I came to the same conclusion as James, put the air pump in the upper sealed section which would be under a pressure less than atmospheric due to the pull of the water column, and recycle the air in the water column.

One of the things I find interesting, and I believe common, between the two tanks is how they were filled in the first place. There are only 2 ways I can figure to fill these things:
1. Pull a vacuum at the highest point (a very strong vacuum to lift the water column) while feeding water into the lower tanks to make up for the water going into the upper ones.
2. Cap the upper tank end(s) under the lower tank water lines, fill the upper tanks with water, cap the filler hole and remove the capped ends under the water line. This is the more likely method. If this is the method, then cleaning would just be a matter of sealing the bottom, opening the top and wiping the glass. Detrius would just fall into the lower tank during normal running so cleaning the upper section should just amount to algae etc. Probably not as much of a nightmare as it looks, and the "wow" factor definitely helps offset the trouble of cleaning in a conversation piece like that.
Aaron