1. 3D Radiative Transfer in Cloudy Atmospheres: Diffusion Approximation and Monte Carlo Simulation for Thermal Emission K. N. Liou, Y. Chen, and Y. Gu Department of Atmospheric and Oceanic Sciences, UCLA 3D Clouds in the Atmosphere and in Climate Models 3D Radiative Transfer: Diffusion Approximation 3D Thermal Radiative Transfer: Monte Carlo Simulation 3D Results for Cirrus Clouds: Some Thought on Flux, Heating Rate, and Absorption

2. A Global View of Clouds from A GOES Satellite

3. 3-D Cirrus Observations from Lidar (E. Eloranta, SBIRS ) September 14, 1995 Side View Top View North 24 km 6 km 12 km

4. Figure 3. Illustrative 2D cirrus cloud images located at the Southern Great Plains (SGP/ARM/DOE) derived from a 35 GHz radar on August 14 (top) and March 22, 2001 (bottom).

5. Radiative Transfer/A Unified Theory for Light Scattering by Ice Crystals and Aerosols Cirrus/Contrail Aerosol/Dust

9.  Decomposition of the Basic Equation and Successive Integrations:  First-order Approximation (N=1) in Cartesian Coordinates:

13. Multigrid Method for Solving Diffusion Equation Solving the diffusion equation on a series of coarser grids first and subsequently interpolating the coarse grid correction back to the pre-specified fine grid. Performing the major computational work on the coarse grid. High frequency errors are relaxed on the fine grid and low frequency errors are relaxed on the coarse grid.

14. Schematic Overview for 3D Infrared Monte Carlo Radiative Transfer Model

15. Parameterization of Gaseous and Ice Cloud Emissivities Cubic Gas Cell EmissivityCubic Cirrus Cell Emissivity

16. 3D Inhomogeneous Radiative Transfer Models for Clouds Monte Carlo “exact” method, delta-diffusion approximation (DDA), and independent pixel-by-pixel approximation (IPA) Correlated k-distribution method for incorporation of gaseous absorption in multiple scattering atmosphere: 121 wavelength to cover solar (0.2-5  m) and thermal IR (5-50  m) Parameterization of the single-scattering properties in terms of ice/water content and mean effective size/radius

17. Subarctic WinterTropical Midlatitude SummerUS Standard Broadband Infrared Flux and Cooling Rate for Plane-Parallel Clear Atmosphere: Monte Carlo vs Fu and Liou

18. Subarctic WinterTropical Midlatitude SummerUS Standard Broadband Infrared Flux and Cooling Rate for Plane-Parallel Cirrus Cloudy Atmosphere: Monte Carlo vs Fu and Liou

19. 3-D Cloud Imaging in a Mesoscale Grid Remote Sensing of 3-D Inhomogeneous Clouds June 1, 2002 Combined Satellite and Mm-Wave Radar

20. Input 3D IWC data (Satellite + Mm-wave Radar) for 3D RT Calculation

22. Figure 2 (a) Three-dimensional ice water content (IWC, 0-0.28 g/m 3 ) and mean effective ice crystal size (DE, 0-196 μm) determined from a unification of the optical depth and DE retrieval from the 0.63 and 3.7 μm AVHRR channels aboard the NOAA-14 satellite and the IWC and DE retrieved from the 35 GHz cloud radar over the ARM-SGP CART site at 2023 UTC on April 18, 1997. The 3D IWC and DE results are presented in xy, yz, and xz planes over a 40 km x 40 km x 4.5 km domain. (b) Time series of the flight altitude and the position of the flight track of the North Dakota Citation over the ARM-SGP CART site on April 18, 1997 (upper panel). Comparison of the mean (symbols) and standard deviations (bars) of the retrieved IWC and DE values from the unification approach involving satellite and cloud radar observations derived from in situ measurements taken on board the University of North Dakota Citation, as functions of aircraft leg height (lower panels) (Liou et al., 2002). (a) 3D Cloud Mapping in a Mesoscale Grid (b) Validation

23. 3D Cloud Mapping in a Mesoscale Grid

24. 3D Radiative Heating Rate in a Mesoscale Grid Figure 2. The left panels illustrate three-dimensional solar heating and IR heating/cooling rates in a mesoscale grid, presented in the xy, yz, xz planes computed from the 3D inhomogeneous radiative transfer model developed by Gu and Liou (2001). The input 3D cloud IWC and DE fields were from those presented in Fig. 1a. The solar constant, solar zenith angle, and surface albedo used were 1366 W/m 2, 60 o, and 0.1 respectively. The standard atmospheric temperature and gaseous profiles were employed in the calculations. The right panels represent the domain-averaged (xy plane) solar heating and IR heating/cooling rates as functions of cloud height.

25. Comparison of 3D broadband Solar Heating Rates 3D DDA relative difference (%)3D Monte CarloIPA relative difference (%)

26. Comparison of 3D broadband IR Heating Rates 3D DDA relative difference (%)3D Monte CarloIPA relative difference (%)

27. Solar Heating Thermal IR Heating Domain Average Heating Rate in a Cirrus Cloud

28. 3D Radiative Transfer in Cloudy Atmospheres: Diffusion Approximation and Monte Carlo Simulation for Thermal Emission K. N. Liou, Y. Chen, and Y. Gu Department of Atmospheric and Oceanic Sciences, UCLA 3D Clouds in the Atmosphere and in Climate Models 3D Radiative Transfer: Diffusion Approximation 3D Thermal Radiative Transfer: Monte Carlo Simulation 3D Results for Cirrus Clouds: Some Thought on Flux, Heating Rate, and Absorption