A review of trend models applied to sea level data with reference to the acceleration-deceleration debate

Global sea levels have been rising through the past century and are projected to rise at an accelerated rate throughout the 21st century. This has motivated a number of authors to search for already existing accelerations in observations, which would be, if present, vital for coastal protection planning purposes. No scientific consensus has been reached yet as to how a possible acceleration could be separated from intrinsic climate variability in sea level records. This has led to an intensive debate on its existence and, if absent, also on the general validity of current future projections. Here we shed light on the controversial discussion from a methodological point of view. To do so, we provide a comprehensive review of trend methods used in the community so far. This resulted in an overview of 30 methods, each having its individual mathematical formulation, flexibilities, and characteristics. We illustrate that varying trend approaches may lead to contradictory acceleration-deceleration inferences. As for statistics-oriented trend methods, we argue that checks on model assumptions and model selection techniques yield a way out. However, since these selection methods all have implicit assumptions, we show that good modeling practices are of importance too. We conclude at this point that (i) several differently characterized methods should be applied and discussed simultaneously, (ii) uncertainties should be taken into account to prevent biased or wrong conclusions, and (iii) removing internally generated climate variability by incorporating atmospheric or oceanographic information helps to uncover externally forced climate change signals.