Most of the time, the sky forms an unobtrusive back-drop that silently sways our moods. But there aretimes when the sky assumes such vivid colors andstriking contrasts of light it commands our attention.Simulating the great range of sky color and bright-ness and the changes that take place as the Sun risesor sets is therefore an exercise in both science andaesthetics. Beautiful photographs and simulations ofsky colors abound on the Internet and in books onatmospheric optics.1–4 Still, there is value in the sim-ple but relatively robust, user friendly model de-scribed in this paper (called SKYCOLOR) thatcaptures the essence of and animates sky color undera wide range of conditions.
Observing the sky is a time-honored practice. Onpristine days when the Sun is high in the sky, theclear sky grades from deep blue at the zenith to al-most white near the horizon. On hazy days the skyappears pale but is very bright near the Sun so longas the size and number of aerosol particles is notunduly large. Aerosol laden skies can take on earthtones, as when strong winds cross the Sahara Desert.
The sky frequently puts on a majestic show around
sunrise or sunset, when a vibrant, spectral play ofcolors marks the horizon. Clouds amplify the beautyand majesty of the sky at these times by reflecting ortransmitting the warmer colors from horizon to ze-nith. Less common but equally dramatic sky showstake place when dark thunderstorms pass overhead.The horizon sky then turns a dirty orange color thatwe associate with the ominous weather. Even morelurid are the green or yellow cloud colors that some-times accompany severe hail producing or tornadicthunderstorms.5 Major volcanic eruptions producefantastic crimson twilight skies that last for months.J. M. W. Turner felt that the painted twilight skies ofClaude were inimitable until the eruption of Tam-bora in 1815 provided him with a working model.6
The main factors that determine sky color andbrightness are well known.7,8 Lord Rayleigh providedthe theory for John Tyndall’s observations that thesky is blue because tiny air particles (molecules) scat-ter shorter waves preferentially.9,10 As the numberand size of aerosol particles increase, the sky becomesless blue and brighter near the Sun. Aerosol particlesare generally comparable in size to the wavelengthsof visible light and scatter light in a manner bestdescribed by Mie theory. Quantifying the optical be-havior of aerosol particles is quite a difficult matterbecause the particles vary in shape and complex in-dex of refraction.11
The model developed here, named SKYCOLOR,contains highly simplified scattering behavior foraerosols. Most aerosol particles in the troposphereare less than 0.5 �m in diameter. They scatter lightless selectively versus wavelength (typically ���1)
S. D. Gedzelman ([email protected]) is with the De-partment of Earth and Atmospheric Sciences and the NOAACREST Center, City College of New York, New York, New York10031.
Received 7 January 2005; revised manuscript received 12 May2005; accepted 12 May 2005.
than air molecules ���4� and by smaller angles, butmuch more efficiently in relation to their cross-sectional area. Volcanic eruptions and large forestfires infuse the stratosphere or upper tropospherewith micrometer-size sulfuric acid droplets that scat-ter long waves more efficiently than short waves.Volcanic particles also bleach the sky during the day,but as a result of their anomalous scattering mayturn the Sun or moon green or blue and producecrimson twilight skies when the troposphere lies inshadow, but the particle-laden stratosphere is stillbathed in sunlight.
Sky brightness and color is also affected by theatmosphere’s optical thickness. As tropospheric aero-sol optical thickness increases, the sky reddens andbrightens at first, particularly in the direction of theSun, but ultimately grows darker as less sunlightpenetrates the atmosphere. The optical path throughthe atmosphere also lengthens as the Sun goes down.The golden and red colors of sunset and twilight re-sult from major loss of short waves by scattering as alight beam penetrates a great optical thickness ofatmosphere.
In cloudless, clean skies, the warmer colors areconfined near the horizon, where optical thickness islarge. But when the Sun nears the horizon in anatmosphere laden with aerosols or laced with opencloud decks or translucent clouds, red, golden, andpurple colors can fill skies from horizon to zenith asthe Sun approaches the horizon.
In addition to the common and the spectacular ap-pearances of the sky, there are subtle effects. On cleardays, maximum sky brightness tends to occur a shortdistance above, rather than at, the horizon.12 Pastelpurple twilights occur when aerosols occupy bothstratosphere and troposphere and when light that
has been reddened in its long passage through thetroposphere is not blocked by distant high clouds.13–15
During twilight, a modest amount of aerosols makethe zenith sky bluer than when the air is pure. And,during many volcanic twilights, a golden strip sepa-rates the red horizon from the crimson sky aloft.
This paper presents a relatively simple, userfriendly model (SKYCOLOR) written in Visual Basicthat simulates or approximates all of the features ofsky color and brightness mentioned above and ani-mates them as the Sun sinks in the sky. The model isdescribed in Section 2 and is available.16 Results ofsimulations are presented and discussed in Section 3.
2. Model
SKYCOLOR animates changes of sky and cloud colorand brightness as the Sun sinks in the sky under awide range of conditions chosen by the user, listed inTable 1. The Sun’s color is also shown, but not itsrelative brightness. Results are displayed either as ascene of the vertical plane including the Sun and theobserver from the horizon facing the Sun up as far asdesired through the zenith to the opposite horizon orin a chromaticity diagram.
Simulations start at an initial solar elevation an-gle, �00, and continue with steps, d�, until the desiredfinal solar-elevation angle. Brightness of the sky andclouds are displayed relative to the maximum valueat the initial solar-elevation angle [see Eq. (1)] so thatthey grow progressively darker (but not too dark onthe monitor) as the Sun sinks.
The geometry and main features of SKYCOLORare shown in Fig. 1. An observer on a spherical Earthat height ho and solar-elevation angle, �0, looks up atan elevation angle, �v, in the vertical plane that in-cludes the Sun. A field of clouds appears at a single
Table 1. Parameter Choices Available to a User of SKYCOLOR
Parameter Choice or Range
Display 0 � Chromaticity Diagram, 1 � PanoramaClouds 0 � No, 1 � YesCloud shadows 0 � No, 1 � YesOzone 0 � No, 1 � YesAtmospheric refraction 0 � No, 1 � YesScattering 0 � Single, 1 � MultipleSolar eclipse 0 � No, 1 � Yes
elevation angle, �cld, and height, hcld. Sunlight ap-proaches from the right and is initially parallel to thex axis. As light passes through the atmosphere, it isrefracted and may be absorbed by ozone (absorptionby aerosols is not included in SKYCOLOR) or scat-tered. Sunbeams are displaced downward by refrac-tion by an amount z. Light reaching the observerconsists of a beam of singly scattered sunlight, whichis depleted by absorption or by a second scattering asit approaches the observer.
Sunlight entering the atmosphere is approximatedby a Planck radiator at 5700 K and is treated as apoint source since few aspects of sky color changemuch over an angular width equal to the Sun’s an-gular radius ��0.25°�. SKYCOLOR is run for 61wavelengths from 0.4 to 0.7 �m, giving a wavelengthresolution of 5 nm. Following the standard approachused in earlier papers, tristimulus values are used tocalculate the 1931 CIE x�y chromaticity coordinatesand to display the phenomena.17,18 In every scene thered-green-blue (RGB) value of each color is given by
RGB � 255� I(�, �0)Imax(�, �00)�
0.15
, (1)
where IRGB��, �0� is the irradiance of red, green, orblue light at a point in the sky and Imax��, �0� is themaximum irradiance when the Sun is at its highpoint in a simulation. The power, 0.15, is used be-cause it gives visually convincing results on a moni-tor.
Refraction is only important when the Sun is nearthe horizon or when the observer is looking near thehorizon. The main impact of refraction on sky colorand brightness is to alter the optical thickness of thepath of light through the atmosphere. Refraction ofthe light beam seen by the observer is calculateddirectly. However, because calculating refraction foreach sunbeam along the path of the observer’s beam
is very time consuming, a heuristic equation is devel-oped to parameterize the impact of refraction.
Because sunbeams are refracted downward, theyalways have a shorter effective optical path throughthe atmosphere than a line straight from the Sun.Therefore, the ratio of optical path length, rat of arefracted sunbeam to that of a straight sunbeamreaching point �xp, zp� is always less than unity and isapproximated by the heuristic equations,
rat � 0.5�1 � tanh�zp � 10500 � 100Texp
2650T
q ��,
q � 66T � 0.0004xp, Hscl �RdT
g ,
q � 19000exp
1800000, Hscl � 2500,
(2)
where Hscl is the scale height or height over whichdensity decreases to a factor, e�1. Equation (2) wasobtained by finding the best fit with calculated valuesof optical path lengths of refracted sunbeams in iso-thermal atmospheres for both pure air and aerosols.Values of rat for various values of xp when T� 273 K are shown in Fig. 2, where the solid curvesare based on Eq. (2) and the dashed curves are basedon a model that calculates refraction of sunbeams inthe atmosphere. When only solid curves appear, theerrors of rat associated with Eq. (2) are too smallto distinguish. In general, the errors are less than1% but are as large as 6% in deep twilight when xp
� �7�10�5 m.Light in SKYCOLOR is scattered by air molecules,
aerosol particles (either near the ground or at ele-vated layers, such as volcanic aerosols), and hydro-meteors (raindrops, cloud droplets, or ice crystals).Air molecules are assumed to be Rayleigh scattererswith wavelength dependence ��4. Polarized compo-nents of scattered light are combined to produce thetotal angular phase function for Rayleigh scattering.An isothermal atmosphere with scale height Hscl
� RdT�g m �Rd � 287, g � 9.8 m s�2� is used for
Fig. 1. Geometry of the sky color model. Light reaching an ob-server looking up at angle �v on a spherical Earth consists ofsunlight at true elevation angle, �0, scattered by air molecules,aerosol particles near the ground, volcanic particles in the strato-sphere, and clouds at height hcld and apparent elevation angle �cld.Sunbeams are refracted downward by an amount z. Shading dueto a total solar eclipse or a broken or opaque cloud deck is includedif desired.
Fig. 2. The ratio of optical path length of a refracted sunbeam tothat of a straight sunbeam reaching point �xp, zp� when T � 273.Dashed curves are based on a refraction model, solid curves, fromEq. (2).
mathematical simplicity to calculate density ��h�� ��0�e�h�Hscl as a function of elevation. The aerosolloading of the atmosphere is expressed in terms of theturbidity, �, which is defined as the ratio of the opti-cal depth of the aerosol-laden atmosphere integratedover the visible spectrum to that of a pure, Rayleigh-scattering atmosphere. Loading by volcanic aerosolsis input into SKYCOLOR using an optical depth, vul,integrated over the visible spectrum. Typical valuesof vul following major eruptions range up to 0.5.
In most runs, aerosol concentration decreases fromthe ground up with a scale height Haer � 2.5 km. Tosimulate the reddening of the horizon sky during the30 June 1973 total solar eclipse at Loiyengalani Oa-sis, it was necessary to assume Haer � 5 km.19 Formost runs involving volcanic aerosols in the strato-sphere, concentration was maximum at hvul� 25 km and decreased both above and below with ane-folding distance of 2 km.
In all runs, light is scattered with wavelength de-pendence ��1 by tropospheric aerosols and ��1 by vol-canic aerosols. The latter value corresponds todroplets of radius roughly 0.4 �m, which fall in theanomalous region of Mie scattering where red light isscattered more efficiently than blue (Fig. 3). Whenthe index of refraction is 1.5, as is more characteristicof aerosol particles, the anomalous red region has amore pronounced peak and occurs for smaller parti-cles.11 The lengthy calculations associated with theMie angular-scattering phase functions for all aero-sols are approximated by the heuristic equation
P( ) �2(1 � a2)
1 � e�a� (1 � e�a�
2 )e�a � e�a�
2 e�a(�� ). (3)
Equation (3) was designed to mimic the major for-ward and minor backward peaks of Mie scattering inSKYCOLOR at a great saving of time. The constanta � 1.5 for near-ground aerosols (typical of particleswith radius 0.15 �m), and a � 3.3 for volcanic aero-
sols (Fig. 4). These yield values of the asymmetryparameter of 0.466 and 0.296, respectively.20
On days of clean (pure) air far from the horizon,optical thickness is so small that multiple scatteringis negligible. But near the horizon or when the Sun islow in the sky, the optical thickness and relativecontribution of multiply scattered light increase. Be-cause air molecules and most aerosols scatter shortwaves more efficiently than long waves, a model thatneglects multiply scattered light produces undue red-dening that increases with the optical path length oflight through the atmosphere. This makes single-scattering simulations least reliable near the horizonand at twilight, precisely where and when color ef-fects are most interesting.
The impact of multiple scattering is included in allruns, but only in parameterized form because directcalculation would drastically slow SKYCOLOR. Asimple parameterization based on output of a one-dimensional channel atmosphere model was found toapproximate the contribution of multiply scatteredlight. In the channel model, light beams continueuntil they exit the channel at top, bottom, or sideends. At any point the light has an equal probabilityto be scattered up, down, forward, or backward. Lightscattered up is treated as lost to space. Light iscounted as skylight at the point where it is scattereddown. Skylight in this channel model decreases withdistance as e�0.70. Because singly scattered skylightdecreases with distance as e�, multiple scattering isparameterized in SKYCOLOR by reducing the scat-tering coefficient of sunlight available for scatteringand of skylight in Earth’s shadow by 30%. This elim-inates the undue depletion of the more readily scat-tered waves in a single-scattering model that causeexcessive redness of normal (nonvolcanic) skies toincrease as the optical path length through the atmo-sphere increases. The shortcoming of this formula-tion is that it does not include multiple scattering asa source of illumination.
Clouds affect sky color by increasing the effectiveoptical thickness of the atmosphere. Clouds transmit
Fig. 3. Mie-scattering efficiency (ratio of scattering cross sectionto geometric cross section) and color of scattered sunlight as afunction of particle-size parameter (ratio of circumference to wave-length at � � 0.55 �m) for spherical water droplets.
Fig. 4. Comparison of angular-scattering phase function usinga � 3.3 in Eq. (3) (thick curve) with Mie-scattering solution forspheres of radius 0.4 �m, at wavelength � � 0.5 �m and index ofrefraction n � 1.33 (thin curve).
light when they appear between the Sun and theviewer and reflect light when seen opposite the Sunor from their bases when the Sun is below the hori-zon. Model clouds consist of an optically thick core(cld � 20 in most runs) and a more translucent fringeto account for the dark core and silver (or golden)lining. Multiple scattering with a � 3 in Eq. (3) iscalculated directly inside clouds. The albedo of thecloud fringe is assigned 20% of the albedo of the cloudcore. Since rainbows, coronas, and halos are extin-guished when clouds are optically thick, clouds aretreated as spectrally nonselective, diffuse reflectorsand transmitters of the incident light.17,18,21
Because broken cloud fields produce some of themost beautiful skies, SKYCOLOR includes the effectof cloud shadows as an option by reducing sunlightintensity below the cloud deck to 1% of the clear skyvalue. This enables it to simulate the impact of athick cloud cover with a distant opening. The impactof the moon’s shadow cast on the Earth during a solareclipse is also included as an option. In this case,sunlight intensity in the umbra is reduced to 0.1% ofits unblocked value and increases linearly with in-creasing distance from the umbra.19
The only absorption included directly in SKY-COLOR occurs in the Chappuis bands of ozone, whichpeaks at about � � 0.59 �m (Fig. 5). Ozone absorp-tion has little effect on sky color during the day. How-ever, during twilight it makes the zenith sky bluerand modulates the purple.22,23 In SKYCOLOR, ozoneconcentration peaks at hzmx � 26 km and decreasesboth up and down with e-folding height 3 km, and isconstant below the tropopause at htrop � 15 km (Fig.6). Reducing hzmx and htrop by 5 km in model runs haslittle impact on sky color. Varying total ozone has amajor impact on sky color during twilight, but is setequal to 300 Dobson units in all model runs unlessmentioned otherwise.
Absorption by aerosol particles and gases otherthan ozone is included indirectly when SKYCOLORis run both with and without scattering because alllight scattered more than once is extinguished. Thisgives an excessive but qualitatively accurate esti-mate of the effects of absorption on sky color becauseboth scattering and absorption spectra of typical
aerosols are roughly proportional to ��1.24,25 Whenatmospheric turbidity is high, model runs with andwithout multiple scattering assume earth-tone colorsseen in dusty skies. This suggests that in most cases,sky color is determined largely by scattering and isnot grossly altered by absorption.
3. Results of Simulations
SKYCOLOR simulates most observed features of thecolor and brightness of the sky, Sun, and clouds. Thedominant feature of the sky when the Sun is wellabove the horizon is a deep blue that whitens towardthe horizon when the air is free of aerosols. Aerosolladen air is distinctly brighter near the Sun andmuch less blue in much of the sky. When the lowertroposphere is clean but smoke from forest fires ispresent in the upper troposphere or volcanic dropletsoccupy the stratosphere, the sky facing the Sun alsoloses its blue color, and takes on warm tones, but theSun (or moon) can become blue-green. Photographs ofclean and hazy skies and a blue, volcanic Sun follow-ing Pinatubo are shown in Fig. 7. Simulated views ofclean, hazy, and postvolcanic skies for solar elevationangle, �0 � 40°, are depicted in the panels of Fig. 8.The view extends from the horizon facing the Sun��v � 0°� at bottom through the zenith to the oppositehorizon ��v � 180°� at top. The simulated color purity,defined as the percent of distance of the chromaticitycoordinate �x, y� from the achromatic point (1⁄3, 1⁄3to the boundary of the chromaticity diagram, isshown as a function of �v for these situations inFig. 9.
The pure Rayleigh-scattering atmosphere (Fig. 8,left panel) has maximum color purity �40% in a largeregion around the zenith, which matches the estab-lished value.26 The darkest part of the sky occursabout 80° from the Sun where Rayleigh-scatteredskylight is almost purely polarized. Maximum bright-ness occurs at each horizon, which has a faint tur-quoise color, and the Sun is pale yellow.
The aerosol-laden sky (center panel, � � 5), ismuch paler blue and markedly asymmetric. The Sunand horizon sky have a faint orange tint while blue
Fig. 5. Absorption coefficient in the Chappuis bands of ozone as afunction of wavelength, �, used in SKYCOLOR. Fig. 6. Vertical distribution of ozone number density used in
SKYCOLOR when the total ozone in the atmospheric column is300 Dobson units.
only appears above about �v � 15°. Maximum skybrightness occurs near the Sun, while a secondarymaximum occurs opposite the Sun about 8° above thehorizon ��v � 182°�, and maximum blue color purity(12%) occurs about 30° above the horizon opposite theSun ��v � 150°�, because aerosols scatter little lightby large angles.
Light and color of the postvolcanic sky (right panel,vul � 0.10) is highly asymmetric. The pale orangetone of the sky around and below the Sun contrastssharply with the pale blue-green of the Sun. Maxi-mum brightness on the side of the sky facing the Sunoccurs at the same height as the Sun while a second-ary brightness maximum occurs at the horizon oppo-site the Sun. The deepest blue part of the sky occursopposite the Sun about �v � 155°, and its high colorpurity ��38%� is consistent with the assumption thatvolcanic droplets scatter little light by large angles.
The impact of turbidity, �, on integrated skybrightness is shown in Fig. 10 for solar elevationangles �0 � 40° and 5°. As aerosol particles are in-troduced and � increases from 1 to about 2, scatteringand sky brightness increase at the expense of sun-light at all elevation angles, �v. As � increases from 2
to about 5, the sky continues to brighten aloft, butdarkens near the horizon, and the brightest part ofthe sky approaches the Sun. As � increases aboveabout 5, the brightest part of the sky surrounds theSun when the Sun is relatively high in the sky ��0� 40°�, but is situated above the Sun when the Sun islow in the sky ��0 � 5°�. Maximum sky brightnessreaches a peak value around � � 8 when �0 � 40°, butonly � � 1.5 when �0 � 5° because the slant path ofthe Sun greatly increases the effective optical thick-ness.
In highly turbid air, the Sun disappears when it isstill well above the horizon. As the Sun nears thehorizon, maximum sky brightness always occursabove the horizon, even in pure air. When the Sunrests on the horizon, the sky is brightest about 2°above the horizon. Lee reported that maximum skybrightness to the side or opposite the Sun occurs at anincreasing angle above the horizon as turbidity andsolar zenith angle increase. SKYCOLOR predictsthat maximum sky brightness occurs above the hori-zon, but at a lower elevation angle than observed(Table 2).12 Neglect of surface albedo in SKYCOLORas well as oversimplified parameterizations of
Fig. 7. Photographs of the sky for clean air in Sydney Australia (left), highly polluted air in New York City (center), and turbidstratosphere after Pinatubo producing a blue Sun (right).
multiple-scattering and scattering phase functionsare likely sources of the discrepancies.
SKYCOLOR simulates the sequence of sunset andtwilight sky colors, including the oft observed butsubtle purple twilight (Fig. 11). In pure air (� � 1,vul � 0), the warm colors begin to appear near thehorizon once the Sun sinks below �0 � 10° and be-come pronounced once the Sun sinks below �0 � 4°.Green first appears in the sky near the horizon when�0 � 8°, and the chromaticity curve of sky color has itsgreatest displacement toward green when 0 � �0� 3° (Fig. 12). The highest chromatic purity (percentof distance from the achromatic point to x � 0.1547,y � 0.8049) of the green band is 6.3%. As twilightdeepens, the maximum purity of the green band de-creases in pure air.
During the day, increasing turbidity reddens thesky near the horizon and shifts the chromaticity
curve of sky light from green toward white. But intwilight the chromaticity curve shifts back towardgreen as turbidity increases when the stratosphere isclean.
As the Sun approaches the horizon, the sky gradesfrom orange at the horizon through yellow, green,and blue. During twilight, the horizon sky facing theSun is reddest when �0 � �2.5°. As twilight deepensfurther, the horizon sky grows less red because anincreasing fraction of light reaching the observeroriginates high in the atmosphere, where scatteringexacts a smaller loss. The brightest part of the twi-light sky tends to be yellow for a wide range of �0 and� and occurs from �v � 1.5° in pure air to �v � 10°� 15° when � � 5. The twilight arch is most pro-nounced about 20 minutes after sunset in moderatelyturbid air, i.e., when �0 � �6° and � � 1.5.27
Twilight purple occurs in SKYCOLOR under twodistinct situations. In pure air, very pale purple ap-pears on the side of the sky facing the Sun deep intwilight. The purple begins just above Earth’sshadow opposite the Sun and advances through thezenith to �v � 45° when �0 � �7°. If the stratosphereremains clean, tropospheric aerosols eliminate thepurple of deep twilight but produce a pale pink colorjust before and shortly after sunset from about �v
� 10°�15° for moderate values of turbidity �� � 2� to�v � 45° when � � 5. The pink of shallow twilightalso appears if the troposphere remains clean butvolcanic droplets occupy the stratosphere. Volcanicaerosols acting alone also produce a richer pink in
Fig. 8. SKYCOLOR simulations of the appearance of the sky fromhorizon facing the Sun at the bottom through the zenith to theopposite horizon at top when the Sun’s elevation angle, �0 � 40°, foran atmosphere with no aerosols (left), turbidity � � 5 and aerosolscale height 2.5 km (center), and sulfuric acid droplets of opticaldepth vul � 0.1 centered in the stratosphere at 25 km withe-folding height 2.0 km (right).
Fig. 9. Simulated color purity as a function of observer elevationangle, �v, for the cases modeled in Fig. 8.
Fig. 10. Integrated sky brightness for values of turbidity, �, from1 to 8 as a function of viewer elevation angle for solar elevationangles �0 � 5° (top) and �0 � 40° (bottom).
deep twilight ��0 � �7°� that tends toward purplewhen vul � 0.2. The richest purple of deep twilightoccurs when the atmosphere contains a modest quan-tity of both tropospheric aerosols and stratosphericdroplets. When � � 1.2 and vul � 0.01, purple ap-pears at �v � 60° when �0 � �4.5°. As twilight con-tinues to deepen, the purple band migratesdownward to �v � 10° when �0 � �7.5°, at whichpoint it rapidly fades. The richest purple occurs when�0 � �5.5° for a wide range of � �1.2 � � � 3�, and ��0.01 � vul � 0.2� has a color purity about 10%. As vulincreases, the purple band appears higher in the sky
and in shallower twilight and also fades more rapidlywith deepening twilight.
The purple of twilight can be diagnosed by examin-ing the skylight spectra (Fig. 13). The purple spectrumis bimodal, with a primary red peak at the edge of thevisible spectrum and a smaller blue peak at �� 0.48 �m. The peaks are separated by a trough foryellow light at � � 0.57 �m. The blue light originatesnear the top of the viewer beam and the red originatesnear the observer. Any combination of �, vul, and �0that enhances one of the red or blue peaks dispropor-tionately or fills the yellow trough destroys the purple.
Table 2. Comparison of Simulated (fSKYCOLOR) and Measured (fv) Elevation Angles of Brightest Elevation Angle of Sky for Cases Measured by Lee12
Fig. 11. Sequence of sky colors in pure air for �s � �0 � 15° to �6° at 3° intervals from the horizon to �v � 45° for four different pairsof � and vul.
Spectra of selected situations are displayed for fourdistinct situations in Fig. 13. The purple twilightspectrum in modestly hazy air (�0 � �6°, �v � 29°,� � 1.2, vul � 0.01) has the bimodal peak. The spec-trum for the deep blue sky of pure air far above thehorizon when the Sun is high in the sky (�0 � 42°,�v � 30°) decreases monotonically with �, while thespectrum for the red twilight horizon sky in pure air(�0 � �3°, �v � 1°) increases monotonically with �.The spectrum for the green band of sky in pure airshortly before sunset (�0 � 2°, �v � 2.1°) peaks at �� 0.50 �m.
The colors of cloud-laced skies either facing (Fig.14) or opposite (Fig. 15) the Sun near sunrise or sun-set have been admired and described from time im-memorial. Simulated sky and cloud colors are shownfor pure air �� � 1� in the three panels of Fig. 16. Thecloud deck, which is representative of altocumulus,has base hcld � 8000 m, and is seen at �cld � 3°.Shadows are not included so that no reduction ofnearby sunlight intensity is included below the cloud
deck. When �0 � 30° (left panel), the sky grades fromdeep blue above to near white at the horizon, and theclouds have a blue tint. When �0 � 2° (center panel),the pristine sky grades from an orange-red at thehorizon through yellow and pale green around �v
� 2° to blue aloft and clouds with golden fringes.When �0 � �3°, the horizon sky and clouds are
much redder. Despite sunlight’s long optical paththrough the atmosphere around sunset, the zenithsky is blue principally because ozone absorbs longerwaves more efficiently. When the Sun is at the hori-zon, the sky’s maximum blue color purity decreases toabout 22% but would be only 7% if there were noozone. Maximum blue purity at the zenith increasesas the Sun continues sinking below the horizon be-cause the lower atmosphere lies in shadow and nolonger contributes reddened light. Aerosols that areconcentrated in the lower troposphere Haer �� Hsclalso increase the purity of the blue zenith by blockingreddened light from the lower troposphere.
Clouds always expand the sky’s color gamut whenthe Sun is near the horizon because they alter theeffective optical thickness of the path taken by lightbeams as they pass through the atmosphere. Theprincipal factors affecting cloud color are solar height,�0, atmospheric turbidity, �, cloud height, hcld, eleva-tion angle, �v, and optical thickness, cld, and whetherthe cloud light is transmitted or reflected. For exam-ple, near sunset, altocumulus cloud elements oftenhave translucent fringes that are bright red andopaque shaded sides or bases that are purple.
Vivid golden cloud elements are almost exclusivelyconfined very near the horizon, at or shortly beforesunset. As the Sun sinks, clouds seen higher abovethe horizon turn orange and red. Spectacular cloudcolors are seen when the Sun has dipped below thehorizon but the clouds are still bathed in direct sun-light. After clouds fall into Earth’s shadow as twilightdeepens, they remain red in pure air. But when tro-pospheric aerosols are present, reddened light fromthe lower troposphere is almost completely extin-guished. Then, clouds turn purple at �cld � 15° when�0 � �3° or �4° and blue for �0 � �5°, while when�cld � 3°, clouds turn yellow for �0 � 5°. Clouds nearthe zenith are the last to turn, but both shaded andilluminated sides take on the deepest red colors.
The greatest play of color on a single cloud occurswhen it spans a great height, as when a toweringcumulonimbus is seen opposite the setting or risingsun. In that case, the cloud will grade from white attop to red at its base. A recent photo of a contrail fromthe space shuttle showed this gradation in dramaticfashion.28,29 But because SKYCOLOR uses a singlevalue of �cld and hcld, it cannot display this gradationin a single run.
Cloud shadows play a significant role in determin-ing sky color. Striking changes in sky color occurwhen an opaque cloud deck covers all but the distanthorizon facing the Sun. Most light then reaches theobserver after passing through a great optical thick-ness of air and is consequently reddened by scatter-ing, even if the air is pure. This is the principal cause
Fig. 12. Maximum green sky color purity defined as fraction ofdistance from the achromatic point (x � 0.3333, y � 0.3333) to the“green” point (x � 0.1547, y � 0.8049) as a function of solarelevation angle, �0, for � � 1 and 2, and for an eclipse sky with� � 1.
Fig. 13. Skylight spectra for the Blue of clean air at �v � 44°,�0 � 60° (heavy solid curve), Green sky at �v � 2.4°, �0 � 2° inclean air (thin solid curve), Red horizon sky at twilight, �v
� 0.06°, �0 � 2° in clean air (thin dotted curve), and Purple sky at�v � 29.4°, �0 � �6°, with � � 1.2 and vul � 0.01.
of the ominous orange tone of the sky in the minutesbefore rain begins when a severe thunderstorm ac-companied by an arc cloud has passed overhead. Sim-ilarly, when the Sun is low in the sky and analtocumulus deck covers all but the horizon, the ho-
rizon sky is apt to turn bright yellow. FredericChurch depicted such a scene in his painting, “Twi-light in the Wilderness,” and there are many photo-graphs that match the sky of the painting.6 In thiscase, the yellow horizon sky appears more vivid be-cause it contrasts with blue openings in the sky aboveand red clouds. Nevertheless, model simulations con-firm that shading by a cloud deck does indeed yellowthe horizon sky and redden the cloud, as in the chro-maticity diagram of Fig. 17, where cloud base, hcld
� 6 km and �cld � 2°, when the Sun is at �0 � 20°.The extreme example of the impact of shading oc-
curs during total solar eclipses. Not only is the nearbysky shaded, but sunlight intensity decreases almostlinearly with distance from the outer edge of the pen-umbra to the umbra.19 As a result, skylight near thehorizon that reaches an observer during a total solareclipse is markedly reddened because it penetratesfrom a great optical distance. For this reason, twi-light colors mark the eclipse horizon sky even whenthe Sun is high in the sky and when the air is pure(Fig. 18).30
Extraordinary twilight skies follow volcanic erup-tions because the stratosphere is filled withmicrometer-size particles that scatter long wavespreferentially. During the day, as Fig. 9 shows, skycolor is washed out in the direction of the Sun. In thetwo years following the eruption of Mt. Pinatubo,volcanic haze reduced the number of halos, coronas,
Fig. 14. Photographs of sky and cloud color when the Sun is near the horizon: (a) Color of the horizon sky when the Sun is above thehorizon and an opaque cloud layer shades the observer; (b) yellow and orange clouds when the Sun is 2° above the horizon.
Fig. 15. Photograph showing color gradation on a thunderstorm(15 August 1988) facing the setting Sun over New York City.SKYCOLOR can only show one cloud height and viewer elevationangle per run.
and iridescence observed and faded those that wereseen. But during twilight, when the stratosphere isstill illuminated, anomalous scattering turns the skycrimson to a great height above the horizon. When�4 � �0 � 7°, a distinct golden strip appears at
�v � 5° sandwiched between layers of red sky (Fig.19). Increasing turbidity to � � 2 turns the volcanictwilight sky �v � 25°�30° from orange-red to purple(Fig. 20).
The height of volcanic aerosols has only a second-ary effect on the appearance of the twilight sky solong as they are located in extremely tenuous strato-spheric air. The crimson of simulated skies wasslightly deeper and persisted later into twilight whenhvul � 25 km than when hvul � 18 km.
The observer’s altitude has a major impact on skycolor and brightness because it strongly affects the
Fig. 16. Simulated appearances of the sky from horizon facing the Sun to viewer elevation angle, �v � 45°, with pure air �� � 1� and anopen altocumulus deck with base, hcld � 8 km, at �cld � 3° without shadows for �0 � 30° (left), 2° (center), and �3° (right). Each cloudconsists of a core on bottom and a fringe on top.
Fig. 17. Chromaticity diagrams with dotted contours of color pu-rity illustrating the impact of shading. Top: Sky and cloud color fora cloud deck with base, hcld � 6 km and �cld � 2°, when the Sun isat �0 � 20°. Thin lines represent sky color below cloud base, heavylines represent cloud color. Sky and clouds with shadows are yel-lower and redder. Bottom: Sky color during a total solar eclipsewhen the Sun’s altitude is �0 � 53° and distance to the penumbra� 100 km for � � 1 (thick line) and � � 2.5, haer � 5 km (thin line).
Fig. 18. Fisheye photograph of the sky during the 11 August 1999total solar eclipse in Bagdere, Turkey showing spectral colors nearthe horizon. Reproduced with permission of Bob Yen, photogra-pher. E-mail: http://www.comet-track.com/eclipse/.
optical path length of light beams in the atmosphere(compare Fig. 21 with the top left panel of Fig. 11).When the Sun is high in the sky, maximum blue colorpurity increases with viewer altitude because the op-tical thickness is reduced. At h0 � 10 km, maximumcolor purity is 42.5%. Conversely, if sea-level pres-sure doubled, maximum color purity of the blue partof the sky at h0 � 0 would decrease to 38%, but thewarm twilight colors would be richer. Blue skies arethus a property of an optically thin atmosphere.
Altitude enhances the red twilight colors of thehorizon sky because the optical path length of a light
beam grazing the surface exceeds and can be as muchas double that at sea level. But increasing the observ-er’s altitude also enhances the blue of the twilight skymore than about 10° above the horizon because thetotal optical path length of sunlight plus a light beamreaching the twilight observer decreases with alti-tude (right panel, Fig. 21). The net effect of the colorenhancing is to dramatize twilight skies seen fromthe air (Fig. 22).
It is appropriate to conclude the simulations with aprediction of the appearance of the twilight volcanicsky when viewed from the air. For observers aboveabout 5 km the golden strip of sky seen when �0 ��6° transforms to a blue strip at �v � 5° that remainssandwiched between layers of red sky (Fig. 23).
4. Summary and Conclusions
A model called SKYCOLOR that captures many as-pects of the light and color of the sky over the spher-ical Earth in the plane of the Sun and animates thechanges as the Sun goes down has been presented.Light in SKYCOLOR is refracted, absorbed by ozone,scattered by air molecules, aerosol particles, andclouds, and shaded by clouds or by the moon during asolar eclipse. Model skylight consists of sunlight thathas been scattered toward the observer but in turn isextinguished by scattering and absorption as it ap-proaches the observer.
SKYCOLOR contains many approximations. Sur-face albedo is not included. Multiple scattering istreated directly in clouds but is represented in clearair by reducing the extinction of light from scatteringby 30%, but provides no direct illumination. The at-mosphere is assumed to be isothermal and horizon-tally uniform. Vertical distributions of aerosols andozone decay exponentially from prescribed maximumlevels. Heuristic equations are used to represent theimpact of refraction on the optical path length ofsunbeams reaching the light beam seen by the ob-server, as well as for the Mie angular scattering
Fig. 19. Postvolcanic twilights: (a) Predawn sky over New YorkCity in October 1991 after Mt. Pinatubo. (b) Postsunset sky overSarasota, Fla., in January, 1984, after El Chichon.
Fig. 20. Chromaticity diagram showing the impact of turbidity onvolcanic twilight skies for �0 � �6° and vul � 0.01 when � � 1(thick line) and � � 1.2 (thin line). Only a small amount of aerosolsin stratosphere and troposphere turn the feeble light aloft fromorange-red to purple.
Fig. 21. SKYCOLOR simulated appearances of the sky for anobserver at hobs � 10 km, for �s � �0 � 15° to �6° (3° below thehorizon) in clean air.
phase functions, while simple approximations areused for the wavelength dependence of scattering bytropospheric ���1� and stratospheric ��1� aerosols.
Despite these limitations and approximations,which greatly increase animation speed but intro-duce errors, SKYCOLOR reproduces many featuresof skylight and color including the following high-lights. When the Sun is high in the sky and the air isclean, sky color grades from relatively deep blue atthe zenith to almost white at the horizon whilebrightness increases toward the horizon. As atmo-spheric turbidity increases due to aerosols, the skywhitens and brightens, particularly around the Sunbut eventually grows darker near the horizon, andsunlight at the ground decreases and reddens.
As the Sun nears the horizon, sky color ranges fromblue above through green, yellow, and orange or redat the horizon, but the twilight colors can appearwhen the Sun is high in the sky provided the nearbysky is shaded by an opaque cloud deck or by the moonduring a solar eclipse. Clouds near the horizon turngold and then red as the Sun dips below the horizon.When aerosols render the atmosphere hazy, clouds
higher than about 15° above the horizon or oppositethe Sun turn rosy purple and ultimately blue as twi-light deepens. Typical tropospheric aerosols shift thepalette of clear sky colors toward white (and awayfrom green) during the day, but shift it toward greenduring twilight.
Volcanic aerosols high in the stratosphere dull thesky during the day and turn the Sun or moon slightlygreen or blue. During twilight when the stratosphereremains directly illuminated, anomalous scatteringfrom volcanic particles turns the sky more than about5° above the horizon crimson red while a golden layeris sandwiched between the crimson sky aloft and thered horizon. Vivid purple twilight skies require thepresence of both volcanic droplets and troposphericaerosols. The purple spectrum is bimodal. Distantlight is primarily blue, and nearby light is primarilyred.
Observer altitude has a profound effect on the ap-pearance of the sky. The elevated observer sees aredder horizon and bluer zenith than an observer atsea level.
In summary, while simulations produced by thesimplified model presented here can never capturethe full range or beauty of sky colors, they can quicklyprovide insight into the factors that affect sky colorand brightness under many varied conditions, andcan brighten the spirits on dark, rainy nights.
References and Notes1. The Sky Color model is available from the author at
[email protected]. Internet Sites for sky color simu-lations include http://www.vterrain.org/Atmosphere/ and http://ucsu.colorado.edu/�kuestern/Rtweb/startRT/html and http://www.ati.com/developer/SIGGRAPH03/PreethamSig2003CourseNotes.pdf and http://webexhibits.org/causesof-color/14B.html.
2. A. Meinel and M. Meinel, Sunsets, Twilights and EveningSkies (Cambridge Univ., London, 1983).
3. D. K. Lynch and W. Livingston, Color and Light in Nature, 2nded. (Cambridge Univ., London, 2001).
4. P. Candy, Le Meraviglie del Cielo (II Castello, Milano, 1997).5. F. W. Gallagher, W. H. Beasley, and C. F. Bohren, “Green
Fig. 22. Photograph of a clear twilight sky seen from the air.
Fig. 23. SKYCOLOR simulated appearances of the volcanic skywith vul � 0.1 for �0 � �6° showing the impact of turbidity andobserver height. � � 1.5 at ho � 0 km (left panel) with purple skynear �v � 45°, � � 1.0 at ho � 0 km (center panel), and � � 1.0 athobs � 10 km (right panel). The golden strip of sky seen by anobserver at sea level changes to blue for an airborne observer,whose horizon appears at �v � �3°.
17. S. D. Gedzelman, and J. Lock, “Simulating coronas in color,”Appl. Opt. 42, 497–504 (2003).
18. S. D. Gedzelman, “Simulating glories and cloudbows in color,”Appl. Opt. 42, 429–335 (2003).
19. S. D. Gedzelman, “Sky color near the horizon during a totalsolar eclipse,” Appl. Opt. 14, 2831–2837 (1975).
20. C. F. Bohren and D. R. Huffman, Absorption and Scattering ofLight by Small Particles (Wiley, New York, 1983).
21. S. D. Gedzelman, “Simulating rainbows and halos in color,”Appl. Opt. 33, 4607–4614, 4958 (1994).
22. C. N. Adams, G. N. Plass, and G. W. Kattawar, “The influenceof ozone and aerosols on the brightness and color of the twilightsky,” J. Atmos. Sci. 31, 1662–1674 (1974). Raymond Leepointed this out to me.
23. K.-N. Liou, An Introduction to Atmospheric Radiation, Vol. 26of International Geophysics Series, (Academic, New York,1980), p. 55.
24. S. T. Henderson, Daylight and its Spectrum (Elsevier, NewYork, 1970), pp. 34–43.
25. R. W. Bergstrom, P. B. Russell, and P. Hignett, “Wavelengthdependence of the absorption of black carbon particles: predic-tions and results from the TARFOX experiment and implica-tions for the aerosol single scattering albedo,” J. Atmos. Sci. 59,567–577 (2002).
26. C. F. Bohren and A. B. Fraser, “Colors of the sky,” Phys.Teacher 23, 267–272 (1985).
27. Ref. 3, pp. 33–45.28. D. L. Chandler, “The mystifying shuttle shadows,” Weather-
wise 54(4), 14–15 (2001).29. R. Greenler, “The NASA, Shuttle-launch dark-moon-ray mys-
tery,” presented at the Topical Meeting in Meteorological Op-tics, Boulder, Colo., 6–8 June 2001.
30. Many photographs of the sky near the horizon during totalsolar eclipses that show twilight colors are available at http://www.comet-track.com/eclipse. Courtesy of Bob Yen.
