Physics of flood frequency analysis. II. Convective diffusion model versus lognormal model

The similarity between the convective diffusion (CD) model and the log-normal (LN) distributions is shown by comparison of their moment estimates. Both models are tested using annual peak discharges observed at 39 gauging -sections of Polish rivers. The average value of the ratio of the coefficient of skewness to the coefficient of variation equals about 2.52, a value closer to the ratio of the CD model than to the gamma or the lognormal model. The likelihood ratio indicates the preference of the CD model over the LN model for 27 out of 39 cases. Applying the maximum likelihood (ML) method, one should take into account the consequences of the wrong distributional assumption on the estimate of moments. In the case of CD, the ML-estimate of the mean is unbiased for any true distribution, which is not the case with the LN model. Moreover the ML-estimate of the two first moments of CD remains asymptotically unbiased if LN is true, while there is small bias in the opposite case. To check the objectivity of our inferences from empirical findings, a simulation experiment was carried out, which comprised generated CD- and LN-distributed samples and both the moment and likelihood criteria for the distribution choice. Its results clearly show that normal hydrological sample sizes are far too small for selecting the true distribution.

Physics of flood frequency analysis. II. Convective diffusion model versus lognormal model Academic Article