2. Radiant 2.0: An Introduction Mick Christi OCO Science Meeting March 2004

3. Why Another Radiative Transfer Solver? Wide use of (1) Doubling & Adding and (2) DISORT

4. The Problem  The optical depth sensitivity of doubling.  The necessity of re-computing the entire RT solution if using a code such as DISORT if only a portion of the atmosphere changes.  Our Goal: Employ the strengths of both while leaving the undesirable characteristics behind.

5. Radiant Overview  Plane-parallel, multi-stream RT model.  Can compute either radiances or spectral radiances as appropriate.  Allows for computation of radiances for user-defined viewing angles.  Includes effects of absorption, emission, and multiple scattering.  Can operate in a solar only, thermal only, or combined fashion for improved efficiency.  Allows stipulation of multiple phase functions due to multiple constituents in individual layers. Capability to surgically select delta-m scaling as needed by the user for those constituents.  Allows stipulation of the surface reflectivity and surface type (lambertian or non- lambertian). Simulating Radiative Processes

6. Radiant Overview  Incorporates layer-saving to greatly improve efficiency when the computation of Jacobians by finite difference is required.  Accuracy tested against established tables and codes (e.g. van de Hulst (1980), doubling codes, and DISORT).  Speed tested against doubling codes and DISORT with encouraging results. Simulating Radiative Processes

7. RTE Solution Methodology employed in Radiant  Convert solution of the RTE (a boundary value problem) into a initial value problem  Using the interaction principle.  Applying the lower boundary condition for the scene at hand.  Build individual layers (i.e. determine their global scattering properties) via an eigenmatrix approach.  Combine layers of medium using adding to build one “super layer” describing entire medium.  Apply the radiative input to the current scene to obtain the RT solution for that scene. The Interaction Principle I + (H) = T(0,H)I + (0) + R(H,0)I - (H) + S(0,H) I - (0) = T(H,0)I - (H) + R(0,H)I + (0) + S(H,0) Lower Boundary Condition: I + (0) = R g I - (0) + a g f o e -  /  o

8. Operational Modes: Normal Mode

9. Operational Modes: Layer-Saving Mode

10. Obtaining Radiances at the TOA I + (z*) = {T(0,z*)R g [E-R(0,z*) R g ] -1 T(z*,0) + R(z*,0) } I - (z*) + R(z*,0) } I - (z*) + T(0,z*)R g [E-R(0,z*) R g ] – 1 S(z*,0) + T(0,z*)R g [E-R(0,z*) R g ] – 1 S(z*,0) + S(0,z*) + S(0,z*) I - (z*) I - (0) I + (z*) I + (0) z* 0 T(z*,0) R(0,z*) R(z*,0) T(0,z*) I + (z*) = {T(0,z*)R g [E-R(0,z*) R g ] -1 T(z*,0) + R(z*,0) } I - (z*) + {T(0,z*)R g [E-R(0,z*) R g ] –1 R(0,z*) + T(0,z*)}a g f o e -  /  o + T(0,z*)R g [E-R(0,z*) R g ] –1 S(z*,0) + S(0,z*) S(z*,0) S(0,z*) RT Solution:

11. Numerical Efficiency: Eigenmatrix vs. Doubling

12. Numerical Efficiency: Radiant vs. DISORT

13. Radiant: Program Structure  Subroutines:  DATA_INSPECTOR – Input Data Checker  PLKAVG – Integrated Planck  PLANCK – Monochromatic Planck  RAD – Computes radiances for normal & layer-saving modes  Singularity Busting:   o = 1   =  o or  =  i

14. Radiant: Program Structure  Subroutines  BUILD_LAYER - Determines global scattering properties of layer being built  COMBINE* - Combines Global Transmission, Reflection, & Source Matrices  SURF* - Surface Depiction:  1_3 (Lambertian)  2_2 (Non-lambertian)  Layer-Saving – Global Transmission, Reflection, & Sources for each layer (& atmospheric block) saved for later use

15. Radiant: Program Structure  Subroutines:  LOCAL – Determines local (i.e. intrinsic) scattering properties of layer being built  SGEEVX – Solves the eigenvalue problem to use in determination of global scattering properties

16. Radiant: Program Structure  Subroutines:  GETQUAD2 – Provides Lobatto, Gauss, or Double Gauss quadrature parameters  PLEG – Provides legendre polynomial information for computation of constituent phase functions

17. Summary  Radiant developed in response to some weaknesses in doubling & adding and in the discrete ordinate method as implemented by DISORT.  Radiant employs “eigenmatrix & adding”.  The method allows Radiant to obtain an accurate RT solution that can be much more efficient depending on the problem at hand.

18. Your Questions & Comments