Dataset for: Spatio-temporal modelling of hydrological return levels. A quantile regression approach

Extreme river flows can lead to inundation of floodplains, with consequent impacts for society, the environment and the economy. Extreme flows are inherently difficult to model, being infrequent, irregularly spaced and affected by non-stationary climatic controls. To identify patterns in extreme flows a quantile regression approach can be used. This paper introduces a new framework for spatio-temporal quantile regression modelling, where the regression model is built as an additive model that includes smooth functions of time and space, as well as space-time interaction effects. The model exploits the flexibility that P-splines offer and can be easily extended to incorporate potential covariates. We propose to estimate model parameters using a penalized least squares regression approach as an alternative to linear programming methods, classically used in quantile parameter estimation. The model is illustrated on a data set of flows in 98 rivers across Scotland.

极端河道径流可引发漫滩淹没，进而对社会、环境及经济造成连带影响。极端径流本身建模难度较高，其发生频率低、分布无规律，且受非平稳气候因素调控。为识别极端径流的变化模式，可采用分位数回归方法。本文提出一种全新的时空分位数回归建模框架：将回归模型构建为加性模型，涵盖时间、空间的平滑函数及时空交互效应项。该模型充分利用P样条（P-splines）的灵活性优势，且可便捷扩展以纳入潜在协变量。相较于经典分位数参数估计中常用的线性规划方法，本文提出采用惩罚最小二乘回归方法完成模型参数估计。本文以苏格兰境内98条河流的径流数据集为例，对所提模型进行了实例演示与验证。