We calculated $R$ on the basis of the radiative transfer simulation for all the combinations of optical conditions shown in Table 1 ($4\xd71\xd73\xd73\xd715\xd711\xd71=5940$ combinations). $\theta i$ values of 0, 30, and 60 deg represent direct sunlight with different solar elevations, and $\theta i=uniform$ (the incident radiance is uniformly distributed over the sky) approximates diffuse sky light. $\theta L$ was fixed at zero to simulate observation by quasi-zenith satellites. Three values of $b/c$ (0.2, 0.5, and 0.8) and three types of $\beta \u02dc$ (“Mob,” “M01,” and “P02”) were used to represent various in-situ measurements.^{19}^{–}^{21} Here, “Mob” indicates the scattering phase function described in Refs. ^{17} and ^{18} obtained by averaging the measurements of ^{19}. The probability of backscattering $B$ (the ratio of the backward scattering coefficient to $b$) was 0.0178 in our implementation. “M01” and “P02” are the scattering phase functions presented in ^{20} and named in ^{21}, characterized by small (0.00453) and large (0.0445) $B$, respectively. We set $c\xb7h$ in geometric progression from $10\u22122(=0.01)$ to $100.6(=3.981)$ with a ratio of $100.2(=1.585)$. This is because the scale of $h$ of interest in shallow-water remote sensing using multispectral satellite imagery is diverse: sometimes very shallow ranges such as 0 to 0.3 m^{13} are discussed in a centimeter scale; in other cases, wide ranges of about 1 to 20 m^{1}^{,}^{22} are targeted. The $c\xb7h$ range handled in this paper corresponds to 0.05 to 19.91 m when $c=0.2$ (a possible value for clear seawater at blue and green wavelengths).^{18}^{,}^{19}^{,}^{23} We set $rb$ to cover a wide range of 0.1 to 0.6 with a small interval of 0.05. An $rb$ value of 0.6 is possible for carbonate sand at green and red wavelengths.^{24} Although an $rb$ of $<0.1$, such as 0.05, is common for algae and corals,^{24} this condition was not considered because it is not suitable for the use of model (1) in the form of Eq. (2): $R\u2212R\u221e$ becomes nonpositive when $Rb\u2264R\u221e$, and we cannot calculate the logarithm in Eq. (2). Because $naw$ is rather stable in natural waters,^{18} it was fixed at a typical value (1.333).