| Abstract: | Exact probability distribution functions (PDF) of critical droughts in stationary second-order Markov chains are derived for finite sample lengths on the basis of the enumeration technique. These PDF are useful in predicting the possible critical drought durations that may result from any hydrologic phenomenon during any future period provided that the second-order Markov chain is representative of the underlying probability generation mechanism. Necessary charts are provided for the expectation and variance of critical droughts. The application of the developed methodology is given for three representative annual flow series from different parts of the world. It is observed that their critical droughts confirm well with the second-order Markov chain. |
