Manfred Birk, Georg Wagner

Remote Sensing Technology Institute (IMF) Deutsches Zentrum für Luft- und Raumfahrt (DLR)

Lorenzo Lodi, Jonathan Tennyson

Department of Physics and AstronomyUniversity College London

Water intensities: ab initio versus experiment

IntroductionRoutes to line intensities in spectroscopic databases• Minimal approach: Line intensities are derived from laboratory

spectroscopy measurementsDisadvantage: not all lines included, precision limited by noise

• Effective Hamiltonian approach: Quantum mechanical data reduction of experimental line intensitiesOnly useful when experimental data are reproduced within their precisionAdvantage: Intensities for lines not in the experiment can be calculated when avoiding large extrapolation towards higher quantum numbersFurther advantages: Noise of experimental line intensities is reduced, experimental line intensities are checked for consistency

• Pure ab initio approach: Semi-empirical PES, purely ab-initio DMSAdvantage: All transitions coveredDisadvantage: Experimental validation mandatory

How accurate are ab initio calculations?• Intercomparison between ab initio and experimental line intensities

required

But:

• Experimental line intensities from different labs often differ outside error margins (see below)

Thus:

• High quality experimental data with known uncertainty needed

• Best case: At least two experimental data sets from independent labs agree within error margins

Ab initio calculation of H2O line intensities • Lorenzo Lodi, Jonathan Tennyson, and Oleg L. Polyansky, “A global, high

accuracy ab initio dipole moment surface for the electronic ground state of the water molecule”, J. Chem. Phys. 135, 034113 (2011).

• Quality estimate: 2 different PES and DMS 4 combinations fractional ab initio uncertainty = (largest value/smallest value -1)

• The authors state line intensity errors of 1% for most lines validated by average agreement with HITRAN 2008 (ab initio/HITRAN=1.01±4.5%, S>1e-22,11% of HITRAN lines with J<13) and agreement of 15 lines measured with CRDS by Lisak and Hodges (NIST) (ab initio/NIST=1.004±0.6%)

• But: Systematic line intensity errors in HITRAN 2008 S>1e-22 are very likely Example: Update 2004 2008 2 line intensities changed up to 6% (see below). Other regions???

• Thus, agreement of 1% between ab initio and HITRAN is not very conclusive

This work: Intercomparison of ab initio and high quality experimental water line intensities

DLR measurements – strategy• Goal: Accurate data with defined error margins

• Redundancy is important since hidden systematic errors may depend on line width and optical depths. Chi tests and investigation of residuals of redundant data may help to quantify/identify error sources

• Line intensities retrieved from many measurements with different optical depths (<4) for redundancy

• Combination of pure water and air-broadened measurements used for increasing redundancy (width and optical depth independently selectable)

• Influence of instrumental lineshape function is minimized by choosing high resolution

• Mostly ambient temperature measurements used

DLR measurements – experimental set-up

800 l mixing

chamber FT

spectrometer White cell 21m, 85 m

N2 Flow controller

Cooler/Heater

Pt100 sensor

H2O liquid

Synth. air

Pt100 sensor

Water/air mixtures Pure water

DLR measurements – 1 µm region• Multireflection cell at 85 m• High signal-to-noise by narrow band pass (10000-11000 cm-1)• Double-sided interferograms• Line intensity analysis included ambient and non-ambient temperature

measurements• Line fitting of individual spectra on

micro window basis applying speed-dependent Voigt profile yielding line intensities for each measurement and transition

0 2 4 6 8 10 12

0.96

0.98

1.00

1.02

1.04

Water Water/air

mea

n(S m

eas/S

HIT2

008)

Voigt fit speed-dep. Voigt fit

PH2O/mb Ptot/mb Tmess/K MOPD/cm Scaling 3.999 199.6 295.98 20 0.988

4.0340 496.8 296.51 20 0.978 16.382 992.3 296.00 10 1.005 15.96 998.2 315.29 10 1.003 3.987 998.0 315.83 10 1.001 3.916 997.7 276.75 10 0.992 1.993 498.9 316.16 20 1.001 1.969 501.8 275.70 20 0.990

0.7822 199.3 276.63 20 0.998 5.002 5.002 296.25 20 0.989 1.001 1.001 295.20 45 1.000

DLR measurements – 1 µm region• Line intensities of up to 11 measurements averaged• Reference: 1 mb pure water measurement at ambient temperature – 5 mb

pure water measurement not used as reference due to insufficient spectral resolution

• Individual measurements (except reference) scaled for 0% mean measurement omc in averaging

• Quality check: Temperature/scaling factor (Sref x scaling factor = Smeas) fit from line intensities of individual measurements using averaged line intensities as reference

• Air-broadened measurements: 7 scaling factors less than 1% off 1, 2 scaling factors between 1 and 2%

Linestrength intercomparison in 1 µm region

• NIST: cavity ringdown by Daniel Lisak and Joseph T. Hodges• HIT: HITRAN 2008, mainly experimental data by Robert A. Toth• Excellent agreement DLR-NIST, mostly <1%• HITRAN 2008 shows bias and large scatter

H2O linestrengths

-4.0

-3.0

-2.0

-1.0

0.0

1.0

2.0

3.0

4.0

10580 10600 10620 10640 10660 10680 10700 10720 10740

Wavenumber (cm-1)

rela

tive

diffe

renc

e (%

)

NIST vs DLRHIT vs DLR

Ab initio vs. experiment 1 µm• Only transitions shown with experimental precision < 1%

Vib transition # of lines Mean diff./% Scatter about mean/meas

Mean(ab initio)/%

1 2 1 0 0 0 78 +4.0 1.9 7.2

2 0 1 0 0 0 189 -0.3 1.6 2.1

3 0 0 0 0 0 76 +4.3 2.3 2.0

1 0 2 0 0 0 17 -8.9 1.4 7.1

0 0 3 0 0 0 12 -0.7 1.1 1.2

Ab initio vs. experiment 1 µm• Bias for entire vibrational bands, cannot be related to experimental error

• Mean differences of bands up to 9%

• Larger scatter for 3 0 0 0 0 0 band

• Isolated outliers with up to 30% difference (see below)

• Average ab initio uncertainties mostly conservative (exception 3 0 0 0 0 0)

Ab initio vs. experiment 1 µmLargest difference for 2 0 1 0 0 0, 120,12 110,11

Sab initio - Sexp= -26.5%, Smean= 0.6%, =1.5, Sab initio= 1.4%

PH2O/mb Ptot/mb T/K % peak abs S/% (S-Smean)/% (S-Smean)/S In av.

4.0 199.6 296.0 15.7 0.64 -0.59 -0.93 1

4.0 496.8 296.5 13.0 2.27 -0.06 -0.03 1

16.1 998.2 315.9 36.3 10.38 2.11 0.20 1

4.0 998.0 316.4 10.7 2.57 5.42 2.00 1

3.9 997.7 277.6 6.1 2.84 5.81 1.93 1

2.0 498.9 317.3 8.5 1.70 -8.63 -5.56 0

2.0 501.8 277.6 4.9 3.64 10.47 2.60 1

0.8 199.3 275.9 2.6 4.38 -3.48 -0.82 1

1.0 1.0 295.2 4.7 2.46 -2.23 -0.93 1

Ab initio vs. experiment 1 µmSubband J’’+10,J’’+1 J’’0,J’’

Ab initio: Resonance at J’’=6, experiment: resonance at J’’=11

Apparently, energy level of resonating states not correctly predicted from PES

J‘‘ (Sab initio)/% (Sab initio – Sexp)/%

0 4.0 0.0

2 1.8 0.3

4 1.7 0.1

6 5630.3 0.3

7 8.7 0.2

8 1.6 -0.6

9 1.5 -0.8

11 1.4 -26.5

H216O linestrength intercomparison in 2 region

• HIT04: HITRAN 2004, mainly experimental data by Robert A. Toth

• Lodi: ab initio calculations

• DLR: 9 pure water, 16 air-broadened measurements, ambient temperature,Voigt profile analysis

• HITRAN 2004 – DLRdifferences up to 6% forstrong and weak lines

• Ab initio – DLR agreement< 2% for S > 1e-23

• 010 000, 020 010

    Ab initio – DLR HITRAN 2004 - DLRlg(Smin) lg(Smax) % %unc ndata % %unc ndata

-24.5 -24.0 3.66 0.80 23 5.90 0.79 24-24.0 -23.5 4.23 0.23 77 5.46 0.24 75-23.5 -23.0 2.12 0.10 94 3.56 0.10 95-23.0 -22.5 1.19 0.04 105 1.87 0.04 106-22.5 -22.0 0.76 0.02 109 0.91 0.02 108-22.0 -21.5 0.74 0.02 72 0.27 0.02 73-21.5 -21.0 0.85 0.02 50 -1.52 0.01 53-21.0 -20.5 1.13 0.02 52 -2.63 0.01 50-20.5 -20.0 1.14 0.02 51 -2.73 0.02 50-20.0 -19.5 1.62 0.02 51 -3.80 0.01 51-19.5 -19.0 1.74 0.01 53 -5.79 0.01 55

H218O linestrength intercomparison in 2 region

• HIT04: HITRAN 2004, mainly experimental data by Robert A. Toth• Lodi: ab initio calculations

% L

odi-D

LR

    Ab initio - DLR HITRAN 2004 - DLRlg(Smin) lg(Smax) % %unc ndata % %unc ndata

-24.5 -24.0 2.84 1.09 12 4.04 1.14 11-24.0 -23.5 3.82 0.32 44 3.27 0.32 45-23.5 -23.0 1.00 0.13 53 -1.20 0.13 53-23.0 -22.5 0.28 0.06 50 -3.30 0.06 53-22.5 -22.0 0.16 0.03 53 -4.75 0.03 55-22.0 -21.5 0.27 0.02 47 -5.11 0.02 42-21.5 -21.0 0.63 0.03 17 -5.43 0.03 17

Brand new quick-look 3 results obtained by our PhD student Joep Loos

• Only single pure water measurement analyzed

• Only 21 transitions, line intensity >1e-19

• Ab initio – experiment: mean -0.96%, scatter 0.25%

• HITRAN 2008 – experiment: mean -2.44%, scatter 0.39%

Conclusion• Good agreement of ab initio and DLR experimental line intensities:

• H216O, 2, S>1e-23: <2%

• H218O, 2, S>1e-23: <2%

• H216O, 3, S>1e-19: <1% (preliminary)

• H216O, 1 µm region, S>1e-22: <2%

• Agreement of ab initio and DLR data much better than with older HITRAN versions• Good agreement of ab initio and DLR data indicates reliability of both data sources• But there exist overtones and combination bands with biases between ab initio and

experiment up to 9%. The origin for the differences can be unambiguously attributed to the ab initio calculation

• Furthermore, singular large differences up to 30% (resonances) and vibrational transition specific scatter related to the ab initio calculations exist

• Ab initio uncertainties were found to be helpful in assessing data quality. In cases of resonances they may be misleading

• Further intercomparison between high quality laboratory measurements and ab initio calculations are required