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The probability plot correlation coefficient test for the normal, lognormal, and Gumbel distributional hypotheses,” (1986)

by R M Vogel
Venue:Water Resources Research,
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Estimation of baseflow recession constants

by Richard M. Vogel, Charles N. Kroll - Water Resources Management , 1996
"... Abstract. Hydrograph recession constants are required in rainfall-runoff models, base flow augmen-tation studies, geohydrologic investigations and in regional low-flow studies. The recession portion of a streamflow hydrograph is shown to be either an autoregressive process or an integrated moving av ..."
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Abstract. Hydrograph recession constants are required in rainfall-runoff models, base flow augmen-tation studies, geohydrologic investigations and in regional low-flow studies. The recession portion of a streamflow hydrograph is shown to be either an autoregressive process or an integrated moving average process, depending upon the structure of the assumed model errors. Six different estimators of the base flow recession constant are derived and tested using thousands of hydrograph recessions available at twenty-three sites in Massachusetts, U.S. When hydrograph recessions are treated as an autoregressive process, unconditional least squares or maximum likelihood estimators of the base-flow recession constant are shown to exhibit significant downward bias due to the short lengths of hydrograph recessions. The precision of estimates of hydrograph recession constants is shown to depend heavily upon assumptions regarding the structure of the model errors. In general, regression procedures for estimating hydrograph recession parameters are generally preferred to the time-series alternatives. An evaluation of the physical significance of estimates of the baseflow recession con-stant is provided by comparing regional regression models which relate low-flow statistics to three independent variables: drainage area, basin slope and the baseflow recession constant. As anticipated, approximately unbiased estimators of the baseflow recession constant provide significant information regarding the geohydrologic response of watersheds.
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...mally distributed. These four estimators assume that the model errors are additive in log space. The model residuals were tested for normality using the probability plot correlation coefficient test (=-=Vogel, 1986-=-) with a 5% significance level. Interestingly, the model residuals associated with the estimators Kbl and Kb3, based on (3) and (8), respectively, were not homoscedastic and were not normally distribu...

A stochastic index flow model of flow duration curves.Water Resources Research

by Attilio Castellarin, Richard M. Vogel, Armando Brath , 2004
"... [1] Annual flow duration curves (AFDCs) are used increasingly because unlike traditional period of record flow duration curves (FDCs), they provide confidence intervals for the median AFDC, they enable one to assign return periods to individual AFDCs, and they offer opportunities for developing a ge ..."
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[1] Annual flow duration curves (AFDCs) are used increasingly because unlike traditional period of record flow duration curves (FDCs), they provide confidence intervals for the median AFDC, they enable one to assign return periods to individual AFDCs, and they offer opportunities for developing a generalized stochastic model of daily streamflow. Previous stochastic models of FDCs and AFDCs were unable to reproduce the variance of AFDCs. We introduce an index flow approach to modeling the relationship between an FDC and AFDCs of daily streamflow series, which is able to reproduce the FDC, as well as the mean, median, and variance of the AFDCs without resorting to assumptions regarding the seasonal or persistence structure of daily streamflow series. Our approach offers additional opportunities for the regionalization of flow duration curves and for the generation of time series of daily streamflows at ungauged sites. Our approach is tested on three river basins in eastern central
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...en more efficient than the maximum likelihood when used with small to moderate length samples [Hosking et al., 1985; Hosking and Wallis, 1987]. A probability plot correlation coefficient (PPCC) test [=-=Vogel, 1986-=-] was used to test the goodness of fit at the 5% significance level. As Table 1 shows, the PPCC test statistic rLO is always higher than the 5% level test statistic for the logistic distribution, r5LO...

Generalized storage-reliability-yield relationships

by Richard M. Vogel, Jery R. Stedinger - J. Hydrol , 1987
"... ..."
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Flood flow frequency model selection in southwestern U.S.A

by M. Vogel, L Member, Wilbert Thomas, Thomas A. Mcmahon - Journal of Water Resources Planning and Management ASCE , 1993
"... ABSTRACT: Uniform flood frequency guidelines in the United States recommend the use of the log Pearson type 3 (LP3) distribution in flood frequency investiga-tions. Many investigators have suggested alternate models such as the generalized extreme value (GEV) distribution as an improvement over the ..."
Abstract - Cited by 4 (0 self) - Add to MetaCart
ABSTRACT: Uniform flood frequency guidelines in the United States recommend the use of the log Pearson type 3 (LP3) distribution in flood frequency investiga-tions. Many investigators have suggested alternate models such as the generalized extreme value (GEV) distribution as an improvement over the LP3 distribution. Using flood-flow data at 383 sites in the southwestern United States, we explore the suitability of various flood frequency models using L-moment diagrams. We also repeat the experiment performed in the original Water Resource Council report (Bulletin 17B, issued in 1982), which led to the LP3 mandate. All our evaluations consistently reveal that the LP3, GEV, and the two- and three-parameter lognormal models (LN2 and LN3) provide a good approximation to flood-flow data in this region. Other models such as the normal, Pearson, and Gumbel distributions are shown to perform poorly. Recent research indicates that regional index-flood pro-cedures should be more accurate and more robust than the type of at-site procedures evaluated here. Nevertheless, this study reveals that index-flood procedures need not be restricted to the GEV distribution because the LN2, LN3, and LP3 distri-butions appear to be suitable alternatives, at least in the southwestern United States.
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.... A third approach to evaluating the fit of alternative probability models to a regional data base is to employ probability plots and associated probability plot correlation coefficient (PPCC) tests (=-=Vogel 1986-=-; Vogel and Kro111989; Vogel and McMartin 1991; Chowdhury et al. 1991). Such tests are usefu., simple, and powerful for most two-parameter distributional alternatives, (VogeI1986; Vogel and KrollI989)...

BMP Modeling Concepts and Simulation

by Wayne C. Huber, Lamarr Cannon, Matt Stouder , 2004
"... managed the research described here. It has been subjected to the Agency’s peer and administrative review and has been approved for publication as an EPA document. Any opinions expressed in this report are those of the authors and do not, necessarily, reflect the official positions and policies of t ..."
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managed the research described here. It has been subjected to the Agency’s peer and administrative review and has been approved for publication as an EPA document. Any opinions expressed in this report are those of the authors and do not, necessarily, reflect the official positions and policies of the EPA. Any mention of products or trade names does not constitute recommendation for use by the EPA. ii Foreword The U.S. Environmental Protection Agency (EPA) is charged by Congress with protecting the Nation's land, air, and water resources. Under a mandate of national environmental laws, the Agency strives to formulate and implement actions leading to a compatible balance between human activities and the ability of natural systems to support and nurture life. To meet this mandate, EPA's research program is providing data and technical support for solving environmental problems today and building a science knowledge base necessary to manage our ecological resources wisely, understand how pollutants affect our health, and prevent or reduce environmental risks in the future. The National Risk Management Research Laboratory (NRMRL) is the Agency's center for investigation of technological and management approaches for preventing and reducing risks from pollution that threaten human health and the environment. The focus of the Laboratory's research program is on methods and their costeffectiveness
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...ariate, z) (Burton and Pitt 2001, Bedient and Huber 2002). Tests for normality itself include tests directly related to probability plots, such as the probability plot correlation coefficient (PPCC) (=-=Vogel 1986-=-) and the Shapiro-Wilk test (Helsel and Hirsch 1992). Tests not related to probability plots include the Kolomogorov-Smirnov test and the chi-square test (Benjamin and Cornell 1970, Helsel and Hirsch ...

Estimating the flood frequency distribution at seasonal

by Hydrology, E. Baratti, A. Montanari, A. Castellarin, J. L. Salinas, A. Viglione, A. Bezzi , 2012
"... www.hydrol-earth-syst-sci.net/16/4651/2012/ ..."
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www.hydrol-earth-syst-sci.net/16/4651/2012/
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...t al., 2012; Kochanek et al., 2012). 3.2 Estimation of seasonal and annual flood frequency distributions Table 1 reports the results of the Plotting Position Correlation Coefficient (PPCC) test (e.g. =-=Vogel, 1986-=-; Castellarin et al., 2004) that was carried out to test the suitability of the Gumbel distribution (also called EV1 distribution) to simulate the flood frequency behaviours in each season. For all se...

Application of Harmony Search to Design Storm Estimation from Probability Distribution Models

by Sukmin Yoon , Changsam Jeong , Taesam Lee
"... The precision of design storm estimation depends on the selection of an appropriate probability distribution model (PDM) and parameter estimation techniques. Generally, estimated parameters for PDMs are provided based on the method of moments, probability weighted moments, and maximum likelihood (M ..."
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The precision of design storm estimation depends on the selection of an appropriate probability distribution model (PDM) and parameter estimation techniques. Generally, estimated parameters for PDMs are provided based on the method of moments, probability weighted moments, and maximum likelihood (ML). The results using ML are more reliable than the other methods. However, the ML is more laborious than the other methods because an iterative numerical solution must be used. In the meantime, metaheuristic approaches have been developed to solve various engineering problems. A number of studies focus on using metaheuristic approaches for estimation of hydrometeorological variables. Applied metaheuristic approaches offer reliable solutions but use more computation time than derivative-based methods. Therefore, the purpose of the current study is to enhance parameter estimation of PDMs for design storms using a recently developed metaheuristic approach known as a harmony search (HS). The HS is compared to the genetic algorithm (GA) and ML via simulation and case study. The results of this study suggested that the performance of the GA and HS was similar and showed more accurate results than that of the ML. Furthermore, the HS required less computation time than the GA.
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...used to assess the adequacy of the proposed parameter estimation method: the correlation coefficient (CC), coefficient of efficiency (CE), and rootmean square error (RMSE) [27, 28].The mathematical forms of these criteria are as follows: CC = ∑ ...

unknown title

by Md. Abdul Karim, Jafflr Uddin Chowdhury , 1995
"... A comparison of four distributions used in ..."
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A comparison of four distributions used in
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...ing probability and i is the rank in ordered observations with / = 1 for the smallest observation in the sample. In this study, the Gringorten formula (a = 0.44) was used for the Gumbel distribution (=-=Vogel, 1986-=-); the Blom formula (a = 0.375) for the LN and LP3 distributions (Vogel & Kroll, 1989); and the Cunnane formula (Cunnane, 1978) (a = 0.4) for the GEV distribution (Chowdhury etal, 1991). The mean and ...

Nonparametric Kernel Estimation of Annual Maximum Stream Flow Quantiles

by Ani Shabri
"... ..."
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...relation coefficient will be near to one. If ¯x denotes the average value of the observations and ¯w denotes the average value of computed flood, then correlation coefficient sample can be defined as =-=[6]-=- ∑ (xT − ¯x)(ˆxT − ¯w) r = √∑ (xT − ¯x) 2 ∑ (ˆxT − ¯w) 2 (12) A comparison of the bandwidths for the Gaussian Kernel using OPT and CV for each stations is shown in Table 3. i=1 xT Table 3: Comparison ...

ACKNOWLEDGEMENTS

by Rajesh Sudarsan Computer Engineering
"... We sincerely thank our guide Mr.A.K.Bhattacharjee for his earnest help and for his patient attitude towards our queries. We also would like to thank him for his expedient advice towards our project that helped us a lot. We would also like to thank Mr. S.D.Dhodapkar, Head, Software Reliability Sectio ..."
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We sincerely thank our guide Mr.A.K.Bhattacharjee for his earnest help and for his patient attitude towards our queries. We also would like to thank him for his expedient advice towards our project that helped us a lot. We would also like to thank Mr. S.D.Dhodapkar, Head, Software Reliability Section, RCnD, BARC and Mr.R.K.Patil, Head, Reactor Control Division for their unfailing support, the initiative and the guidance given by them. We also express our sincere gratitude to Prof. O.R.Kale, Project Counselor, Dr.R.P.Kulkarni, Principal, RAIT for their enthusiastic support and guidance towards our project. 2 The task of designing large real-time reactive systems, which interact continuously with their environment and exhibit concurrency properties, is a challenging one. Statecharts is a visual formalism for specification and development of reactive systems and has been in wide use in the industry. These charts are intended to capture the
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...diagrams. These are described in Chapter 10. Hypothesis testing of goodness-of-fit is outside the scope here; readers are directed3 to basic statistical texts (Verzani, 2005, Section 9.3) and papers (=-=Vogel, 1986-=-). Sawitzki (2009, pp. 10–34) provides considerably relevant attention to “distribution diagnostics.” Finally, the R language has several built-in functions for goodness-of-fit testing, such as ks.tes...

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