Environmental processes can exhibit non-stationary properties due to prevailing weather patterns that propagate in a particular direction. Such processes are challenging to model, and computationally expensive when the size of space-time observations is large. An alternative is to fit a simpler local-stationary-model to disjoint subsets of the data, or "regions" of the area-of-interest. Choosing the size of the regions requires a trade-off between larger regions for accuracy in parameter estimation and smaller regions for approximating the local non-stationarity. In this work, we devise a three-step approach which allows for smaller regions that are computationally cheap without compromising much the parameter estimates. In the first step, we estimate stationary models for each region. In the second step, we improve the parameter estimates by borrowing strength from neighboring regions. In the third step, we refit the models to each region, accounting for the posterior uncertainty of the parameters in each region. We apply the proposed method on simulated high-resolution wind speed data and demonstrate improvements in predictions after accounting for non-stationarity.