The statistical relation of sea-level and temperature revisited

• Proposes semi-empirical state-space model for relation of global temperature and global sea-levels that extracts smooth trend components similar to singular spectrum analysis.
• Allows for joint estimation of trend components and interaction term as well as valid statistical inference on the interaction term.
• Shows substantial influence of temperature increases on sea-levels in long-term projections, with wider confidence regions and more statistical uncertainty than previously reported.

We propose a semi-empirical model for the relation between global mean surface temperature and global sea-levels. In contradistinction to earlier approaches to this problem, the model allows for valid statistical inference and joint estimation of trend components and interaction term of temperature and sea-level. Estimation of the model on the data set used in Rahmstorf (2007) yields a proportionality coefficient of 4.6 mm/year per °C at a one-sided significance level of 7.6 percent or higher. Long-term simulations of the model result in a two-sided 90-percent confidence interval for the sea-level rise in the year 2100 of [15 cm, 150 cm] above the 1990 level. This is a wider margin of error than was reported in the previous literature, and it reflects the substantial uncertainty in relating two trending time series.