeira T. L., Mello, C. R., Faria, L. C. and Guedes,
H.A.S. 2015. “Multiparameter probability distribution
for heavy rainfall modeling in extreme southern Brazil”.
Journal of Hydrology: Regional Studies 4:123-133.
Bougadis, J. and Adamowski, K. 2006. “Scaling a model of
a rainfall intensity-duration-frequency relationship”.
Hydrological Processes 20(17):3747-3757.
Chalmer,, B.J. 1987. Understanding Statistics. Marcel-Dekker,
Inc, New York.
Chow, V.T., Maidment, D.R. and Mays, L.W. 1988. Applied
Hydrology. McGraw-Hill, New York, 572.
Dolsak, D., Bezak, N. and Sraj, M. 2016. “Temporal
characteristics of rainfall events under three climate types
in Slovenia”. Journal of Hydrology 541:1395-1405.
DPWH-JICA. 2003. Manual on Flood Control Planning.
Retrieved August 1, 2017 from https://www.jica.go.jp/
project/philippines/0600933/04/pdf/Manual_on_FC_
Planning.pdf
Ghazimezade, M., Mohammadi, K. and Eslamian, S. 2011.
“Estimation of design ood hydrograph for an ungauged
watershed”. Journal of Flood Engineering 2(1-2):27-36.
Guo, J. C. and Hargadin, H. 2009. “Conservative design
rainfall distribution”. Journal of Hydrologic Engineering
14(5):528-530.
Huff, F.A. 1967. “Time distribution of rainfall in heavy
storms”. Water Resources Research 3(4):1007–1019.
Israel, D. C and Briones, R. M. 2012. Impacts of Natural
Disasters on Agriculture, Food Security, and Natural
Resources and Environment in the Philippines. Retrieved
December 13, 2015 from https://dirp4.pids.gov.ph/ris/dps/
pidsdps1236.pdf
Keifer, C. J. and Chu, H. 1957. “Synthetic storm pattern for
drainage design”. Journal of the Hydraulics Division
ASCE 83(HY4):1–25.
Koutsoyiannis, D. 1994. “A stochastic disaggregation
method for design storm and ood synthesis”. Journal of
Hydrology 156(1-4):193-225.
Kruskal, W.H and Wallis, W.A. 1952. “Use of ranks in one-
criterion variance analysis”. Journal of the American
Statistical Association 47(260):583-621.
Lee, K. T. and Ho, J-Y. 2008. “Design hyetograph for typhoon
rainstorms in Taiwan”. Journal of Hydrologic Engineering
13(7):647-651.
Levy, B. and McCuen, R. 1999. “Assessment of Storm Duration
for hydrologic design”. ASCE Journal of Hydrologic
Engineering 4(3):209-213.
PAGASA. 2014. Rainfall Intensity Duration Frequency
Analysis Data for UPLB, Laguna. Hydrometeorological
Data Application Section, Hydro-Meteorology Division,
PAGASA. Purchased August 13, 2015.
Palynchuk, B.Y. and Guo Y. 2011. “A probabilistic description
of rain storms incorporating peak intensities”. Journal of
Hydrology 409:71-80.
Pan, C., Wang, X., Liu, L., Huang, H. and Wang, D. 2017.
“Improvement to the Huff curve for design storms and
urban ooding simulations in Guangzhou, China”. MPDI
Water 411(9)1-18.
Placer County Flood Control and Water Conservation District.
1999. Stormwater Management Manual. Auburn,
California, USA.
Pochwat, K., Slys, D. and Kordana, S. 2017. “The temporal
variability of a rainfall synthetic hyetograph for the
dimensioning of stormwater retention tanks in small urban
catchments”. Journal of Hydrology 549:501-511.
Prodanovic, P. and Simonovic, S. 2004. Generation of Synthetic
Design Storms for the Upper Thames River Basin CFCAS
Project: Assessment of Water Resources Risk and
Vulnerability to Changing Climatic Condition. Project
Report V. The University of Western Ontario, Canada.
Santra, P. and Das, B. S. 2013. ‘Modeling runoff from an
agricultural watershed of western catchment of Chilika
Lake through ArcSWAT”. Journal of Hydro-environment
Research 7:261-269.
USACE. 2000. Hydrologic Modelling System HEC-HMS.
Technical reference manual, United States Army Corps of
Engineers, Davis, California, USA.
Wright, D. B., Smith, J. A., Villarini, G. and Baeck, M. L.
2013. “Estimating the frequency of extreme rainfall using
weather radar and stochastic storm transposition”. Journal
of Hydrology 488:150-165.
Yeh, H-C, Chen, Y-C and Wei, C. 2013. “A new approach
to selecting regionalizes design hyetograph by principal
component analysis and analytic hierarchy process”.
Paddy Water Environment 11:73-85.
Yen, B. C. and Chow, V. T. 1980. “Design hyetographs for small
drainage structures”. Journal of Hydraulic Engineering
106:1055-1076.