Nonparametric approach for estimating return periods of droughts in arid regions

Droughts cause severe damage in terms of both natural environments and human lives, and hydrologists and water resources managers are concerned with estimating the relative frequencies of these events. Univariate parametric methods for frequency analysis may not reveal significant relationships among drought characteristics. Alternatively, nonparametric methods provide local estimates of the univariate and multivariate density function by using weighted moving averages of the data in a small neighborhood around the point of estimation and opposed to parametric methods. A methodology for estimating the return period of droughts using a nonparametric kernel estimator is presented in order to examine the univariate as well as the bivariate behavior of droughts. After evaluating and validating a nonparametric kernel estimator, a drought frequency analysis is conducted to estimate the return periods of droughts for the Conchos River Basin in Mexico. The results show that, for the univariate analysis, the return periods of the severe drought occurring in the 1990s are 100 years or higher. For the bivariate analysis, the return periods are approximately 50 years for joint distributions and more than 120 years for the conditional distributions of severity and duration.