# Some Approaches for Light and Color on the Surface of Mars
## 2 Materials and Methods  
From the COMIMART model, we obtained 43 \(\times\) 73 = 3139 total (direct + diffuse) spectral irradiances on the surface of Mars with a spectral range of 300-830 nm at steps of 5 nm (see Supplementary Material). Specifically, we considered 43 values for the 'opacity' (parameter named 'Tau', ranging from 0.1 to 8.5 in steps of 0.2) and 73 values for the'solar zenith angle' (parameter named 'Angle', ranging from 0\({}^{\circ}\) to 72\({}^{\circ}\) in steps of 1\({}^{\circ}\)), assuming a latitude of 0\({}^{\circ}\), a solar longitude of 0\({}^{\circ}\) (spring equinox in the Northern Hemisphere), and a surface albedo of 0.2. In the COMIMART model, the parameters of opacity and solar zenith angle are related to the amount of dust in the atmosphere and the time of day, respectively. For each of these 3139 spectral irradiances, we computed \(x\),\(y\) chromaticity coordinates for the CIE 1931 colorimetric observer [3], values of CCT from a binary search method described in [17], distances from the Planckian locus (\(D_{uv}\)) [18], and values of the general color fidelity index (\(R_{f}\)) [19]. Positive/negative values of \(D_{uv}\) in the range of \(\pm\)0.05 indicate 'white lights' with chromaticities above/below the Planckian locus. The index \(R_{f}\) improves the old CIE general color rendering index \((R_{a})\), representing how closely the color appearances of 99 samples are reproduced on average by a test light as compared to those under a reference illuminant with the same CCT. The higher the value of \(R_{f}\) (always in the range of 0-100), the closer the color appearance produced by the test source is to the reference source. An object is said to be 'color inconstant' when its color appearance changes because of variations in the color and level of illumination [20]. This occurs with changes in the spectral irradiance of light on the surface of Mars (current the case), or when comparing objects on the surfaces of Mars and Earth. The definition of 'corresponding colors' is pairs of color stimuli that look alike when one is seen in one set of adaptation conditions and the other is seen in a different set [20]. Corresponding colors are computed using chromatic adaptation transforms (CATs), the core of color appearance models (CAMs) used in advanced colorimetry [21]. Here, we computed corresponding colors using the chromatic adaptation transform CIECAT16 embedded in CIECAM16 [22], assuming a constant adaptation luminance \(L_{A}\) of 63.7 cd/m\({}^{2}\), which is equivalent to an illuminance of 1000 lx, an average surround adaptation factor (\(F\) = 1), and with illuminant D65 and CIE 1964 colorimetric observer (\(X_{n}\) = 94.81, \(Y_{n}\) = 100.00, \(Z_{n}\) = 107.28) as reference conditions. From corresponding colors, we computed color inconstancy in CIELAB units, using as reference white illuminant D65 with CIE 1964 colorimetric observer. For homogeneous object colors, visual thresholds for human observers with normal color vision fall within the range of 0.55-1.10 CIELAB units [23]. The input of the CIE method to compute spectral power distributions of daylight illuminants is a value of CCT in the range of 4000 K-25,000 K [3]. The CIE method follows the next four steps: (1) Compute the \(x\) chromaticity coordinate using a third-degree polynomial equation of the inverse of CCT, which depends on the input CCT value being in the range of 4000 K-7000 K or 7000 K-25,000 K. This leads to values of \(x\) chromaticity coordinates in the range of 0.250-0.380. (2) Compute the \(y\) chromaticity coordinate using a two-degree polynomial equation from the value of the \(x\) chromaticity coordinate. (3) Compute coefficients \(M_{1}\) and \(M_{2}\) from values of \(x\),\(y\) chromaticity coordinates. (4) Compute the spectral power distribution of the illuminant from \(M_{1}\) and \(M_{2}\) using tabulated values of three specific functions (average and two eigenvectors) obtained by principal component analysis [3].