1. Radiative Transfer in Clouds: 3D and 1D Approaches Brian Cook University of Maryland, College Park August 10, 2006

2. Why do we care? • 3D approaches are accurate but require much more computer time than their 1D counterparts; • GOAL: Determine how well 1D calculations approximate the 3D radiative fields for various scenarios, namely: • What is the magnitude of 1D errors? • Where do the errors come from?

3. Inputs and outputs • Inputs: • Cloud field • Solar angles • Viewing angles • Surface albedo • Scattering phase function • Output: • Radiation fields

4. Cloud/Photon Interactions Incoming Shortwave Radiation Reflected Shortwave Radiation (Forward Scattering) Reflected Shortwave Radiation (Backward Scattering) Transmitted Short Wave Radiation

5. Cumulus Cloud field from 9 viewing angles

6. 3D vs. 1D simulations 3D • 3D simulations allow photons to move between cloud regions with different properties • 1D simulations treat each column independently as a horizontally infinite cloud layer 1D

7. Photon Leakage 1D 3D

8. 3D / 1D Backward vs. Forward Scattering Bias • The direction of scatter is skewed towards forward for 1D simulations compared to 3D simulations 3D 1D • This bias is dampened at high sun • For 3D, surface reflectance increases the difference between backward and forward scattering.

9. “Mie” vs. “Henyey-Greenstein” Phase Function If the sun is low, for both 1D and 3D simulations, R(HG) > R(Mie) for all viewing azimuth angles except back-scattering

10. “Mie” vs. “Henyey-Greenstein” Phase Function 1D 3D RMS BACK BACK BACK HG RMS FRWD FRWD FRWD Mie Solar Zenith Angle - 60° Albedo = 0.2 For all scattering angles the 1D approximation works better for the real (Mie) phase function than for the HG one

11. Conclusions • The 1D approximation works better for nadir and sideways viewing angles than for backward and forward viewing directions; • The 1D approximation is better for high sun than for low one. • In general, the 1D radiative transfer approximation works better for the real (Mie) phase function than for its HG counterpart;

12. Future Research . . . • Extend analysis to more viewing and illumination conditions; • Try different cloud fields / cloud types • Compare different wavelengths of solar radiation • Add atmospheric affects

13. Acknowledgments Special Thanks to : • Alexander Marshak • Tamas Varnai • Guoyong Wen • Christine Chiu • Cathy Newman • Larry Wharton