A study of snow optical properties with a multiplescattering radiative transfer model for theatmosphere-snow system and spectral albedo observations
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A multiple scattering radiative transfer model in the shortwave wavelength region has been developed for the atmosphere-snow system in which the absorption and scattering by the realistic gases， aerosols and clouds were included and a radiative interaction between the atmosphere and the snow was simulated. Using this model the atmospheric effects on spectral albedo and radiation budget at the snow surface and the top of the atmosphere were investigated. Furthermore, observations of spectral albedo and bidirectional reflection distribution function (BRDF) with the spectrometer have been made together with the snow pit works on some snowfields. The results of spectral observations were compared with the theoretically calculated ones with a multiple scattering model for the atmosphere-snow system and the effects of snow physical parameters on spectral albedo and BRDF were investigated．<br /> 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°. <br /> 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<i>μm</i> by the Rayleigh scattering and at almost all wavelengths by the atmospheric aerosols and cloud cover. <i>H<small>2</small>O</i> rich atmosphere decreased the spectral surface albedo at large solar zenith angle in the <i>H<small>2</small>O</i> bands, while the additional reduction of downward solar flux in the near infrared region by <i>H<small>2</small>O</i> absorption caused the spectrally integrated surface albedo to increase by several percent. Aerosols increased the spectrally integrated surface albedo at small solar zenith angles and reduced it at large solar zenith angles, however they reduced the spectrally integrated planetary albedo except at large solar zenith angles. Optically-thick cloud cover increased both the spectrally integrated surface and planetary albedos at any solar zenith angle. In the visible region at small solar zenith angles the downward solar flux on the snow surface under cloudy sky could exceed that for clear case， and both further could exceed the extraterrestrial solar flux, resulting from the multiple reflection between snow surface and the atmosphere (cloud cover). <br /> 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.<br /> 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. <br /> 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<i>μm</i> were made together with snow pit work on a flat snowfield under the clear sky in eastern Hokkaido, Japan in February, 1998. The effects of snow impurities, density, layer structure, and grain size attained by in situ and laboratory measurements were taken into account in snow models for which spectral albedos were calculated using a multiple scattering model for the atmosphere-snow system. Comparisons of these theoretical albedos with measured ones suggest that the snow impurities were concentrated at the snow surface by dry fallout of atmospheric aerosols. The optically equivalent snow grain size was found to be of the order of a branch width of dendrites or of a dimension of narrower portion of broken crystals as was same in Chapter3. This means that the optical equivalent snow grain size is smaller than the so-called snow grain size measured glaciologically. The observational results for the BRDF normalized by the radiance at the nadir showed that the anisotropic reflection was very significant in the near infrared region especially at the wavelengths longer than 1.4<i>μm</i>, while the visible normalized BRDF (NBRDF) patterns were relatively flat. Comparison of this result with two kinds of theoretical NBRDFs, where one having been calculated using single scattering parameters by the Mie theory and the other using the same parameters except for Henyey-Greenstein (HG) phase function obtained from the same asymmetry factor as in the Mie theory, showed that the observed NBRDF agreed with the theoretical one using HG phase function rather than with that using Mie phase function, while the albedos calculated with both phase functions agreed well with each other. This suggests that the optically effective snow grain shape is neither the sphere nor the ordinary hexagonal column, by which respectively the rainbow or halo appear in the theoretical BRDF pattern, but is the nonspherical particle having the smooth phase function．