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Some properties of variance reduction techniques where hydrological extremes are estimated by Monte Carlo Simulation
Author(s) -
Moore R. J.,
Clarke R. T.
Publication year - 1978
Publication title -
water resources research
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.863
H-Index - 217
eISSN - 1944-7973
pISSN - 0043-1397
DOI - 10.1029/wr014i001p00055
Subject(s) - control variates , variance reduction , monte carlo method , variance (accounting) , random variate , reduction (mathematics) , importance sampling , computer science , reliability (semiconductor) , sampling (signal processing) , streamflow , statistics , mathematics , algorithm , hybrid monte carlo , random variable , markov chain monte carlo , drainage basin , power (physics) , physics , geometry , accounting , cartography , filter (signal processing) , quantum mechanics , business , computer vision , geography
An estimate F ˆ of a water resource system's performance, when it is derived by simulation using synthetic streamflow sequences, is subject to at least three errors: first, model errors, arising from the approximation to the ‘true’ streamflow mechanism which the model represents; second, sampling errors in the model parameters θ when they are calculated from the historic records; and third, errors introduced by the Monte Carlo calculation from which F ˆ is derived. This paper presents some observations on the effects of the first two types of error on the estimate F ˆ but concentrates on the application of variance reduction techniques to the derivation of Monte Carlo estimates F ˆ for given θ. These techniques are, first, the use of control variates and, second, the use of antithetic variates, and their application is illustrated by using some hypothetical examples of the calculation of probabilities of extreme hydrological events and of the calculation of reliability measures for a much oversimplified storage system. Considerable reduction in the variance of F ˆ resulted from the application of the control variate method; the reduction in Var F ˆ resulting from the use of antithetic variates was much less but still probably worth the small additional programing effort required. It is concluded that the promise of the control variate method suggests that it should be applied to assist in the efficient simulation of more realistic water resource systems than the trivial ones considered in this paper.