Quantifying the uncertainty of wind energy potential from climate models is a time-consuming task and requires considerable computational resources. A statistical model trained on a small set of runs can act as a stochastic approximation of the original climate model, and can assess the uncertainty considerably faster than by resorting to the original climate model for additional runs. While Gaussian models have been widely employed as means to approximate climate simulations, the Gaussianity assumption is not suitable for winds at policy-relevant (i.e., subannual) time scales. We propose a trans-Gaussian model for monthly wind speed that relies on an autoregressive structure with a Tukey g-and-h transformation, a flexible new class that can separately model skewness and tail behavior. This temporal structure is integrated into a multi-step spectral framework that can account for global nonstationarities across land/ocean boundaries, as well as across mountain ranges. Inferences are achieved by balancing memory storage and distributed computation for a big data set of 220 million points. Once the statistical model was fitted using as few as five runs, it can generate surrogates rapidly and efficiently on a simple laptop. Furthermore, it provides uncertainty assessments very close to those obtained from all available climate simulations (40) on a monthly scale.