Super-resolving the coarse outputs of global climate simulations, termed downscaling, is crucial in making political and social decisions on systems requiring long-term climate change projections. Existing fast super-resolution techniques, however, have yet to preserve the spatially correlated nature of climatological data, which is particularly important when we address systems with spatial expanse, such as the development of transportation infrastructure. Herein, we show an adversarial network-based machine learning enables us to correctly reconstruct the inter-regional spatial correlations in downscaling with high magnification of up to 50 while maintaining pixel-wise statistical consistency. Direct comparison with the measured meteorological data of temperature and precipitation distributions reveals that integrating climatologically important physical information improves the downscaling performance, which prompts us to call this approach piSRGAN (Physics Informed Super-Resolution Generative Adversarial Network). The proposed method has a potential application to the inter-regionally consistent assessment of the climate change impact. Additionally, we present the outcomes of another variant of the deep generative model-based downscaling approach in which the low-resolution precipitation field is substituted with the pressure field, referred to as psiSRGAN (Precipitation Source Inaccessible SRGAN). Remarkably, this method demonstrates unexpectedly good downscaling performance for the precipitation field.