Accelerated Bayesian Calibration and Uncertainty Quantification of RANS Turbulence Model Parameters for Stratified Atmospheric Boundary Layer Flows

Abstract In operational weather models, the effects of turbulence in the atmospheric boundary layer (ABL) on the resolved flow are modeled using turbulence parameterizations. These parameterizations typically use a predetermined set of model parameters that are tuned to limited data from canonical flows. Using these fixed parameters results in deterministic predictions that neglect uncertainty in the unresolved turbulence processes. In this study, we perform a machine learning-accelerated Bayesian inversion of a single-column model of the ABL. This approach is used to calibrate and quantify uncertainty in model parameters of Reynolds-averaged Navier–Stokes turbulence models. To verify the data-driven uncertainty quantification methodology, we test in an idealized setup in which a prescribed but unobserved set of parameters is learned from noisy approximations of the model output. Following this verification, we learn the parameters and their uncertainties in two different turbulence models conditioned on scale-resolving large-eddy simulation data over a range of ABL stabilities. We show how Bayesian inversion of a numerical model improves flow predictions by investigating the underlying mean momentum budgets. Further, we show that uncertainty quantification based on neutral ABL surface layer data recovers the relationships between parameters that have been predicted using theoretical modeling, but that learning the parameters based on stable ABL data or data from outside the surface layer can lead to different parameter relationships than neutral surface layer theory. Efforts to systematically reduce parameter uncertainty reveal that (1) sampling wind speed up to the ABL height can reduce uncertainty in key model parameters by up to $$84\%$$ , and (2) assimilating fluid flow quantities beyond first-order moment statistics can further reduce uncertainty in ways that baseline wind speed assimilation alone cannot achieve. The parameters learned using Bayesian uncertainty quantification generally yield lower error than standard deterministic parameters in out-of-sample tests and also provide uncertainty intervals on predictions.