P.hd Research Proposal
CANDIDATE NAME:
Mohammad Nura
SUPERVISOR:
Associate Professor Dr. Zahrahtul Amani Zakaria
RESEARCH TITLE:
Regional Analysis of annual maxmum rainfall Via TL-Moment method
INTRODUCTION:
Rainfall data have been collected for decades long in Malaysia through hydrological stations installed
across the country. The Hydrology and Water Resources Division of the Department of Irrigation and
Drainage (DID), Malaysia is responsible for handling the rainfall data collection and had done a great
job in recording the rainfall data for decades long. In this research, the rainfall data is to be analysed
while improving the prediction of large values in extreme precipitation frequency analysis.
Rainfall pattern analysis is a critical component in understanding climate dynamics,
particularly in regions where weather patterns significantly impact the environment and human
activities. Conventional L-moment method of analyzing rainfall data often focus on annual maximum
values, a practice that has provided valuable insights in various climatic contexts. However, this
approach may not fully capture the nuances of rainfall patterns in regions with distinct climatic
characteristics, such as tropical areas. This research proposal focuses on Terengganu, a state in
Malaysia, situated near the equator, known for its tropical climate and consistent rainfall patterns.
Terengganu's equatorial location results in a unique precipitation regime, characterized by
frequent and intense rainfall events. This climatic feature challenges the conventional L-moment
method of rainfall analysis, which often fail to account for the regularity and intensity of such events
in tropical regions. The L-moment method, traditionally used for datasets with significant outliers,
presents an opportunity for a more nuanced analysis when applied to daily rainfall data in such a
setting. While the L-moment method has shown effectiveness in various hydrological studies, its
application in analyzing daily rainfall data in a tropical climate is less explored.
The primary motivation behind this research is the hypothesis that daily rainfall data in a
tropical climate like Terengganu's may offer more insightful information about extreme weather
events compared to annual maximum data. This is especially pertinent in understanding the return
periods of extreme events, which are critical in flood risk management and water resource planning.
The frequent occurrence of heavy rainfall in Terengganu contrasts with the less frequent extreme
events in temperate regions like the USA and UK, necessitating a reevaluation of standard analytical
approaches.
This research aims to bridge this gap by adapting and applying the L-moment method to daily
rainfall data in Terengganu. Through this approach, the study seeks to provide a more accurate
representation of the rainfall patterns and extreme events in this tropical region. The findings of this
research could offer significant implications not only for local climate and environmental studies but
also for broader applications in similar tropical settings globally.
PROBLEM STATEMENT
The conventional methods of rainfall data analysis, particularly in the field of hydrology, typically
utilize annual maximum data to study extreme weather events. However, in tropical climates like
that of Terengganu, Malaysia, these methods may not accurately capture the true nature of rainfall
patterns. The frequent and intense rainfall events in these regions challenge the traditional
analytical frameworks, which are more suited to temperate climates where extreme weather events
are less frequent and more variable. This discrepancy raises a critical issue: there is a potential
misrepresentation of rainfall characteristics in tropical regions when using conventional methods,
possibly leading to inadequate understanding and mismanagement of water resources and flood
risk.
STUDY RATIONALE
This research aims to address the gap in current methodologies by adapting the L-moment and
frequency analysis method for daily rainfall data analysis in Terengganu, Malaysia. The rationale for
this study is threefold:
1. Methodological Adaptation for Tropical Climates: There is a pressing need for
methodological innovations that account for the unique characteristics of tropical climates.
By focusing on daily rainfall data, this research seeks to provide a more nuanced
understanding of precipitation patterns, which is crucial for accurate weather forecasting,
water resource management, and disaster preparedness in these regions.
2. Enhanced Understanding of Extreme Weather Events: The analysis of daily data using the Lmoment method may offer new insights into the frequency, intensity, and return periods of
extreme rainfall events in Terengganu. This understanding is vital for infrastructure planning,
agricultural activities, and developing effective strategies to mitigate the impacts of climate
change.
3. Global and Local Relevance: While this study is geographically focused on Terengganu, the
findings could have broader implications. Adapting analytical techniques for tropical climates
can benefit other regions with similar climatic conditions. Moreover, the methodological
insights gained from this study could contribute to the global discourse on climate science,
particularly in understanding and managing the impacts of extreme weather events in
tropical regions.
In conclusion, this research is not only methodologically innovative but also of significant practical
importance. It aims to enhance the accuracy of rainfall data analysis in tropical climates and
contribute to more informed environmental and climatic decision-making processes, both locally in
Terengganu and in other parts of the world facing similar climatic challenges.
RESEARCH QUESTIONS
1. What are the Distributional Characteristics of Annual Maximum and Daily Rainfall Data in
Terengganu, Malaysia?

This question corresponds with the first objective of characterizing the distributional
properties of the datasets. It aims to understand the inherent differences in the
distribution patterns of annual maximum and daily rainfall data, providing a basis for
selecting the appropriate analysis method.
2. How Effective are Different Performance Metrics in Evaluating the Fit of Assumed
Distributions to the Original Rainfall Data?

Aligned with the second objective, this question investigates the effectiveness of
various statistical metrics (such as the Kolmogorov-Smirnov and Anderson-Darling
tests) in assessing the adequacy of the distribution models applied to the rainfall
data.
3. Which Distribution Model Provides the Best Fit for Rainfall Data in Terengganu, and How
Does This Vary Between Annual Maximum and Daily Data?

This question is designed to address the third objective. It focuses on identifying the
most suitable distribution model for the rainfall data and explores whether the bestfit model differs when comparing annual maximum and daily datasets.
4. What Insights Can Be Gained From Return Period Analysis in Predicting the Frequency of
Extreme Rainfall Events in Terengganu?

Linked to the fourth objective, this question aims to understand how return period
analysis, based on the best-fit distribution, can be used to predict the frequency and
magnitude of extreme rainfall events. This question is crucial for practical
applications in areas like disaster management and urban planning.
RESEARCH OBJECTIVES
1. To Characterize the Distributional Properties of Annual Maximum and Daily Rainfall
Datasets: This objective involves analyzing the probability distribution functions (PDFs) of
both datasets. The focus will be on identifying the normal-like distribution of annual
maximum data and the heavy right-tailed nature of daily data, thereby justifying the use of
L-moment analysis for the latter. This step is crucial as it lays the foundational understanding
of the data characteristics and supports the rationale for selecting appropriate analytical
methods.
2. To Implement and Evaluate Performance Metrics for Distribution Fit Assessment: This
entails applying statistical metrics to evaluate how well the assumed distributions (derived
from L-moment analysis) fit the original rainfall data. Metrics such as goodness-of-fit tests
(e.g., Kolmogorov-Smirnov, Anderson-Darling) will be utilized. This objective is essential for
validating the effectiveness of the chosen analytical approach and ensuring the reliability of
your results.
3. To Identify the Optimal Distribution Model for Rainfall Data: The goal here is to compare
different potential distributions (like 4-parameter kappa, GEV, GLO, GPA) and determine
which provides the best fit for both annual maximum and daily rainfall datasets. This
objective is vital for ensuring that the most accurate and representative distribution is used
for further analysis, particularly for extreme event characterization.
4. To Conduct Return Period Analysis for Extreme Rainfall Event Prediction: This involves
using the best-fit distribution to perform frequency analysis and calculate return periods for
extreme rainfall events. This step is crucial for practical applications, such as flood risk
assessment and water resource management, providing valuable insights for policy and
planning in relation to extreme weather events.
OPERATIONAL DEFINITION
1. L-Moment: L-moment refers to a statistical method used for analyzing probability
distributions and characterizing the behavior of hydrological data. It is particularly effective
in handling skewed distributions and datasets with outliers. L-moments are used to estimate
distribution parameters and to provide summaries of the data such as mean, variance,
skewness, and kurtosis.
2. Extreme Precipitation Events: These are defined as rainfall events that significantly exceed
the average patterns in terms of intensity and duration. For this study, 'extreme' is
operationally defined based on local historical rainfall data thresholds, which are identified
as events that surpass the 95th percentile of daily rainfall data in Terengganu.
3. Tropical Climate: This term refers to the climate characterized by consistent high
temperatures and significant rainfall throughout the year, as experienced in Terengganu,
Malaysia. It includes the seasonal variations due to monsoons, but generally lacks the wide
temperature extremes seen in temperate climates.
4. Daily vs. Annual Maximum Rainfall Data: 'Daily rainfall data' refers to precipitation
measurements recorded on a daily basis, whereas 'annual maximum rainfall data' compiles
the maximum recorded rainfall data for each year. This distinction is crucial in this research
for comparing the applicability and effectiveness of the L-moment analysis on different data
scales.
5. Goodness-of-Fit Tests (Kolmogorov-Smirnov and Anderson-Darling Tests): These are
statistical tests used to assess the fit of a chosen probability distribution to the observed
data. In this study, they are used to evaluate the effectiveness of L-moment method in
modeling rainfall data distributions.
6. Return Periods: In hydrological context, the return period refers to the average interval of
time between occurrences of a given rainfall event (e.g., a specific intensity and duration) at
a particular location. It is a statistical measure used in this research to assess the frequency
of extreme rainfall events.
LITERATURE REVIEW
a) Precipitation Behavior in Temperate and Tropical Climate Regions
Temperate Climate Precipitation Patterns: In temperate climate regions, precipitation patterns are
typically characterized by a more uniform distribution throughout the year, although they can exhibit
significant seasonal variations depending on the geographical location. According to Dai et al. (1997),
temperate regions often experience distinct wet and dry seasons, with rainfall patterns influenced by
mid-latitude cyclones and frontal systems. These regions can also experience extreme precipitation
events, but such events are generally less frequent and less intense compared to tropical climates.
The variability in precipitation in these regions is often linked to larger-scale atmospheric circulation
patterns like the El Niño Southern Oscillation (ENSO) and the North Atlantic Oscillation (NAO) (Hurrell,
1995).
Tropical Climate Precipitation Patterns: Tropical climates, on the other hand, are characterized by
high temperatures and significant rainfall, often resulting in a distinct wet season and a relatively dry
season. As described by Hastenrath (1991), tropical regions typically exhibit more intense and
frequent rainfall events, largely due to convective processes associated with high temperatures. These
regions are often subject to monsoons, tropical cyclones, and other systems that can lead to heavy
rainfall events. The distribution and intensity of rainfall in tropical climates are influenced by factors
such as the Intertropical Convergence Zone (ITCZ) and monsoonal flows, which can lead to significant
spatial and temporal variability in precipitation (Ramage, 1971).
Comparative Analysis: The contrast in precipitation behavior between temperate and tropical
climates has significant implications for hydrological modeling and frequency analysis. While
temperate regions may often use annual maximum data to analyze extreme precipitation events, this
approach may not be adequate in tropical regions where extreme events are more frequent and the
daily variation in rainfall is higher. This difference necessitates tailored approaches to rainfall data
analysis in tropical climates, considering the higher frequency and intensity of extreme events
(Madsen et al., 2014).
b) Probability Distributions in Extreme Precipitation Frequency Analysis
In the field of extreme precipitation frequency analysis, probability distributions are fundamental tools
for describing and predicting the frequency and intensity of extreme rainfall events. Among these, the
Generalized Extreme Value (GEV), Generalized Logistic (GLO), Generalized Pareto (GPA), and Kappa
distributions are widely recognized for their flexibility and applicability in modeling diverse types of
hydrological data.
The GEV distribution, a unifying model for the block maxima method, is particularly useful in extreme
value theory and has been extensively applied in analyzing the maximum or minimum values of
meteorological data series (Coles, 2001). The GLO distribution, with its ability to model asymmetric
data, is another critical tool in hydrology, offering an effective means of representing skewed
distributions often observed in rainfall data (Katz et al., 2002).
Similarly, the GPA distribution is frequently employed in peak-over-threshold analysis, a method that
focuses on extreme values exceeding a specific threshold, making it highly relevant for studying
intense rainfall events (Pickands, 1975). This distribution is particularly valued for its adaptability in
representing the tail behavior of a wide range of data types.
In addition to these distributions, the four-parameter Kappa distribution, as discussed by Hosking
(1994), presents a comprehensive framework that can be used both to fit experimental data
accurately and as a basis for generating artificial data in simulation studies. This distribution is notable
for its versatility, encompassing a wide range of distribution shapes including those of the threeparameter models, and thus offering a more encompassing approach to modeling rainfall data.
Hosking's work emphasizes the importance of selecting appropriate probability distributions in
frequency analysis, acknowledging that certain extreme weather data may require the flexibility
offered by a four-parameter model like the Kappa distribution. The choice of distribution is crucial in
accurately capturing the characteristics of extreme precipitation events and in predicting their
frequency and intensity.
Each of these distributions - GEV, GLO, GPA, and Kappa - plays a pivotal role in the analysis of extreme
precipitation, offering distinct advantages and catering to different aspects of the data. Their
combined use and comparison in studies provide a comprehensive understanding of extreme rainfall
patterns, essential for effective water resource management and disaster mitigation strategies.
METHODOLOGY
a) Data Collection
This research utilizes annual maximum rainfall series over rainfall stations in Peninsular Malaysia. The
data from 120 water level stations in Peninsular Malaysia which range from 1960 to 2019 will be
collected from Department of Irrigation and Drainage, Ministry of Natural Resources and
Environment, Malaysia. At early stage of analysis, it is important to identify the unusual sites and their
potential data errors. Hosking and Wallis (1997) identified the outliers through a statistical screening
test called discordancy measure test. The main goal of the discordancy measure is to identify those
data for which point sample PL-moments are markedly different from the most of other data in a site.
b) Concepts of L-Moments
i. L-Moments
The L-moments, introduced by Hosking (1990) is another way of summarizing the statistical properties
of hydrological data. L-moments can be expressed as linear combinations of PWMs. The PWMs of
order r was formally defined by Greenwood et al. (1979) as  r 
1
 x( F ) F dF
r
0
where F  F (x ) is a cumulative distribution function, x (F ) is an inverse distribution function or so
called quantile function of random variables x and r  0,1,2,... is a nonnegative integer The first four
L-moments, expressed as linear combinations of PWMs, are
1   0
2  2 1   0
3  6 2  61   0
4  20 3  30 2  121   0
The L-moments ratios are identified by L-coefficient of variation (L-Cv,  2 ); L-coefficient of
skewness (L-Cs,  3 ) and L-coefficient of kurtosis (L-Ck,  4 ), and are computed as  2  2 1 ,
 3  3 2 and  4  4 2 respectively. For an ordered sample x(1)  x( 2)    x( n) , Wang
(1990a) stated that the following statistic as an unbiased estimator of  r
1 n (i  1)(i  2)...(i  r )
br  
x( i )
n i 1 (n  1)(n  2)...( n  r )
Hence, the first four sample L-moments are l1 , l 2 , l3 and l 4 , and sample L-moments ratios
are noted as t 2  l 2 l1 , t 3  l3 l 2 and t 4  l 4
2
.
iii. Framework of Parameter Estimation Model
Theoretical PLmoments
Theoretical Lmoments
Parameter derivation of
probability distributions
Parameter derivation of
probability distributions
Parameter estimation
for each distribution
Parameter estimation
for each distribution
Prediction for large
values event
Prediction for large
values event
Comparison performance
of PL-moments and Lmoments
PLAN OF WORK AND TIME SCHEDULE:
No.
Description of Milestones
Expected End
Date
1.
2.
Completion of literature reviews on past research
Completion of parameters derivation of several
probability distributions
Completion of data collection of annual maximum
streamflow for several stations in Malaysia
Completion of streamflow prediction for four different
levels of PL-moments
Completion of identification of best fitted probability
distribution to represent streamflow series in Malaysia
Completion of performance comparison between PLmoments and L-moments approaches
Completion of result analysis and discussion
Completion of journal writing
December 2022
May 2023
Cumulative
Project
Completion
Percentage
10
30
July 2023
40
October 2023
60
March 2024
70
June 2024
85
July 2024
August 2024
95
100
3.
4.
5.
6.
7.
8.
BIBLIOGRAPHY
Ahmad, I., Abbas, A., Saghir, A., and Fawad, M. (2016). Finding probability distributions for
annual daily maximum rainfall in Pakistan using linear moments and variants. Polish
Journal of Environmental Studies. 25(3), 925-937.
Bhat, M. S., Alam, A., Ahmad, B. and Kotlia, B. S. (2019). Flood Frequency Analysis of River
Jhelum in Kashmir Basin. Quaternary International. 507: 288-294.
Bhattarai, K.P. (2004). Partial L-moments for the Analysis of Censored Flood Samples.
Hydrological Sciences Journal. 49(5): 855-868.
Bobée, B. and Rasmussen, P. F. (1995). Recent Advances in Flood Frequency Analysis. U.S. Nalt.
Rep. Int. Union Geol. Geophys. Rev. Geophys. 33: 1111-1116.
Chow, V.T., Maidment, D.R. and Mays, L.W. (1988). Applied Hydrology. New York: McGrawHill.
Cunnane, C. (1988) Methods and Merits of Regional Flood Frequency Analysis. Journal of
Hydrology, 100: 269-290
Deng, J.and Pandey, M.D. (2009). Using Partial Probability Weighted Moments and Partial
Maximum Entropy to Estimate Quantile from Censored Samples. Probalistic Engineering
Mechanics. 24: 407-417.
Drissia, T.K., Jothiprakash, V. And Anitha, A.B. (2019). Flood Frequency Analysis Using L
Moments: a Comparison Between At-Site and Regional Approach. Water Resources
Manangement. DOI: 10.1007/s11269-018-2162-7
Hosking, J.R.M. (1990). L-moments: Analysis and Estimation of Distributions Using Linear
Combinations of Order Statistics. Journal of the Royal Statistical Society. 52: 105-124.
Hosking, J.R.M (1994). The four-parameter kappa distribution. IBM Journal of Research and
Development. 38(3): 251-258.
Hosking, J. R. M. and Wallis J. R. (1997). Regional Frequency Analysis: An Approach Based
on L-moments, Cambridge University Press, Cambridge, UK.
Khan, S.A., Hussain, I., Hussain, T., Faisal, M., Muhammad, Y.S. and Shouk, A.M. (2017).
Regonal Frequency Analysis of Extrene Precipitation using L-moments and Partial Lmoments. Advances in Meteorology. 2017: 1-21
Moisello, U. (2007). On the Use of Partial Probabiility Weighted Moments in the Analysis of
Hydrological Extremes. Hydrological Processes. 21: 1265—1279.
Rao, A.R. and Hamed, K.H. (2000). Flood Frequency Analysis. Boca Raton, London, New York,
Washington, D.C: CRC Press.
Sandeep, S. and Abinash, S. (2020). Estimation of Flood Frequency using Statistical Method:
Mahanadi River Basin, India. H2 Open Journal. 3(1): 189-207.
Sharafi, M., Rezaei, A. and Tavangar, F. (2021). Comparing Estimation Methods for ThreeParameter Kappa Distribution with Application to Precipitation Data. Hydrological
Sciences Journal, 66(2): 991-1003.
Wang, J. (2018). The Application of Partial L-moments for Flood Frequency Analysis in the
South of Guizho. Journal of Water Resources Research. 7(4): 418-425.
Wang, Q. J. (1997). LH Moments for Statistical Analysis of Extreme Events. Water Resources
Research. 33(12): 2841-2848.
Zakaria, Z.A. and Shabri, A. (2013). Regional Frequency Analysis of Extreme Rainfalls using
Partial L-moments Method. Theoretical and Applied Climatology. 113(1-2): 83-94.
Zakaria, Z.A., Suleiman, J. M. A. and Mohamad, M. (2018) .Rainfall Frequency Analysis using
LH-Moments Approach: A Case of Kemaman Station, Malaysia. International Journal of
Engineering Technology. 7(2): 107-110.