1. Temperature dependence of N 2 -, O 2 -, and air-broadened half- widths of water vapor transitions R. R. Gamache, B. K. Antony and P. R. Gamache Dept. of Environmental, Earth, and Atmospheric Sciences and Intercampus Graduate School of Marine Sciences and Technology

2. NASA’s Earth Observing System Atmospheric Infrared Sounder (AIRS) on Aqua Tropospheric Emission Spectrometer (TES) and the High Resolution Dynamics Limb Sounder (HIRDLS) on AURA

3. NASA’s Earth Observing System TES - spectral coverage - 3.2 to 15.4  m HIRDLS - spectral coverage - 6.12 to 17.76  m. Calculations for transitions taken from HITRAN 2001 from 563 to 3125 cm -1 for the principal isotopologue of water vapor and J≤18 (5442 transitions)

4. H 2 16 O transitions in the 3.2-17.6  m region v 1 ’ v 2 ’ v 3 ’ v 1 ” v 2 ” v 3 ”# transitions 000000506 010010144 0100001885 020010872 100010532 030020382 001010484 020000326 030010146 10000090 00100075

5. Theory Semi-classical formalism of Robert and Bonamy Complex formalism - halfwidths and line shifts Free from cut-off procedure and adjustable parameters Trajectories from solution of Hamilton’s eqs. or R-B parabolic approximation General spherical tensor expansion for the intermolecular potential

6. Radiator - Perturber trajectory determined via the potential 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 b v V[ R(t),  (t) ]

7. Intermolecular Potential H 2 O-N 2 and H 2 O-O 2 n Leading electrostatic components n Atom-atom potential, expanded to 8 th order n The vibrational dependence of the isotropic potential uses the induction and London dispersion potentials

8. S 1 term Depends strongly on the vibrational dependence of polarizability. The coefficients for H 2 O are taken from the work of Luo et al. J. Chem. Phys. 98, 7159 (1983).

9. S 1 term Depends strongly on the vibrational dependence of polarizability. The coefficients for H 2 O are taken from the work of Luo et al. J. Chem. Phys. 98, 7159 (1983). Note, stretch modes have roughly the same contribution.

10. Air-broadening of H 2 O Calculations were made for N 2 - and O 2 -broadening of H 2 O at 225 and 296 K. At each temperature air-broadening is determined from

11. Connecting states i i’ f f’ optical transitions collisionally induced transitions J2J2 J2’J2’  E i  i’ EJ2J2’EJ2J2’ Absorbing Molecule Perturbing Molecule V

12. Low J transitions  E small  E J2  J2’  E i  I’ On resonance collisions, collisional contributions dominate the half-width

13. Off-resonance collisions, collisional contributions small, half-width dominated by vibrational terms.   E large  E J2  J2’  E i  I’ High J transitions

14. 2 H 2 O-N 2 P and R Doublet Transitions (J  1 1,J  1  J 0,J and J  1 0,J  1  J 1,J ) and  are calculated values associated with P and R lines such that (Ka’-Ka”)=(J’-J”) and (Ka’-Ka”)=-(J’-J”), respectively. The horizontal dashed line indicates the pure dephasing contribution Gamache and Hartmann, JQSRT 83, 119– 147 (2004).

15. H 2 O-air N Exp =1 N Exp >1 Band# lines% error# lines% error 0000001248.841178.86 010010131.32 0100002851.041441-3.57 020010111-3.858-15.21 10001013-1.52 00101027-2.36 02000091.092-1.42 1000001-0.37

16. Intercomparison and Comparison with CRB for H 2 O-N 2 N=2 Exp-ExpExp-CRB SD : 7.32 8.44 AAPD : 4.80 5.96 Number of points : 596 298 SD = Standard Deviation AAPD = Average Absolute % Difference

17. Intercomparison and Comparison with CRB for H 2 O-N 2 N=2 Exp-ExpExp-CRB SD : 7.32 8.44 AAPD : 4.80 5.96 Number of points : 596 298 N=3 Exp-ExpExp-CRB SD:7.12 6.66 AAPD : 5.71 5.99 Number of points :6321 SD = Standard Deviation AAPD = Average Absolute % Difference

18. T-dependence “Rule-of-thumb” For “on resonance” collisions the temperature dependence of the half- width is given by InteractionnInteractionn d-d 4d-q, q-d6 q-q8dispersion10

19. Temperature Dependence of  n Power law form n In practice plot (fit)

20. H 2 O-N 2 system “Dipole-Quadrupole” system – “rule-of- thumb” gives temperature dependence of 5/6

21. H 2 O-N 2 system “Dipole-Quadrupole” system – “rule-of- thumb” gives temperature dependence of 5/6

22. H 2 O doublet transitions The rotational contribution to the half- widths decreases as J” increases.

23. H 2 O doublet transitions At low J” half-widths are dominated by rotational contributions (S 2, on resonance).

24. 2

25. 2

26. H 2 O doublet transitions At high J” half-widths are dominated by vibrational contributions (S 1, off resonance).

27. 2

28. 2

29. Power law is not theoretically correct. However, it gives a reasonable fit. 2

30. H 2 O doublet transitions Intermediate J” – a mixture of rotational and vibrational contributions. (S 1 and S 2 )

31. 2

32. 2

33. 2

34. 2

35. 2

36. 2

37. Temperature exponents on the HITRAN database JNJN 00.7890.49 10.78100.45 20.78110.41 30.77120.39 40.73130.37 50.69140.36 60.64150.36 70.59160.38 80.53170.41

39. 0.83>N>-1.3

41. Acknowledgments The authors are pleased to acknowledge support of this research by the National Aeronautics and Space Administration (NASA) through Grant No. NAG5-11064 and by the National Science Foundation (NSF) through Grant No. ATM-0242537. 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 NASA or NSF.