Model selection techniques for the frequency analysis of hydrological extremes

Abstract

[1] The frequency analysis of hydrological extremes requires fitting a probability distribution to the observed data to suitably represent the frequency of occurrence of rare events. The choice of the model to be used for statistical inference is often based on subjective criteria, or it is considered a matter of probabilistic hypotheses testing. In contrast, specific tools for model selection, like the well-known Akaike information criterion (AIC) and the Bayesian information criterion (BIC), are seldom used in hydrological applications. The objective of this study is to verify whether the AIC and BIC work correctly when they are applied to identifying the probability distribution of hydrological extremes, i.e., when the available samples are small and the parent distribution is highly asymmetric. An additional model selection criterion, based on the Anderson-Darling goodness-of-fit test statistic, is here proposed, and the performances of the three methods are compared through an extensive numerical analysis. The capability of the three criteria to recognize the correct parent distribution from the available data samples varies from case to case, and it is rather good in some cases (in particular when the parent is a two-parameter distribution) and unsatisfactory in others. An application to flood peak time series from 1000 catchments located in the United Kingdom provides some further information on the qualities and drawbacks of the considered criteria. From the numerical simulations and data-based analyses it can be concluded that the three model selection techniques considered here produce results of comparable quality.

Finding Probability Distributions for Annual Daily Maximum Rainfall in Pakistan Using Linear Moments and Variants

“…Different methods have been used for the goodness-of-fi t measure such as including the Chi-square method, quantile-quantile plots, mean absolute deviation index, LMRD, RMSE, KST, and ADT. These tests have been used by many authors [8,16,36,[41][42][43][44][45][46][47]. In this study we implemented three GOF tests -RMSE, KS, and AD -and one graphical method, i.e., LRD for visual inspection.…”

Large-scale attribution of trend in UK flood flow data

“…The LN2 distribution has previously been found to provide a reasonable fit to UK flood data (Laio et al, 2009). Assuming a stationary flood series, the LN2 quantile function, q r , is defined for a return period T as…”

Parent Flood Frequency Distribution of Turkish Rivers

“…Empirical appropriateness also plays a significant role in PD selection [18]. However, the aforementioned tests show some obvious restrictions, including non-objective and uncertain results, as reflected in the fact that more than one PD frequently passes the tests [22,7].…”

“…Identifying the appropriate PD of floods is probably the most important step in flood frequency analysis. Accordingly, many studies all over the world have investigated how to determine an appropriate PD of floods [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16]. The selection of techniques for assessing flood frequency in specific conditions depends on several dynamics, including national tradition, knowledge of the modeler, the aim of a study, governmental necessities, and data accessibility [17].…”