MODTRAN6, 2022 and Pseudo-aerosol determination 2023

Sept 1, 2022

Bought 4 seat licenses for MODTRAN6. 

Downloaded MODTRAN6, additional utilities, and atmosphere generation tool. 

These come as g'zipped tar files with a utility called 7z. It evidently does an install based on a repository. To get this installed on a Mac had to go into Preferences→ Security → General and allow 7z to be an OK thing to run. 
Once that was done this ran to completion: 

                   sudo ./macos/7za x ~/Downloads/Mod6_0_2r3full_allplat/Mod6_0_2r3full_allplat.7z.001 -o/usr/local/bin

MODTRAN6 Manual : MODTRAN 6 User's Manual.pdf

**************

HUIT-FAS-MacBook-Stubbs:MODTRAN6.0 cstubbs$ cat README_installation.txt 

MODTRAN6 Linux Installation for Release MODTRAN6.0

==================================================

For the public release of MODTRAN6, data files are shipped as

binaries, precompiled binary executables are included for Linux,

MacOS, and Windows, and some additional software tools have been

included. These program files can be found in the "bin" sub-

directory for each of the supported platforms.

Setup instructions are given below, first for installation on

MacOS, then Linux, and finally for Windows.

MODTRAN Setup for MacOS:This 

========================

  1) Create an environment variable MODTRAN_DATA to define the absolute path to MODTRAN's data directory.

  Most MacOS systems load environment variables from the user's 

  .bash_profile configuration file.  Open this file with your

  preferred text editor, such as TextEdit or nano.

  Add this parameter to the .bash_profile:

    export MODTRAN_DATA=/home/user/Modtran6/DATA (use your actual path)

  2) Register your license key

  Modtran 6 includes a standalone license management utility to enter

  and register a license key.  To open the utility, enter the Modtran

  "bin/macos" subdirectory and run this script:

./mod6lic

  Enter your 28-digit key in the text field and press the "Activate"

  button to register the key.  The license status will display

  "Genuine" if the action is successful.

  The Modtran console application can also register the license from a

  terminal/command prompt.  To register the license with this program,

  enter the Modtran "bin/macos" subdirectory and type this command:

./mod6c_cons -activate_license <28-digit product key>

  The program will report a message indicating the status of the 

  license.

MODTRAN Setup for Linux:

========================

  1) Create an environment variable MODTRAN_DATA to define the absolute 

  path to MODTRAN's data directory.

  Most Linux profiles use either bash or csh/tcsh shells.  These shells

  load environment variables from the user's .bashrc or .cshrc 

  configuration files.

  (BASH) Add this parameter to the .bashrc:

    export MODTRAN_DATA=/home/user/Modtran6/DATA (use your actual path)

  (T/CSH) Add this parameter to the .cshrc:

    setenv MODTRAN_DATA /home/user/Modtran6/DATA (use your actual path)

  2) Register your license key

  Modtran 6 includes a standalone license management utility to enter

  and register a license key.  To open the utility, enter the Modtran

  "bin/linux" subdirectory and run this script:

./mod6lic

  Enter your 28-digit key in the text field and press the "Activate"

  button to register the key.  The license status will display

  "Genuine" if the action is successful.

  The Modtran console application can also register the license from a

  terminal/command prompt.  To register the license with this program,

  enter the Modtran "bin/linux" subdirectory and type this command:

./mod6c_cons -activate_license <28-digit product key>

  The program will report a message indicating the status of the 

  license.

MODTRAN Setup for Windows:

==========================

  The Windows installation program will typically perform all setup

  necessary to configure and license Modtran 6.  The manual steps

  outlined below are carried out by that program. 

  1) Create an environment variable named MODTRAN_DATA to define the

  absolute path to the DATA directory.

  If the MODTRAN data files were installed to:

C:\ProgramDATA\SSI\MODTRAN6DATA\

  Using an command prompt:

    1. Type the command:

    setx /M MODTRAN_DATA "C:\ProgramDATA\SSI\MODTRAN6DATA\"

or

setx MODTRAN_DATA "C:\ProgramDATA\SSI\MODTRAN6DATA\"

(use your actual installation path)

  Using the Windows control panel:  

1. Click the START button and select "Control Panel"

2. Click on "System and Security"

3. Click on "System"

4. On the left panel, click on "Advanced system settings"

5. The "System Properties" window should display. Under the 

  "Advanced" tab, click on "Environment Variables ..."

6. Check that the variable MODTRAN_DATA is not already

  assigned a value under either "User variables for ..."

  or "System variables". If it is not already defined,

  click "New ..." under "System variables"

7. In the "New System Variable" window, set "Variable name:" 

  to MODTRAN_DATA and set "Variable value:" to 

      C:\ProgramDATA\SSI\MODTRAN6DATA\ 

  (use your actual installation path)

8. Click OK in the Environment Variables window.

9. Click OK in the System Properties window.

You can verify that the environment variable was created by

opening a command window and typing "set".

  2) Register your license key

  Modtran 6 includes a standalone license management utility to enter

  and register a license key.  To open the utility, navigate to the 

  Modtran 6 program group and select the license manager shortcut:

Start -> MODTRAN 6 -> Settings -> Manage License

  Enter your 28-digit key in the text field and press the "Activate"

  button to register the key.  The license status will display 

  "Genuine" if the action is successful.

*****************************************************

our license key is NZT2-96IQ-FZ4A-4GVU-3JSD-QEDA-NWTA

sent request for offline authorization

************************************

added environment variable with data path to .bash_profile, and sourced that file. 

HUIT-FAS-MacBook-Stubbs:~ cstubbs$ echo $MODTRAN_DATA 
/Users/cstubbs/data/Modtran6/data/

Java interface startup is in 

/usr/local/bin/MODTRAN6.0/bin/macos

OK, that didn't work. It looks for a lot of stuff in the data directory, so need to use

/usr/local/bin/MODTRAN6.0/DATA

that did work, got an initial run to work. Here is a useful ref: http://dirsig.cis.rit.edu/docs/new/modtran.html 

Sept 5, 2022

TAPAS online atmospheric throughput generation tool:

http://cds-espri.ipsl.fr/tapas/project?methodName=home_en 

RUNNING MODTRAN6

Feb 20, 2023

Go to 

/usr/local/bin/MODTRAN6.0/bin/macos

then do mod6gui

which will bring up this (JAVA) screen: 

Clicking on Edit function brings up a range of panels

Unit conversions

It wants Ozone content as gm/cm^2 and we have it in Dobson units. Wikipedia says 1 DU is 2.69×10²⁰ molecules per meter squared.
Molecular weight of O_3^16 is 47.992 gm/mole. One mole is 6.023E23 molecules. One square meter is 1E4 cm^2. So: 

1 DU = 2.69E20 molecules/m^2 * (1m^2/1e4 cm^2) * ( 47.992 gm/mole) * (1 mole/6.023E23 molecules) = 2.1434e-06 gm/cm^2

so to get O3 in gm/cm^2 do (DU*2.1434e-06) 

250 DU = 5.3586e-04 gm/cm^2

PWV is in mm, collapsing entire column density into some depth of liquid. MODTRAN6 wants gm/cm^2 of H2O. Density of water is 1 gm/cc, so 1 cm of water is 1 gm/cc. 
So for this the conversion is 10 mm PWV → 1 gm/cc. Typical Pachon PWV is a few mm. Let's use a default 5mm PWV which corresponds to 0.5 gm/cm^2. 

Set up point-to-point geometry from LSST elevation to 80 km, straight up.

Data go to ~/MODTRAN6

rename .tp7 output files with X.XX***.dat where X.XX is airmass to 3 sig figures
Matlab code ReadModtran6.m will then read in and act on these files. Need at least 4 of them. 

The ***.psc output file is really simple; nm, T in two columns. 

Default Atmosphere at zenith

Used MODTRAN6 to generate transmission data for Rubin elevation up to 100 km. Used 5mm PWV and 250 Dobson units. Used ReadModtran6.m MATLAB code to convert from cm^-1 to nm and extract total transmission, ozone, and water. 
Stable Transmission is Transmission/(water*Ozone), and is basically the Rayleigh scattering portion in blue. 
The quadnotch filter avoids the O2 lines, doesn't go that far into the red. 

Looked up pressure vs. altitude for US Standard Atmosphere, did a fit vs. altitude and evaluated at Rubin elevation of 2647 m. Result is 7.3269 E 4 N/m^2 which is 0.73269  bar = 732.69 millibar

From Wikipedia:

If we add more material, need to use the product of transmissions. So compute a dimensionless quantity EAM, effective airmass, where EAM=(X)*(P/0.73269) and X is computed from zenith angle using formulation given above. 
Also compute OEAM, Ozone effective airmass, as OEAM=(X)*(O3/250) where O3 is in Dobson units. This has no pressure dependence since Ozone is already total column density
Also compute WEAM, Water effective airmass, as WEAM=sqrt(X*PWV/5). 

Wrote MakeAtmosphere.m that takes default transmission. 

Here is the result of doubling water content, going from 250 to 300 Dobson units of ozone, and pointing at 60 degree zenith angle

Expected range of PWV is given by  The GPS water vapor monitor and thermal astronomy at Gemini South (note this is an estimate from Paranal). So 5mm is a sensible default value. 

Targets

Calspec standards that are both bright and rather AB-flat.
From https://www.eso.org/sci/observing/tools/standards/spectra/stanlis.html 

HR9087 00 01 49.42 -03 01 39.0 5.12 B7III
HR718 02 28 09.54 +08 27 36.2 4.28 B9III
HR1996 05 45 59.92 -32 18 23.4 5.17 O9V = Mu Col
HD60753 07 33 27.26 -50 35 03.7 6.70 B3IV
HR3454 08 43 13.46 +03 23 55.1 4.30 B3V
HR4468 11 36 40.91 -09 48 08.2 4.70 B9.5V
HR5501 14 45 30.25 +00 43 02.7 5.68 B9.5V
HR7001 18 36 56.33 +38 47 01.1 0.00 A0V = Alpha Ly
HR7950 20 47 40.55 -09 29 44.7 3.78 A1V
HR8634 22 41 27.64 +10 49 53.2 3.40 B8V

In general, A0V stars are good spectra for this purpose. 

Here's a list of bright A0 stars from Simbad in the right dec band: 

Polar A0 stars: 

Exposure times

HD 185975 is V=8.1
In 30 sec integration it gets hologram peak of 2500, sum of 60K ADU at peak, in typical seeing. A mag 6 star is 7X brighter so we'd get peak of 17K ADU, not saturated. So 30 sec seems good for V=6-8.

March 5 2023- synthetic photometry

Downloaded MuCol CalSpec data files from STSCI. https://archive.stsci.edu/hlsps/reference-atlases/cdbs/current_calspec/ 
data files are mucol_mod_004.fits and mucol_stis_006.fits:
mucol_stis_006.fits
mucol_mod_004.fits

used the TopCat utility to strip out columns of data from the model atmosphere file, resulting in MuCol.dat with extracted columns. wavelength is in Angstroms, fluxes are F_lambda, in Watts/m^2/A (I presume). 
Also pulled out the data from the STIS observations of Mu Col, which is evidently better to use at CCD wavelengths. Columns in that file are

Called it MuColSTIS.dat

The data are energy per nm so to convert to photons per wavelength bin need to multiply by lambda- it takes more photons at longer wavelength to make same amount of energy. 

BEWARE! Step size of wavelength intervals changes!!

Here is a plot of (lambda/8000)*F_lambda, which is photon spectrum for this source: 

LATISS throughput estimates, ab initio

data files are in  laptop directory /Users/cstubbs/data/AuxTel/throughput

Quadnotch curve is from Semrock, and is adjusted for Aux tel f/17 beam

Grating was digitized from Edmund catalog image using WebPlotDigitizer, https://www.edmundoptics.com/f/uv-transmission-gratings/14332/

Grating is fused silica substrate, presumably included in throughput curve

LATISS entrance window is quartz, dewar window is fused silica. Quartz uncoated is 90% flat across all our bands. Fused silica is same.

Aluminum Mirror reflectance from Subaru data, digitized from https://www.naoj.org/Observing/Telescope/Parameters/Reflectivity/

AuxTel primary mirror reflectance from https://confluence.lsstcorp.org/display/LTS/Aux+Tel+Reflectivity+Status

ITL QE curve is from BNL test stand data. Note AR coating could be different... it's a first estimate.

Aux Tel secondary and tertiary are Ag coated, better reflectance at 45 deg. Note there will be polarization effects!! Data from 6_30_45DEG UV350AG_UV-VIS-NIR-IR.xls 

Secondary reflectance limits UV throughput of overall system, 10% at 323 nm, 665 AT 330 nm. 

Hard to reconcile Al mirror from Subaru with our reflectance data: 

These splined data sets are really only valid for 310-1100 nm. But the data run from 300-1200 nm. 

Default atmosphere: 
Zenith angle = 0
PWV = 5 mm
Ozone = 250 Dobson units
Barometric Pressure = 0.73269 bar

NO AEROSOLS!

Wrote SynPhot.m that integrates Mu Col photon spectrum against instrumental throughput and though various atmospheric columns, including top of atmosphere. 

Linear fits to magnitudes of extinction vs. airmass produce:

Color-airmass terms:

For a color difference of Mu Col -flat =  delta(B1-B2) = (22.4303 - 21.9940) - (20.5042 - 20.4675) = 0.4363 - 0.0367 = +0.3996, we get an extinction difference of 3.5 mmag/airmass. 
For a color difference of Mu Col -flat = delta(B3-B4) =   (21.9831-21.5152) - (23.1427-22.3052) = 0.4679 - 0.8375 = -0.3696 we get an extinction difference of 0.7 mmag/airmass
                                                   

Compare to photon-flat source:

Quick-look comparison with observations from March 2, 2023

SEE BELOW FOR ERROR FOUND AND CORRECTED IN BAND 4

Observations of Mu Col

If m=0 star is at row 339,

B1 starts at 1876+339 and goes to 2263+339
B2 starts at 2263+339 and goes to 2746+339
B3 starts at 2746+339 and goes to 2995+339
B4 starts at 2295+339 and goes to 3562+339

seq num	airmass	B1	B2	B3	B4
1 is single bias frame for that night	NA
052-054 (omitted from fits)	1.029	2.0363	1.8454	3.3374	1.2848
106-108	1.086	2.0365	1.8413	3.3213	1.2730
142-144	1.152	2.0664	1.8548	3.3253	1.2833
204-206	1.298	2.1417	1.8917	3.3636	1.3193
298-300	1.852	2.3909	2.0284	3.4647	1.4349
extinction coeff extracted from observations		0.4620+- 0.015	0.2458+-0.005	0.1913	0.2131+-0.01
TOA magnitude from observations		1.5365	1.5729	3.1110	1.0406
extinction excess: observed-predicted		0.073	0.0559	0.0742	0.1161

(assuming photometric conditions on that night... actually lowest airmass points look anomalous, omit them) 

Problem in B4 could be hard-wired aperture photometry missing flux?
Or throughput curve being quite wrong?
Or more ozone than assumed? 
Or code error somewhere? *note added: yes this was the issue. see below
Or a real physical aerosol effect?? 

What about spectrophotometry, at top of atmosphere? Compare colors since overall magnitude has zeropoint uncertainty

color	predicted	observed	difference
B1-B2	0.0367	-0.0364	0.0731
B1-B3	-1.4789	-1.5745	0.0956
B1-B4	-1.0110	0.4959	-1.5069

March 12 2023

I found and fixed an error in photometry extraction code used above, for the band-4 photometry. Redoing it correctly gives

TOA colors:

A toy example of determining excess extinction. 
March 13 2023

Determined effective band center for observations of Mu Col by computing, band per band, lambda_eff=sum(lambda*detected photon spectrom on ground)/sum(photon specrum on ground) for atmosphere at 1.4 airmasses and Mu Col photon spectrum and estimated throughput. 
Resulting band centers are

MuCol45B1Center =
372.4688

MuCol45B2Center =
444.4264

MuCol45B3Center =
507.9065

MuCol45B4Center =
574.9926

plot extinction excess vs. wavelength: 

So overall there is scatter but a decreasing trend with wavelength. Note this is for single-image analysis and no flatfielding and no correction for m=0 contaminating stars. Let's pretend like the value at 507 is anomalous, and continue to get fit parameters: 

define lambdanorm=lambda/500. 

March 19 2023, wavelength solution for quadnotch + 300 l/mm disperser. 

 Images from March 16 2023 seq num 477 has a star with nice stellar atmosphere features. HD 73495 = Eta Pyxidis HR 3420. HD 73495. HIP 42334 is an A0V star.
Spectrum from RubinTV is

Copied images from 20230316 to local disk on laptop. Need to include bias frames as well as images of interest. Note that dispersion depends critically on disperser-to-CCD spacing so we should solve for it each time. 
Note apparent m=0 stellar contamination at blue end of band3. We need to either subtract those out or median-filter with rotations. 

Balmer lines are at

486.135
434.047
410.173
397.007
388.906
383.540

Downloaded seqnums
477
745-755 bias frames

Ran InjestAndAnalyze.m to create bias frames and full frame debiased images. 

Ran Specexam2.m on frame AT_O_20230316_000477.full.debias.fits. m=0 star centroid is row 300.4 and col 1737.1

zoom on spectrum at absorption lines

March 21, 2023

Looking at band edges to get a broader estimate of wavelength solution. Plot of spectrum in black, abs(diff(spectrum)) in red: 

Manual extraction of pixel row where flux begins to fall. This is notch band edge when convolved with seeing. 

This gives what seems to be a decent dispersion solution, at 0.177 nm/pixel. 
If seeing is of order 1 arcsec and we have 0.1 arcsec per pixel then spectral FWHM is around 10 pixels which gives a spectral resolution of around 1.8 nm. Not bad!

Center of m=0 star is row 312, add that in and see how it looks... wow! Still a really linear relationship. 

lambda=(pix - m=0 row) * 0.1769.

uncertainties: 

Coefficients (with 95% confidence bounds):
       p1 =      0.1769  (0.1744, 0.1795)
       p2 =      -55.15  (-62.48, -47.82)

Compare two images at different airmasses and therefore different parallactic angles to see stellar contamination:

image 299 from 20230302: 

Extract full spectrum from 3 images, align in wavelength and then fit for TOA spectrum. We can then divide by Mu Col spectrum and get overall transmission function of telescope and instrument. A simple offset in pixel space ought to align the spectra since dispersion is so linear. 
Pick images 107, 143, 205, 299 from 2023-03-02. 

We want the cross-correlation of the resulting spectrum vectors. Do xcorr(spec,full107) and find offset for best match. We are already finely sampled at 0.177 nm/pixel. 

circular shift of spectra: template=zeros(length(full107,1));

shift107=template;

shift107(1:end-5)=full107(5:end-1);

etc

save('shiftedspectra.mat','shift107','shift143','shift205','shift299')

verify by plotting shifted spectra: 

'

Highest airmass curve has degraded seeing, we'd have to correct for that. 

For now, just fit to the three lowest airmass curves. In future, good to pick stars with no stellar features. K type stars perhaps? 

Wrote TOAAuxTel.m that picks out subset of spectra and find extinction and top of atmosphere (TOA) photon spectrum. Cuts imposed in slope & TOA space: 

March 31, 2023 

Eske ran DM reductions on a more extensive data set of Mu Col observations, and we still see excess extinction but with non-power law wavelength dependence. 

There also seems to be a dependence of color anomalies on az smearing ie.e PSF.
We need to validate the photometry code being used. One good comparison is to run Source Extractor and compare 

Relevant Seq Nums are:

Mar 14 2023, HD 38666

403, 404, 405, 436, 437, 438, 444, 445, 446, 477, 478, 479, 485,
            486, 487, 512, 513, 514, 536, 537, 538, 560, 561, 562, 595, 596,
            597, 695, 696, 697

November 23, 2023 - revisions for quadband paper 1. 

We've done an analysis of observations from Oct 10, 2023 on Aux Tel with masked quadband filter. There is about a 1% discrepancy between photometry and MODTRAN predictions. 

This looks like the place to find Ozone dobson units: https://disc.gsfc.nasa.gov/datasets/OMPS_NPP_NMTO3_L3_DAILY_2/summary

NASA Ozone data https://urs.earthdata.nasa.gov/home cstubbs cat4Earthdata stubbs@g

do geographical search on latitude -30:14:40.68 longitude -70:44:57.90; = -30.245, -70.75

Well, that didn't work so well. Try this: 
https://www.esrl.noaa.gov/gmd/grad/neubrew/SatO3DataTimeSeries.jsp 

That works! Can get plots as well as CSV data files:

For our site: 

Ozone data file for Rubin site: Ozone2023.csv

I used MAtlab program MakeAtmosphereExtinction.m to generate band-integrated extinctions for stars of different temperatures. This used GPT to help with generation of MATLAB code. 

best current estimate of Aux tel throughput: TotalAuxtelThroughput.dat. Note that this include the quadband filter as well as telescope and optics and detector QE. 

angle-corrected quadband throughput: Quadband.dat

Ozone for Oct 10 2023 is 283.7 Dobson units, interpolated to our site location.

Try to get barometric pressure right. Used https://weatherspark.com/h/d/25822/2023/10/10/Historical-Weather-on-Tuesday-October-10-2023-in-La-Serena-Chile#Figures-Pressure for barometric pressure at La Serena airport. 

On Oct 10 2023 at 10 pm local the pressure at airport was 30.06 inches of mercury which is 1018 mbar. On Nov 23 2023 at 10 pm local it was the same value (precision is 0.01 inches). And at the summit we had 744.35 at that same time. 
So a good pressure value to use for Oct 10 2023 is 0.74435 mbar. 

Let's explore sensitivity to MODTRAN parameter choices. 

Over the course of a year, barometric pressure at La Serena airport ranged from 29.8 in to 30.3 in of mercury. That's less than +- 1% variation.
PWV varies (very conservatively) from 0- 10 mm
Ozone varies from (see plot above)  250 to 300 Dobson units
Stellar colors go from -1 to 1. 

So introduce perturbations that amount to mean-to-peak excursions, i.e. half the peak-to-peak value. This will show peak extinction excursions about the mean. 

Let's explore sensitivity to MODTRAN parameter choices. 
MATLAB program takes Star temperature, PWV, barometric pressure, and Ozone as inputs. 
Pressure first: 

T in 1000K.  Dobson.   PWV (mm). P(mbar) m1-m4.    E1.          E2.        E3.             E4.         E14.         E24.          E34

10.5000  298.0000    5.0000    0.7327    0.0036    0.3892    0.1887    0.1194    0.1030    0.2862    0.0857    0.0164
10.5000  298.0000    5.0000    0.7400    0.0068    0.3930    0.1906    0.1205    0.1037    0.2894    0.0869    0.0168
10.5000  298.0000   10.0000    0.7400    0.0067    0.3930    0.1906    0.1205    0.1038    0.2892    0.0868    0.0167
10.5000  275.0000    5.0000    0.7400    0.0096    0.3930    0.1905    0.1195    0.1008    0.2922    0.0896    0.0187
10.5000  250.0000   10.0000    0.7400    0.0125    0.3930    0.1904    0.1185    0.0980    0.2950    0.0924    0.0206
  6.0000  250.0000   10.0000    0.7400    1.0046    0.3872    0.1875    0.1184    0.0976    0.2896    0.0900    0.0208

E1 is extinction in band 1 in mag per airmass, bluest band. E14=E1-E4, etc. 

We see color-extinction changes of 

Final selection for Oct 10 2023:

which gives: 

10.5000  283.7000    5.0000    0.7443    0.0105    0.3953    0.1916    0.1205    0.1023    0.2930    0.0893    0.0182
5.0000  283.7000    5.0000    0.7443    1.4842    0.3868    0.1875    0.1203    0.1018    0.2850    0.0857    0.0185
15.0000  283.7000    5.0000    0.7443   -0.3492    0.3975    0.1927    0.1206    0.1024    0.2951    0.0902    0.0181
8.0000  283.7000    5.0000    0.7443    0.4131    0.3929    0.1905    0.1205    0.1022    0.2908    0.0883    0.0183

Except OOPS we are using c34 as the definition of color, to reduce airmass sensitivity, recreate table with c34 in final column: 

  5.0000  283.7000    5.0000    0.7443    1.4842    0.3868    0.1875    0.1203    0.1018    0.2850    0.0857    0.0185    1.0369
10.5000  283.7000    5.0000    0.7443    0.0105    0.3953    0.1916    0.1205    0.1023    0.2930    0.0893    0.0182    0.6828
15.0000  283.7000    5.0000    0.7443   -0.3492    0.3975    0.1927    0.1206    0.1024    0.2951    0.0902    0.0181    0.5998

Fitting to C34 color (typcially around 0.5) gives

 E14=  0.3090   -0.0231*C34
 E24=  0.0964   -0.0103*C34
 E34=  0.0176    +0.0009*C34

and for an A star we get E14=0.2930, E24=0.0893, E34=0.0182. 

MATLAB program is here: MATLAB MODTRAN code

Nov 25, 2023. 

Looked up some papers on short term ozone fluctuations Typical RMS daily flluctuations at -30 latitude is around 5%. 
Also looked at ESA Sentinel satellite data for Ozone. See https://dataspace.copernicus.eu/browser/?zoom=6&lat=-29.84835&lng=-71.2672&themeId=DEFAULT-THEME&visualizationUrl=https%3A%2F%2Fsh.dataspace.copernicus.eu%2Fogc%2Fwms%2F0b0f5a61-f3d1-4c6e-8d11-4e58e2d454ef&datasetId=S5_O3_CDAS&fromTime=2023-11-24T00%3A00%3A00.000Z&toTime=2023-11-24T23%3A59%3A59.999Z&layerId=O3_VISUALIZED&demSource3D=%22MAPZEN%22&cloudCoverage=30

stubbs@g.harvard.edu, cat4Tropomi!

Sentinel 5 has ozone data with 3 day sliding averages. Can place a pin and download data file. 

they use different units, moles/m^2. Value for 10 Oct 2023 was 0.13. 

So the conversation factor is  2.2379e+03. The Sentinel5 ozone value for Oct 10 2023 is therefore 0.1248*  2.2379e+03 = 279.3 Dobson units. NASA said 284. 

The conversion factor is 2.2379e+03 to go from Sentinal 5 units to Dobson units. 

For Oct 10 2023 the Sentinel 5 value was 0.1248 (better precision obtained by downloading CSV file) which corresponds to 279.3 Dobson units. This is to be compared to NASA OMI value of 283.7. 

November 26, 2023

Trying to understand how MODTRAN makes excess extinction prediction. An excellent paper is Patat et al about extinction above Paranal. They also see, even after accounting for aerosols, and excess extinction predicted by LBLRTM (line by line radiative transfer model). 
Their Figure 4: 

If observed - model is negative, then model extinction is > observed. Difference between 570 nm and 380 nm is 0.75 percent. We see about 1% 
So this is indeed possibly a real discrepancy, and our measurement might not be the culprit. 

How about aerosols? Take our band centers as 373,  445, 508, 575. Patat aerosol estimate from 2011 would imply (see figure below)