In Chapter 1, the approximation methods for Mie phase function were discussed in calculating the spectral albedo of snow surface by taking account of the multiple scattering by snow particles. The particles such as snow grains which are large compared to the wavelength have a strong forward peak in the phase function of single scattering. It has been known that a large error is led by the calculation of multiple scattering directly using such phase function. Therefore, four types of approximations of Mie phase function were investigated in calculating the multiple scattering by snow particles using the "doubling" method. These involve Hansen's renormalization, Grant's renormalization, the delta-M method and the truncation method. Using these approximations, the spectral albedos of snow surface were calculated under the conditions of effective grain radii of 50, 200 and 1000μm in a wavelength region from 0.3 to 3.0μm， and were compared to that calculated using the delta-Eddington approximation. The reason to compare with the delta-Eddington approximation is that this method does not need a phase function and a behavior of the systematic error is understood. In the Hansen's renormalization, the maximum albedo error exceeded 0.1 for the snow with an effective radius of 1000μm at small solar zenith angles. The delta-M method overestimated the snow albedos at all solar zenith angles at the wavelengths less than 1.4μm for the snow with an effective radius of 1000μm. Reasonable results were obtained by the Grant’s renormalization and the truncation method for all three cases of effective grain radii studied. It was also found that these methods save computation time and memory because sufficient accuracy was obtained even with an angle resolution of 0.1° in the forward peak region of phase function. In case of truncation method, the result was not sensitive to the choice of a truncation angle between 5° and 20°.

In Chapter 2, the atmospheric effects on spectral and spectrally integrated snow albedos at the snow surface and the top of the atmosphere were investigated. A multiple scattering radiative transfer model based on the "doubling and adding" method combined with the Mie theory was applied to estimate the effects of absorption and scattering by the atmospheric molecules, absorptive gases, aerosols and clouds. Based on the result of Chapter 1, the truncation method with a truncation angle of 10ﾟ was employed to correct the anisotropic Mie phase function. It was shown that the spectral surface albedo was reduced by the atmospheric absorptive gases at large solar zenith angles. The solar zenith angle dependence was weakened at the wavelengths less than 0.5

It is concluded, from what has been said above, that the snow surface albedo is affected by the appearances of cloud or aerosols of high concentration. It is also found that the snow surface albedo is affected by the Rayleigh scattering at shorter wavelengths and by the atmospheric absorption at large solar zenith angles. Thus, it is necessary to take the atmospheric effects into account for comparison of the theoretical albedo of snow surface with the measured one, according to the conditions of clouds，aerosols, water vapor and solar zenith angle.

In Chapter3, the spectral albedo in the wavelength region of 0.35-2.5μm observed on the snowfield under the cloudy sky at Barrow, Alaska in April, 1997 was discussed. The observed spectral albedo was compared with the theoretical ones calculated by a multiple scattering model for the atmosphere-snow system using the snow physical parameters obtained from the snow pit work. It was found that for new snow consisting of dendrites the optically effective snow grain size was not a crystal size, but of the order of a branch width. The observed spectral albedo was lower than theoretically calculated one for "pure snow" in the visible region and a part of the near infrared region; such reduction was explained by the internal mixture of soot and the external mixture of dust for snow particles. The theoretical spectral albedo calculated for a two-layer snow model that contains impurities agreed well with the measured one at all wavelengths.

In Chapter 4, the effects of snow physical parameters on spectral albedo and bidirectional reflectance of snow surface were discussed by comparing the observed spectral data with the theoretical ones. The observations of spectral albedo and bidirectional reflectance in the wavelength region of 0.35 - 2.5