Nora - I see these little guys resting on daylilies quite a bit during the summer, and have taken a number of photos of them over the years. And I've noted that they tend to hang around in one area for days sometimes. I'd come back and see them day after day in the same planting. And have you heard them sing? They have a voice that is amazingly loud - the first time I ever heard one, I thought it was some new kind of bird and had to track it down. I was floored to see that sound was coming from a little green frog!
The ones we have around here are more of a browny- green, but you are right - they have an amazingly loud voice.
Not too many are around here - it is very dry.