Atmospheric transmittance at the oxygen A-band

The oxygen A-band is a spectral band of molecular oxygen $O_2$ in the wavelength region of about 759 nanometers to 771 nanometers. Molecular oxygen is quite remarkable because its ground state is a triplet configuration for the electrons and as everything would oxidize quite rapidly in our atmosphere if this would not be the case, we should be happy for this fact. The A-band is basically formed by the electronic transition from the ground state to the second excited singlet state in its lowest vibrational state. The band consists of a lot of individual transitions involving different rotational quantum states. For further reading pick your favorite spectroscopy textbook and have a look at the details (it is a rabbit hole with no end... and that's the fun part ;)).

Let's say we want to know the A-band spectrum at standard HITRAN conditions ($T=296\,\text{K}, p=1.0\,\text{atm}$) and what is the maximum transmittance through a 100 m air column. For simplicity we assume that the conditions (and abundance does not change along this air column.

Getting started

We start by loading the module:

julia> using HITRAN

Now we could specify a database using the function open_database or just stick to the default database. If no database is specified, the package will just use a default database in a file named HITRAN.sqlite in your current environment folder.

Populating the local database

We need line-by-line data, so let's fetch it using:

julia> fetch!("StdAtm", iso_id(["N2", "O2", "CO2", "H2O", "CH4"]), 12900, 13200, [:standard, :ht_self]);[ Info: No custom HITRAN database specified, opening 'HITRAN.sqlite' (default)
2630

Now this command needs some explanation. First of all it is named fetch!with exclamation mark because it modifies the underlying database and is therefore considered "mutating". The parameters are the following:

Now that we have a table called "StdAtm" (for Standard Atmosphere) with some of the more relevant atmospheric constituents, we can already calculate a spectrum. One more important detail: The fetch commands generates a hash of the url used to query the HITRAN database. If you make a consecutive fetch! call with exactly the same parameters, no new download will be initiated. This is also handy because you do not need to comment/uncomment fetch! commands in your code to disable download. As soon as you change the parameters (for example the wavenumber limit) new data will be downloaded.

Calculating a spectrum

The most simple approach would be to just straight away call this command:

julia> wavenumbers, absorption_coefficient = α(
           ["StdAtm"]
       )(12900.269191:0.01:13199.939191, [1.4903946624960187e-9, 1.2266333962521325e-9, 6.850773033507631e-10, 2.6358418367654267e-10, 7.581870359272896e-11, 2.5420227204685723e-11, 2.6434725864692407e-11, 6.81664848505016e-11, 1.9275110052664767e-10, 4.248277246656541e-10  …  7.553659996865661e-12, 8.335221227383e-12, 1.0292840140433695e-11, 1.9721445609075427e-11, 8.687101879563264e-11, 4.836010846013798e-10, 2.111724044035105e-9, 6.505288356125817e-9, 1.3854707655923233e-8, 2.030366539922462e-8])

As you can see, we get a range of wavenumber values and values for the absorption coefficient right away. But wait, how does the module know the atmospheric composition we are interested in? In short: It does not! If you just specify a table name to the α function it will just calculate all spectral lines withing the table assuming their natural isotopologue abundance and does not take the proper gas mixture into account. See the function description of α for all details. For this example, we can use a neat shortcut:

julia> wavenumbers, absorption_coefficient = α(
           ["StdAtm"];
           components=default_environments[:dry_air]
       )(12900.269191:0.01:13199.939191, [2.832690943125633e-9, 3.231158338723144e-9, 3.7166093935579818e-9, 4.3148493526887175e-9, 5.061127570521185e-9, 6.0039005691102835e-9, 7.209715633414868e-9, 8.768520796948074e-9, 1.0796293705719397e-8, 1.3425807293242e-8  …  2.7073190974006877e-15, 2.5625129614225664e-15, 2.4290980092873225e-15, 2.305920647548923e-15, 2.191967992395459e-15, 2.086348024620865e-15, 1.9882728910833393e-15, 1.89704480360403e-15, 1.8120440894652065e-15, 1.7327190312314336e-15])

The default_environment variable is a Dict containing standard mixtures. For now this is only dry air by using the key :dry_air. See Environments for details for the environments.

The final code

To sum it all up, the correct code (besides the warning above) for this example is:

julia> wavenumbers, absorption_coefficient = α(["StdAtm"];
               components=(default_environments[:dry_air])
           )(12900.269191:0.01:13199.939191, [2.832690943125633e-9, 3.231158338723144e-9, 3.7166093935579818e-9, 4.3148493526887175e-9, 5.061127570521185e-9, 6.0039005691102835e-9, 7.209715633414868e-9, 8.768520796948074e-9, 1.0796293705719397e-8, 1.3425807293242e-8  …  2.7073190974006877e-15, 2.5625129614225664e-15, 2.4290980092873225e-15, 2.305920647548923e-15, 2.191967992395459e-15, 2.086348024620865e-15, 1.9882728910833393e-15, 1.89704480360403e-15, 1.8120440894652065e-15, 1.7327190312314336e-15])

This specifies that our oxygen is dilutet by the surrounding air mass which tells the module how to properly calculate the collision-broadening of the spectral lines.

To get the transmittance along our air column we can use the little helper function and specifying the air path length in centimeters:

julia> transmittance = transmittance_spectrum(absorption_coefficient, 100e2);

Full code & plotting

Let's put everything so far together and create a plot:

using HITRAN, Plots

fetch!("StdAtm", iso_id(["N2", "O2", "CO2", "H2O", "CH4"]), 12900, 13200, [:standard, :ht_self]);
wavenumbers, absorption_coefficient = α(["StdAtm"];
        components=default_environments[:dry_air]        
    )
transmittance = transmittance_spectrum(absorption_coefficient, 100e2)

plot(
    wavenumbers,
    transmittance,
    xlabel="Wavenumbers [1/cm]", 
    ylabel="Transmission", 
    title="Transmission along a 100 m air column",
    leg=false
)