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

University of Copenhagen Discussion Papers No. 11-26

37 Pages Posted: 29 Oct 2011

See all articles by Torben Schmith

Torben Schmith

Danish Meteorological Institute

Soren Johansen

University of Copenhagen - Department of Economics; Aarhus University - CREATES

Peter Thejll

Danish Meteorological Institute

Date Written: October 24, 2011

Abstract

Global sea levels are rising which is widely understood as a consequence of thermal expansion and melting of glaciers and land-based ice caps. Due to physically-based models being unable to simulate observed sea level trends, semi-empirical models have been applied as an alternative for projecting of future sea levels. There is in this, however, potential pitfalls due to the trending nature of the time series. We apply a statistical method called cointegration analysis to observed global sea level and surface air temperature, capable of handling such peculiarities.

We 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. We further find that the warming episode in the 1940s is exceptional in the sense that sea level and warming deviates 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, we use the total radiative forcing as an explanatory variable, but unexpectedly find that the sea level does not depend on the forcing. We 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 ten.

Suggested Citation

Schmith, Torben and Johansen, Soren and Thejll, Peter, Statistical Analysis of Global Surface Air Temperature and Sea Level Using Cointegration Methods (October 24, 2011). University of Copenhagen Discussion Papers No. 11-26, Available at SSRN: https://ssrn.com/abstract=1950555 or http://dx.doi.org/10.2139/ssrn.1950555

Torben Schmith

Danish Meteorological Institute ( email )

Lyngbyvej 100
Copenhagen Ø, 2100
Denmark

Soren Johansen (Contact Author)

University of Copenhagen - Department of Economics ( email )

Øster Farimagsgade 5
Bygning 26
1353 Copenhagen K.
Denmark

Aarhus University - CREATES ( email )

Nordre Ringgade 1
Aarhus, DK-8000
Denmark

Peter Thejll

Danish Meteorological Institute ( email )

Lyngbyvej 100
Copenhagen Ø, 2100
Denmark

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