Hi,
We had an inground pool growing up, and we used chlorine for years. Unless you dump the water out after each use, you will have algae. Water will grow algae unless treated with chemicals. Even our pool, with pump and filter running would grow green stuff without the chlorine.You MIGHT, find that you could use GSE...but that would take a lot, and cost way more than chemicals. I have used it in animals water dishes, and it does cut down on the algae growth.