Efficient spin-up of Earth System Models using sequence acceleration

The ocean and land carbon cycles plays a critical role in the climate system and are key components of the Earth System Models (ESMs) used to project future changes in the environment. However, their slow adjustment time also hinders effective use of ESMs because of the enormous computational resources required to integrate them to a pre-industrial quasi-equilibrium, a prerequisite for performing any simulations with these models and, in particular, identifying the human impact on climate. Here, a novel solution to this ``spin-up'' problem, regarded as one of the grand challenges in climate science, is shown to accelerate the equilibration of state-of-the-art marine biogeochemical models typical of those embedded in ESMs by over an order of magnitude. Based on a ``sequence acceleration'' method originally developed in the context of electronic structure problems, the new technique can be applied in a ``black box'' fashion to any existing model. Even under the challenging protocols used to spin-up ESMs for the IPCC Coupled Model Intercomparison Project, which can take up to two years on even some of the most powerful supercomputers, the new algorithm can reduce simulation times by a factor of 5, with preliminary results suggesting that complex land surface models can be similarly accelerated. The ability to efficiently spin-up ESMs would enable for the first time a quantification of major parametric uncertainties in these models, lead to more accurate estimates of metrics such as climate sensitivity, and allow increased model resolution beyond what is currently feasible.