Simulations of Sky Radiances in Red and Blue Channels at Various Aerosol Conditions Using Radiative Transfer Modeling

: We conducted a theoretical analysis of the relationship between red-to-blue (RBR) color intensities and aerosol optical properties. RBR values are obtained by radiative transfer simulations of diffuse sky radiances. Changes in atmospheric aerosol concentration (parametrized by aerosol optical depth, AOD), particle’s size distribution (parametrized by Ångström exponent, AE) and aerosols’ scattering (parametrized by single scattering albedo—SSA) lead to variability in sky radiances and, thus, affect the RBR ratio. RBR is highly sensitive to AOD as high aerosol load in the atmosphere causes high RBR. AE seems to strongly affect the RBR, while SSA effect the RBR, but not to such a great extent.


Introduction
The accurate knowledge of the angular distribution of the diffuse sky radiance is crucial for many applications, particularly in building design [1], in design and performance investigation of photovoltaic (PV) systems [2,3], solar collectors and other spectral selective energy devices [4].
Aerosols' impact on the radiative balance of the Earth-Atmosphere system is caused by direct scattering and absorption (attenuation) of incoming solar radiation (direct impact) and through aerosol-cloud interactions (indirect impact). These interactions depend significantly on the aerosol load and aerosol optical properties like the aerosol optical depth (AOD), the Ångström exponent (AE) or the single scattering albedo (SSA) [5].
The diffuse sky radiance or luminance is strongly affected by aerosol optical properties under clear sky conditions [6,7]. Olmo et al. [8] used sky radiance measurements to study mineral dust optical properties, while Deering and Eck [9] investigated the effect of AOD in bi-directional reflectance distributions of vegetation canopies. Inversion algorithm has been implemented by different authors [10], e.g., Ref. [11] measured sky radiance to retrieve aerosol optical properties. Later, Dubovik et al. [12] and Olmo et al. [8] included non-spherical particles approximation in the previous proposed inversion codes to derive other aerosol properties, namely, size distribution, SSA, phase function (PF) and asymmetry parameter (g) from radiance measurements. The variation in sky radiance has been analyzed under various atmospheric conditions using measurements with instruments, such as spectroradiometers [13,14]. These spectral radiance observations have been compared with the results from radiative transfer models (RTM) mostly under clear sky conditions. However, the limited number of radiometric stations around the globe and the cost of the equipment make it essential to explore alternative techniques. Recently, all-sky imagers (ASI) have been proven very useful for atmospheric applications since they automatically take series of hemispheric sky images.
All-sky images are devices that combine a digital camera with a fisheye lens that takes pictures of the full hemispherical sky and are based on measurements of radiance at three different wavelengths, which correspond to the red, green and blue spectral range. Furthermore, the red, green and blue (RGB) color intensity has gradually become one of the most widely used characteristics. Therefore, they can be used to obtain the spectral radiance distribution of the sky [15,16] and cloud and aerosol optical properties as well [17][18][19]. Specifically, the red-to-blue ratio (RBR) has been implemented in cloud detection algorithms of whole sky imagers [20][21][22][23], cloud segmentation [24,25], cloud classification [26], retrieving cloud characteristics [23,27], solar irradiance prediction and forecasting [28,29] and constructing clear-sky libraries (CSL) [30]. Image RBR is shown to be affected by aerosol conditions under cloud free sky conditions [31]. Reference [32] proposed a method that estimates the aerosol amount using the blue-to-red ratio within a vertical pixel line and compares it with AOD and particulate matter (PM) measurements.
This study aims to investigate the relationship between the RBR and aerosol optical properties, namely, AOD, AE and SSA, using simulated values of the red and blue color channels using a radiative transfer model (libRadtran) [33,34].

Methodology
The libRadtran software package (Mayer, B., Emde, C., and Kylling, A., LMU Munich, Munich, Germany) is widely used for radiative transfer calculations [33]. It enables the user to compute radiances, irradiances and actinic fluxes in both the solar and the thermal spectrums. The libRadtran package includes numerous tools that may be used to calculate the radiation field for given atmospheric and surface conditions.
In the current work, the libRadtran version 2.0.1 [34] and the UVSPEC radiative transfer model are adopted. The UVSPEC model includes various methods to solve the radiative transfer equations. The discrete ordinate solver DISORT (Discrete-Ordinate-Method Radiative Transfer) [35], which considers the atmosphere a non-isothermal, vertically inhomogeneous but horizontally homogeneous medium, is selected. AOD at 500 nm and AE are the varying input parameters. Using the "output rgb" option in libRadtran, sky radiances are automatically converted to RGB values. For every simulation, the solar zenith angle (SZA) is 30 • , and the RBR is calculated at the zenith point of the image and a number of scattering angles. Figure 1 display the scatter plots between RBR and AOD 500nm (a), AE (b) and SSA (c) for four different sky scattering angles. Based on Figure 1a, it can be observed that the RBR exhibits a quadratic growth as AOD increases, revealing that the red and blue radiances are equal for high AOD values. The RBR values were also related to scattering angles, encompassing lower values for lower scattering angles, which is strongly related to the aerosol scattering processes around the circumsolar region. Regarding AE, the RBR values followed a decreasing trend for coarse aerosol particles (AE < 0.6). Nevertheless, for higher AE values, the trends switch to increasing when the aerosol size becomes smaller. Finally, the RBR values documented a marginal linear decrease with increases in the SSA for all scattering angles. It is apparent that the wavelength-dependent scattering of light, and thus the RBR, is strongly related to the aerosol burden and to the aerosol size distribution.

Conclusions
Clear sky RBR varies significantly because of changes in atmospheric composition. The main objective of this study was to determine the impact of aerosol optical properties on RBR using radiative transfer modeling. High sensitivity between RBR and AOD was found; high aerosol burden in the atmosphere causes high RBR. As aerosol load increases, Mie scattering dominates over Rayleigh; thus, light is scattered equally along all wavelengths resulting in high RBR values even close to 0.9, when AOD at 500 nm reaches values higher than the unity, for large scattering angles. Aerosol particle size, parameterized by the AE, seems to strongly affect the ratio too, with high values of RBR detected for large particles (AE < 0.5). This is because most aerosols are of the same order of size or larger than the wavelength of incoming light. The single scattering albedo of the aerosols affects RBR, but not to such a great extent.

Data Availability Statement:
The data presented in this study is available on request from the corresponding author.

Conclusions
Clear sky RBR varies significantly because of changes in atmospheric composition. The main objective of this study was to determine the impact of aerosol optical properties on RBR using radiative transfer modeling. High sensitivity between RBR and AOD was found; high aerosol burden in the atmosphere causes high RBR. As aerosol load increases, Mie scattering dominates over Rayleigh; thus, light is scattered equally along all wavelengths resulting in high RBR values even close to 0.9, when AOD at 500 nm reaches values higher than the unity, for large scattering angles. Aerosol particle size, parameterized by the AE, seems to strongly affect the ratio too, with high values of RBR detected for large particles (AE < 0.5). This is because most aerosols are of the same order of size or larger than the wavelength of incoming light. The single scattering albedo of the aerosols affects RBR, but not to such a great extent.