scholarly journals Introducing empirical and probabilistic regional envelope curves into a mixed bounded distribution function

2010 ◽  
Vol 14 (12) ◽  
pp. 2465-2478 ◽  
Author(s):  
B. Guse ◽  
Th. Hofherr ◽  
B. Merz
Keyword(s):  
Distribution Function ◽  
Upper Bound ◽  
Inflection Point ◽  
Flood Frequency ◽  
Quantile Estimation ◽  
Flood Frequency Analysis ◽  
Envelope Curve ◽  
Recurrence Intervals ◽  
Flood Quantiles ◽  
Selection Of

Abstract. A novel approach to consider additional spatial information in flood frequency analyses, especially for the estimation of discharges with recurrence intervals larger than 100 years, is presented. For this purpose, large flood quantiles, i.e. pairs of a discharge and its corresponding recurrence interval, as well as an upper bound discharge, are combined within a mixed bounded distribution function. The large flood quantiles are derived using probabilistic regional envelope curves (PRECs) for all sites of a pooling group. These PREC flood quantiles are introduced into an at-site flood frequency analysis by assuming that they are representative for the range of recurrence intervals which is covered by PREC flood quantiles. For recurrence intervals above a certain inflection point, a Generalised Extreme Value (GEV) distribution function with a positive shape parameter is used. This GEV asymptotically approaches an upper bound derived from an empirical envelope curve. The resulting mixed distribution function is composed of two distribution functions which are connected at the inflection point. This method is applied to 83 streamflow gauges in Saxony/Germany. Our analysis illustrates that the presented mixed bounded distribution function adequately considers PREC flood quantiles as well as an upper bound discharge. The introduction of both into an at-site flood frequency analysis improves the quantile estimation. A sensitivity analysis reveals that, for the target recurrence interval of 1000 years, the flood quantile estimation is less sensitive to the selection of an empirical envelope curve than to the selection of PREC discharges and of the inflection point between the mixed bounded distribution function.

scholarly journals Introducing empirical and probabilistic regional envelope curves into a mixed bounded distribution function

2010 ◽  
Vol 7 (4) ◽  
pp. 4253-4290
Author(s):  
B. Guse ◽  
T. Hofherr ◽  
B. Merz
Keyword(s):  
Distribution Function ◽  
Upper Bound ◽  
Inflection Point ◽  
Flood Frequency ◽  
Quantile Estimation ◽  
Flood Frequency Analysis ◽  
Envelope Curve ◽  
Recurrence Intervals ◽  
Flood Quantiles ◽  
Selection Of

Abstract. A novel approach to consider additional spatial information in flood frequency analyses, especially for the estimation of discharges with recurrence intervals larger than 100 years, is presented. For this purpose, large flood quantiles, i.e. pairs of a discharge and its corresponding recurrence interval, as well as an upper bound discharge, are combined within a mixed bounded distribution function. Large flood quantiles are derived using probabilistic regional envelope curves (PRECs) for all sites of a pooling group. These PREC flood quantiles are introduced into an at-site flood frequency analysis by assuming that they are representative for the range of recurrence intervals which is covered by PREC flood quantiles. For recurrence intervals above a certain inflection point, a Generalised Extreme Value (GEV) distribution function with a positive shape parameter is used. This GEV asymptotically approaches an upper bound derived from an empirical envelope curve. The resulting mixed distribution function is composed of two distribution functions, which are connected at the inflection point. This method is applied to 83 streamflow gauges in Saxony/Germany. Our analysis illustrates that the presented mixed bounded distribution function adequately considers PREC flood quantiles as well as an upper bound discharge. The introduction of both into an at-site flood frequency analysis improves the quantile estimation. A sensitivity analysis reveals that, for the target recurrence interval of 1000 years, the flood quantile estimation is less sensitive to the selection of an empirical envelope curve than to the selection of PREC discharges and of the inflection point between the mixed bounded distribution function.

scholarly journals On accuracy of upper quantiles estimation

2010 ◽  
Vol 7 (4) ◽  
pp. 4761-4784
Author(s):  
I. Markiewicz ◽  
W. G. Strupczewski ◽  
K. Kochanek
Keyword(s):  
Distribution Function ◽  
Population Distribution ◽  
Model Misspecification ◽  
Estimation Method ◽  
Flood Frequency ◽  
Likelihood Method ◽  
Flood Frequency Analysis ◽  
Estimation Methods ◽  
Hypothetical Model ◽  
Log Normal

Abstract. Flood frequency analysis (FFA) entails estimation of the upper tail of a probability density function (PDF) of annual peak flows obtained from either the annual maximum series or partial duration series. In hydrological practice the properties of various estimation methods of upper quantiles are identified with the case of known population distribution function. In reality the assumed hypothetical model differs from the true one and one can not assess the magnitude of error caused by model misspecification in respect to any estimated statistics. The opinion about the accuracy of the methods of upper quantiles estimation formed from the case of known population distribution function is upheld. The above-mentioned issue is the subject of the paper. The accuracy of large quantile assessments obtained from the four estimation methods are compared for two-parameter log-normal and log-Gumbel distributions and their three-parameter counterparts, i.e., three-parameter log-normal and GEV distributions. The cases of true and false hypothetical model are considered. The accuracy of flood quantile estimates depend on the sample size, on the distribution type, both true and hypothetical, and strongly depend on the estimation method. In particular, the maximum likelihood method looses its advantageous properties in case of model misspecification.

Handling non-stationary flood frequency analysis using TL-moments approach for estimation parameter

2019 ◽  
Vol 11 (4) ◽  
pp. 966-979
Author(s):  
Nur Amalina Mat Jan ◽  
Ani Shabri ◽  
Ruhaidah Samsudin
Keyword(s):  
Frequency Analysis ◽  
Moment Method ◽  
Estimation Method ◽  
Flood Frequency ◽  
Flood Frequency Analysis ◽  
Moments Method ◽  
Flood Estimation ◽  
L Moments ◽  
Flood Quantiles ◽  
Quantile Estimates

Abstract Non-stationary flood frequency analysis (NFFA) plays an important role in addressing the issue of the stationary assumption (independent and identically distributed flood series) that is no longer valid in infrastructure-designed methods. This confirms the necessity of developing new statistical models in order to identify the change of probability functions over time and obtain a consistent flood estimation method in NFFA. The method of Trimmed L-moments (TL-moments) with time covariate is confronted with the L-moment method for the stationary and non-stationary generalized extreme value (GEV) models. The aims of the study are to investigate the behavior of the proposed TL-moments method in the presence of NFFA and applying the method along with GEV distribution. Comparisons of the methods are made by Monte Carlo simulations and bootstrap-based method. The simulation study showed the better performance of most levels of TL-moments method, which is TL(η,0), (η = 2, 3, 4) than the L-moment method for all models (GEV1, GEV2, and GEV3). The TL-moment method provides more efficient quantile estimates than other methods in flood quantiles estimated at higher return periods. Thus, the TL-moments method can produce better estimation results since the L-moment eliminates lowest value and gives more weight to the largest value which provides important information.

scholarly journals A study on selection of probability distributions for at-site flood frequency analysis in Australia

2013 ◽  
Vol 69 (3) ◽  
pp. 1803-1813 ◽  
Author(s):  
Ayesha S. Rahman ◽  
Ataur Rahman ◽  
Mohammad A. Zaman ◽  
Khaled Haddad ◽  
Amimul Ahsan ◽  
...  
Keyword(s):  
Frequency Analysis ◽  
Probability Distributions ◽  
Flood Frequency ◽  
Flood Frequency Analysis ◽  
Selection Of

Flood frequency analysis for the Red River at Winnipeg

2001 ◽  
Vol 28 (3) ◽  
pp. 355-362 ◽  
Author(s):  
Donald H Burn ◽  
N K Goel
Keyword(s):  
Flood Frequency ◽  
Red River ◽  
Noise Model ◽  
Flood Frequency Analysis ◽  
Data Series ◽  
Correlation Structures ◽  
Flood Magnitude ◽  
Mixed Noise ◽  
Flood Quantiles

This paper reviews the flood frequency characteristics of the Red River at Winnipeg. The impacts of persistence in the flood series on estimates of flood quantiles and their associated confidence intervals are examined. This is done by generating a large number of data sequences using a mixed noise model that preserves the short-term and long-term correlation structures of the observed flood series. The results reveal that persistence in the data series can lead to a slight increase in the expected flood magnitude for a given return period. More importantly, persistence is shown to dramatically increase the uncertainty associated with estimated flood quantiles. The 117-year flood series for the Red River at Winnipeg is demonstrated to be equivalent to roughly 45 years of independent data.Key words: flood frequency, extreme events, simulation, historical data.

scholarly journals Local and regional flood frequency analysis based on hierarchical Bayesian model: application to annual maximum streamflow for the Huaihe River basin

2018 ◽  
Author(s):  
Yenan Wu ◽  
Upmanu Lall ◽  
Carlos H.R. Lima ◽  
Ping-an Zhong
Keyword(s):  
Bayesian Model ◽  
Flood Frequency ◽  
Flood Frequency Analysis ◽  
Hierarchical Bayesian Model ◽  
Annual Maximum ◽  
Huaihe River Basin ◽  
Huaihe River ◽  
Index Flood ◽  
Flood Quantiles ◽  
The Huaihe River

Abstract. We develop a hierarchical, multilevel Bayesian model for reducing uncertainties in local (at-site) and regional (ungauged or short data sites) flood frequency analysis. This model is applied to the annual maximum streamflow of 17 gauged sites in the Huaihe River basin, China. A Generalized Extreme Value (GEV) distribution is considered for each site, and its location and scale parameters depend on the site’s drainage area. We assume the hyper-parameters come from Non-informative (independent, uniform) prior distribution and sample values from posterior distribution by the MCMC method using Gibbs sampling. For comparison, the ordinary GEV fitting by Maximum Likelihood Estimate (MLE) and index flood method fitted by L-moments are also applied. The local simulation results show that for most sites the 95 % credible interval simulated by the Hierarchical Bayesian model are narrower than the at site GEV outputs thus reducing uncertainty. By comparison, the homogeneity assumption of the index flood method often leads to large deviations from the empirical flood frequency curve. Cross validated flood quantiles and associated uncertainty intervals are also derived. These results show that the proposed model can better estimate the flood quantiles and their uncertainty than the index flood method.

scholarly journals On accuracy of upper quantiles estimation

2010 ◽  
Vol 14 (11) ◽  
pp. 2167-2175 ◽  
Author(s):  
I. Markiewicz ◽  
W. G. Strupczewski ◽  
K. Kochanek
Keyword(s):  
Distribution Function ◽  
Population Distribution ◽  
Model Misspecification ◽  
Estimation Method ◽  
Flood Frequency ◽  
Likelihood Method ◽  
Flood Frequency Analysis ◽  
Estimation Methods ◽  
Annual Peak ◽  
Log Normal

Abstract. Flood frequency analysis (FFA) entails the estimation of the upper tail of a probability density function (PDF) of annual peak flows obtained from either the annual maximum series or partial duration series. In hydrological practice, the properties of various methods of upper quantiles estimation are identified with the case of known population distribution function. In reality, the assumed hypothetical model differs from the true one and one cannot assess the magnitude of error caused by model misspecification in respect to any estimated statistics. The opinion about the accuracy of the methods of upper quantiles estimation formed from the case of known population distribution function is upheld. The above-mentioned issue is the subject of the paper. The accuracy of large quantile assessments obtained from the four estimation methods is compared to two-parameter log-normal and log-Gumbel distributions and their three-parameter counterparts, i.e., three-parameter log-normal and GEV distributions. The cases of true and false hypothetical models are considered. The accuracy of flood quantile estimates depends on the sample size, the distribution type (both true and hypothetical), and strongly depends on the estimation method. In particular, the maximum likelihood method loses its advantageous properties in case of model misspecification.

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