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FLODRO 4.0: SPREADSHEETS BASED FLOOD FREQUENCY ANALYSIS COMPUTER PACKAGE
JOSE A. RAYNAL-VILLASENOR
Department of Civil and Environmental Engineering Universidad de las Americas, Puebla 72820 Cholula, Puebla, Mexico Tel.: (52-222) 229-2647 FAX: (52-222) 229-2031 E-mail: josea.raynal@udlap.mx
ABSTRACT
A computer package for flood frequency analysis, based on the application of common use spreadsheets framework provided by Excel
(Excel is a registered trademark of Microsoft Corporation, Inc.), is presented using several probability distribution functions. The computer package addresses the issues of model parameter estimation by the methods of moments (MOM), maximum likelihood (ML) and, for those with invertible probability distribution functions, the probability weighted moments (PWM), too. The computer model uses two measures of goodness of fit tests. When the ML method is applied, the value of a third is provided. The computer package also computes design events for several return periods and confidence limits for two of the three estimation methods for all the distributions considered in the package, and when possible, by the PWM method, too. The computer model is able to produce several graphic displays which aid visual comparison. A full example of application, using a particular probability distribution function with a particular estimation method, is presented in the paper to show the easy way to use this computer package.
Key words:
Flood frequency analysis, spreadsheets, probability distribution functions, estimation of parameters, confidence limits
INTRODUCTION
A subject of paramount interest in planning and design of water works is that related with flood frequency analysis. Due to the characteristic that design values have, given that they are linked to a return period or to a non-exceedance probability, the use of mathematical models known as probability distribution functions is a must. Among the most widely used probability distribution functions for hydrological analysis, related with flood frequency analysis, are (Kite, 1988, Salas and Smith, 1980, Rao and Hamed, 2000 and Raynal-Villasenor, 2009): a)
Normal (NOR) b)
Two parameters Log-Normal (LN2) c)
Three parameters Log-Normal (LN3) d)
Gamma (GAM) e)
Pearson type III (PIII) f)
Log-Pearson Type III (LPIII) g)
Extreme Value Type I (EVI) h)
General Extreme Value (GEV) In the light of the personal computer applications in education and training in all the fields of science, a personal computer program was developed to take care of the processes of flood frequency analyses, in particular in engineering hydrology but easily extended to other fields related with frequency analyses dealing with the maxima. The computer code provides a wide number of options in the models to be used as in the analyses that can be done with such a tool as well. The resulting code has been named FLODRO 4.0, as it will be referred herein and it is the latest version of the FLODRO family of computer codes, Raynal-Villasenor (1992, 1998 and 2002). The paper contains the key features of FLODRO 4.0 and one example of application for flood frequency analysis is included to show the main results that FLODRO 4.0 can supply to the user.
FRAMEWORK OF FLODRO 4.0
FLODRO 4.0 has been developed under the computer framework provided by Excel
(Excel is a registered trademark of Microsoft Corporation, Inc.). The interactive mode in which FLODRO 4.0 is used makes it to have a high user-friendly component typical of the Windows
(Windows is a registered trademark of Microsoft Corporation, Inc.) environment. In any step, the user has the control on the processes that he/she is performing, from data input to printing of results of the analysis. The personal computer package FLODRO 4.0 has the structure shown in figure 1. All the probability distribution functions mentioned in the previous section are contained in FLODRO 4.0. FLODRO 4.0 can perform the following computations, as shown in figure 2: a)
Estimation of parameters, by the methods of moments and maximum likelihood for all the distributions, and probability weighted moments where this method is applicable, e.g. EVI and GEV distributions b)
Computation of design events, for several return periods, by the methods of moments and maximum likelihood for all the distributions, and probability weighted moments where this method is applicable, e.g. EVI and GEV distributions c)
Estimation of confidence limits for design events, by the methods of moments and maximum likelihood for all the distributions, and probability weighted moments where this method is applicable, e.g. EVI and GEV distributions d)
Goodness of fit tests based in the standard error of fit (SEF), Kite (1988), the mean absolute relative error (MARD), Sing and (1987), and the Akaike Information Criterion (AIC) in the case of the method of maximum likelihood, Akaike (1974) e)
A graphical comparison between the empirical and theoretical probability density functions Personal computer program FLODRO 4.0 has been designed to use a minimum of memory and computer peripherals. The graphs provided by FLODRO 4.0 are printed in a common printer there is no need to use costly plotters to get a hard copy of these graphs. In the case of the graphs plotted in a electronic version of the Gumbel’s probability paper, the limitations of Excel
with regard to be unable to use a probability or a return period axis, has been overcome by the use of the Gumbel’s reduced value as the abscissa axis, as can be seen in figures 8 and 9. These features make FLODRO 4.0 very suitable in programs of hydrological education, training and in continuing education as well, particularly in developing countries.
NUMERICAL EXAMPLE
Gauging station Huites is located in the El Fuerte River in Northwestern Mexico and has been selected to analyze its sample of annual floods, using the GEV probability distribution function and the ML method of estimation of its parameters, design values and confidence limits. The geographical location of gauging station Huites, Mexico is shown in figure 3. The first step in the computations is to obtain basic statistics of the flood sample and such statistics are shown in figure 4. The parameters and the goodness of fit measures obtained through the use of FLODRO 4.0 are shown in figure 5. The design values and its confidence limits are displayed in figure 6. The comparison between the histogram of flood data and the theoretical probability density function is shown in figure 7. The figure 8 shows the different results obtained by the application of the methods of MOM, ML and PWM for the estimation of parameters with application of the GEV probability distribution function to the flood sample. In figure 9 is shown a graphical representation of the best method of estimation for the design values and their confidence limits.
CONCLUSIONS
A personal computer program has been presented for flood frequency analyses in education and training. Due to the minimum requirements of central memory and computer peripherals that the personal computer program has, as it has been shown in the paper, makes it a versatile tool to train students or technical personnel in the field with a personal
computer and a printer. The use of Excel
, a standard computational tool, as the main computational environment of the computer code, makes it available to anybody with access to a personal computer.
ACKNOWLEDGMENTS
The author wishes to express his deepest gratitude to the Universidad de las Americas, Puebla for the support given to produce this paper.
REFERENCES
Akaike, H., 1974, A New Look at the Statistical Model Identification, IEEE Trans. Autom. Control, AC-19 (6) 716-723. Jain, D. y Singh, V.P., 1987, Estimating Parameters of EV1 Distribution for Flood Frequency Analysis”, Water Resources Bulletin, Vol. 23, No. 1, 59-71 Kite, G.W., 1988, Flood and Risk Analyses in Hydrology, Water Resources Publications, Littleton, Colorado, USA, 187 Rao, A. R. and Hamed, K. H., 2000, Flood Frequency Analysis, CRC Press, Boca Raton, Florida, USA Raynal-Villasenor, J. A. and Escalante Sandoval, C. A., 1992, FLODRO: A Personal Computer Package for Flood and Drought Frequency Analyses Education and Training, Hydrology and Water Resources Education, Training and Management, Jose A. Raynal, ed., Water Resources Publications, 87-94 Raynal-Villasenor, J.A., 1998, FLODRO 2.0: A User-Friendly Personal Computer Package for Flood and Drought Frequency Analyses, Computer Techniques to Environmental Studies, WIT Press, Southampton, UK, 181-187, 1998 Raynal-Villasenor, J.A., 2002, FLODRO 3.0: A User-friendly Personal Computer Package for Flood and Drought Frequency Analyses, in Surface Water Hydrology, V.P. Singh et al, eds., A. A. Balkema Pub.Lisse, Holanda, 599-608. 2002 Raynal-Villasenor, J. A., 2009, Frequency Analysis of Hydrologic Extremes, Aqua-Terra Consultores, Chihuahua, Mexico Salas, J. D. and Smith, R., 1980, Computer Programs of Distribution Functions in Hydrology, Colorado State University, Fort Collins, Colorado, USA
FIGURE 1. Framework of computer package FLODRO 4.0 FIGURE 2. Options of analysis in computer package FLODRO 4.0
FLODRO 4.0 DATA
PROBABILITY DISTRIBUTION FUNCTION RESULTS PROBABILITY DISTRIBUTION FUNCTION ESTIMATION OF PARAMETERS ESTIMATION OF CONFIDENCE LIMITS
GOODNESS OF FIT TESTS
ESTIMATION OF DESIGN COMPARISON BETWEEN HISTOGRAM AND PDF

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