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Drought is a slow and creeping phenomenon that occurs more frequently in arid and semi-arid regions. In recent decades, among natural disasters influencing human societies the number or frequency of drought event has increased more than others. In this context, the prediction of drought intensity, duration and frequency can help to take the necessary precautions and reduce drought risk. This study employs Markov chains of different orders (0, 1, 2 and 3) to analyze hydrological drought characteristics. Hydrological drought is identified based on the streamflow drought index (SDI) at 3-, 6-, 9- and 12-month time scales using data from 21 hydrometric stations located in the Karkheh River Basin in Iran. According to the Akaike Information Criterion (AIC) and the Bayesian Information Criterion (BIC), first-order Markov chain models are adequate to reproduce the statistical structure of SDI-based hydrological droughts. Moreover, the steady state probabilities and expected residence time of drought severity for all time scales increase as the degree of severity decreases. The results also indicate that the expected frequency of drought occurrence is higher for smaller time scales (i.e., 3-month and 6-month). [ABSTRACT FROM AUTHOR]

A certain Markov chain which was encountered by T. L. Hill in the study of the kinetics of a linear array of enzymes is studied. An explicit formula for the steady state probabilities is given and some conjectures raised by T. L. Hill are proved. [ABSTRACT FROM AUTHOR]