Statistical Analysis of Global Surface Temperature and Sea Level Using Cointegration Methods

Abstract

Abstract Global sea level rise is widely understood as a consequence of thermal expansion and the melting of glaciers and land-based ice caps. Because of the lack of representation of ice-sheet dynamics in present-day physically based climate models, semiempirical models have been applied as an alternative for projecting future sea levels. There are, however, potential pitfalls in this because of the trending nature of the time series. A statistical method called cointegration analysis that is capable of handling such peculiarities is applied to observed global sea level and land–ocean surface temperature. The authors find a relationship between sea level and temperature and find that temperature causally depends on the sea level, which can be understood as a consequence of the large heat capacity of the ocean. They further find that the warming episode in the 1940s is exceptional in the sense that sea level and warming deviate from the expected relationship. This suggests that this warming episode is mainly due to internal dynamics of the ocean rather than external radiative forcing. On the other hand, the present warming follows the expected relationship, suggesting that it is mainly due to radiative forcing. In a second step, the total radiative forcing is used as an explanatory variable, but it is unexpectedly found that the sea level does not depend on the forcing. The authors hypothesize that this is due to a long adjustment time scale of the ocean and show that the number of years of data needed to build statistical models that have the relationship expected from physics exceeds what is currently available by a factor of almost 10.