Tropospheric Haze and Colors of the Clear Twilight Sky

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Research Article Vol. 56, No. 19 / July 1 2017 / Applied Optics G179

Tropospheric haze and colors of the clear twilight sky

RAYMOND L. LEE,JR.* AND DUNCAN C. MOLLNER Mathematics and Science Division, United States Naval Academy, Annapolis, Maryland 21402, USA *Corresponding author: [email protected]

Received 31 January 2017; revised 21 March 2017; accepted 23 March 2017; posted 24 March 2017 (Doc. ID 285879); published 12 June 2017

At the earth’s surface, clear-sky colors during civil twilights depend on the combined spectral effects of molecular scattering, extinction by tropospheric aerosols, and absorption by ozone. Molecular scattering alone cannot produce the most vivid twilight colors near the solar horizon, for which aerosol scattering and absorption are also required. However, less well known are haze aerosols’ effects on twilight sky colors at larger scattering angles, including near the antisolar horizon. To analyze this range of colors, we compare 3D Monte Carlo simulations of skylight spectra with hyperspectral measurements of clear twilight skies over a wide range of aerosol optical depths. Our combined measurements and simulations indicate that (a) the purest antisolar twilight colors would occur in a purely molecular, multiple-scattering atmosphere, whereas (b) the most vivid solar-sky colors require at least some turbidity. Taken together, these results suggest that multiple scattering plays an important role in determining the redness of the antitwilight arch. © 2017 Optical Society of America

OCIS codes: (010.1290) Atmospheric optics; (010.1310) Atmospheric scattering; (010.1690) Color; (010.3920) Meteorology; (330.1730) Colorimetry.

https://doi.org/10.1364/AO.56.00G179

τ 1. INTRODUCTION optical depths aer;λ) affect colors throughout the clear twilight sky? One plausible idea is that redder direct sunlight from larger Students of sky color learn early on that sunrise and sunset col- τ aer;λ will produce redder features in the antisolar direction, ors become redder as concentrations of small particles increase – in the lower troposphere [1–5]. Scattering by solid and liquid much as it does for the alpenglow and rainbow [13 15]. particles that are small compared with the wavelengths λ of vis- Similarly, could large changes in molecular surface pressures ible light (here taken as 400 ≤ λ ≤ 700 nm) greatly increases and number densities ever yield twilight colors that rival those of the real atmosphere? the reddening of direct and forward-scattered sunlight com- – pared with that due to molecular scattering alone. Hulburt In Sections 2 4 below, we address these questions by com- showed in 1953 that spectral absorption by ozone’s Chappuis paring measured and modeled twilight chromaticities and color bands helps to explain colors and spectra in sunlit regions of the maps. However, we start by considering the effective optical clear twilight sky, including at the zenith [6]. However, in 1974 properties of real and simulated tropospheric haze particles, as Adams et al. used a single-scattering model to demonstrate that well as those for atmospheric ozone. In principle, each of our a purely molecular atmosphere, whether it includes ozone or twilight hyperspectral scans should be accompanied by detailed, not, would yield only yellowish-orange sunset skies rather than directly sampled soundings of aerosols and ozone throughout red ones (see [7], Figs. 16 and 17). When they added a normal the local atmosphere. Although this ideal exceeds our equipment and personnel resources, Fig. 1 illustrates one satisfactory alter- amount of tropospheric aerosol to their model, this change did τ indeed produce an orangish-red solar sky near sunset (see [7], native: normal aer;λ data acquired by AERONET sun photom- Fig. 19). eters [16] near our coastal site in North Beach, Maryland Yet such single-scattering twilight models [7–9] by defini- (38.710° N, 76.529° W). Although AERONET data is mea- tion cannot produce multiple-scattering features (e.g., the dark sured at five discrete wavelengths across the visible, it is well segment [10,11]), and they may omit important spectral and approximated by the continuous Angström function [17] colorimetric details in the sunlit atmosphere [12]. In fact, τ βλ−α aer;λ ; (1) tropospheric haze aerosols’ profound effects on circumsolar twilight colors suggest a corollary question: how do changes with β ∝ spectrally integrated τaer and α specifying aerosols’ in aerosol concentrations (as measured by, say, aerosol spectral effective spectral dependence. Thus aerosol optical depth

0.15 0.15 non-sea-salt sulfates, sodium, ammonium, and chloride, along

North Beach, Maryland with soluble ferrous species [21]. Consistent with these data, τ our twilight simulations use the spectral extinction properties AERONET normal aer,λ 0.12 0.12 of what Shettle labels a “tropospheric” mixture of water-soluble and dust-like aerosol species [22]. This broad category is acceptable for our colorimetric and photometric modeling of 0.09 0.09 North Beach twilights because the pre-sunset AERONET normal τ τ aer;λ data quantifies their effective bulk spectral extinction aer,λ properties. 0.06 0.06 On ozone changes and twilight colors, Lee previously ana- 11-27-2016 10-20-2013 lyzed [12] whether large seasonal variations in 2005 Antarctic 11-3-2013 ozone concentrations (O3) could affect twilight chromaticities, 0.03 0.03 and he found only weak correlations between the two quantities. In fact, changes in polar aerosol composition and concentrations had as much influence on twilight colors as 0.00 0.00 400450500550600650700 did changes in either column total O3 or its vertical distribu- λ wavelength (nm) tion. In addition, a local Maryland site exhibited weak corre- τ O Fig. 1. Aerosol normal optical depths aer;λ measured as a function lations between 3 concentrations and spectrally measured of wavelength λ by the NASA Goddard Space Flight Center’s zenith colors [12]. Finally, note that the 2005 variations in AERONET sun photometers at Greenbelt, Maryland (2013 dates) Antarctic O3 concentrations were much larger than those and Edgewater, Maryland (11-27-2016), the two sites closest to for Fig. 1: in the Antarctic, the ozone coefficient of variation our twilight measurements in North Beach, Maryland. CVO3s∕x ∼ 36%, whereas CVO3 ∼ 8.6% near North Beach in October–November 2013 [23]. Given (a) the moot effects of large ozone variations on measured twilight colors and ’ O increases as β increases, and its spectral selectivity increases as (b) the North Beach site s much stabler 3 concentrations, α increases. we use a fixed (and realistic) ozone level of 300 Dobson units Among the twilights measured with our Pika II imaging for its simulated twilights. ’ τ spectrometer [18], Fig. 1 s three aer;λ spectra are from dates that have minimal, intermediate, and high amounts of tropospheric aerosols. In 56 clear skies from 2007–2016 for which 2. MEASURED AND MODELED ANTITWILIGHT Lee has measured spectra and colors, local AERONET data COLORS yields a sample mean xα1.5203 and a sample standard On 21 clear evenings from November 2012–November 2016, deviation sα0.3925. Note that molecular scattering has the Pika II was used to measure twilight spectra of clear skies α ∼ 4.09 τ ∝ λ−4.09 so that mol;λ [19]. Table 1 lists the best- at two sites: the United States Naval Academy in Annapolis, fit aerosol α and β parameters for Fig. 1’s three twilights. Maryland and at North Beach. Both sites are on the Lacking direct samples of North Beach’s local aerosol col- Chesapeake Bay’s western shore. For each scan, the Pika II umn, we do not know precisely what its dispersed-phase species camera’s optical axis panned along an almucantar at a fixed are for a particular twilight. However, measurements from a view-elevation angle of h 15°–16° above the astronomical coastal Delaware site in 1982–1983 indicate that its aerosols horizon. A calibrated digital inclinometer with a repeatability were predominated by small haze droplets that contained of 0.1° was used to determine h, and each scan’s lateral width sulfate and organic compounds, plus lesser amounts of fine dust of 196° included both the solar and antisolar skies. Because the and soil grains [20]. A 2007–2008 study at a coastal New Jersey North Beach site includes a wide, unobstructed view of the site found that most of its aerosol droplets included nitrate, Chesapeake Bay, we used its astronomical horizon (including

Table 1. Color Gamuts for Measured and Modeled Antitwilights ° ° τ β τ α ˆ Figure Measurement Date or Model Parameters Surface h0 ( ) h Interval ( ) aer;λ [Eq. (1)] aer;λ [Eq. (1)] gamut g 1, 3a 11-3-2013 −1.56 0–30 0.0061076 1.766 0.055410 1, 3a 10-20-2013 −1.77 0–30 0.018211 1.802 0.041579 1, 3a 11-27-2016 −1.74 0–30 0.030695 1.741 0.033644 4 aerosol, z 0km −1.56 0.5–30 0.0061076 1.766 0.045822 4 molecular, z 0km −1.56 0.5–30 N/A N/A 0.065206 5 aerosol, z 10 km −1.56 −3.2–30 0.0061076 1.766 0.10737 5 molecular, z 10 km −1.56 −3.2–30 N/A N/A 0.12547 6 8-4-2013 −3.03 −2.1–30 N/A N/A 0.088551 6 8-9-2013 −2.89 −2.1–30 N/A N/A 0.061952 aFigure 3’s maxima of β and gˆ are in boldface, whereas its minimum values are in italics. Entries labeled N/A indicate “not applicable” for purely molecular atmospheres or “not available” for Fig. 6. Research Article Vol. 56, No. 19 / July 1 2017 / Applied Optics G181

Fig. 2. Visible-wavelength images calculated from hyperspectral scans made along almucantars at view-elevations h 15°–16° at North Beach on (a) 11-3-2013 at unrefracted sun elevation h0 −1.56°, (b) 10-20-2013 at h0 −1.77°, and (c) 11-27-2016 at h0 −1.74°. From Fig. 1, (a) has the minimum spectrally integrated τaer and (c) has the maximum τaer. a small dip-angle correction [24]) to refine inclinometer mea- locus and its corresponding color-temperature limits. Figure 3’s surements of the camera’s h angle. perceptual scale for color difference is a MacAdam just- Figures 2(a)–2(c) are twilight images calculated from hyper- noticeable difference (JND) ellipse for this part of the UCS spectral scans made on three different evenings at North Beach. diagram [27,28]. In Fig. 2,thedigitalred–green–blue (or RGB) values for each Plotted in Fig. 3 are u0v 0h chromaticity curves for Fig. 2’s pixel are determined by its CIE tristimulus values, and these in three antisolar meridians (i.e., at constant ϕrel 180°), with turn are calculated from the pixel’s radiance spectrum as mea- chromaticity coordinates at each h averaged across an azimuthal 0 0 sured by the Pika II. Lee and Laven [25] describe such spec- window of width Δϕrel 4°. Collectively, these u v h curves trum-to-RGB calculations in more detail. In Figs. 2(a)–2(c), illustrate the wide range of antisolar color gamuts typically seen h ∼ 30° at image top, the mean unrefracted sun elevation at the earth’s surface. In particular, note that the normalized 0 0 h0 ∼ −1.6°[26], and measured aerosol optical depths τaer in- colorimetric gamut gˆ [29] for any given u v h curve decreases crease from Fig. 2(a)–2(c). In particular, τaer380 nm as τaer increases, which is consistent with the color patterns seen 0.033182 for Fig. 2(a), 0.10286 for Fig. 2(b), and 0.16249 in Fig. 2. Table 1 summarizes the relationship between gˆ and τ for Fig. 2(c). See Fig. 1 for the corresponding aer;λ spectra. Although the antitwilight arch (or ATA) and dark segment occur at different maximum elevation angles and in slightly dif- – ferent compass directions in Figs. 2(a) 2(c), these maxima are 0.495 0.495 all at azimuth relative to the sun ϕrel 180°or∼1∕3 of the North Beach, Maryland ’ clear-sky antitwilight distance from each image s left edge. Sun elevation h0 only dif- colors (φ =180°) ATA ∼0.2 – rel fers by ° in Figs. 2(a) 2(c), but their twilight colors are 0.485 0.485 strikingly different: the ATA and dark segment are most vivid h increasing for Fig. 2(a)’s minimum τaer, whereas its sunlit blue sky is the ’ least chromatic of the three evenings. For Fig. 2(c) s maximum 0.475 MacAdam 0.475 τ ATA aer, the ATA is barely distinguishable from the surrounding * h = 0° JND sky, even though solar-sky colors are vivid near the image’s † h = 30° right edge. This pattern is not coincidental: in all of our hyper- CIE 1976 v' 0.465 0.465 spectral scans, the ATA and dark segment become less h increasing chromatic as τaer increases. * ≤ ≤ {-1.77° h0 -1.56°} ’ 0.455 † 0.455 Some of Fig. 2 s colorimetric data is plotted in Fig. 3, which 11-3-2013, τ(380 nm)=0.0332 shows the interior of the CIE 1976 uniform-chromaticity- * 10-20-2013, τ(380 nm)=0.103 scale (or UCS) diagram. To good approximation, this * 11-27-2016, τ(380 nm)=0.162 0 † † diagram’s v ordinate is a light source’s proportion of blue to 0.445 0.445 0 0 0.185 0.195 0.205 0.215 0.225 0.235 0.245 yellow–green (smaller v is bluer), and its u abscissa is the pro- CIE 1976 u' 0 portion of bluish-green to red (larger u is redder). Another Fig. 3. Smoothed meridional chromaticity curves of the antitwilight metric of color, correlated color temperature (or CCT), can arch (or ATA) and dark segment (near h 0°) from hyperspectral scans be used as a proxy for a source’s spectral energy distribution. made at North Beach on the twilight dates in Figs. 1 and 2. For each For this reason, Fig. 3 also includes part of the Planckian curve, azimuth relative to the sun ϕrel 180°andh 0°–30°. G182 Vol. 56, No. 19 / July 1 2017 / Applied Optics Research Article

0.49 0.49 we use MYSTIC’s backward mode in which photons are scat- MYSTIC antitwilight tered from the observer back toward the sun [32,33]. We colors at z = 0 km model A 0.48 φ 5.1° 0.48 model MYSTIC’s τaer λ using Eq. (1) and for now set its ( rel= 180°, h0= -1.56°) ; Lambertian surface reflectance r 0.2 at all λ. 0.47 reddest h 0.47 ’ MacAdam Figure 4 plots the colorimetric consequences for MYSTIC s JND 6.1° antisolar twilight of either eliminating aerosols entirely (i.e.,a h ’ 0.46 increasing 0.46 purely molecular atmosphere) or adopting Fig. 1 s minimum model B aerosol amount. We designate these as MYSTIC atmosphere 0.45 h = 30° 0.45 models A and B, respectively. In Fig. 4 and later simulations, CIE 1976 v' we set unrefracted h0 −1.56° to aid comparisons among 0 ’ τaer 0.44 0.44 figures [this h value is for Fig. 2(a) s minimum case]. As shown by the perceptibly large distance between Fig. 4’s min aerosol + O 0 0 h = 0.5° 3 two u v h curves at their respective minimum CCTs, at 0.43 molecular + O 0.43 3 0km ’ Planckian locus the surface (altitude z ) the ATA in model As molecular atmosphere would have visibly purer reds than those from 0.42 0.42 0.17 0.18 0.19 0.20 0.21 0.22 0.23 0.24 model B (minimum τaer of 11-3-2013). In other words, the CIE 1976 u' smallest antitwilight CCT in a molecular atmosphere Fig. 4. MYSTIC Monte Carlo simulated meridional u0v 0h curves (∼4050 K at h 5.1° and ϕrel 180°) would be visibly red- for a purely molecular atmosphere (designated atmosphere model A) der than the most vivid ATA simulated for North Beach and one with minimal τaer (atmosphere model B based on 11-3-2013; (∼5390 K at h 6.1°). see Fig. 1). The observer is at z 0km, ϕrel 180°, and While we cannot visually experience a purely molecular −1.56 h0 ° as in Fig. 2(a). atmosphere, we can approximate its antitwilight colors from an airplane in the lower stratosphere (at, say, z ∼ 10 km). Combined with Table 1’s gˆ values, Fig. 5 shows just how much τ α β surface values of aer;λ parameters and , with the latter values this higher altitude can improve antitwilight colors: at the same requiring λ in Eq. (1)tobeinμm. h0, not only has gˆ for model B nearly doubled from the ob- To simulate twilight colors, we use a multiple-scattering served North Beach value, but its minimum CCT in the strato- Monte Carlo model that (a) includes the spherical atmosphere spheric antitwilight arch is now reduced (i.e., further reddened) needed for twilight, (b) specifies surface and atmospheric scat- to ∼3740 K at h 0.8°[34]. Although an observer at tering and absorption either just radially or in all three dimen- z 10 km is far above boundary layer aerosols, their optical sions, and (c) simulates skylight spectral radiances at and far effects are still visible due to backscattering of direct sunlight above the earth’s surface [30,31]. This MYSTIC model (from that has been reddened after traversing the troposphere at low “Monte carlo code for the phYSically correct Tracing of pho- (or even surface-grazing) altitudes. tons In Cloudy atmospheres”) has been developed over two Figure 6 shows that the increases in gˆ due to an observer’s decades and used on many atmospheric radiative transfer prob- large z can be pronounced: on two different airline flights, Lee lems from the ultraviolet to the thermal infrared. For efficiency, used a colorimetrically calibrated RGB camera [12] to measure

0.48 0.48 antitwilight colors seen 0.52 0.52 from lower stratosphere clear-sky antitwilight colors model A (φ = 180°, h = -1.56°) 0.46 8-4-2013, z=11.0 km 0.46 rel 0 8-9-2013, z=11.3 km 0.50 model B 0.50 ATA 0.44 MacAdam CCT ~ 5350 K 0.44 h increasing JND min 0.48 0.48 {Wyoming, h = -3.0°} h = 32° 0 h = -3.2° 0.42 0.42 0.46 h=0° 0.46 CIE 1976 v' CIE 1976 h increasing

CIE 1976 v' 0.40 0.40 MacAdam CCT = 0.44 JND 0.44 ∞ min h = 12390 K {Yukon, 30° h increasing h = -2° h0 = -2.89°} 0.38 0.38

0.42 MYSTIC(molec+O3, z=10 km) 0.42 MYSTIC(molec+aeros+O3, z=10 km) North Beach, MD 11-3-2013 (z=0 km) 0.36 0.36 0.40 0.40 0.15 0.16 0.17 0.18 0.19 0.20 0.21 0.22 0.23 0.17 0.18 0.19 0.20 0.21 0.22 0.23 0.24 0.25 CIE 1976 u' CIE 1976 u' Fig. 6. Smoothed meridional chromaticity curves of the ATA and 0 0 Fig. 5. Meridional u v h curves measured for the minimum τaer dark segment calculated from calibrated RGB camera images taken at case on 11-3-2013 (observer at z 0km) or simulated by airplane flight altitudes z ∼ 11 km near Burlington, Wyoming MYSTIC models A and B with the observer at z 10 km. (8-4-2013) and near Sterlin Lake, Yukon (8-9-2013). Research Article Vol. 56, No. 19 / July 1 2017 / Applied Optics G183

Fig. 8. Simulated twilight colors mapped as f ϕrel in a plane that is tilted up slightly from the solar horizon at ϕrel 0°, h 0° for Fig. 7. Geometrical relationship of the observer’s tangent plane to MYSTIC (a) purely molecular model A, (b) minimum τaer model the tilted plane of maximum circumhorizontal redness and to the ver- B, and (c) model C, which has the maximum τaer observed in tical principal plane. For clarity, the tilt angle hmax is exaggerated here, Figs. 1 and 2(c). and the small rectangle indicates that the tangent and principal planes are perpendicular.

h hmax sinϕrel∕2. Figure 7 illustrates the relationships antitwilight colorimetric gamuts that were ∼12%–60% larger among this tilted plane, the observer’s horizontal tangent plane, than the largest gˆ from surface observations (see Table 1). and the vertical principal plane (the latter is defined by the sun, However, one consequence of Fig. 6’s lower h0 is that its zenith, and observer). In astronomical terms, the reddish band minimum antitwilight CCTs are in fact larger than those simu- is a celestial small circle that is tilted slightly with respect to the −1.56 lated in Figs. 4 and 5 for h0 °. This increase in mini- local tangent plane. During civil twilight, hmax increases as h0 mum CCT as h0 decreases is similar to that measured for decreases and as τaer increases at a given h0. surface-based twilights [10]. Thus the reddest part of the anti- Because this band is the reddest part of the circumhorizontal solar sky (the ATA) becomes steadily bluer as evening twilight twilight sky, using MYSTIC to map its colors is quite instruc- progresses, just as it does in Fig. 6. For naked-eye observers, the tive. We do so in Fig. 8 for three different atmospheres, each practical import of Figs. 5 and 6 is that to see the best antitwi- with simulated h0 −1.56°atz 0km: (a) model A’s purely ˆ light colors (i.e., antitwilights with the largest g), one should molecular atmosphere, (b) the minimum and (c) maximum τaer climb a tall mountain or, more conveniently, take a high- cases (models B and C, respectively) whose measured antisolar altitude airplane flight. τ chromaticities are graphed in Fig. 3. The aer;λ spectra for models B and C are plotted in Fig. 1 and their best-fit α and β values 3. MODELING COLORS OF THE are listed in the first and third rows of Table 1. As noted above, CIRCUMHORIZONTAL TWILIGHT SKY each atmosphere model is given the same surface O3 concen- Our experience to date is that the MYSTIC model tends to tration of 300 Dobson units. Thus Fig. 8 directly displays the 0 0 O shift antitwilight u v h curves along the Planckian locus to color consequences of having fixed 3 and no, minimal, or color temperatures slightly higher than those measured by large amounts of tropospheric haze aerosols. the Pika II. However, the simulated chromaticity curves’ shapes Readers will of course experience slightly different chroma- and gamuts are quite realistic, meaning that MYSTIC consis- ticities than we do when looking at Fig. 8, depending on their tently produces accurate relative, as distinct from absolute, particular display device or on the illuminant for their printed chromaticities. This is no small accomplishment, given the page. Those important caveats aside, we created Fig. 8 using τ (a) inherent difficulties of determining aer;λ spectra exactly standard projective geometry techniques that map twilight and (b) marked sensitivity of chromaticities to even small chromaticities into their RGB equivalents on a computer’s cali- differences in skylight spectra. Bearing these caveats firmly brated color display [36], for which we made white (or maxi- 0 in mind, we now extend the model’s reach across the sky to mum gray level R G B) correspond to an equal-energy u , 0 get a more complete picture of civil twilight’s underlying color v . Because twilight’s overall luminance dynamic range far ex- structure. ceeds that of most computer displays, we made Fig. 8’s lumi- As observed earlier [10], the ATA is in fact part of a reddish nances proportional to the square root of MYSTIC model band of light that encircles the horizon during civil twilight. For luminances. Furthermore, some twilight colors may be purer a surface observer, this band’s lowest point is the astronomical than a particular display can reproduce [37]. Thus Fig. 8 pro- horizon at the sun’s azimuth where it forms part of what vides a diligent, but not exact, color reproduction of the Minnaert calls the “bright glow” [35]. The band’s highest point MYSTIC twilights. is in the antisolar direction (see Figs. 2 and 3), where its h is What qualitative optical insights can Fig. 8 provide? First, as several degrees above the astronomical horizon at elevation Fig. 4 shows graphically, the molecular atmosphere in Fig. 8(a) angle hmax. Visualize this reddish band as the intersection of has the reddest antisolar colors (see the color map’s left side), a tilted plane with the observer’s celestial sphere, with followed by the far less saturated ones of the minimum τaer case the plane’s tilt angle being hmax and at any ϕrel its (model B) shown in Figs. 2(a) and 8(b). Note that Fig. 2(a)’s G184 Vol. 56, No. 19 / July 1 2017 / Applied Optics Research Article reddest colors are confined to a very narrow, slightly purplish model B 0.535 band just above the horizon near the scan’s left side. Yet what 0.535 φ = 0°, h = 0° Fig. 8(b)’s minimum τaer atmosphere lacks in antisolar vivid- rel (solar horizon) ness, it gains in its solar sky’s more saturated oranges. model A 0.515 0.515 For the maximum τaer atmosphere (model C) in Figs. 2(c) MYSTIC tilted azimuthal and 8(c), the ATA is marginally visible at best. And although paths through middle ’ ’ of ATA for h = -2.78° Fig. 8(c) s solar sky is now visibly redder than those in Fig. 8 s 0.495 0 0.495 two smaller-τaer cases, this red is less saturated. Note too that Fig. 8(c)’s midpoint where ϕrel 90° is the bluest of models – ’ A C. Thus taken as a whole, Fig. 8 s colors suggest that (a) CIE 1976v' 0.475 min aerosol + O3 (hmax= 11.3°) 0.475 adding even a little of Shettle’s tropospheric aerosol [22]to molecular + O3 (hmax= 11.0°) a molecular atmosphere makes the circumsolar sky redder at sunlight above the expense of the antisolar sky and (b) adding more aerosol 0.455 atmosphere 0.455 will eventually eliminate any visible redness in the antisolar φ = 180°, h = h sky while not necessarily making the solar sky a vivid red. rel max (reddest part of ATA) These two trends are clearly evident in Fig. 2’s observed 0.435 0.435 0.18 0.20 0.22 0.24 0.26 0.28 0.30 0.32 twilights. CIE 1976 u' Figure 9 translates Fig. 8’s azimuthal trends to the UCS dia- Fig. 10. Same as Fig. 9 for models A and B, but here for gram. In Fig. 9, the model A molecular atmosphere has the −2.78 x 0 ≤ ϕ ≤ 180 h0 °. As a point of reference, an marks the chromaticity smallest ° rel ° circumhorizontal colorimetric gamut of sunlight above the atmosphere. while model B (minimum τaer) has the largest gamut. Two important color consequences of this larger gamut are that, compared with model A’s molecular atmosphere, model B ’ has a less-red ATA (i.e., its CCTs are larger) and a redder rather than at the suns azimuth, a displacement that is just sky near the solar horizon. This suggests that, unlike the alpen- discernible in Fig. 8(c). Figure 10 shows the colorimetric results of lower h0 on glow or rainbow, reddening of direct sunlight does not by itself ’ explain the redder ATAs that result from having little or no Fig. 9 s tilted-plane azimuthal colors. For both the molecular and minimum τaer atmospheres, the 0° ≤ ϕrel ≤ 180° colori- aerosol. A plausible explanation is that in the molecular atmos- −2.78 phere, redder indirect sunlight from the solar sky (i.e., multiple metric gamut is larger at h0 °. This expansion neces- scattering) gives model A the reddest ATA in Figs. 4 and 9. For sarily means that the (a) reddest part of each ATA is now bluer (note Fig. 10’s higher CCTs at ϕrel 180°) and (b) solar skies Fig. 9’s model C (maximum τaer), the entire chromaticity curve is shifted toward higher CCTs (i.e., it is bluer at all h) and its are now redder. Thus in either atmosphere, as the sun moves solar half lies farther from the Planckian locus. In fact, the farther below the horizon the ATA fades into its blue-sky surroundings and circumsolar colors become more vivid. reddest part of this circumhorizontal sky occurs at ϕrel ∼ 16° 4. MODELING COLORS OF THE TWILIGHT SKY’S PRINCIPAL PLANE 0.53 0.53 Figure 11 rotates the plane of simulated twilight colors so that it φ = 0°, h = 0° rel passes through the zenith. In other words, this color map shows 0.52 (solar horizon) 0.52 twilight colors of the clear-sky principal plane, again using MYSTIC tilted azimuthal Fig. 8’s atmospheres and h0 −1.56°. As in Fig. 8, we make 0.51 paths through middle 0.51 ’ of ATA for h = -1.56° Fig. 11 s displayed luminances proportional to the square root 0 of MYSTIC model luminances. The ATA for Fig. 11(a)’s 0.50 0.50 model C

0.49 0.49 φ rel= 0°, h = 0° CIE 1976CIE v' 0.48 model A 0.48

φ (reddest part of ATA) rel= 180°, h = hmax 0.47 0.47 min aerosol + O (h = 6.1°) model B 3 max molecular + O (h = 5.1°) 0.46 3 max 0.46 max aerosol + O3 (hmax= 7.8°) h = hmax 0.45 0.45 0.18 0.20 0.22 0.24 0.26 0.28 0.30 0.32 CIE 1976 u' 0 0 Fig. 9. MYSTIC simulated azimuthal u v ϕrel curves for Fig. 8’s tilted-plane maps of reddest twilight colors for h0 −1.56° that cor- Fig. 11. MYSTIC simulated twilight colors mapped in the clear- respond to models A (purely molecular), B (minimum τaer), and C sky principal plane at h0 −1.56° for (a) models A (purely molecu- (maximum τaer). lar), (b) B (minimum τaer), and (c) C (maximum τaer). Research Article Vol. 56, No. 19 / July 1 2017 / Applied Optics G185 purely molecular atmosphere (model A) clearly has the largest vertical extent and most vivid, saturated colors. However, this is paired on the solar horizon (map’s right edge) with a bright glow that is both narrower and slightly less orange than for either aerosol atmosphere [Figs. 11(b) and 11(c); models B and C, respectively]. In Fig. 11(c)’s maximum τaer case, the bright glow has its largest vertical extent although its lower edge is dull-looking and desaturated, and the ATA is barely visible above the antisolar horizon. Both color deficiencies stem from this turbid atmosphere’s increased multiple scattering. Figure 12 graphs the colorimetric data that underlies Fig. 11’s color map. In Fig. 12, we extend Fig. 4’s antisolar features and also include chromaticities from model C (maximum τaer). Much like its Fig. 9 cousin for circumhorizontal colors, Fig. 12 indicates that the reddest solar-sky colors will occur for some unknown minimum τaer (note that both the molecular and maximum τaer cases are less red near the solar τ ψ horizon). Exactly what spectrally integrated aer value yields Fig. 13. MYSTIC simulated principal-plane luminances Lv for these minimum CCT colors likely depends on the shape of the Fig. 11’s maps of twilight colors that correspond to models A (purely τ molecular), B (minimum τaer), and C (maximum τaer). corresponding aer;λ spectrum. However, MYSTIC simulations show that in a purely molecular atmosphere, redder solar-sky colors can also be pro- duced by increasing surface pressure and thus increasing Equally noteworthy in Fig. 11 are differences among the ’ molecular number density N mol. This enhanced redness is rea- three zeniths local minima of luminance Lv. The zenith is best sonable given that molecular single scattering extinguishes di- defined for Fig. 11(b)’s minimum τaer case (model B), since its −4.09 rect sunlight at a rate ∝ λ , whereas our local aerosols combined scattering yields a slightly narrower dark region near −1.52 typically do so only at a rate ∝ λ . Thus from the standpoint the zenith than do models A and C. Figure 13 helps to explain of spectral extinction by single scattering, aerosols typically are this subtlety. In it, we plot MYSTIC Lv as a function of single- less effective than molecules in reddening sunlight scattered in scattering angle ψ, which equals 1.56° on the solar horizon and near-forward directions. (As is often true, though, multiple 91.56° at the zenith for h0 −1.56°. Not only is the near- scattering complicates this simple picture.) The reason that zenith sky slightly darker for model C (maximum τaer), but ψ aerosols redden sunlight is not that they are more effective its Lv curve is also slightly wider here. Taken together, these at doing so per unit optical depth. Instead, the distinction is details describe a darker zenith sky that has lower contrast than between the possible and impossible: while τaer can vary widely model B. The zenith of the model A molecular atmosphere is in the real atmosphere, its counterpart τmol cannot given that also less well-defined because it too has a broader local mini- ψ changes in surface N mol are proportionally much smaller. mum in Lv . However, model A has the brightest zenith because molecular scattering is symmetric about ψ 90°. Put another way, single scattering of direct sunlight is stronger 0.54 0.54 for model A near ψ 90° than for either model B or C. MYSTIC principal-plane colors Although the minimum CCTs that define the ATA tend not (z = 0 km, h0 = -1.56°) 0.52 0.52 to occur at the same h as their corresponding luminance maxima [10], Fig. 13 shows that these nearby local maxima solar horizon ψ in Lv also behave predictably at constant h0. As aerosol 0.50 model C 0.50 ψ amount increases, the local maxima in antisolar Lv widen and move to higher h at a given h0. As a result, the ATA has 0.48 0.48 lower color and luminance contrast as τaer increases (see Figs. 2 ψ ATA and 8). Figure 13 has similar Lv patterns in the solar sky, but CIE 1976 v' model A with one important difference: some unknown minimum τaer 0.46 0.46 produces the brightest glow. This is because as τaer increases, sky antisolar model B horizon brightness near the sun responds to a changing balance between min aerosol + O 0.44 3 0.44 (a) relatively weak forward scattering by molecules, which is molecular + O 3 eventually surpassed by (b) stronger forward scattering from max aerosol + O3 zenith aerosols, which in turn is (c) reduced by increased extinction 0.42 0.42 from ever-larger aerosol slant-path optical thicknesses. 0.16 0.18 0.20 0.22 0.24 0.26 0.28 0.30 0.32 CIE 1976 u' 5. CONCLUSIONS Fig. 12. MYSTIC simulated meridional u0v 0h curves for Fig. 11’s maps of twilight principal-plane colors that correspond to models A Our analysis of calibrated RGB camera images and ∼80 (purely molecular), B (minimum τaer), and C (maximum τaer). hyperspectral scans made during 21 clear evenings reveals G186 Vol. 56, No. 19 / July 1 2017 / Applied Optics Research Article several little-known features of civil twilights. First, our data 8. G. V. Rozenberg, Twilight: A Study in Atmospheric Optics (Plenum, ’ 1966), pp. 245–249. clearly shows that at a given h0, the antitwilight archs vertical “ τ 9. J. V. Dave and C. L. Mateer, The effect of stratospheric dust on the extent, colorimetric purity, and redness all increase as aer de- ” 73 – 0 0 color of the twilight sky, J. Geophys. Res. , 6897 6913 (1968). creases, with redness calculated either by CCT or u , v chro- 10. R. L. Lee, Jr., “Measuring and modeling twilight’s Belt of Venus,” Appl. maticities (Figs. 2–4). Second, to make the ATA even more Opt. 54, B194–B203 (2015). vivid, one can either wait for exceptionally clear, unturbid skies 11. D. K. Lynch, D. S. P. Dearborn, and S. C. Richtsmeier, “Antitwilight I: structure and optics,” Appl. Opt. 56, G156–G168 (2017). or ascend above boundary layer aerosols in an airplane or on a 12. R. L. Lee, Jr., W. Meyer, and G. Hoeppe, “Atmospheric ozone and mountaintop (Figs. 5 and 6). Either approach provides a real- colors of the Antarctic twilight sky,” Appl. Opt. 50, F162–F171 (2011). atmosphere approximation to the even more visually striking 13. J. C. Naylor, Out of the Blue: A 24-hour Skywatcher’s Guide ATAs of the theoretical molecular atmosphere. Third, for most (Cambridge University, 2002), pp. 69–73, 101–102. turbidities the ATA and dark segment both become visibly 14. See Ref. 2, p. 12. 15. See Ref. 4, p. 106. bluer as h0 decreases (Figs. 6, 9, and 10). ’ τ 16. Figure 1 s aer;λ data is archived by the AErosol RObotic NETwork Fourth, MYSTIC simulations indicate that twilight’s most (AERONET) at http://aeronet.gsfc.nasa.gov. vivid solar-sky colors require some, but not too much, turbidity 17. K.-N. Liou, An Introduction to Atmospheric Radiation (Academic, (Figs. 8–12). The additional spectrally selective extinction by 1980), p. 239. 18. Pika II hyperspectral imaging system from Resonon, Inc., 123 aerosols further reddens skylight near the sun, albeit not as ef- Commercial Drive, Bozeman, Montana 59715 (http://www.resonon. ficiently as an equivalent (but unrealistic) increase in molecular com). The system consists of a digital camera that has an internal dif- scattering would. Fifth, the model A molecular atmosphere fraction grating and is coupled to a rotation stage controlled by a pre- would simultaneously produce (a) a redder ATA and (b) cision stepper motor and laptop computer. In this pushbroom system, less-reddened direct sunlight than our model B minimum the laptop acquires 640 different skylight spectra at each rotation stage τ ’ position (i.e., for each line of the resulting hyperspectral datacube). aer case (Figs. 9 and 12). Because the molecular ATAs greater 19. See Ref. 5, p. 398. redness must come from somewhere other than direct sunlight, 20. G. T. Wolff, N. A. Kelly, M. A. Ferman, M. S. Ruthkosky, D. P. Stroup, the MYSTIC simulations lead us to think that reddish multiple and P. E. Korsog, “Measurements of sulfur oxides, nitrogen oxides, ” scattering plays an important role in determining the colors of haze and fine particles at a rural site on the Atlantic coast, J. Air ’ Pollut. Control Assoc. 36, 585–591 (1986). the antitwilight arch and the dark segment. Sixth, MYSTIC s 21. L. Xia and Y. Gao, “Chemical composition and size distributions of principal-plane profiles of twilight Lv (Fig. 13) are realistic and coastal aerosols observed on the US East Coast,” Mar. Chem. instructive: not only does the model B minimum τaer case (c) 119,77–90 (2010). produce the real atmosphere’s brightest, most vivid ATA, but 22. E. P. Shettle, “Models of aerosols, clouds and precipitation for atmospheric propagation studies,” in Conference Proceedings No. 454 on (d) its strong (and minimally attenuated) forward scattering Atmospheric Propagation in the UV, Visible, IR and mm-Wave Region yields the brightest twilight glow above the solar horizon. and Related Systems Aspects (Copenhagen, 1989), pp. 1–13. Taken together, these measured and modeled results add nu- 23. The Meteorological Service of Canada archives surface-based Dobson ance to our understanding of how molecular and aerosol scat- spectrophotometer data (www.woudc.org/data_e.html), and its mean O – tering affect the coloring of the twilight sky. column total 3 for October November 2013 from nearby Wallops ’ Island, Virginia is 296.2 Dobson units. For 11-27-2016, the closest Raymond Lee s research has been generously supported by available data is at Raleigh, North Carolina, where column-integrated United States National Science Foundation grant AGS- O3 ∼ 290 Dobson units (archived at esrl.noaa.gov/gmd/grad/neubrew). 0914535, as well as by the United States Naval Academy’s 24. A. T. Young and G. W. Kattawar, “Sunset science. II. A useful dia- Departments of Mathematics and Oceanography. Opinions, gram,” Appl. Opt. 37, 3785–3792 (1998). 25. R. L. Lee, Jr. and P. Laven, “Visibility of natural tertiary rainbows,” findings, and conclusions or recommendations expressed in this Appl. Opt. 50, F152–F161 (2011). See the discussion of its paper are those of the authors and do not necessarily reflect the Fig. 11, but note that in our paper Fig. 2’s achromatic stimulus is given views of the National Science Foundation. by the equal-energy spectrum. 26. During the 3.5 min needed to acquire a scan at twilight lighting levels, ∼0.65 ’ Funding. National Science Foundation (NSF) (AGS- h0 changes by ° in Fig. 2. As a result, each of Fig. 2 s vertical scanlines occurs at a slightly different sun position, and this is used 0914535). in calculating the scanline’s azimuth relative to the sun ϕrel. 27. CCT and the MacAdam JND are described in G. Wyszecki and W. S. Stiles, Color Science: Concepts and Methods, Quantitative Data and REFERENCES AND NOTES Formulae, 2nd ed. (Wiley, 1982), pp. 224–225, 306–310. “ 1. M. G. J. Minnaert, Light and Color in the Outdoors (Springer-Verlag, 28. J. Hernández-Andrés, R. L. Lee, Jr., and J. 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32. B. Mayer, S. W. Hoch, and C. D. Whiteman, “Validating the MYSTIC below the local tangent plane, which corresponds to h<0° three-dimensional radiative transfer model with observations from the in Fig. 5. complex topography of Arizona’s Meteor Crater,” Atmos. Chem. Phys. 35. See Ref. 1, p. 296. 10, 8685–8696 (2010). 36. See Ref. 27, pp. 138–139. 33. C. Emde, R. Buras, B. Mayer, and M. Blumthaler, “The impact of aero- 37. Figure 8 was developed for a Sony Trinitron display with the sols on polarized sky radiance: model development, validation, and following CIE 1976 primaries: u0(red) 0.4289, v 0(red) 0.5268, applications,” Atmos. Chem. Phys. 10, 383–396 (2010). u0(green) 0.1169, v 0(green) 0.5594, u0(blue) 0.1721, and v 0(blue) 34. For notational consistency, all h and h0 values in Fig. 5 are given as if 0.1744; each color channel has a gray-level gamma of 1.8. All of the observer were still on the z 0kmtangent plane. However, at Fig. 8’s colors are well within the triangular u0, v 0 gamut spanned z 10 km one can see the bluish skylight that comes from just by this display’s three primaries.