FREQUENCY-ANALYSIS OF LOW FLOWS USING THE AKAIKE INFORMATION CRITERION

It is the current practice in frequency analysis of low flows to consi der only three-parameter distributions in which one of the parameters represents a nonzero lower bound. When applied to the small samples ty pically available, this practice results in incorrect low flow estimat es. These errors are related to errors in the estimated lower bound. T o preclude this possibility, it is proposed that the current practice be changed to include the selection of a two-parameter distribution in certain situations. To assess this proposal, the Akaike information c riterion (AIC) is used to compare the suitability of the most commonly used three-parameter distribution (three-parameter Weibull) and three two-parameter distributions (two-parameter Weibull, Gumbel, and logno rmal) to low flow data for 51 long-term hydrometric stations across Ca nada. For 75% of the stations, a two-parameter distribution is selecte d over the three-parameter distribution if the selection criterion is minimum AIC. In about one third of the remaining 25% of the stations w here the three-parameter Weibull distribution gave the minimum AIC, th e estimated lower bound is sufficiently close to the minimum observed low flow to indicate overfitting and hence unreliable quantile estimat es. When the AIC is supplemented with visual examination of goodness o f fit on probability plots, it is found that the lognormal distributio n could very well fit those cases where the AIC selected the three-par ameter Weibull distribution.