1. Purpose and objectives
To present and use a new approach to annual maximum floods analysis for countries that have both types of floods, i.e. snowmelt and rainfall origin. That is the prerequisite condition to employ the Guidelines to estimate annual maximum flood with given probability of exceedence (T-year return period) for water management structures designing.
The proposed Guidelines for calculating annual maximum discharges with given probability of exceedance Qmax,p are based on the following major assumptions and principles:
· Correctness of annual maximum discharge of summer and winter seasons, defined on the grounds of reliable rating curves;
· Maximum use of non-statistical information to verify the reliability of measurement series for statistical calculations;
· Maximum use of information about the statistical properties of measurement series to select the most credible function of probability distribution.
Principles and procedures for carrying out calculations relate to two issues, namely: analysis of measurement series and calculation of maximum discharges with a given probability of exceedance.
The measurement data analysis procedure includes the following:
· Examination of homogeneity of maximum discharge series with the use of genetic (physical) methods:
- Set up of observations from a period of N >= 30 years and plotting a graph of the run of two series of floods of various origin, i.e. annual maximum flood in winter season and maximum flood in summer season; floods consolidated in each of these series are homogeneous in terms of origin (a priori homogeneous),
- in each series, checking and elimination of measurement nonhomogeneity, which could have resulted from any change in measurement method or instruments,
- in each series, checking and elimination of time nonhomogeneity, which could have resulted from any change in basin or river bed development over the observation period,
· Examination of homogeneity of maximum discharge series with the use of statistical methods:
- investigation of so-called outliers with the use of the Grubbs-Beck test,
- investigation of independence of elements of series with the use of the test of series,
- investigation of stationarity of the series of maximum discharges with the use of three non-parametric tests: the Kruskal-Wallis test, the Spearman rank correlation coefficient test for trend of mean value and the Spearman rank correlation coefficient test for trend of variance.
In case of recognising non homogeneity of the series, such series cannot be subject to further processing, i.e. it cannot be used as a basis for calculating Qmax,p.
The Qmax,p calculating procedure may be used solely for homogeneous measurement series of size N
>= 30years of observation:
· The following four types of probability distribution functions have been adopted as models of statistical properties of each studied series: Gamma, log-Normal, Weibull, log-Gamma.
· For all the above listed types of distributions a condition was assumed that left side lower bound may adopt values from the interval between 0 and the lowest value of maximum discharge observed in the studied series,
· Estimation of two remaining parameters, with defined different values of lower bound, is carried out with the use of the maximum likelihood method,
· Testing of the hypothesis of goodness of fit of theoretical probability distribution function with the empirical distribution, with the use of
Chi2 Pearson test, at a = 0.05 significance level, leads to selection of non-rejected distribution functions which form a set of uncontradicted probability distribution functions, acceptable as theoretical distributions of the studied measurement series,
· Selection of the best fitted distribution function, one for each adopted type of distribution, is done with the use of minimum Dmax Kolmogorov distance criterion, between the theoretical and empirical distribution,
· Selection of one most credible function of probability distribution, from the set of best fitted distribution functions, is done with the use of Akaike Information Criterion (AIC),
· The function of probability of exceedance of annual maximum discharges is defined as a probability function of alternative of two non-eliminated independent events, based on the most credible function of probability distribution of the annual maximum discharges of the winter season and the most credible function of probability distribution of the annual maximum discharges of the summer season,
· The upper bound of interval of confidence, resulting from randomness of maximum discharge series, is calculated by simulation method,
· Checking whether the size of the measurement series is sufficient to calculate the annual maximum discharge with probability p, i.e. Qmax,p, where the error resulting from sample randomness does not exceed 20 %,
· Procedure is completed with estimation of zone of uncertainty of quantile Qmax,p of the annual maximum discharge distribution, selected from among best fitted functions in specific types of distributions.
The computing program FLOODS ANALYSIS has been implemented for microcomputers operating in Windows environment.
Two measurement series of size N >= 30 years of annual maximum floods of snowmelt and rainfall origin, i.e. one series for winter season and one for summer season.
The report contains statistical characteristics and graphs of measurement series, tables of quantiles Qmax,p and probability distribution plots for winter and summer seasons as well as for the year.
5. Operational requirements and restrictions
The program can be implemented for computers with operating system as WINDOWS 98/NT/2000/XP. For edition of final report the Microsoft Word ver. 2000 or higher is necessary.
6. Form of presentation
The Guidelines are in English they consist of 44 pages plus computing program.
7. Operational experience
During the study period both the assumptions and technical basis for the Guidelines as well as research results were presented and discussed during various scientific seminars. A series of discussion articles were also published in professional journal Water Management.
The present Guidelines have been developed following a year of practical application, a working seminar at the Cracow Branch of IMGW in March 2001 and after incorporation of technically justified remarks. The Guidelines are in operational use at the Institute of Meteorology and Water Management (IMGW) in Poland since year 2002.
8. Originator and technical support
Institute of Meteorology and Water Management (IMGW), Warsaw, Poland.
The Guidelines are available as a HOMS component free of charge from HNRC for Poland at the Institute of Meteorology and Water Management.
10. Conditions on use
Cost of reproduction (if any) and mailing.