Probability distribution, risk, and return period of dependent hydrologic events

Estimates of event occurrence probabilities, risks, and return periods of hydrologic processes such as monthly and annual streamflow provide fundamental information for decision making in water resources planning, management and engineering design. Traditionally, such properties of time dependent processes were obtained by using Markov chain models. While they are generally adequate to represent processes with short term dependence, they are inadequate for hydrologic processes exhibiting longer time dependence. In this study, low order DARMA and PDARMA models are used for modeling the variability of hydrologic wet and dry series. These models are more useful than simple Markov chain models for preserving long memory persistence of the historical data.; The methodology developed here are centered on the occurrence of events particularly their duration by using the concept of runs. The probability distribution of the time occurrence, expected values and variances of first arrival and interarrival times of events and the associated risks are derived based on the model properties. The derived equations and algorithms are verified by Monte Carlo simulation experiments. The applicability of the proposed methods is demonstrated by using a variety of hydrologic and environmental data. The results show that, in general, as long as the persistence characteristics of the binary sample are described by the fitted DARMA or PDARMA model, the historical return periods are likely to be well preserved.; Also involved in this study is the relationship between the continuous valued process and the clipped binary process. A method is presented for relating their autocorrelation functions. The method includes both stationary and periodic-stochastic series. In addition, the relationships between the lag-1 autocorrelations of the continuous and discrete processes and the crossing rate gamma are derived. The applicability of the methods and derived relationships are examined and tested by using streamflow series at several sites and by simulation experiments. Application results show that the event occurrence properties obtained by using the converted binary series correlogram based on the relationship are reliable.; It is concluded that the proposed methods are quite useful for modeling hydrologic or environmental events such as droughts or water quality episodes assuming that low order DARMA or PDARMA models can describe their clipped binary series.