If it is anthracite, I assume it is a dual media filter. You need to work out the bed expansion for all the types of media during the backwash, or the re-grade wash if you are doing one. Once you have the bed expansion, assuming you have a reasonably low weir loading rate, 100mm-150mm above the top of the expanded bed should be alright.
4'6" sounds a little on the high side. Sand filters expand about 30% bed of depth and anthracite filters expand about 40% of bed depth at maximum backwash rates.
Anthracite filters would need a minimum freeboard of approximately 50% anthracite bed depth.
