Numerical implementation of ESMs: an additional source of uncertainty in climate prediction?

Modern research in climate science relies heavily on Earth System Models (ESMs), which are highly complex and nonlinear mathematical representations of the planet Earth. Because ESMs are too complicated to be tractable analytically, one must resort to computers in order to extract useful information from them. Numerically solving these models is, however, a non-trivial task, with two key practical consequences. First, being complex and nonlinear, ESMs require the use of several numerical schemes and involve different computational strategies to accommodate for the multiplicity of scales and components present in such models. These numerical choices vary from model to model and are also dependent on the user needs, as well as the computing resources available to them. Second, being chaotic means that its initial value problem is sensitive to the finest details in the model (e.g. initial condition), and so any future state can only be characterised as a distribution, requiring an ensemble of simulations instead of a single one. Hence, different numerical approximations could in principle lead to differences in the resulting distributions, particularly in shape and extreme values. This is important, as such numerical scheme dependence can cause ambiguity in our interpretation of future climate within a model. Despite that, this issue has been largely neglected in both climate and mathematical literature. In this presentation, we will briefly review and discuss the use of numerical schemes in ESMs and individual components. Using a conceptual but low-dimensional representation of the climate system 1,2, we will then present a systematic study of how different numerical methods can indeed change the resulting climate distribution. In addition to the uncertainties from initial condition, parameter and model formulation, our results suggest a fourth level of structural uncertainty in climate modelling in the numerical (or computational) implementation. This has implications to the design and interpretation of climate ensembles, suggesting that the computational formulation must be accounted as a source of uncertainty when producing climate distributions, particularly for high-end stakeholders such as decision makers. References: 1 de Melo Virssimo, F. and Stainforth, D.: A low-dimensional dynamical systems approach to climate ensemble design and interpretation, EGU General Assembly 2023, Vienna, Austria, 2428 Apr 2023, EGU23-14755, https://doi.org/10.5194/egusphere-egu23-14755, 2023. 2 de Melo Virssimo, F., Stainforth, D. A. and Brcker, J.: The evolution of a non-autonomous chaotic system under non-periodic forcing: a climate change example, Chaos, 34, 2024, http://doi.org/10.1063/5.0180870, 2024