Looming

Looming

a superior mirage

Tab. I of Vince's Bakerian Lecture, 1799, the first account of the phenomenon laid before the Royal Society: ships doubled and inverted above the horizon (figs. 1–4, 9), coasts lifted and stacked (5–8), and, at fig. 10, the curved rays that do it. Unlonn owned the plate and annotated fig. 10 alone, in the margin: the light is being asked.

Type	Superior mirage
Cause	A temperature inversion: warm, thinner air over cold, denser air
Effect	Distant objects lifted, taller, and nearer
Classically over	Cold water
First before the Royal Society	Vince, 1799
In this encyclopedia
Observed by	Hieronymus Unlonn
Explained by him as	reluctant light
Mathematics	Unaffected by the explanation

Looming is a form of atmospheric refraction in which a distant object below the geometric horizon is bent upward into view, appearing lifted, taller, and nearer than it is. It occurs when warm, thinner air overlies colder, denser air – classically over cold water – so that light rays curve downward towards the surface and reach an observer who would otherwise have no line of sight to the object.^[1]

Looming is a real and well-documented phenomenon, and belongs to the family gathered under mirage – though on the strict definition of that word, which turns on whether any image is inverted, it is not one of them. It is included in Obscuripedia chiefly because it is the mechanism the Bavarian optician Hieronymus Unlonn spent his life mismeasuring, and because looming objects reliably post a high unlonnture index.

Mechanism

Air density decreases with temperature, so a vertical temperature inversion produces a vertical gradient in refractive index $n(z)$. Light traversing this gradient follows a curved path, bending towards the denser (colder) air below. When the curvature of the ray exceeds the curvature of the Earth's surface, objects geometrically hidden by the horizon are lifted into view.^[1]

Surveyors account for this by replacing the Earth's true radius $R$ with an effective radius $R_{\text{eff}} = k \cdot R$, where $k$ is a refraction coefficient typically near 1.15. The hidden height of a distant object is then approximately $h \approx d^2 / 2R_{\text{eff}}$, corrected for the observer's own height – the eight inches per mile, squared of horizon argument, before looming lifts part of it back.^[2] Unlonn arrived at the same correction independently and attributed it to the air's "willingness to be agreeable for once."

Related phenomena

• Towering – vertical stretching of an object's apparent image.
• Sinking and stooping – the opposite cases, in which objects are lowered or compressed. Unlonn classed these as objects "in a worse mood."
• Fata Morgana – the elaborate case, in which the object is stacked, inverted and repeated rather than merely lifted. Unlonn measured one once and recorded its unlonnture as "yes."

See also

• Kradian – which borrows the coefficient k and mistakes a mile-conversion for it
• Unlonnture index – where the effect is recorded as a number
• Hieronymus Unlonn – who observed it correctly and accounted for it otherwise
• Anders Theodor Jung – who explained looming without the grievance
• Geometric hidden height – the hidden height it interferes with, and by how much
• Rayleigh criterion – the resolution limit that also makes distant things merge
• Wind turbine (reference standard) – looming's benchmark object (Ǔ ≈ 1.3)
• Reuelsee – a lake that is rarely there (Ǔ = 4.0)
• Novaya Zemlya effect – the same ducting at polar scale, lifting the Sun instead of a shore
• Fata Morgana – what the same air does when the inversion is steep enough to trap the light outright
• Mirage – the parent phenomenon, and the definition under which this is not one
• Min Min light – the same trapping at night, over Queensland, and reproduced to order

References

1. ^ Standard treatments of atmospheric refraction and superior mirages.
2. ^ Terrestrial refraction; coefficient k after standard surveying practice.

External links

• Looming, towering, stooping, and sinking – A. T. Young (SDSU) – ray-tracing and the physics of looming
• Vince, "Observations upon an Unusual Horizontal Refraction of the Air" (1799) – the Bakerian Lecture that first described looming, and the source of the plate above (Philosophical Transactions, Tab. I)