An investigation of the implications of lunar illuminationspectral changes for Day/Night Band-basedcloud property retrieval due to lunarphase transitionMin Min1 , Jianbo Deng2, Chao Liu3 , Jianping Guo4 , Naimeng Lu1, Xiuqing Hu1, Lin Chen1,Peng Zhang1 , Qifeng Lu1, and Ling Wang1

1Key Laboratory of Radiometric Calibration and Validation for Environmental Satellites, National Satellite MeteorologicalCenter, China Meteorological Administration, Beijing, China, 2Hunan Institute of Meteorological Sciences, Changsha, China,3Key Laboratory for Aerosol-Cloud-Precipitation of China Meteorological Administration, School of Atmospheric Physics,Nanjing University of Information Science and Technology, Nanjing, China, 4State Key Laboratory of Severe Weather,Chinese Academy of Meteorological Sciences, Beijing, China

Abstract The Moon reflects sunlight like a huge mirror hanging in the sky at night, which presents theobviously periodical changes in its luminance or irradiance due to Sun-Earth-Moon geometry variation.The potential effect of the periodical changes in lunar phase angle on nighttime Day/Night Band (DNB)radiative transfer simulation in the presence of cloud has seldom been reported thus far. In this study, aradiative transfer model is developed by coupling the lunar light source with various Sun-Earth-Moongeometries. To elucidate the stability of DNB-averaged cloud bulk scattering properties, we simulatenighttime reflectance and radiances under four typical lunar phase angles (0°, 45°, 90°, and 135°) from 7 April2016 to 8 May 2016 (e.g., two lunar cycles). Explicit simulation analyses indicated that DNB-averaged cloudbulk scattering properties exhibit weak sensitivity to lunar phase angles. The maximum DNB reflectancedifferences between any and 90° lunar phase angles are less than 0.05% (0.01%) in the presence of water (ice)clouds, indicating a negligible effect of periodically changes on lunar spectral irradiances. Our findingssuggest that the differences of reflectance at lunar phase angle = 90° are less than approximately 0.05%(water cloud)/0.01% (ice cloud), much smaller than 11% radiometric calibration uncertainties of DNB. Thismeans that these differences could be ignored in both nighttime cloud property retrieval and DNB radiativetransfer modeling.

1. Introduction

The Moon as a unique light source in the sky at night can directly reflect sunlight to the Earth’s surface, whichcan be well measured by some particular-designed satellite sensors [Miller et al., 2005]. However, in contrastwith the almost constantly apparent solar spectral irradiances, the obvious periodical changes in lunar spec-tral irradiances (LSI) are likely to introduce complexities and uncertainties into quantitative remote sensing atnight, which are closely associated with Moon phase angle, Sun-Earth-Moon distances, and Moon libration[Kieffer and Stone, 2005; Miller and Turner, 2009]. In particular, the changes in spectral distribution shapes oflunar irradiances are closely associated with the lunar phase-dependent Moon surface materials (or albedo)that reflect incident solar light [Kieffer and Stone, 2005]. As a first-ever attempt to observe the reflected moonlight, the low-light imager of Operational Linescan System (OLS) has been installed on the U.S. DefenseMeteorological Satellite Program (DMSP) constellation since the late 1960s [Miller et al., 2005; Miller et al.,2012b]. The low-light imager centered around visible and near-infrared wavelengths (about 0.4–1.0 μm) isable to measure radiances with the extremely low magnitudes at Earth’s surface in the range from 10�5 to10�3 W cm�2 sr�1 (e.g., reflected moonlight, polar aurora, and city light), which is approximately 10�6 timesfainter than sunlight [Miller et al., 2005;Miller et al., 2012b;Miller et al., 2013]. As a successor to the DMSP/OLS,a new Day/Night Band (DNB) with improved performance on the Visible/Infrared Imager/Radiometer Suite(VIIRS) is carried by the Suomi National Polar-orbiting Partnership (SNPP) satellite as the first-generationpolar-orbiting satellite of the Joint Polar Satellite System, which was successfully launched on 28 October2011 [Cao et al., 2014; Lee et al., 2014; Lee et al., 2006]. Furthermore, the Chinese FengYun-3 (FY-3) Early-Morning-Orbit (EMO) satellite will also carry a DNB or low-light band on its key payload MEdium

MIN ET AL. CLOUD SIMULATION FOR DAY/NIGHT BAND 1

PUBLICATIONSJournal of Geophysical Research: Atmospheres

RESEARCH ARTICLE10.1002/2017JD027117

Key Points:• The DNB-averaged bulk cloudscattering properties do not varyconsiderably with different lunarphase angles

• The maximum DNB reflectancedifferences between any and90{degree sign} lunar phase angles areless than 0.05% (0.01%) for water (ice)cloud

• The periodical changes in lunarspectral irradiances exert a minoreffect on DNB radiative transfercalculations under cloudy conditions

Supporting Information:• Supporting Information S1

Correspondence to:J. Guo,jpguocams@gmail.com

Citation:Min, M., J. Deng, C. Liu, J. Guo, N. Lu,X. Hu, L. Chen, P. Zhang, Q. Lu, andL. Wang (2017), An investigation of theimplications of lunar illumination spec-tral changes for Day/Night Band-basedcloud property retrieval due to lunarphase transition, J. Geophys. Res. Atmos.,122, doi:10.1002/2017JD027117.

Received 11 MAY 2017Accepted 21 AUG 2017Accepted article online 24 AUG 2017

©2017. American Geophysical Union.All Rights Reserved.

Resolution Spectral Imager (MERSI) [Hu et al., 2012; Min et al., 2016], which is scheduled for launch in 2018[Zhang et al., 2015]. One of most crucial purposes of DNB observations on FY-3 EMO/MERSI is to providehigh-quality subpixel cloud test information for some passive microwave and infrared hyperspectral sensors,which act as a key data sources for assimilation module in numerical weather prediction model.

To date, the nocturnal visible and near-infrared lights measured by DNB from space have been extensivelyused in various important aspects of Earth’s many “spheres” from cryosphere to biosphere [Miller et al.,2013]. Previous scientific literatures [e.g., Miller et al., 2013] has elucidated the principle applications of DNBdata at nighttime, such as observing hurricanes, snow and sea ice, fire, lightning, coastal waters turbidity, soilmoisture, polar aurora, and city light [Bankert et al., 2011; Li et al., 2013]. Compared with the traditional solarreflective bands, the wider spectral response and high-gain detector of DNB make it possible for detectingboth the reflected sunlight at daytime and weak moonlight at nighttime. Besides, in the night, DNB is ableto capture more detailed features on the Earth’s surface through reflected moonlight than infrared bands[Miller et al., 2013]. Furthermore, more recent researchers [e.g., Johnson et al., 2013; Walther et al., 2013]attempted to use the VIIRS/DNB observation data to retrieve aerosol and cloud optical and microphysicalproperties. Themethod used to retrieve aerosol optical depth at night using VIIRS/DNBmeasurements largelydepends on the contrast between regions with and without artificial surface lights [Johnson et al., 2013]. Also,the nighttime inversion algorithms of cloud optical and microphysical properties take advantage of thedependence of DNB (a visible band) on cloud optical depth in a way analogous to those derived from sun-light [Hu et al., 2012;Walther et al., 2013]. However, to the best of our knowledge, both absolute radiometriccalibration precision and forward low-light radiative transfer model (RTM) at night have increasingly becomekey prerequisites for promoting effective quantitative applications of DNB data. Current SNPP VIIRS/DNBspans three dynamics radiance gains during the daytime, twilight, and nighttime with measured radiometriccalibration uncertainties of 11% at night [Liao et al., 2013; Miller et al., 2012b]. Despite the potential effect ofradiometric calibration precision on quantitative applications of DNB observation data, it goes beyond thescope of this study.

Some forward or fast radiative transfer models (FRTM), such as Community Radiative Transfer Model [Liu andBoukabara, 2014], have been found to be able to precisely simulate radiance, reflectance, or brightness tem-perature observed by visible, infrared, and microwave bands of satellite imaging sensors under clear andcloudy conditions with sunlight [Greenwald et al., 2016; Liu et al., 2015; Wang et al., 2013; Zhang et al.,2007]. The implementation of FRTM requires the application of some parameterization schemes in calculat-ing gas absorption or aerosol/cloud absorption and scattering effects, which helps improve original RTMoperation efficiency [Baum et al., 2007; Fu and Liou, 1992, 1993]. In the RTM parameterization schemes, solarspectral irradiances at visible and infrared bands have to be subject to convolution and normalization[Greenwald et al., 2016; Liu et al., 2015; Liu and Boukabara, 2014]. For the FRTM simulations under cloudysky condition, cloud (both water and ice phases) bulk scattering properties are required to determine theabsorption and scattering properties of cloud layers. For solar reflective or infrared band, band-averagedcloud bulk scattering property calculations are preaveraged and convolved over normalized band spectralresponse function (SRF) and relatively constantly solar spectral irradiance as the fixed parameters for RTM cal-culations [Baum et al., 2005; Baum et al., 2007]. Generally speaking, cloud optical and microphysical propertyretrieval algorithms often use a precalculated look-up table (LUT) instead of a forward model to interpret therelationship between satellite observations and cloud optical and microphysical properties [e.g., Waltheret al., 2013]. This LUT is calculated based on a precise radiative transfer model with the band-averaged cloudbulk scattering property model [Baum et al., 2007], which is required to convolve over both band SRF andnormalized light source spectral irradiances [Baum et al., 2007], representing the band-averaged cloud opticaland microphysical properties.

Nevertheless, due to the aforementioned phase-dependent LSI, the DNB-averaged cloud bulk scatteringproperties for RTM might be affected by the Moon motion. It is worth to note that most of the current night-time cloud retrieval algorithms do not consider or discuss this effect of variable phase-dependent LSI [e.g.,Walther et al., 2013]. Therefore, the primary objective of our investigation is to figure out the extent to whichthe variable phase-dependent LSI alters the cloud bulk scattering properties in nighttime cloud propertyretrieval and DNB radiative transfer simulations. The next sections will sequentially introduce the LSI andRTM models we use, followed by the effects of LSI on cloud bulk scattering properties, RTM simulations,

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and cloud bidirectional reflectance distribution function (BRDF) effect. Finally, the key findings willbe summarized.

2. Models2.1. Lunar Spectral Irradiance Model

The Moon, as a well-defined target and an excellent radiometric reference, is often used in the radiometricstability monitoring for solar reflected bands because of the stable spectral reflected sunlight over its surface[Sun et al., Jul. 2007]. For quantitative remote sensing, the Moon is no longer an excellent radiometric targetbut is still an important light source at night. It is a challenge to determine the incoming downwelling lunarspectral irradiances at the top of the atmosphere (TOA) [Miller et al., 2012a]. The TOA lunar spectral irradiances(ETOA) is a function of a number of components, including the lunar phase angle, and the Sun-Moon-Earthdistances, which can be expressed by equation (1) [Miller and Turner, 2009]. The lunar spectral irradiancemodel, covering the spectral range from 0.202 μm to 2.80 μm with 1 nm resolution, is developed anddescribed in detail by Miller and Turner [2009].

ETOA ¼ αEoRseRsm

� �2rm

Rme � re

� �2

f θð Þ; (1)

where α is the mean lunar visual albedo (0.105< α< 0.125); Eo is the solar constant;Rse is the mean Sun-Earthradius; Rsm and Rme are the Sun-Moon and Moon-Earth distances; rm and re are the radius of the Moon andEarth, respectively; and f(θ) represents the phase function which describes lunar brightness with lunar phaseangle θ.

This LSI model is based on a standard Sun-Earth-Moon geometry and geocentric viewing assumptions, whichare used to interpolate scaling results from an auxiliary look-up table (LUT) of time-dependent variables[Miller and Turner, 2009]. In this way, the TOA lunar spectral irradiances have been simulated at lunar phaseangles θ = 0°, 45°, 90°, and 135° (Figure 1a). It is worth noting that the four cases (θ = 0°, 45°, 90°, and 135°)applied here come from the simulations of two lunar cycles for the period 7 April 2016 to 8 May 2016.Also, the magnitudes of LSI are found to be negatively associated with lunar phase angle. Figure 1b

Figure 1. Simulated TOA lunar spectral irradiances at lunar phase angles θ = 0°, 45°, 90°, and 135° and NPP/VIIRS-DNB SRF (black solid line) and its associated lunarphase angle, (a) the changing appearance of the lunar disk [Miller and Turner, 2009], and (b) its corresponding normalized weighting values of DNB. Note that theilluminated sides of lunar bodies are shown in white and shaded sides in black.

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compares the SNPP/VIIRS DNB-averaged (spectral) and convolved normalized weighting (NW) values usingLSI and DNB SRF at four typical lunar phase angles shown in Figure 1a for cloud bulk scattering propertiescalculations [Baum et al., 2005; Baum et al., 2007], based on the following formula:

NW λð Þ ¼ SRF λð Þ�ETOA λð Þ∫λ2λ1SRF λð Þ

; (2)

where λ1 (0.4 μm) and λ2 (1.0 μm) are the bounding wavelengths of DNB SRF and LSI. Afterward, to obtainDNB SRF/LSI-dependent cloud bulk scattering properties, we convolve NW with cloud scattering parameters(CP) at the wavelengths from λ1 to λ2 using the following equation:

NCP ¼ ∫λ1λ2NW λð Þ�CP λð Þ; (3)

where NCP represents spectral normalized cloud scattering parameter.

Figure 1b also reveals remarkable differences in the normalized weighting values at four different lunarphase angles and a turning point at 0.7 μm. Figure 1a shows that the peak of the lunar irradiances spectraldistribution (θ = 0°) shifts from the 0.50–0.55 μm (solar spectral irradiance) to roughly 0.60 μm, which isprimarily attributed to the Moon surface albedo variation [Kieffer and Stone, 2005]. This Moon surfacealbedo variation is directly caused by the changes in reflected incoming sunlight by Moon surface, whichare closely associated with lunar phase angle and Sun-Moon-Earth geometry. As a consequence, this effectresults in differences of the normalized weighting values between four different lunar phase angles(Figure 1b).

Figure 2 shows the normalized weight ratios (10 min interval) with that at lunar phase angle θ = 90°, the lunarphase angle, the changing appearance of the lunar disk, and the Earth-Moon geometry in two lunar cyclesfrom 7 April 2016 to 8 May 2016. In Figure 2, we suppose the normalized weight at lunar phase angle

Figure 2. (top) Normalized weight ratios (at 10min intervals) between a given lunar phase angle and the lunar phase angle θ = 90° in two lunar cycles ranging from 7April 2016 to 8 May 2016, and (bottom) its associated lunar phase angle, the changing appearance of the lunar disk, and the Earth-Moon geometry [Miller and Turner,2009] as well.

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θ = 90° as a standard LSI for cloud bulk scattering property calculations, which shows an obviously periodicaldifference in two lunar cycles with a turning point at 0.7 μm.

2.2. Coupled Radiative Transfer Model

To simulate the radiance or reflectance under cloudy conditions at night, an accurate RTM that incorporatesboth gaseous absorption andmultiple scattering within cloud layers is indispensable. A new radiative transfermodel combined with the discrete ordinates radiative transfer (DISORT) model and the line-by-line (LBL)radiative transfer model (LBLRTM) is coupled with lunar incoming light source at night [Clough et al., 2005;Miller and Turner, 2009; Stamnes et al., 1988]. We define the simulated DNB apparent reflectance, RDNB, asfollow:

RDNB ¼ πLμlEl

; (4)

where L is the measured TOA band-averaged radiance using DNB, El is the lunar flux or irradiance at the TOA,μl = cos(θl), and θl is the lunar zenith angle. Following equation (2), El can be computed by convolving theDNB SRF at different wavelengths.

In this RTM, seven major atmospheric absorptive gases (H2O, CO2, O3, O2, CH4, CO, and N2O) have been cal-culated using a rigorous LBLRTM. A parameterization formula is used to compute Rayleigh scattering opticaldepth [Bodhaine et al., 1999; Srivastava et al., 2009]. Considering that this study only focuses on the primaryeffects of variable phase-dependent LSI on the RTM simulations under cloudy conditions, we simplify theissue to average and convolve the high-spectral gas absorption optical depths at every atmospheric layerwith VIIRS/DNB SRF, as calculated based on the following equation:

τDNBgasþray ¼∫λ2λ1 τgasþray λð ÞSRF λð Þdλ

∫λ2λ1SRF λð Þdλ; (5)

whereτDNBgasþray is the total gas and Rayleigh absorption optical depth for DNB at any layers and τgas + ray(λ) is thetotal gas absorption and Rayleigh scattering optical depth at the wavelength λ. Note that we use the midla-titude summer atmospheric profile data to calculate the gas absorption optical depths for each atmosphericlayer, assuming the cloud top height of 6.0 km and the Lambert surface with an albedo of 0.05 for the follow-ing study.

3. Simulations and Discussion3.1. Cloud Bulk Scattering Properties

Liquid/water cloud (WC) is assumed to be spheres with the scattering properties given by the classicalLorenz-Mie theory. The water cloud droplets are assumed to follow a gamma distribution [Zhang, 2013],and the cloud effective radii (CER) ranging from 1 to 60 μmare used for bulk scattering properties [Baum et al.,2005; Liu et al., 2014]. For ice cloud (IC), the spherical hypothesis is no longer applicable because the micro-physical and optical properties of ice clouds are very sensitive to crystal particle habits. The single-scatteringproperties of ice clouds are obtained from the forward database developed by Yang et al. [2013], and those ofhexagonal aggregates with severely roughened surface are used for this study. Similar to water cloud size dis-tributions, the bulk scattering properties for ice clouds are averaged based on the gamma size distributionwith effective radii ranging from 5 to 60 μm.

Figure 3 compares the DNB-averaged bulk scattering properties at four lunar phase angles θ = 0°, 45°, 90°,and 135°, and the extinction efficiency, Qe; single-scattering albedo, ω; asymmetry factor, g; and phase func-tion, P11, are shown here. These DNB-averaged cloud bulk scattering properties with single-scatteringapproximation [Baum et al., 2007] execute a convolution using the spectral NW values in Figure 1b at fourdifferent lunar phase angles. Therefore, the possible differences in DNB-averaged bulk scattering propertiesare mainly contributed to the variations in the NW with different lunar phase angles. From the enlarged sub-figures in Figures 3a, 3b, and 3d, it is noticeable that there are slight differences on the Qe, g, and P11 of watercloud at relatively small CERs (<2 μm). This finding is mainly attributed to the band averaging and convolu-tion calculations using the relatively larger absolute values of Qe, g, and P11 at small CERs. In contrast, due tothe minimum effective radius of ice cloud is 5 μm, we cannot find the obvious differences in Qe, g, and P11 for

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ice clouds duo to relatively small absolute values. The differences inω are close to 1.0 with relative differencesless than 0.001% (Figure 3b), which could be ignored in the RTM calculation with 32 bit floating-point precision.

3.2. Radiative Transfer Numerical Simulations

We use the coupled DNB radiative transfer model mentioned above to simulate reflectance or radiances(see equation (4)) at the TOA under cloudy conditions at four typical lunar phase angles θ = 0°, 45°, 90°,and 135°, which needs the precalculated cloud bulk scattering properties in section 3.1 as input to com-pute absorption and scattering properties of cloud layer. Figure 4a shows the simulated DNB reflectance atthe TOA at θ = 0°, 45°, 90°, and 135° for (CER = 1, 10, and 40 μm) water and ice (CER = 5, 10, and 40 μm)clouds with lunar zenith angle (LZA) = 60°, view zenith angle (VZA) = 50°, and relative azimuth angle(RAA) = 40° as a function of cloud optical depth. Similar to Figure 4a, Figure 4b demonstrates the simu-lated DNB radiances at the TOA under constant CER (i.e., 5 μm) conditions. It also can be seen that thesimulated DNB reflectance at the four lunar phase angles at the TOA is almost the same. This minor dif-ference is primarily attributed to the slight differences in cloud bulk scattering properties shown inFigure 3. The significant differences in simulated radiances are likely due to the magnitudes of incominglunar irradiances in Figures 4c and 4d. We also find that the simulated DNB radiances at θ = 0° are about103 times brighter than those at θ = 135° for ice/water clouds, indicative of its unique significance andhigh sensitivity of the LSI model to the simulated irradiances of DNB.

Instead of physical radiances, the normalized satellite reflectance data are typically used to retrieve level 2science products, such as cloud mask and cloud optical depth [Heidinger et al., 2012; Platnick et al., 2003].In the light of its key applications in level 2 science products and the differences in bulk scattering

Figure 3. Water (solid lines, WC)/ice (dashed lines, IC) cloud bulk scattering properties comparisons: the DNB-averaged (a) extinction efficiency, Qe; (b) single-scatter-ing albedo, ω; (c) asymmetry factor, g, as a function of cloud effective radius; and (d) phase function (WC CER = 1 μm, IC CER = 5 μm), P11, as a function ofscattering angle, as stratified by four lunar phase angles of θ = 0° (in red), 45°(in green), 90°(in blue), and 135°(in brown). “CER” represents cloud effective radius.The inset plots in Figures 3a, 3c, and 3d show the enlarged water cloud results at small CER and scattering angle. Note that the illuminated sides of lunar bodiesare shown in white and shaded sides in black.

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properties (Figure 3), wecompute the differences ofsimulated DNB reflectance inthe presence of water and iceclouds between any lunarangle and θ = 90° (as astandard reference of lunarphase condition), as illustratedin Figure 5. A closer lookshows that the maximumdifference in simulated watercloud DNB reflectance, roughlyequaling 0.05%, occurs atcloud optical depth (COD) = 2(Figure 5a). The differencelevels off at approximately0.01% (for CER = 1, 10, and40 μm) when COD is greaterthan 10, which is mainlyattributed to the stablereflectance at the TOA ofoptically thick cloud (Figure 4a).More importantly, the changesin the DNB reflectancedifferences with CERs (=1, 10,and 40 μm) are not significant,indicative of a weak effect ofcloud particle size. In addition,

Figure 4. Simulated DNB reflectance at the TOA at θ = 0°(in red), 45°(in green), 90°(in blue), and 135°(in brown) under (a) water (CER = 1, 10, and 40 μm) and (b) ice(CER = 5, 10, and 40 μm) cloudy conditions with lunar zenith angle (LZA) = 60°, view zenith angle (VZA) = 50°, and relative azimuth angle (RAA) = 40°. SimulatedDNB radiances at the TOA at four lunar phase angles: θ = 0°, 45°, 90°, and 135° under water (CER = 5 μm; Figure 4c)/ice (CER = 5 μm; Figure 4d) cloudy condition withthe same observation geometry as Figures 4a and 4b. Note that the illuminated sides of lunar bodies are shown in white and shaded sides in black.

Figure 5. Deviation of simulated DNB reflectance at θ = 0° (in red), 45°(in green),90°(in blue), and 135°(in brown) under (a) water (CER = 1, 10, and 40 μm) and(b) ice (CER = 5, 10, and 40 μm) cloudy conditions relative to that at θ = 90° withLZA = 60°, VZA = 50°, and RAA = 40°. Note that the illuminated sides of lunarbodies are shown in white and shaded sides in black.

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the simulation experiment in Figure 5b for ice cloud shows that the maximum differences in DNBreflectance are <0.01% for cloud droplets with different sizes.

Despite this minor effect due to the changes in lunar phase angles, strong gas absorption lines can befound in the DNB, such as Oxygen A-band (near 760 nm) and B-band (near 680 nm), as shown inFigure S1 in the supporting information. In this case, we resimulate the high-spectral atmospheric gasabsorption or transmittance using a line-by-line model instead of the DNB spectral convolution calculation(i.e., equation (5)). Based on the transmittance curves in Figure S1, we simulated the reflectance (Figure S2,top) and radiances (Figure S2, bottom) at the TOA for a typical water cloud case, as illustrated in Figure S2.

Figure 6. Distributions of simulated TOA DNB reflectance differences between the lunar phase angle of (left column) 0°, (middle column) 45°, and (right column) 135°versus the lunar phase angle of 90° for water cloud (CER = 1, 10, and 40 μm, COD = 10) under different observational geometries conditions. (top, middle, andbottom rows) Results at RAA = 0°, 40°, and 120°, respectively. The integer numbers (with the floor function calculation) at CER = 1 μm in Figure 6 (left column)represent the corresponding scattering angles between incoming and outcoming lunar light beams.

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Results show that the simulated reflectance does not change too much with lunar phase angles, incontrast to large difference in radiance due to changes in lunar phase angles. Then, we convolvesimulated reflectance over DNB SRF and thus get the simulated band-averaged DNB reflectance at thelunar phase angle of 0°, 45°, 90°, and 135°, and their corresponding differences in reflectance relative tothat at the lunar phase angle of 90° for a typical water cloud case (Table S1 in the supportinginformation). From this table, it is found that the largest difference of 0.118% occurs at theta = 135°,more than two times the magnitude of the DNB band-averaged difference (a maximum of 0.05%) usingequation (5). However, the difference at theta = 45° is only 0.017% (about one third of 0.05%).Therefore, the difference of band-averaged reflectance can be ignored, as compared with difference ofband-averaged radiance. But the latter is not what we concern about in this study. This implies thatlunar phase angles have indiscernible effect on the simulated band-averaged reflectance.

Figure 7. Same as Figure 6 but for the ice cloud (CER = 5, 10, and 40 μm, COD = 10).

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3.3. Cloud BRDF Effect

Although the absolute differences in simulated DNB reflectance of water/ice clouds from the periodical var-iations in phase-dependent LSI are seemly insignificant (in section 3.2), the bidirectional reflectance distribu-tion function effect of cloud on radiative transfer simulation should not be negligible. For instant, theprecisely and strictly calculation on BRDF effect is indispensable in the radiometric calibrations of satelliteimaging sensor solar reflective bands using deep convective cloud as an ideal and relatively invariantEarth target [Chen et al., 2014; Doelling et al., 2013]. Therefore, we test this BRDF effect of water and ice cloudswith different particle sizes under different observation geometries on the differences in simulated DNBreflectance. It is noteworthy that the maximum sensor view zenith angle (VZA) simulated is 50° here becausethe maximum scanning angles of traditional imaging sensor are always smaller than 55° [Xiong et al., 2009].

Figure 6 shows the distributions of simulated TOA DNB reflectance differences between the lunar phaseangle of 0°, 45°, and 135°versus the lunar phase angle of 90° for water cloud (CER = 1, 10, and 40 μm,COD = 10) under different observational geometries conditions. The BRDF effects for ice clouds are presentedin Figure 7. Apparently, the averaged DNB reflectance differences between lunar phase angles of 45° and 90°are the smallest because of the closest distribution of spectral normalized weighting values between themshown in Figure 1b. Both results in water and ice clouds illustrate a significant increasing trend in differencewith the decreasing of lunar and view zenith angles, but it shows a weak dependence on relative azimuthangle. This finding is probably attributed to the increasing of DNB reflectance at small LZA or VZA. As a con-sequence, it illustrates a significant cloud BRDF effect in simulating DNB reflectance under cloudy sky.However, the maximum absolute reflectance differences of water and ice clouds are approximately 0.05%and 0.01% from Figures 6 and 7 due to the changes in lunar phase angles relative to 90° lunar phase angle,which is also much less than DNB radiometric calibration uncertainty of 11% [Miller et al., 2012b]. Apparently,this uncertainty of 11% is more than 200 times of maximum 0.05% difference of water cloud caused by thechanges in lunar phase angle, which implies that the impact of lunar phase can be ignored for retrievingcloud properties using DNB measurements at night. Therefore, we should further improve the DNB calibra-tion accuracy for quantitative remote sensing applications at night in the future. A closer look at Figure 6 doesnot reveal any obvious relationship between the DNB reflectance difference and the scattering angles, indi-cating that there exist no large reflectance differences near cloud bow and back scattering angles. Finally, itsuggests that the cloud BRDF effect can be negligible despite its importance, and any typical LSI (e.g., θ = 90°)can be used as a standard or baseline for calculating and averaging cloud bulk scattering properties of DNBat night.

4. Conclusions

This study investigates the implications of lunar illumination spectral changes for Day/Night Band-basednighttime cloud property retrieval or radiative transfer modeling due to lunar phase transition. Based on anew RTM by coupling with a lunar light source and water/ice cloud bulk scattering properties, we selectedthe cases with four different lunar phase angles from two lunar cycles for the period 7 April 2016 to 8 May2016 to analyze the feasible influences of the changes in phase-dependent lunar spectral irradiances oncloud bulk scattering properties and associated DNB RTM calculations.

Through a series of concrete sensitivity tests for the DNB-averaged cloud bulk scattering properties, thenighttime radiative transfer calculations, and cloud BRDF effect, the effect of changes in phase-dependentlunar spectral irradiances has been quantitatively evaluated. The key findings of this study are summarizedas follows:

1. We find slight differences in DNB-averaged extinction efficiency; asymmetry factor; phase function atdifferent size cloud effective radius between four different lunar phase angles θ=0°, 45°, 90°, and 135°;and ignorable differences at relatively large CERs (>2 μm).

2. A minor effect of periodically changes in phase-dependent lunar spectral irradiances was found on DNBradiative transfer calculations with different observation geometries for reflectance under cloudy condi-tions. It can also be ignored despite that it will be increased with the decrease of view and lunar zenithangles from the results of cloud BRDF test. These differenceswith the reflectance at lunar phase angle = 90°are less than approximately 0.05% (water cloud)/0.01% (ice cloud), much smaller than 11% radiometriccalibration uncertainties of DNB.

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3. The lunar spectral irradiances at any typical lunar phase angle (e.g., lunar phase angle θ = 90°) can be usedto precalculate DNB-averaged water/ice cloud bulk scattering properties for DNB radiative transfermodeling, implying the potential application in retrieving cloud optical and microphysical propertiesand DNB observation numerical simulation at night.

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AcknowledgmentsThe authors would like to acknowledgeSteven. Miller for making his lunar irra-diance model publicly available (http://lasp.colorado.edu/sorce/index.htm). Wealso thank the STEVENS Institute ofTechnology Laboratory (http://lllab.phy.stevens.edu/disort) for providingDISORT-V2.0, the Atmospheric andEnvironmental Research Company(http://rtweb.aer.com/lblrtm_frame.html) for providing LBLRTM, andNESDIS/NOAA for providing SNPP/VIIRS-DNB spectral response function online(https://www.star.nesdis.noaa.gov/smcd/GCC/instrInfo-srf.php). This studywas supported by the ChinaMeteorological Special Funding undergrant GYHY201506074, the NationalNatural Science Foundation of Chinaunder grants 41405035, 41471301,41571348, 41771399, and 41401417,and Chinese Academy of MeteorologicalSciences under grant 2017Z005. Lastbut not least, we would also like tothank the anonymous reviewers fortheir thoughtful suggestions andcomments.

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