1. Diffuse reflection coefficient or diffuse reflectance of light from water body is an informative part of remote sensing reflectance of light from the ocean. Diffuse reflectance contains information on content of dissolved and suspended substances in seawater. Diffuse reflectance is an apparent optical property that depends not only on inherent optical properties of the seawater, but also on the parameters of illumination. The dependence on inherent optical properties is expressed as a dependence on a ratio of backscattering coefficient b b to absorption coefficient a. In the open ocean under diffuse illumination of the sky diffuse reflectance R is linearly proportional to the ratio of b b to a, i. e. R=k b b /a, with k=0.33 according to Morel and Prieur. The abovementioned linear equation is very good for the Type I open ocean waters. It is also acceptable for certain types of coastal waters. In fact, it is valid for all types of waters when the ratio of b b to a is less than 0.1. From physical considerations R should always lie between zero and one for any ratio b b /a between zero and infinity. The linear equation fails to pass this criterion, i. e. it exceeds unity when b b /a becomes greater than 1/k, or a < k b b (highly scattering water with a lot of very small particles). It means that indiscrete use of the linear equation for coastal waters, when parameter b b /a exceeds limitations of smallness, can cause unacceptable errors in processing of in situ and remote sensing optical information. In order to estimate possible errors in determining diffuse reflectance we used different approaches to generate diffuse reflectance as a function of b b /a, or g = b b /(a+b b ). One approach is based on numerical calculations using Monte Carlo simulation, and other approaches were theoretical. The input values of b b /a have been varied from very small to very large numbers. It was found that numerically and theoretically generated results for all varieties of input parameters satisfactory correspond to the available experimental data. It was found both theoretically and using Monte Carlo that diffuse reflectance strongly depends on backscattering coefficient and has very weak dependence on the shape of the phase function used. The widely used linear model is very good for b b /(a+b b ) 0.2. The majority of coastal water and almost all open ocean water cases fall in the range of applicability of linear model. But the linear model may be very inadequate in some important and interesting coastal water conditions like hazardous blooms, spills, etc. For the reasons to avoid possible unacceptable errors and missing interesting optical events it is advisable to avoid using linear model to process information related to coastal (Type II and III) waters. All presented non-linear equations (except the Kubelka- Munk equation that is not acceptable for seawater at small values of b b /(a+b b ) 0.2, and at b b /(a+b b ) < 0.0001) are capable to produce values of R that are correct for all possible values of b b /(a+b b ). In order to detect special optical cases the non-linear equations should be used in automatic processing of in-situ and remotely obtained optical information. The author thanks continuing support at the Naval Research Laboratory through the Spectral Signatures 73-5939-A1 program. This article represents NRL contribution AB/7330-01-0168. (Morel-Prieur, 1977): Exact (Haltrin, 1988) Self-Consistent Asymptotic (Haltrin, 1985, 1993, 1997) Self-Consistent Diffuse (Haltrin, 1985) Two-Stream: (Gamburtsev, 1924; Kubelka-Munk, 1931; Sagan and Pollack, 1967) Monte Carlo (Gordon, Brown, and Jackobs, 1975) Semi-Empirical (Haltrin and Weidemann, 1996) Direct Diffuse e-m: e-m: ; nrlssc.navy.mil Because we do not have reliable in situ measurements of diffuse reflectances that represent the whole range of variability of inherent optical properties, 0 < b b /(a+b b ) < 1, we have to choose a dependence which can be regarded as sufficiently “precise one” in order to be a basis for error estimation. Such dependence exists in literature (Haltrin, 1988) and represents an exact solution of radiative transfer for diffuse reflection of light in a medium with delta-hyperbolic phase function. This solution lies exactly in the middle of two Monte Carlo and two theoretical solutions for diffuse reflections for small values of b b /(a+b b ) < 0.2, and it gives precise and asymptotically correct values for 1 - b b /(a+b b ) < < 1 (see first two figures). 1. G. A. Gamburtsev, “On the problem of the sea color,” Zh. RFKO, Ser. Fiz. (Journal of Russian Physical and Chemical Society, Physics Series), 56, 226-234 (1924). 2. P. Kubelka and F. Munk. “Ein Beitrag zur Optik der Farbanstriche,” Zeit. Techn. Phys., 12, 593-607 (1931). 3. C. Sagan and J. B. Pollack, “Anisotropic nonconservative scattering and the clouds of Venus,” J. Geophys. Res., 72, 469-477 (1967). 4. H. R. Gordon, O. B. Brown, and M. M. Jacobs, “Computed relationships between the inherent and apparent optical properties of a flat homogeneous ocean,” Appl. Optics, 14, 417-427 (1975). 5. A. Morel, L. Prieur, “Analysis of variations in ocean color,” Limnol. Oceanogr., 22, 709-722 (1977). 6. V. I. Haltrin (a.k.a. V. I. 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