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:
[email protected] 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) b) c) d) e) f) g) h) Normal (NOR) Two parameters Log-Normal (LN2) Three parameters Log-Normal (LN3) Gamma (GAM) Pearson type III (PIII) Log-Pearson Type III (LPIII) Extreme Value Type I (EVI) 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. 0. has been overcome by the use of the Gumbel’s reduced value as the abscissa axis.g. as it has been shown in the paper. EVI and GEV distributions d) Goodness of fit tests based in the standard error of fit (SEF). e. In any step. design values and confidence limits. Sing and (1987).0 has the structure shown in figure 1. as shown in figure 2: a) Estimation of parameters. These features make FLODRO 4. The design values and its confidence limits are displayed in figure 6. The figure 8 shows the different results obtained by the application of the methods of MOM. The interactive mode in which FLODRO 4. from data input to printing of results of the analysis. FLODRO 4. In figure 9 is shown a graphical representation of the best method of estimation for the design values and their confidence limits.0 has been designed to use a minimum of memory and computer peripherals.0 are shown in figure 5.0 very suitable in programs of hydrological education. CONCLUSIONS A personal computer program has been presented for flood frequency analyses in education and training. The parameters and the goodness of fit measures obtained through the use of FLODRO 4. The geographical location of gauging station Huites. the limitations of Excel with regard to be unable to use a probability or a return period axis. makes it a versatile tool to train students or technical personnel in the field with a personal .0 has been developed under the computer framework provided by Excel (Excel is a registered trademark of Microsoft Corporation. e. In the case of the graphs plotted in a electronic version of the Gumbel’s probability paper. by the methods of moments and maximum likelihood for all the distributions. the user has the control on the processes that he/she is performing. The first step in the computations is to obtain basic statistics of the flood sample and such statistics are shown in figure 4.FRAMEWORK OF FLODRO 4. particularly in developing countries.0 is used makes it to have a high userfriendly component typical of the Windows (Windows is a registered trademark of Microsoft Corporation. All the probability distribution functions mentioned in the previous section are contained in FLODRO 4.g. by the methods of moments and maximum likelihood for all the distributions. EVI and GEV distributions b) Computation of design events. Due to the minimum requirements of central memory and computer peripherals that the personal computer program has. training and in continuing education as well. by the methods of moments and maximum likelihood for all the distributions. 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. and probability weighted moments where this method is applicable. Mexico is shown in figure 3.0 are printed in a common printer there is no need to use costly plotters to get a hard copy of these graphs. The graphs provided by FLODRO 4. as can be seen in figures 8 and 9. Kite (1988). e. The comparison between the histogram of flood data and the theoretical probability density function is shown in figure 7. Akaike (1974) e) A graphical comparison between the empirical and theoretical probability density functions Personal computer program FLODRO 4. and probability weighted moments where this method is applicable.0 FLODRO 4. and probability weighted moments where this method is applicable. and the Akaike Information Criterion (AIC) in the case of the method of maximum likelihood. EVI and GEV distributions c) Estimation of confidence limits for design events.0 can perform the following computations.) environment. Inc. using the GEV probability distribution function and the ML method of estimation of its parameters. the mean absolute relative error (MARD).). The personal computer package FLODRO 4. for several return periods.g. ML and PWM for the estimation of parameters with application of the GEV probability distribution function to the flood sample. Inc. J. Flood Frequency Analysis. A. K. H. and Hamed. Water Resources Publications. eds. Jain. Colorado. a standard computational tool. Water Resources Publications. 187 Rao. USA Hydrology. A. and Escalante Sandoval. J. G. 1988.. 59-71 Kite.. 1980. Chihuahua.0: A User-Friendly Personal Computer Package for Flood and Drought Frequency Analyses.. Colorado State . Water Resources Bulletin. 2002. 87-94 Raynal-Villasenor.computer and a printer. Frequency Analysis of Hydrologic Extremes. 1... Training and Management.0: A User-friendly Personal Computer Package for Flood and Drought Frequency Analyses. Aqua-Terra Consultores. y Singh. 2002 Raynal-Villasenor. Control. 23. Boca Raton. Florida. A.P. Holanda.P. A... in Surface Water Hydrology. Jose A. Colorado. CRC Press. Estimating Parameters of EV1 Distribution for Flood Frequency Analysis”. H. 1998 Raynal-Villasenor. AC-19 (6) 716-723. Southampton... makes it available to anybody with access to a personal computer. 2000. Littleton.W. A. 1998. Flood and Risk Analyses in Hydrology. USA Raynal-Villasenor.. Balkema Pub. Singh et al. WIT Press. R. REFERENCES Akaike. UK. V.. IEEE Trans. as the main computational environment of the computer code. 1992. Puebla for the support given to produce this paper. Computer Techniques to Environmental Studies.A. Vol. Raynal. Computer Programs of Distribution Functions in University. USA. and Smith. 599-608. J. ed. 1987. J. R. Autom. No. 1974. FLODRO 3. V. 181-187. 2009. D. FLODRO: A Personal Computer Package for Flood and Drought Frequency Analyses Education and Training. Mexico Salas.A. ACKNOWLEDGMENTS The author wishes to express his deepest gratitude to the Universidad de las Americas. FLODRO 2. A.Lisse. A New Look at the Statistical Model Identification. The use of Excel. C. Hydrology and Water Resources Education. D. J. Fort Collins. 0 .0 ESTIMATION OF PARAMETERS GOODNESS OF FIT TESTS PROBABILITY DISTRIBUTION FUNCTION ESTIMATION OF DESIGN EVENTS ESTIMATION OF CONFIDENCE LIMITS COMPARISON BETWEEN HISTOGRAM AND PDF FIGURE 2. Options of analysis in computer package FLODRO 4.FLODRO 4.0 DATA PROBABILITY DISTRIBUTION FUNCTION RESULTS FIGURE 1. Framework of computer package FLODRO 4. FIGURE 3. Data statistics computed by FLODRO 4.0 . Mexico FIGURE 4. Location of gauging station Huites. FIGURE 5. Mexico . Estimation of parameters (GVE-ML) and their goodness of fit measures for gauging station Huites. Mexico FIGURE 6. Computation of design events and their confidence limits (GVE-ML) for gauging station Huites. 5E-04 20 2. Mexico Flood Frequency Analysis Gauging Station: Huites.0E+00 422 1809 3195 4582 5969 7356 8743 10129 Bin FIGURE 7.0E-04 Frequency 25 2. (1942-1992) 30 3. Mexico (1942-1992) General Extreme Value Distribution 15000 10000 Q (m3/s) MOM ML PWM1 PWM2 5000 Flood Data 0 -2 -1 1 2 3 4 5 Gumbel's Reduced Variate FIGURE 8.Histogram Gauging Station: Huites. Empirical and theoretical frequency curves for gauging station Huites.0E-04 5 5.0E-05 0 0.5E-04 3. Mexico .5E-04 10 1.0E-04 15 Em pirical Frequency GEV-ML 1. Mex. Histogram and theoretical probability density function for gauging station Huites. 5 0.5 6. Mexico .5 2.5 Gumbel's Reduced Value FIGURE 9.5 4.5 -0.5 5.5 3.Flood Frequency Analysis Gauging Station: Huites (1942-1992) Confidence Limits: GEV Distribution (ML) 50000 Q (m3/s) 40000 30000 Upper Confidence Lim it GEV-ML 20000 Low er Confidence Lim it Flood Data 10000 0 -1.5 1. Empirical and theoretical frequency curves and their confidence limits for gauging station Huites.