In gridded combat, how many squares/cubes above ground can the caster of Earth Tremor be in order to affect the ground?

Question

Our campaign uses the optional Using Miniatures rules (Dungeon Master's Guide Ch. 8) and the variant Playing on a Grid rules (Player's Handbook Ch. 9). If a spellcaster is not on the ground (due to Fly, a fly speed, levitation, etc.), what is the vertical square furthest from the ground that a creature/character can occupy while casting Earth Tremor and still affect the ground to cause damage to creatures beneath them?

The relevant part of Earth Tremor (Xanathar's Guide to Everything Ch. 3) is represented here for convenience:

Range: 10 feet
You cause a tremor in the ground within range. [...]

In case it helps discussion, consider the following to be a visual representation of a vertical slice of the map. The ground level 5-foot cube (where a goblin might stand) is represented as G, with the 5-foot cube above that being represented as 2 and so forth (as in European storey numbering). Could the caster affect the ground with Earth Tremor if they occupy a cube on level 3, or must they be as low as 2 (and why)?

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Answer 1

The range is 10 feet

Range is not changed by grid combat. Whether you use a grid or not, if the spell or effect has a range of 10 feet, it has a range of 10 feet. The only difference with a grid is that you target the corner of a square with the spell, but it still needs to be in range. Here is how grids change how you can place the area of effect (DMG p. 251):

The area of effect of a spell, monster ability, or other feature must be translated onto squares or hexes to determine which potential targets are in the area and which aren't. Choose an intersection of squares or hexes as the point of origin of an area of effect, then follow its rules as normal. If an area of effect is circular and covers at least half a square, it affects that square.

So here, you only an affect the ground within 10 feet or yourself. If there is no ground within 10 feet, you cannot affect it. If you fly higher, you cannot affect the ground. The game has pretty iffy consideration of vertical space in combat, but this is not one of the ambiguous cases.

How many squares do you affect?

You affect the ground in within a range of 10 feet , which will be measured from yourself (or around a corner of your square).

You can use the math approach of this answer to calculate how many squares are affected. Since the area of effect here is circular around a corner of your square, you calculate the intersection of the sphere around that point with the grid on the floor depending on your height, and each square that is covered by more than 50% is affected.

Since the floor is only touched at a single point if you are 10 foot up, that will affect no squares. If you are 0 feet up, it will affect the normal radius. So we really only need to calculate what squares are affected if you are 5 feet up.

Here (other than in the schematic depiction above to illustrate the idea) h is 5 feet, and r is 10 feet, so r' is $$ r' = \sqrt{r^2 - h^2} = r' = \sqrt{10^2 - 5^2} \approx 8.66 $$

Generally, if the center of a square is within range, more than half of the square will be covered - it is not quite exact but easier check (you can use the detail math in the linked answer if you want to know exactly). Here are the approximate distances in feet of the centerpoint of each square around the corner directly underneath you:

From this you can see that both for the green area, and for the yellow ara, the center points are well under the range for r' = 8.66, and all of these areas would be affected if you are five feet up. That incidentally is the same area, as if you were on the ground (because then, you have the full 10 feet radius around the corner, but the red square centers are a good bit further out than 10 feet, so those squares are still not affected).

So, you affect the same plus-shaped area if you are on level G or 2, and no area if you are on level 3 or 4.

(This assumes that the grid has the same dimensions vertically, i.e. each level is 5 feet high, so one on level G is at 0 feet, on level 2 at 5 feet, on level 3 at 10 feet and on level 4 at 15 feet above ground with the space they fly in. This is however not required to work this out. You just need to decide how high above the ground the caster is, i.e. where the spot to center the 10 feet radius is).

Answer 2

DM's decision

There are no explicit rules for verticality as far as I know of. But what we do have:

1. Pure geometry: 5-foot cubes are 5 foot high.
2. The origin of a spell can usually be chosen from the four corners of a tile (2D), so we could say in 3D that the origin can be chosen from the eight corners of a cube.
3. A spell effects a certain space if at least 50% of its space is within the range of the spell - but there are different rules out there.

According to this, the caster of a spell with a range of 10 ft. must be in the 'floor' designated by you with 3 - or lower.

Of course, one can argue that the space a medium sized, bi-pedal creature controls is higher than 5 ft. But, as said in the beginning, there are no rules for verticality.