The word aerial has long been in common usage as an adjective to describe things having to do with the sky and atmosphere. Although documented in English as early as the 1670s, the word areal is fairly new in popular usage. The first time I encountered it, my misspelling detector tingled, but I soon realized that it could have nothing to do with the air because it was being used to describe such things as computer memory and flooding.
Aerial has to do with air, but areal has to do with area.
aerial: adj. relating to the air or atmosphere. From Latin aerius “airy,” from Greek aerios “of the air.” As a noun, an aerial is a wire, rod or other structure by which airborne radio waves are transmitted or received.
Aerial View of Oil Leak Shows Size
Branching of Aerial Roots in Aranda Orchids
Air Power: World War I Aerial Combat
areal: adj. of, pertaining to, or of the nature of, an area. Linguistics: of, pertaining, or relating to the comparative study of languages or dialects in terms of geographical distribution and contact rather than historical development.
Areal Flood Watch in Force
Effects of pulse duration and areal density on ultrathin foil acceleration
Evidentials and Areal Typology: A Case Study from Amazonia
In computer speak, “areal density” is defined by PC Magazine as
The number of bits per square inch of storage surface. It typically refers to disk drives, where the number of bits per inch (bpi) times the number of tracks per inch (tpi) yields the areal density.
In meteorology, “areal flooding” differs from “flash flooding’ in that it covers a larger area and is of longer duration.
Like aerial, the name Ariel is related to air. An early meaning of the noun aerial was “a creature or spirit of the air.” The 1800 reference in the OED tells us that some aerials have feathers, like pigeons, and others have wings of skin, like bats.
Long before the 1989 Disney movie in which Ariel is the name of a mermaid, writers were using the name for supernatural creatures. The sprite in Shakespeare’s The Tempest is named Ariel. Milton made his Ariel into an evil angel. Alexander Pope’s mock epic The Rape of the Lock is narrated by a playful spirit named Ariel. For a very long list of real people, places, and fictional characters all named Ariel, see the Wikipedia article with the title “Ariel.”