Observing system simulation experiments (OSSEs) have been widely used as a cost-effective way to guide the development of new observing systems, and to evaluate the performance of new data assimilation algorithms. Nature runs (NRs), which are outputs from deterministic models, play an essential role in building OSSE systems for global atmospheric processes because they are used both to create synthetic observations at high resolution and to represent the "true" atmosphere against which forecasts are verified. However, most NRs are generated at resolutions coarser than actual observations. We propose a principled statistical downscaling framework to construct high-resolution NRs via conditional simulation from the coarse-resolution numerical model output. We use nonstationary spatial covariance function models with data-driven adaptive basis functions. This approach not only explicitly addresses the change-of-support problem but allows fast computation with large volumes of numerical model output. These techniques are demonstrated by downscaling global CO2 concentrations at 1-degree latitude by 1.25-degree longitude to high-resolution fields over 655,362 equal-area hexagons.