Emulating long-term CMIP6 projections of sterodynamic sea-level change using a three-layer energy balance model

Multi-century projections of sea-level change are crucial for understanding long-term climate impacts. However, projecting ocean dynamic processes affecting sea-level change faces two main challenges: (1) the ocean’s thermal inertia and dynamics can lead to substantial nonlinearities both on a global (thermal expansion) and regional scale (dynamic sea level); and (2) simulating ocean dynamic sea-level change over multiple centuries with global climate models is computationally intensive. To address these challenges, we use an energy balance model (EBM) to emulate the thermal responses of models participating in the Coupled Model Intercomparison Project 6 (CMIP6) and evaluate its optimal layer configuration for reproducing both thermal expansion and dynamic sea-level change. We compare results between a two and a three-layer EBM configuration, as fitting more than three layers can lead to EBM parameter overfitting. We find that both configurations perform similarly when emulating thermal expansion, with performance being highly dependent on accurate EBM forcing. To emulate dynamic sea level, we couple the EBM to a multivariate pattern scaling approach that relates the response of layer temperatures to regional changes in dynamic sea level. The latter demonstrates clear advantages of a three-layer configuration under high-emission scenarios, leading to an 18% reduction in emulator error at 2300 while capturing nonlinearities more effectively. Coupling the regional emulator with a simple climate model to propagate climate uncertainties further highlights the advantage of using a three-layer approach, leading to more stable parameter fitting and reducing uncertainty in probabilistic projection by up to one global mean standard deviation. Our findings suggest that multi-layer EBMs can more accurately mimic long-term (up to 2300) CMIP6 projections of sterodynamic sea-level changes while limiting computational burden and reducing uncertainty in emulators due to statistical fitting.