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Retracing the evolution of Earth’s surface temperatures

How can the evolution of the Earth’s surface temperatures over several centuries be modelled? Biomathematics researchers have found a way to identify the relevant climate model parameters using data obtained through ice core analysis.

An Icelandic iceberg on exhibit in front of the Palais de la Découverte science museum in Paris. © INRA, MAITRE Christophe
By Pascale Mollier, translated by Teri Jones-Villeneuve
Updated on 12/01/2015
Published on 11/13/2015

Biomathematics researchers at INRA have developed an original modelling approach. The aim is to identify the parameters of a model that describes the dynamic of a variable of interest: the Earth’s temperature over time and space. First, a statistical correlation was established between data obtained through ice core analysis and the Earth’s surface temperature. Next, a climate model was selected: a simplified model called an energy balance model (EBM), which included various parameters. Lastly, the statistical correlation was used to estimate the parameter values that would lead to the most accurate results based on observations and temperatures obtained using the climate model.

It is hoped that modelling the Earth’s surface temperature over time will provide a better understanding of global climate changes, glacial periods and the determining factors of such events.

Using a statistical model to identify relevant parameters

Ice core data provide indications about the Earth’s surface temperature for a specific time and place based on analyses of the heavy and light isotopes present and observations of the type of ice. Nevertheless, some uncertainty remains with regards to the temperature and date estimates, because the farther back in time one goes (i.e., towards the base of the ice core), the more compacted the layers are and the harder it is to distinguish the strata.

“We built a probabilistic model that describes the observations as random variables that depend on the temperature,” explain Lionel Roques and Samuel Soubeyrand. “Despite some uncertainty regarding the data, this allows us to estimate the most likely parameter values of the climate model – in other words, those that would best explain the observations. Once these values are estimated, the climate model estimates the temperature for any latitude and at any date in time.”

Inputting the climate model parameters

The climate model is based on a partial differential equation created using energy balances, i.e., the differences in incoming and outgoing solar radiation. The main parameters that determine energy balance are:

  • The greenhouse effect, due to the layer of atmospheric gases preventing the reflection of solar radiation and which is a factor in global warming.
  • Albedo, which is the ability of the Earth’s surface to reflect solar energy, determined by the type of surface and temperature. A white surface, such as ice, reflects much more solar energy, making it a factor in cooling. Dark surfaces, such as the ocean, absorb radiation and are a factor in warming. Albedo depends not only on current temperatures but also on past temperatures, which complicates modelling due to delayed influences.
  • Other parameters include temperature distribution patterns across the Earth, etc.

“Our approach has been validated using simulated ice core data. We hope to apply this method to real data as part of our joint research with the Department of Atmospheric and Oceanic Sciences at UCLA.

“In applied mathematics, the research is rather compartmentalised. On the one side, there is the world of empirical statistical models, which describe a reality but not the underlying mechanisms, and on the other, the world of dynamical models, which describe a phenomenon using a mechanic description. The originality of our approach lies in combining the two,” say Lionel Roques and Samuel Soubeyrand.

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Applied Mathematics and Informatics
Associated Centre(s):
Provence-Alpes-Côte d'Azur

An approach that can be applied to other problems

Using a statistical approach to input parameters in a spatio-temporal dynamic model is an approach that can also be applied to other problems, such as biological invasions. For example, the approach was used to create a model of the spread of the pine processionary and tiger mosquito to understand the determining factors of these invasions.