Should ADS-B airborne and surface squitter transponder registers both be updated regards air/ground status? ADS-B have two position squitters, airborne and surface. As far as i know, airborne position is broadcasted on air and surface position broadcasted on ground.

There is a "Squitter Capability Subfield" in BDS Register 10, which needs to be set if both airborne and surface position registers are updated within last 10 seconds. This kinda implies both registers shall be updated all the times.

Is providing data for both squitters necessary regardless of aircraft's vertical status? Can we select one of these squitters and provide data only for it?
I don't have the 1090ES MOPS at hand here, but it makes sense to me that both should be updated. 

At the moment that the registers are updated, it is not necessarily clear whether an airborne or a surface squitter will be transmitted next. In the period between update of the register and transmission of its contents, the vertical status of the aircraft can change.