Quantum machine learning-based parametrization for boundary layer turbulence

In light of the urgent need to accelerate measures for the adaptation to and mitigation of climate change, accurate Earth system models are more important than ever, for technology assessment and the identification of the most effective climate protection strategies. Global climate models have successfully projected consequences of different future scenarios, but the spread in projections remains large, with subgrid-scale parametrizations being the main origin of these uncertainties. Recently, machine learning-based hybrid models have successfully enhanced parametrizations - their directly data-driven structure can more effectively capture the empirical aspects of the parametrizations. Especially for the more complex parametrizations, such as microphysics or turbulence, which we study here, quantum computing could bring decisive further improvements as a part of hybrid models. Atmospheric turbulence strongly affects weather and climate because it determines the rates of exchange of heat, moisture, and momentum between the earth surface and the atmosphere. However, due to the chaotic nature of turbulence and the wide range of turbulent regimes in the atmospheric boundary layer from deep convection to nearly laminar stable conditions, it is notoriously hard to predict and model.
Here, we develop a prototype of a quantum machine learning-based subgrid-scale parametrization for the vertical temperature flux caused by atmospheric turbulence based on semi-idealized Large-Eddy-Simulations. We run experiments with dry convective boundary layers with the PALM model system. The setups span an 8x8 km² domain with a resolution of 10 m and horizontal periodic boundary conditions and an imposed surface heat flux, combining runs with different surface heat fluxes and geostrophic winds in our training data set. We train quantum and classical neural networks with different architectures, and find that quantum models based on parametrized circuits with just 2 or 3 qubits achieve accuracies similar to classical models with the same number of trainable parameters, highlighting the possibility to use quantum computing for parametrizations in the near future. In contrast, the Smagorinsky closure deviates strongly from the true flux in this setup. Our quantum and classical cell-based models both generalize well to data from PALM runs with unseen parameters close to the seen range. We further analyze the feature importance in quantum and classical models and find that most of our quantum models show better stability of the Shapley values with respect to varying the random initial conditions of the training runs. Since the number of required qubits to capture the idealized setting is low, it is promising to extend our model to more complex settings with realistic topography and varied weather conditions in the future, e.g. by using ICON boundary conditions in PALM, opening the possibility to exploit quantum advantages anticipated by the more stable interpretability of our prototype models.