Introducing the Mixed Distribution in Fitting Rainfall Data

Suhaila, Jamaludin; Ching-Yee, Kong; Yusof, Fadhilah; Hui–Mean, Foo

doi:10.4236/ojmh.2011.12002

Cited by 25 publications

(16 citation statements)

References 20 publications

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“…The development of the model for the amount process was based on the recommendations by Fernandes et al [9] and Suhaila et al [18]. Specifically, a number of distributions were selected for the purpose of identifying and evaluating the ideal distribution for this process.…”

Section: Amount Processmentioning

confidence: 99%

Bayesian Time Series Modelling of the Italian Daily Rainfall Data using Mixed Distribution

Bin Ibrahim*,

Jalal

2019

IJRTE

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A combination of continuous and discrete elements is referred to as a mixed distribution. For example, daily rainfall data consist of zero and positive values. We aim to develop a Bayesian time series model that captures the evolution of the daily rainfall data in Italy, focussing on directly linking the amount and occurrence of rainfall. Two gamma (G1 and G2) distributions with different parameterisations and lognormal distribution were investigated to identify the ideal distribution representing the amount process. Truncated Fourier series was used to incorporate the seasonal effects which captures the variability in daily rainfall amounts throughout the year. A first-order Markov chain was used to model rainfall occurrence conditional on the presence or absence of rainfall on the previous day. We also built a hierarchical prior structure to represent our subjective beliefs and capture the initial uncertainties of the unknown model parameters for both amount and occurrence processes. The daily rainfall data from Urbino rain gauge station in Italy were then used to demonstrate the applicability of our proposed methods. Residual analysis and posterior predictive checking method were utilised to assess the adequacy of model fit. In conclusion, we clearly found that our proposed method satisfactorily and accurately fits the Italian daily rainfall data. The gamma distribution was found to be the ideal probability density function to represent the amount of daily rainfall.

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Section: Amount Processmentioning

confidence: 99%

Bayesian Time Series Modelling of the Italian Daily Rainfall Data using Mixed Distribution

Bin Ibrahim*,

Jalal

2019

IJRTE

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“…For instance, Generalized Pareto has been found to be the best distribution of rainfall intensity in Peninsular Malaysia (Dan'azumi et al, 2010) to model the rainfall intensity. Another study found that Mixed Lognormal distribution was the best distribution model for most of the rain gauge stations in Peninsular Malaysia (Suhaila et al, 2011). However, studies by Abas et al (2014) and Daud et al (2016) using Neyman Scott methodology showed that Mixed Exponential was the best distribution to describe the intensity of rainfall in Peninsular Malaysia.…”

Section: Introductionmentioning

confidence: 97%

Stochastic generation of hourly rainfall series in the Western Region of Peninsular Malaysia

Syafrina

2018

Int. j. adv. appl. sci.

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Comprehensive analysis and modeling of rainfall distribution is essential in capturing the characteristics of high intense rainfall. The western region of Peninsular Malaysia which is more urbanized and densely populated is prone to flash flood occurrences due to the high intense rainfall brought by a convective rainfall during the inter-monsoon season. Convective rain is usually short live and intense. Therefore, knowledge pertaining to the distribution of rainfall intensity at short time scale is crucial in planning and decision making prior to, during and after a flood event, thereby minimizing the potentially catastrophic impact of flooding. The selection of appropriate probability distribution to represent rainfall intensity is highly critical to get a better indication of seasonal contribution to the annual rainfall. This study aimed to determine the better distribution of rainfall intensity to represent extreme rainfall events in the western region using Advanced Weather Generator (AWE-GEN). Model development consists of using hourly rainfall data and other meteorological data from three stations located within the studied region. Two probability distributions incorporated in the AWE-GEN model, namely, Weibull and Gamma were fitted to the historical data. Numerical evaluation using Root Mean Square Error goodness-of-fit test was used to compare the performance of the distributions. Results showed that AWE-GEN model is capable of simulating the monthly rainfall series at the west coast region with Weibull being the better distribution representing intensity. It was found that high values in model parameters , and contribute to the higher intense rainfall within the studied region. The AWE-GEN model also performs quite well in reproducing the hourly and 24 hour extremes rainfall as well as generating the extreme wet spell; however the model slightly underestimates the extreme dry spell. Results can be beneficial, particularly, for a better rainfall forecasting at watersheds and urban areas.

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“…Characterizing variability by fitting a function to some empirical form of the distribution of daily rainfall is another established technique. Whether the function is fit to the empirical frequency distribution [e.g., May, 2004a;Suhaila et al, 2011], the normalized rainfall curve [e.g., Burgueño et al, 2010], or the concentration index [e.g., Martin-Vide, 2004;Jiang et al, 2016;Caloiero, 2014] the result is the same: the actual form of the distribution of daily rainfall variability is summarized by a function with just a few parameters. In order to keep in line with previous work on the importance of climatic variability on long-term landscape evolution [Tucker and Bras, 2000;Tucker, 2004;Lague, 2005;Rossi et al, 2016], we fit a mixture of gamma distributions to the empirical frequency distribution of daily rainfall.…”

Section: Introductionmentioning

confidence: 99%

Rainfall variability in the Himalayan orogen and its relevance to erosion processes

Deal

Favre

Braun

2017

Water Resources Research

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Rainfall is an important driver of erosion processes. The mean rainfall rate is often used to account for the erosive impact of a particular climate. However, for some erosion processes, erosion rate is a nonlinear function of rainfall, e.g., due to a threshold for erosion. When this is the case, it is important to take into account the full distribution of rainfall, instead of just the mean. In light of this, we have characterized the variability of daily rainfall over the Himalayan orogen using high spatial and temporal resolution rainfall data sets. We find significant variations in rainfall variability over the Himalayan orogen, with increasing rainfall variability to the west and north of the orogen. By taking into account variability of rainfall in addition to mean rainfall rate, we find a pattern of rainfall that, from a geomorphological perspective, is significantly different from mean rainfall rate alone. Using these findings, we argue that short‐term rainfall variability may help explain observed short and long‐term erosion rates in the Himalayan orogen.

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Introducing the Mixed Distribution in Fitting Rainfall Data

Cited by 25 publications

References 20 publications

Bayesian Time Series Modelling of the Italian Daily Rainfall Data using Mixed Distribution

Bayesian Time Series Modelling of the Italian Daily Rainfall Data using Mixed Distribution

Stochastic generation of hourly rainfall series in the Western Region of Peninsular Malaysia

Rainfall variability in the Himalayan orogen and its relevance to erosion processes

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