Regional flood frequency analysis by nonparametric methods.

Abstract

Parametric methods, currently used in regional flood frequency analysis, have numerous drawbacks and limitations, especially with regard to flood distribution selection and regional relationship form. Alternative approaches involving nonparametric methods are investigated in this thesis on a set of New Brunswick annual maximum floods. Nonparametric methods were employed at the three steps of regional analysis: at-site flood frequency analysis, homogeneous region delineation and regional relationship development. Nonparametric flood frequency analysis indicated that an annual maximum flood data set from New Brunswick contained some unimodal distributions along with many mixed distributions of bimodal and heavy-tailed shapes. A simulation study showed that sampling variability from a unimodal distribution could not account for the bimodality in nonparametric frequency analysis, confirming the existence of mixed distributions. L-moment analysis, a parametric method, confirmed that the entire set of floods from New Brunswick could not be appropriately described by a unimodal distribution. In this study, a new method is proposed for the purpose of homogeneous region delineation which effectively combines geographical considerations and flood data characteristics. The technique is based on the grouping of stations with similar density function shape, which reflect similar flood generating mechanisms. In New Brunswick, flood densities of three different shapes were grouped on a geographical basis to delineate homogeneous regions. Statistical tests based on L-moment analysis confirmed that the stations within a homogeneous bimodal region came from the same distribution. But L-moment analysis would propose either the Generalized Logistic or the Generalized Extreme Value as the regional distribution. Nonparametric frequency analysis revealed, however, that the floods within that region actually came from a mixed distribution. Nonparametric regression was employed for regional relationship development in New Brunswick; however, no significant improvement over the parametric approach of linear regression resulted. Using bootstrapping of pairs, a new method to compute the confidence interval at the center of a nonparametric regression was investigated. A comparison of linear and nonparametric regression confidence intervals can assist in evaluating the appropriateness of a linear model, and thus the need to employ nonparametric regression. Nonparametric regression was shown to be useful in screening irrational relationships that could be developed with the parametric approach. A new regional analysis methodology, involving nonparametric methods at the three steps of regional analysis, is proposed in this study, resulting in improved homogeneous region delineation, in more accurate at-site quantile estimates, and more realistic regional relationships.