We calculated on the basis of the radiative transfer simulation for all the combinations of optical conditions shown in Table 1 ( combinations). values of 0, 30, and 60 deg represent direct sunlight with different solar elevations, and (the incident radiance is uniformly distributed over the sky) approximates diffuse sky light. was fixed at zero to simulate observation by quasi-zenith satellites. Three values of (0.2, 0.5, and 0.8) and three types of (“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 (the ratio of the backward scattering coefficient to ) 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) , respectively. We set in geometric progression from to with a ratio of . This is because the scale of of interest in shallow-water remote sensing using multispectral satellite imagery is diverse: sometimes very shallow ranges such as 0 to 0.3 m13 are discussed in a centimeter scale; in other cases, wide ranges of about 1 to 20 m1,22 are targeted. The range handled in this paper corresponds to 0.05 to 19.91 m when (a possible value for clear seawater at blue and green wavelengths).18,19,23 We set to cover a wide range of 0.1 to 0.6 with a small interval of 0.05. An value of 0.6 is possible for carbonate sand at green and red wavelengths.24 Although an of , 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): becomes nonpositive when , and we cannot calculate the logarithm in Eq. (2). Because is rather stable in natural waters,18 it was fixed at a typical value (1.333).