02 May 2024
 | 02 May 2024
Status: this preprint is currently under review for the journal NPG.

Solving a North-type energy balance model using boundary integral methods

Aksel Samuelsberg and Per Kristen Jakobsen

Abstract. Simplified climate models such as energy balance models (EBMs) are useful conceptual tools, in part because their reduced complexity often allows for studies using analytical methods. In this paper, we solve a North-type EBM using a boundary integral method (BIM). The North-type EBM is a diffusive one-dimensional EBM with a non-linear albedo feedback mechanism. We discuss this approach in light of existing analytical techniques for this type of equation. Subsequently, we test the proposed method by solving multiple North-type EBMs with a zonally symmetric continent featuring an altered ice-albedo feedback dynamic. We demonstrate that the introduction of a continent results in new equilibrium states characterized by multiple ice edges and ice belts. Furthermore, we show that the BIM serves as an efficient framework for handling unconventional ice distributions and model configurations for North-type EBMs.

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Aksel Samuelsberg and Per Kristen Jakobsen

Status: open (until 27 Jun 2024)

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Aksel Samuelsberg and Per Kristen Jakobsen

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Aksel Samuelsberg and Per Kristen Jakobsen


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Short summary
We explored a simplified climate model based on Earth's energy budget. One advantage of such models is that they are easier to study mathematically. Using a mathematical technique known as boundary integral methods, we have found a new way to solve these climate models. This method is particularly useful for modeling climates very different from Earth's current state, such as those on other planets or during past ice ages.