Yes, it is possible for a large enough enclosed area to have its own weather system. Weather is primarily driven by the interaction of various factors such as temperature, humidity, air pressure, and wind patterns. If these factors are present within an enclosed space, such as a large building, a dome, or even a planetary-scale structure like a biodome, it can give rise to localized weather phenomena.
For example, if the enclosed area has a controlled temperature and humidity, it can lead to the formation of clouds, precipitation, and even localized storms. Air circulation within the space can generate winds, and temperature gradients can create convection currents. The size and complexity of the enclosed area, as well as the availability of energy sources, can further influence the intensity and variety of the weather patterns that develop.
An excellent real-world example is the Eden Project in Cornwall, United Kingdom. It features massive biomes that house different climate zones, including rainforest and Mediterranean environments. These enclosed spaces have their own weather systems with regulated temperature, humidity, and even rainfall to mimic the conditions of the natural ecosystems they represent.
While creating a fully self-contained and sustainable weather system within an enclosed area is a significant engineering challenge, it is theoretically possible to simulate various weather conditions on a smaller scale.