region 5000 5600 cm : Evidence for water dimers

Q J R Meteorol Soc (2004) 130 pp 2391ndash2408 doi 101256qj03178

Laboratory measurements of water vapour continuum absorption in spectralregion 5000ndash5600 cmminus1 Evidence for water dimers

By IGOR V PTASHNIK1lowast KEVIN M SMITH2 KEITH P SHINE1 and DAVID A NEWNHAM2

1Department of Meteorology University of Reading UK2Space Science and Technology Department Rutherford Appleton Laboratory UK

(Received 9 September 2003 revised 28 May 2004)

SUMMARY

In spite of decades of extensive studies the role of water dimers (WD) in the atmospheric radiation budget isstill controversial In order to search for evidence of the dimer in the solar near infrared high spectral resolutionpure water vapour absorption spectra were obtained in laboratory conditions for two different pressures andtemperatures in the spectral region 5000ndash5600 cmminus1 (1785 to 2 microm) The residual was derived as a differencebetween the measured optical depth and the calculated one for water monomer using the modified HITRANdatabase and two different representations of the water vapour continuum CKD-24 (CloughndashKneizysndashDavies)and the Ma and Tipping continuum In both cases the residuals obtained are very similar to those expectedfrom a recent theoretical calculation of the WD absorption However the WD band half-width at half maximum(HWHM) and dimerization equilibrium constant Keq required to provide a best fit to the residual differ for eachcase To be in best agreement with the residual calculated by using the Ma and Tipping continuum the WD bandsHWHM should be sim28 cmminus1 and Keq = 002 plusmn 00035 atmminus1 and 0043 plusmn 00055 atmminus1 for temperatures 342and 299 K respectively For the residual calculated using the CKD-24 continuum the fitted value of the HWHMis sim18 cmminus1 and Keq = 0011 plusmn 00025 atmminus1 (342 K) and 0018 plusmn 0003 atmminus1 (299 K) It is concluded thata substantial part of the WD absorption is already implicitly included within the CKD-24 continuum model Theincrease in estimated clear-sky global mean absorption of solar radiation due to WD varies from 05 to 20depending on the set of WD parameters used On the basis of a comparison of the derived Keq values with othersin the literature the higher estimate is favoured

KEYWORDS CKD continuum Dimerization equilibrium constant Ma and Tipping continuum Radia-tive transfer

1 INTRODUCTION

Water vapour is one of the most important substances in the atmosphere Theabsorption of solar radiation in the near infrared and visible spectral region is dominatedby H2O molecular absorption In addition to the water monomer (WM) water clusterssuch as water dimers (WD) or trimers have been investigated very intensively in recentyears (Mhin et al 1993 Huisken et al 1996 Low and Kjaergaard 1999 Evans andVaida 2000 Vaida and Headrick 2000) In particular the role of WD in the atmosphereis still controversial in spite of many theoretical and experimental investigations Anoverview can be found in Vaida et al (2001)

There are two interrelated issues in estimating the role of WD in the radiationbudget Firstly it is necessary to know the parameters (intensity width position andshape) of the WD absorption bands secondly it is important to know the abundance ofthe dimers There is significant uncertainty in both these aspects

WD have recently been investigated (Arking 1999 Chylek et al 1999 Daniel et al1999 Hill and Jones 2000 Goldman et al 2001 Vaida et al 2001) as a possiblereason for the discrepancy between atmospheric absorption measurements and modelcalculations (Kato et al 1997 Ramanathan and Vogelmann 1997 Conant et al 1998Arking 1999 Pilewskie et al 2000) The upper limit of solar radiation absorption byWD varies between different authors from 15 to 6 W mminus2 for a clear-sky tropicalatmosphere and overhead sun (Chylek et al 1999 Daniel et al 1999 Vaida et al2001 Kjaergaard et al 2003) According to the Goldman et al (2001) calculation of

lowast Corresponding author present affiliation Institute of Atmospheric Optics Akademicheskii 1 Tomsk 634055Russia e-mail piviaoruccopy Royal Meteorological Society 2004

2391

2392 I V PTASHNIK et al

2000 4000 6000 8000 10000 12000 14000

10-6

10-5

10-4

10-3

10-2

10-1

100

101

102

Opt

ica

l dep

th HITRAN v11 with CKD-24 Dimer Low and Kjaergaard (1999) Dimer Schofield and Kjaergaard (2003) CKD-24 only

Wavenumber (cm-1)

Figure 1 Optical depth of the water monomer including CKD-24 continuum two recent theoretical estimatesfor the water dimer and CKD-24 self-broadening continuum separately for optical path length 10 m purewater vapour pressure 15 hPa and T = 293 K The dimer absorption band half-width at half maximum =25 cmminus1 (Lorentzian profile) and the dimerization equilibrium constant Keq = 0041 atmminus1 are used for the

dimer calculation

the water dimerization equilibrium constant Keq that defines WD amount for a givenWM amount the value of WD radiative absorption could even be two to three timeshigher

Finally WD has also been discussed as a possible component of the self-broadeningpart of the water vapour continuum (Penner and Varanasi 1967 Devir et al 1994) Thesimilarity in the self-broadened continuum absorption and the calculated one due to WDcan be seen in Fig 1 here the optical depth of the CKD-24 (CloughndashKneizysndashDavies)water continuum model (Mlawer et al 1999) as well as the total WM absorbance ispresented together with WDrsquos optical depth for the spectral region 1000ndash15 000 cmminus1The latest calculations by Schofield and Kjaergaard (2003) of WD fundamental andovertone OH-stretching and HOH-bending vibrational transition frequencies and in-tensities were used to simulate the WD absorption The WD band half-width at half-maximum (HWHM) was chosen to be 25 cmminus1 for all WD bands together with theassumption that the wings are Lorentzian The Curtiss et al (1979) WDrsquos enthalpy andentropy parameters (H =minus359 kcal molminus1 S =minus1859 cal Kminus1molminus1) were usedto calculate Keq

Keq = exp(SR minusHRT) (1)

where R is the universal gas constant and T is temperature It is worth mentioning thatthe temperature dependence Keq(T ) is very similar to that for water CKD continuumMoreover the self-broadened water vapour continuum has the same quadratic depen-dence on WM partial pressure pWM as the WD

pWD =Keq middot p2WM (2)

WATER VAPOUR CONTINUUM ABSORPTION 2393

This causes a very similar relation between WD and CKD continuum absorption for theother pressures and temperatures to that presented in Fig 1

Theoretical and experimental investigations of WDrsquos thermodynamic and chemicalproperties can be found in Curtiss et al (1979) Goldman et al (2001) Headrickand Vaida (2001) Mhin et al (1993) Munoz-Caro and Nino (1997) and Slanina andCrifo (1992) The different approaches to derive WD spectroscopic parameters weredescribed by Huang and Miller (1989) Huisken et al (1996) Low and Kjaergaard(1999) Perchard (2001) Schofield and Kjaergaard (2003) Tso et al (1998) and manyother authors

In spite of this interest in WD two attempts to detect direct WD absorption in theatmosphere have failed (Daniel et al 1999 Hill and Jones 2000) There are two mainreasons why it is so difficult to detect WD in the atmosphere First WD absorptionis usually masked by strong WM absorption (see Fig 1) second there is a largeuncertainty in knowledge of the main WD parameters For example estimates of Keqvary from sim001 atmminus1 (Mhin et al 1993) to sim012 atmminus1 (Goldman et al 2001)for room temperature The theoretically predicted and observed WD fundamental andovertone bands HWHM can vary from 6 to 100 cmminus1 (Vaida et al 2001) The abinitio calculated WD cross-section spectrum has also changed markedly during recentyears (Tso et al 1998 Low and Kjaergaard 1999 Schofield and Kjaergaard 2003)Such uncertainty makes it very difficult to predict the best spectral region to detectWD For example the two experimental attempts mentioned above failed to reproducethe calculations of Tso et al (1998) in the spectral region 10 600ndash15 000 cmminus1 (066ndash094 microm) Vaida et al (2001) attribute this mostly to the lack of a suitable dipole momentfunction in the Tso et al (1998) model

The only work to date that describes the detection of WD absorption in theatmosphere (the |0〉f|4〉b overtone transition) in the spectral region near 13 330 cmminus1

(075 microm) has recently appeared (Pfeilsticker et al 2003) Apart from this workno other measurements (neither laboratory nor atmospheric) of WD absorption inequilibrium close to atmospheric conditions have been reported The technique ofcreation of supersonic molecular beams is usually used to investigate WD properties(Huang and Miller 1989 Huisken et al 1996 Paul et al 1997) which however does notallow any definite conclusion to be reached about possible WD amounts in atmosphere

In the present work we discuss the results of measurements and numerical sim-ulation aimed at the direct detection of WD absorption in the spectral region 5000ndash5600 cmminus1 (1785ndash20 microm) in a pure water vapour cell in laboratory conditions In spiteof relatively strong overlapping with the WM absorption a significant absolute value ofWD absorption is predicted in this regionlowast The measurement in a WM absorption bandcould also help to investigate the possible relation between WD and present models ofwater vapour continuum absorption

2 EXPERIMENTAL SET-UP

The near-infrared absorption spectra of pure water vapour for conditions presentedin Table 1 have been characterized at the Rutherford Appleton Laboratory MolecularSpectroscopy Facility using a combination of high-resolution Fourier transform spec-troscopy with fixed and variable-path-length absorption cells Measurements made at a

lowast Part of the reason for choosing the 5000ndash5600 cmminus1 region is that the theoretical WD spectrum in Vaida et al(2001 H G Kjaergaard personal communication) indicated more intense and distinct WD absorption in thisspectral region (Fig 1) than the recent more precise calculation (with a better representation of HOH-bendingmodes) by the same group (Schofield and Kjaergaard 2003) which was reported after our measurements


TABLE 1 MEASUREMENT CONDITIONS

Water vapour pressure Temperature Path length Resolution1

(hPa) (K) (m) (cmminus1)

1 98 342 974 003 (SPAC2)

2 20 299 128 00068 (LPAC3)3 20 297 029 00068

1Spectral resolution is defined here as 09(maximum optical path difference in cm)2Short-path-length cell (Remedios 1990)3Long-path-length cell (Ballard et al 1994)

path length of 29 cm have been described in detail previously (Smith et al 2004) Herewe report two additional measurements made using two variable-path-length absorptioncells The long-path-length absorption cell (LPAC) described previously (Ballard et al1994) is capable of providing optical path lengths in the range 32 m to 1 km at temper-atures between 200 and 300 K A short-path-length cell (SPAC Remedios 1990) givesoptical paths in the range 5 to 20 m and temperatures in the range 200 to 350 K For thiswork the Bruker IFS 120HR Fourier transform spectrometer (FTS) was configured witha 150 W quartz tungsten halogen source a calcium fluoride beam-splitter and a liquid-nitrogen-cooled indium antimonide detector The LPAC and SPAC fitted with calciumfluoride windows and gold coated reflective optics were used

The optical path length in the LPAC was 128 m at 299 K (see Table 1) TheSPAC was operated at an optical path of 974 m and electrically heated to 342 KGood stability of the water vapour partial pressure was achieved by virtue of thesmall surface-area to volume ratio of both the cells NortonndashBeer strong apodization(Norton and Beer 1976) and Mertz phase correction (Mertz 1967) were applied to all ofthe measured interferograms Where appropriate optical filters were used to limit theoptical bandwidth to the spectral range of the measurement The interferometer inputaperture diameter was set such that the intensity of radiation at the detector was sufficientto give excellent information-to-noise ratios whilst avoiding saturation of the detectoror loss of spectral resolution The alignment of the interferometer was optimized and thephotometric accuracy tested before carrying out the measurements reported here TheFTS was maintained at a pressure below 04 Pa by a turbo-molecular pump to minimizethe amount of carbon dioxide and water vapour in the optical path of the interferometerA calcium fluoride window separated the FTS from the SPAC transfer optics A rotaryand turbo-molecular pump evacuated the transfer optics to a pressure below 002 Pa

Details of the sensors used to measure gas temperature pressure and humiditywithin the LPAC and SPAC are given in Table 2 The 10 and 1000 Torr full-scaleBaratron gauges (calibration traceable to the US National Institute of Standards andTechnology) were used to monitor pressure during sample preparation and throughoutthe measurements The atmospheric pressure reading of the 1000 Torr Baratron wascompared with that of a calibrated (traceable to UK National Physical Laboratory stan-dards) precision aneroid barometer Low-pressure readings of the 10 and 1000 TorrBaratron gauges were compared by measuring identical pressures with both gaugesRelative humidity (RH) was measured by two humidityplatinum-resistance thermome-ter sensors positioned at opposite ends inside of either the LPAC or the SPAC

Water vapour samples were prepared using a clean glassPTFElowast vacuum linefrom distilled liquid water (analar grade BDH Chemicals) which had previously beenpurified to remove dissolved air using at least three repeat 200 K freezendashpumpndashthaw

lowast Polytetrafluoroethylene


TABLE 2 DETAILS OF TEMPERATURE PRESSURE AND HUMIDITY SENSORS

Measurement Manufacturer and type Stated uncertainty

TemperatureLPAC1 HeraeusNulectrohms Platinum resistance plusmn01K at 273 K

thermometers (14 positions)

SPAC2 RS Components R-T curve matched plusmn02K at 296 Knegative temperature coefficient thermistorstype UUA41J1 (6 positions)

Signal logger Laplace Instruments Model SPC-801 plusmn03K

Pressure0ndash10 hPa MKS-390 (10 Torr Baratron) plusmn008 of reading10ndash1000 hPa MKS-390 (1000 Torr Baratron) plusmn008 of readingAtmospheric Negretti aneroid barometer M2236A plusmn40 Pa

HumidityRelative humidity Vaisala HMP2340ndash9090ndash100 plusmn1plusmn2Temperature Vaisala HMP234 plusmn01K

1Long-path-length cell (Ballard et al 1994)2Short-path-length cell (Remedios 1990)

cycles Agreement between the humidity sensor and pressure gauge readings (to withinthe humidity sensor accuracy) confirmed the purity of the water vapour introduced tothe gas cells The vapour pressure RH and temperature were recorded at 5 s intervalsduring spectroscopic measurements on water vapour samples

Evacuated-cell background spectra were recorded before and after each filling ofthe LPAC or SPAC at a spectral resolution of 003 cmminus1 Before each backgroundspectrum was recorded high-resolution test measurements were made to check thatthe water vapour had been adequately removed from the gas cell Taking the ratio ofthe sample and averaged background spectra minimized errors in the transmittance orabsorbance spectra arising from changes in baseline signal level eg due to drifts in thenear-IR source intensity

The measured water vapour transmittance τ (ν T ) at wave number ν and tempera-ture T was calculated using τ (ν T )= I (ν T )Io(ν T ) where I (ν T ) and Io(ν T )are the intensities of the sample and background spectra respectively Napierianabsorbance spectra Aobs(ν T ) were calculated from the transmittance data asAobs(ν T )=minuslnτ (ν T )

The rms signal-to-noise ratio in each of the transmittance spectra exceeded 10001across the entire spectral range of the water vapour absorption features giving aninformation-to-noise ratio in excess of 1001 for absorbances between 02 and 35The maximum information-to-noise ratio at an absorbance of around 10 was 3701

3 RESULTS AND DISCUSSION

(a) Preliminary data treatmentThe observed laboratory spectra were compared with calculated absorbance spec-

tra generated for the measured laboratory conditions using HITRAN v11 (httpwwwhitrancom Rothman et al 2003) the line-by-line (LBL) code of Mitsel et al(1995) and the Reference Forward Model LBL code of Dudhia (1997) Detailed in-formation about the optical configuration of the FTS and the numerical apodization


000

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5000 5100 5200 5300 5400 5500 5600000

002

(a)O

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al d

ep

th

Experiment - HITRANwith_CKD

5 points smoothing

(b)

(c)

Wavenumber (cm-1)

Figure 2 (a) Initial view of the residual optical depth for the experiment with water vapour pressure 20 hPa pathlength 128 m and temperature 299 K The spectral resolution is 5 cmminus1 (b) Contribution to the residual in (a) thatshould be subtracted because of the new spectral line parameters fitting (c) contribution that should be subtracted

from the residual because of the impact of weak lines Thick lines in (a) and (b) show five-point smoothing

function was used to calculate a wavelength-dependent instrument line shape and thenconvolute it with the calculated molecular spectrum

An example of the initial residual between optical depth derived from experimentand the calculated WM optical depth including the CKD-24 water vapour continuumis shown in Fig 2(a) The residual is presented with a spectral resolution of 5 cmminus1

It should be mentioned that there is no significant difference between HITRAN-96and HITRAN v11 for H2O spectral lines in the spectral region 3500ndash6000 cmminus1 (seefor example Ptashnik and Shine (2003)) It means that using CKD-24 with HITRANv11 is quite justified in this case in spite of the fact that originally HITRAN-96 wassupposed to be used with this version of CKD continuum

To calculate the residual only parts of the spectrum (both measured and calculated)below an optical depth threshold (ODT) of 2 were used in order to exclude the impactof regions of the spectrum which are saturated Such a method of data processing doesnot affect the continuum part of the residual we are interested in here because for bothmeasurement conditions this part is much less than the threshold level

The bars in Fig 2(a) show only experimental error However there are two othermain sources of error which should be taken into account to get the final residual

(i) Uncertainty of spectral line parameters It was found that any systematic error inthe initial HITRAN lines parameters for example a 15 error either in line intensityS or self-broadening half-width parameter γself could lead to a similar shape and sizeof the residual shown in Fig 2(a) This is especially important as HITRAN does nothave the information about self-broadening parameters for this spectral region In suchcircumstances LBL codes usually use the approximation γself = k middot γair where γair is


51193 51194 51195 51196 5119700

01

02

03

04

54752 54753 54754 54755 54756 5475700

10

20

(a)O

ptic

al d

ep

th

Measurement HITRAN new line parameters

(b)

Wavenumber (cm-1)

Figure 3 Examples of comparisons of the calculated optical depth using HITRAN (v11) modified-HITRAN(new line parameters) and the measured optical depth for pure water vapour pressure 20 hPa path length 29 cm

and temperature 297 K See text for details

the air-broadening coefficient and k sim 5 While this approximation is not normallyimportant for atmospheric calculations where air-broadening prevails it is of muchgreater importance when interpreting pure water spectra in laboratory conditions

To exclude the possibility that such errors were the cause of the residual we decidedto derive γself and the line-intensity parameters by fitting the calculated spectrum to themeasured one The measured spectrum for water vapour pressure 20 hPa and path length29 cm was used to fit parameters of the 460 strongest lines (S gt 2times 10minus23 cm molminus1)in this spectral region that determined from numerical experiment are most importantwhen computing the residual We used the LevenbergndashMarquardt least-square algorithmto fit three parameters (centre position intensity and self-broadening coefficient) foreach spectral line The Voigt profile was used for the fitting Additionally the baselinewas fitted for every three consecutive spectral lines The mean error of the S and γselfparameters determination was estimated to be about 5

Figure 3 shows parts of a measured high-spectral-resolution spectrum comparedwith the calculation using HITRAN and the modified HITRAN (we will refer to thisdatabase with newly fitted lines as lsquomodified-HITRANrsquo or lsquoHITRAN(m)rsquo) Figure 2(b)displays the correction that should be subtracted from the initial residual (Fig 2(a)) totake into account the impact of the new line parameters Comparison of Figs 2(a) and(b) shows that the impact of the correction of line parameters on the original residualis significant and accounts for much of the residual at wave numbers above 5500 andbelow 5150 cmminus1 This indicates the importance of a careful assessment of the qualityof line parameters in this work The other details of the line fitting as well as the fittedline parameters will be reported elsewhere They can be found in HITRAN format at theBritish Atmospheric Data Centre (httpbadcnercacukdatacwvchitranindexhtml)


To minimize the possible impact of parameter errors in weaker (S lt 2times 10minus23 cmmolminus1) unfitted HITRAN lines we did not include in the residual calculation (inaddition to the ODT limitation mentioned above) parts of the spectra (both measuredand calculated) near the centres of these lines The width of the cut-off areas was derivedso that the line contribution was less then 5 of the maximum residual value Such anapproach is quite reasonable since we are interested only in the smooth (continual) partof the residual Taking into account that the maximum cut-off distance (for the strongestof the unfitted lines) that satisfies the 5 requirement is about 03 cmminus1 for 20 hPa and06 cmminus1 for 98 hPa measurements we still have enough data points in the each 5 cmminus1

spectral region to be processed

(ii) Contribution from weak-lines HITRAN does not include parameters of veryweak lines (S lt 10minus26 to 10minus27 cm molminus1) Schwenke and Partridge (2000) haverecently updated their ab initio calculation of water vapour line parameters (Partridgeand Schwenke 1997) which includes such weak lines and allows an estimation of theircontribution To assess the impact of these weak lines it is necessary to account forthe fact that many of the lines in the PartridgendashSchwenke (hereafter PS) database arealso in HITRAN There are several possible ways in which the weak-line contributioncan be estimated (see Ptashnik and Shine 2003) We believe that the best method is toreplace all the lines in the PS database by their HITRAN equivalent if they have onethis ensures that differences between the PS and HITRAN databases are solely due tolines which are uncatalogued on HITRAN rather than because of differences in spectralparameters of catalogued lines between PS and HITRAN This is the PSlarr HITRANcase of Ptashnik and Shine (2003)

Figure 2(c) shows the contribution of the PS weak lines where it can be seen to begenerally significantly smaller than the residual in Fig 2(a)

It should be mentioned again that only those parts of corrections due to lineparameters fitting and PS weak lines which are below the ODT = 2 are presented inFigs 2(b) and (c) The total weak-lines contribution (ie without using ODT) is severaltimes larger

(b) Water dimer as a lsquoseparatersquo absorberThe corrected optical depth residual which takes into account the new line pa-

rameters the weak lines and CKD-24 continuum is shown in Fig 4 together with theexpected dimer absorption Error bars include in this case both the measurement errorand estimated uncertainty (standard deviation) caused by errors in the line parametersrsquofitting Two WD parameters Keq and HWHM were fitted to best match the central(bigger) peak of the residual (near 5340 cmminus1) Keq was found to be 0018plusmn 0003 and0011 plusmn 00025 atmminus1 for the 20 hPa 299 K and for the 98 hPa 342 K measurementrespectively whereas the mean HWHM value is found to be 18 plusmn 3 cmminus1

To be in best agreement with the residual the |0〉f|1〉b|1〉 and two close (unre-solved) |10〉|1〉 and |1〉f|0〉b|1〉 stretching + bending WD bands (using Schofield andKjaergaardrsquos (2003) notation) are red-shifted in Fig 4 with respect to their positionspredicted by Schofield and Kjaergaard (2003) (5231 5341 and 5357 cmminus1 respectively)by 12 cmminus1 (Fig 4(a)) and 5 cmminus1 (Fig 4(b)) These shifts are much less than the uncer-tainty of the prediction The low-temperature experimental study by Perchard (2001) ofthe water trapped in a nitrogen matrix has revealed the |10〉|1〉WD band to be positionednear 5296 cmminus1 indicating that there is uncertainty in the precise position of the WDbands which can also depend on the ambient conditions


5000 5100 5200 5300 5400 5500 5600

000

005

010

(a) Residual Measurement - HITRAN(m)_with_CKD-24 Dimer K

eq=0018 atm-1 HWHM=20 cm-1 Shift=-12 cm-1

CKD-24 continuum

Opt

ical

dep

th

5000 5100 5200 5300 5400 5500 5600

000

005

010

(b) Residual Measurement - HITRAN(m)_with_CKD-24

Dimer Keq=0011 atm-1 HWHM=16 cm-1 Shift=-5 cm-1

CKD-24 continuum

Wavenumber (cm-1)

Opt

ical

dep

th

Figure 4 Corrected residual between measurement and modified-HITRAN calculations with CKD-24 includedBars show the measurement errors and errors of spectral line parameters fitting (a) Pure water vapour pressure20 hPa path length 128 m temperature 299 K measurement (b) 98 hPa 97 m 342 K measurement To best fit

the residual the dimer spectrum is red-shifted by 12 and 5 cmminus1 for (a) and (b) respectively

Taking also into account uncertainty in the knowledge of the main WD parametersquite good agreement between residuals and expected WD signatures can be seen forboth measurements apart from the part of the residual between 5400 and 5500 cmminus1This part can be attributed either to extra CKD continuum or non-predicted WD orhigher-order water clusters absorption features (for example trimers) The higher-ordercluster explanation may be favoured because of the stronger dependence on watervapour pressure than is the case for the dimer as can be seen for this part of the residualif one compares Figs 4(a) and (b)


(c) Water dimer as a part of CKD continuumAn alternative interpretation of the residual and its relationship with the expected

dimer absorption can be suggested Taking into account that the CKD continuum isa semi-empirical model which has been fitted to observation in only some parts ofthe spectrum (Clough et al 1989 Mlawer et al 1999) we can suggest that it maycontain absorption of some other components (in addition to the WM line far wings)such as WDs In spite of the fact that no experimental data in the spectral region underour investigation were used for CKD parameters fitting these parameters could includesome WD contribution through the presence of WD absorption in the spectral regionswhere the CKD parameters were fitted (for example below 2500 cmminus1)

Figure 5 shows the residual between measurement and modified-HITRAN calcu-lation using the Ma and Tipping (1999 2002 henceforth MT) continuum instead ofCKD The MT continuum model is distinct from the CKD model in the sense that itis based on far wing line shape theory which does not rely on adjustable parametersor fitting to observation thus it cannot include any other components in addition tothe far wing contribution It can be seen from Fig 5 that the MT continuum is aboutone quarter of CKD in this spectral region The values of WD equilibrium constant thatbest match the residuals in this case were found to be Keq = 0043plusmn 00055 atmminus1 for299 K 20 hPa and Keq = 002plusmn 00035 atmminus1 for 342 K 98 hPa and are thereforesignificantly higher than the values derived in subsection 3(b) The mean value of theWD band HWHM = 28 plusmn 4 cmminus1 matches the central residual peak quite well

Again the residual in the spectral region 5400ndash5500 cmminus1 cannot be explainedeither by the MT continuum or by the present WD feature The WD band shifts in Fig 5are similar to those obtained in Fig 4

(d) Implication for the dimerization equilibrium constantFigure 6 displays two sets of Keq we have obtained together with several other

calculated and experimentally derived values of water dimerization equilibrium con-stant It is clear from the plot that our upper estimation of Keq temperature de-pendence Kequp(T ) derived from the residual lsquoMeasurement minus HITRAN(m) withMT continuumrsquo is in much better agreement with the Curtiss et al (1979) measure-ments and extrapolation than the lower Keqlow(T ) estimation which was obtainedfrom the residual with CKD continuum subtracted The Kequp(T ) is also very closeto the Slanina and Crifo (1992) calculations and is in a very good agreement with theKeq (2924 K)= 005 atmminus1 derived by Pfeilsticker et al (2003)lowast (K Pfeilsticker 2003personal communication) in an independent measurement and in a rather different spec-tral region However both the Pfeilsticker et al (2003) and our measurements do notsupport the Goldman et al (2001) prediction of the strong Keq dependence on temper-ature (Fig 6) Munoz-Caro and Nino (1997) explain the low values of their calculatedKeq(T ) (Fig 6) by the lack of interaction in the vibrational model they used

The low set of our Keq estimation when combined with the Curtiss et al (1979)experimental data points by contrast shows very small nearly zero temperaturedependence which is in contradiction with all theoretical predictions This all indicatesthat WD absorption is most probably included partlymostly in the modern CKD con-tinuum model (self-broadening part) through the fitting of CKD continuum parametersto the experimental data which included some component of WD absorption Taking

lowast Keq(2924 K)= 0047 atmminus1 was obtained from the experiment assuming the band intensity calculated by Lowand Kjaergaard (1999) S = 304times10minus22 cm molecminus1 This corresponds to Keq = 005 atmminus1 if the value of S =284times10minus22 cm molecminus1 calculated more recently by Schofield and Kjaergaard (2003) is used for the same band


5000 5100 5200 5300 5400 5500 5600

000

005

010

(a) Residual Measurement - HITRAN(m)_with_MT

Dimer Keq

=0043 atm-1 HWHM=30 cm-1 Shift=-9 cm-1

CKD-24 continuum Ma amp Tipping continuum

Opt

ical

dep

th

5000 5100 5200 5300 5400 5500 5600

000

005

010

(b) Residual Measurement - HITRAN(m)_with_MT


CKD-24 Ma amp Tipping continuum

Wavenumber (cm-1)

Op

tical

de

pth

Figure 5 Corrected residual between measurements and modified-HITRAN calculations with the Ma and Tip-ping (1999 2002) continuum included Bars show the measurement errors and errors of spectral line parametersfitting (a) Pure water vapour pressure 20 hPa path length 128 m temperature 299 K measurement (b) 98 hPa97 m 342 K measurement To best-fit the residual the dimer spectrum is red-shifted by 9 and 5 cmminus1 for (a) and

(b) respectively

into account that WDs can be regarded to some degree as colliding water moleculeswith very long collision duration the contribution of WD absorption can causethe lsquochi-functionrsquo correction in the CKD continuum (Clough et al 1989) very similar tothe one caused by deviation from the impact collision model

(e) Implication for short-wave absorption by the atmosphereVaida et al (2001) have shown that the spectral regions 4000ndash5000 and 5600ndash

6500 cmminus1 should give the main contribution to WD short-wave absorption Thiscontribution is caused mainly by far wings of the |0〉f|1〉b|0〉 |1〉f|0〉b|0〉 and |10〉 |0〉


280 300 320 340 360 380 400000

002

004

006

008

Ke

q (

atm

-1)

Curtiss et al (1979) experiment Curtiss et al (1979) extrapolation MCaro and Nino (1997) Slanina and Crifo (1992) MCY-B potential Slanina and Crifo (1992) BJHG potential Goldman et al (2001) Pfeilsticker et al (2003) This work Measurement - HITRAN(m)_with_CKD This work Measurement - HITRAN(m)_with_MT

T (K)

Figure 6 Different theoretical and experimental determinations of the dimerization equilibrium constant Keqtemperature dependence including the current work The shaded area shows the uncertainty of the Curtiss et al(1979) extrapolation caused by experimental and calculation errors The dash-dotted lines display the temperature

interpolationextrapolation of the lower and upper set of the Keq derived in this paper

WD bands centred near 3600 3730 and 3745 cmminus1 respectively and by wings of|0〉f|1〉b|1〉 |10〉 |1〉 and |1〉f|0〉b|1〉 bands centred near 5230 5340 and 5357 cmminus1respectively We applied our derived values of WD bandwidth and Lorentzian line shapeto all WD bands and used this approximation together with the derived sets of Keq andSchofield and Kjaergaard (2003) WD spectroscopic information to estimate the globalmean extra short-wave absorption caused by WD

The fast LBL code of Mitsel et al (1995) was used for high (0001 cmminus1) spectral-resolution calculation of optical depth for each of 17 atmospheric layers of clear-skymid-season zonal-mean atmospheric profiles at a latitudinal resolution of 10 Apartfrom the H2O monomer and dimer the model also includes CO2 O3 CH4 and O2 Theoptical depth spectra were then used as input to the Discrete Ordinate (DISORT) codeof Stamnes et al (1988) for irradiance calculations Rayleigh scattering was taken intoaccount using DISORT with four-streams approximation The solar irradiance at the topof the atmosphere compiled by Kurucz (1992 httprtwebaercomsolarframehtml) isemployed which presents the solar spectrum at the spectral resolution of 1 cmminus1 (totalsolar irradiance = 13688 W mminus2)

The WD partial pressure profile for each atmospheric WM profile was cal-culated from Eq (2) We used the value Hup =minus378 kcal molminus1 and Sup =minus1889 cal Kminus1molminus1 in Eq (1) to interpolateextrapolate our Kequp(T ) and Curtisset al (1979) data to atmospheric temperatures (upper dash-dotted line in Fig 6)These values are very close to those derived by Curtiss et al (1979 H =minus359plusmn05 kcal molminus1 and S =minus1859plusmn 13 cal Kminus1molminus1) Similarly the values Hlow =minus1590 kcal molminus1 and Slow =minus1329 cal Kminus1molminus1 were used to extrapolateinter-polate the Keqlow(T ) together with Curtiss et al (1979) data (lower dash-dotted line in


-80 -60 -40 -20 0 20 40 60 80

0

1

2

3

4

Global mean 042 W m-2


Wa

ter

dim

er

abso

rptio

n (

W m

-2)

Latitude (degree)

Keq up(T) HWHM=28 cm-1

Keq low(T) HWHM=18 cm-1

Figure 7 The latitudinal dependence of water dimer solar absorption in the spectral region 1500ndash17 000 cmminus1

for MarchndashMay for the lower and upper set of the dimerization equilibrium constant Keq derived in this paper

Fig 6) However these H and S values are too far from those derived by differentauthors (see Curtiss et al 1979) thus they can only be regarded as fitting parameters ofour investigation

In Fig 7 the calculated latitudinal dependence of WD absorption of solar irradiancein the spectral region 1500ndash17 000 cmminus1 is presented for MarchndashMay for both sets ofthe Keq and HWHM obtained For the other seasons the dependencies look similarapart from a +10(minus10) shift for the winter (summer) seasons The global-meanvalue of extra absorption due to WD is sim042 W mminus2 (for the Keqlow and HWHM= 18 cmminus1) and sim15 W mminus2 (for the Kequp and HWHM = 28 cmminus1) or about05 and 2 of the total clear-sky absorption respectively Calculation with the Curtisset al (1979) extrapolation of Keq(T ) (dashed line in Fig 6) with HWHM = 28 cmminus1

gives sim13 W mminus2 global-mean WD absorptionFigure 8 displays the calculated spectrum of the solar direct flux at the surface and

WD contribution to the flux for a tropical atmosphere case with overhead sun for acolumn water vapour amount of 47 kg mminus2 The dashed lines display the cumulativeWD absorption (ie the extra absorption integrated from 1500 cmminus1 to the given wavenumber) that reaches 2 and 72 W mminus2 for the low and upper sets of the Keq(T )respectively The latter value is about twice as high as the upper estimate of Vaida etal (2001) which is mainly due to the fact that our Keq is approximately twice as bigThe estimate by Chylek et al (1999) of WD absorption of 6 W mminus2 for the tropicalatmosphere is by contrast very close to ours However this is largely coincidental astheir value is obtained with a value of Keq about 30 lower than ours which reflects thefact that WD overtone intensities predicted by Tso et al (1998) are significantly largerthan the ones calculated by Schofield and Kjaergaard (2003)

Figure 8 shows that the main contribution to the extra absorption comes from thewings of the WD bands referred to above rather than from the band centres Figure 1


2000 4000 6000 8000 10000 12000 14000 160000000

0005

0010

0015

Flu

x (W

m-2

cm-1

)

Wavenumber (cm-1)

Direct solar surface flux 5 no WD absorption WD absorption

0

1

2

3

4

5

6

7

8

9

Cumulative WD absorption

Cu

mulative

WD

abso

rption

(W m

-2)

Figure 8 The calculated spectrum of the solar direct flux at the surface and water dimer (WD) spectral andcumulative (right axis) contribution to the absorption for an overhead sun in a tropical atmosphere The upperand lower curves for the WD absorption correspond to the upper and lower sets of dimerization equilibrium

constant Keq

1000

800

600

400

200

0

00 05 10 15 20

Heating rate (K day-1)

Pre

ssur

e (

mb)

(1) HITRAN (2) HITRAN + WDup [(2) - (1)] 5 Keq up [(2) - (1)] 5 Keq low

Figure 9 The calculated atmospheric heating rate due to water dimer (WD) absorption (lower and upperestimate) for the midlatitude summer atmospheric profile and solar zenith angle of 30


indicates that the CKD-24 continuum is much weaker than the theoretical estimates ofthe WD absorption in these wings Therefore even if CKD-24 is included in radiationbudget calculations the extra absorption due to WD is more likely to be closer to ourupper estimate assuming that the Lorentzian approximation of the WD bands is valid

Finally in Fig 9 the calculated atmospheric heating rate due to WD absorptionis presented for the midlatitude summer profile (Ellingson et al 1991) It can be seenthat the main WD contribution to short-wave absorption appears near the surface It iscaused by the fact that the quadratic dependence of WD amount on that of WM (Eq (2))is stronger than the growth of Keq(T ) when temperature falls with height

It is worth reiterating that all assessments of WD absorption are highly dependenton the widths and far wing shapes of the strongest WD bands centred near 3600 3730and 3745 cmminus1 For example decreasing the HWHM of these three bands alone fromthe values of 28 and 18 cmminus1 used here to sim6 cmminus1 (Huisken et al 1996) will decreaseall WD absorption values presented in Figs 7ndash9 by a factor of 2 to 25

4 CONCLUSIONS

In spite of the quite strong overlapping lines of the WM a quasi-continual resid-ual absorption very similar to that expected from the WD |0〉f|1〉b|1〉 |10〉 |1〉 and|1〉f|0〉b|1〉 stretching + bending combination bands was observed in a series of lab-oratory measurements for different pressures and temperatures in the spectral region5000ndash5600 cmminus1 The measured residuals have a 5ndash10 cmminus1 red shift in comparisonwith the Schofield and Kjaergaard (2003) theoretical prediction The dimerization equi-librium constants (Keq(299 K) = 0043 plusmn 00055 atmminus1 and Keq(342 K) = 002 plusmn00035 atmminus1) derived from the residual lsquoMeasurementminusmodified HITRAN with Maand Tipping continuumrsquo are in a good agreement with the main theoretical predictionsand with all experimental observations of the value It can mean that a substantial part ofWD absorption is most probably already included as part of the present self-broadeningCKD continuum model at least near the band centres The lower and upper estimationsof WD contribution to the global-mean solar radiation absorption are found to be about05 and 2 of the total atmospheric absorption However on the basis of a comparisonof the derived Keq values with others in the literature we believe that dimer contributionis closer to the higher estimate Our upper limit is 2ndash25 times the upper estimation ofVaida et al (2001) however it is much less than would follow from the Goldman et al(2001) calculation of water dimerization equilibrium constant

On the basis of the latest Schofield and Kjaergaard (2003) calculation it can besuggested that the largest WD contribution to the water vapour continuum shouldbe expected from the strongest WD bands |0〉f|1〉b|0〉 |1〉f|0〉b|0〉 and |10〉 |0〉 near3700 cmminus1 (see Fig 1) However for atmospheric radiation budget applications itseems more important to investigate the absorptionshape of the far wings of these WDbands as well as the bands investigated in our work The far wing absorption of thesebands gives the main contribution to WD global radiative impact The Lorentzian wingapproximation for the WD bands used in our work (and for example in the workof Vaida et al 2001) should probably be regarded as a first approximation and canbe a source of significant uncertainty when estimating the WD absorption (see alsoKjaergaard et al 2003)

An additional absorption was registered in the spectral region 5400ndash5500 cmminus1 thatcannot be explained either by CKD-24 water continuum or by the currently predictedWD spectrum


ACKNOWLEDGEMENTS

We are very grateful to Henrik Kjaergaard Eli Mlawer Klaus Pfeilsticker RichardTipping Anu Dudhia Boris Fomin Olga Naumenko and Ahilleas Maurellis forfruitful discussions and help in providing us with up-to-date datasets The authorsthank the UK Natural Environment Research Council (grants NERTS200000982NERTS200100194 and NERTS200101117) for support and the technical assis-tance of R G Williams at the Rutherford Appleton Laboratory Molecular SpectroscopyFacility

REFERENCES

Arking A 1999 Bringing climate models into agreement with observations ofatmospheric absorption J Climate 12 1589ndash1600

Ballard J Strong KRemedios J Page M andJohnston W B

1994 A coolable long path absorption cell for laboratory spectroscopicstudies of gases J Quant Spectrosc Radiat Transfer 52677ndash691

Chylek P Fu Q Tso H C Wand Geldart D J W

1999 Contribution of water vapor dimers to clear sky absorption of solarradiation Tellus 51A 304ndash313

Clough S A Kneizys F X andDavies R W

1989 Line shape and water vapor continuum Atmos Res 23 229ndash241

Conant W C Vogelmann A Mand Ramanathan V

1998 The unexpected solar absorption and atmospheric H2O A directtest using clear-sky data Tellus 50A 525ndash533

Curtiss L A Frurip D J andBlander M

1979 Studies of molecular association in H2O and D2O vapors bymeasurement of thermal conductivity J Chem Phys 712703ndash2711

Daniel J S Solomon SSanders R WPortmann R W andMiller D C

1999 Implication for water monomer and dimer solar absorption fromobservations at Boulder Colorado J Geophys Res 10416785ndash16791

Devir A D Neumann MLipson S G andOppenheim Uri P

1994 Water vapor continuum in the 15 to 25 microm spectral region Evi-dence for (H2O)2 in the atmosphere Opt Eng 33 746ndash750

Dudhia A 1997 lsquoReference forward model version 3 Software userrsquos manualrsquoEuropean Space Technological Centre (ESTEC) DocumentPO-MA-OXF-GS-0003 European Space Agency (ESA)Paris France

Ellingson R G Ellis J andFels S

1991 The intercomparison of radiation codes used in climate modelsLongwave results J Geophys Res 96 8929ndash8953

Evans G T and Vaida V 2000 Aggregation of water molecules Atmospheric implicationsJ Chem Phys 113 6652ndash6659

Goldman N Fellers R SLeforestier C andSaykally J

2001 Water dimers in the atmosphere Equilibrium constant forwater dimerization from the VRT(ASP-W) potential surfaceJ Phys Chem 105 515ndash519

Headrick J E and Vaida V 2001 Significance of water complexes in the atmosphere Phys ChemEarth 26 479ndash486

Hill C and Jones R 2000 Absorption of solar radiation by water vapor in clear and cloudyskies Implications for anomalous absorption J GeophysRes 105 9421ndash9428

Huang Z S and Miller R E 1989 High-resolution near infrared spectroscopy of water dimerJ Chem Phys 91 6613ndash6631

Huisken F Kaloudis M andKulcke A

1996 Infrared spectroscopy of small size-selected water clustersJ Chem Phys 104 17ndash25

Kato S Ackerman T PClothiaux E E Mather J HMace G G Wesley M LMurcray F and Michalsky J

1997 Uncertainties in modelled and measured clear-sky surface shortwave irradiances J Geophys Res 102 25881ndash25898

Kjaergaard H G Robinson T WHoward D L Daniel J SHeadrick J E and Vaida V

2003 Complexes of importance to the absorption of solar radiationJ Phys Chem A 107 10680ndash10686

Kurucz T L 1992 Synthetic infrared spectra Infrared solar physics IAU Sym-posium 154 Eds D M Rabin and J T Jefferies KluwerAcademic Norwell Massachusetts USA


Low G R and Kjaergaard H G 1999 Calculation of OH-stretching band intensities of the water dimerand trimer J Chem Phys 110 9104ndash9115

Ma Q and Tipping R H 1999 The averaged density matrix in the coordinate representationApplication to the calculation of the far-wing line shape forH2O J Chem Phys 111 5909

2002 The frequency detuning correction and the asymmetry of lineshapes The far wing of H2O-H2O J Chem Phys 1164102ndash4115

Mertz L 1967 Auxiliary computation for Fourier transform spectrometryInfrared Phys 7 17ndash23

Mhin B J Lee S J andKim K S

1993 Water-cluster distribution with respect to pressure and tempera-ture in the gas phase Phys Rev A 48 3764ndash3770

Mitsel A A Ptashnik I VFirsov K M and Fomin A B

1995 Efficient technique for line-by-line calculating the transmittanceof the absorbing atmosphere Atmos Oceanic Opt 8 847ndash850

Mlawer E J Clough S ABrown P D and Tobin D C

1999 lsquoRecent developments in the water vapor continuumrsquo Pp 1ndash6in Proceedings of the ninth ARM Science Team meetingMarch 22ndash26 San Antonio Texas Eds N Burleigh andD Carrothers US Department of Energy Richland WAUSA

Munoz-Caro C and Nino A 1997 Effect of anharmonicities on the thermodynamic properties of thewater dimer J Phys Chem 101 4128ndash4135

Norton R H and Beer R 1976 New apodizing functions for Fourier spectrometry J Opt SocAm 66 259ndash264

Partridge H and Schwenke D W 1997 The determination of an accurate isotope potential energy surfacefor water from extensive ab initio calculation and experimen-tal data J Chem Phys 106 4618ndash4639

Paul J B Collier C PSaykally R J Scherer J Jand OrsquoKeefe A

1997 Direct measurement of water cluster concentration by infraredcavity ringdown laser absorption spectroscopy J PhysChem A 101 5211ndash5214

Penner S S and Varanasi P 1967 Spectral absorption coefficient in the pure rotational spectrumof water vapor J Quant Spectrosc Radiat Transfer 7687ndash690

Perchard J P 2001 Anharmonicity and hydrogen bonding IImdashA near infrared studyof water trapped in nitrogen matrix Chem Phys 266109ndash124

Pfeilsticker K Lotter APeters C and Bosch H

2003 Atmospheric detection of water dimers via near-infraredabsorption Science 300 2078ndash2080

Pilewskie P Rabbette MBergstrom R Marquez JSchmid B and Russell P B

2000 The discrepancy between measured and modelled downwellingsolar irradiance at the ground Dependence on water vaporGeophys Res Lett 27 137ndash140

Ptashnik I V and Shine K P 2003 Calculation of solar radiative fluxes in the atmosphere The effectof updates in spectroscopic data Atmos Oceanic Opt 16251ndash255

Ramanathan V andVogelmann A M

1997 Greenhouse effect atmospheric solar absorption and the earthrsquosradiation budget From ArrheniusndashLangley era to the 1990sAmbio 26 38ndash46

Remedios J J 1990 lsquoSpectroscopy for remote sounding of the atmospherersquo D PhilThesis Oxford University

Rothman L S Barbe A ChrisBenner D Brown L RCamy-Peyret CCarleer M R Chance KClerbaux C Dana VDevi V M Fayt AFlaud J-M Gamache R RGoldman A Jacquemart DJucks K W Lafferty W JMandin J-Y Massie S TNemtchinov VNewnham D A Perrin ARinsland C P Schroeder JSmith K M Smith M A HTang K Toth R A VanderAuwera J Varanasi P andYoshino K

2003 The HITRAN molecular spectroscopic database Edition of 2000including updates through 2001 J Quant Spectrosc RadiatTransfer 82 5ndash44


Schofield D P andKjaergaard H G

2003 Calculated OH-stretching and HOH-bending vibrational transi-tions in the water dimer Phys Chem Chem Phys 5 3100ndash3105

Schwenke D W and Partridge H 2000 Convergence testing of the analytic representation of an ab initiodipole moment function for water Improved fitting yieldsimproved intensities J Chem Phys 113 6592ndash6597

Slanina Z and Crifo J-F 1992 A refined evaluation of the gas-phase water-dimerizationequilibrium constant within nonrigid BJH- and MCY-typepotentials Int J Thermophys 13 465ndash476

Smith K M Ptashnik I VNewnham D A andShine K P

2004 Absorption by water vapour in the 1 to 2 microm region J QuantSpectrosc Radiat Transfer 83 735ndash749

Stamnes K Tsay S CWiscombe W andJayaweera K

1988 A numerically stable algorithm for Discrete-Ordinate-Methodtransfer in multiple scattering and emitting layered mediaAppl Opt 27 2502ndash2509

Tso H C W Geldart D J andChylek P

1998 Anharmonicity and cross section for absorption of radiation bywater dimer J Chem Phys 108 5319ndash5329

Vaida V and Headrick J E 2000 Physicochemical properties of hydrated complexes in the earthrsquosatmosphere J Phys Chem A 104 5101ndash5412

Vaida V Daniel J SKjaergaard H G Goss L Mand Tuck A F

2001 Atmospheric absorption of near infrared and visible solar radi-ation by the hydrogen bonded water dimer Q J R MeteorolSoc 127 1627ndash1643


2000 4000 6000 8000 10000 12000 14000

10-6

10-5

10-4

10-3

10-2

10-1

100

101

102

Opt

ica

l dep

th HITRAN v11 with CKD-24 Dimer Low and Kjaergaard (1999) Dimer Schofield and Kjaergaard (2003) CKD-24 only

Wavenumber (cm-1)

Figure 1 Optical depth of the water monomer including CKD-24 continuum two recent theoretical estimatesfor the water dimer and CKD-24 self-broadening continuum separately for optical path length 10 m purewater vapour pressure 15 hPa and T = 293 K The dimer absorption band half-width at half maximum =25 cmminus1 (Lorentzian profile) and the dimerization equilibrium constant Keq = 0041 atmminus1 are used for the

dimer calculation

the water dimerization equilibrium constant Keq that defines WD amount for a givenWM amount the value of WD radiative absorption could even be two to three timeshigher

Finally WD has also been discussed as a possible component of the self-broadeningpart of the water vapour continuum (Penner and Varanasi 1967 Devir et al 1994) Thesimilarity in the self-broadened continuum absorption and the calculated one due to WDcan be seen in Fig 1 here the optical depth of the CKD-24 (CloughndashKneizysndashDavies)water continuum model (Mlawer et al 1999) as well as the total WM absorbance ispresented together with WDrsquos optical depth for the spectral region 1000ndash15 000 cmminus1The latest calculations by Schofield and Kjaergaard (2003) of WD fundamental andovertone OH-stretching and HOH-bending vibrational transition frequencies and in-tensities were used to simulate the WD absorption The WD band half-width at half-maximum (HWHM) was chosen to be 25 cmminus1 for all WD bands together with theassumption that the wings are Lorentzian The Curtiss et al (1979) WDrsquos enthalpy andentropy parameters (H =minus359 kcal molminus1 S =minus1859 cal Kminus1molminus1) were usedto calculate Keq

Keq = exp(SR minusHRT) (1)

where R is the universal gas constant and T is temperature It is worth mentioning thatthe temperature dependence Keq(T ) is very similar to that for water CKD continuumMoreover the self-broadened water vapour continuum has the same quadratic depen-dence on WM partial pressure pWM as the WD

pWD =Keq middot p2WM (2)















1 98 342 974 003 (SPAC2)

2 20 299 128 00068 (LPAC3)3 20 297 029 00068

























000

002

004

006

008

-002

000

002

5000 5100 5200 5300 5400 5500 5600000

002

(a)O

ptic

al d

ep

th


5 points smoothing

(b)

(c)

Wavenumber (cm-1)










51193 51194 51195 51196 5119700

01

02

03

04

54752 54753 54754 54755 54756 5475700

10

20

(a)O

ptic

al d

ep

th


(b)

Wavenumber (cm-1)
















5000 5100 5200 5300 5400 5500 5600

000

005

010



CKD-24 continuum

Opt

ical

dep

th

5000 5100 5200 5300 5400 5500 5600

000

005

010



CKD-24 continuum

Wavenumber (cm-1)

Opt

ical

dep

th














5000 5100 5200 5300 5400 5500 5600

000

005

010


Dimer Keq



Opt

ical

dep

th

5000 5100 5200 5300 5400 5500 5600

000

005

010




Wavenumber (cm-1)

Op

tical

de

pth


(b) respectively





280 300 320 340 360 380 400000

002

004

006

008

Ke

q (

atm

-1)


T (K)







-80 -60 -40 -20 0 20 40 60 80

0

1

2

3

4



Wa

ter

dim

er

abso

rptio

n (

W m

-2)

Latitude (degree)











2000 4000 6000 8000 10000 12000 14000 160000000

0005

0010

0015

Flu

x (W

m-2

cm-1

)

Wavenumber (cm-1)


0

1

2

3

4

5

6

7

8

9


Cu

mulative

WD

abso

rption

(W m

-2)


constant Keq

1000

800

600

400

200

0

00 05 10 15 20


Pre

ssur

e (

mb)







4 CONCLUSIONS





ACKNOWLEDGEMENTS


REFERENCES
























































































1 98 342 974 003 (SPAC2)

2 20 299 128 00068 (LPAC3)3 20 297 029 00068

























000

002

004

006

008

-002

000

002

5000 5100 5200 5300 5400 5500 5600000

002

(a)O

ptic

al d

ep

th


5 points smoothing

(b)

(c)

Wavenumber (cm-1)










51193 51194 51195 51196 5119700

01

02

03

04

54752 54753 54754 54755 54756 5475700

10

20

(a)O

ptic

al d

ep

th


(b)

Wavenumber (cm-1)
















5000 5100 5200 5300 5400 5500 5600

000

005

010



CKD-24 continuum

Opt

ical

dep

th

5000 5100 5200 5300 5400 5500 5600

000

005

010



CKD-24 continuum

Wavenumber (cm-1)

Opt

ical

dep

th














5000 5100 5200 5300 5400 5500 5600

000

005

010


Dimer Keq



Opt

ical

dep

th

5000 5100 5200 5300 5400 5500 5600

000

005

010




Wavenumber (cm-1)

Op

tical

de

pth


(b) respectively





280 300 320 340 360 380 400000

002

004

006

008

Ke

q (

atm

-1)


T (K)







-80 -60 -40 -20 0 20 40 60 80

0

1

2

3

4



Wa

ter

dim

er

abso

rptio

n (

W m

-2)

Latitude (degree)











2000 4000 6000 8000 10000 12000 14000 160000000

0005

0010

0015

Flu

x (W

m-2

cm-1

)

Wavenumber (cm-1)


0

1

2

3

4

5

6

7

8

9


Cu

mulative

WD

abso

rption

(W m

-2)


constant Keq

1000

800

600

400

200

0

00 05 10 15 20


Pre

ssur

e (

mb)







4 CONCLUSIONS





ACKNOWLEDGEMENTS


REFERENCES














































































1 98 342 974 003 (SPAC2)

2 20 299 128 00068 (LPAC3)3 20 297 029 00068

























000

002

004

006

008

-002

000

002

5000 5100 5200 5300 5400 5500 5600000

002

(a)O

ptic

al d

ep

th


5 points smoothing

(b)

(c)

Wavenumber (cm-1)










51193 51194 51195 51196 5119700

01

02

03

04

54752 54753 54754 54755 54756 5475700

10

20

(a)O

ptic

al d

ep

th


(b)

Wavenumber (cm-1)
















5000 5100 5200 5300 5400 5500 5600

000

005

010



CKD-24 continuum

Opt

ical

dep

th

5000 5100 5200 5300 5400 5500 5600

000

005

010



CKD-24 continuum

Wavenumber (cm-1)

Opt

ical

dep

th














5000 5100 5200 5300 5400 5500 5600

000

005

010


Dimer Keq



Opt

ical

dep

th

5000 5100 5200 5300 5400 5500 5600

000

005

010




Wavenumber (cm-1)

Op

tical

de

pth


(b) respectively





280 300 320 340 360 380 400000

002

004

006

008

Ke

q (

atm

-1)


T (K)







-80 -60 -40 -20 0 20 40 60 80

0

1

2

3

4



Wa

ter

dim

er

abso

rptio

n (

W m

-2)

Latitude (degree)











2000 4000 6000 8000 10000 12000 14000 160000000

0005

0010

0015

Flu

x (W

m-2

cm-1

)

Wavenumber (cm-1)


0

1

2

3

4

5

6

7

8

9


Cu

mulative

WD

abso

rption

(W m

-2)


constant Keq

1000

800

600

400

200

0

00 05 10 15 20


Pre

ssur

e (

mb)







4 CONCLUSIONS





ACKNOWLEDGEMENTS


REFERENCES




























































































000

002

004

006

008

-002

000

002

5000 5100 5200 5300 5400 5500 5600000

002

(a)O

ptic

al d

ep

th


5 points smoothing

(b)

(c)

Wavenumber (cm-1)










51193 51194 51195 51196 5119700

01

02

03

04

54752 54753 54754 54755 54756 5475700

10

20

(a)O

ptic

al d

ep

th


(b)

Wavenumber (cm-1)
















5000 5100 5200 5300 5400 5500 5600

000

005

010



CKD-24 continuum

Opt

ical

dep

th

5000 5100 5200 5300 5400 5500 5600

000

005

010



CKD-24 continuum

Wavenumber (cm-1)

Opt

ical

dep

th














5000 5100 5200 5300 5400 5500 5600

000

005

010


Dimer Keq



Opt

ical

dep

th

5000 5100 5200 5300 5400 5500 5600

000

005

010




Wavenumber (cm-1)

Op

tical

de

pth


(b) respectively





280 300 320 340 360 380 400000

002

004

006

008

Ke

q (

atm

-1)


T (K)







-80 -60 -40 -20 0 20 40 60 80

0

1

2

3

4



Wa

ter

dim

er

abso

rptio

n (

W m

-2)

Latitude (degree)











2000 4000 6000 8000 10000 12000 14000 160000000

0005

0010

0015

Flu

x (W

m-2

cm-1

)

Wavenumber (cm-1)


0

1

2

3

4

5

6

7

8

9


Cu

mulative

WD

abso

rption

(W m

-2)


constant Keq

1000

800

600

400

200

0

00 05 10 15 20


Pre

ssur

e (

mb)







4 CONCLUSIONS





ACKNOWLEDGEMENTS


REFERENCES











































































000

002

004

006

008

-002

000

002

5000 5100 5200 5300 5400 5500 5600000

002

(a)O

ptic

al d

ep

th


5 points smoothing

(b)

(c)

Wavenumber (cm-1)










51193 51194 51195 51196 5119700

01

02

03

04

54752 54753 54754 54755 54756 5475700

10

20

(a)O

ptic

al d

ep

th


(b)

Wavenumber (cm-1)
















5000 5100 5200 5300 5400 5500 5600

000

005

010



CKD-24 continuum

Opt

ical

dep

th

5000 5100 5200 5300 5400 5500 5600

000

005

010



CKD-24 continuum

Wavenumber (cm-1)

Opt

ical

dep

th














5000 5100 5200 5300 5400 5500 5600

000

005

010


Dimer Keq



Opt

ical

dep

th

5000 5100 5200 5300 5400 5500 5600

000

005

010




Wavenumber (cm-1)

Op

tical

de

pth


(b) respectively





280 300 320 340 360 380 400000

002

004

006

008

Ke

q (

atm

-1)


T (K)







-80 -60 -40 -20 0 20 40 60 80

0

1

2

3

4



Wa

ter

dim

er

abso

rptio

n (

W m

-2)

Latitude (degree)











2000 4000 6000 8000 10000 12000 14000 160000000

0005

0010

0015

Flu

x (W

m-2

cm-1

)

Wavenumber (cm-1)


0

1

2

3

4

5

6

7

8

9


Cu

mulative

WD

abso

rption

(W m

-2)


constant Keq

1000

800

600

400

200

0

00 05 10 15 20


Pre

ssur

e (

mb)







4 CONCLUSIONS





ACKNOWLEDGEMENTS


REFERENCES











































































51193 51194 51195 51196 5119700

01

02

03

04

54752 54753 54754 54755 54756 5475700

10

20

(a)O

ptic

al d

ep

th


(b)

Wavenumber (cm-1)
















5000 5100 5200 5300 5400 5500 5600

000

005

010



CKD-24 continuum

Opt

ical

dep

th

5000 5100 5200 5300 5400 5500 5600

000

005

010



CKD-24 continuum

Wavenumber (cm-1)

Opt

ical

dep

th














5000 5100 5200 5300 5400 5500 5600

000

005

010


Dimer Keq



Opt

ical

dep

th

5000 5100 5200 5300 5400 5500 5600

000

005

010




Wavenumber (cm-1)

Op

tical

de

pth


(b) respectively





280 300 320 340 360 380 400000

002

004

006

008

Ke

q (

atm

-1)


T (K)







-80 -60 -40 -20 0 20 40 60 80

0

1

2

3

4



Wa

ter

dim

er

abso

rptio

n (

W m

-2)

Latitude (degree)











2000 4000 6000 8000 10000 12000 14000 160000000

0005

0010

0015

Flu

x (W

m-2

cm-1

)

Wavenumber (cm-1)


0

1

2

3

4

5

6

7

8

9


Cu

mulative

WD

abso

rption

(W m

-2)


constant Keq

1000

800

600

400

200

0

00 05 10 15 20


Pre

ssur

e (

mb)







4 CONCLUSIONS





ACKNOWLEDGEMENTS


REFERENCES




















































































5000 5100 5200 5300 5400 5500 5600

000

005

010



CKD-24 continuum

Opt

ical

dep

th

5000 5100 5200 5300 5400 5500 5600

000

005

010



CKD-24 continuum

Wavenumber (cm-1)

Opt

ical

dep

th














5000 5100 5200 5300 5400 5500 5600

000

005

010


Dimer Keq



Opt

ical

dep

th

5000 5100 5200 5300 5400 5500 5600

000

005

010




Wavenumber (cm-1)

Op

tical

de

pth


(b) respectively





280 300 320 340 360 380 400000

002

004

006

008

Ke

q (

atm

-1)


T (K)







-80 -60 -40 -20 0 20 40 60 80

0

1

2

3

4



Wa

ter

dim

er

abso

rptio

n (

W m

-2)

Latitude (degree)











2000 4000 6000 8000 10000 12000 14000 160000000

0005

0010

0015

Flu

x (W

m-2

cm-1

)

Wavenumber (cm-1)


0

1

2

3

4

5

6

7

8

9


Cu

mulative

WD

abso

rption

(W m

-2)


constant Keq

1000

800

600

400

200

0

00 05 10 15 20


Pre

ssur

e (

mb)







4 CONCLUSIONS





ACKNOWLEDGEMENTS


REFERENCES











































































5000 5100 5200 5300 5400 5500 5600

000

005

010



CKD-24 continuum

Opt

ical

dep

th

5000 5100 5200 5300 5400 5500 5600

000

005

010



CKD-24 continuum

Wavenumber (cm-1)

Opt

ical

dep

th














5000 5100 5200 5300 5400 5500 5600

000

005

010


Dimer Keq



Opt

ical

dep

th

5000 5100 5200 5300 5400 5500 5600

000

005

010




Wavenumber (cm-1)

Op

tical

de

pth


(b) respectively





280 300 320 340 360 380 400000

002

004

006

008

Ke

q (

atm

-1)


T (K)







-80 -60 -40 -20 0 20 40 60 80

0

1

2

3

4



Wa

ter

dim

er

abso

rptio

n (

W m

-2)

Latitude (degree)











2000 4000 6000 8000 10000 12000 14000 160000000

0005

0010

0015

Flu

x (W

m-2

cm-1

)

Wavenumber (cm-1)


0

1

2

3

4

5

6

7

8

9


Cu

mulative

WD

abso

rption

(W m

-2)


constant Keq

1000

800

600

400

200

0

00 05 10 15 20


Pre

ssur

e (

mb)







4 CONCLUSIONS





ACKNOWLEDGEMENTS


REFERENCES




















































































5000 5100 5200 5300 5400 5500 5600

000

005

010


Dimer Keq



Opt

ical

dep

th

5000 5100 5200 5300 5400 5500 5600

000

005

010




Wavenumber (cm-1)

Op

tical

de

pth


(b) respectively





280 300 320 340 360 380 400000

002

004

006

008

Ke

q (

atm

-1)


T (K)







-80 -60 -40 -20 0 20 40 60 80

0

1

2

3

4



Wa

ter

dim

er

abso

rptio

n (

W m

-2)

Latitude (degree)











2000 4000 6000 8000 10000 12000 14000 160000000

0005

0010

0015

Flu

x (W

m-2

cm-1

)

Wavenumber (cm-1)


0

1

2

3

4

5

6

7

8

9


Cu

mulative

WD

abso

rption

(W m

-2)


constant Keq

1000

800

600

400

200

0

00 05 10 15 20


Pre

ssur

e (

mb)







4 CONCLUSIONS





ACKNOWLEDGEMENTS


REFERENCES











































































5000 5100 5200 5300 5400 5500 5600

000

005

010


Dimer Keq



Opt

ical

dep

th

5000 5100 5200 5300 5400 5500 5600

000

005

010




Wavenumber (cm-1)

Op

tical

de

pth


(b) respectively





280 300 320 340 360 380 400000

002

004

006

008

Ke

q (

atm

-1)


T (K)







-80 -60 -40 -20 0 20 40 60 80

0

1

2

3

4



Wa

ter

dim

er

abso

rptio

n (

W m

-2)

Latitude (degree)











2000 4000 6000 8000 10000 12000 14000 160000000

0005

0010

0015

Flu

x (W

m-2

cm-1

)

Wavenumber (cm-1)


0

1

2

3

4

5

6

7

8

9


Cu

mulative

WD

abso

rption

(W m

-2)


constant Keq

1000

800

600

400

200

0

00 05 10 15 20


Pre

ssur

e (

mb)







4 CONCLUSIONS





ACKNOWLEDGEMENTS


REFERENCES











































































280 300 320 340 360 380 400000

002

004

006

008

Ke

q (

atm

-1)


T (K)







-80 -60 -40 -20 0 20 40 60 80

0

1

2

3

4



Wa

ter

dim

er

abso

rptio

n (

W m

-2)

Latitude (degree)











2000 4000 6000 8000 10000 12000 14000 160000000

0005

0010

0015

Flu

x (W

m-2

cm-1

)

Wavenumber (cm-1)


0

1

2

3

4

5

6

7

8

9


Cu

mulative

WD

abso

rption

(W m

-2)


constant Keq

1000

800

600

400

200

0

00 05 10 15 20


Pre

ssur

e (

mb)







4 CONCLUSIONS





ACKNOWLEDGEMENTS


REFERENCES











































































-80 -60 -40 -20 0 20 40 60 80

0

1

2

3

4



Wa

ter

dim

er

abso

rptio

n (

W m

-2)

Latitude (degree)











2000 4000 6000 8000 10000 12000 14000 160000000

0005

0010

0015

Flu

x (W

m-2

cm-1

)

Wavenumber (cm-1)


0

1

2

3

4

5

6

7

8

9


Cu

mulative

WD

abso

rption

(W m

-2)


constant Keq

1000

800

600

400

200

0

00 05 10 15 20


Pre

ssur

e (

mb)







4 CONCLUSIONS





ACKNOWLEDGEMENTS


REFERENCES











































































2000 4000 6000 8000 10000 12000 14000 160000000

0005

0010

0015

Flu

x (W

m-2

cm-1

)

Wavenumber (cm-1)


0

1

2

3

4

5

6

7

8

9


Cu

mulative

WD

abso

rption

(W m

-2)


constant Keq

1000

800

600

400

200

0

00 05 10 15 20


Pre

ssur

e (

mb)







4 CONCLUSIONS





ACKNOWLEDGEMENTS


REFERENCES














































































4 CONCLUSIONS





ACKNOWLEDGEMENTS


REFERENCES











































































ACKNOWLEDGEMENTS


REFERENCES


































































































































Documents

region 5000 5600 cm : Evidence for water dimers