Non-Gaussian spatial modeling in index flood estimation

Abstract

Index flood estimation is important in regionalization procedure to solve an issue of ungauged catchment that has received great attention among hydrologists. The UK index flood estimation model known as the FEH-QMED model is a well established one with nonlinear effect of explanatory variables identified. However the shortcomings of current research in literature such as not taking into account a spatial dependency and non-Gausianity that exist in the flooding data motivated us to investigate further. This thesis aims to improve the existing methodology in index flood estimation model, where FEH-QMED model is chosen as the benchmark. Three objectives that have been developed in this thesis are: (i) to explore the shortcomings of the current research with a possibly improved model in estimating the UK index flood, (ii) to develop a more efficient statistical model in estimating the index flood that better fits the UK flooding data, and (iii) to discover more relevant predictive catchment characteristics that may improve the index flood estimation model. To answer the objectives, statistical methods have been proposed and applied into the UK flooding data analysis to establish new index flood regression models detailedly discussed in chapters of the thesis respectively. In Chapter 2 we apply the spatial additive and spatial error analyses into the UK flooding data to explore possibly improved models for the UK index flood estimation. Chapter 3 proposes a new spatial error model with skewed normal distribution for residuals and develops a maximum likelihood computational algorithm to apply into the UK flooding data for the purpose of establishing a new index flood estimation model. Chapter 4 is focused on model selection of index flood estimation model by proposing a panelized likelihood estimation method that utilizes adaptive Lasso as a regularization tool in variable selection of all available catchment characteristics in the UK flooding data source. We also present the simulations to investigate the finite sample performance of the proposed statistical methods. In comparison study, AIC scores have been used as model selection criteria, while to measure the performance of different models, the percentage improvement in mean square prediction error relative to the updated FEH-QMED model in Kjeldsen and Jones (2010) is applied. The obtained results demonstrate that the skewed spatial error flood model that is established by using statistical method suggested in Chapter 4 outperforms the others and can significantly improve the FEH-QMED model in estimating the UK index flood.

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ORCID for Zudi Lu: orcid.org/0000-0003-0893-832X

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