A stochastic model of low flows

A model is developed for annual low flow hydrographs. Its two primary components reflect the fact that hydrologic processes during streamflow rise (function of water input) and recession (function of basin storage) are different. Durations of periods of rise (wet intervals) and recession (dry intervals) are modelled by discrete probability distributions — negative binomial for dry intervals and negative binomial or modified logarithmic series for wet intervals depending on goodness of fit. During wet intervals, the total inflow is modelled by the lognormal distribution and daily amounts are allocated according to a pattern-averaged model. During dry intervals, the flow recedes according to a deterministic-stochastic recession model. The model was applied to three Canadian basins with drainage area ranging from 2210 to 22000 km² to generate 50 realizations of low flow hydrographs. The resulting two standard-error confidence band for the simulated probability distribution of annual minimum 7-day flows enclosed the probability distribution estimated from the observed record. A sensitivity analysis for the three basins revealed that in addition to the recession submodel, the most important submodel is that describing seasonality. The state of the basin at the beginning of the low flow period is of marginal importance and the daily distribution of input is unimportant.