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1.
Random variable simulation has been applied to many applications in hydrological modelling, flood risk analysis, environmental impact assessment, etc. However, computer codes for simulation of distributions commonly used in hydrological frequency analysis are not available in most software libraries. This paper presents a frequency‐factor‐based method for random number generation of five distributions (normal, log–normal, extreme‐value type I, Pearson type III and log‐Pearson type III) commonly used in hydrological frequency analysis. The proposed method is shown to produce random numbers of desired distributions through three means of validation: (1) graphical comparison of cumulative distribution functions (CDFs) and empirical CDFs derived from generated data; (2) properties of estimated parameters; (3) type I error of goodness‐of‐fit test. An advantage of the method is that it does not require CDF inversion, and frequency factors of the five commonly used distributions involves only the standard normal deviate. Copyright © 2006 John Wiley & Sons, Ltd.  相似文献   

2.
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 η 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. Copyright © 2012 John Wiley & Sons, Ltd.  相似文献   

3.
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   

4.
The index flood procedure coupled with the L‐moments method is applied to the annual flood peaks data taken at all stream‐gauging stations in Turkey having at least 15‐year‐long records. First, screening of the data is done based on the discordancy measure (Di) in terms of the L‐moments. Homogeneity of the total geographical area of Turkey is tested using the L‐moments based heterogeneity measure, H, computed on 500 simulations generated using the four parameter Kappa distribution. The L‐moments analysis of the recorded annual flood peaks data at 543 gauged sites indicates that Turkey as a whole is hydrologically heterogeneous, and 45 of 543 gauged sites are discordant which are discarded from further analyses. The catchment areas of these 543 sites vary from 9·9 to 75121 km2 and their mean annual peak floods vary from 1·72 to 3739·5 m3 s?1. The probability distributions used in the analyses, whose parameters are computed by the L‐moments method are the general extreme values (GEV), generalized logistic (GLO), generalized normal (GNO), Pearson type III (PE3), generalized Pareto (GPA), and five‐parameter Wakeby (WAK). Based on the L‐moment ratio diagrams and the |Zdist|‐statistic criteria, the GEV distribution is identified as the robust distribution for the study area (498 gauged sites). Hence, for estimation of flood magnitudes of various return periods in Turkey, a regional flood frequency relationship is developed using the GEV distribution. Next, the quantiles computed at all of 543 gauged sites by the GEV and the Wakeby distributions are compared with the observed values of the same probability based on two criteria, mean absolute relative error and determination coefficient. Results of these comparisons indicate that both distributions of GEV and Wakeby, whose parameters are computed by the L‐moments method, are adequate in predicting quantile estimates. Copyright © 2011 John Wiley & Sons, Ltd.  相似文献   

5.
The impact of climate change on the behaviour of intensity–duration–frequency curves is critical to the estimation of design storms, and thus to the safe design of drainage infrastructure. The present study develops a regional time trend methodology that detects the impact of climate change on extreme precipitation from 1960 to 2010. The regional time trend linear regression method is fitted to different durations of annual maximum precipitation intensities derived from multiple sites in Ontario, Canada. The results show the relationship between climate change and increased extreme precipitation in this province. The regional trend analysis demonstrates, under nonstationary conditions arising from climate change, that the intensity of extreme precipitation increased decennially between 1.25% for the 30‐min storm and 1.82% for the 24‐h storm. A comparison of the results with a regional Mann–Kendall test validates the found regional time‐trend results. The results are employed to extrapolate the intensity–duration–frequency curves temporally and spatially for future decades across the province. The results of the regional time trend assessment help with the establishment of new safety margins for infrastructure design in Ontario. Copyright © 2016 John Wiley & Sons, Ltd.  相似文献   

6.
Truncated moment expressions (TMEs), defined as moment equations for truncated or incomplete distributions, are derived for several continuous univariate distributions commonly applied to hydrologic problems, including normal, lognormal, Pearson type III, log Pearson type III, and extreme value (Weibull and Gumbel) distributions. Solutions for gamma, tanks-in-series, and exponential distributions result as special cases. For most of the distributions considered here, closed form TMEs are presented for Nth order moments for the general case of double truncation (both upper and lower bounds). For the normal and Gumbel distributions, TMEs are presented only for moments of order N={0,1,2,3} and {0,1}, respectively. The derived TMEs are used to evaluate the effect of truncation on measured moments. The relative error between the first four truncated and complete moments is calculated as a function of both upper and lower truncation point.  相似文献   

7.
An approach for nonstationary low‐flow frequency analysis is developed and demonstrated on a dataset from the rivers on the Loess Plateau of China. Nonstationary low‐flow frequency analysis has drawn significant attention in recent years by establishing relationships between low‐flow series and explanatory variables series, but few studies have tested whether the time‐varying moments of low flow can be fully described by the time‐varying moments of the explanatory variables. In this research, the low‐flow distributions are analytically derived from the 2 basic explanatory variables—the recession duration and the recession coefficient—with the assumption that the recession duration and recession coefficient variables follow exponential and gamma distributions, respectively; the derived low‐flow distributions are applied to test whether the time‐varying moments of explanatory variables can explain the nonstationarities found in the low‐flow variable. The effects of ecosystem construction measures, that is, check dam, terrace, forest, and grassland, on the recession duration and recession coefficient are further discussed. Daily flow series from 11 hydrological stations from the Loess Plateau are used and processed with a moving average technique. Low‐flow data are extracted following the pit under threshold approach. Six of the 11 low‐flow series show significant nonstationarities at the 5% significance level, and the trend curves of the moments of low flow are in close agreement with the curves estimated from the derived distribution with time‐dependent moments of the recession duration and time‐constant moments of the recession coefficient. It is indicated that the nonstationarity in the low‐flow distribution results from the nonstationarity in the recession duration in all 6 cases, and the increase in the recession duration is resulted from large‐scale ecosystem constructions rather than climate change. The large‐scale ecosystem constructions are found to have more influence on the decrease in streamflow than on the increase in watershed storage, thus resulting in the reduction of low flow. A high return period for the initial fixed design value decreases dramatically with an increasing recession duration.  相似文献   

8.
Abstract

Regional frequency analysis of annual maximum flood data comprising 407 stations from 11 countries of southern Africa is presented. Forty-one homogeneous regions are identified. The L-moments of the observed data indicate that the possible underlying frequency distributions are Pearson type 3 (P3), lognormal 3-parameter (LN3), General Pareto (GPA) or General Extreme Value (GEV). Simulation experiments for the selection of the most suitable flood frequency procedure indicate that Pearson type 3/Probability Weighted Moments (P3/PWM) and log-Pearson type 3/Method of Moments (LP3/MOM) are suitable procedures for the region.  相似文献   

9.
A consistent approach to the frequency analysis of hydrologic data in arid and semiarid regions, i.e. the data series containing several zero values (e.g. monthly precipitation in dry seasons, annual peak flow discharges, etc.), requires using discontinuous probability distribution functions. Such an approach has received relatively limited attention. Along the lines of physically based models, the extensions of the Muskingum‐based models to three parameter forms are considered. Using 44 peak flow series from the USGS data bank, the fitting ability of four three‐parameter models was investigated: (1) the Dirac delta combined with Gamma distribution; (2) the Dirac delta combined with two‐parameter generalized Pareto distribution; (3) the Dirac delta combined with two‐parameter Weibull (DWe) distribution; (4) the kinematic diffusion with one additional parameter that controls the probability of the zero event (KD3). The goodness of fit of the models was assessed and compared both by evaluation of discrepancies between the results of both estimation methods (i.e. the method of moments (MOM) and the maximum likelihood method (MLM)) and using the log of likelihood function as a criterion. In most cases, the DWe distribution with MLM‐estimated parameters showed the best fit of all the three‐parameter models. Copyright © 2005 John Wiley & Sons, Ltd.  相似文献   

10.
This study presents copula‐based multivariate probabilistic approach to model severity–duration–frequency (S‐D‐F) relationship of drought events in western Rajasthan, India. Drought occurrences are analysed using standardized precipitation index computed on monthly mean areal precipitation, aggregated at a time scale of 6 months. After testing with a series of probability density functions, the drought variable severity is found to be better represented with log‐normal distribution, whereas duration is well fitted with exponential distribution. Four different classes of bivariate copulas – Archimedean, extreme value, Plackett, and elliptical families are evaluated for modelling joint distribution of drought characteristics. It is observed that the extreme value copula – Gumbel–Hougaard copula – performed better as compared with other classes of copulas, based on results of various statistical tests and upper tail dependence coefficient. The joint distribution obtained from best performing copula is then employed to determine conditional return period and to derive drought severity‐duration‐frequency (S‐D‐F) curves for the study region. The results of the study suggests that the copula method can be used effectively to derive the drought S‐D‐F curves, which can be helpful in planning and adopting suitable drought mitigation strategies in drought‐prone areas. Copyright © 2011 John Wiley & Sons, Ltd.  相似文献   

11.
《水文科学杂志》2013,58(5):863-877
Abstract

The method of L-moment ratio diagrams and the average weighted distance (AWD) are used to determine the probability distribution type of annual, seasonal and monthly precipitation in Japan. For annual precipitation, the log-Pearson type III (LP3) distribution provides the best fit to the observations with the generalized-extreme value (GEV), three-parameter lognormal (LN3) and Pearson type III (P3) distributions as potential alternatives. For seasonal precipitation, the P3 distribution shows the best fit to the observations of spring precipitation; the LP3 the best fit for summer and winter precipitation; and the LN3 the best fit for autumn precipitation with the LP3 as a potential alternative. For monthly precipitation, the P3 distribution fits the precipitation best for January, February, March, May, July, October and December; the LP3 for June; and the LN3 for April, August, September and November. The identified probability distribution types of annual, seasonal and monthly precipitation are basically consistent. Overall, the P3 and LP3 distributions are acceptable distribution types for representing statistics of precipitation in Japan with the LN3 distribution as a potential alternative.  相似文献   

12.
Two well-known methods for estimating statistical distributions in hydrology are the Method of Moments (MOMs) and the method of probability weighted moments (PWM). This paper is concerned with the case where a part of the sample is censored. One situation where this might occur is when systematic data (e.g. from gauges) are combined with historical data, since the latter are often only reported if they exceed a high threshold. For this problem, three previously derived estimators are the “B17B” estimator, which is a direct modification of MOM to allow for partial censoring; the “partial PWM estimator”, which similarly modifies PWM; and the “expected moments algorithm” estimator, which improves on B17B by replacing a sample adjustment of the censored-data moments with a population adjustment. The present paper proposes a similar modification to the PWM estimator, resulting in the “expected probability weighted moments (EPWM)” estimator. Simulation comparisons of these four estimators and also the maximum likelihood estimator show that the EPWM method is at least competitive with the other four and in many cases the best of the five estimators.  相似文献   

13.
A new method of parameter estimation in data scarce regions is valuable for bivariate hydrological extreme frequency analysis. This paper proposes a new method of parameter estimation (maximum entropy estimation, MEE) for both Gumbel and Gumbel–Hougaard copula in situations when insufficient data are available. MEE requires only the lower and upper bounds of two hydrological variables. To test our new method, two experiments to model the joint distribution of the maximum daily precipitation at two pairs of stations on the tributaries of Heihe and Jinghe River, respectively, were performed and compared with the method of moments, correlation index estimation, and maximum likelihood estimation, which require a large amount of data. Both experiments show that for the Ye Niugou and Qilian stations, the performance of MEE is nearly identical to those of the conventional methods. For the Xifeng and Huanxian stations, MEE can capture information indicating that the maximum daily precipitation at the Xifeng and Huanxian stations has an upper tail dependence, whereas the results generated by correlation index estimation and maximum likelihood estimation are unreasonable. Moreover, MEE is proved to be generally reliable and robust by many simulations under three different situations. The Gumbel–Hougaard copula with MEE can also be applied to the bivariate frequency analysis of other extreme events in data‐scarce regions.  相似文献   

14.
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   

15.
Stationarity is often assumed for frequency analysis of low flows in water resources management and planning. However, many studies have shown that flow characteristics, particularly the frequency spectrum of extreme hydrologic events, were modified by climate change and human activities. Thus, the conventional frequency analysis that fails to consider the nonstationary characteristics may lead to costly design. The analysis presented in this paper was based on the more than 100 years of daily flow data from the Yichang gauging station 44 km downstream of the Three Gorges Dam. The Mann–Kendall trend test under the scaling hypothesis showed that the annual low flows had a significant monotonic trend, whereas an abrupt change point was identified in 1936 by the Pettitt test. The climate‐informed low‐flow frequency analysis and the divided and combined method were employed to account for the impacts from related climate variables and nonstationarities in annual low flows. Without prior knowledge of the probability density function for the gauging station, six distribution functions including the generalized extreme values (GEV), Pearson Type III, Gumbel, Gamma, Lognormal and Weibull distributions have been tested to find the best fit, in which the local likelihood method is used to estimate the parameters. Analyses show that GEV had the best fit for the observed low flows. This study has also shown that the climate‐informed low‐flow frequency analysis is able to exploit the link between climate indices and low flows, which would account for the dynamic feature for reservoir management and provide more accurate and reliable designs for infrastructure and water supply. Copyright © 2014 John Wiley & Sons, Ltd.  相似文献   

16.
Hydrological drought analysis is very important in the design of hydrotechnical projects and water resources management and planning. In this study, a methodology is proposed for the analysis of streamflow droughts using the threshold level approach. The method has been applied to Yermasoyia semiarid basin in Cyprus based on 30‐year daily discharge data. Severity was defined as the accumulated water deficit volume occurring during a drought event, in respect with a target threshold. Fixed and variable thresholds (seasonal, monthly, and daily) were employed to derive the drought characteristics. The threshold levels were determined based on the Q50 percentiles of flow extracted from the corresponding flow duration curves for each threshold. The aim is to investigate the sensitivity of these thresholds in the estimation of maximum drought severities for various return periods and the derivation of severity–duration–frequency curves. The block maxima and the peaks over threshold approaches were used to perform the extreme value analysis. Three pooling procedures (moving average, interevent time criterion, and interevent time and volume criterion) were employed to remove the dependent and minor droughts. The application showed that the interevent time and volume criterion is the most unbiased pooling method. Therefore, it was selected to estimate the drought characteristics. The results of this study indicate that monthly and daily variable thresholds are able to capture abnormal drought events that occur during the whole hydrological year whereas the other two, only the severe ones. They are also more sensitive in the estimation of maximum drought severities and the derivation of the curves because they incorporate better the effect of drought durations.  相似文献   

17.
In this study, the parameter estimations for the 3-parameter generalized logistic (GL) distribution are presented based on the methods of moments (MOM), maximum likelihood (ML), and probability weighted moments (PWM). The asymptotic variances of the MOM, ML, and PWM quantile estimators for the GL distribution are expressed as functions of the sample size, return period, and parameters. A Monte Carlo simulation was performed to verify the derived expressions for variances and covariances between parameters and to evaluate the applicability of the derived asymptotic variances of quantiles for the MOM, ML and PWM methods. The simulation results generally show good agreement with the analytical results estimated from the asymptotic variances of parameters and quantiles when the shape parameter (β) of the GL distribution is between −0.10 and 0.10 for the MOM method and between −0.25 and 0.45 for the ML and PWM methods, respectively. In addition, the actual sample variances and the root mean square error (RMSE) of asymptotic variances of quantiles for various sample sizes, return periods, and shape parameters were presented. In order to evaluate the applicability of the estimation methods to real data and to compare the values of estimated parameter, quantiles, and confidence intervals based on each parameter estimation method, the GL distribution was fitted to the 24-h annual maximum rainfall data at Pohang, Korea.  相似文献   

18.
Q.J. Wang 《Journal of Hydrology》1990,120(1-4):115-124
Unbiased estimators of probability weighted moments (PWM) and partial probability weighted moments (PPWM) from systematic and historical flood information are derived. Applications are made to estimating parameters and quantiles of the generalized extreme value (GEV) distribution. The effect of lower bound censoring, which might be deliberately introduced in practice, is also considered.  相似文献   

19.
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. Copyright © 2014 John Wiley & Sons, Ltd.  相似文献   

20.
The probability weighted moment (PWM) method can generally be used in estimating parameters of a distribution whose inverse form cannot be expressed explicitly. For several distributions, such as normal, log-normal and Pearson Type Three distributions, the expressions relating PWM to parameters have the same forms. Such expressions may be readily employed in practice for estimating the parameters.  相似文献   

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