The Tenser's floating disk spell allows its caster to be followed around by a pretty useful force disk:

This spell creates a circular, horizontal plane of force, 3 feet in diameter and 1 inch thick, that floats 3 feet above the ground in an unoccupied space of your choice that you can see. The disk remains for the duration and can hold up to 500 pounds. If more weight is placed on it, the spell ends and everything falls to the ground.

The disk is immobile while you are within 20 feet of it. If you move more than 20 feet away, it follows you so that it remains within 20 feet. It can move across uneven terrain, up or down stairs, slopes and the like, but it can't cross an elevation change of 10 feet or more. For example, the disk can't move across a 10-foot-deep pit, nor could it leave such a pit if it was created at the bottom.

If you move more than 100 feet from the disk (typically because it can't move around an obstacle to follow you), the spell ends.

My question is: if the caster of floating disk happens to be flying in a diagonal fashion (going forward and up) above a flat ground, would the disk vertically follow him as well as horizontally ?

I have highlighted the parts relevant to the question and a possible "yes" answer:

• the description does state that the disk floats 3 feet above ground, but I think this is less a height restriction than a default state;

• it also states that the disk follows you, but does not specify that the following is exclusively horizontal;

• there is a restriction about an elevation change of 10 feet or more, but I think this is for sudden changes, like walls or holes, for instance, rather than the progressive height change of a diagonal flight (as explained above).