  Low-fidelity wake models are used for wind farm design and control
optimization. To generalize to a wind farm model, individually-modeled wakes
are commonly superimposed using approximate superposition models. Wake models
parameterize atmospheric and wake turbulence, introducing unknown model
parameters that historically are tuned with idealized simulation or
experimental data and neglect uncertainty. We calibrate and estimate the
uncertainty of the parameters in a Gaussian wake model using Markov chain Monte
Carlo (MCMC) for various wake superposition methods. Posterior distributions of
the uncertain parameters are generated using power production data from large
eddy simulations (LES) and a utility-scale wake steering field experiment. The
posteriors for the wake expansion coefficient are sensitive to the choice of
superposition method, with relative differences in the means and standard
deviations on the order of 100%. This sensitivity illustrates the role of
superposition methods in wake modeling error. We compare these data-driven
parameter estimates to estimates derived from a standard turbulence-intensity
based model as a baseline. To assess predictive accuracy, we calibrate the
data-driven parameter estimates with a training dataset for yaw-aligned
operation. Using a Monte Carlo approach, we then generate predicted
distributions of turbine power production and evaluate against a hold-out test
dataset for yaw-misaligned operation. Compared to the deterministic predictions
of the baseline parameter estimates, we find that the MCMC-calibrated
parameters reduce the total error of the power predictions by roughly 50%. An
additional benefit of the data-driven parameter estimation is the
quantification of uncertainty, which enables physically-quantified confidence
intervals of wake model predictions.
