# Terms for aerial versus ground surface area

Are there accepted area terms that concisely distinguish aerial area (e.g., from a Google Earth satellite photo) from ground surface area? (For sloped ground, the ground surface area is larger than the aerial area; if the ground is planar then the ratio is the hypotenuse to base ratio of a triangle having a hypotenuse along the ground gradient and having as base the projection of that gradient down to the horizontal plane).

Context: My water department is asking me for a report on irrigated area as part of their California-mandated customer micro-management scheme. I have some highly sloped land (1:1) that requires a hypotenuse calculation. So my report needs to be indisputably clear which area numbers are from the satellite photo, and which area numbers are ground surface area. (Lest the water department treats the satellite photo area as the irrigated area, leading to conflict, unintentionally or otherwise).

A simple (albeit extreme) example: a 40ft tall, 50ft wide succulent wall planter placed within a section of vertical self-retaining ground (a.k.a. cliff face) has 2,000 square feet of ground surface area (and consumes water in proportion to that area) but 0 square feet of aerial area. What would be the accepted terms for these two areas?

• The report should include definition of terms. Ground area might be the area of the ground measured in the mean plane of the ground (this definition allows for the ground being rough). And you could define plan area as the area of the projection of ground area onto the horizontal plane. Even if you find conventional terms for these concepts you should include them as definitions so that there is no doubt as to meaning as used in the report. May 1, 2022 at 7:44
• @Anton Great suggestions. I will define my terms as you suggest. "ground area" and "plan area" seem like good choices, and I like your idea to define ground area in the mean plane (otherwise the whole concept of area is arbitrary - I'm pretty sure I'm not supposed to count blades of grass, microtextures thereon, etc.). May 1, 2022 at 18:42
• Thanks. It does not make an answer because an answer is to some extent a matter of opinion. I am glad to have helped. May 1, 2022 at 21:25
• I’m voting to close this question because it's obviously asking for technical terms well outside everyday English. Perhaps Mathematics.SE? Gardening and Landscaping? May 2, 2022 at 15:30
• gis.stackexchange.com would be a better home for this question May 2, 2022 at 21:03

Jeness (2004) distinguishes between "surface area" and "planimetric area". I'd also call them "3D-surface area" and "2D-surface area", respectively. Please see also citing articles and related articles in Google Scholar

If you'd like to put emphasis, you may call the former "landscape surface area", "ground surface area" or "DEM surface area" (after digital elevation model). Incidentally, "DEM" is a very useful term for narrowing the search in the GIS literature. Part of the difficulty also stems from the fact that "area" (a scalar or single number) is often used informally as a synonym of "surface region" (the surface patch bounded by a closed curve).

The latter quantity, "planimetric area" or "2D-surface area", is based on a well established term, as in "planimetric map" (Glossary of the Mapping Sciences). It can be further defined slightly different ways:

• a) plane area in tangent plane coordinates (local east and north)
• b) plane area in map projection coordinates (grid east and north)
• c) surface area on the ellipsoid (involving latitude and longitude)

"Plane area" is simply the result of the shoelace formula to 2D coordinates. Definition (a) is a crude approximation, accurate only for very small areas; it may be called "tangent area" or "normal area". Definitions (b) and (c) are supposed to agree for an equal-area map projection. Definition (c) follows may be called "geodetic area" or "ellipsoidal area" and in general involves "ellipsoidal polygons" allowing meridians, parallels, and other rhumb lines as polygon sides; alternatively, it can be restricted to "geodesic polygons" delimited only by geodesic lines; see geod for details.

• May 1, 2022 at 21:29
• Indeed, "3D area" seems fairly popular. For example this paper talks about the "surface area ratio" A_3D/A_2D (by "_" I mean subscript). An abstract geometrist might complain that all area is 2D, but I think most people would understand that 3D means you're talking about a surface embedded in 3D, whose practical area calculation uses 3D. May 2, 2022 at 19:40

In Google Earth's Ruler, there is "Map Length" and "Ground Length". By extension one might assume there is "map area" and "ground area".