Radiant 2.0:Radiant 2.0:An Introduction An Introduction

Mick ChristiMick ChristiOCO Science MeetingOCO Science Meeting

March 2004March 2004

Why Another Radiative Why Another Radiative Transfer Solver?Transfer Solver?

Wide use of (1) Doubling & Adding and (2) DISORTWide use of (1) Doubling & Adding and (2) DISORT

The ProblemThe Problem

The optical depth sensitivity of doubling.The optical depth sensitivity of doubling. The necessity of re-computing the entire RT solution if The necessity of re-computing the entire RT solution if

using a code such as DISORT if only a portion of the using a code such as DISORT if only a portion of the atmosphere changes.atmosphere changes.

Our GoalOur Goal: Employ the strengths of both while leaving : Employ the strengths of both while leaving

the undesirable characteristics behind.the undesirable characteristics behind.

Radiant Overview Radiant Overview Plane-parallel, multi-stream RT model.Plane-parallel, multi-stream RT model. Can compute either radiances or spectral Can compute either radiances or spectral

radiances as appropriate.radiances as appropriate. Allows for computation of radiances for Allows for computation of radiances for

user-defined viewing angles. user-defined viewing angles. Includes effects of absorption, emission, Includes effects of absorption, emission,

and multiple scattering.and multiple scattering. Can operate in a solar only, thermal only, or Can operate in a solar only, thermal only, or

combined fashion for improved efficiency.combined fashion for improved efficiency. Allows stipulation of multiple phase Allows stipulation of multiple phase

functions due to multiple constituents in functions due to multiple constituents in individual layers. Capability to surgically individual layers. Capability to surgically select delta-m scaling as needed by the select delta-m scaling as needed by the user for those constituents.user for those constituents.

Allows stipulation of the surface reflectivity Allows stipulation of the surface reflectivity and surface type (lambertian or non-and surface type (lambertian or non-lambertian).lambertian).

Simulating Radiative Processes

Radiant Overview Radiant Overview Incorporates layer-saving to greatly improve Incorporates layer-saving to greatly improve

efficiency when the computation of efficiency when the computation of Jacobians by finite difference is required.Jacobians by finite difference is required.

Accuracy tested against established tables Accuracy tested against established tables and codes (e.g. van de Hulst (1980), and codes (e.g. van de Hulst (1980), doubling codes, and DISORT).doubling codes, and DISORT).

Speed tested against doubling codes and Speed tested against doubling codes and DISORT with encouraging results.DISORT with encouraging results.

Simulating Radiative Processes

RTE Solution Methodology RTE Solution Methodology employed in Radiantemployed in Radiant

Convert solution of the RTE (a Convert solution of the RTE (a boundary value problem) into a boundary value problem) into a initial value problem initial value problem Using the interaction principle.Using the interaction principle. Applying the lower boundary Applying the lower boundary

condition for the scene at hand.condition for the scene at hand. Build individual layers (i.e. Build individual layers (i.e.

determine their global scattering determine their global scattering properties) via an eigenmatrix properties) via an eigenmatrix approach.approach.

Combine layers of medium using Combine layers of medium using adding to build one “super layer” adding to build one “super layer” describing entire medium.describing entire medium.

Apply the radiative input to the Apply the radiative input to the current scene to obtain the RT current scene to obtain the RT solution for that scene.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) = RgI-(0) + agfoe-/o

Operational Modes:Operational Modes:Normal ModeNormal Mode

Operational Modes:Operational Modes:Layer-Saving ModeLayer-Saving Mode

Obtaining Radiances at the Obtaining Radiances at the TOATOA

II++(z*) = {T(0,z*)R(z*) = {T(0,z*)Rgg[E-R(0,z*) R[E-R(0,z*) Rgg] ] -1-1T(z*,0) T(z*,0)

+ R(z*,0) } I+ R(z*,0) } I--(z*) (z*)

+ + T(0,z*)RT(0,z*)Rgg[E-R(0,z*) R[E-R(0,z*) Rgg] ] ––

11S(z*,0)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*)Rg[E-R(0,z*) Rg] -1T(z*,0)

+ R(z*,0) } I-(z*)

+ {T(0,z*)Rg[E-R(0,z*) Rg] –1R(0,z*)

+ T(0,z*)}agfoe-/o

+ T(0,z*)Rg[E-R(0,z*) Rg] –1S(z*,0)

+ S(0,z*)S(z*,0)

S(0,z*)

RT Solution:

Numerical Efficiency:Numerical Efficiency:Eigenmatrix vs. DoublingEigenmatrix vs. Doubling

Numerical Efficiency:Numerical Efficiency:Radiant vs. DISORTRadiant vs. DISORT

Radiant: Program StructureRadiant: Program Structure Subroutines:Subroutines:

DATA_INSPECTOR – Input DATA_INSPECTOR – Input Data CheckerData Checker

PLKAVG – Integrated Planck PLKAVG – Integrated Planck PLANCK – Monochromatic PLANCK – Monochromatic

PlanckPlanck RAD – Computes radiances RAD – Computes radiances

for normal & layer-saving for normal & layer-saving modesmodes

Singularity Busting:Singularity Busting: oo = 1 = 1

= = oo or or = = ii

Radiant: Program StructureRadiant: Program Structure Subroutines Subroutines

BUILD_LAYER - Determines BUILD_LAYER - Determines global scattering properties of global scattering properties of layer being builtlayer being built

COMBINE* - Combines Global COMBINE* - Combines Global Transmission, Reflection, & Transmission, Reflection, & Source MatricesSource Matrices

SURF* - Surface Depiction:SURF* - Surface Depiction: 1_3 (Lambertian)1_3 (Lambertian) 2_2 (Non-lambertian)2_2 (Non-lambertian)

Layer-Saving – Global Layer-Saving – Global Transmission, Reflection, & Transmission, Reflection, & Sources for each layer (& Sources for each layer (& atmospheric block) saved for atmospheric block) saved for later uselater use

Radiant: Program StructureRadiant: Program Structure Subroutines:Subroutines:

LOCAL – Determines local LOCAL – Determines local (i.e. intrinsic) scattering (i.e. intrinsic) scattering properties of layer being builtproperties of layer being built

SGEEVX – Solves the SGEEVX – Solves the eigenvalue problem to use in eigenvalue problem to use in determination of global determination of global scattering propertiesscattering properties

Radiant: Program StructureRadiant: Program Structure Subroutines:Subroutines:

GETQUAD2 – Provides GETQUAD2 – Provides Lobatto, Gauss, or Double Lobatto, Gauss, or Double Gauss quadrature parametersGauss quadrature parameters

PLEG – Provides legendre PLEG – Provides legendre polynomial information for polynomial information for computation of constituent computation of constituent phase functions phase functions

SummarySummary

Radiant developed in response to some weaknesses in Radiant developed in response to some weaknesses in doubling & adding and in the discrete ordinate method doubling & adding and in the discrete ordinate method as implemented by DISORT.as implemented by DISORT.

Radiant employs “eigenmatrix & adding”.Radiant employs “eigenmatrix & adding”. The method allows Radiant to obtain an accurate RT The method allows Radiant to obtain an accurate RT

solution that can be much more efficient depending on solution that can be much more efficient depending on the problem at hand.the problem at hand.

Your QuestionsYour Questions& Comments& Comments