If you are talking about Anatolia, I don't know. If you are talking about the Forestiere Underground Gardens in Fresno, CA, there is not much to worry about. Fresno receives less than 10 inches of rain per year. Mr. Forestiere designed his excavations so that the watter drained down to the lowest level -- 3 levels down. From their web page: "Forestiere built three underground levels; the first level is about 10 feet deep, the second is about 22 feet deep, and the third is around 23 feet deep. The lower levels also act as the main drainage point for most of the underground rooms and passageways." Apparently, he had no formal training in architecture and was self taught. He designed his gardens from memory of underground structures that he knew in Italy and learned his engineering from working on subways in Boston.
Huell Howser did a thing on those gardens. Looked really cool.