Hi Amy! Welcome.
I too have a 13,500 AGP, but ours is 24' round. I always put a pool pillow in the middle before covering it. Kinda guides the rain/snow/sludge a little closer to the edge. If you either have one, or are willing to invest in one (approx. $50), a small utility pump with a garden hose attachment will get most of it off. I always use my pool net to scoop out most of the sludge. Before putting my pump on the cover, I use a hairnet or filter sock to cover the pump's intake holes; keeps the remaining silt that's on the cover mostly out of the pump. When your filter gets dirty, throw it away/wash it and replace. If a spring top-off is in order, I have been known to duct-tape another hairnet over the end of the outlet hose and stuff it under the cover and let 'er rip. My pool is always very clear upon opening as well, and this "free" fill up has never yet impacted it. Normal pool opening vacuum and you're done! Hope this helps.