Analysis of a two-layer EBM

Cristina Urbani

A simple yet extremely valuable approach to the study the climate system are Energy Balance Models (EBMs), first introduced independently by Budyko and Sellers in the 1960s. These models offer a simplified but effective framework for capturing the evolution of zonally averaged surface temperatures on Earth, reducing the complexity of the climate system to a one-dimensional spatial field.

To enhance the classical EBM, one can increase the model’s vertical resolution. In this talk, I will present a two-layer energy balance model that incorporates vertical energy exchanges between the Earth's surface and the atmosphere. I will discuss the stability and long time behavior of solutions, as well as the model's sensitivity to key parameters, particularly those associated with the greenhouse effect.

This talk is based on the following works:

P. Cannarsa, V. Lucarini, P. Martinez, C. Urbani, J. Vancostenoble, "Analysis of a two-layer energy balance model: Long time behavior and greenhouse effect", CHAOS, vol. 33, p. 113111, 2023.

P. Cannarsa, V. Lucarini, P. Martinez, C. Urbani, J. Vancostenoble, "Well-posedness and comparison results for a diffusion Energy Balance Model with vertical resolution", submitted, 2025.