==== Comparison of spectra averaged over 3 bands in O2A band ====

For the retrieval, averages over three spectral bands within the
O2A band are used. Therefore, in order to reduce data storage requirements,
we decided to store only the 3 values of each
spectrum.

The REPTRAN absorption parameterization included in libRadtran should be sufficient
for this purpose. If it can be applied (instead of full line-by-line simulations),
this would also save a
significant amount of computational time. 

Huan suggested the following:

Average both radiance and solar irradiance over 758-759nm (6points:
758, 758.2, 758.4, 758.6, 758.8, 760)/760-761/765-766nm as rad_aver, irr_aver.
Finally to get normalized radiance = rad_aver/irr_aver

Question: Is it not possible to obtain the normalized radiance from
LIDORT, so that you do not need to average the irradiance?


** MYSTIC simulation **

US standard atmosphere, 1e6 photons (quite accurate, for test calculation with LES data 1e5 where used), albedo 0.5, sza 40, vza 60, phi 196.3

cloud from 3-4km altitude, tau=2, reff=10um


MYSTIC calculation gives normalized radiance from 755-775nm at different spectral resolutions. The parameterization is set up in such a way, that if one integrates over a spectral interval, the result is approximately the same as if integrated over line-by-line simulations. Therefore I integrated the results over the 1nm intervals to obtain the following values: 

|          ^ CPU time ^ 758-759nm ^ 760-761nm ^ 765-766nm ^
^ clear | | | | |
^ line-by-line | 260s | 0.1222 | 0.0058 | 0.0660 |        
^ REPTRAN fine | 41s | 0.1227 | 0.0063 | 0.0672 |
^ REPTRAN medium | 15s | 0.1226 | 0.0066 | 0.0714 |
^ cloudy | | | | |
^ line-by-line | 70m51s | 0.1335 | 0.0102 | 0.0765 |   
^ REPTRAN fine | 10m43s | 0.1334 | 0.0108 | 0.0773 |
^ REPTRAN medium | 3m5s | 0.1340 | 0.0113 | 0.0825 |

Simulated values for the 3 spectral bands proposed by Huan calculated using REPTRAN (fine spectral resolution) are very close to the values obtained from line-by-line simulation. Similar statistical error to be expected when 1e5 photons are used.
REPTRAN (medium spectral resolution) not sufficiently accurate for 765-766nm band.

CPU time can be decreased by a factor of approx. 7 => Use REPTRAN fine for O2A band simulations?
CPU time can further be decreased, because simulation not necessary outside these bands. 

Next step: Intercomparison setups (clear and cloudy) for the 3 bands?

[{{ :projects:3dcats:wp_200:o2a_clear.png?600 | O2A band simulation, clear-sky, line-by-line vs. REPTRAN absorption parameterization.}}]
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[{{ :projects:3dcats:wp_200:o2a_clear_bands.png | O2A band simulation, clear-sky, line-by-line vs. REPTRAN absorption parameterization, integration over three 1nm-wide bands. }}]
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[{{ :projects:3dcats:wp_200:o2a_cloud.png?600 | O2A band simulation, cloud, line-by-line vs. REPTRAN absorption parameterization.}}]
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[{{ :projects:3dcats:wp_200:o2a_cloud_bands.png | O2A band simulation, cloud, line-by-line vs. REPTRAN absorption parameterization, integration over three 1nm-wide bands. }}]
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[{{ :projects:3dcats:wp_200:o2a_layer_amf.png | Layer-AMF calculated at 756nm. Check whether the same result is obtained independent of absorption parameterization. }}]