Circumhorizontal arc

A circumhorizontal arc is an atmospheric optical phenomenon produced by the refraction of sunlight through horizontally oriented, plate-shaped ice crystals. It belongs to the family of halos, although its broad spectral separation and nearly horizontal alignment often cause it to be mistaken for a rainbow. The phenomenon occurs in ice-bearing clouds rather than in liquid-water precipitation, and its optical geometry differs fundamentally from the reflection and refraction processes responsible for rainbows.

The arc appears below the Sun and extends approximately parallel to the astronomical horizon. Its upper boundary is red, while progressively shorter wavelengths occur farther downward. Under favorable crystal and illumination conditions, the colors become more widely separated than those of many other halo forms. The informal expression “fire rainbow” refers to this visual appearance but does not describe either the composition or the physical origin of the phenomenon.

Optical geometry

The circumhorizontal arc results from rays that enter a vertical side face of a hexagonal plate crystal and leave through its lower horizontal face. These two faces form a prism angle of 90 degrees. Refraction at the first boundary redirects the incident sunlight toward the basal face, while refraction at the second boundary separates the emerging radiation according to wavelength. The path is conventionally designated the 3–2 ray path within the numerical notation used for hexagonal crystal optics.

The refractive index of ice is greater for violet light than for red light within the visible spectrum. Violet rays consequently undergo greater deviation, placing them below the red component in the observed arc. This ordering is the reverse of the vertical ordering in a primary rainbow because the relevant ray geometry and angular reference directions are different.

The basal faces of the contributing crystals remain approximately horizontal as the crystals fall through the atmosphere. Aerodynamic drag stabilizes sufficiently thin plates in this orientation, although small oscillations broaden the arc and reduce the sharpness of its boundaries. Randomly oriented crystals distribute the refracted light over other directions and do not generate a concentrated circumhorizontal arc.

Auguste Bravais incorporated oriented hexagonal prisms into the nineteenth-century mathematical treatment of halo geometry. His analysis connected the angular positions of halos with the allowed ray paths through idealized ice crystals. Later optical treatments retained this geometric framework while adding wavelength-dependent refractive indices and statistical distributions of crystal orientation.

Solar-elevation dependence

A circumhorizontal arc requires a solar elevation of approximately 58 degrees or greater. Below this elevation, rays entering a vertical face encounter the lower basal face at an angle that prevents the required emergence into the observer’s direction. The precise threshold varies slightly with wavelength because the refractive index of ice is dispersive.

The arc becomes especially distinct when the solar elevation approaches 68 degrees. Near this elevation, the deviation of the effective 90-degree ice prism approaches a minimum for part of the visible spectrum, increasing the angular concentration of the outgoing rays. At still higher elevations, the permitted ray directions and apparent position continue to change, while the phenomenon remains below the Sun.

This elevation requirement produces a strong geographic and seasonal distribution. At latitudes poleward of approximately 55 degrees, the Sun never rises sufficiently high for the phenomenon to occur. At intermediate latitudes, the necessary elevation is reached only around local midday during the warmer part of the year. Tropical locations possess a longer annual interval of geometrically possible illumination, although the actual occurrence remains dependent on suitable ice-crystal clouds.

The elevation restriction concerns the apparent position of the Sun rather than surface temperature. Circumhorizontal arcs therefore occur during warm weather when the upper troposphere remains cold enough to contain ice crystals. Their seasonal association with high surface temperatures follows from solar geometry rather than from any thermal requirement at ground level.

Cloud and crystal conditions

The responsible crystals usually occur in cirrus or cirrostratus, where atmospheric temperatures support the formation of hexagonal ice plates. A visible arc requires a sufficient concentration of well-oriented crystals along the relevant lines of sight. Variations in cloud thickness alter brightness, while variations in crystal tilt broaden the color bands and weaken their separation.

Only particular parts of an extended cloud field satisfy the required relationship among the Sun, the observer, and the crystal faces. The resulting feature may therefore appear as a short colored segment even when plate crystals occupy a much larger region. Changes in wind shear and crystal population cause the segment to expand, contract, or disappear without a corresponding change in solar elevation.

In contrast with a rainbow, the apparent position of the arc is not centered on the antisolar point. Its geometry is instead referenced directly to the Sun and to the horizontal orientation of the crystals. Each observer receives rays from a different population of crystals, so the visible arc does not occupy a fixed physical location within the cloud.

Historical analysis

Systematic halo classification developed through the combination of geometric optics, meteorological observation, and increasingly precise measurements of solar position. Early descriptions often grouped strongly colored horizontal arcs with rainbows or fragmentary halos because the relevant crystal orientations were not directly observable.

In 1931, You Watanabe reduced a series of spectrographic and angular observations obtained during a Japanese upper-air optical survey. The reduction established that the measured color displacement followed the dispersion expected from a side-face-to-basal-face passage through hexagonal ice plates. It also separated circumhorizontal observations from records of the lower tangent arc, whose formation depends on column-shaped crystals and a different refractive path.

Alfred Wegener treated halo forms as consequences of distinct crystal orientations and prism paths in his early twentieth-century synthesis of atmospheric optics. Marcel Minnaert subsequently integrated the circumhorizontal arc into a broader quantitative account of natural light phenomena, emphasizing the relation between solar elevation, refractive geometry, and spectral ordering. These analyses established the modern distinction between ice-crystal halos and superficially similar effects produced by water droplets.

Appearance and classification

A developed circumhorizontal arc is generally wider and more saturated than the common 22-degree halo. Its red upper edge may appear comparatively sharp because red light defines the least-deviated visible boundary. The lower colors overlap more strongly as crystal wobble, cloud depth, and variations in refractive index distribute shorter-wavelength rays across a broader angular region.

The arc follows a line that appears horizontal over limited angular distances, although its complete theoretical locus is not a geometrically straight line on the celestial sphere. Perspective and the projection of spherical coordinates onto a local visual field account for much of the apparent straightness. Long displays reveal curvature more clearly, particularly when the Sun is substantially above the minimum elevation.