The use of the Akaike Information Criterion in the identification of an optimum flood frequency model

Abstract

For a long time now, the hydrologist has been faced with the problem of finding which of the many possible probability distribution functions can be used most effectively in flood frequency analyses. This problem has been mainly due to the insufficiency of the conventional goodness-of-fit procedures when used with the typically skewed flood probability distributions. In this study, the Akaike Information Criterion (AIC) goodness-of-fit test is used to identify more objectively the optimum model for flood frequency analysis in Kenya from a class of competing models. The class is comprised of (a) seven three-parameter density functions, namely, log-normal, Pearson, log-Pearson, FisherTippet, log-Fisher-Tippet, Walter Boughton and log-Walter Boughton; and (b) two five-parameter density functions, namely, Wakeby and log-Wakeby. The AIC is also used in this study as a method of testing for the existence of outlier peak-flow values in the peak annual data used. A modified version of the chi-square goodness-of-fit test is also used, but only for the sake of comparison with the AIC. Utilisation du Critère d'Information d'Akaike pour identifier un modèle optimal de fréquence de cruesRésumé II y a bien longtemps que les hydrologues sont confrontés dans l'analyse de la fréquence des crues au problème du choix, parmi les nombreuses fonctions proposées dans la littérature, de la fonction de distribution la plus appropriée. Ce problème est essentiellement dû aux insuffisances des procédures habituelles d'appréciation de la qualité d'un ajustement lorsqu'elles sont utilisées pour des distributions dissymétriques comme le sont systématiquement celles des crues. Dans cette étude le Critère d'Information d'Akaike (CIA) a été utilisé pour identifier objectivement le modèle optimum d'analyse des fréquences de crues au Kenya parmi un ensemble de fonctions densité de probabilité concurrentes, à savoir sept fonctions à trois paramètres (log-normale, Pearson, logPearson, Fisher-Tippet, log-Fisher-Tippet, Walter Boughton et log-Walter Boughton) et deux fonctions à cinq paramètres (Wakeby, log-Wakeby). Le CIA a aussi été utilisé dans cette étude pour détecter l'existence de valeurs exceptionnelles (outliers) parmi les valeurs annuelles maximales utilisées. Une version modifiée du test d'ajustement du chi-2 a également été utilisée mais uniquement dans le but d'une comparaison avec le CIA.

Model selection techniques for the frequency analysis of hydrological extremes

“…[6] Applications of model selection criteria within the field of the frequency analysis of hydrological extremes are rare and nonmethodical: In the works by Turkman [1985], Mutua [1994], Hache et al [1999], Strupczewski et al [2001Strupczewski et al [ , 2002 and Cahill [2003] the Akaike information criterion is applied to single case studies without, however, analyzing the properties of such criterion for small samples or comparing its selection efficiency with that of other criteria. Mitosek et al [2006] applied three model discrimination procedures in order to find the best fitting distribution.…”

Introducing the Mixed Distribution in Fitting Rainfall Data

“…The result of AIC is directly dependent with the sample size of observation [23]. AIC is asymptotically effective and unbiased since the test is based on the maximum likelihood function and if the sample size is sufficiently larger than 30, the test will yield fairly accurate result [24]. The sample size of this study is greater than 30, hence AIC can be applied to determine the best model.…”

Modelling of Hydrological Drought Events in the Upper Tana Basin of Kenya

“…In Kenya, hydrological drought frequency studies are few and scattered and except for work by Mutua (1993) and Opere (1999) who fitted several distributions to maximum flow in the Lake Victoria, Rift Valley, Athi and the Tana basins and found the Wakeby and the three-parameter lognormal distributions to be the best models for flood frequency analysis, no comprehensive study has been done to fit frequency distribution models to hydrological drought events. In examining hydrological drought events using stream flow records, it is necessary to differentiate droughts from low flows.…”

“…Low flows differ from droughts in that the duration in low flows is of the order of days or weeks, flows occur instantaneously and only one event is selected from an annual period of data. The various frequency distributions used by Mutua (1993) and Opere (1999) in modelling floods in the country are useful in hydrological drought frequency analysis. However, their suitability or otherwise has not been examined and except for preliminary studies by Sharma (1996) who has shown drought duration and severity at selected gauging stations in the country to follow the three parameter lognormal distribution, no previous attempt has been made to test the suitability of various frequency distribution models in modelling drought duration and severity in the Tana basin.…”