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 datadriven 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 centurylong) tide gauge dataset (