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A Stochastic Analysis of Shasta Dam Storage Level using Truncated Power Function Distribution

Harshil J. Patel, Manharlal N. Patel

Abstract


The main objective of this research study is to predict the monthlydam storage level of Shasta dam on Sacramento river at Northern California by Markov chain model based on 59 years of monthly data of the water storage level of dam from June 1960 to October 2019.The total water storage capacity is as 45,52,000 acre-feet at 1067 feet elevation.The overall data is divided by the total storage level of the dam. Then the data is separated in 12 states of small intervals. Further with the help of historical data of monthly water storage,12 x 12 transition probability matrix (TPM) is developed. The truncated power function distribution is fitted to estimate the monthlywater storage values. The fitting of distribution is confirmed with the chi square test for the goodness of fit.Moment estimate and Bayes estimate of the parameter of the distribution are used with Markov chain model.The prediction is being done for the values of water storage of the dam from November 2019 to October 2020and compared with the original values of the same period.


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