Frequency Analysis of Low Flows: Hypothetical Distribution Methods and a Physically Based Approach

A mixed log Pearson type III distribution, a double bounded probability density function, partial duration series and a physically based approach are analyzed for frequency estimates of low flows. The mixed log Pearson III involves a point probability mass at zero for intermittent streams. The double bounded probability distribution has lower and upper bounds with a point mass at the lower bound. Two approaches are used in partial duration series i) truncation, and ii) censoring which represent curtailing of the population and the sample respectively. The parameters are estimated by maximum likelihood procedure. Considering low flows as part of the recession limb of stream flow hydrographs a physically based approach is formulated. By using the exponential decay of stream recessions and considering the initial recession flows, recession durations, and recharge due to incoming storms as statistically independent random variables, a first order random coefficient Markov model for initial recession flows is formed. The resulting steady state probability distribution for initial recession flows is combined with the probability distribution of the exponential decay to obtain the probabilities of low flow events. The methods are applied to both perennial and intermittent streams.