I asked a similar question and I am not aware of any tile server to support a time dimension.

The best solution I came up with, was to have different layers with the time dimension, see our demo version.

Weather.com seems to have a similar approach as you can see in their tile ulrs (with a timestamp in the folder/layer structure):

http://tiles.weather.com/201212/en-US/0009/0001/Pi5CSuQ6xoV0MVoQ/0040/0/20160111061500/1/5/8/18/layer.png

I asked a similar question and I am not aware of any tile server to support a time dimension.

The best solution I came up with, was to have different layers with the time dimension, see our demo version.

Weather.com seems to have a similar approach as you can see in their tile ulrs (with a timestamp in the folder/layer structure):

http://tiles.weather.com/201212/en-US/0009/0001/Pi5CSuQ6xoV0MVoQ/0040/0/20160111061500/1/5/8/18/layer.png