Case 1: Angle-Value phase function vs. Legendre-expansion vs. Legendre-expansion  truncation

The input scattering phase function for I3RC model can be specified in two ways: 1) as scattering angle-value 2) as Legendre polynomial expansion. The objective of this task is to test whether these two ways of phase function specification yield consistent results.

Case setup:

Phase function;                Mie; wavelength 0.84µm~0.88µm averaged; gamma distribution re = 10µm & veff=0.1

Extinction efficient:          159.123/km/(g/m^3)

Single-scattering albedo: 0.999958

Cloud parameters:          0.5km~1.5km, LWC=0.1g/m^3; no atmosphere, black surface

Total optical depth:         159.123 * 1km * 0.1g/m^3 = 15.9123

Solar angles:                   µ0=0.9397 (20 degree); phi0 = 0 degree

original

truncated

input files for I3RC (click to download):

Angle-value phase function inputs:

Mie_w0.86_Re10_AngVal.phasetab: scattering properties and phase function (angle-value) to generate domain optics

single_cell_AnglVale_w0.86.dom: Domain optical property based on Mie_w0.86_Re10_AngVal.phasetab

Legendre expansion (w/o truncation) inputs:

Mie_w0.86_Re10_LegCoef.phasetab: scattering properties and phase function (Legendre expansion  w/o truncation) to generate domain optics

single_cell_LegCoef_w0.86.dom:Domain optical property based on Mie_w0.86_Re10_LegCoef.phasetab

Legendre expansion (with truncation) inputs:

Mie_w0.86_Re10_LegCoef_truncated.phasetab: scattering properties and phase function (Legendre expansion with truncation) to generate domain optics

single_cell_LegCoef_truncated_w0.86.dom: Domain optical property based on Mie_w0.86_Re10_LegCoef_truncated.phasetab

RT simulation outputs(click to download):

run_I3RC.nml: driver name list file for running I3RC

single_cell_AnglVale_w0.86_I3RC.nc: Radiative transfer simulation results based on single_cell_AnglVale_w0.86.dom

single_cell_LegCoef_w0.86_I3RC.nc: Radiative transfer simulation results based on single_cell_LegCoef_w0.86.dom

single_cell_LegCoef_truncated_w0.86_I3RC.nc: Radiative transfer simulation results based on single_cell_LegCoef_truncated_w0.86.dom

Input phase function

blue asterisks indicate the comparison between RT simulation using Angle-Value phase function vs. using Legendre-Expansion Phase function (w/o truncation) in I3RC

red  diamonds indicate the comparison between RT simulation using Angle-Value phase function vs. using Legendre-Expansion Phase function with truncation

Correlation: 0.92

Std of Relative difference: 2.24%

Correlation: 0.96

Std of Relative difference: 1.57%

Results: RT simulations based on Legendre-Expansion phase function (with or w/o truncation) agree closely results based on Angle-Value phase function. The relative difference is within 5%

Case 2: Component-Method vs. external mix

I3RC allows several “components” in each grid cell. Each component can have its own scattering properties. In Monte-Carlo RT simulation, the probability of each component interacting with incoming phonons is weighted by the extinction of each component in a given cell. The objective of this task is to test whether RT simulation based on component-method is consistent with that based on manually mixed scattering properties.

Case setup:

Component #1

Phase function;                Mie; wavelength 0.84µm~0.88µm averaged; gamma distribution re = 10µm & veff=0.1

Extinction efficient:          159.123/km/(g/m^3)

Single-scattering albedo: 0.999958

Component #2

Phase function;                Non-spherical Ice (Baum et al. 05); wavelength 0.84µm~0.88µm averaged; re = 30µm

Extinction efficient:          55.5333/km/(g/m^3)

Single-scattering albedo: 0.9999

Cloud parameters:          0.5km~1.5km, LWC =0.1g/m^3; IWC=0.1g/m^3 no atmosphere, black surface

Total optical depth:         159.123 * 1km * 0.1g/m^3 + 55.5333 *1km *0.1g/m^3= 21.46

Solar angles:                   µ0=0.9397 (20 degree); phi0 = 0 degree

ice

water

mixed

input files for I3RC (click to download):

Angle-value phase function inputs:

Mie_w0.86_Re10_AngVal.phasetab: scattering properties and phase function (angle-value) for water

ice_PF_w0.86_Re30.00_AngVal.phasetab: scattering properties and phase function (angle-value) for ice

PF_w0.86_AngVal_Water_Ice_mixed.phasetab: scattering properties phase function (angle-value) for water & ice mix

Legendre expansion (with truncation) inputs:

Mie_w0.86_Re10_LegCoef_truncated.phasetab: scattering properties and phase function (Legendre expansion with truncation)  for water

ice_PF_w0.86_Re30.00_LegCoef_truncated.phasetab: scattering properties and phase function (Legendre expansion with truncation) for ice

Domain optics:

single_cell_AnglVale_w0.86_Water_Ice_Components.dom: Domain optics based on “component method” & Angle-Value phase function

single_cell_LegCoef_truncated_w0.86_Water_Ice_Components.dom:  Domain optics based on “component method” & Legendre expansion with truncation

single_cell_AnglVale_w0.86_Water_Ice_mixed.dom: Domain optics based on “mixed method” & Angle-Value phase function

RT simulation outputs(click to download):

run_I3RC.nml: driver name list file for running I3RC

single_cell_AnglVale_w0.86_Water_Ice_Components_I3RC.nc: RT simulation based on “component-method” & Angle-Value phase function

single_cell_LegCoef_truncated_w0.86_Water_Ice_Components_I3RC.nc: RT simulation based on “component-method” & Legendre expansion phase function with truncation

single_cell_AnglVale_w0.86_Water_Ice_mixed_I3RC.nc: RT simulation based on “mixed method” & Angle-Value phase function

External mix of components

blue asterisks:

external mix & Angle-Value PF

vs.

component method & Angle-Value PF

Correlation: 0.92

Std of Relative difference: 1.78%

red  diamonds:

external mix & Angle-Value PF vs.

component method & Legendre-expansion with truncation PF

Correlation: 0.97

Std of Relative difference: 0.93%