2010-06-07: Mie Calculations Verification

From Federation of Earth Science Information Partners

Mie scattering calculations that were carried out on MODIS reflectance data [ http://wiki.esipfed.org/index.php/2010-05-30:_MODIS_aerosol_reflectance_Mie_simulation] using MieTab7.24 [downloaded from http://sourceforge.net/projects/mietab/ ] are compared here with similar computations done with MieTab 4.1 available from http://capita.wustl.edu/CAPITA/People/RHusar/MIE/ folder.

Before discussing the results of this comparison, I would like to point out some of the basic differences in the computation abilities of MieTab4.1 and MieTab7.24

1) MieTab 7.24 can calculate volume (extinction/scattering/absorption) cross sections in cm-1 for various particle size distribution (PSD) models. MieTab 4.1 only provides cross sections (extinction/scattering/absorption) in square centimeters.

2) MieTab7.24 calculates the four elements (M2, M1, S21 and D21) of F’ Matrix [ notations are similar to that used by Van de Hulst ] at each specified scattering angle and displays them under the generic term "intensities" together with the “phase function”. This facility is not available in MieTab 4.1. Mie Tab 4.1 only provides relative intensities at specified scattering angles.

3) The number of angles (NANG) at which the phase function(s) are calculated can be upto maximum 361 in MieTab 7.24. In MieTab 4.1, NANG is maximum 181.

4) MieTab7.24 has a function called NBIN which can subdivide the overall computational range (RMIN to RMAX) in to number of radius intervals (or “bins”). The maximum number of bins that are allowed in MieTab7.24 is five. MieTab 4.1 doesn’t have this function. NBIN is only used with analytic particle distribution models.

5) MieTab 7.24 provides Modified Stokes Vector for given input Stokes Vector. Apart from the four elements {I(parallel), I(perpendicular), U, V} of the stokes vector , the out put also include polarization and ellipticity.

In-order to verify the earlier Mie calculations,most of them was re-checked using the MieTab 4.1. However, only a sample calculation is provided in this note here.

As MieTab 4.1 only provides “cross sections” and MieTab 7.24 only provides “volume cross sections” for PSD models, they could not be compared.

Therefore it was decided to compare the Phase functions computed by these two Mie programs.

Following are the out puts from these two programs for one of the aerosol models (Model 23) used in the earlier calculations.

Details of the Model:

Refractive Index: 1.55+0.0035i; RMIN= 0.05 μm; RMAX= 5 μm; Rbar= 0.5 μm; Std.Dev (σ )= 0.5; Wavelength= 0.469μm

scattering angle of interest is about 150 degree. Therefore the results of Mie computations are provided around that angle.

Output from Mie Tab 4.1

Cross Sections (cm2):

Waveln.     Cext      Csca      Cabs      Cbak       M         K  
--------- --------- --------- --------- --------- --------- ----------
4.690E-01 5.258E-06 4.686E-06 5.714E-07 4.730E-06 1.550E+00 3.500E-03

Variation of scattered intensity with specified angle [a subset of actual output]:

 Angle(deg) Relative Intensity                                                           
 --------   ------------------
 148.83     1.317E-04
 149.83     1.305E-04
 150.84     1.279E-04
 151.84     1.246E-04
 152.85     1.237E-04
 153.85     1.307E-04

Output from Mie Tab 7.24

Number of radius intervals (bins) = 5; Number of radii used = 45

Interval   Rmin      Rmax     k(ext)    k(sca)    k(abs)  k(radar)  NRADI  CNVG
 1      5.000E-02 1.040E+00 1.932E-06 1.810E-06 1.222E-07 3.069E-06   9   Yes              
 2      1.040E+00 2.030E+00 1.735E-06 1.531E-06 2.043E-07 6.325E-07   9   Yes              
 3      2.030E+00 3.020E+00 6.749E-07 5.583E-07 1.166E-07 3.686E-07   9   Yes              
 4      3.020E+00 4.010E+00 2.671E-07 2.086E-07 5.844E-08 8.772E-08   9   Yes              
 5      4.010E+00 5.000E+00 1.161E-07 8.649E-08 2.957E-08 2.215E-08   9   Yes

Volume Cross Sections (cm-1):

k(ext)=4.725E-06; k(sca)=4.194E-06; k(abs)=5.311E-07;

Assymetry g= 7.585E-01

F' Matrix[a subset of actual output]

Angle   Phase Fn.     M2         M1        S21        D21
148.8   1.331E-02   1.056E-02   1.607E-02 -3.945E-04 -6.492E-03
149.8   1.411E-02   1.132E-02   1.689E-02 -5.330E-04 -7.159E-03
150.8   1.502E-02   1.211E-02   1.793E-02 -6.863E-04 -7.964E-03
151.8   1.608E-02   1.295E-02   1.921E-02 -8.167E-04 -8.928E-03
152.8   1.731E-02   1.387E-02   2.076E-02 -9.141E-04 -1.007E-02
153.9   1.874E-02   1.485E-02   2.262E-02 -9.947E-04 -1.139E-02

It is clear from these outputs that the Phase Function given by MieTab 7.24 is larger (by two orders of magnitude) than the angular relative intensity given by MieTab 4.1 for similar scattering angles,wavelength and aerosol model. The reason for this (from my investigations!!!) is that the relative intensity output by MieTab 4.1 is normalized to particle number density. The Phase function computed from both the Mie programs matched when particle number density was used as a multiplier to the relative intensity values provided by MieTab 4.1.