Hydrologic time series of annual minimum mean monthly rainfall and annual minimum 1-day and 7-day discharge, considered as drought indices, were used to study the distribution of droughts with respect to time. The rainfall data were found to be nearly random. The discharge data, however, were found to be nonrandomly distributed in time and generated by a first-order Markov process. The expected value of the variance for a time series generated by a first-order Markov process was compared with the expected value of the variance for a random time series. This comparison showed that the expected value of the variance for a nonrandom time series converged to the population variance with an increase in sample size at a slower rate than for a random time series.
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USGS Numbered Series
Autocorrelation of rainfall and streamflow minimums