A regime switch error correction model to project sea level rise

Climate scientists employ various techniques to study the sea level rise (SLR), one of which is semi-empirical approach where the historical relationship between the SLR and global temperature is extracted from the data and parameterized for future SLR projections. It has been documented that semi-empirical models tend to have large variations in the projections depending on the data and methodologies. This study examines the statistical properties of the data used to construct the semi-empirical models and propose a new specification as a regime switch error correction model. We show that the proposed model has sound statistical foundation and good performance. The out-of-sample model projection of cumulative SLR from 2001–2020 is within 10% of the actual SLR. The model projects that in 21 st century, the average and the 5%-95% range (in parenthesis) cumulative sea level rise will be 0.28m (0.20–0.36m), 0.41m (0.33–0.48m), or 0.68m (0.60–0.76m), respectively, under the SSP1-2.6/2-4.5/5-8.5 scenarios. These projections are aligned with IPCC AR5 while lower than IPCC AR6. They are also within the range of the projections in recent studies.