High-resolution meteorological fields are essential for assessing local climate change impacts. In recent years, deep learning (DL) downscaling techniques have shown increasing potential in emulating dynamical downscaling, with advanced techniques capable of reconstructing fine-scale features and flow characteristics. These methods offer substantial computational advantages over numerical approaches, making them a viable, sustainable option, especially for applications to climate projections, which are usually coarse, long term, and scenario rich. However, despite these successes and advantages, the spatio-temporal physical consistency of DL-downscaled fields remains underexplored. This PhD research will investigate the consistency of high-resolution downscaled climate data (e.g. temperature, wind, precipitation) through theoretical and empirical approaches, enhancing credibility and enabling broader applications of DL-based approaches in climate science.