Multi-fidelity modeling and uncertainty quantification of heterogeneous roughness*

Operational models of the atmosphere used for decision-making, such as numerical weather prediction, cannot resolve atmosphere-surface interactions. Instead, these models use surface parameterizations that typically use deterministic estimates of required input parameters based on morphometric, geometry-based approaches. In this study, we present a method to improve lower fidelity operational models through a closed-loop workflow. We leverage geometry-resolving high-fidelity large eddy simulations (LES) to learn the uncertainties in both mid-fidelity (wall modeled LES) and low-fidelity (RANS) models that parameterize the surface roughness. We achieve this in a computationally tractable manner using a machine learning-accelerated inverse uncertainty quantification approach that reduces the required model evaluations by a thousand-fold. To enhance lower fidelity operational atmospheric models, we address two questions: (1) How can we quantify and reduce uncertainty in parameterizing heterogeneous roughness? (2) To what extent does this reduction lead to improved atmospheric predictions? Focusing on a case study in an idealized urban environment, we evaluate the predictions, with confidence intervals from uncertainty quantification, against morphometric approaches across a range of roughness geometries. Further, we investigate the impact of spatial averaging on assimilated statistics and the assimilation of turbulence statistics beyond wind speed on inversion accuracy.