Flood Frequency Analysis

Khaled Hamed, A. Ramachandro. Rao

• Publisher: CRC Press
• Year: 2019
• Print ISBN: 9780849300837
• eBook ISBN: 9780429525308
• Topic: Computer Science
• Subtopic: Computer Engineering
• Index: Computer Science

After five decades, the field of Statistical Hydrology continues to evolve and remains a very active area of investigation. Researchers continue to examine various distributions, methods of estimation of parameters, and problems related to regionalization. However, much of this research appears in journals and reports and usually in a form not easily accessible to practitioners and students. Flood Frequency Analysis answers this need by presenting the most popular and promising distributions and estimation procedures in a unified format. It offers the details that provide the basis for the computations, and illustrates each procedure with real data.

CHAPTER 1

Introduction

1.1 Hydrologic Frequency Analysis

The primary objective of frequency analysis is to relate the magnitude of extreme events to their frequency of occurrence through the use of probability distributions (Chow et al., 1988). Data observed over an extended period of time in a river system are analyzed in frequency analysis. The data are assumed to be independent and identically distributed. The flood data are considered to be stochastic and may even be assumed to be space and time independent. Further, it is assumed that the floods have not been affected by natural or manmade changes in the hydrological regime in the system.

In practice, the true probability distribution of the data at a site or a region is unknown. The assumption that data in a given system arise from a single-parent distribution may be questionable when data from large watersheds are analyzed. In such cases, more than one type of rainfall or flow may contribute to extreme events in a region. How-ever, for the analysis to be of practical use, simpler distributions are often used to characterize the relation between flood magnitudes and their frequencies. The performance of distributions is evaluated by using different statistical tests. Quite often, many assumptions made in flood frequency analysis may be invalid. At any rate these assumptions have been questioned and discussed extensively (Klemes, 1987a; Klemes, 1987b; Yevjevich, 1968).

1.2 General Aspects and Approaches

There have been many discussions of general aspects of frequency analysis. There are also several summaries and discussions of flood frequency analysis: Chow (1964), Yevjevich (1972), Haan (1977), Kite (1977), Singh (1987), Potter (1987), Bobee and Ashkar (1991), McCuen (1993), and Stedinger et al. (1993). The literature in this field is vast and growing.

Todd (1957) discussed the basic principles of frequency analysis of stream flow data and outlined computational procedures. Construction of probability papers for the exponential, bounded exponential and log Pearson (3) distributions were discussed by Burkhardt and Prakash (1976). Linsley (1986) discussed the accuracy of flood estimates. The gap between research and practice in flood research and strategies to close them were discussed by Pilgrim (1986). One of Pilgrim’s conclusions was that inadequate attention was given by researchers to problems which are important to practitioners.

Flood frequencies have also been estimated by using observed or simulated rainfall data and valid watershed models. A technique of using rainfall data to obtain flood frequencies was tested as early as 1957. The TR-20 computer program was used by Danushkodi (1979) to simulate floods. Alexander (1963) discussed the method of storm transposition to estimate the frequency of rare floods. Fleming and Franz (1971) compared different methods of estimation of flood frequencies. They concluded that the Hydrocomp Simulation Program was most successful in reproducing flood frequency curves determined from historic streamflow records. The distribution of simulated floods matched that of observed floods.

Two derived distribution techniques to derive flood frequency distributions were investigated by Moughamian et al. (1987). Both of them were found to perform poorly and it was concluded that fundamental improvements were needed before the derived distribution approach could be used with confidence for flood frequency analysis.

Raines and Valdes (1993) evaluated two methods based on derived distributions. Neither of these methods gave consistently better results than those obtained by using the log Pearson (3) distribution. Bradley and Potter (1991) developed a new statistical procedure using approximate relationships between flood quantities which could be compared for different scenarios. Bradley and Potter (1992) presented a new approach for flood frequency analysis of flows simulated by using models. In this method, peak discharges are conditioned on runoff volumes. The effect of changes in temperature and precipitation on frequency of extreme runoff was studied by Krasouskaia (1993).

Earlier work in flood frequency analysis covered a wide range. For example, Snyder (1958) developed an approach based on the rational method, the time of concentration and unit hydrograph interpretation, to compute the flood discharge probability. Benson (1959) investigated the effect of channel slope on flood frequencies and found it to be second in importance to drainage area. Alexander et al. (1969) discussed the problem of estimating the relationship between the magnitude and frequency of rare floods. The use of moment ratio diagrams was also discussed by them. The random occurrence of rare floods and the use of Poisson distribution in flood frequency analysis was discussed by Kirby (1969). The relationship between flood data and watershed characteristics in small basins in Pennsylvania was discussed by White and Reich (1970). A method of incorporating past water levels at a site into probability analysis was developed by Gerard and Karpuk (1979). The importance of visual i...

Table of contents

• Cover
• Half Title
• Title Page
• Copyright Page
• Table of Contents
• List of Tables
• List of Figures
• Preface
• Acknowledgments
• 1 Introduction
• 2 Selection and Evaluation of Parent Distributions: Conventional Moments
• 3 Selection and Evaluation of Parent Distributions: Probability Weighted Moments and L-Moments
• 4 Parameter and Quantile Estimation
• 5 Normal and Related Distributions
• 6 The Gamma Family
• 7 Extreme Value Distributions
• 8 The Wakeby Distribution
• 9 The Logistic Distribution
• 10 Computer Program
• References
• Index