What is a word for the length of sky between directly overhead and horizon?

What is a word that is closely defined to "the vertical length of sky between directly overhead and the horizon"?

Example for definition: "The sun shown through the fog in the |between-zenith-horizon|"

It may also be defined as "the range of directions between directly overhead and the horizon."

Example for definition: "The sun shown through the fog in the |between-overhead-horizon| sky"

I would prefer one word.

You could call that range of angles the first quadrant, using quadrant in one or more of the following senses. I don't know of a more-specific term for altitudes between horizon and zenith.

1. One of the four sections made by dividing an area with two perpendicular lines.
2. (mathematics) The four regions of the Cartesian plane bounded by the x-axis and y-axis.
3. (geometry) One fourth of a circle or disc; a sector with an angle of 90°.

In sense 2, the region where both x and y are positive is quadrant 1; quadrant 2 is counterclockwise from 1; etc.

In the context “The sun shown through the fog in the |between-overhead-horizon| sky”, one might say “The sun shown through the fog in the quadrant of sky before us”.

Measuring the length of the arc wouldn't make any sense, as its length would vary depending on the distance of the arc from the observer.

You can speak of the angle of the arc as its altitude or elevation in astronomical terms, usually measured in degrees. So from the horizon to the zenith, your altitude is 90 degrees. The arc itself is a part of a meridian.

In mathematics the term appears to be polar angle, represented by φ.