Level vs horizontal — which statements correctly describe level surfaces/lines and horizontal surfaces/lines in geodetic terms? Choose the most comprehensive option.

Introduction / Context:
“Level” and “horizontal” are often used casually as synonyms, but in geodesy and precise surveying they have distinct meanings tied to the Earth’s gravity field. Understanding the difference is essential when transferring elevations and when aligning instruments over significant distances.

Given Data / Assumptions:

• Direction of gravity is defined by the plumb line (local vertical).
• Level surfaces approximate equipotential surfaces of the Earth’s gravity field.
• Horizontal planes/lines are defined locally at a point.

Concept / Approach:
A level surface is everywhere perpendicular to gravity (plumb line) and thus curves with the Earth. A level line lies on this surface. A horizontal surface is a plane perpendicular to gravity at a single point; extended far from that point, it departs from the level surface due to curvature. A horizontal line is a straight line in that plane and is tangential to the level surface at the point of tangency.

Step-by-Step Solution:

Verification / Alternative check:
Precise levelling over long distances uses level lines (curved) rather than straight horizontal lines; curvature corrections exemplify this distinction.

Why Other Options Are Wrong:
Each of A–D is correct; only the combined option fully captures the relationship.

Common Pitfalls:
Assuming a horizontal plane is globally level; the “level” concept is inherently tied to the curved equipotential surface.

Final Answer:
All of the above