BALWOIS 2004 Ohrid, FY Republic of Macedonia, 25-29 May 2004 Method Of Composition Applied For Selected Karstic Springs In Bulgaria Elena Kirilova Bojilova National Institute of Meteorology and Hydrology Sofia, Bulgaria Abstract In the study empirical and theoretical distribution of the yearly spring flow data are evaluated. The estimations of statistical parameters of distribution functions using analytical methods are not with equal level of accuracy. In the present contribution for obtaining best fit to the empirical data the method of composition of the constituting casual values is used. For testing of the method some karstic springs are selected. The data originated from Bulgarian National Hydrological and Hydro- geological Network located in National Institute of Meteorology and Hydrology, Sofia, Bulgaria. The method of composition for specifying the frequency curves is possible to use in three cases. In the research two cases are applied and discussed – composition in case of function between two arguments and correlation between two variables. Our conclusion is that, the method of composition is proved itself to be very powerful for extending probability curve of the empirical distribution. With this method is possible to estimate the quantiles in the range of very low probability of occurrence. Introduction In the study empirical and theoretical distribution of the yearly spring flow data are executed. For applying the method of composition some karstic springs are selected. Spring flow data originated from Bulgarian National Hydrological and Hydro-geological Network located in National Institute of Meteorology and Hydrology, Sofia, Bulgaria. The method of composition for specifying the frequency curves is possible to use in three cases - composition in case of function between two arguments and correlation between two and three variables. The object of the study is an application of method of composition in case of function between two arguments and correlation between two variables for selected karstic springs. Method of composition From the group of methods for specifying the frequency curves of empirical distribution and their theoretical approximation we are introducing and applying the method of composition. The method gives the possibility in case of functional relationship between the study set and l-independent components (sets) to obtain effective estimation of probability curve. The number of numerical realizations form n real numbers rises to N=n l - Bojilova (2003a). In probabilistic theory the method of composition is executed and is possible to apply in existence of the following conditions: functional relationship between study random variables and its arguments and independence between the arguments. The method of composition can follow the next steps: Increasing (decreasing) order of the set of functional time series X 0 and its components ; l X X X X ,..., , , 3 2 1 Calculation of X i values of the function ( ) l X X X f X ,..., , 2 1 0 = applying to step by step arrangement of every argument X i with all others ; l i i X X X X ,..., , ,..., 1 1 2 + − X , 1 Ordering of all N calculated values of X i in increasing (decreasing) order; Building of the empirical composed probability curve ( ) [ ] 0 0 0 x M X P P x < = using one of existing methods (graphical, analytical or graph–analytical). The method of composition for specifying the frequency curves is possible to apply only in three cases: correlation between two and three variables and function of two arguments. Bojilova (2003b) applied the method of composition for selected rivers in Bulgaria. In this research two of the three possible cases are applied and discussed for chosen karstic springs. Water bodies protection and Ecohydrology 1