Linear diaphragm type pumps are one of the most energy efficient
at shallow depths. They might be suitable for a situation where energy requirements are at a premium.
Problem is, they put out loads of air (for the energy used) at 5 feet, a fair amount at 10 feet, and pretty much stall out with no air at around 11 or 12 feet. Their output is very sensitive to back pressure (I.E. water head pressure or in other words water depth).
They also would not likely have the lifespan of a higher end compressor.
Their strengths are 1. relatively low initial cost and 2. a lot of cfm for the energy used when operated within their design capabilities.
Their weaknesses are likely shorter overall life and likely will require a diaphragm kit maintenance every year or two (about $20 for my particular pump model). And they simply do not work at greater depths.
I'm running four Pondmaster AP100's. Three of them are each supplying a dual 9" diffuser in my 3 acre pond, all set at about 9'. I should be getting somewhere between 2 and 2.5 cfm each at that 9'depth (Edit: the chart actually shows about 3 cfm at that depth, but I always try to be conservative in my estimations, because I figure the companies selling the product might not be and they might not live up to advertised specs. Also, I'm using specs from a similar pump, not my actual pump model). The fourth pump is split between two single 9" diffusers, one in my sediment pond (half of a tenth acre) and one in my forage pond, both around 7-8' depth. I use a splitter valve to direct more air to the sediment pond because it is the larger of the two (about 1/10th acre).
I don't have a lot of experience with these pumps. They have been running about 3 months straight with no problems, but that is not much evidence as to what their eventual life will be. They may not last well enough in the long term. But they are working very well for the time being, and I like the fact that I can reduce my electricity requirements at any time by one fourth by simply shutting one of the four pumps off. This gives me a lot of flexibility as far as energy requirement goes.
Each pump is putting out the 2-2.5 cfm (at my particular depth, less deeper and more shallower) for a rated 108 watts. Just slightly more than a 100 watt light bulb. I don't think there is any other type of pump that can touch that for energy efficiency
at shallow depths.
Most people would not want to use these type pumps, because of their questionable service life and the hassle of needing to be rebuilt regularly. I mention it to you because of their energy efficiency, which might fit well in a solar application.
Here is an earlier post with a performance curve for a similar pump. Unfortunately the pump I am actually using does not supply a performance curve, but I think this one should be very similar. Notice how the output drops with depth. I would not recommend their use for anything over 10' at the most. I'm getting very strong boils of water with mine at 9'.
Pressure calculation thread If you could live with diffusers at 10' depth in might be a possibility for a pump that uses little energy for the output it produces. I'm not an expert by any means and have only limited experience with these pumps, so use anything I say at your own risk and do your own due diligence.
Edit: the Pondmaster AP100 mfg recommends a maximum operating depth of 11 ft. It might be fine at that depth, but I've tried to do everything with a margin of safety/error to make sure it works ok and has reasonable service life.