Flooding is one of the major natural hazards in the UK. Accurate flood estimation at ungauged catchment is an important component to understand and mitigate flood hazards, but still a difficult issue. This study therefore attempts to explore and improve an index flood estimation model, known as the FEH-QMED model, popular in the UK. It was developed under the assumption that the index flood of QMED, i.e., the median of the set of annual maximum (AMAX) flood data, standing for a flooding level of 2-year return period, can be explained by catchment descriptors. In this study, two fundamentals are empirically explored, including assessing reliability of the nonlinear functional impacts of the catchment descriptors on the logarithmic transformation of QMED, specified by the FEH-QMED model, and the potential to improve the model for more accurate index flood estimation, based on the flooding data of 586 gauged stations across the UK. Through a spatial additive regression analysis, we empirically find that the nonlinear impacts of the catchment descriptors in an updated FEH-QMED model appear reliable. However, spatial correlation tests including Moran’s I and Lagrange multiplier tests show that strong spatial dependence exists in the residuals of, but was not fully taken into account by, the QMED type models. We have therefore empirically established new spatial index flood estimation models by proposing spatial autoregressive models to model the impacts of the neighboring sites. Cross-validation assessments demonstrate that the suggested spatial error-based index flood model outperforms the updated FEH-QMED model with a significant improvement, which is robust in the sense of different error measures, say by a reduction of 13.8% of the mean squared error of prediction, for the UK index flood estimation.

洪水是英国的主要自然灾害之一。在未受污染的集水区进行准确的洪水估算是了解和减轻洪水危害的重要组成部分，但仍然是一个难题。因此，本研究试图探索和改进在英国流行的索引洪水估计模型，即FEH-QMED模型。它是在假设QMED的指标洪水（即代表2年回归期洪水水平的年度最大洪水数据集的中位数）可以由流域描述符来解释的前提下开发的。在这项研究中，我们从经验上探索了两个基础，包括评估集水区描述符对QMED的对数转换（由FEH-QMED模型指定）的非线性功能影响的可靠性，基于英国586个测站的洪水数据，有可能改进该模型以进行更准确的指数洪水估算。通过空间加性回归分析，我们从经验上发现，在更新的FEH-QMED模型中，流域描述符的非线性影响显得可靠。但是，空间相关性测试包括Moran'sI和Lagrange乘数检验表明，QMED类型模型的残差中存在很强的空间依赖性，但并未充分考虑。因此，我们通过提出空间自回归模型来模拟相邻站点的影响，从而建立了新的空间指数洪水估计模型。交叉验证评估表明，建议的基于空间误差的索引泛洪模型具有明显的改进，优于更新的FEH-QMED模型，这在不同的误差度量的意义上是稳健的，例如，均方误差减少了13.8％预测，用于英国指数洪水估算。