Ah, this one works.
So yes, much of what you're seeing is related to low AA. In general we recommend "power of 2" values for AA, so 6 or 8. 7 can be OK to try, but I think you may need 8 to really get rid of the noise. If you're using Soft Shadows, I also noticed that some of the noise may be coming from that, so you'd need to increase the samples there, again increasing render time unfortunately. Finally, in the bottom left I also see a shadow changing, which is due to out-of-frame geometry simplification that improves render speed. Unless your animation will eventually show the terrain that is out of camera and casting that shadow (or maybe it's a cloud?), I would try to eliminate it (the terrain). If you do need to keep it, then you'll need to use Ray Detail Region Padding in the Renderer node to get rid of that popping shadow. Probably a detail of 0.5 will work, but you can try up to a value of 1. This too will increase render time.
The simple reality is that rendering an animation, *especially* one with water in it, may not be very practical on a single home computer. That's true for almost any 3D software though, at least for scenes of this scale and complexity (with water, thousands of 3D model instances, atmosphere, etc.). You might check out Pixel Plow for render farm services. They're quite affordable. Do a project on low priority and you could spend no more than $20 or so to get your entire animation rendered, and much faster than you could do yourself:
http://www.pixelplow.net/- Oshyan
