oh-einstein-temp-convert 1.0.0

Tool to convert temperatures OH*(6-2) between two sets of Einstein A coefficients.

oh_einstein_temp_convert

oh_einstein_temp_convert is a Python package which translates temperatures originally calculated from OH*(6-2) transiton spectra using a certain set of Einstein coefficients to a new set of Einstein coefficients with no need of the original data.

Author

Rowan Dayton-Oxland University of Southampton Github

Installation

Use the package manager pip to install oh_einstein_temp_convert.

pip install oh_einstein_temp_convert

Requirements

• Python >= 3.10
• numpy, pandas
• OS independent

Einstein A coefficient sources

Ain (int) - Original Einstein coefficient source index (see table)
Aout (int) - Desired output Einstein coefficient source index (see table)

Einstein A Source	Index
Mies et al., 1974	0
Loo and Groenenboom, 2008	1
Langhoff et al., 1986	2
Goldman et al., 1998	3
Turnbull and Lowe, 1989	4

Usage

import oh_einstein_temp_convert as oh

Temperatures = []  # List of temperatures

# Temperatures originally calculated from e.g. Mies et al., 1974 coefficients
Ain_index = 0  # Choose index of input temperatures
# Output temperatures calculated from e.g. Loo and Groenenboom, 2008 coefficients. 
Aout_index = 1  # Choose index of output temperatures

# returns list of converted temperatures
Result = oh.convert_temperatures(Temperatures, Ain_index, Aout_index)

Algorithm

• Get the original temperature and original Einstein coefficient set
• Calculate $ln(\frac{I}{Ain \cdot 2(2J' + 1)})$ and add a correction term for the new Einstein coefficient set $ln(\frac{Ain}{Aout})$ for each $F(J')$ value in the OH*(6-2) P-branch.
• Plot the corrected $ln(\frac{I}{Aout \cdot 2(2J' + 1)})$ term against $F(J')$
• Extract the output temperature from the gradient of the line by linear fit

This comes from the following equation; $$ ln(\frac{I}{A \cdot 2(2J' + 1)}) = \frac{-(h c)}{(k T)} * F(J') + ln(\frac{N}{QR}) $$

$I$ The spectral line intensity $A$ The Einstein A coefficient $J'$ The rotational quantum state $h$ The Planck constant $c$ The speed of light in the vacuum $k$ The Boltzmann constant $T$ The rotational temperature $F(J')$ The rotational energy term $ln(\frac{N}{QR})$ The partition function (constant for any single branch in the spectrum)

Contributing

Pull requests are welcome on Github. For major changes, please open an issue first to discuss what you would like to change.

References

Einstein and other quantum coefficients, and general inspiration from the Synthetic Hydroxyl Spectrum Generator Sigernes, F., Shumilov, N., Deehr, C.S., Nielsen, K.P., Svenøe, T., and Havnes, O., The Hydroxyl rotational temperature record from the Auroral Station in Adventdalen, Svalbard (78°N, 15°E) , Journal of Geophysical Research, Vol 108 (A9), 1342, doi 1029/2001JA009023, 2003.

Holmen, S., Trends and variability of polar mesopause region temperatures attributed to atmospheric dynamics and solar activity, PhD Thesis, UiT The Arctic University of Norway, 2016.

Mies, F. H. (1974). Calculated vibrational transition probabilities of OH($X^2\Pi$). Journal of Molecular Spectroscopy,53(2), 150–188.

Mark P. J. van der Loo, Gerrit C. Groenenboom (2008) Theoretical transition probabilities for the OH Meinel system. J. Chem. Phys. 21 March 2007; 126 (11): 114314.

Langhoff, S. R., Werner, H. J., & Rosmus, P. (1986). Theoretical transition probabilities for the OH Meinel system. Journal of Molecular Spectroscopy, 118(2), 507-529

Goldman, A., Schoenfeld, W. G., Goorvitch, D., Chackerian, J., C., Dothe, H., Mélen, F., … Selby, J. E. A. (1998). Updated line parameters for $OH X^2II-X^2II$ ($\upsilon″\upsilon’$) transitions. Journal of Quantitative Spectroscopy and Radiative Transfer, 59(3–5), 453–469.

D.N. Turnbull, R.P. Lowe, New hydroxyl transition probabilities and their importance in airglow studies, Planetary and Space Science, 37(6), 1989, 723-738, 0032-0633

License

GNU GPLv3.0