Intercomparison of millimeter-wave radiative transfer models

This study analyzes the performance at millimeter-wave frequencies of five radiative transfer models, i.e., the Eddington second-order approximation with and without δ-scaling, the Neumann iterative method with and without geometric series approximation, and the Monte Carlo method. Three winter time precipitation profiles are employed. The brightness temperatures calculated by the Monte Carlo method, which considers all scattering angles, are considered as benchmarks in this study. Brightness temperature differences generated by the other models and sources of those differences are examined. In addition, computation speeds of the radiative transfer calculations are also compared. Results show that the required number of quadrature angles to generate brightness temperatures consistent with the Monte Carlo method within 0.5 K varies between two and six. At least second to 15th orders of multiple scattering, depending on the significance of scattering, are required for the Neumann iterative method to represent accurately the inhomogeneous vertical structure of the scattering and absorbing components of precipitating clouds at millimeter-wave frequencies. The δ-scaling in the Eddington second-order approximation improves brightness temperatures significantly at nadir for cloud profiles that contain snow due to the correction for strong scattering, while it did not make any difference at 53° off-nadir. The computational time comparisons show that the Neumann iterative method generates accurate brightness temperatures with better computational efficiency than the Monte Carlo method for cloud profiles with weak scattering. However, it can consume computational time that is even greater than the Monte Carlo method for some millimeter-wave frequencies and cloud profiles with strong scattering. A geometric series approximation can improve computational efficiency of the Neumann iterative method for those profiles. In view of the ease of introducing scaled parameters into the Eddington second-order approximation, good computational time efficiency, and better than within 2 K accuracy when compared with the Monte Carlo method, we recommend its use for brightness temperature calculations at millimeter-waves in precipitating atmospheres.