Selection of the best fit flood frequency distribution and parameter estimation procedure: a case study for Tasmania in Australia

Haddad, Khaled; Rahman, Ataur

doi:10.1007/s00477-010-0412-1

Cited by 102 publications

(46 citation statements)

References 46 publications

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“…MADI and PPCC have been used in different studies (for example see [23], [9,[25][26][27], and many others). Similarly, the AD test is frequently used in many studies such as [12] and [28][29][30][31].…”

Section: Goodness Of Fit Testsmentioning

confidence: 99%

At-Site Flood Frequency Analysis of Annual Maximum Stream Flows in Pakistan Using Robust Estimation Methods

Ahmad¹,

Fawad²,

Mahmood³

2015

Pol. J. Environ. Stud.

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IntroductionFloods, droughts, and heavy storms are some of the manifestations of environmental events that cause tremendous destruction and bring misery to human existence. Flooding can bring havoc to property, infrastructure, animals, plants, and human lives. Floods have been a major challenge in Pakistan for many years. The main reason for these floods is extreme monsoon rainfall due to the unusual climate-change-led seasonal cycle of land temperature in Pakistan that has made the monsoon rainfall more severe and produced a large volume of water in the northern mountainous region of the country. Summer monsoon in the subcontinent is going to be extreme. Temperature, CO 2 , and CH 4 records of past decades represent this change [1]. The monsoon in Pakistan starts in early July and remains until the end of September. Besides human loss, the financial loss in the last six decades is estimated at $37.554 billion US.In construction of flood protection projects, information on flood magnitude and their frequencies is critical [2]. Frequency analysis is the estimation of how often a specified event will happen. The main objective of FFA is to relate the magnitude of extreme events to their frequency of happening through the use of probability distributions [3].This study is interesting in two aspects, first by selecting a robust estimation method and second by selecting a best distribution for at-site FFA using AMSF data in the country using different goodness fit tests. The first aspect is a prerequisite for the second, in the sense that we need estiPol. J. Environ. Stud. Vol. 24, No. 6 (2015), [2345][2346][2347][2348][2349][2350][2351][2352][2353] AbstractOur paper compares the L-moments (MLM), TL-moments (MTLM), and maximum likelihood estimation (MLE) methods in order to select the best-fit distribution of annual maximum stream flow (AMSF) data for at-site flood frequency analysis (FFA) in Pakistan. Initially this study considered different probability distributions. Best distribution for each site is identified using different goodness of fit tests such as mean absolute deviation index (MADI), Anderson darling (AD) test, probability plot correlation coefficient (PPCC), and L-moments ratio diagram. Results show that GPA distribution is the most suitable distribution for most of the sites, followed by GLO and GEV distributions, respectively. MLM is found to be the most suitable estimation method in finding the best-fit distribution for most of the sites in this study, followed by MTLM and MLE. For at-site FFA we also estimated different return periods associated with given flood magnitudes (quantiles of best fit distribution/maximum annual discharge values). It is found that estimated flows based on fitted distribution are in close agreement with observed flows.

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Section: Goodness Of Fit Testsmentioning

confidence: 99%

At-Site Flood Frequency Analysis of Annual Maximum Stream Flows in Pakistan Using Robust Estimation Methods

Ahmad¹,

Fawad²,

Mahmood³

2015

Pol. J. Environ. Stud.

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“…Different methods have been used for the goodness-of-fi t measure such as including the Chi-square method, quantile-quantile plots, mean absolute deviation index, LMRD, RMSE, KST, and ADT. These tests have been used by many authors [8,16,36,[41][42][43][44][45][46][47]. In this study we implemented three GOF tests -RMSE, KS, and AD -and one graphical method, i.e., LRD for visual inspection.…”

Section: Goodness-of-fi T Criteriamentioning

confidence: 99%

Finding Probability Distributions for Annual Daily Maximum Rainfall in Pakistan Using Linear Moments and Variants

Ahmad

Abbass²,

Saghir

et al. 2016

Pol. J. Environ. Stud.

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In this study, at-site frequency analysis (AFA) of an annual daily maximum rainfall (ADMR) series was carried out using the method of linear moments (L-moments) and their variants such as trimmed linear moments (TL-moments) and higher order linear moments (LH-moments). The ADMR series we investigated was observed at 28 meteorological observatories across Pakistan as retrieved from the Pakistan Meteorological Department (PMD). The basic aim of the study was to fi nd best-fi t (i.e., the most suitable) probability distribution among the class of various probability distributions. Initially different goodness-offi t (GOF) measures such as the Kolmogorov-Smirnov test (KST), Anderson-Darling test (ADT), root mean square error (RMSE) and L-moments ratio diagram (LRD) were applied to determine not only the best-fi t distributions but also the best linear estimation method for AFA. We observed that no single probability distribution could be declared as the best-fi t distribution for all the stations. Five distributions were found to be the most appropriate: generalized extreme value (GEV), three parameter lognormal (LN3), Pearson type III (P3), generalized logistic (GLO), and generalized pareto (GPA). The TL-moments method was also applied for parameter estimation to mitigate the effect of outliers on fi nal estimates. LH-moments were used for estimating the upper part of probability distributions and larger events in the data samples. LH moments alleviate the unwanted affects due to small sample values that may be obvious during estimation of events related to larger return periods. Using different GOF tests, we observed that the L-moments method was best for eight stations, TL-moments with trimming (1, 0), and LH-moments with level η =2, 3, 4 were best for six and 14 stations, respectively. A theoretical relationship between TL-moments and LH-moments was also revisited, which revealed that LH-moments are special cases of TL-moments when we are motivated to make trimming only from the lower side.

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“…At this point it is worth emphasizing that the accuracy with which the quantiles are estimated is a fundamental criterion for selecting a distribution (MADSEN et al, 1997). By considering that the MAE and MSE are scalar measures of agreement (WILKS, 2011) that evaluates the reliability of quantile estimates made by a given model (HADDAD & RAHMAN, 2011), we may assume that the GPD fits better than the GEV to the extreme dry SPI values obtained from the weather station of Ribeirão Preto. Considering the 95% confidence interval, the visual analysis of Figure 2 clearly indicates that the GEV model is inconsistent with the most extremes SPI values obtained from the weather station of Ribeirão Preto.…”

Section: Block Maxima and Peaks-over-thresholdmentioning

confidence: 99%

Dry months in the agricultural region of Ribeirão Preto, state of São Paulo-Brazil: an study based on the extreme value theory

Blain

2014

Eng. Agríc.

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ABSTRACT:The application of the Extreme Value Theory (EVT) to model the probability of occurrence of extreme low Standardized Precipitation Index (SPI) values leads to an increase of the knowledge related to the occurrence of extreme dry months. This sort of analysis can be carried out by means of two approaches: the block maxima (BM; associated with the General Extreme Value distribution) and the peaks-over-threshold (POT; associated with the Generalized Pareto distribution). Each of these procedures has its own advantages and drawbacks. Thus, the main goal of this study is to compare the performance of BM and POT in characterizing the probability of occurrence of extreme dry SPI values obtained from the weather station of Ribeirão Preto-SP (1937. According to the goodness-of-fit tests, both BM and POT can be used to assess the probability of occurrence of the aforementioned extreme dry SPI monthly values. However, the scalar measures of accuracy and the return level plots indicate that POT provides the best fit distribution. The study also indicated that the uncertainties in the parameters estimates of a probabilistic model should be taken into account when the probability associated with a severe/extreme dry event is under analysis. KEYWORDS:Extreme Value distribution, Pareto distribution, goodness-of-fit tests. TEORIA DOS VALORES EXTREMOS APLICADA À OCORRÊNCIA DE MESES SECOS EM UMA REGIÃO AGRÍCOLA DO ESTADO DE SÃO PAULO RESUMO:A aplicação da Teoria dos Valores Extremos (EVT) para modelar a probabilidade de ocorrência dos extremos inferiores do Índice Padronizado de Precipitação (SPI) leva ao aprofundamento do conhecimento relativo à ocorrência de meses secos. Esse tipo de análise pode ser realizado com base nos métodos dos máximos em bloco (BM; associado à distribuição Geral dos Valores Extremos) e dos peaks-over-threshold (POT; associado à distribuição Pareto Generalizada). Considerando que cada um desses procedimentos apresenta vantagens e desvantagens, o objetivo principal do trabalho foi comparar o desempenho de ambos os métodos na caracterização da probabilidade de ocorrência dos extremos secos do SPI obtidos a partir da estação meteorológica de Ribeirão Preto-SP (1937. De acordo com os testes de aderência, o BM e o POT podem ser usados para avaliar a probabilidade de ocorrência de valores mensais extremamente secos do SPI obtidos na referida localidade. Entretanto, medidas escalares de precisão e gráficos de nível de returno indicam que o POT resulta no melhor ajuste. O estudo também demonstrou que as incertezas na estimação dos parâmetros de modelos probabilísticos devem ser consideradas quando a probabilidade de ocorrência dos eventos em análise estiver sendo avaliada.

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Selection of the best fit flood frequency distribution and parameter estimation procedure: a case study for Tasmania in Australia

Cited by 102 publications

References 46 publications

At-Site Flood Frequency Analysis of Annual Maximum Stream Flows in Pakistan Using Robust Estimation Methods

At-Site Flood Frequency Analysis of Annual Maximum Stream Flows in Pakistan Using Robust Estimation Methods

Finding Probability Distributions for Annual Daily Maximum Rainfall in Pakistan Using Linear Moments and Variants

Dry months in the agricultural region of Ribeirão Preto, state of São Paulo-Brazil: an study based on the extreme value theory

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