Drought Occurrence Probabilities and Risks of Dependent Hydrologic Processes

The occurrence probabilities, return periods, and risk of drought events are estimated for dependent hydrologic processes. Traditionally, Markovian models have been used for modeling hydrologic processes having short-term time dependence. However, they are inadequate for processes exhibiting longer time dependence. In this paper, low-order discrete autoregressive moving average (DARMA) models are used for modeling the variability of wet and dry years. Specifically, we center our attention on the occurrence of drought events, particularly their duration, by using the concept of runs. The probability distribution of drought occurrence, expected values and variances of first arrival and interarrival times of drought events, and the associated risks are derived. The derived equations and algorithms are verified by Monte Carlo simulation experiments. The applicability of the proposed methods is demonstrated by using annual streamflow data of the South Platte River in Colorado and the Niger River in Africa. It is concluded that the proposed methods are quite useful for modeling drought events, assuming that low-order DARMA models can describe wet and dry years.