Spatial patterns of linear and nonparametric long-term quantile trends in Baltic sea level during the 20th century

The study of long-term trends in tide gauge data is important for understanding the present and future risk of changes in sea-level variability on coastal zones, particularly with respect to the ongoing debate on climate change impacts. Traditionally, most corresponding analyses have exclusively focused on trends in mean sea-level. However, such studies are not able to provide sufficient information about changes in the full probability distribution (especially in the more extreme quantiles). As an alternative, we apply quantile regression (QR) for studying changes in arbitrary quantiles of sea-level variability. For this purpose, we chose two different QR approaches and discuss the advantages and disadvantages of different settings. In particular, linear QR poses very restrictive assumptions that are often not met in reality. For monthly data from 47 tide gauges from the Baltic Sea, we find that results obtained via QR in a linear and nonparametric (spline-based) framework display marked differences, which need to be understood in order to fully assess the impact of future changes in sea-level variability.