Troughs under threshold modeling of minimum flows in perennial streams

Troughs under threshold analysis has so far found little application in the modeling of minimum streamflows. In this study, all the troughs under a certain threshold level are considered in deriving the probability distribution of annual minima through the total probability theorem. For the occurrence of minima under the threshold, Poissonian, binomial or negative binomial processes are assumed. The magnitude of minima follows the generalized Pareto, exponential or power distribution. It is shown that asymptotic extreme value distributions for minima or the two-parameter Weibull distribution is obtained for the annual minima, depending on which models are assumed for the occurrence and magnitude of troughs under the threshold. Derived distributions can be used for modeling the minimum flows in streams which do not have zero flows. Expressions for the T-year annual minimum flow are obtained. An example illustrates the application of the troughs under threshold model to the minimum flows observed in a stream.