The mixture of water cloud droplets with black carbon impurities is modeled by external and internal mixing models. The internal mixing model is modeled with a two-layered sphere (water cloud droplets containing black carbon (BC) inclusions), and the single scattering and absorption characteristics are calculated at the visible wavelength of 0.55 µm by using the Lorenz-Mie theory. The external mixing model is developed assuming that the same amount of BC particles are mixed with the water droplets externally. The multiple scattering characteristics are computed by using the Monte Carlo method. The results show that when the size of the BC aerosol is small, the reflection intensity of the internal mixing model is bigger than that of the external mixing model. However, if the size of the BC aerosol is big, the absorption of the internal mixing model will be larger than that of the external mixing model.

A method for determining the optical thickness and effective particle radius of spherical aerosols with sun light of a single wavelength is presented. Based on the vector radiative transfer theory, the reflection matrix of the aerosols is calculated by using the adding-doubling method for λ=0.75μm and 3.3μm, the effective radii of aerosol particles were 0.01—1.5μm, and the optical thickness were 0.05—1. We modeled the retrieval process by computer simulation. From the numerical results, we conclude that the radiance combined with polarization is capable of uniquely retrieving optical thickness and effective radius with high accuracy. Especially, when the effective radius is less than 0.4μm, a visible light wavelength can be used for retrieval; when the effective radius is larger than 1.0μm, an infrared light wavelength can be used for retrieval; when the effective radius lies between 0.4 and 1.0μm, both of the two wave bands can be used to obtain a unique result with high accuracy.

Based on the Mie theory，the light scattering properties in the visible regions of clouds consisting of pure water, pure ice spheres and concentric water_ice spheres are computed respectively. The reflection function and plane albedo, transmissivity, absorptivity of the three types of clouds are evaluated with the adding_doubling method by solving the radiative transfer equation. The numerical results show that the reflection function and plane albedo of ice clouds and ice_water clouds are slightly less than those of water clouds at most scattering angles, when the transmissivity is larger. A detailed theoretical analysis of the numerical results is presented, which explains the phenomenon of cloud absorption anomaly.

Based on the radiative transfer theory, the backscattering characteristics of water clouds and ice-water two layers clouds irradiated by infinite narrow collimated light beam are studied by using the Monte Carlo method. The incident wavelength is 0.532 μupm, and the cloud particle shape is assumed to be of sphere or plate. The single scattering characteristics of the clouds are computed based on the Mie theory, and the scattering angle sampling is based on the Mie phase function. The photon step adjustment is considered when the step is large enough to cross the cloud layer. The variations of reflection functions of the water clouds and ice-water two layers clouds with the radial length r and zenith angle are given, and the interior light intensity distribution of clouds are given in two dimensions. From the computed results, we find that the reflection characteristics of the two layer clouds are greatly different from those of the pure water clouds. The reflection intensity of ice clouds covered with water clouds is bigger than that of ice clouds covered with water clouds. This reason is that the sizes of ice clouds are larger than those of the water clouds, so more photons will be scattered into the interior of the clouds.#br#The cloud layer is assumed to be linear and invariant, so the response to an infinitely narrow photon beam will be described by a Green's function of the clouds, and the response to the Gaussian beam can be computed from the convolution of the Green's function according to the profile of the Gaussian photon beam. The multiple scattering characteristics of the Gaussian photon beam are computed from the convolution of the impulse response, i.e., the response to an infinitely narrow photon beam, according to the profile of the Gaussian light photon beam. From the computed results, we find that the reflection function of clouds for Gaussian incidence has a great difference from that for the infinite narrow beam incidence. The reflected light intensity is inversely proportional to the size of the Gaussian beam at the location near r=0. So the laser spot must be considered when detecting the clouds by using of the lidar, and the method presented in this paper can give theoretical support.

The melting snow particles on top of clouds form the melting layer of precipitation. The melting process starts with the snow particles falling, so the microphysical characteristics of the melting layer vary continuously in vertical direction. In this paper, a Monte Carlo simulation model for the melting layer is developed, and the melting snow particles are modeled by more practical three-layered spherical particles. The size distribution of the melting snow particles is derived from the raindrops size distribution. Vertical profiles of radar reflectivity and specific attenuation factor are computed at 5, 10, 35 and 94 GHz using the Mie theory at rain rates below 12.5 mm/h. It is shown that the radar bright band can be absent in the melting layer at frequencies above 20 GHz. This agrees with radar observations at 35 and 94 GHz. Base on the radiative transfer theory, the Monte Carlo method is used to compute the reflectivity of the melting layer whose microphysical characteristics are continuous in vertical direction. We compared the reflectivity of the melting layers with two different size-distributions (Gamma size distribution and Marshall-Palmer size distribution). These provided theoretical and numerical basis for radar remote sensing of the melting layer with high frequencies electromagnetic waves.