coronas and iridescence in mountain wave cloudscoronas and iridescence in mountain wave clouds...

Coronas and iridescence in mountain wave clouds

Joseph A. Shaw and Paul J. Neiman

We use Fraunhofer diffraction theory and meterological data to determine the nature of cloud-particledistributions and the mean particle sizes required for interpreting photographs of coronas and iridescencein mountain wave clouds. Traditional descriptions of coronas and iridescence usually explain theseoptical phenomena as diffraction by droplets of liquid water. Our analysis shows that the photographeddisplays have mean particle sizes from 7.6 to 24.3 �m, with over half the cases requiring diffraction bysmall ��20 �m� quasispherical ice particles rather than liquid water droplets. Previous documentationof coronas produced by ice particles are limited to observations in cirrus clouds that appear to be composedof small ice crystals, whereas our observations suggest that coronas and iridescence quite often can becreated by tiny quasispherical ice particles that might be unique to mountain wave clouds. Further-more, we see that the dominant colors in mountain wave-cloud coronas are red and blue, rather than thetraditionally described red and green. © 2003 Optical Society of America

OCIS codes: 010.1290, 010.1310, 010.3920.

1. Introduction

When light from the Sun or the Moon passes throughan optically thin cloud, scattering toward the forwarddirection can produce spectacular displays of color.Coronas and iridescence are two closely related col-orful displays that can result from scattering inclouds.1–7 A corona exhibits concentric colored ringsaround the light source, which range from blue orgreen on the inside to red on the outside. Irides-cence is a more random, swirling patchwork of colors.The size, shape, and color purity of either displaydepend on the cloud particle size and distribution andon the optical thickness of the cloud. Generally thecolors are of a pastel nature, with low purity, becauseof the high content of white light combined with thediffracted colors. These optical phenomena usuallyexist over an angular range of only several degreesaround the light source, so they can be explained andanalyzed by use of Fraunhofer diffraction theory.Circular �or quasi-circular� coronas with concentriccolored rings centered on the light source are partic-ularly amenable to this analysis. Coronas exhibit

J. A. Shaw �[email protected]� is with the Department ofElectrical and Computer Engineering, Montana State University,Bozeman, Montana 59717. P. J. Neiman is with the National Oce-anic and Atmospheric Administration Environmental TechnologyLaboratory, 325 Broadway, Boulder, Colorado 80305.

Received 29 January 2002; revised manuscript received 29 April2002.

0003-6935�03�030476-10$15.00�0© 2003 Optical Society of America

476 APPLIED OPTICS � Vol. 42, No. 3 � 20 January 2003

the traditional Fraunhofer diffraction inverse rela-tionship between cloud particle size and corona-ringdiameter. There is no similarly simple relationshipthat can be used to predict or analyze the randomswirling patterns of iridescent clouds.

Mie scattering analysis by Lock and Yang3 sug-gests that multiple-ring coronas can be visible whenthe cloud particle-size distribution is narrow and uni-form throughout the cloud within several degrees ofthe light source, with a mean particle size of less than�25 �m. A more random, swirling pattern of irides-cence results when the mean particle size varieswithin the cloud region near the source or when themean particle size is particularly small. Lock andYang3 used their scattering model for spherical waterdroplets to analyze corona photographs and foundexamples of visible multiple-ring coronas created bymean cloud-particle diameters within a narrow rangeof approximately 6.5–15 �m. Because their scatter-ing model predicted multiple-ring coronas with meancloud particles as large as 25 �m, while their photo-graphic analysis inferred drop sizes not exceeding 15�m, they wondered if perhaps these larger drop sizeswere accompanied by a broadening of the drop-sizedistribution or an increase in multiple scattering, de-stroying the visibility of multiple-ring coronas. Forparticles smaller than their 6.5-�m lower limit, theiranalysis suggested that multiple-ring displays wouldnot be visible because the combination of refractedand diffracted light results in the colors being highlysensitive to particle size, such that any reasonabledrop-size distribution destroys the colored rings.Lock and Yang3 also showed that the simpler Fraun-

hofer diffraction theory could be used with resultscomparable with the Mie scattering calculations, aslong as a blue wavelength of 0.49 �m was used for thedominant short wavelength instead of the traditionalgreen 0.57 �m.1–5 This is in agreement with manyof their chromaticity diagrams, which show the prin-cipal plane of oscillation being between red and bluecoordinates �not red and green�.

We find this particularly interesting because,whereas traditionally coronas are described as dif-fraction phenomena with dominant colors of pink andgreen, our observations strongly favor pink and blue,at least in mountain wave clouds. We do not believethat previous observations of pink and green coronasand iridescence are in error but rather that there is afundamental difference in the dominant colors formountain wave clouds and nonorographic clouds.

Gedzelman and Lock7 extended the Mie scatteringmodel to include a Rayleigh scattering atmospherebelow and above a geometrically thin cloud of vari-able optical thickness. As with previous simula-tions,3 the clouds contain spherical drops of liquidwater. This model provides the valuable capabilityof performing the most-complete simulations yet ofcoronas and should provide a significant step forwardin understanding how variables such as cloud parti-cle size distribution and cloud optical depth combineto create corona displays. The scattering calcula-tions made so far by Gedzelman and Lock7 suggestthat the corona color purity is maximized for a cloudoptical depth of 0.2 and becomes effectively zero for a

cloud optical depth of 4. They also show that colorsother than the first-order ring usually cannot be per-ceived in very thin clouds �optical depth � 0.05� be-cause of the competing blue daytime skylight. Inagreement with this interpretation, we have notedthat the most intensely blue multiple-ring coronasoccur in extremely thin wave clouds at night, whenthe visible background is black.6

As illustrated in Fig. 1, mountain wave clouds8–12

can produce particularly vivid coronas and irides-cence because of their narrow particle-size distribu-tion and small mean particle sizes.13–15 Mountainwave clouds, especially of the vertically propagatingvariety, tend to be geometrically thin in the verticaldirection and have a large ratio of horizontal-to-vertical air motion within them. These conditionsresult in a limited amount of time for cloud particlesto fall as they are quickly transported through thewave cloud, which results in such lenticular cloudsbeing optically thin and often lens shaped. In thispaper we show photographs of coronas and irides-cence observed within mountain wave clouds alongthe steep lee side of the Rocky Mountains over north-eastern Colorado. Such clouds are commonly ob-served in this location, as well as on the downstreamside of many other prominent mountain ranges, andtend to have small cloud particles with narrowparticle-size distributions. These conditions lead torelatively frequent, high-quality optical displays�e.g., Fig. 1� that are remarkably more colorful and

Fig. 1. Photograph of iridescent standing lenticular wave clouds above Boulder, Colorado, on 8 November 1995. This cropped photo wastaken with a 70–210-mm focal length lens; the exact focal length is unknown.

20 January 2003 � Vol. 42, No. 3 � APPLIED OPTICS 477

intense than what we have seen in nonorographicclouds.

Regardless of the particular cloud type, it has beenaccepted traditionally that spherical liquid clouddroplets are primarily responsible for coronas andiridescence. For example, in 1912 Simpson1 re-ported on corona observations in Antarctica duringCaptain Scott’s first British Antarctic expedition,concluding that supercooled liquid water dropletswere the diffracting objects leading to the colorfuldisplays observed in air temperatures ranging from�26 to �29 °C. Simpson’s conclusion was based ona combination of corona and fogbow observations thatled him to believe that the clouds during that displaycould not have contained ice crystals. Much later,Sassen2 analyzed a photograph of iridescence in anairplane contrail, also concluding that the particlesinvolved were most likely liquid water drops and notice. However, later observations of a corona in ahigh cirrus cloud exhibiting large depolarization ra-tios in lidar backscatter led Sassen4 to conclude thatdiffraction by unusually small ��25 �m� ice crystalswas indeed the source of that corona. Sassen et al.5described a similar observation and further docu-mented it by collecting and photographing the smallice crystals, collected by an airborne sampler at thetop of a high cirrus cloud with a temperature near�70 °C.

In this paper we add further documentation ofvivid corona displays being created by small ice-phase cloud particles. In over half our photographsthat we describe, the meteorological conditions re-quire the cloud particles to consist of ice, not liquidwater, on the basis of the homogeneous freezing point��36 °C� of supercooled droplets.13,14 The uniquefeature of our observations is that they are all inmountain wave clouds. Microphotographs of parti-cles collected from the interior of similar mountainwave clouds show that such clouds do indeed quiteoften contain small and monodisperse ice particles,but that these particles are quasispherical with ef-fective diameters less than 25 �m �Fig. 2�.16,17 Thissmall size, much smaller than typical ice crystals innonorographic clouds, provides a mechanism for thehigh-quality displays to be generated within waveclouds at high altitudes with temperatures below�36 °C. Therefore our analysis shows that visiblediffraction displays caused by such small ice particlesare more common than previously documented.Our observations of mean particle sizes from 7.6 to24.3 �m also help fill in the gap of large-particlemultiring coronas in the Lock and Yang3 observationset. It will be particularly interesting in the futureto use scattering models to explore the possible effectof the different complex refractive index of ice andliquid water on the visual appearance of coronas andiridescence.

2. Diffraction Theory for Corona Analysis

Closed-form solutions of electromagnetic scatteringtheory generally are limited to special cases, such asparticles that have spherical �Mie scatter�, cylindrical,

or otherwise simple geometry or symmetry.18 Amuch simpler approach to modeling coronas, however,is to use scalar diffraction theory, which provides apolarization-independent �scalar� approximate solu-tion for scattering by objects or apertures that arelarger than the optical wavelength.19 Some of thelight impinging on such an object is deviated from itsprior course, or diffracted, into a new direction thatdepends on wavelength and object size.

The simplest form of scalar diffraction theory isobtained in the Fraunhofer approximation, valid fordiffraction patterns observed at a distance muchgreater than �d2��, where d is the maximum trans-verse object dimension �i.e., particle diameter� and �is the optical wavelength. At such distances, thediffraction pattern is proportional to the spatial Fou-rier transform of the object. Corona and iridescence

Fig. 2. In situ observations of frozen cloud particles in an upper-tropospheric mountain wave cloud at a pressure altitude and tem-perature of �a� 339.3 mb and �34.4 °C, and �b� 319.3 mb and�40.0°C. The classical ice crystals in �a�, whose �100-�m size isshown for scale, are associated with a nearby nonorographic cirruscloud, while the much smaller quasispherical particles in �b� arefrozen wave-cloud particles �freezing of supercooled droplets oncollection can be ruled out because drops larger than a few mi-crometers cannot exist colder than the homogeneous nucleationpoint of about �36 °C�.17 These ice particles were collected inmountain wave clouds similar to the ones that produced the opticaldisplays illustrated with photographs in this paper. Photos cour-tesy of Andy Heymsfield at the National Center for AtmosphericResearch, Boulder, Colorado.17


in clouds typically satisfy this condition for ground-based observers.

The irradiance �W m�2� in a Fraunhofer diffractionpattern for a uniformly illuminated circular object ofdiameter d is described by the Airy function,

I�r� � ��d2

4�z�2�2J1��dr

�z ��dr

�z � �2

(1)

where r is the radial coordinate in the observationplane �i.e., the radius of the diffraction pattern�, � isthe optical wavelength, z is the distance from thediffracting object to the observer, and J1 is a first-order Bessel function of the first kind. The Airy pat-tern in Eq. �1� is a set of concentric rings, oftendescribed in terms of their angular radius �the angleby which the light is deviated upon encountering theparticle�. Because Fraunhofer theory is valid onlyfor small angles, some sort of small-angle approxima-tion is common, resulting in the Bessel function ar-gument being written in one of the following forms:

�dr�z

��d tan��

��

�d sin��

��

�d

�. (2)

We choose to use the sin�� version of Eq. �2�, describ-ing the angular position of maxima and minima inthe oscillating Airy pattern with

sin�� m��d , (3)

where m is a constant �0, 1.635, 2.679, 3.699,4.710, . . . for maxima and 1.220, 2.233, 3.238, . . . forminima�. Note that, according to Eq. �3�, the ringswill have shorter-wavelength blue on the inside andlonger-wavelength red on the outside. Further-more, large corona rings result from small particles,whereas small rings result from large particles.Thin clouds minimize multiple scattering and narrowparticle-size distributions avoid excessive overlap ofcolored rings, leading to the best visual displays.Mountain wave clouds often meet these stringentconditions.

In this paper we infer the mean cloud-particle sizesfrom the measured maxima for red and blue light incorona photographs taken with lenses of known focallength. We use the maxima because we feel it al-lows us to identify most reliably the wavelength ap-propriate for any point in the photograph. Thisapproach differs only in minor respects from that ofprevious studies,1–5 which describe the approximateangular minima in circular diffraction patterns withsin�� n � 0.22��d. This equation approximatesthe angular location of the nth-order minimum, andtraditionally has been used with a green wavelengthof 0.57 �m, which is assumed to coincide with the redmaximum �however, a blue wavelength of 0.49 �mnow seems to be more appropriate3�.

3. Analysis of Corona and Iridescence Photographs

We have observed many displays of corona and iri-descence through mountain wave clouds in the vicin-ity of Boulder and Nederland, Colorado, on theeastern �leeward� edge of the Rocky Mountains, dur-ing more than a decade of careful observing. Allexamples presented in this paper occurred with west-to-northwest flow near mountain top in the layer be-tween 700 and 500 mb �Table 1�, or approximately 3.0to 5.5 km above mean sea level �MSL�. The associ-ated cross-mountain �west-to-east� component of thislayer-mean flow was significant �7.1 to 17.4 m s�1�and quite likely contributed to the generation ofmountain-wave activity and the wave clouds.8,9,20

We used the heights and temperature ranges ofprominent moist layers in soundings at Denver, Col-orado, and Grand Junction, Colorado, to deduce theapproximate height and temperature characteristicsof these wave clouds. It is reasonable to assume,though impossible to confirm, that the wave cloudsthat produced the diffraction patterns resided withinthese moist layers, all of which were colder than themelting level �i.e., �0 °C�.

These mountain wave clouds are formed by airpushed upward as winds blow across the ContinentalDivide, usually are optically thin, and tend to havenarrower particle-size distributions than other cloudtypes. Mountain wave clouds typically contain liquidwater drops at temperatures down to approximately�36 °C.14,15 However, when the temperature fallsbelow a threshold near this value, the water particlesin these wave clouds freeze rapidly, forming small,quasispherical ice particles with diameters that ap-proach 25 �m. Such ice particles from Coloradomountain wave clouds �Fig. 2�17 are slightly largerthan the original liquid water droplets but are muchsmaller than typical ice crystals found in nonoro-graphic clouds �sizes �100 �m�.21–23 These smallwave-cloud ice particles have sufficiently sphericalshapes to produce coronas that are similar to liquid-generated ones. As far as we know, this is the firstdocumentation of this kind of small quasispherical iceparticle coronas in mountain wave clouds.

Figures 3–8 are photographs of six different opticaldisplays in wave clouds on the lee side of the RockyMountains near Boulder and Nederland, Colorado.In this subsection we use Eq. �3� from Fraunhoferdiffraction theory, along with mean wavelengths of0.63 and 0.48 �m, to determine the mean particlediameter from the angular radii of the red and theblue coronal rings, respectively �the angular radiusfor each ring is determined as tan�1�ring radius onthe slide�focal length of the lens� . A common at-tribute linking these examples, and many other dis-plays that we have observed in mountain waveclouds, is the vividness of the blue color, often at theexpense of green. All photographs were taken with-out neutral-density, polarizer, or other filters otherthan simple skylight filters used to protect the frontlens surface. Unfortunately, we do not have exactexposure data for all photographs, but they all were


taken by handheld cameras on 35-mm slide film atreasonably typical exposure time and F�# settings�for example, the iridescent cloud in Fig. �8b� wasphotographed at approximately F�8 and 1�125 s; co-rona photographs, especially ones in which the sur-rounding sky appears very dark, were typicallyphotographed with substantially lower exposure tobring out the colors from the bright light near theSun .

A. Circular Corona

Figure 3 shows a corona with multiple brightly col-ored concentric rings, resulting from diffraction in a

thin cloud with a highly monodisperse particle-sizedistribution. The highly uniform colors and circularshape both suggest further that the particle-size dis-tribution was quite uniform throughout this portionof the cloud. The Sun is at the center of the rings,blocked by the top of the tree. To the right of theSun are numbers that represent the average angularradii �in degrees� of the rings determined for the first-order red ring and the second-order blue and redrings at four locations in the photograph. From Eq.�3� these values correspond to a mean cloud particlesize of 20.4 �m ��0.5 �m�, which is comparable to insitu aircraft observations of frozen particle sizeswithin wave clouds.14,15

On the basis of the meteorological data summa-rized in Table 1, this wave cloud could have resided in

Fig. 3. Photograph of a circular corona above Nederland, Colo-rado, on 5 November 1989. The first-order red ring and thesecond-order blue and red rings are marked to the right of the Sun,and their radii are labeled in degrees. This cropped photo wastaken with a 70-mm focal-length lens.

Fig. 4. Photograph of an oblong corona above Boulder, Colorado,on 29 January 1987. The first-order red ring and the second-order blue and red rings are marked below and above the Sun, andtheir radii are labeled in degrees. This cropped photo was takenwith a 70-mm focal-length lens.

Fig. 5. Photograph of an asymptotic corona at the upwind edge ofa wave cloud above Nederland, Colorado, on 31 May 1987. Thefirst-order red ring is marked above and to the sides of the Sun, andthe second- through fourth-order red rings are marked above theSun; their angular radii are labeled in degrees. This croppedphoto was taken with a 70-mm focal-length lens.

Fig. 6. Photograph of a stepwise discontinuous corona aboveBoulder, Colorado, on 31 October 1989. The first-order red ringand the second-order blue and red rings are marked below andabove the Sun, and their radii are labeled in degrees. Thiscropped photo was taken with a 70-mm focal-length lens.


one of three layers that extended collectively througha deep layer of the troposphere from �650 to 320 mb�i.e., from approximately �5 to �40 °C�. However,the contrail in this photo can be used to constrain theestimate of the vertical position and temperature ofthe cloud. Because contrails form at temperaturesbelow approximately �43 °C,24 we know from thenearby soundings that this contrail could not haveresided lower than �9 km MSL, or �6.4 km aboveground. Furthermore, in the original photographthe contrail cast a sharp but very narrow ��0.3° ofarc� shadow on the wave cloud, with the shadow lo-cated directly above the contrail and to the left of theSun, suggesting that the contrail was slightly abovethe wave cloud in the left portion of the photo andwithin the cloud on the right side. Knowing that themaximum possible solar angle for the date of thephoto is �33.5° and then performing the appropriatesimple geometry, we determined that the contrailcould not have extended more than �25 m above thecloud �this is reasonable since the flow is usuallyhighly laminar and not excessively turbulent in waveclouds away from the wave-breaking region near thetropopause and away from the lower-level rotor cir-culations�. Also, given that the wave cloud wasquite thin �i.e., note the sharp detail of the contrailthrough the wave cloud�, the wave cloud effectivelyresided at the level of the contrail, i.e., at a temper-ature ��43 °C or slightly above the uppermost moistlayer measured by the soundings. At these very coldtemperatures the wave-cloud particles can exist only

in solid form.13 The relatively large wave-cloud par-ticle size of 20.4 �m inferred from the angular radii ofthe coronal rings further supports this conclusion.Sassen4 and Sassen et al.5 previously documentedice-crystal coronas within non-wave-like cirrus cloudsheets, though these displays are relatively uncom-mon since the ice crystals in cirrus clouds are non-spherical and often too large �i.e., ��100 �m�21–23 toproduce visible coronas.

B. Noncircular Coronas

Wave-cloud particles can be sufficiently uniform insize to produce noticeable diffraction rings, but theymay vary enough in size across the cloud that theserings are noncircular. This subsection highlightsfour variants of noncircular coronas. Where possi-ble, we use Eq. �3� to determine the particle diametercorresponding to the “radius” at different pointswithin the noncircular diffraction pattern.

1. Oblong CoronaThe diffraction rings of the oblong-shaped corona inFig. 4 have a larger diameter at the top of the pho-tograph and become gradually smaller toward thebottom. This is caused by the mean cloud particlesizes becoming steadily larger from top to bottom.

Fig. 7. Photograph of a ragged corona above Nederland, Colorado,on 15 January 1996. This cropped photo was taken with a 70–210-mm focal-length lens; the exact focal length is unknown.

Fig. 8. Photographs of iridescence above Boulder, Colorado, on �a�8 November 1995 and �b� 25 December 1998. These cropped pho-tos were taken with 70–210- and 28–200-mm focal-length lenses,respectively. The exact focal length in �a� is unknown, and thefocal length in �b� is �120 mm.


The mean particle diameters deduced from the angu-lar radii of these rings ranged from 19.5 �m at the topof the corona to 24.3 �m at the bottom. These rel-atively large sizes suggest that the wave clouds werecomposed of ice particles, which is supported by theobservation that the upper portion of the highermoist layer in nearby soundings was colder than thehomogeneous nucleation point. It is unclear pre-cisely why the ice particles gradually changed sizeacross the corona. However, it is possible that thischange reflected the growth of ice particles in theupward-motion portion of the wave cloud, especiallygiven that a small component of the upper-tropospheric flow was directed from the top of thecorona to the bottom.

Several other authors have documented oblong co-ronas that appear in a clear sky from diffraction bypollen.25–27 The shape of these coronas reflects theshape of the pollen spores: circular for juniper, ob-long or otherwise asymmetric and noncircular forpine and birch, and so forth. However, the oblongcorona described here results from a local gradient inmean cloud particle diameter.

2. Asymptotic CoronaThe uniquely shaped high-order corona shown in Fig.5 is an extreme example of a noncircular corona. Itcontains a series of colored bands at the upwind edgeof a wave cloud, whose radii expand continuously�never closing� as the upwind edge is approachedfrom the cloud interior. This sharp spatial gradientin diffraction ring radius indicates rapid particlegrowth downwind of the cloud edge �i.e., toward thetop of the photograph�. The angular radii of thefirst- through fourth-order red rings above the Suncorrespond to cloud particle sizes of 12.3, 14.5, 15.8,and 16.6 �m, respectively, while the mean radius ofthe first-order red ring near the edge of the cloud �tothe sides of the Sun� was produced by an average

particle size of 7.6 �m. The relatively small size ofthese particles and the fact that the prominent moistlayers remained well below the altitude of the homo-geneous nucleation point �Table 1� indicate that thewave cloud was composed of water droplets. Be-cause the upwind edge of the cloud is where the limitof the droplet size goes to zero, the angular radii ofthe diffraction rings here approach infinity. There-fore, we refer to this particular diffraction display asan asymptotic corona.

The fortuitous location and unique shape of thesediffraction rings, in tandem with knowledge fromrawinsonde observations that midtropospheric flowof �10 m s�1 was directed nearly perpendicular tothe cloud edge from bottom to top, provide usefulinformation about the distribution of cloud particlesand their mean growth rate at the upwind edge orupdraft region of this wave cloud. The decrease inradii of the diffraction rings �i.e., the increase in drop-let size� from the upstream edge of the cloud to itsinterior clearly documented the growth of cloud drop-lets. Assuming steady horizontal flow of 10 m s�1

through the wave cloud, the most rapid growth rateoccurred at the leading edge of the cloud where drop-lets initially formed and reached a mean size of 7.6�m in less than �5 s. Thereafter the droplets in-creased in size much more slowly to 16.6 �m in either�34 or �70 s, depending on whether the cloud wasassumed to reside in the lower or the upper moistlayer summarized in Table 1. The initial rapidcloud-droplet growth and subsequent slow growthwithin the updraft region of the wave cloud’s upwindedge is fully consistent with in situ aircraft observa-tions of droplet growth in the same region of otherliquid-phase wave clouds.14

3. Stepwise Discontinuous CoronaThe corona in Fig. 6 exhibits a step discontinuity indiffraction-ring radius near the top of the corona,

Table 1. Mean Wind, Moisture, and Temperature Characteristics from the Relevant Denver and Grand Junction Rawinsonde Soundings for theDiffraction Displays Shown in Our Photographsa

Date�day-month-year�

Fig.No.

700–500-mb Mean WindInformation

Moist Layersb

�mb�

Temperature Rangeof Moist Layers

��°C�

InferredCloud

ParticleSize ��m�

CloudParticlePhase

Direction�deg�

Speed�m s�1�

CrossMountain

�m s�1�

29-Jan-87 4 301 13.6 11.7 565–429; 400–331 15.5–28.2; 31.9–39.9 19.5–24.3 Ice31-May-87 5 262 7.2 7.1 638–562; 550–500;

420–3630.1–8.2; 6.7–9.1;

18.3–25.77.6–16.6 Liquid

31-Oct-89 6 283 14.0 13.6 559–493; 474–443;457–341

6.9–24.5; 23.2–26.1;24.1–39.8

14.4–18.1 Liquid�ice

05-Nov-89 3 280 17.7 17.4 650–547; 511–386;450–322

5.1–14.4; 16.0–29.7;22.0–39.9

20.4 Ice

08-Nov-95 1, 8�a� 294 15.0 13.7 315–100 38.9–70.7 — Ice15-Jan-96 7 271 14.4 14.4 552–529; 387–100 12.0–13.6; 31.1–65.2 — Ice25-Dec-98 8�b� 310 17.3 13.3 579; 440–420; 300–250 15.9; 30.7–33.5;

52.5–58.3— Liquid

aInferred cloud particle sizes are also shown for each display �where applicable�, as is the estimated cloud particle phase.bA moist layer is defined by a local minimum in a vertical profile of dewpoint depression.


indicating a sudden change of mean cloud-particlesize. The relatively circular rings in the lower two-thirds of this corona correspond to a mean particlesize of 18.1 �m, a value that is representative offrozen wave-cloud particle sizes. In contrast, thepartial rings possessing larger angular radii abovethe Sun were created by a much smaller mean par-ticle size of 14.4 �m that is more characteristic ofwave-cloud water droplets. Multiple moist layerswere observed during this event �Table 1�, the highestof which extended above the homogeneous nucleationpoint. Heymsfield and Miloshevich14 presented insitu observations of a rapid change in phase of wave-cloud particles from supercooled liquid to ice, and acorresponding jump in particle size, associated withhomogeneous nucleation. Therefore it is plausiblethat the discrete change in the angular radii of thecoronal rings in this photograph marks the location ofa phase change from supercooled liquid �larger rings,top� to ice �smaller rings, bottom�.

4. Ragged-Edge CoronaThe use of a zoom lens to photograph the corona inFig. 7 without recording the exact focal length pre-vents us from accurately determining the meancloud-particle sizes that produced this corona. Nev-ertheless, the photo clearly shows the ragged edges ofthe diffraction rings. This distinctive trait indicatesthat the cloud particles were sufficiently uniform insize to produce visible colored rings but that the par-ticles also exhibited enough variability in size acrossthe cloud to create undulations within these rings.

This case is unique among those presented in thissection because it was characterized by a superposi-tion of high-level wave clouds east of the ContinentalDivide and synoptic-scale cirrus �as cold as �51 °C �streaming overhead from southern California �deter-mined from satellite imagery not shown here�. Thesoundings clearly documented this upper-level mois-ture up to 100 mb or ��65 °C, as well as a very thinmoist layer in the middle troposphere �Table 1�.When this photo was taken, however, midtropo-spheric wave clouds were not evident in the immedi-ate vicinity. Therefore it is quite likely that both thewave clouds and cirrus in the area were composed ofice particles. Because the cirrus was quite cold, itsice crystals might have been small enough to producea corona4,5,22 in tandem with the upper-level waveclouds. On the basis of the microphysical character-istics of nonorographic cirrus clouds outlined earlier,we observe the cirrus ice particles in this case toexhibit a comparatively large range of sizes relativeto wave-cloud ice particles, and they probably werenonspherical and randomly oriented. Therefore thecirrus ice crystals were quite likely responsible forthe ragged appearance of the coronal rings.

C. Iridescence

When sunlight or moonlight passes through a trans-lucent cloud containing clusters of uniformly sizedsmall particles, and each cluster is characterized by aunique mean particle size, a patchwork of colors

known as iridescence can be produced, sometimesrelatively far from the light source. Iridescence mayalso occur by means of anomalous diffraction arisingfrom interference effects associated with sunlight ormoonlight passing through a cloud composed of verysmall particle sizes, thus resulting in irregular colorpatterns quite far from the light source.3 The twoiridescence displays shown in Fig. 8 were distin-guished by smooth and mottled cloud textures, re-spectively. During the first display �Fig. 8�a� , aphoto was also taken of iridescent wave clouds intheir entirety �Fig. 1�. During this display moistconditions existed only at high levels where thetemperature was colder than the homogeneous nu-cleation point �Table 1�. These rawinsonde observa-tions are supported by infrared satellite imagery �notshown�, showing a localized north–south-orientedwave-cloud band east of the Continental Divide overBoulder with cloud-top temperatures of �52 to�58°C. Hence the iridescence in Figs. 8�a� and 1were almost certainly produced by ice particles. Asis often the case with iridescence, green is more ap-parent than in many mountain wave-cloud coronas,but all three iridescence photographs in Figs. 1 and 8also exhibit a significant amount of blue.

Rawinsonde measurements relevant to the displayshown in Fig. 8�b� reveal two moist layers that werewarmer than the homogeneous nucleation point andone layer that was colder �Table 1�. Our qualitativeimpression was that during this display the irides-cent cloud was situated no higher than the middletroposphere, i.e., in a layer where supercooled drop-lets would have existed. In all three iridescencephotos �Figs. 1, 8�a�, 8�b� , iridescent colors were ob-served at least 10°–15° from the Sun, indicating thatthe cloud particles producing these displays werequite small �i.e., the result of large-angle and possiblyhigh-order diffraction�. The corona rings showcasedearlier in this paper subtended smaller angles rela-tive to the Sun, indicating larger particle sizes.

4. Discussion and Conclusions

The meteorological conditions for the wave-cloud dif-fraction displays shown here strongly suggest that inmost cases the diffracting objects were small quasi-spherical ice particles with mean sizes of approxi-mately 7–25 �m �only several of these examples arelikely generated by supercooled liquid water�. Pre-vious documentation of coronas produced by ice par-ticles are limited to observations in cirrus clouds thatappear to be composed of small ice crystals,4,5

whereas our observations suggest that corona andiridescence quite often can be created by tiny quasi-spherical ice particles that might be unique to moun-tain wave clouds �we discuss mountain wave-cloudmicrophysics in more detail in a similar manuscriptbeing prepared as a review of coronas and iridescencefor the meteorological community28�. Furthermore,the quasispherical shape of these tiny ice particlesmay not produce a significant depolarization signa-ture, meaning that remote identification of these


wave-cloud ice particles may require techniquesother than polarization lidar alone.

The particle diameters that we infer from coronaphotographs agree well within the particle-sizeboundaries suggested by Lock and Yang3 at the smallend, but we have several cases of inferred particlediameters significantly larger than the 15-�m upperlimit of their observations. This, in fact, helps fill inthe large-particle region where the modeling of Lockand Yang3 predicted that good visible coronas couldbe created, but for which they found no photographicevidence.

Even beyond the examples included in this paper,our observations �mostly in mountain wave clouds�favor blue over green as the dominant shortwavecorona color, but many comments in the communityand the popular literature favor green. The bluepreference may be unique to diffraction in mountainwave clouds. We see a tendency for iridescence dis-plays to have more green content than coronas, evenin mountain wave clouds; sometimes the green isaccompanied by blue, but sometimes—especiallywhen the clouds appear to be composed of liquidwater—there is significantly less blue. In waveclouds that appear to be extremely thin and high inthe atmosphere, the resulting coronas almost alwaysappear as vivid blue rings, rarely exhibiting anygreen at all. The most striking examples of theseblue coronas occur in thin wave clouds at night, withthe full or nearly full moon as the light source.

We believe that further observation and modelingwill provide much more insight into the cloud micro-physics accompanying corona and iridescence dis-plays and into the perceived optical nature of thesedisplays. In particular, we wonder whether there isa connection between the cloud particle-size distribu-tion, or perhaps the type of cloud particle involved,and the perceived short-wavelength dominant color�green versus blue�. Given that previous scatteringmodels of coronas have been for liquid spheres,whereas many of the larger particles in our examplesappear to be quasispherical ice particles, there isclearly an opportunity to explore what effect the dif-fering refractive indices of ice and liquid water mighthave on the color and visibility of coronas. However,any such effect will likely be limited to the smallestparticles, for which reflection, transmission, and dif-fraction by the particles tend to be comparable. Thisanalysis will require a scattering formulation insteadof diffraction analysis, because diffraction theory con-siders only the shape and size of the objects and nottheir optical properties. This future research shouldbe accompanied by a quantitative analysis of the col-orimetric properties of coronas and iridescence inmountain wave clouds and other cloud types.

The authors thank Andy Heymsfield �NationalCenter for Atmospheric Research� for providing thewave-cloud particle microphotograph in Fig. 2 and forinsightful discussions about wave-cloud microphys-ics, Ken Sassen �University of Alaska� and Stan Ged-zelman �City University of New York� for engaging us

in stimulating discussions of coronas and iridescence,and Jim Churnside �National Oceanic and Atmo-spheric Administration �NOAA��EnvironmentalTechnology Laboratory and two reviewers for pro-viding helpful and encouraging suggestions for themanuscript. J. A. Shaw acknowledges support froma NOAA Presidential Early Career Award for Scien-tists and Engineers for his participation in this study.

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