INTRODUCTION
Problem Statement
Climate change refers to alterations in the climate system driven by both natural and human factors In recent years, the effects of climate change have intensified due to human activities, particularly the reliance on fossil fuels for transportation and industrial processes, which release greenhouse gases Consequently, climate change has emerged as a critical global issue that demands urgent attention.
Vietnam ranks first in ASEAN and sixth globally in vulnerability to climate change, as reported by Genamwatch at COP 24 The country is experiencing an increase in the frequency of extreme weather events, making their prediction increasingly challenging Notably, the highest monthly rainfall has seen a significant rise.
270 mm in the period of 1901 to 1930 to 281 mm in the period of 1991 to 2015, while the highest monthly temperature increased from 27.1 o C to 27.5 o C (WorldBank, 2018)
In recent years, new records are still being set every year The words “record heavy rain”,
Vietnamese media frequently report on "record hot weather" and "record flooding," highlighting the increasing occurrence of extreme rainfall This trend indicates a significant shift in weather patterns, with notable changes in frequency and intensity over recent years.
In 2017, Vietnam experienced an unprecedented number of natural disasters, recording over 16 storms and severe floods This year marked a significant increase in changes to water resources, including heightened rainfall and river water levels, compared to previous years.
Climate change significantly impacts rainfall patterns, increasing both the intensity and frequency of precipitation As global warming warms the oceans, more water evaporates into the atmosphere This moisture-laden air, when it moves inland or converges in storm systems, can result in heavy rainfall and flooding, which heightens risks to human safety, economic stability, and environmental health, as well as the potential spread of diseases.
To effectively estimate flood risk at the basin scale, it is essential to enhance research methods and models that account for changes in rainfall characteristics Additionally, developing multiple risk indicators, including scale and frequency, is crucial for effective flood management.
2 etc Together with research on appropriate indicators for flood risk communication in order to minimize negative impacts from extreme weather events and climate change.
Motivation
Vietnam is highly vulnerable to climate change, making it essential to understand changes in rainfall characteristics for effective flood management and adaptation This research analyzes rainfall patterns across various return periods using historical data and the Hydrological Frequency Analysis model, specifically focusing on the Cau River basin The findings aim to serve as a pilot study for the broader Red River Delta and the entire country of Vietnam.
Study Area
The Cau River basin spans coordinates between 21.11 to 22.3 latitude and 105.47 to 106.13 longitude, encompassing areas within the provinces of Bac Kan, Thai Nguyen, Bac Ninh, Bac Giang, Vinh Phuc, and Hanoi.
The Cau River basin, spanning an area of 6,030 km², is the most significant basin within the Thai Binh River system, representing about 8% of the Red River - Thai Binh River basin in Vietnam With approximately 1,600 km of tributaries, the basin boasts an annual water flow of 4.2 billion cubic meters The river's flow is managed by Nui Coc Lake, located on the Cong River, which is a key tributary, holding hundreds of millions of cubic meters of water.
The main river Cau River originates from the Van On mountain range (105 0 37’40”-
22 0 15’40”) at an altitude of 1175 m in Cho Don district, Bac Kan province
The river upstream flows in the North-South direction, the basin average elevation is
The river features a narrow and steep bed, particularly between 300 to 400 meters, characterized by numerous waterfalls and rapids During the dry season, the river averages 50 to 60 meters in width, while this can expand to 80 to 100 meters during the flood season The riverbed has a slope of approximately 10 ‰ and exhibits a meandering degree of 2.0.
The middle class descends from Cho Moi as the river meanders in a Northwest-Southeast direction over a considerable distance Eventually, it reverts to its original North-South course, leading to Thai Nguyen, where the river valley widens and the mountains become less elevated.
3 height is 100 - 200 m, the bottom slope decreases to 0.5 ‰ The river bed in the dry season is about 80-100 m wide, and the meandering value is still large (1.90)
The river flows from Huong Waterfall to Pha Lai in a Northwest-Southeast direction, with an average basin height of just 10-25 meters and a minimal riverbed slope of 0.1 ‰ During the dry season, the riverbed width ranges from 70 to 150 meters, with water depths between 3 to 4 meters The banks are lined with dikes, allowing the water surface to expand during the flood season.
The Cau River features 27 tributaries measuring 10 km or more, with the majority being small Among these, five significant tributaries stand out due to their catchment areas, including the Cong River (951 km²), Ca Lo River (891 km²), Nghinh Tuong River (465 km²), Cho Chu River (437 km²), and Du River (360 km²) Notably, the Thuong and Luc Nam Rivers have even larger catchment areas than the Cau River itself, which spans 6,650 km² Excluding these two, the Cau River's most substantial tributaries are the Cong and Ca Lo Rivers, both originating from the Tam Dao mountain range, which exceeds 1,000 m in elevation, before meandering through the expansive plains of Dai Tu and Phuc Yen.
The Cau River flows through a narrow valley in Bac Kan, surrounded by mountains and waterfalls, before gradually expanding as it reaches Thai Nguyen Along the riverbank, there are low-lying and flood-prone areas that are susceptible to heavy flooding, which is why a dyke has been constructed from Thai Nguyen downstream to protect the region.
The hydrological regime of rivers in the Cau River basin is divided into 2 seasons:
(1) The flood season starts from June to September and accounts for 70-80% of the total flow in the year
(2) The dry season starts from October to May and accounts for only 20-30% of the total flow of the year
The average flow of each month of the year varies by 10 times, the difference between the high and the low water level is quite large, possibly up to 5–6 m
Figure 1.1 Map of the Cau River Basin
The Cau River basin experiences significant flooding primarily due to storms and the polar front, with 42% of large floods between 1960 and 2000 attributed to these weather events Data from the Thac Buoi station indicates that major floods, characterized by peak discharges exceeding 2,000 m³/s, are exclusively caused by storm-related rainfall These floods have detrimental impacts on both property and human lives Consequently, this study aims to evaluate changes in rainfall patterns within the Cau River basin to enhance flood prediction simulations and emphasize the critical role of risk communication in disaster prevention.
The Cau River basin features a diverse and complex topography characterized by three distinct types of terrain: mountainous, midland, and plain Overall, the elevation of the basin decreases from the Northwest towards the Southeast.
- The upstream side of the river valley is between the Gam River bow and the Ngan Son
The Yen Lac arc features a distinctly defined water distribution line within the Cau River basin In the northern and northwestern regions, notable peaks exceed 1,000 meters, including Hoa Sen at 1,525 meters, Phia Đeng at 1,527 meters, and Pianon at 1,125 meters Meanwhile, the eastern area showcases peaks over 700 meters, with Coc Xe reaching 1,131 meters, Lung Giang at 785 meters, and Khao Khien measuring 1,107 meters.
The middle-class area of Cho Moi is characterized by the Cau River, which flows through the Ngan Son arc in a Northwest-Southeast direction for a considerable distance before returning to its original course towards Thai Nguyen In this section, the river valley widens, and the surrounding mountains are notably low, with an average altitude of only 100 to 200 meters above sea level.
Downstream from Huong Waterfall to Pha Lai, the riverbanks rise to heights of 10-25 meters, with the Tam Dao mountain range to the west, featuring the peak of Tam Dao at 1,592 meters This area is also the source of two significant tributaries, the Cong River and the Ca Lo River.
Figure 1.2 Topography of the Cau River basin
Research Objectives
The purpose of this research is to estimate the changes in rainfall characteristics in the Cau river basin The specific objectives of this research are as follows:
- Estimation of the probable rainfall using Hydrological Frequency Analysis
- Assessment of the rainfall characteristics using specific rainfall indices
- Create risk maps to use for flood risk communication based on the probable rainfall
Scope of Research
Simulating river flows with hydrological models is crucial, but this thesis primarily evaluates rainfall parameters due to data limitations Understanding rainfall characteristics is essential, as they directly influence river flow in the Cau River basin, particularly during the rainy season in the Red River Delta from June to September, when flood flows typically occur.
LITERATURE REVIEW
Flood and Rainfall Situation in RRD and Cau River Basin
The Red River Delta (RRD) in northern Vietnam spans 1.7 million hectares and experiences a climate heavily influenced by the monsoon system It has two distinct seasons: a dry season from October to April and a rainy season from May to October, with average annual rainfall ranging from 1,600 to 1,800 mm The rainy season contributes to 80 to 85% of the total rainfall, with intensities reaching 300 to 600 mm over just 3 to 5 days Additionally, the RRD is situated downstream of major rivers, relying on water flow from neighboring countries, which often leads to challenges in water supply management, especially during the dry season when upstream nations extract significant amounts This situation results in frequent flooding and water shortages due to seasonal variations.
Figure 2.1 Geographical Location of the Red River Delta
The RRD, situated in a tropical monsoon region with an extensive coastline, frequently experiences storms that cause prolonged heavy rainfall This extreme precipitation often results in flooding, with an average of six typhoons impacting the coast annually The overlap of the monsoon and typhoon seasons leads to significant damage, loss of life, and the destruction of vital infrastructure and services (Pilarczyk & Nuoi, 2005).
The RRD's irrigation and drainage system, originally constructed in the 1950s and 1960s, features 3,000 km of river dikes and 1,500 km of sea and estuary dikes Despite renovations, rapid urbanization has hindered the system's ability to effectively drain water during heavy rainfall, resulting in significant flooding in major cities like Hanoi The rainy season, lasting from May to November, accounts for 70% to 75% of the annual runoff, while the dry season contributes only 20% to 25%.
The RRD experiences seasonal and localized water shortages, while the downstream areas of most basins face frequent flooding, including flash floods during storms in October and November (Thái, 2009).
Water-related disasters pose a significant threat, primarily because a large portion of the population resides in flood-prone areas, often near major rivers or coastal regions vulnerable to storms and heavy rainfall Statistics reveal that from 1970 to 2000, Vietnam experienced 5,858 storm-related deaths, 4,859 fatalities from floods, and 1,310 from other disasters (Pilarczyk & Nuoi, 2005) Consequently, floods emerge as the most critical natural disaster risk facing Vietnam.
The Cau River basin, characterized by its feather-like shape, experiences uneven rainfall distribution, leading to frequent flooding that does not concentrate in specific areas Major floods often occur simultaneously along the Cau River and its tributaries, including the Du River, Cong River, and the smaller Ca Lo River.
+ Big flood in Rieng Waterfall meets big flood in Gia Bay about 40%
+ The big flood in Gia Bay meets the big flood in Giang Tien (Du river) about 75%
The recent flooding in Tan Cuong (Cong River) coincides with significant flooding in Gia Bay, which is approximately 25% more severe The flood dynamics in the Cau River system vary across smaller basins, particularly in river branches with catchment areas under 500 km², such as the Nghinh Tuong, Du, and Chu Rivers These smaller rivers exhibit steep catchment slopes (greater than 10%), leading to rapid water concentration during floods Consequently, they experience quick flood rises and falls, with flood peaks varying significantly and transmission times ranging from 1 to 3 days The intensity of flooding in these tributaries is often substantial, especially within smaller watersheds.
10 transmission time is usually longer, so the flood process path is gentle, and the flood intensity is only about 0.5 - 1.0 m/h (Thái, 2009)
The Cau River basin experiences significant flooding primarily due to storms and polar fronts, with storms accounting for 42% of major floods recorded between 1960 and 2000 Data from the Thac Buoi station indicates that all major floods, characterized by peak discharges exceeding 2,000 m³/s, are a direct result of rainfall during these storms.
Table 2.1 The major floods on the Cau River (Nhất, 2010)
(m 3 /s) Rainy days Amount of rain (mm)
Vietnam's water resource management is significantly affected by its dependence on upstream flows from neighboring countries, particularly China, which contributes 60% of the water to the Red River and Thai Binh River systems The lack of access to critical information regarding hydroelectric plants in the Chinese basin complicates this reliance Furthermore, insufficient data on flood discharge from the Da, Thao, and Lo Rivers hampers effective control of water sources in the Red and Thai Binh River basins, ultimately impacting the flow dynamics of the Cau River basin.
To address the threat of flooding, the Vietnamese government has implemented a combination of structural solutions, such as dykes and reservoirs, alongside non-structural measures like flood delta management and regulations Recently, there has been an increased focus on involving communities in flood management efforts.
The Probability Distributions to Analyze Rainfall/ Extreme Rainfall in Vietnam 11 2.3 Hydrological Frequency Analysis
Precipitation is a key variable in climate research, essential for balancing the energy budget and challenging for climate modeling, particularly in convection precipitation parameterization Accurate assessments of precipitation distribution, quantity, and intensity are vital for understanding climate impacts on sectors like water and agriculture at various scales Recent studies have focused on extreme rainfall characteristics, particularly in a mountainous region of Vietnam, utilizing over 30 years of daily precipitation data Researchers analyzed statistical characteristics such as maximum, minimum, mean, standard deviation, skewness, and kurtosis, employing various distributions including Normal, Lognormal, and Gamma to determine the best fit for the data based on goodness of fit tests like Anderson-Darling and Shapiro-Wilks The optimal distribution for extreme precipitation indices was identified for each station, while rainfall intensity, duration, and frequency analyses in Huong Khe district utilized the Pearson III distribution to develop empirical and theoretical exceedance frequencies for heavy rainfall events lasting 24 to 96 hours.
Rainfall frequency and magnitude are crucial parameters for assessing flood risks, designing reservoirs, and evaluating potential downstream flood impacts In 1999, the Vietnam Institute of Meteorology, Hydrology, and Environment created a map of the highest one-day rainfall for the Central Region and Central Highlands, based on 1% frequency data available at that time However, due to the emergence of new observational data and the effects of climate change, these findings may no longer be applicable This research utilizes long-term rainfall data from 1960 to 2010 to provide updated insights.
A study was conducted to determine the values of calculated daily rainfall based on design frequency at 12 selected meteorological stations, addressing the impacts of climate change in accordance with TCVN9845:2013 standards Research by Doan Thi Noi analyzed the temporal characteristics of floods and the development of rainfall frequency and intensity-duration-frequency (IDF) curves for Northern Vietnam, focusing on one-day maximal rainfall relevant to transport design Given the significant changes in rainfall intensity due to climate change, relying on historic rainfall data for IDF curves may underestimate risks in drainage system design The investigation in the Da River Basin evaluated various probability distributions, including Gumbel, generalized extreme value, generalized Laplace, and generalized exponential, revealing that while generalized Laplace fit the observational data best, the generalized extreme value distribution is most suitable for generating IDF curves in a changing climate.
In October 2020, Central Vietnam experienced devastating flooding and landslides due to five tropical depressions and typhoons, resulting in over 200 fatalities, more than 500 injuries, and approximately 1.2 billion USD in damages Analyzing the Rx15day rainfall trends through PRIMAVERA and CORDEX-CORE ensembles, the generalized extreme value (GEV) method was applied to assess precipitation intensity, defining the event as the regional maximum of annual maximum 15-day average rainfall This analysis highlights the urgent need for increased investment in disaster risk reduction strategies to mitigate the impacts of rainfall-induced flood hazards (Luu et al., 2021).
Flood frequency analysis is a technique used by hydrologists to predict flow values corresponding to specific return periods or probabilities along a river (Sarhadi, Soltani,
& Modarres, 2012) Flood frequency analysis is commonly used to predict the
The probability of flood recurrence is crucial for determining the intensity of potential floods, guiding decisions on the construction of disaster prevention structures These estimates are frequently utilized to assess possible damages associated with varying flood intensities A key application of flood frequency analysis is the categorization of flood zones into different levels, which plays a vital role in effective flood management.
Hydrological events are often unique, making it challenging to predict their future occurrence based on past records Frequency analysis serves as a crucial method for assessing the likelihood of hydrological events, particularly for planning and constructing infrastructure such as dams, bridges, and drainage systems Despite the inherent irregularity of rainfall, it is possible to accurately estimate design rainfall for specific return periods using various probability distributions Numerous studies have been conducted on rainfall data frequency analysis across different locations, focusing on validating statistical procedures for various probability distribution functions, including Normal, Log-Normal, and Gamma.
The unpredictability of rainfall patterns underscores the importance of research and forecasting to effectively manage significant flood and drought events It is essential to assess future probabilities of these occurrences based on historical data, particularly for various return periods that align with a structure's lifespan Statistical methods, such as frequency analysis in hydrology, are employed to evaluate the likelihood of flood and drought events This analysis correlates the magnitude of extreme occurrences with their frequency, revealing that more severe events are less likely to happen For this purpose, annual maximum flood peaks serve as key input data, while rainfall data series are utilized to analyze extreme storm events when extensive discharge gauge records are unavailable.
14 matching to a certain return period, and then to calculate discharge using various rainfall- runoff models (Bhakar et al., 2006; Kwaku & Duke, 2007; Upadhaya & Singh, 1998)
In hazard assessment, understanding the frequency of dangerous events is crucial for predicting their likelihood in the future By analyzing historical data, scientists can determine when specific hazards of varying magnitudes are likely to occur in particular locations Typically, there is a clear relationship between the magnitude and frequency of natural occurrences, allowing for more accurate risk assessments.
Figure 2.2 The magnitude - frequency relation for rainfall related events (Gilleland,
Frequency is commonly expressed through exceedance probability, which indicates the chance of a particular event size occurring within a year Alternatively, the return period can be calculated, reflecting the average number of years between occurrences of specific hazards based on historical data.
Figure 2.3 Frequency magnitude return period and probability (Gilleland et al., 2013)
The frequency-magnitude connection is grounded in historical records of hazardous incidents, as illustrated in Figure 2.3 This figure presents the annual maximum discharge data organized from highest to lowest, with a regression line representing the magnitude-frequency relationship Due to the absence of observed data for longer return periods, the regression line must be extrapolated, leading to increased uncertainty, particularly when the observed time frame is shorter.
Yearly peak flow data is essential for flood frequency analysis, which provides statistical insights such as mean, standard deviation, and skewness to create frequency distribution diagrams Various statistical distributions, including Gumbel, Normal, Log-normal, Exponential, Weibull, Pearson, and Log-Pearson, can be selected to identify the most suitable frequency distribution Once the appropriate probability distribution is determined, flood frequency curves are generated based on the yearly maximum data.
To ensure accuracy and reliability, there are several important issues to consider when analyzing flood frequencies including (Takara, 2009)
(2) Sample size (effect of years of records on accuracy and appropriate estimation method),
(3) Parameter estimation (selection of parameter values of distribution functions),
(4) Model evaluation (selection of a distribution), and
(5) Accuracy of quantile estimates (unbiasedness, estimation error)
Hosking (1994) explored the four-parameter kappa distribution, categorizing it into one, two, and three parameters, and applied it to annual maximum precipitation data from Washington using parameters determined by the LMM In their 1995 study, Hosking and Wallis compared unbiased estimators derived from L-moments with plotting-position estimators, concluding that the unbiased estimators frequently outperformed the latter in regional frequency analysis Additionally, Singh and Deng (2003) employed the entropy approach to further examine the four-parameter kappa distribution for predicting floods with significant return periods based on lower bound censored data.
16 samples, Wang (1996) used extreme value type I, II, and III distributions with parameters calculated using probability weighted moments
Chowdhury et al (1991) investigated the goodness-of-fit statistics for the generalized extreme value (GEV) distribution, using unbiased probability-weighted moment (PWM) estimators for small samples to derive variances for the L-moment coefficient of variation (L-CV) and coefficient of skewness (L-CS) Their findings indicated that these techniques struggled to identify thin-tailed alternatives, although they successfully employed the chi-square test to detect severely skewed distributions Meanwhile, Williams and Yeh (1983) proposed various methods for estimating rainfall-runoff model parameters, including linear programming (LP) for minimizing the sum of absolute errors (MSAE), quadratic programming (QP) for ordinary least squares (OLS), and generalized least squares (GLS), which were tested on the Williams River in New South Wales, Australia Additionally, Ding et al (1989) utilized weighted probability moments (PWM) to estimate parameters of the Pearson type III distribution, demonstrating that PWM estimators were nearly unbiased and superior to standard moment techniques Lastly, Arora and Singh (1989) examined the Log-Pearson type 3 distribution, which was endorsed by the United States Water Resources Council (USWRC) in 1967.
Natural disasters, particularly floods, can have severe negative impacts, making flood prediction models crucial for effective warning and damage mitigation Given the complexity of climate as a variable, numerous flood prediction models have been developed globally to forecast floods and hydrological phenomena over both short and long-term periods.
Frequency analysis is essential for risk mapping and calculating design return periods, such as the 100-year flood event (Salas & Obeysekera, 2014) Numerous efforts have been made to conduct multivariate hydrologic frequency analysis, considering the interdependence of variables like rainfall, floods, droughts, and water quality Various methods have been employed to perform this comprehensive multivariate analysis in hydrology.
Risk Communication Model
Risk Communication is the timely sharing of information and advice between experts and individuals facing threats to their health, safety, or well-being Its main goal is to empower those at risk to make informed decisions that help reduce the impact of hazards, such as disease outbreaks, and to take necessary protective and preventive measures.
Risk communication refers to the two-way exchange of information between stakeholders aimed at making informed decisions for effective risk management This process encompasses various risk-related communications, alongside non-risk-related messages that express concerns, opinions, or reactions to risk messages and legal or institutional risk management frameworks (Krewski, Turner, & Tyshenko, 2011).
Risk communication emerged as a distinct concept in the early 1970s and was first documented in scientific literature in 1984, driven by an interest in risk perception theory that explored how individuals and groups develop varying views on risk acceptability Initially, the focus was on providing objective information about hazards through clear and precise descriptions of risk probabilities based on scientific facts and assessments Over time, the scope of risk communication expanded to include the explanation of technical information and risk assessments, alongside fostering public engagement in risk dialogues Throughout the 1990s, the emphasis shifted towards building public trust through relationship-building, open conversations, and collaborative decision-making.
Risk factors and communication styles can be categorized into three distinct types The first category encompasses routine risk circumstances, which are well-defined by risk scientists The second category involves risks that carry significant ambiguity, where the consequences and potential interactions leading to further dangers are not fully understood, necessitating effective risk communication to alleviate concerns about the unknown This approach is crucial for maintaining public trust through caution and transparency Lastly, the third category includes hazards that are likely to provoke controversy (Krewski et al., 2011).
Figure 2.4 The role of risk communication in the risk management cycle
The concept of risk highlights that humans face various threats daily, a reality that is ingrained in modern industrialized society (Palenchar & Heath, 2002) Risk communication encompasses actual dangers, public perceptions of these risks, and the thoughts and opinions surrounding them It is essential for public relations professionals, especially risk communicators, to understand not only the real dangers but also how people perceive these risks, the factors influencing those perceptions, and the communication that shapes and is shaped by them.
There are many risk communication models in the world, but they are mainly built according to the following phases There are 03 phases in risk communication:
Effective preparedness involves proactive risk communication before an event, emphasizing practical measures to enhance safety It is crucial to educate the public about the unique characteristics of various threats, such as distinguishing between the risks posed by an improvised nuclear device terrorist attack and those associated with an earthquake.
Response (Imminent Warnings): crisis communication and guidance regarding protective actions to take immediately prior to, in the midst of, or during the hours immediately following an event;
Recovery: messages communicating needs and guidance in the weeks, months, and years following an event
The effectiveness of risk communication initiatives is significantly influenced by the components of the communication process Research highlights the importance of the risk messenger, emphasizing that increased trust in the communicator enhances the overall efficacy of the communication.
The message's substance and format are also important, since it has been shown that the same danger presented or framed in different ways can have distinct consequences
When communicating risks, contrasting them with other hazards can be effective, as various factors influence audience perception Research indicates that people are more engaged when risks are compared across different times and locations.
The communication route plays a crucial role in the communication process, as research indicates varying levels of trust among different channels Studies have shown that individuals exhibit differing degrees of confidence in various media, including print, radio, television, magazines, and advertising.
Last but not least, the recipient's impression is crucial to the process and is a well-studied part of risk communication
THEORIES AND METHODOLOGIES
Theory of Hydrological Frequency Analysis
3.1.1 Rainfall depths expected for specific probability ( 𝑿 𝒑 )
Effective management and planning of irrigation and drainage projects necessitate accurate estimates of rainfall depths (𝑋 𝑝 ) or intensities These estimates should be predicted for a specific probability during defined reference periods, which can range from hours to years.
The exceedance probability highlights the likelihood that actual rainfall will meet or exceed the projected depth, denoted as 𝑋 𝑝 This predicted rainfall depth, often termed 'dependable rainfall' in irrigation sciences, represents the amount of rain expected or potentially surpassed during a specific timeframe, reflecting its significance in effective irrigation planning.
Exceedance probability refers to the likelihood of experiencing a rainfall depth greater than a specific threshold, denoted as 𝑋 𝑝 This probability, represented as a fraction between 0 and 1 or as a percentage from 0 to 100, indicates the chances of surpassing a certain rainfall amount When forecasting rainfall for a specific year based on historical data, these predictions can be expressed as a fixed number of years within a defined reference period.
The return period, or recurrence interval (𝑇 𝑥), is the timeframe expressed in years during which a specific annual event is anticipated to occur again This period can also be viewed as the reciprocal of the event's probability.
Application of HFA
The HFA model, as illustrated in Figure 3.1, is applicable to the Cau River basin, drawing from its theoretical and practical use in Japan The implementation of the HFA model involves four essential steps: data collection, application of probability density functions (PDFs), conducting a goodness-of-fit test, and determining the optimal PDF.
Figure 3.1 The HFA model application in the Cau River Basin
In the first step of the study, data collection involved gathering annual daily maximum rainfall values from 11 monitoring points within the Cau River basin, spanning the years 2005 to 2019 These monitoring points included locations such as Bac Giang, Bac Kan, Bac Son, Dinh Hoa, Hiep Hoa, Huu Lung, Luc Ngan, Son Dong, Tam Dao, Thai Nguyen, and Vinh Yen The rainfall data were sourced from the long-term datasets maintained by local monitoring centers.
In step 2, the study applied annual daily maximum rainfall values to five candidate probability distribution functions (PDFs), specifically Gumbel, Generalized Extreme Value (GEV), Weibull, Exponential, and Generalized Pareto (GP).
In step 3, the results after PDF calculation will be checked for fit through Standard Least- Squares Criterion (SLSC)
In the last step, the optimal PDF values to describe the analytical values are selected based on the SLSC value
Figure 3.2 shows the locations of 11 rainfall monitoring points in the Cau River basin The monitoring points belonged to the provinces of Bac Kan (02 points), Thai Nguyen
(02 points), Vinh Phuc (02 points), and Bac Giang (05 points) Daily rainfall data at the points were collected from 2005 to 2019
Rainfall data is collected in Excel format and processed to determine key metrics such as maximum daily rainfall, the number of rainy days, and total annual rainfall, which are essential for research purposes.
Points: 11 points (Bac Giang, Bac Kan, Bac Son, Dinh Hoa, Hiep Hoa, Huu Lung, Luc Ngan, Son Dong, Tam Dao, Thai Nguyen, Vinh Yen)
Source: Vietnam Meteorological and Hydrological administration
Figure 3.2 Rainfall monitoring points in the Cau river basin
3.2.2 Application of probability density functions (PDFs)
The Gumbel distribution (Generalized Extreme Value Distribution Type-I) is used to simulate the distribution of a number of samples of various distributions' maximum (or minimum)
The Gumbel distribution graph in Figure 3.3 illustrates the impact of varying parameters μ and β, with green and red curves representing increasing μ, which correlates with higher magnitudes, while the blue curves indicate the effect of increasing β, associated with a broader range This distribution is valuable for predicting the probability of significant natural disasters, such as earthquakes and floods (Bhagat, 2017).
Figure 3.3 The Gumbel probability density function
Figure 3.4 The GEV probability density function
The Gumbel's distribution equation, as well as the process with a return period T, is as follows:
Where, 𝜎 𝑋 = Standard deviation of the Sample Size
K = Frequency Factor, which is expressed as, 𝐾 = 𝑌𝑡−𝑌𝑛 ̅̅̅̅
The values 𝑌𝑛̅̅̅̅ of and S n are selected from Gumbel’s Extreme Value Distribution considered depending on the sample size
The GEV distribution, also known as type I, type II, and type III extreme value distributions, is a family of continuous probability distributions developed in extreme
The Generalized Extreme Value (GEV) distribution serves as a valuable approximation for modeling the maxima of finite sequences of random variables, effectively combining the Gumbel, Fréchet, and Weibull families As illustrated in Figure 3.4, the probability density function of the GEV distribution is depicted for parameters -0.5, 0, and 0.5, showcasing its versatility in extreme value theory.
In 1955, Jenkinson introduced the Generalized Extreme Value (GEV) distribution, which has since been utilized in various studies to analyze flood and rainfall frequencies Notable applications include flood frequency analysis in the United Kingdom (NERC, 1975), rainfall frequency assessments in the United States (Willeke, 1995), and sea wave frequency studies (De Haan & De Ronde, 1998) The GEV distribution is defined by a specific equation that characterizes extreme value behavior.
𝜶 ]} 𝒌 = 𝟎 (4) Where 𝜀, 𝛼, and k are the location, scale and shape parameters, respectively
Quantiles of the GEV distribution are given in terms of the parameters and the cumulative probability p by
The Weibull distribution is a versatile continuous probability distribution widely utilized in reliability and life data analysis Its adaptability allows it to simulate various life behaviors based on specific parameter values Additionally, the Weibull distribution, which has applications in hydrology, was derived from the principle of maximum entropy (Chow, 1953; V P Singh, 1987).
The Weibull distribution function, illustrated in Figure 3.5, features two parameters: the shape parameter (k > 0) and the scale parameter (λ > 0) When k < 1, represented by the blue curve, the hazard rate decreases over time In contrast, a value of k = 1, shown by the red curve, also indicates a decreasing hazard rate Additionally, a value of k > 1, depicted by the pink curve, suggests an increasing hazard rate over time.
26 green curves) indicates that the hazard rate increases with time After that decrease and stable with time
Figure 3.5 Weibull probability density function
Figure 3.6 Exponential distribution probability density function
The random variable x is said to have a Weibull distribution if its probability density function is given by
In which, a and b are parameters
In a Poisson point process, events occur continuously and independently at a constant average rate, with the time between these events following an exponential distribution This distribution is commonly utilized for analyzing the frequency of rainfall characteristics, including depth, intensity, duration, and the number of rainfall events (Eagleson, 1972; V Singh).
& Rajagopal, 1986; Todini, 1988) If the PDF of a random variable X, it is said to have an exponential distribution is given by
The exponential distribution graph represents a probability density function that illustrates the distribution of time or distance between events In this graph, two key variables are used: Lambda (λ), which indicates the rate of occurrences per unit of time, and x, which represents time The graph specifically displays values for λ = 0.5, λ = 1, and λ = 1.5, as illustrated in figure 3.6.
Figure 3.7 GP probability density function
The Generalized Pareto (GP) distribution is a family of continuous probability distributions commonly used to model the tails of various distributions As illustrated in Figure 3.7, the GP distribution varies with different values of the scale parameter (𝜎) and shape parameter (ɛ), particularly when the shape parameter is set to zero This distribution was initially proposed by the economist Vilfredo Pareto, highlighting its significance in statistical analysis.
2017) The definition of GP is given by:
3.2.3 Goodness-of-fit test and decision of the optimum PDF
The least-squares criteria is a mathematical formula used to assess the accuracy of a straight line in representing the underlying data, effectively identifying the best-fit line for data analysis.
Figure 3.8 Linear least squares Figure 3.9 Ellips least squares
The least squares criteria is established by minimizing the sum of squares of a mathematical function This involves squaring the distance between each data point and the regression line or the mean value of the dataset.
A least-squares analysis begins with a graph of data points, where the horizontal x-axis represents independent variables and the vertical y-axis represents dependent variables To accurately describe the relationship between these variables, analysts use the least squares formula to determine the best-fitting straight line For instance, Figure 3.8 illustrates a quadratic function fitting a set of data points, while Figure 3.9 demonstrates the use of least-squares approximation to fit an ellipse to another set of points.
Analysis of Rainfall Characteristics
Annual rainfall refers to the total amount of rainfall recorded over a year In contrast, average annual rainfall indicates the typical monthly rainfall for that year, calculated by dividing the total annual rainfall by 12 months.
Rainfall is measured in millimeters (mm), indicating that 1 mm of rain corresponds to 1 liter of water falling on a unit area, resulting in a rainwater layer with a thickness of 1 mm.
According to the General Department of Meteorology and Hydrology of Vietnam, rainfall within 12 hours greater than or equal to 0.3mm will be counted as rainy day
3.3.3 The simple precipitation intensity index (SDII)
The simple precipitation intensity index is calculated by summing the precipitation amounts on wet days (days with over 1mm of rain) and dividing this total by the number of wet days within the specified period This method provides the average precipitation during wet days.
Let RRwj be the daily precipitation amount on wet days, w (RR ≥ 1mm) in period j If
W represents number of wet days in j, then:
Spatial Interpolation and Mapping Using GIS
This is an important method applied to present research results in a general way in the form of diagrams and maps
In this thesis, we have used DEM data using ArcGIS 10.1 and Mapinfo 15.0 software to build a map of the Cau River basin
Figure 3.10 Applying GIS in research
This study utilized rainfall monitoring data collected from 11 locations within the Cau River basin and employed ArcGIS 10.1 software to model precipitation factors using the Inverse Distance Weighting (IDW) interpolation method Additionally, the reclassification method was applied to assess the hierarchy of rainfall levels across the region.
Rainfall Classification
According to the General Department of Meteorology and Hydrology, in the warning, rainfall is divided into 6 levels, including:
Table 3.1 Rainfall levels according to the
General Department of Meteorology and Hydrology
No Rainfall level Amount of rain mm/12 hours mm/24 hours
However, due to data limitations, the exact timing of the observation and the monitoring method was not known, so the study divided rainfall into 6 levels, including:
Table 3.2 Rainfall levels using in thesis
No Rainfall level Amount of rain (mm/day)
Determining Return Periods for Rainfall
The geographical and temporal characteristics of events are crucial elements of risk assessment One key temporal feature is the frequency of occurrence, which indicates how often hazardous events take place In this study, frequency is defined as the likelihood of a specific magnitude rainfall event occurring in a particular location over a designated time frame (measured in years).
Frequency plays a crucial role in assessing the probability of future rainfall events By analyzing historical rainfall data, we can gain insights into past rainfall characteristics and utilize this information to estimate probable rainfall for specific return periods.
This study involves the creation of a continuous annual dataset of maximum daily rainfall values spanning from 2005 to 2019 Each peak duration is then organized into a ranked table, listing durations from highest to lowest.
The value tables in turn are used to calculate according to 05 probability density functions, including Gumbel, GEV, Weibull, Exponential, and GP
The SLSC values for each probability density function are calculated and combined To determine the optimal probability density function for each monitoring point, the SLSC values are compared, with the minimum value indicating the best fit.
After confirming the appropriate density function Tx (Return period) values will be chosen to calculate the possible rainfall in each period (Tx = 20, 40, 60, 80, 100)
Alternatively, Tx values can also be calculated by entering probable precipitation values
FINDING AND DISCUSSION
Estimation of The Probable Rainfall Using HFA
According to the HFA model theory, rainfall data collection and calculations are conducted, with Table 4.1 presenting the SLSC calculation results The values highlighted in yellow indicate the optimal PDF values selected for each monitoring point.
Table 4.1 Standard Least-Squares Criterion (SLSC) Point Gumbel GEV Weibull Exponential GP
The GEV distribution is predominantly chosen for most monitoring points, including Bac Kan, Dinh Hoa, Huu Lung, Luc Ngan, Thai Nguyen, and Vinh Yen In contrast, the Weibull and GP distributions are selected for two points each, with Weibull applied to Ban Son and Hiep Hoa, while GP is used for Bac Giang and Tam Dao Additionally, the Gumbel distribution is designated for the Son Dong monitoring point, whereas the Exponential distribution is not utilized for any monitoring points.
Table 4.2 presents the estimated probable rainfall based on the optimum probability density functions (PDFs), while Figure 4.1 illustrates the corresponding graphical results The findings indicate that an increase in the return period duration correlates with a higher estimated probable rainfall amount.
During each return period, rainfall varies significantly across different locations For T x = 20, Hiep Hoa records the lowest rainfall at 166.5 mm/day, while Tam Dao experiences nearly double that amount at 321.4 mm/day, indicating that rainfall exceeding 200 mm has become increasingly common As for T x = 40, 60, and 80, Hiep Hoa consistently remains the site with the lowest rainfall, whereas Tam Dao continues to have the highest rainfall in the region.
With T x = 80, the entire region has experienced rainfall exceeding 200 mm, and amounts greater than 300 mm are likely to persist In contrast, at T x = 100, Hiep Hoa records a lower rainfall average of 185.7 mm per day, while Tam Dao has seen peak rainfall levels surpassing 400 mm per day.
>300 mm/day is almost covering the Cau river basin
Over the next century, projected rainfall is expected to range from 150 mm to nearly 400 mm, with continuous rainfall increasing over time In flat regions like Hiep Hoa, the rise in rainfall is gradual, while mountainous areas such as Vinh Yen and Tam Dao experience a rapid increase Extreme rainfall events are particularly concentrated in these mountainous regions, where precipitation levels exceed significant thresholds.
200 mm and nearly 400 mm While the probable rainfall in flat areas such as Hiep Hoa ranges from 150 mm to 180 mm
Figure 4.1 Estimated probable rainfall in the Cau river Basin
This study categorizes rainfall into six levels, ranging from light to violent rain, as detailed in Table 4.3, which presents the return periods for each level Rainfall below 100 occurs with a rapid frequency of less than 1.5 years, while heavy rain shows significant variations in frequency across different monitoring points Specifically, Tam Dao, Vinh Yen, and Son Dong experience the highest frequency of heavy rain, occurring every 1.5 to 2 years, alongside lashing rain, which averages similarly.
In Bac Kan and Hiep Hoa, the return period for heavy rain is significantly elevated, averaging between 7 to 10 years, while lashing rain occurs every 40 to 190 years, and violent rain has a return period exceeding 1000 years.
Table 4.3 Return period for each rain level
Bac Kan Bac Son Dinh
Assessment of The Rainfall Characteristics
4.2.1 Analysis of rainfall in the period 2005 – 2019
From 2005 to 2019, the Cau River basin experienced annual rainfall ranging from a high of 2,159 mm in 2013 to a low of 1,319 mm in 2007, with an overall average annual rainfall of approximately 1,900 mm.
Over a 15-year period, the total rainfall averaged 1700 mm, with a standard deviation of 250 mm The number of rainy days fluctuated, ranging from 180 days in 2006 to 234 days in 2012, with an overall average of 207 days The standard deviation for the total number of rainy days during this period was 14 days.
Figure 4.2 Total annual rainfall and number of rainy days recorded in the Cau River basin for the period 2005 - 2019
To analyze the relationship between total rainfall and the number of rainy days annually, the SDII index was calculated, as illustrated in Figure 4.3 for 11 monitoring points in the Cau River basin Between 2005 and 2019, the average rainfall on rainy days in this basin varied from 8 to 16 mm/day, with notable fluctuations observed during this period.
37 increase in values such as in Vinh Yen in 2006, the average rainfall value on rainy days is up to nearly 21 mm/day
Figure 4.3 SDII in the Cau River basin in the period 2005 - 2019
Figure 4.4 shows the average rainfall in rainy days in the Cau River basin the period
From 2005 to 2019, rainfall patterns in the region showed significant changes In 2005, the most extensive rainfall area recorded was between 10-11 mm/day, with higher concentrations of rain (11-13 mm/day and above) primarily in Vinh Phuc and Bac Giang provinces By 2010, average rainfall had decreased to between 9-11 mm/day, although Bac Giang continued to experience the highest levels, particularly in the 11-13 mm/day range In 2015, the area receiving rainfall from 11 to 13 mm/day became predominant, with Bac Giang still reporting averages exceeding 13 mm/day However, by 2019, there was a noticeable decline in average rainfall, with the majority of the area experiencing rain levels between 9-11 mm/day.
Figure 4.4 Average rainfall in rainy days in Cau River basin in the period 2005 – 2019
Between 2005 and 2019, average rainfall on rainy days can be effectively predicted by analyzing the correlation between total rainfall and the number of rainy days each year Notably, the years 2005, 2010, and 2019 experienced low rainfall despite having a high number of rainy days In contrast, 2015 saw a significant decrease in rainy days, which led to a sharp increase in average rainfall in the Cau River basin.
The Cau River basin, situated in the high rainfall region of Bac Kan and Thai Nguyen provinces, receives between 1,500 to 2,700 mm of rain annually This rainfall is unevenly distributed, with nearly 80% occurring during the rainy season.
39 total rainfall in the whole region in a year Figure 4.5 shows seasonal rainfall in the Cau River basin
Figure 4.5 Seasonal rainfall in the Cau river basin
Figure 4.6 illustrates the rainfall patterns across the Cau River basin from 2005 to 2019, with recorded values ranging from a minimum of 58 mm to a maximum of 278 mm The rainfall data is categorized into four levels, with daily rainfall between 100 to 150 mm being the most prevalent, particularly in delta regions In contrast, rainfall amounts of 150 to 200 mm are less common and primarily occur in mountainous areas.
Figure 4.6 Spatial rainfall characteristics in the Cau river basin from 2005 to 2019
In 2005, the entire area experienced rainfall ranging from 100 to 150 mm, with some locations recording less than 100 mm; only a small portion of the Cau river basin saw rainfall between 150 and 200 mm, while amounts exceeding 200 mm were virtually nonexistent However, by 2010, there was a notable increase in rainfall, particularly in the regions receiving between 150 and 200 mm and higher.
200 mm expanded to a large area in the whole area Rainfall was reduced in the following years 2010 and 2019, heavy rain areas are replaced by smaller rainfall rains
Rainfall patterns in the Cau River basin are notably unpredictable and exhibit significant annual variability From 2005 to 2019, the region experienced daily rainfall fluctuations primarily between 100 to 150 mm, although certain areas may deviate from this range.
Heavy rainfall is frequently observed in mountainous regions, particularly in the Tam Dao area, which lies within the monsoon trough where the East-North and South-West monsoon zones converge This geographical positioning contributes to the occurrence of large-scale rain in the North.
There is a clear correlation between historical rainfall patterns and the frequency of heavy rainfall events In regions like Vinh Phuc and Tam Dao, daily rainfall often reaches 150mm, leading to a shorter return period for extreme rain occurrences.
This study categorizes rainfall into six levels, ranging from spitting rain to violent rain, as detailed in Table 4.7, which outlines rainfall amounts for various return periods At a return period of T x = 20, spitting and pouring rain are no longer observed, with heavy rain becoming the dominant type in Vinh Phuc province, while lashing to violent rain remains minimal As the return period increases to T x @, rainfall levels between 200 - 300 mm have expanded, particularly in densely populated areas like Thai Nguyen, Bac Kan, and Bac Ninh, with occurrences of rainfall exceeding 300 mm becoming more frequent in Vinh Phuc Furthermore, at T x `, heavy rainfall continues to spread, with Bac Giang province recording significant rainfall amounts exceeding 200 mm.
In the Cau River basin, areas experiencing rainfall exceeding 200 mm have become predominant, particularly during intense rainstorms affecting all of Thai Nguyen province Conversely, regions with rainfall below 200 mm have seen a significant decline, as heavy and violent rain persists throughout the area.
Figure 4.7 Spatial probable rainfall characteristics in the Cau river basin
Risk Communication
Based on the division of 6 levels of rainfall, the danger of rain on Cau River basin is divided into 6 levels from very safe to disaster
Between 2005 and 2019, the Cau River basin experienced varying levels of rainfall-related danger Initially, in 2005, the entire region was deemed safe due to manageable rainfall levels However, by 2010, certain areas, particularly in Vinh Phuc province and Hanoi, were classified as dangerous A subsequent decrease in rainfall by 2015 led to a reassessment of the entire area as safe, a status that continued through to 2019.
Figure 4.8 Warning of dangerous levels due to rain in Cau River basin in the period 2005 - 2019
The area is consistently on high alert due to a significant rise in rainfall during return periods Throughout the T x = 20 and 40-year intervals, dangerous levels of rainfall are widespread Moreover, for return periods extending to T x = 100 years, warning levels predominantly reach disaster levels.
Figure 4.9 Warning about the dangerous levels due to rain in the Cau River basin in each return period
Figure 4.9 presents user-friendly products for communicating risks, which are essential for raising awareness and serve as key components in integrated heavy rain risk management Heavy rains, a primary cause of flooding in residential areas, can occur unexpectedly and are often accompanied by limited warning times However, early warning maps are available to assist authorities in effectively disseminating information from hazard analyses and risk assessments to at-risk populations These maps also enable individuals to compare their area's risk level through a clearly defined mapping system.
The Cau River basin is predominantly situated in a high-risk zone, with a significant portion classified as a disaster area, affecting over half of the population and the capital city To mitigate potential harm, early warning systems and danger zoning have been established for each region, aiding in the relocation of individuals and assets This framework also serves as a critical foundation for government decision-making concerning the enhancement of water supply and drainage infrastructure investments.
Heavy rain poses significant hazards that can lead to extensive damage to individuals and property, impacting various professions and communities To ensure safety and mitigate the effects of natural disasters, it is crucial to enhance infrastructure and implement evacuation plans when necessary Additionally, effective risk communication strategies should be tailored to address the needs of different target groups.
CONCLUSION AND RECOMMENDATION
Conclusion
This study aims to estimate changes in rainfall characteristics within the Cau River basin, a key river system in the Red River Delta (RRD) influenced by a monsoon climate with distinct rainy and dry seasons Utilizing rainfall data for hydrological frequency analysis, the research calculates rainfall patterns for various repeating periods The findings reveal significant insights into the rainfall dynamics of the region.
Over the next century, expected rainfall will vary significantly, ranging from 150mm to nearly 400mm Mountainous regions like Vinh Yen and Tam Dao are likely to experience extreme rainfall, with totals exceeding 200mm and approaching 400mm In contrast, flatter areas such as Hiep Hoa are projected to receive lower rainfall amounts, between 150mm and 180mm.
Rainfall measuring less than 100 exhibits a rapid recurrence rate of less than 1.5 years, with notable variations in frequency across different monitoring points Tam Dao, Vinh Yen, and Son Dong experience the highest frequency of heavy rain, occurring every 1.5 to 2 years, while lashing rain has an average return period of 15 years, and violent rain events occur approximately every 100 years.
- The average rainfall on rainy days in the basin fluctuates from 8 to 16 mm/day in the period 2005 to 2019
Rainfall in the Cau River basin is characterized by its uneven distribution, with approximately 80% of the total annual precipitation occurring during the rainy season.
Daily rainfall in most regions typically ranges from 100 to 150 mm, which is representative of delta areas In contrast, rainfall amounts between 150 and 200 mm are rare and primarily occur in mountainous regions.
- In 2005 - 2019, the whole area was assessed as safe with corresponding rainfall
- In return periods, with a rapid increase in rainfall, the whole area is always alerted from the dangerous level
During the research process, a limitation was encountered as follows:
- The lack of data leads to limitations in the process of assessing and analyzing the characteristics of rainfall, the correlation of rainfall and runoff in the Cau River basin
The risk communication model primarily focuses on rainfall as a key factor, neglecting other critical elements such as infrastructure, including dykes and drainage systems, as well as current land use This oversight limits the model's effectiveness in providing a comprehensive assessment of flood risks.
Recommendation
This study assessed rainfall characteristics and quantified rainfall amounts for various return periods in the Cau River basin To gain a comprehensive understanding and enable early forecasting, this methodology should be extended to the entire Red River Delta region.
The study acknowledges limitations stemming from insufficient data, highlighting the need for a comprehensive plan to synchronize and disseminate meteorological, hydrological, and environmental datasets This initiative is essential not only for the Cau River basin but also for the broader Red River Delta (RRD) region, facilitating more thorough research across the entire area.
The risk warning results from the study may not be entirely reliable, as they do not account for critical factors such as dikes, drainage systems, and land development that significantly influence hydrological processes Consequently, the dependability of these results varies based on the study's objectives and the availability of data for enhancing early warning models.
2 Agarwal, M., Katiyar, V., & Babu, R 1988 Probability Analysis of Annual Maximum Daily Rainfall for Up Himalayas
3 Anh, N T 2014 Studying the determination of a number of rain parameters to make contributions to completing the formula of design flow of small sized drain works on road under the climatic conditions of Vietnam Ph.D thesis Hanoi university of transportation
4 Barry, M M., Sixsmith, J., & Infanti, J J 2013 A literature review on effective risk communication for the prevention and control of communicable diseases in Europe: ECDC
5 Bhagat, N 2017 Flood frequency analysis using Gumbel's distribution method: a case study of Lower Mahi Basin, India Journal of Water Resources and Ocean Science, 6(4), 51-54
6 Bhakar, S., Bansal, A K., Chhajed, N., & Purohit, R 2006 Frequency analysis of consecutive days maximum rainfall at Banswara, Rajasthan, India ARPN Journal of Engineering and Applied Sciences, 1(3), 64-67
7 Bhatt, V., Tiwari, A., & Sharma, A 1996 Probability models for prediction of annual maximum daily rainfall of data Indian Journal of Soil Conservation, 24(1), 25-27
8 Chow, V T 1953 Frequency analysis of hydrologic data with special application to rainfall intensities Retrieved from
9 De Haan, L., & De Ronde, J 1998 Sea and wind: multivariate extremes at work Extremes, 1(1), 7-45
10 Eagleson, P S 1972 Dynamics of flood frequency Water Resources Research, 8(4), 878-898
11 Gilleland, E., Ribatet, M., & Stephenson, A G 2013 A software review for extreme value analysis Extremes, 16(1), 103-119
12 Krewski, D., Turner, M C., & Tyshenko, M G 2011 Risk management in environmental health decision
13 Kwaku, X S., & Duke, O 2007 Characterization and frequency analysis of one day annual maximum and two to five consecutive days maximum rainfall of Accra, Ghana ARPN J Eng Appl Sci, 2(5), 27-31
14 Luu, L N., Scussolini, P., Kew, S., Philip, S., Hariadi, M H., Vautard, R., Otto,
F 2021 Attribution of typhoon-induced torrential precipitation in Central Vietnam, October 2020 Climatic change, 169(3), 1-22
15 Mohanty, S., Marathe, R., & Singh, S 1999 Probability analysis of annual maximum daily rainfall for Amravati Indian J Soil Conser, 43(1), 15-17
16 Mosavi, A., Ozturk, P., & Chau, K.-w 2018 Flood prediction using machine learning models: Literature review Water, 10(11), 1536
17 Nguyen, T T., & Nguyen, T S 2022 Investigation of design rainfall distribution for Lower Da River Basin under climate change International Journal of Global Warming, 27(1), 71-91
18 Nguyen, V L., Le Quang, D., Dong, T V., Pham, L H., & Le Thanh, T 2017 Study on the Frequency of Heavy Rainfall in Huong Khe District, Ha Tinh Province VNU Journal of Science: Earth and Environmental Sciences, 33(2)
19 Nhất, P T 2010 Đánh giá ngưỡng chịu tải nước sông Cầu, làm cơ sở xây dựng các quy hoạch kinh tế xã hội và bảo vệ môi trường (Assessing the water load-bearing threshold of Cau River, serving as a basis for building socio-economic and environmental protection plans)
20 Noi, D T 2016 Study on flooding variation and scientific basis for flood calculation for transportation in the Northeast region of Vietnam PhD Thesis Water Resources University
21 Organization, W H 2018 Managing epidemics: key facts about major deadly diseases: World Health Organization
22 Palenchar, M J., & Heath, R L 2002 Another part of the risk communication model: Analysis of communication processes and message content Journal of Public Relations Research, 14(2), 127-158
23 Pilarczyk, K W., & Nuoi, N S 2005 Experience and practices on flood control in Vietnam Water International, 30(1), 114-122
24 Ritzema, H., Thinh, L D., Anh, L Q., Hanh, D N., Chien, N V., Lan, T N., Kim, B T 2008 Participatory research on the effectiveness of drainage in the Red River Delta, Vietnam Irrigation and Drainage Systems, 22(1), 19-34
25 Salas, J D., & Obeysekera, J 2014 Revisiting the concepts of return period and risk for nonstationary hydrologic extreme events Journal of Hydrologic Engineering, 19(3), 554-568
26 Sarhadi, A., Soltani, S., & Modarres, R 2012 Probabilistic flood inundation mapping of ungauged rivers: Linking GIS techniques and frequency analysis Journal of Hydrology, 458, 68-86
27 Sheppard, B., Janoske, M., & Liu, B 2012 Understanding risk communication theory: a guide for emergency managers and communicators
28 Singh, V., & Rajagopal, A 1986 A new method of parameter estimation for hydrologic frequency analysis Hydrological Science and Technology, 2(3), 33-40
29 Singh, V P 1987 On application of the Weibull distribution in hydrology Water Resources Management, 1(1), 33-43
30 Stewardson, M J., & McMahon, T A 2002 A stochastic model of hydraulic variations within stream channels Water Resources Research, 38(1), 8-1-8-
31 Takara, K 2009 Frequency analysis of hydrological extreme events and how to consider climate change Water Resources and Water-Related Disasters under Climate Change,-Prediction, Impact Assessment and Adaptation-, 19th UNESCO-IHP Training Course, Kyoto University.