BillD's pump house is a good idea. One can simplify it by down sizing it and using just a hinged slant roof instead of the A frame roof. Actually BillD would not need to have a separate cover for the compressor. The compressor could easily operate in the open sitting inside the pump house. Set the pump on an piece of foam rug padding to help dampen the sound.
I also built a similar smaller pump house of the ground out of a large plastic dog house. Lid lifts off for access. Added screening on the bottom and louvered house vents near the roofline. Screened the dog entry way to keep the insects out.
+1 to what Bill C. said. Definitely can downsize. I went oversize to provide some minimal storage at the pond and have room should I want to put any other equipment in the house in the future. I keep the cover on the pump during times of high pollen or when farmers are working the fields as it has a cleanable filter built in that traps alot of the stuff before it gets to the paper filter at the compressor inlet. Those little paper filters are expensive (The manufacturer of my system has several bells and whistles, like special air filter cartridges, that you can only get from them.). I need to modify that area and adapt a cheaper lawn mower type paper filter assembly to the inlet.
Anybody know someone that sells filter adapter kits for compressors? The compressor is essentially a 1/3 HP Gast rocking piston.