# Connecting complex and simplified models of tipping elements: a nonlinear two-forcing emulator for the Atlantic meridional overturning circulation

## TL;DR

This paper introduces a new emulator for simulating the Atlantic Meridional Overturning Circulation (AMOC) that captures tipping points using two climate forcings, enabling faster and more efficient climate scenario analysis.

## Contribution

The study introduces a novel two-forcing AMOC emulator calibrated against complex models, enabling accurate and low-cost simulation of AMOC tipping dynamics.

## Key findings

- The emulator captures additional AMOC collapses and tipping overshoots under high-emission scenarios.
- The tool enables rapid simulation of AMOC trajectories while maintaining alignment with complex model behavior.
- The methodology is generalizable for studying other climate tipping elements.

## Abstract

Despite its far-reaching implications, accurately characterizing the tipping dynamics of the Atlantic Meridional Overturning Circulation (AMOC) remains a significant challenge. Complex models, including Earth System Models (ESMs) and Earth System Models of Intermediate Complexity (EMICs), offer valuable insights; however, they are computationally expensive and subject to substantial uncertainties in identifying AMOC tipping points. In contrast, simple conceptual models based on non-linear dynamics have been developed to represent tipping elements such as the AMOC. These models can be calibrated against complex models to explore various scenarios and forcing spaces, functioning as emulators. Traditionally, such emulators have focused on a single forcing variable, typically global mean temperature, despite the well-established influence of freshwater fluxes on AMOC dynamics. Moreover, existing two-forcing AMOC emulators lack robust calibration methods against complex models.

In this study, we develop and validate a two-forcing AMOC emulator that incorporates global mean temperature and freshwater flux, grounded in non-linear dynamics. The emulator is calibrated against the AMOC response within the EMIC cGENIE. After validation, the emulator is integrated into SURFER, a reduced-complexity climate model, enabling rapid simulation of AMOC trajectories under diverse emission scenarios.

By considering Greenland Ice Sheet melt, the emulator captures two additional collapses and one overshoot without tipping trajectories for emission scenarios ranging from SSP3-7.0 to SSP5-8.5. Furthermore, the emulator allows the assessment of the critical forcing manifold of the AMOC in the complex model, enabling the identification of combined forcing thresholds for the AMOC and serving as a tool for comparing the sensitivities of complex models.

With its low computational cost and calibration accuracy, our tool represents a significant advancement in exploring AMOC dynamics in future climatic scenarios. Finally, the methodology used to develop this emulator is generalizable, providing a framework for studying other tipping elements in research.

As global temperatures rise due to greenhouse gas emissions, certain key components of the Earth’s climate system are approaching critical thresholds known as tipping points, beyond which significant changes may occur. One such tipping element is the Atlantic Meridional Overturning Circulation (AMOC), a crucial ocean current responsible for redistributing heat between the hemispheres. If the AMOC were to collapse, it could result in substantial regional changes in temperature, precipitation, and other critical aspects of the climate. However, the exact location of the AMOC tipping point and the time it would take to collapse remain uncertain due to limitations in complex climate models. Additionally, running these complex models is computationally expensive, making it difficult to explore a wide range of potential future scenarios. In this study, we developed an emulator—a simplified conceptual model calibrated using a complex model—to reproduce the behaviour of the AMOC during a potential collapse. This emulator is built on a new methodology that improves the alignment between simplified dynamics and complex models. The resulting tool enables the production of numerous AMOC simulations under various emission scenarios with low computational cost, while remaining consistent with our understanding of the physical processes that govern the AMOC. For example, this new emulator simulate AMOC collapse under future high emission pathways. This emulator and methods enables researchers to better explore the potential responses of the AMOC to future emissions and strengthens our ability to predict and prepare for abrupt changes in the climate system.