ALBERT

Description: 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.

Description: A Monte Carlo model is developed to calculate the microwave emissivity of the sea surface based on the Kirchhoff approximation combined with modified Fresnel coefficients. The modified Fresnel coefficient depends on the incident angle of the electromagnetic wave and the height variance of small‐scale roughness, which is an approximation to account partly for the scattering effect from small ripples. The advantage of the Monte Carlo model is its inherent capability to treat multiple scattering events. Using a two‐dimensional Gaussian distribution for the sea surface slope variability, the model is capable of simulating the azimuthal dependency of the microwave emission caused by the alignment of waves perpendicular to the wind direction. Good agreement between model calculations and measurements is obtained.

Description: A radiative transfer model, the matrix operator method, is discussed here. The matrix operator method is applied to a plane-parallel atmosphere within three spectral ranges: the visible, the infrared, and the microwave. For a homogeneous layer with spherical scattering, the radiative transfer equation can be solved analytically. The vertically inhomogeneous atmosphere can be subdivided into a set of homogeneous layers. The solution of the radiative transfer equation for the vertically inhomogeneous atmosphere is obtained recurrently from the analytical solutions for the subdivided layers. As an example for the application of the matrix operator method, the effects of the cirrus and the stratocumulus clouds on the net radiation at the surface and at the top of the atmosphere are investigated. The relationship between the polarization in the microwave range and the rain rates is also studied. Copies of the FORTRAN program and the documentation of the FORTRAN program on a diskette are available.