Parameter uncertainty quantification of wake models to analyze effects of wake superposition

Low-fidelity wake models are used for control of wind turbines and layout optimization for wind farms. Wake models contain parameters that are tuned with experimental data, but their uncertainty is often neglected. We estimate the parameter uncertainty of a Gaussian wake model using Markov-chain Monte Carlo, and we consider the effects of different superposition methods and atmospheric stability. Posterior distributions of the uncertain parameters are generated using data from large eddy simulations and physically-constrained Gaussian priors. Then, Monte Carlo wake model predictions are generated using samples from the posterior distributions. The results show that the mean and variance of the wake expansion coefficient tend to increase in the downstream region of a wind farm. The posteriors for the wake expansion coefficient are sensitive to the choice of superposition method: four of the five superposition methods under consideration demonstrated this trend, but a sum-of-squares method was an outlier. Furthermore, we examine the influence of atmospheric stability on the posterior distribution of wake model parameters. Quantifying the uncertainty of wake model parameters enables the uncertainty quantification of wake model predictions, such as annual energy production.