Estimating cloud particle size using the moon

1. Estimating cloud particle size usingthe moon Robin Hogan

2. What causes the coloured rings around the moon? • Huygens’ principle states that any part of a “wave front” can be treated as its own source of spherical waves. • This predicts that light (and many other types of wave) will diffract around an obstacle (e.g. cloud particles) A “wave front”: Maxwell’s interpretation of this is the point of maximum electric field Direction of incidence of electromagnetic radiation

3. Superposition principle • From this we deduce that • The scattering amplitude of the obstacle (NOT including unscattered radiation) is the negative of the scattering amplitude from the equivalent hole • But intensity = amplitude squared! • Babinet’s principle: the pattern of scattered intensity from an obstacle is the same as that from the equivalent hole + = Scattering amplitude from an obstacle (including unscattered radiation) Scattering amplitude from the equivalent hole Original plane wave

4. Fraunhofer diffraction The first Bessel function in WCD! • The scattering pattern from a hole is easier to calculate than a particle • The first minimum occurs when light from opposite sides of hole destructively interferes • Occurs when the distance travelled differs by half a wavelength • The scattering pattern will be broader for • Smaller holes (i.e. particles with smaller radius r) • Longer wavelengths l

5. What about the colours? • Red light has a longer wavelength, so forms a broader pattern and the characteristic red ring Ring radius 2° -> particle radius r=9 mm Ring radius 3.5° -> particle radius r=5 mm Ring radius 7° -> particle radius r=2.5 mm • For reference, note that the sun and moon both have an angular diameter in the sky of 0.5° • The effect is known variously as • Corona • Aureole • Iridescence

6. How well do the predicted colours match the observations? Droplets must be nearly all the same size so that the colours don’t wash out

7. Estimating particle size Diameter of moon: 0.5° Radius of red-ring: 3° Droplet diameter: 4.3 mm Ice crystals are larger so produce a smaller aureole

8. Examples with the sun

9. Bishop’s ring • Produced by stratospheric aerosol, usually from a volcano • First exact description of the associated corona was after the Krakatoa volcano on August 27, 1883 • Sereno Bishop observed it on September 5, 1883 in Honolulu: • Let me draw your special attention to the very strange corona or halo that extends about 20 to 30 degrees away from the sun. It could be seen here every day, and the whole day long. A whitish veil with a shade of pink and violet or purple shadow in front of the blue background. I don‘t know any other report on such a corona. It is a hardly remarkable object. • This corresponds to particles of around 1-2 micron in size “The Scream” (Munch 1893) shows Krakatoa-induced red skies?

10. Bishop’s ring after Pinatubo in 1991 • Photo taken in Finland in May 1992

12. Texas aureole from Saharan dust?