Author(s): Bonifacio Fernandez
Linked Author(s): Bonifacio Fernandez L.
Keywords: No Keywords
Abstract: This paper is concerned with the estimation of the probability of occurrence of a drought of given duration detected in a systematic record of length N. Systematic records of hydrometeorological variables related to water supply are usually considered in the design of hydraulic systems to evaluate its behavior under the extreme conditions observed in the available series. Nevertheless it is known that for extreme conditions related to droughts, which can last for several periods of the record, the probability of occurrence of the worst observed drought can not be directly related to the length of the systematic record in which it is observed. The sample properties that characterize droughts are stochastic variables and hence its probability distribution function, pdf, must be known in order to obtain the exceedance probability of its characteristics. To evaluate the pdf of the properties of droughts Llamas and Siddiqui (1969) used analytical methods and Millan and Yevjevich (1971) intended statistical experiments. A set of analytical procedures to evaluate probabilities of several drought properties has been tested by Guerrero-Salazar and Yevjevich (1975). In a series of papers Sen (1976, 1980a, 1980b) used the theory of runs to develop analytical expressions to determine the probabilities of runs lengths including the case of a first order autoregressive process. From the statistical point of view several procedures have been recently presented to evaluate properties of runs in a fixed amount of trials in Markov- dependent series. Some of these methods can be applied in the evaluation of properties of droughts. References about them can be found in Banjevic (1988). Among them method developed by Schwager (1983) is specially well oriented to be used in characterizing probabilities of run length in general and droughts duration as a particular case, and has a great potential for developing alternative expressions to evaluate the probabilities of observed droughts. He developed method of computing the probability of the occurrence of a given run, as a function of the composition of the run, the number of trials, and the probabilities of the possible outcomes at each trial. This method is presented here and used to estimate probabilities of observed drought in systematic records of precipitation and streamflow. Examples with actual records from Central Chile are shown.
Year: 1993