Bayesian uncertainty quantification of engineering models for wind farm–atmosphere interaction

Abstract. Accurate modeling of wind-farm atmosphere interactions is critical for reliable energy yield assessments and flow control strategies. However, formal model comparison methodologies that quantify model form uncertainty by also accounting for parameter uncertainty are still lacking. This study presents an enhanced Bayesian uncertainty quantification framework for the calibration and validation of engineering wind farm flow models. Building on previous work, the framework explicitly incorporates model inadequacy through a parameterized model error distribution, enabling the separation of model and measurement uncertainties. The improved framework is demonstrated using a large-eddy simulation dataset for wind-farm blockage and atmospheric gravity waves in conventionally neutral boundary layers. Two models of differing fidelity – a standard Gaussian wake model and an atmospheric perturbation model (APM) – are calibrated and compared. The posterior distribution of the model parameters reveals insights into model behavior and highlights areas for further improvement, for instance, when estimated parameter values are inconsistent across the model chain. In addition, it is shown that not explicitly incorporating model inadequacy results in an overly confident posterior distribution, and renders derived stochastic flow models incapable of representing model uncertainty. A comparison of the quantified model uncertainty shows that the APM has significantly lower uncertainty than a standard wake model for this dataset, as the wake model is unable to represent wind-farm blockage effects. This demonstrates the utility of the framework for objective model comparison with quantified parameter and model uncertainty given a reference dataset. Both the framework and the parallelized sequential Monte Carlo algorithm for accelerated posterior sampling are made available through the open-source Python package UMBRA.