Total internal partition sums for molecules in the terrestrial atmosphere

Gamache, Robert R.; Kennedy, Stephen J.; Hawkins, R. L.; Rothman, Laurence S.

doi:10.1016/s0022-2860(99)00266-5

Cited by 154 publications

(85 citation statements)

References 70 publications

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“…The RMS relative deviation of MIRART (Figure 4) exceeds 2% in bands 8, 9, and 12 at altitudes around 30 km. The reason is very likely the temperature conversion scheme of the line strengths: MIRART uses the scheme from the ATMOS software [Norton and Rinsland, 1991], whereas ARTS and the other models use the TIPS scheme [Gamache et al, 2000] or other polynomial interpolations of the partition functions. It has been observed that line strengths converted to other temperatures with the ATMOS and the TIPS scheme agree for some molecule species, while there are differences of up to about ±10% for other molecule species.…”

Section: Discussion Of Results (Exercise 1a)mentioning

confidence: 99%

“…[108] For the temperature conversion of the line strength, partition functions are calculated from an internal polynomial representation, which is taken from the TIPS-dst97 FORTRAN program [Gamache et al, 2000] for those species included in TIPS. For the other species, a polynomial fit to the tabulated partition function values of JPL is used.…”

Section: A1 Atmospheric Radiative Transfer Simulator (Arts)mentioning

confidence: 99%

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Intercomparison of general purpose clear sky atmospheric radiative transfer models for the millimeter/submillimeter spectral range

et al. 2005

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[1] We compare a number of radiative transfer models for atmospheric sounding in the millimeter and submillimeter wavelength range, check their consistency, and investigate their deviations from each other. This intercomparison deals with three different aspects of radiative transfer models: (1) the inherent physics of gaseous absorption lines and how they are modeled, (2) the calculation of absorption coefficients, and (3) the full calculation of radiative transfer for different geometries, i.e., up-looking, down-looking, and limblooking. The correctness and consistency of the implementations are tested by comparing calculations with predefined input such as spectroscopic data, line shape, continuum absorption model, and frequency grid. The absorption coefficients and brightness temperatures calculated by the different models are generally within about 1% of each other. Furthermore, the variability or uncertainty of the model results is estimated if (except for the atmospheric scenario) the input such as spectroscopic data, line shape, and continuum absorption model could be chosen freely. Here the models deviate from each other by about 10% around the center of major absorption lines. The main cause of such discrepancies is the variability of reported spectroscopic data for line absorption and of the continuum absorption model. Further possible causes of discrepancies are different frequency and pressure grids and differences in the corresponding interpolation routines, as well as differences in the line shape functions used, namely a prefactor of (n/n 0 ) or (n/n 0 ) 2 of the Van-Vleck-Weisskopf line shape function. Whether or not the discrepancies affect retrieval results remains to be investigated for each application individually.Citation: Melsheimer, C., et al. (2005), Intercomparison of general purpose clear sky atmospheric radiative transfer models for the millimeter/submillimeter spectral range, Radio Sci., 40, RS1007,

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Section: Discussion Of Results (Exercise 1a)mentioning

confidence: 99%

Section: A1 Atmospheric Radiative Transfer Simulator (Arts)mentioning

confidence: 99%

Intercomparison of general purpose clear sky atmospheric radiative transfer models for the millimeter/submillimeter spectral range

et al. 2005

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“…The most commonly used (Tatum 1966;Sauval & Tatum 1984;Rossi et al 1985;Gamache et al 1990;Goorvitch 1994;Gamache et al 2000;Fischer et al 2003) value is 40 000 cm −1 :…”

Section: Casementioning

confidence: 99%

“…) presented total internal partition functions for a number of molecules and their isotopes for the temperature range 70-3000 K. The methods used in this study are based on (Gamache et al 2000;Fischer et al 2003). Rotational partition functions were determined using the formulae in (McDowell 1988;McDowell 1990).…”

Section: Laraia Et Al (2011 L2011mentioning

confidence: 99%

Partition functions

Popovas

Jørgensen

2016

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Context. Hydrogen is the most abundant molecule in the Universe. Its thermodynamic quantities dominate the physical conditions in molecular clouds, protoplanetary disks, etc. It is also of high interest in plasma physics. Therefore thermodynamic data for molecular hydrogen have to be as accurate as possible in a wide temperature range. Aims. We here rigorously show the shortcomings of various simplifications that are used to calculate the total internal partition function. These shortcomings can lead to errors of up to 40 percent or more in the estimated partition function. These errors carry on to calculations of thermodynamic quantities. Therefore a more complicated approach has to be taken. Methods. Seven possible simplifications of various complexity are described, together with advantages and disadvantages of direct summation of experimental values. These were compared to what we consider the most accurate and most complete treatment (case 8). Dunham coefficients were determined from experimental and theoretical energy levels of a number of electronically excited states of H 2 . Both equilibrium and normal hydrogen was taken into consideration. Results. Various shortcomings in existing calculations are demonstrated, and the reasons for them are explained. New partition functions for equilibrium, normal, and ortho and para hydrogen are calculated and thermodynamic quantities are reported for the temperature range 1-20 000 K. Our results are compared to previous estimates in the literature. The calculations are not limited to the ground electronic state, but include all bound and quasi-bound levels of excited electronic states. Dunham coefficients of these states of H 2 are also reported. Conclusions. For most of the relevant astrophysical cases it is strongly advised to avoid using simplifications, such as a harmonic oscillator and rigid rotor or ad hoc summation limits of the eigenstates to estimate accurate partition functions and to be particularly careful when using polynomial fits to the computed values. Reported internal partition functions and thermodynamic quantities in the present work are shown to be more accurate than previously available data.

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“…E m is the lowerstate energy and c 2 the second radiation constant (=1.439 cm/K). The spectral line transition frequency v mn corresponds to the energy of a photon emitted or absorbed by a transition between lower and upper states m and n. The total internal partition sum Q(T) can be approximated by a polynomial expression in the temperature T with high accuracy [Gamache, 2000]:…”

Section: Appendix Amentioning

confidence: 99%

Tropospheric water vapor from solar spectrometry and comparison with Jason microwave radiometer measurements

et al. 2006

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[1] Atmospheric water vapor is a crucial factor in achieving highest accuracies in the field of space geodesy, particularly in the determination of height. A new instrumental approach to high-precision determination of tropospheric water vapor has been investigated and realized in the construction of a mobile solar spectrometer. The optical approach as applied to the spectrometer allows the simultaneous measurement of single vibrational-rotational absorption lines in the wide wavelength range between 728 nm and 915 nm. Dedicated field experiments have been carried out in the frame of an EU project for calibrating the Jason onboard microwave radiometer. A comparison of the spectrometer results with a conventional ground-based water vapor radiometer and radiosondes revealed a fit on the order of 10 mm for the wet path delay, which corresponds to 1.6 kg/m 2 integrated water vapor content (IWV). The comparison with the measurements from the radiometer of Jason reveals an even better agreement for the wet path delay. Long time series are foreseen for a detailed statistical analysis. The mobile solar spectrometer can be considered as a novel portable tool for determining tropospheric water vapor and as an excellent space-borne radiometer calibration and validation system.

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Total internal partition sums for molecules in the terrestrial atmosphere

Cited by 154 publications

References 70 publications

Intercomparison of general purpose clear sky atmospheric radiative transfer models for the millimeter/submillimeter spectral range

Intercomparison of general purpose clear sky atmospheric radiative transfer models for the millimeter/submillimeter spectral range

Partition functions

Tropospheric water vapor from solar spectrometry and comparison with Jason microwave radiometer measurements

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