  Studies agree on a significant global mean sea level rise in the 20th century
and its recent 21st century acceleration in the satellite record. At regional
scale, the evolution of sea level probability distributions is often assumed to
be dominated by changes in the mean. However, a quantification of changes in
distributional shapes in a changing climate is currently missing. To this end,
we propose a novel framework quantifying significant changes in probability
distributions from time series data. The framework first quantifies linear
trends in quantiles through quantile regression. Quantile slopes are then
projected onto a set of four $orthogonal$ polynomials quantifying how such
changes can be explained by $independent$ shifts in the first four statistical
moments. The framework proposed is theoretically founded, general and can be
applied to any climate observable with close-to-linear changes in
distributions. We focus on observations and a coupled climate model (GFDL-CM4).
In the historical period, trends in coastal daily sea level have been driven
mainly by changes in the mean and can therefore be explained by a shift of the
distribution with no change in shape. In the modeled world, robust changes in
higher order moments emerge with increasing CO2 concentration. Such changes are
driven in part by ocean circulation alone and get amplified by sea level
pressure fluctuations, with possible consequences for sea level extremes
attribution studies.
