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

Strupczewski W., Singh V., Węglarczyk S., Mitosek H.

Acta Geophysica Polonica

2003

Vol. 51, nr 1

85-106

The similarity between the convective diffusion (CD) model and the lognormal (LN) distribution 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 ration of the coefficient of skew ness to the coefficient of variation equals about 2.52, a value closer to the ration of the CD model than to the gamma or the lognormal model. The likelihood ratio indicates the preference of the CD over the LN model for 27 out of 39 cases. Applying the maximum likelihood (ML) method, one should take into account the consequence of the wrong distributional assumption on the estimate of moments. In the case of CD, the ML-estimate of the means is unbiased for any true distribution, which is not the case with the LN model, moreover the ML-estimate of the two fist 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. Part I. Linear convective diffusion wave model

Strupczewski W., Węglarczyk S., Singh V.

Acta Geophysica Polonica

2002

Vol. 50, nr 3

433-455

It is hypothesized that the impulse response of a linearized convective diffusion wave (CD) model is a probability distribution suitable for flood frequency analysis. This flood frequency model has two parameters, which are derived using the methods of moments and maximum likelihood. Also derived are errors in quantiles for these methods of parameter estimation. The distribution shows an equivalency of the two estimation methods with respect to the mean value - an important property in the case of unknown true distribution function. As the coefficient of variation tends to zero (with the mean fixed), the distribution tends to a normal one, similar to the lognormal and gamma distributions.