Studies on the spatial and temporal distribution characteristics of global atmospheric profiles are currently limited. In this study, we analyzed the statistical characteristics of the mean and standard deviation of global specific humidity vertical profiles during 1979 to 2016, using ERA-Interim monthly means of daily means reanalysis data published by the European Centre for Medium-Range Weather Forecasts (ECMWF). The results are as follows. (1) The mean and standard deviation of the specific humidity profiles exponentially decrease with height. (2) There are latitudinal and seasonal differences in both the Northern and Southern Hemispheres. The specific humidity is higher in low latitudes than in high latitudes, and the summer is the wettest and the winter is the driest. (3) The mean and standard deviation of specific humidity are larger over the ocean than over land in the lower atmosphere. This study provides support for evaluating the application performance, radiation transmission algorithm and atmospheric inversion method of new satellite instruments. It can also be used to update and complete current standard atmospheric profiles, and for their comparative analysis.
In this paper, delta-M and delta-fit approximation methods for the scattering phase function in a radiative-transfer equation are reviewed. Radiance in different streams was calculated by a discrete-ordinate algorithm, and the single-variate factor method was used to investigate the influence of phase-function expansion terms on the scattering intensity. The radiance obtained by the delta-M and delta-fit methodologies was compared and discussed under different optical-depth conditions. The results show that, from the aspect of relative error, these two methods come close to standard intensity as optical depth increases, and the bias error of delta-fit is always smaller than that of delta-M for a fixed optical thickness. Delta-fit does well for all of optical depths, whereas delta-M is only good for thick optical depth. From the aspect of absolute error, delta-M is better than delta-fit under small optical depth, whereas the reverse is true when the optical depth is large.
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