Divergence criteria in extreme rainfall series frequency analyses

Haktanır, Tefaruk

doi:10.1623/hysj.48.6.917.51427

Cited by 7 publications

(8 citation statements)

References 13 publications

(12 reference statements)

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“…One other plausible reason for the possible crossover of IDF curves is that frequency analysis of rainfall data is performed separately for each duration without considering the inter-correlations that are intrinsically embedded in rainfall data of different durations. Haktanir [53] earlier pointed out that rainfall frequency analysis of different durations in the process of establishing IDF relationships should not be performed independently of each other, but did not propose a mechanism to handle the correlation directly. Recently, Gräler et al [54] applied D-vine copula, along with the generalized extreme value distributions, to derive rainfall IDF relationships based on rainfalls of five durations.…”

Section: Numerical Examplementioning

confidence: 99%

Third-Order Polynomial Normal Transform Applied to Multivariate Hydrologic Extremes

Tung

You

Yoo

2019

Water

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Hydro-infrastructural systems (e.g., flood control dams, stormwater detention basins, and seawalls) are designed to protect the public against the adverse impacts of various hydrologic extremes (e.g., floods, droughts, and storm surges). In their design and safety evaluation, the characteristics of concerned hydrologic extremes affecting the hydrosystem performance often are described by several interrelated random variables—not just one—that need to be considered simultaneously. These multiple random variables, in practical problems, have a mixture of non-normal distributions of which the joint distribution function is difficult to establish. To tackle problems involving multivariate non-normal variables, one frequently adopted approach is to transform non-normal variables from their original domain to multivariate normal space under which a large wealth of established theories can be utilized. This study presents a framework for practical normal transform based on the third-order polynomial in the context of a multivariate setting. Especially, the study focuses on multivariate third-order polynomial normal transform (TPNT) with explicit consideration of sampling errors in sample L-moments and correlation coefficients. For illustration, the modeling framework is applied to establish an at-site rainfall intensity–duration-frequency (IDF) relationship. Annual maximum rainfall data analyzed contain seven durations (1–72 h) with 27 years of useable records. Numerical application shows that the proposed modeling framework can produce reasonable rainfall IDF relationships by simultaneously treating several correlated rainfall data series and is a viable tool in dealing with multivariate data with a mixture of non-normal distributions.

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Section: Numerical Examplementioning

confidence: 99%

Third-Order Polynomial Normal Transform Applied to Multivariate Hydrologic Extremes

Tung

You

Yoo

2019

Water

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“…But, the frequency analyses of the 14 successive‐duration annual extreme rainfalls series should not be performed independently from each other. The magnitude of extreme rainfall, x 2 , of a longer‐duration, tr 2 , should be greater than that of extreme rainfall, x 1 , of shorter‐duration, tr 1 , both having the same average return period, T , which necessitate that the quantile function of the tr 2 ‐duration annual extreme rainfall must be divergent from that of the tr 1 ‐duration annual extreme rainfall with increasing return periods, as analytically depicted by the following constraints (Haktanir, 2003b): …”

Section: Divergence Criterionmentioning

confidence: 99%

“…Inequality (1) is the revelation of conservation of mass, and inequality (2) assures the frequency curves of successive‐duration annual extreme rainfall series to be diverging from each other with increasing return periods up to T of + ∞ years. Inequalities (1) and (2) define the divergence criterion, and accordingly, the magnitudes of the parameters of the adopted probability distribution for the 14 successive‐duration annual extreme rainfalls must be either increasing or decreasing with increasing rainfall duration, tr (Haktanir, 2003b).…”

Section: Divergence Criterionmentioning

confidence: 99%

“…There are analytical relationships among the distribution parameters and distribution statistics peculiar to the distribution. Accordingly, in order for guaranteed satisfaction of the divergence criterion, the parameters of a distribution must be either increasing or decreasing with increasing tr (Haktanir, 2003b). For the GEV distribution, parameters of each successive‐duration pair of annual extreme rainfalls series must satisfy: a 2 < a 1 , b 2 > b 1 , c 2 > c 1 , and for the LN3 distribution: a 2 > a 1 , b 2 > b 1 , c 2 > c 1 .…”

Section: Modification Of Distribution Parameters Of 14 Successive‐durmentioning

confidence: 99%

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Frequency analyses of annual extreme rainfall series from 5 min to 24 h

Haktanır

Çobaner

Kisi

2010

Hydrological Processes

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Abstract:The parameter estimation methods of (1) moments, (2) maximum-likelihood, (3) probability-weighted moments (PWM) and (4) self-determined PWM are applied to the probability distributions of Gumbel, general extreme values, three-parameter log-normal (LN3), Pearson-3 and log-Pearson-3. The special method of computing parameters so as to make the sample skewness coefficient zero is also applied to LN3, and hence, altogether 21 candidate distributions resulted. The parameters of these distributions are computed first by original sample series of 14 successive-duration annual extreme rainfalls recorded at a rain-gauging station. Next, the parameters are scaled by first-degree semi-log or log-log polynomial regressions versus rainfall durations from 5 to 1440 min (24 h). Those distributions satisfying the divergence criterion for frequency curves are selected as potential distributions, whose better-fit ones are determined by a conjunctive evaluation of three goodness-of-fit tests. Frequency tables, frequency curves and intensity-duration-frequency curves are the outcome.

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“…The generalization approach proposed herein provides the following advantages and innovations for the IDF relationships: In order for the IDF curves not to exhibit 'intersections' in a guaranteed way, both sample mean and sample standard deviation must show increasing trends with increasing rainfall duration. This is called 'divergence criterion' (Haktanir 2003). This criterion is defined as the constraints to be fulfilled by the parameters of a parent distribution in order not to intersect each others with increasing return periods.…”

Section: Introductionmentioning

confidence: 99%

Simple generalization approach for intensity-duration-frequency relationships

Aşıkoğlu

Benzeden

2012

Hydrol. Process.

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ABSTRACT:Rainfall intensity-duration-frequency (IDF) relationships describe rainfall intensity as a function of duration and return period, and they are significant for water resources planning, as well as for the design of hydraulic constructions. In this study, the two-parameter lognormal (LN2) and Gumbel distributions are used as parent distribution functions. Derivation of the IDF relationship by this approach is quite simple, because it only requires an appropriate function of the mean of annual maximum rainfall intensity as a function of rainfall duration. It is shown that the monotonic temporal trend in the mean rainfall intensity can successfully be described by this parametric function which comprises a combination of the parameters of the quantile function a(T) and completely the duration function b(d) of the separable IDF relationship. In the case study of Aegean Region (Turkey), the IDF relationships derived through this simple generalization procedure (SGP) may produce IDF relationships as successfully as does the well-known robust estimation procedure (REP), which is based on minimization of the nonparametric Kruskal-Wallis test statistic with respect to the parameters θ and Z of the duration function. Because the approach proposed herein is based on lower-order sample statistics, risks and uncertainties arising from sampling errors in higher-order sample statistics were significantly reduced. The authors recommend to establish the separable IDF relationships by the SGP for a statistically favorable two-parameter parent distribution, because it uses the same assumptions as the REP does, it maintains the observed temporal trend in the mean additionally, it is easy to handle analytically and requires considerably less computational effort.

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Divergence criteria in extreme rainfall series frequency analyses

Cited by 7 publications

References 13 publications

Third-Order Polynomial Normal Transform Applied to Multivariate Hydrologic Extremes

Third-Order Polynomial Normal Transform Applied to Multivariate Hydrologic Extremes

Frequency analyses of annual extreme rainfall series from 5 min to 24 h

Simple generalization approach for intensity-duration-frequency relationships

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