A three-dimensional Monte Carlo transfer model for polarized radiation is developed and used to study three-dimensional (3-D) effects of raining clouds on the microwave brightness temperature. The backward method is combined with the forward method to treat polarization correctly within the cloud. In comparison with horizontally homogeneous clouds, two effects are observed: First, brightness temperatures from clouds are reduced in the 3-D case due to net leakage of radiation from the sidewalls of the cloud. Second, radiation which is emitted by the warm cloud and then reflected from the water surface increases the brightness temperatures of the cloud-free areas in the vicinity of the cloud. Both effects compete with each other, leading to either lower or higher overall brightness temperatures, depending on the geometry of the cloud, the satellite viewing angle, the coverage, and the position of the cloud within the field of view (FOV) of the satellite. At 37 GHz, for example, up to 10 K differences can occur for a cloud of 50% coverage. Finite homogeneous raining clouds matching the size of the FOV of the satellite show a similar relationship between rain rates and brightness temperatures (TB) as horizontally infinite clouds. Namely, an increase of TB with increasing rain rates at low rain rates, due to emission effects, is followed by a decrease due to temperature and scattering effects. For small horizontal cloud diameter, however, the 3-D brightness temperatures may show a second maximum due to the decrease of the leakage effect with increasing rain rates. At nadir, 3-D brightness temperatures are always lower than the 1-D values with differences up to 20 K for a cloud of 5-km vertical extent and a base of 1 × 1 km. To quantify the 3-D effects for more realistic cloud structures, we used results of a three-dimensional dynamic cloud model as input for the radiative transfer codes. The same 3-D effects are obtained, but the differences between 1-D and 3-D modeling are smaller. In general, most of the differences between the 1-D and 3-D results for off-nadir view angles are pure geometry effects, which can be accounted for in part by a modified 1-D model.
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