A study on selection of probability distributions for at-site flood frequency analysis in Australia

Rahman, Ayesha; Rahman, Ataur; Zaman, Mohammad A; Haddad, Khaled; Ahsan, Amimul; Imteaz, Monzur Alam

doi:10.1007/s11069-013-0775-y

Cited by 125 publications

(99 citation statements)

References 23 publications

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“…Different methods of parameter estimations change the results of the goodness-of-fi t tests to some extent [8].…”

Section: Resultsmentioning

confidence: 99%

“…Only fi ve distributions (such as GEV, GLO, GPA, LN3, and P3) are declared the most suitable for different stations. L-moments, TL-moments with trimming (1, 0), LH-moments with level (η =2), (η =3), (η = 4) are suitable for 8,6, and 14 stations, respectively. A theoretical relationship between TL-moments and LHmoments is also revisited, which persuades us that LHmoments are special cases of TL-moments, when trimming is performed only from the lower side.…”

Section: Discussionmentioning

confidence: 99%

“…All these distributions have been studied in many countries for atsite and regional frequency analysis [6,8,18,[37][38]40]. After this, the next step was to select the most appropriate distribution for each site.…”

Section: Goodness-of-fi T Criteriamentioning

confidence: 99%

“…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%

“…This can result in either under or over estimation, and may have serious implication in practice. [8]. For AFA, we need data from a reasonably large record period, since the available data of rainfall is of shorter length than return periods of interest.…”

Section: Introductionmentioning

confidence: 99%

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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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“…Different methods of parameter estimations change the results of the goodness-of-fi t tests to some extent [8].…”

Section: Resultsmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

Section: Goodness-of-fi T Criteriamentioning

confidence: 99%

Section: Goodness-of-fi T Criteriamentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

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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Imprecise probabilistic estimation of design floods with epistemic uncertainties

Zhang

et al. 2016

Water Resources Research

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An imprecise probabilistic framework for design flood estimation is proposed on the basis of the Dempster-Shafer theory to handle different epistemic uncertainties from data, probability distribution functions, and probability distribution parameters. These uncertainties are incorporated in cost-benefit analysis to generate the lower and upper bounds of the total cost for flood control, thus presenting improved information for decision making on design floods. Within the total cost bounds, a new robustness criterion is proposed to select a design flood that can tolerate higher levels of uncertainty. A variance decomposition approach is used to quantify individual and interactive impacts of the uncertainty sources on total cost. Results from three case studies, with 127, 104, and 54 year flood data sets, respectively, show that the imprecise probabilistic approach effectively combines aleatory and epistemic uncertainties from the various sources and provides upper and lower bounds of the total cost. Between the total cost and the robustness of design floods, a clear trade-off which is beyond the information that can be provided by the conventional minimum cost criterion is identified. The interactions among data, distributions, and parameters have a much higher contribution than parameters to the estimate of the total cost. It is found that the contributions of the various uncertainty sources and their interactions vary with different flood magnitude, but remain roughly the same with different return periods. This study demonstrates that the proposed methodology can effectively incorporate epistemic uncertainties in cost-benefit analysis of design floods.

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Applicability of Wakeby distribution in flood frequency analysis: a case study for eastern Australia

et al. 2014

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Abstract:Parametric method of flood frequency analysis (FFA) involves fitting of a probability distribution to the observed flood data at the site of interest. When record length at a given site is relatively longer and flood data exhibits skewness, a distribution having more than three parameters is often used in FFA such as log-Pearson type 3 distribution. This paper examines the suitability of a five-parameter Wakeby distribution for the annual maximum flood data in eastern Australia. We adopt a Monte Carlo simulation technique to select an appropriate plotting position formula and to derive a probability plot correlation coefficient (PPCC) test statistic for Wakeby distribution. The Weibull plotting position formula has been found to be the most appropriate for the Wakeby distribution. Regression equations for the PPCC tests statistics associated with the Wakeby distribution for different levels of significance have been derived. Furthermore, a power study to estimate the rejection rate associated with the derived PPCC test statistics has been undertaken. Finally, an application using annual maximum flood series data from 91 catchments in eastern Australia has been presented. Results show that the developed regression equations can be used with a high degree of confidence to test whether the Wakeby distribution fits the annual maximum flood series data at a given station. The methodology developed in this paper can be adapted to other probability distributions and to other study areas.

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A study on selection of probability distributions for at-site flood frequency analysis in Australia

Cited by 125 publications

References 23 publications

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

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

Imprecise probabilistic estimation of design floods with epistemic uncertainties

Applicability of Wakeby distribution in flood frequency analysis: a case study for eastern Australia

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