Calculation of lineshape parameters for self- broadening of water vapor transitions via complex Robert-Bonamy theory Bobby Antony, Steven Neshyba* & Robert Gamache Department of Environmental, Earth, and Atmospheric Sciences, Intercampus Graduate School of Marine Sciences and Technology, University of Massachusetts Lowell, MA *Department of Chemistry, University of Puget Sound, Tacoma, WA 98416

Introduction  Studies on atmospheric water vapor by the NASA EOS mission  AIRS on Aqua  TES and HIRDLS on Aura  Lack of sufficient data  On spectral parameters like Half-width & Line Shift  Only 440 out of half-width measurements have uncertainty <10% with more than 3 intercomparisons  Requirement of parameters for thousands of water vapor transitions  The effect of uncertainty in half-widths on the accuracy of retrieved concentration profiles  The effect of the line shift on reducing data from remote sensing measurements

Theory Complex Robert-Bonamy formalism 1,2 1. D. Robert and J. Bonamy, J. Phys. Paris., 40 (1979) R. Lynch, R. R. Gamache and S. P. Neshyba, J. Quant. Spectrosc. Radiat. Transfer, 59 (1998) 595 Where,   half-width &   line shift n 2  number density of perturbers J 2  initial rotational state of the collision partner. S 1 & S 2  I & II order terms from the expression for scattering matrix, S=S 1 +S 2 Two vital features have been incorporated in the present CRB formalism: (i) the elimination of cut-off procedure, and (ii) the improved treatment for close collisions.

Calculation  Self-broadened half-widths and line shifts for H 2 O Classically H 2 O-H 2 O has been considered as a dipole- dipole system. Here, the intermolecular potential is a sum of:  The electrostatic terms (  ),  The atom-atom potential, and  The induction and dispersion terms.

Calculation  Self-broadened half-widths and line shifts for H 2 O  Preliminary studies on 499 transitions to elucidate broadening and shifting mechanisms  Order of atom-atom expansion  Inclusion of complex terms  Effect of trajectory model  Vibrational dependence of the half-width  Temperature dependence of the half-width

Calculation Integrating over Boltzmann distribution of velocities makes calculation slower. And gives difference of only a few percent from the MRTV results at ~300 K for this system  Self-broadened half-widths and line shifts for H 2 O  Preliminary studies on 499 transitions to elucidate broadening and shifting mechanisms  5442 water vapor transitions in the  m ( cm -1 ) wavelength region  Mean relative thermal velocity approximation

Calculation  Self-broadened half-widths and line shifts for H 2 O  Preliminary studies on 499 transitions to elucidate broadening and shifting mechanisms  5442 water vapor transitions in the  m ( cm -1 ) wavelength region  Mean relative thermal velocity approximation  Calculation is performed at 296 & 200K to evaluate temperature dependence  All the molecular parameters used here are the “best” available from the literature.  No parameters are adjusted to give better agreement with measured data.

Calculation  Preliminary studies on 499 transitions to elucidate broadening and shifting mechanisms  Order of atom-atom expansion Order( w ) O =0, 2, 4, 6, 8, …

Effect of atom-atom expansion on  H 2 O-H 2 O

Effect of atom-atom expansion on  H 2 O-H 2 O

Effect of order & complex terms. H 2 O-H 2 O (010  000) 8 08  %

Calculation S 1 – Vibrational dependence only Im(S 2 ) – mostly rotational dependence  Preliminary studies on 499 transitions to elucidate broadening and shifting mechanisms  Order of atom-atom expansion  Inclusion of complex terms

Effect of complex terms on  H 2 O-H 2 O

Effect of order & complex terms. H 2 O-H 2 O (010  000) 4 22  %

Calculation  Preliminary studies on 499 transitions to elucidate broadening and shifting mechanisms  Order of atom-atom expansion  Inclusion of complex terms  Effect of trajectory model b v V[R(t),Y(t)] The isotropic component of the atom-atom potential is used to define the trajectory of the collisions within the parabolic model of Robert and Bonamy

Calculation The isotropic component of the atom-atom potential is used to define the trajectory of the collisions within the parabolic model of Robert and Bonamy For strong interacting systems (like H 2 0-H 2 0), collisions will be dominated by the ReS 2 term (or exp{-ReS 2 }  0) at larger intermolecular separation, before the trajectories start to bend.  Preliminary studies on 499 transitions to elucidate broadening and shifting mechanisms  Order of atom-atom expansion  Inclusion of complex terms  Effect of trajectory model

Calculation  Preliminary studies on 499 transitions to elucidate broadening and shifting mechanisms  Order of atom-atom expansion  Inclusion of complex terms  Effect of trajectory model  Vibrational dependence of the half-width The vibrational dependence of the half-width arises from:  Spectroscopic effect  Purely a vibrational effect Extensive study on vibrational dependence of half-width & line shift Results show the difference is in the range of ±3-5%.

Calculated H 2 O-H 2 O  &  for the J±1 0,J±1  J 0,J & J±1 1,J±1  J 1,J transitions

Calculation Uses the power law form  Preliminary studies on 499 transitions to elucidate broadening and shifting mechanisms  Order of atom-atom expansion  Inclusion of complex terms  Effect of trajectory model  Vibrational dependence of the half-width  Temperature dependence of the half-width

Temperature exponent of  of H 2 O-H 2 O

Comparison with experiments

Results – comparison with experiments 1. Mandin et al, JQSRT, 23 (1980) 351; 26 (1981) Toth et al, JQSRT, 59 (1998) Eng et al, Chem. Phys. Lett, 19 (1973) Eng et al, Molec. Phys. 28 (1974) 653

Results – comparison with experiments 1. Remedios, PhD University of Oxford, (1990)2. Nicolaisen, 1990 ASA workshop, Moscow (1990) 3. Toth et al, JQSRT, 59 (1998) 529

Results – comparison with experiments 1. Mandin et al, JQSRT, 23 (1980) 351; 26 (1981) Toth et al, JQSRT, 59 (1998) Ben, JQSRT, 7 (1967) 211

Results – comparison with experiments 1. Toth et al, JQSRT, 59 (1998) Mandin et al, JQSRT, 23 (1980) 351; 26 (1981) 483

Results – comparison with experiments 1. Eng et al, Chem. Phys. Lett, 19 (1973) Eng et al, Molec. Phys. 28 (1974) 653

Results – comparison with experiments 1. Toth et al, JQSRT, 59 (1998) 529

Results – comparison with experiments 1. Toth et al, JQSRT, 59 (1998) 529

% Diff between Measurement and Calculations Total transitions studied5442 Number transitions with experimental data1207 ExpCRB Average percent difference Average absolute percent difference Standard deviation

 Self-broadening of H 2 O is dominated by the electrostatic contributions of the intermolecular potential.  For a number of lines studied the imaginary components affect the half-widths up to ~12%. This is larger than the uncertainty desired by the spectroscopic and remote sensing communities.  For strong interacting systems (like H20-H20), collisions will be dominated by the ReS 2 term (and hence e -ReS2  0) at larger intermolecular separation, before the atom-atom potential has a chance to bend the trajectories. Thus, the choice trajectory is not significant to present calculation. Conclusions

 There is ~3% change in half-width for higher J transitions from pure rotation to 6 3 and the line shift changes by a factor of 2. However, we should note that these line shifts are too small compared with N 2 broadening.  Because the half-width is determined mostly by rotational contributions, the temperature dependence of  is given by the standard power law expression. The temperature exponents are found to be positive. However, there is a large spread of the exponent from ~0.2 to ~1.4, with an average of 0.8.

Conclusions  The comparison with measurements shows that the present results falls well within the uncertainties of most of the experiments.  The CRB has a standard deviation of 6.9 compared to 5.5 of experiments. It is worth noting that these statistics are drawn with the experiments as the base.

Acknowledgments Research funded by the National Aeronautics and Space Administration (NASA) through Grant No. NAG and by the National Science Foundation (NSF) through Grant No. ATM A Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation or NASA. University of Massachusetts Lowell

Chu et al., J. Geophys. Res. 98 (1993)

Pumphrey and Buhler, JQSRT 64, , 2000.

IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING, 43, , 2005

i i’ f f’ Optical transitions Collisionally induced transitions  E i  i’ EJ2J2’EJ2J2’ Absorbing Molecule Perturbing Molecule V Energy Gap Connecting states Doublet Transitions i i’  E i  i’ EJ2J2’EJ2J2’ Energy Gap H20H20N2N2 i i’  E i  i’ EJ2J2’EJ2J2’ Energy Gap H20H20H2OH2O

J A factor of ~8 Calculated H 2 O-N 2  and  for the J-1 0,J-1  J 1,J transitions

Temperature exponent