Temporal and spatial modelling of extreme river flow values in Scotland

HA Statistics

Franco Villoria, Maria ; Scott, E. Marian

University:University of Glasgow

Department:School of Mathematics and Statistics

关键词: extreme river flow, non-stationary, long range dependence, wavelet analysis, quantile regression, P-splines;   

Others  :  http://theses.gla.ac.uk/4017/1/2013FrancoVilloriaphd.pdf

来源: University of Glasgow

【 摘 要 】

Extreme river flows can lead to inundation of floodplains, with consequent impacts for society, the environment and the economy. Flood risk estimates rely on river flow records, hence a good understanding of the patterns in river flow, and, in particular, in extreme river flow, is important to improve estimation of risk. In Scotland, a number of studies suggest a West to East rainfall gradient and increased variability in rainfall and river flow.This thesis presents and develops a number of statistical methods for analysis of different aspects of extreme river flows, namely the variability, temporal trend, seasonality and spatial dependence. The methods are applied to a large data set, provided by SEPA, of daily river flow records from 119 gauging stations across Scotland. The records range in length from 10 up to 80 years and are characterized by non-stationarity and long-range dependence.Examination of non-stationarity is done using wavelets. The results revealed significant changes in the variability of the seasonal pattern over the last 40 years, with periods of high and low variability associated with flood-rich and flood-poor periods respectively. Results from a wavelet coherency analysis suggest significant influence of large scale climatic indices (NAO, AMO) on river flow.A quantile regression model is then developed based on an additive regression framework using P-splines, where the parameters are fitted via weighted least squares. The proposed model includes a trend and seasonal component, estimated using the back-fitting algorithm. Incorporation of covariates and extension to higher dimension data sets is straightforward. The model is applied to a set of eight Scottish rivers to estimate the trend and seasonality in the 95th quantile of river flow. The results suggest differences in the long term trend between the East and the West and a more variable seasonal pattern in the East.Two different approaches are then considered for modelling spatial extremes. The first approach consists of a conditional probability model and concentrates on small subsets of rivers. Then a spatial quantile regression model is developed, extending the temporal quantile model above to estimate a spatial surface using the tensor product of the marginal B-spline bases. Residual spatial correlation using a Gaussian correlation function is incorporated into standard error estimation. Results from the 95th quantile fitted for individual months suggest changes in the spatial pattern of extreme river flow over time. The extension of the spatial quantile model to build a fully spatio-temporal model is briefly outlined and the main statistical issues identified.