Modeling climate extremes using the four-parameter kappa distribution for <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si53.svg" display="inline" id="d1e813"><mml:mi>r</mml:mi></mml:math>-largest order statistics

Shin, Yire; Park, Jeong‐Soo

doi:10.1016/j.wace.2022.100533

Cited by 12 publications

(8 citation statements)

References 37 publications

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“…Therefore, they have higher uncertainty [1,39], and fitting PDFs' distribution suffers from numerical stability [40]. The most common distribution functions are normal, log-normal, gamma, log-Pearson type III, Gumbel, and log-Gumbel [2,38,[41][42][43][44][45][46].…”

Section: Probability Density Functions (Pdf)mentioning

confidence: 99%

Extreme Runoff Estimation for Ungauged Watersheds Using a New Multisite Multivariate Stochastic Model MASVC

Hernández-Bedolla,

García-Romero,

Franco-Navarro

et al. 2023

Water

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Precipitation is influential in determining runoff at different scales of analysis, whether in minutes, hours, or days. This paper proposes the use of a multisite multivariate model of precipitation at a daily scale. Stochastic models allow the generation of maximum precipitation and its association with different return periods. The modeling is carried out in three phases. The first is the estimation of precipitation occurrence by using a two-state multivariate Markov model to calculate the non-rainfall periods. Once the rainfall periods of various storms have been identified, the amount of precipitation is estimated through a process of normalization, standardization of the series, acquisition of multivariate parameters, and generation of synthetic series. In comparison, the analysis applies probability density functions that require fewer data and, consequently, represent greater certainty. The maximum values of surface runoff show consistency for different observed return periods, therefore, a more reliable estimation of maximum surface runoff. Our approach enhances the use of stochastic models for generating synthetic series that preserve spatial and temporal variability at daily, monthly, annual, and extreme values. Moreover, the number of parameters reduces in comparison to other stochastic weather generators.

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Section: Probability Density Functions (Pdf)mentioning

confidence: 99%

Extreme Runoff Estimation for Ungauged Watersheds Using a New Multisite Multivariate Stochastic Model MASVC

Hernández-Bedolla,

García-Romero,

Franco-Navarro

et al. 2023

Water

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“…The statistical method aims to fit the empirical FDC through appropriate distribution functions (such as gamma distribution, lognormal distribution, generalized Pareto distribution, kappa distribution, etc.) (Almeida et al, 2021; Burgan & Aksoy, 2022; Cheng et al, 2012; Ghotbi, Wang, Singh, Blöschl, & Sivapalan, 2020; Ghotbi, Wang, Singh, Mayo, & Sivapalan, 2020; Shin & Park, 2022), and then find the quantitative and qualitative relationship between the estimated parameters of the fitting function and the characteristics of the local climate and geographical environment of the measured catchment. Villalobos and Neelin explained why the gamma distribution can well fit the daily precipitation distribution.…”

Section: Introductionmentioning

confidence: 99%

Physical controls and regional pattern similarities of precipitation and flow duration curves using the three‐parameter gamma distribution

Zhou,

Zhang

2024

Hydrological Processes

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The flow duration curve (FDC) is the cumulative distribution function, which represents the relationship between the frequency and magnitude of streamflow, and the precipitation duration curves (PDC) follows the same principle. Nowadays, the correlation between the shape of PDC and FDCs, their respective physical control factors including human activities, and their fitting conditions in unmeasured catchments across China have not been fully understood. In this paper, daily precipitation and streamflow data with 30 years records from 224 hydrological stations in the middle and lower Yangtze River basin were chosen to fit PDC and FDCs through gamma distribution. Framework was proposed for modelling FDCs to analyse the relationship, similarity, regional patterns and response mechanism of fitting parameters between PDC and FDCs, dividing the streamflow time series into fast and base flow and stations into three categories in consideration of human activities to attribute the shapes of PDC and FDCs to catchment meteorological and geographical characteristics and physical processes under natural conditions. Results indicate that the parameters of PDC and certain FDCs (TFDC, FFDC, SFDC) share similar spatial patterns but vary for the different duration and interactions of the processes. The climate and catchment characteristics such as extreme properties of precipitation, base flow index (BFI), Pmax*αp and concentration ratio index (CIM) will influence the shape of PDC and FDCs. The relationship between BFI and SFDC/TFDC can be better reflected in “Regulated watersheds”, while CIM/Pmax*αp and PDC/FFDC in “watersheds in the mainstream” are more related. This paper provides a deeper understanding and more accurate way of the application of these parameters in describing and predicting hydrological processes and estimation of PDC and FDCs in unmeasured catchments, and can be applied to more future research about processes based on catchment rainfall‐runoff responses and physical controls.

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“…To estimate the parameters of these types of statistical distributions, the most used methods are the method of ordinary moments (MOM) and the method of linear moments (L-moments), the latter having the advantage that it is less influenced by the length of the data series [7][8][9][10], the extreme values in the data series, or in some cases, outlier values requiring the elaboration of specific verification tests. However, a correction of the statistical parameters (L 1 , τ 2 , τ 3 ) of the short series of maximum flows is necessary because they differ from those of the considered statistical population, that is, of the theoretical probability distribution function.…”

Section: Introductionmentioning

confidence: 99%

Flood Frequency Analysis Using the Gamma Family Probability Distributions

Ilinca

Anghel

2023

Water

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This article presents six probability distributions from the gamma family with three parameters for the flood frequency analysis in hydrology. The choice of the gamma family of statistical distributions was driven by its frequent use in hydrology. In the Faculty of Hydrotechnics, the improvement of the estimation of maximum flows, including the methodological bases for the realization of a regionalization study with the linear moments method with the corrected parameters, was researched and is an element of novelty. The linear moments method performs better than the method of ordinary moments because it avoids the choice of skewness depending on the origin of the flows, and is the method practiced in Romania. The L-moments method conforms to the current trend for estimating the parameters of statistical distributions. Observed data from hydrometric stations are of relatively short length, so the statistical parameters that characterize them are of a sample that requires correction. The correction of the statistical parameters is proposed using the method of least squares based on the inverse functions of the statistical distributions expressed with the frequency factor for L-moments. All the necessary elements for their use are presented, such as quantile functions, the exact and approximate relations for estimating parameters, and frequency factors. A flood frequency analysis case study was carried out for the Ialomita river to verify the proposed methodology. The performance of this distributions is evaluated using Kling–Gupta and Nash–Sutcliff coefficients.

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Modeling climate extremes using the four-parameter kappa distribution for r-largest order statistics

Cited by 12 publications

References 37 publications

Extreme Runoff Estimation for Ungauged Watersheds Using a New Multisite Multivariate Stochastic Model MASVC

Extreme Runoff Estimation for Ungauged Watersheds Using a New Multisite Multivariate Stochastic Model MASVC

Physical controls and regional pattern similarities of precipitation and flow duration curves using the three‐parameter gamma distribution

Flood Frequency Analysis Using the Gamma Family Probability Distributions

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