Prediction of Extreme Events in Hydrologic Processes that Exhibit Abrupt Shifting Patterns

We propose a probabilistic framework for modeling extreme events such as annual maximum floods, and annual low flows. The model assumes that the underlying data sequence exhibits abrupt changes or shifts in the mean, and the data are skewed and autocorrelated. Thus, the stochastic model is assumed to shift abruptly from one “stationary” state to another one around a long-term mean. The proposed modeling framework is based upon the previously suggested shifting mean (SM) models, where the process was assumed to be autocorrelated but the marginal distribution was normally distributed and as a result the model skewness was zero. The main objective of the research reported herein has been to further extend the referred SM models to incorporate skewed marginal distributions so that they can be applicable for frequency analysis of extreme events. For this purpose, two SM models and alternative estimation procedures were developed using the generalized extreme value, Pearson III, and Gumbel distributions. The proposed models utilizing skewed distributions are successfully applied for determining extreme quantiles of the quarter-monthly maximum annual outflows of Lake Ontario and the $7\text{day}$ annual low flows for the Paraná River in Argentina.