Non-stationary extreme value analysis is a powerful framework to address the problem of time evolution of extremes and its link to climate variability as measured by different climate indices CI (like North Atlantic Oscillation NAO index). To model extreme sea levels (ESLs), a widely-used tool is the non-stationary Generalized Extreme Value distribution (GEV) where the parameters (location, scale and shape) are allowed to vary as a function of some covariates like the month-of-year or some CIs. A commonly used assumption is that only a few CIs impact the GEV parameters by using a linear model, and most of the time by focusing on two GEV parameters (location or/and the scale parameter). In the present study, these assumptions are revisited by relying on a data-driven spline-based GEV fitting approach combined with a penalization procedure. This allows identifying the type (non- or linear) of the CI influence for any of the three GEV parameters directly from the data, and evaluating the significance of this relation, i.e. without making any a priori assumptions as it is traditionally done. This approach is applied to the monthly maxima of sea levels derived from eight of the longest (quasi century-long) tide gauge dataset (Brest, France; Cuxhaven, Germany; Gedser, Denmark; Halifax, Canada; Honolulu, US; Newlyn, UK; San Francisco, US; Stockholm, Sweden) and by accounting for four major CIs (the North Atlantic Oscillation, the Atlantic Multidecadal Oscillation, the Niño 1 + 2 and the Southern Oscillation indices). From this analysis, we show that: (1) the links between CIs and different parameters of a GEV distribution fitted to ESL data are most of the time linear, but some of them present significant non-linear shapes; (2) multiple CIs should be considered to predict ESLs, and (3) the CI influence of the GEV distribution is not limited to the location parameter. These results are useful to understand current modes of variability of ESLs, and ultimately to improve coastal resilience through more precise extreme water level assessments.

非平稳极值分析是一个强大的框架，可以解决极端事件的时间演变问题及其与由不同气候指数CI（如北大西洋涛动 NAO 指数）衡量的气候变率的联系。为了模拟极端海平面 (ESL)，一种广泛使用的工具是非平稳广义极值分布 (GEV)，其中允许参数（位置、尺度和形状）作为某些协变量的函数而变化，例如月份-年或一些CI s。一个常用的假设是只有少数CIs 通过使用线性模型影响 GEV 参数，并且大部分时间通过关注两个 GEV 参数（位置或/和尺度参数）。在本研究中，依靠数据驱动的基于样条的 GEV 拟合方法与惩罚程序相结合，重新审视了这些假设。这允许识别CI的类型（非线性或线性）直接从数据中对三个 GEV 参数中的任何一个产生影响，并评估这种关系的重要性，即无需像传统那样做出任何先验假设。这种方法适用于来自八个最长（准百年）潮汐测量数据集（法国布雷斯特；库克斯港，德国；格德瑟，丹麦；哈利法克斯，加拿大；美国檀香山；纽林，英国）的每月海平面最大值；美国旧金山；瑞典斯德哥尔摩）和四个主要CI（北大西洋涛动、大西洋多年代际涛动、Niño 1 + 2 和南方涛动指数）。从这个分析中，我们表明：（1）CI之间的联系s 和拟合 ESL 数据的 GEV 分布的不同参数大部分时间是线性的，但其中一些呈现出明显的非线性形状；(2)应考虑多个CI来预测 ESL，以及 (3) GEV 分布的CI影响不限于位置参数。这些结果有助于了解 ESL 的当前变异模式，并最终通过更精确的极端水位评估来提高沿海弹性。