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1.
Abstract Applicability of log-Gumbel (LG) and log-logistic (LL) probability distributions in hydrological studies is critically examined under real conditions, where the assumed distribution differs from the true one. The set of alternative distributions consists of five two-parameter distributions with zero lower bound, including LG and LL as well as lognormal (LN), linear diffusion analogy (LD) and gamma (Ga) distributions. The log-Gumbel distribution is considered as both a false and a true distribution. The model error of upper quantiles and of the first two moments is analytically derived for three estimation methods: the method of moments (MOM), the linear moments method (LMM) and the maximum likelihood method (MLM). These estimation methods are used as methods of approximation of one distribution by another distribution. As recommended in the first of this two-part series of papers, MLM turns out to be the worst method, if the assumed LG or LL distribution is not the true one. It produces a huge bias of upper quantiles, which is at least one order higher than that of the other two methods. However, the reverse case, i.e. acceptance of LN, LD or Ga as a hypothetical distribution, while the LG or LL distribution is the true one, gives the MLM bias of reasonable magnitude in upper quantiles. Therefore, one should avoid choosing the LG and LL distributions in flood frequency analysis, especially if MLM is to be applied. 相似文献
2.
Pietro Bernardara Daniel Schertzer Eric Sauquet Ioulia Tchiguirinskaia Michel Lang 《Stochastic Environmental Research and Risk Assessment (SERRA)》2008,22(1):107-122
This paper empirically investigates the asymptotic behaviour of the flood probability distribution and more precisely the
possible occurrence of heavy tail distributions, generally predicted by multiplicative cascades. Since heavy tails considerably
increase the frequency of extremes, they have many practical and societal consequences. A French database of 173 daily discharge
time series is analyzed. These series correspond to various climatic and hydrological conditions, drainage areas ranging from
10 to 105 km2, and are from 22 to 95 years long. The peaks-over-threshold method has been used with a set of semi-parametric estimators
(Hill and Generalized Hill estimators), and parametric estimators (maximum likelihood and L-moments). We discuss the respective
interest of the estimators and compare their respective estimates of the shape parameter of the probability distribution of
the peaks. We emphasize the influence of the selected number of the highest observations that are used in the estimation procedure
and in this respect the particular interest of the semi-parametric estimators. Nevertheless, the various estimators agree
on the prevalence of heavy tails and we point out some links between their presence and hydrological and climatic conditions. 相似文献
3.
Knowable moments for high-order stochastic characterization and modelling of hydrological processes 总被引：2，自引：2，他引：0
Demetris Koutsoyiannis 《水文科学杂志》2019,64(1):19-33
4.
J. -H. Heo J. D. Salas 《Stochastic Environmental Research and Risk Assessment (SERRA)》1996,10(3):187-207
The log-Gumbel distribution is one of the extreme value distributions which has been widely used in flood frequency analysis. This distribution has been examined in this paper regarding quantile estimation and confidence intervals of quantiles. Specific estimation algorithms based on the methods of moments (MOM), probability weighted moments (PWM) and maximum likelihood (ML) are presented. The applicability of the estimation procedures and comparison among the methods have been illustrated based on an application example considering the flood data of the St. Mary's River. 相似文献
5.
《水文科学杂志》2013,58(5)
Abstract Abstract A parameter estimation method is proposed for fitting the generalized extreme value (GEV) distribution to censored flood samples. Partial L-moments (PL-moments), which are variants of L-moments and analogous to ?partial probability weighted moments?, are defined for the analysis of such flood samples. Expressions are derived to calculate PL-moments directly from uncensored annual floods, and to fit the parameters of the GEV distribution using PL-moments. Results of Monte Carlo simulation study show that sampling properties of PL-moments, with censoring flood samples of up to 30% are similar to those of simple L-moments, and also that both PL-moment and LH-moments (higher-order L-moments) have similar sampling properties. Finally, simple L-moments, LH-moments, and PL-moments are used to fit the GEV distribution to 75 annual maximum flow series of Nepalese and Irish catchments, and it is found that, in some situations, both LH- and PL-moments can produce a better fit to the larger flow values than simple L-moments. 相似文献
6.
《水文科学杂志》2013,58(2):367-386
Abstract Extremes of streamflow are usually modelled using heavy tailed distributions. While scrutinising annual flow maxima or the peaks over threshold, the largest elements in a sample are often suspected to be low quality data, outliers or values corresponding to much longer return periods than the observation period. In the case of floods, since the interest is focused mainly on the estimation of the right-hand tail of a distribution function, sensitivity of large quantiles to extreme elements of a series becomes the problem of special concern. This study investigated the sensitivity problem using the log-Gumbel distribution by generating samples of different sizes and different values of the coefficient of L-variation by means of Monte Carlo experiments. Parameters of the log-Gumbel distribution were estimated by the probability weighted moments (PWM) method, both for complete samples and the samples deprived of their largest element. In the latter case Hosking's concept of the “A” type PWM with Type II censoring was employed. The largest value was censored above the random threshold T corresponding to the non-exceedence probability F T. The effect of the F T value on the performance of the quantile estimates was then examined. Experimental results show that omission of the largest sample element need not result in a decrease in the accuracy of large quantile estimates obtained from the log-Gumbel model by the PWM method. 相似文献
7.
Comparison of Two Nonstationary Flood Frequency Analysis Methods within the Context of the Variable Regime in the Representative Polish Rivers 总被引：2，自引：0，他引：2
Witold G. Strupczewski Krzysztof Kochanek Ewa Bogdanowicz Iwona Markiewicz Wojciech Feluch 《Acta Geophysica》2016,64(1):206-236
Changes in river flow regime resulted in a surge in the number of methods of non-stationary flood frequency analysis. Common assumption is the time-invariant distribution function with time-dependent location and scale parameters while the shape parameters are time-invariant. Here, instead of location and scale parameters of the distribution, the mean and standard deviation are used. We analyse the accuracy of the two methods in respect to estimation of time-dependent first two moments, time-invariant skewness and time-dependent upper quantiles. The method of maximum likelihood (ML) with time covariate is confronted with the Two Stage (TS) one (combining Weighted Least Squares and L-moments techniques). Comparison is made by Monte Carlo simulations. Assuming parent distribution which ensures the asymptotic superiority of ML method, the Generalized Extreme Value distribution with various values of linearly changing in time first two moments, constant skewness, and various time-series lengths are considered. Analysis of results indicates the superiority of TS methods in all analyzed aspects. Moreover, the estimates from TS method are more resistant to probability distribution choice, as demonstrated by Polish rivers’ case studies. 相似文献
8.
Extremes of stream flow and precipitation are commonly modeled by heavytailed distributions. While scrutinizing annual flow
maxima or the peaks over threshold, the largest sample elements are quite often suspected to be low quality data, outliers
or values corresponding to much longer return periods than the observation period. Since the interest is primarily in the
estimation of the right tail (in the case of floods or heavy rainfalls), sensitivity of upper quantiles to largest elements
of a series constitutes a problem of special concern. This study investigated the sensitivity problem using the log-Gumbel
distribution by generating samples of different sizes (n) and different values of the coefficient of variation by Monte Carlo experiments. Parameters of the log-Gumbel distribution
were estimated by the probability weighted moments (PWMs) method, method of moments (MOMs) and maximum likelihood method (MLM),
both for complete samples and the samples deprived of their largest elements. In the latter case, the distribution censored
by the non-exceedance probability threshold, F
T
, was considered. Using F
T
instead of the censored threshold T creates possibility of controlling estimator property. The effect of the F
T
value on the performance of the quantile estimates was then examined. It is shown that right censoring of data need not reduce
an accuracy of large quantile estimates if the method of PWMs or MOMs is employed. Moreover allowing bias of estimates one
can get the gain in variance and in mean square error of large quantiles even if ML method is used. 相似文献
9.
Abstract A parameter estimation method is proposed for fitting probability distribution functions to low flow observations. LL-moments are variants of L-moments that are analogous to LH-moments, which were defined for the analysis of floods. LL-moments give higher weights to the small observations. Expressions are given that relate them to the probability distribution function for the case of normal, Weibull and power distributions. Sampling properties of the LL-moments and of the distribution parameters and quantiles estimated by them are found by a Monte Carlo simulation study. It is shown on an example that the low flow quantile estimates obtained by LL-moments may be significantly different from those obtained by L-moments. 相似文献
10.
Investigation on the properties of the relationship between rare and extreme rainfall and flood volumes, under some distributional restrictions 总被引：1，自引：1，他引：0
Mauro Naghettini Nebai Tavares Gontijo Maria Manuela Portela 《Stochastic Environmental Research and Risk Assessment (SERRA)》2012,26(6):859-872
The fact that rainfall data are usually more abundant and more readily regionalized than streamflow data has motivated hydrologists to conceive methods that incorporate the hydrometeorologial information into flood frequency analyses. Some of them, particularly those derived from the French GRADEX method, involve assumptions concerning the relationship between extreme rainfall and flood volumes, under some distributional restrictions. In particular, for rainfall probability distributions exhibiting exponential-like upper tails, it is possible to derive the shape and scale of the probability distribution of flood volumes by hypothesizing the basic properties of such a relationship, under rare and/or extreme conditions. This paper focuses on a parametric mathematical model for the relationship between rare and extreme rainfall and flood volumes under exponentially-tailed distributions. The model is analyzed and fitted to rare and extreme events derived from hydrological simulation of long stochastically-generated synthetic series of rainfall and evaporation for the Indaiá River basin, located in south-central Brazil. The paper also provides a sensitivity analysis of the model parameters in order to better understand flood events under rare and extreme conditions. By working with hydrologically plausible hypothetical events, the modeling approach proved to be a useful way to explore extraordinary rainfall and flood events. The results from this exploratory analysis provide grounds to derive some conclusions regarding the relative positions of the upper tails of the probability distributions of rainfall and flood volumes. 相似文献
11.
12.
A gamma distribution is one of the most frequently selected distribution types for hydrological frequency analysis. The bivariate gamma distribution with gamma marginals may be useful for analysing multivariate hydrological events. This study investigates the applicability of a bivariate gamma model with five parameters for describing the joint probability behavior of multivariate flood events. The parameters are proposed to be estimated from the marginal distributions by the method of moments. The joint distribution, the conditional distribution, and the associated return periods are derived from marginals. The usefulness of the model is demonstrated by representing the joint probabilistic behaviour between correlated flood peak and flood volume and between correlated flood volume and flood duration in the Madawask River basin in the province of Quebec, Canada. Copyright © 2001 John Wiley & Sons, Ltd. 相似文献
13.
Frequency analysis of droughts using the Plackett copula and parameter estimation by genetic algorithm 总被引：11，自引：8，他引：3
Songbai Song Vijay P. Singh 《Stochastic Environmental Research and Risk Assessment (SERRA)》2010,24(5):783-805
This study aims to model the joint probability distribution of drought duration, severity and inter-arrival time using a trivariate
Plackett copula. The drought duration and inter-arrival time each follow the Weibull distribution and the drought severity
follows the gamma distribution. Parameters of these univariate distributions are estimated using the method of moments (MOM),
maximum likelihood method (MLM), probability weighted moments (PWM), and a genetic algorithm (GA); whereas parameters of the
bivariate and trivariate Plackett copulas are estimated using the log-pseudolikelihood function method (LPLF) and GA. Streamflow
data from three gaging stations, Zhuangtou, Taian and Tianyang, located in the Wei River basin, China, are employed to test
the trivariate Plackett copula. The results show that the Plackett copula is capable of yielding bivariate and trivariate
probability distributions of correlated drought variables. 相似文献
14.
Md. Sharwar Murshed Sangil Kim Jeong-Soo Park 《Stochastic Environmental Research and Risk Assessment (SERRA)》2011,25(7):897-911
The beta-κ distribution is a distinct case of the generalized beta distribution of the second kind. In previous studies, beta-p and beta-κ distributions have played important roles in representing extreme events, and thus, the present paper uses the
beta-κ distribution. Further, this paper uses the method of moments and the method of L-moments to estimate the parameters
from the beta-κ distribution, and to demonstrate the performance of the proposed model, the paper presents a simulation study
using three estimation methods (including the maximum likelihood estimation method) and beta-κ and non beta-κ samples. In
addition, this paper evaluates the performance of the beta-κ distribution by employing two widely used extreme value distributions
(i.e., the GEV and Gumbel distributions) and two sets of actual data on extreme events. 相似文献
15.
Modelling raindrop size distribution (DSD) is a fundamental issue to connect remote sensing observations with reliable precipitation products for hydrological applications. To date, various standard probability distributions have been proposed to build DSD models. Relevant questions to ask indeed are how often and how good such models fit empirical data, given that the advances in both data availability and technology used to estimate DSDs have allowed many of the deficiencies of early analyses to be mitigated. Therefore, we present a comprehensive follow-up of a previous study on the comparison of statistical fitting of three common DSD models against 2D-Video Distrometer (2DVD) data, which are unique in that the size of individual drops is determined accurately. By maximum likelihood method, we fit models based on lognormal, gamma and Weibull distributions to more than 42.000 1-minute drop-by-drop data taken from the field campaigns of the NASA Ground Validation program of the Global Precipitation Measurement (GPM) mission. In order to check the adequacy between the models and the measured data, we investigate the goodness of fit of each distribution using the Kolmogorov–Smirnov test. Then, we apply a specific model selection technique to evaluate the relative quality of each model. Results show that the gamma distribution has the lowest KS rejection rate, while the Weibull distribution is the most frequently rejected. Ranking for each minute the statistical models that pass the KS test, it can be argued that the probability distributions whose tails are exponentially bounded, i.e. light-tailed distributions, seem to be adequate to model the natural variability of DSDs. However, in line with our previous study, we also found that frequency distributions of empirical DSDs could be heavy‐tailed in a number of cases, which may result in severe uncertainty in estimating statistical moments and bulk variables. 相似文献
16.
Shen Zhenyao Chen Lei Chen Tao 《Stochastic Environmental Research and Risk Assessment (SERRA)》2013,27(1):235-251
Parameter uncertainty involved in hydrological and sediment modeling often refers to the parameter dispersion and the sensitivity of the parameter. However, a limitation of the previous studies lies in that the assignment of range and specification of probability distribution for each parameter is usually difficult and subjective. Therefore, there is great uncertainty in the process of parameter calibration and model prediction. In this study, the impact of probability parameter distribution on hydrological and sediment modeling was evaluated using a semi-distributed model—the Soil and Water Assessment Tool (SWAT) and Monte Carlo method (MC)—in the Daning River watershed of the Three Gorges Reservoir Region (TGRA), China. The classic types of parameter distribution such as uniform, normal and logarithmic normal distribution were involved in this study. Based on results, parameter probability distribution showed a diverse degree of influence on the hydrological and sediment prediction, such as the sampling size, the width of 95% confidence interval (CI), the ranking of the parameter related to uncertainty, as well as the sensitivity of the parameter on model output. It can be further inferred that model parameters presented greater uncertainty in certain regions of the primitive parameter range and parameter samples densely obtained from these regions would lead to a wider 95 CI, resulting in a more doubtful prediction. This study suggested the value of the optimized value obtained by the parameter calibration process could may also be of vital importance in selecting the probability distribution function (PDF). Such cases, where parameter value corresponds to the watershed characteristic, can be used to provide a more credible distribution for both hydrological and sediment modeling. 相似文献
17.
Starting from a recent paper by Murshed (Stoch Environ Res Risk Assess 25:897–911, 2011) in which a good performance of the Beta-k distribution in analyzing extreme hydrologic events is shown, in this paper, we propose the use of two new four-parameters distribution functions strongly related to the Beta-k distribution, namely the Beta-Dagum and the Beta-Singh-Maddala distributions. More in detail, the new distributions are a generalization of a reparametrization of Beta-k and Beta-p distributions, respectively. For these distributions some particular interpretations in terms of maximum and minimum of sequences of random variables can be derived and the maximal and minimal domain of attraction can be obtained. Moreover, the method of maximum likelihood, the method of moments and the method of L-moments are examined to estimate the parameters. Finally, two different applications on real data regarding maxima and minima of river flows are reported, in order to show the potentiality of these two models in the extreme events analysis. 相似文献
18.
Six precipitation probability distributions (exponential, Gamma, Weibull, skewed normal, mixed exponential and hybrid exponential/Pareto distributions) are evaluated on their ability to reproduce the statistics of the original observed time series. Each probability distribution is also indirectly assessed by looking at its ability to reproduce key hydrological variables after being used as inputs to a lumped hydrological model. Data from 24 weather stations and two watersheds (Chute‐du‐Diable and Yamaska watersheds) in the province of Quebec (Canada) were used for this assessment. Various indices or statistics, such as the mean, variance, frequency distribution and extreme values are used to quantify the performance in simulating the precipitation and discharge. Performance in reproducing key statistics of the precipitation time series is well correlated to the number of parameters of the distribution function, and the three‐parameter precipitation models outperform the other models, with the mixed exponential distribution being the best at simulating daily precipitation. The advantage of using more complex precipitation distributions is not as clear‐cut when the simulated time series are used to drive a hydrological model. Although the advantage of using functions with more parameters is not nearly as obvious, the mixed exponential distribution appears nonetheless as the best candidate for hydrological modelling. The implications of choosing a distribution function with respect to hydrological modelling and climate change impact studies are also discussed. Copyright © 2012 John Wiley & Sons, Ltd. 相似文献
19.