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1.
The annual peak flow series of Polish rivers are mixtures of summer and winter flows. As Part II of a sequence of two papers, practical aspects of applicability of seasonal approach to flood frequency analysis (FFA) of Polish rivers are discussed. Taking A Two‐Component Extreme Value (TCEV1) model as an example it was shown in the first part that regardless of estimation method, the seasonal approach can give profit in terms of upper quantile estimation accuracy that rises with the return period of the quantile and is the greatest for no seasonal variation. In this part, an assessment of annual maxima (AM) versus seasonal maxima (SM) approach to FFA was carried out with respect to seasonal and annual peak flow series of 38 Polish gauging stations. First, the assumption of mutual independence of the seasonal maxima has been tested. The smoothness of SM and AM empirical probability distribution functions was analysed and compared. The TCEV1 model with seasonally estimated parameters was found to be not appropriate for most Polish data as it considerably underrates the skewness of AM distributions and upper quantile values as well. Consequently, the discrepancies between the SM and AM estimates of TCEV1 are observed. Taking SM and TCEV1 distribution, the dominating season in AM series was confronted with predominant season for extreme floods. The key argument for presumptive superiority of SM approach that SM samples are more statistically homogeneous than AM samples has not been confirmed by the data. An analysis of fitness to SM and AM of Polish datasets made for seven distributions pointed to Pearson (3) distribution as the best for AM and Summer Maxima, whereas it was impossible to select a single best model for winter samples. In the multi‐model approach to FFA, the tree functions, i.e., Pe(3), CD3 and LN3, should be involved for both SM and AM. As the case study, Warsaw gauge on the Vistula River was selected. While most of AM elements are here from winter season, the prevailing majority of extreme annual floods are the summer maxima. The upper quantile estimates got by means of classical annual and two‐season methods happen to be fairly close; what's more they are nearly equal to the quantiles calculated just for the season of dominating extreme floods. Copyright © 2011 John Wiley & Sons, Ltd.  相似文献   

2.
Quantile estimates of the annual maximum distribution can be obtained by fitting theoretical distributions to the maxima in separate seasons, e.g. to the monthly maxima. In this paper, asymptotic expressions for the bias and the variance of such estimates are derived for the case that the seasonal maxima follow a Gumbel distribution. Results from these expressions are presented for a situation with no seasonal variation and for maximum precipitation depths at Uccle/Ukkel (Belgium). It is shown that the bias is often negligible and that the variance reduction by using seasonal maxima instead of just the annual maxima strongly depends on the seasonal variation in the data. A comparison is made between the asymptotic standard error of quantile estimates from monthlymaxima with those from a partial duration series. Much attention is paid to the effect of model misspecification on the resulting quantile estimates of the annual maximum distribution. The use of seasonal maxima should be viewed with caution when the upper tail of this distribution is of interest.  相似文献   

3.
Ugo Moisello 《水文研究》2007,21(10):1265-1279
The use of partial probability weighted moments (PPWM) for estimating hydrological extremes is compared to that of probability weighted moments (PWM). Firstly, estimates from at‐site data are considered. Two Monte Carlo analyses, conducted using continuous and empirical parent distributions (of peak discharge and daily rainfall annual maxima) and applying four different distributions (Gumbel, Fréchet, GEV and generalized Pareto), show that the estimates obtained from PPWMs are better than those obtained from PWMs if the parent distribution is unknown, as happens in practice. Secondly, the use of partial L‐moments (obtained from PPWMs) as diagnostic tools is considered. The theoretical partial L‐diagrams are compared with the experimental data. Five different distributions (exponential, Pareto, Gumbel, GEV and generalized Pareto) and 297 samples of peak discharge annual maxima are considered. Finally, the use of PPWMs with regional data is investigated. Three different kinds of regional analyses are considered. The first kind is the regression of quantile estimates on basin area. The study is conducted applying the GEV distribution to peak discharge annual maxima. The regressions obtained with PPWMs are slightly better than those obtained with PWMs. The second kind of regional analysis is the parametric one, of which four different models are considered. The congruence between local and regional estimates is examined, using peak discharge annual maxima. The congruence degree is sometimes higher for PPWMs, sometimes for PWMs. The third kind of regional analysis uses the index flood method. The study, conducted applying the GEV distribution to synthetic data from a lognormal joint distribution, shows that better estimates are obtained sometimes from PPWMs, sometimes from PWMs. All the results seem to indicate that using PPWMs can constitute a valid tool, provided that the influence of ouliers, of course higher with censored samples, is kept under control. Copyright © 2007 John Wiley & Sons, Ltd.  相似文献   

4.
ABSTRACT

Flood quantile estimation based on partial duration series (peak over threshold, POT) represents a noteworthy alternative to the classical annual maximum approach since it enlarges the available information spectrum. Here the POT approach is discussed with reference to its benefits in increasing the robustness of flood quantile estimations. The classical POT approach is based on a Poisson distribution for the annual number of exceedences, although this can be questionable in some cases. Therefore, the Poisson distribution is compared with two other distributions (binomial and Gumbel-Schelling). The results show that only rarely is there a difference from the Poisson distribution. In the second part we investigate the robustness of flood quantiles derived from different approaches in the sense of their temporal stability against the occurrence of extreme events. Besides the classical approach using annual maxima series (AMS) with the generalized extreme value distribution and different parameter estimation methods, two different applications of POT are tested. Both are based on monthly maxima above a threshold, but one also uses trimmed L-moments (TL-moments). It is shown how quantile estimations based on this “robust” POT approach (rPOT) become more robust than AMS-based methods, even in the case of occasional extraordinary extreme events.
Editor M.C. Acreman Associate editor A. Viglione  相似文献   

5.
If the maximum annual peak flow series are a mixture of summer and winter flows, a seasonal approach to flood frequency analysis is necessary. While considering seasonal maxima as mutually independent events, the annual maxima distribution is defined as the product of seasonal distributions. However, if the independency assumption does not hold, a bivariate approach with dependent margins should be applied, i.e. the copula approach. The impact of dependency on design quantiles is investigated here in the context of the Fréchet-Hoeffding inequality defining copula bounds and the definition of dependency. The results of the two approaches are compared using six catchments in the San River basin, where in four cases the dependency of seasonal maxima has been identified as positive significant and no strong dominance of any one season is observed. The product model leads to higher estimates of design quantiles than do models where the dependency is taken into account and, therefore, is safe.
EDITOR R. Woods ASSOCIATE EDITOR A. Fiori  相似文献   

6.
Abstract

Seasonal design floods which consider information on seasonal variation are very important for reservoir operation and management. The seasonal design flood method currently used in China is based on seasonal maximum (SM) samples and assumes that the seasonal design frequency is equal to the annual design frequency. Since the return period associated with annual maximum floods is taken as the standard in China, the current seasonal design flood cannot satisfy flood prevention standards. A new seasonal design flood method, which considers dates of flood occurrence and magnitudes of the peaks (runoff), was proposed and established based on copula function. The mixed von Mises distribution was selected as marginal distribution of flood occurrence dates. The Pearson Type III and exponential distributions were selected as the marginal distribution of flood magnitude for annual maximum flood series and peak-over-threshold samples, respectively. The proposed method was applied at the Geheyan Reservoir, China, and then compared with the currently used seasonal design flood methods. The case study results show that the proposed method can satisfy the flood prevention standard, and provide more information about the flood occurrence probabilities in each sub-season. The results of economic analysis show that the proposed design flood method can enhance the floodwater utilization rate and give economic benefits without lowering the annual flood protection standard.

Citation Chen, L., Guo, S. L., Yan, B. W., Liu, P. & Fang, B. (2010) A new seasonal design flood method based on bivariate joint distribution of flood magnitude and date of occurrence. Hydrol. Sci. J. 55(8), 1264–1280.  相似文献   

7.
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   

8.
Multicomponent probability distributions such as the two‐component Gumbel distribution are sometimes applied to annual flood maxima when individual floods are seen as belonging to different classes, depending on physical processes or time of year. However, hydrological inconsistencies may arise if only nonclassified annual maxima are available to estimate the component distribution parameters. In particular, an unconstrained best fit to annual flood maxima may yield some component distributions with a high probability of simulating floods with negative discharge. In such situations, multicomponent distributions cannot be justified as an improved approximation to a local physical reality of mixed flood types, even though a good data fit is achieved. This effect usefully illustrates that a good match to data is no guarantee against degeneracy of hydrological models. Copyright © 2016 John Wiley & Sons, Ltd.  相似文献   

9.
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   

10.
Abstract

Flood frequency analysis can be made by using two types of flood peak series, i.e. the annual maximum (AM) and peaks-over-threshold (POT) series. This study presents a comparison of the results of both methods for data from the Litija 1 gauging station on the Sava River in Slovenia. Six commonly used distribution functions and three different parameter estimation techniques were considered in the AM analyses. The results showed a better performance for the method of L-moments (ML) when compared with the conventional moments and maximum likelihood estimation. The combination of the ML and the log-Pearson type 3 distribution gave the best results of all the considered AM cases. The POT method gave better results than the AM method. The binomial distribution did not offer any noticeable improvement over the Poisson distribution for modelling the annual number of exceedences above the threshold.
Editor D. Koutsoyiannis

Citation Bezak, N., Brilly, M., and ?raj, M., 2014. Comparison between the peaks-over-threshold method and the annual maximum method for flood frequency analysis. Hydrological Sciences Journal, 59 (5), 959–977.  相似文献   

11.
《水文科学杂志》2013,58(5):974-991
Abstract

The aim is to build a seasonal flood frequency analysis model and estimate seasonal design floods. The importance of seasonal flood frequency analysis and the advantages of considering seasonal design floods in the derivation of reservoir planning and operating rules are discussed, recognising that seasonal flood frequency models have been in use for over 30 years. A set of non-identical models with non-constant parameters is proposed and developed to describe flows that reflect seasonal flood variation. The peak-over-threshold (POT) sampling method was used, as it is considered to provide significantly more information on flood seasonality than annual maximum (AM) sampling and has better performance in flood seasonality estimation. The number of exceedences is assumed to follow the Poisson distribution (Po), while the peak exceedences are described by the exponential (Ex) and generalized Pareto (GP) distributions and a combination of both, resulting in three models, viz. Po-Ex, Po-GP and Po-Ex/GP. Their performances are analysed and compared. The Geheyan and the Baiyunshan reservoirs were chosen for the case study. The application and statistical experiment results show that each model has its merits and that the Po-Ex/GP model performs best. Use of the Po-Ex/GP model is recommended in seasonal flood frequency analysis for the purpose of deriving reservoir operation rules.  相似文献   

12.
Abstract

The impulse response of a linear convective-diffusion analogy (LD) model used for flow routing in open channels is proposed as a probability distribution for flood frequency analysis. The flood frequency model has two parameters, which are derived using the methods of moments and maximum likelihood. Also derived are errors in quantiles for these parameter estimation methods. The distribution shows that the two methods are equivalent in terms of producing mean values—the important property in case of unknown true distribution function. The flood frequency model is tested using annual peak discharges for the gauging sections of 39 Polish rivers where the average value of the ratio of the coefficient of skewness to the coefficient of variation equals about 2.52, a value closer to the ratio of the LD model than to the gamma or the lognormal model. The likelihood ratio indicates the preference of the LD over the lognormal for 27 out of 39 cases. It is found that the proposed flood frequency model represents flood frequency characteristics well (measured by the moment ratio) when the LD flood routing model is likely to be the best of all linear flow routing models.  相似文献   

13.
This study examines the 1914–2015 runoff trends and variability for 136 rivers draining British Columbia's Coast and Insular Mountains. Rivers are partitioned into eastward and westward flowing rivers based on flow direction from the Coast Mountains. Thus, eastward and westward runoff trends and influence of topography on runoff are explored. Our findings indicate that rivers flowing eastward to the Nechako and Chilcotin plateaus contribute the lowest annual runoff compared to westward rivers where runoff is high. Low interannual runoff variability is evident in westward rivers and their alpine watersheds, whereas eastward rivers exhibit high interannual runoff variability. On Vancouver Island, some of the rivers with the highest annual runoff exhibit high interannual variability. A significant (p < .05) negative correlation exists between mean annual runoff (Rm) and latitude, gauged area, mean elevation, and its corresponding coefficient of variation. However, a significant positive correlation was found between the glacierized area of mountainous regions and Rm. The mean coefficient of variation in annual runoff is significantly negatively correlated with latitude and glacierized area, but significantly positively correlated with longitude. Annual and seasonal runoff trend analyses of each river were performed for an early (1936–2015), a middle (1966–2015), and a late (1986–2015) period using the Mann–Kendall test. Trend analyses revealed a shift towards more positive detectable (signal‐to‐noise ratio > 1) trends in annual and seasonal runoff from the middle to the late period across the study domain. Most positive detectable seasonal runoff trends in the middle period occur in spring in glacierized westward rivers located >1,200 m, whereas in the late period, they all occur in fall and are regionally coherent around Vancouver Island and south coastal BC. Rivers draining eastward exhibit more positive trends over 1986–2015 compared to westward rivers. This study provides crucial information on the hydrology of mountain watersheds across British Columbia's coast in response to Pacific Decadal Oscillation phase changes, the elevational amplification of regional climate change, and their influences on precipitation and glacier retreat.  相似文献   

14.
ABSTRACT

The index flood method of the regional L-moments approach is adapted to annual maximum rainfall (AMR) series of successively increasing durations from 5 minutes to 24 hours. In Turkey, there are 14 such AMRs having standard durations of 5, 10, 15, 30, 60, 120, 180, 240, 300, 360, 480, 720, 1080 and 1440 min. The parameters of the probability distributions found suitable for these AMR series in a homogeneous region need to be adjusted so that their quantile functions will not cross each other over the entire range of probabilities. This adjustment is done so as to make (1) the derivative of the quantile function with respect to the Gumbel reduced variate of a longer-duration AMR be greater than or equal to that of the shorter-duration AMR, and (2) the quantile of a longer-duration AMR be greater than that of the shorter-duration AMR, both to be satisfied for any specific probability. Accordingly, the parameters of a probability distribution fitted to some AMR series must either increase or decrease or be constant with respect to increasing rainstorm duration; and the parameters of different distributions fitted to two sequential AMR series must be interrelated. The index flood method by the L-moments approach modified in such manner for successive-duration AMR series is applied to the Inland Anatolia region of Turkey using data recorded at 31 rain-gauging stations with recording lengths from 31 to 66 years.
EDITOR Z.W. Kundzewicz; ASSOCIATE EDITOR A. Viglione  相似文献   

15.
The paper deals with the probability estimates of temperature extremes (annual temperature maxima and heat waves) in the Czech Republic. Two statistical methods of probability estimations are compared; one based on the stochastic modelling of time series of the daily maximum temperature (TMAX) using the first-order autoregressive (AR(1)) model, the other consisting in fitting the extreme value distribution to the sample of annual temperature peaks.The AR(1) model is able to reproduce the main characteristics of heat waves, though the estimated probabilities should be treated as upper limits because of deficiencies in simulating the temperature variability inherent to the AR(1) model. Theoretical extreme value distributions do not yield good results when applied to maximum annual lengths of heat waves and periods of tropical days (TMAX 30°C), but it is the best method for estimating the probability and recurrence time of annual one-day temperature extremes. However, there are some difficulties in the application: the use of the two-parameter Gumbel distribution and the three-parameter generalized extreme value (GEV) distribution may lead to different results, particularly for long return periods. The resulting values also depend on the chosen procedure of parameter estimation. Based on our findings, the shape parameter testing for the GEV distribution and the L moments technique for parameter estimation may be recommended.The application of the appropriate statistical tools indicates that the heat wave and particularly the long period of consecutive tropical days in 1994 were probably a more rare event than the record-breaking temperatures in July 1983 exceeding 40°C. An improvement of the probability estimate of the 1994 heat wave may be expected from a more sophisticated model of the temperature series.  相似文献   

16.
Recently amended European (EU) water policies call for an adequate monitoring of the chemical status of sediments and suspended matter (SM) in rivers. In this study, we focus on long‐term time series of particle‐bound hexachlorobenzene (HCB) and selected polychlorinated biphenyls (PCB‐138 and PCB‐153) that were monitored biweekly to monthly at eight stations in the River Rhine catchment. Our aims are (1) to detect trends in the concentration series HCB, PCB‐138 and PCB‐153, (2) to estimate the uncertainty of loads caused by SM collection techniques and load calculation procedures and (3) to detect trends in the subsequently calculated annual load series. HCB concentration in the SM for the period 1995–2008 significantly (p < 0·01) decreased at six of the eight monitoring stations. Decreasing PCB‐138 and PCB‐153 concentrations are significant at six of the eight and seven of the eight monitoring stations, respectively. A two‐way analysis of variance (ANOVA) that tested the effect of two collection techniques and four load calculation procedures on annual loads indicates homogeneity of the methods at four of the five monitoring stations. At Weil, only the loads of HCB, PCB‐138 and PCB‐153 are significantly affected by the collection technique. The trend analysis of an extended series (1985–2007) of annual HCB loads at Koblenz showed a significant decrease from about 110 kg year?1 to about 15–23 kg year?1; however, in the shorter period (1995–2007) only at two of the eight monitoring stations decreasing trends of annual contaminant load could be detected. We conclude that any of the tested load calculation procedures can be applied, as loads do no differ systematically. Although a high uncertainty in load estimation exists (e.g. maximum percentage error of E = [18·1, 122·5]% for HCB), the monitoring programme at the Rhine is adequate for analysing the long‐term chemical status of SM. Copyright © 2011 John Wiley & Sons, Ltd.  相似文献   

17.
To set accurate critical values for the protection of lakes and coastal areas, it is crucial to know the seasonal variation of nutrient exports from rivers. This article presents an improved method for estimating export and in‐stream nutrient retention and its seasonal variation. For 13 lowland river catchments in Western Europe, inputs to surface water and exports were calculated on a monthly basis. The catchments varied in size (21 to 486 km2), while annual in‐stream retention ranged from 23 to 84% for N and 39 to 72% for P. A novel calculation method is presented that quantifies monthly exports from lowland rivers based on an annual load to the river system. Inputs in the calculation are annual emission to the surface waters, average monthly river discharge, average monthly water temperature and fraction of surface water area in the catchment. The method accounts for both seasonal variation of emission to the surface water and seasonal in‐stream retention. The agreement between calculated values and calibration data was high (N: r2 = 0·93; p < 0·001 and P: r2 = 0·81; p < 0·001). Validation of the model also showed good results with model efficiencies for the separate catchments ranging from 31 to 95% (average 76%). This indicates that exports of nitrogen and phosphorus on a monthly basis can be calculated with few input data for a range of West European lowland rivers. Further analysis showed that retention in summer is higher than that in winter, resulting in lower summer nutrient concentrations than that calculated with an average annual input. This implies that accurate evaluation of critical thresholds for eutrophication effects must account for seasonal variation in hydrology and nutrient loading. Our quantification method thus may improve the modelling of eutrophication effects in standing waters. Copyright © 2011 John Wiley & Sons, Ltd.  相似文献   

18.
Graphical application of the Type 1 (Gumbel) extreme value distribution is very simple since the distribution inverse gives a linear x-y plot. In contrast, the Type 2 and Type 3 extreme value distributions have nonlinear functions with respect to the same axes. A simple three-point graphical estimation procedure is described for these two distributions. This approach allows the nonlinear flood magnitude prediction functions to be located in any desirable position relative to the plotted annual maxima, subject to the constraint of having an extreme value form. The computation is very simple and requires only the location of a unique zero of a one-parameter function within a defined interval.  相似文献   

19.
As an alternative to the commonly used univariate flood frequency analysis, copula frequency analysis can be used. In this study, 58 flood events at the Litija gauging station on the Sava River in Slovenia were analysed, selected based on annual maximum discharge values. Corresponding hydrograph volumes and durations were considered. Different bivariate copulas from three families were applied and compared using different statistical, graphical and upper tail dependence tests. The parameters of the copulas were estimated using the method of moments with the inversion of Kendall's tau. The Gumbel–Hougaard copula was selected as the most appropriate for the pair of peak discharge and hydrograph volume (Q‐V). The same copula was also selected for the pair hydrograph volume and duration (V‐D), and the Student‐t copula was selected for the pair of peak discharge and hydrograph duration (Q‐D). The differences among most of the applied copulas were not significant. Different primary, secondary and conditional return periods were calculated and compared, and some relationships among them were obtained. Copyright © 2014 John Wiley & Sons, Ltd.  相似文献   

20.
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   

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