water vapor absorption in the visible and near infrared

Water vapor absorption in the visible and near infrared:results of field measurements

Rodolfo Guzzi and Rolando Rizzi

Measurements of solar irradiance at the ground have been analyzed to obtain information on absorptionfrom water vapor in the visible and near infrared. Great care has been taken in evaluating the aerosol opti-cal thickness to obtain results compatible with theory. An automatic procedure is presented that eliminatesthe recordings in which modifications of the aerosol optical properties not monitored would seriously influ-ence the determination of those of water vapor. Particular care is paid to assessing the error limits of thederived spectral attenuation parameters.

1. Introduction

Measurements of water vapor absorption in thevisible and near infrared have been performed by sev-eral authors using different devices (e.g., monochro-mators, interference filters) both in the laboratory andin the actual atmosphere. Laboratory measurementsare generally not fully compatible with field studiesbecause of the difficulty in constructing path cells longenough and of producing sufficiently high water vaporcontent to simulate real atmospheric conditions.

Howard et al.I measured water vapor band-inte-grated absorption using a long path cell in which thetotal pressure, water vapor, and temperature could bevaried. The results are expressed in terms of two em-pirical relations for weak and strong bands. Burch andGryvnak2 presented high resolution water vaportransmission values in the 0.69-1.98 Am range. Sincethe water content along the path was obtained byheating the sample to 443 K, their results are not easilytransferable to real atmospheres.

Atmospheric attenuation studies started with thework by Fowle3 who analyzed the data at his disposalin terms of water vapor content. His data were subse-quently reprocessed by Eldridge 4 who computed a setof (error function) absorption coefficients and pointedout that the lack of agreement between computed and

Rodolfo Guzzi is with Istituto di Fisica Generale, Ferrara, Italy, andR. Rizzi is with UniversitA degli studi di Bologna, Dipartimento diFisica, 40127 Bologna, Italy.

Received 7 June 1983.0003-6935/84/111853-09$02.00/0.©) 1984 Optical Society of America.

measured transmittances could be due to a concentra-tion of particles of radius >1 um higher than predictedby available model aerosol distributions.

Guzzi, Tomasi, and Vittori5-7 made extensive mea-surements of atmospheric transparency from the visibleto the infrared over several years and in different me-teorological conditions. The amount of precipitablewater along the light path was simultaneously measuredusing an infrared hygrometer. When analyzing the dataobtained in very clear conditions during anticyclonicevents, they found an unexpected increase in spectralattenuation going from morning to noon which couldnot be accounted for by the variation of precipitablewater. This effect was explained (Guzzi et al.5 andVittori et al. 6) in terms of variation of particulate matteroptical properties while water vapor absorption coeffi-cients were presented by Tomasi et al. 7 In the latterpaper it was shown that residual attenuation by watervapor, after elimination of particulate matter effects,was present even in wavelength regions considered mosttransparent. Similar conclusions were reached byFraser.8

More recently Tomasi 9 has reprocessed a subset ofthe data measured by Guzzi, Tomasi, and Vittori todiscriminate between water vapor absorption andwater-dependent particulate-matter attenuation.Seasonal sets of atmospheric optical thicknesses wereselected presenting at each wavelength a linear corre-lation with precipitable water vapor. The dependenceof optical thickness on precipitable water is expressedas the sum of a nonselective absorption coefficient ofatmospheric water vapor and a coefficient expressingthe variation of particulate-matter optical thicknesswith precipitable water. His technique gives absorptioncoefficients smaller than previously reported using thesame set of data. His data are, however, rather coarselyspaced in the wavelength interval.

1 June 1984 / Vol. 23, No. 11 / APPLIED OPTICS 1853

In some of the papers mentioned above the spectraldependence of optical thickness on precipitable wateris assumed to follow a square-root law within the bandswhile, in the so-called windows, a Lambertian law isused. Moskalenko 0 performed a series of laboratorymeasurements using a long path cell. Large thicknessesof water vapor could be obtained in conditions of nullaerosol attenuation. He expressed his transmissiondata using a power dependence of optical thickness onprecipitable water. His results show that no sharpdistinction exists between windows and bands as far asthe precipitable water dependence is concerned, whilethe absorption coefficients changed considerably goingfrom weak to strongly absorbing regions.

Koepke and Quenzel1 performed a single measure-ment of spectral solar irradiance from the ground todetermine the water vapor attenuation coefficient.Instead of using either the weak or strong approxima-tion, they use Moskalenko's data for the dependence ofoptical thickness on precipitable water. They foundno agreement with Moskalenko's spectral attenuationdata at wavelengths smaller than 1 zm.

In light of the previous discussion it is still unclearwhether a Lambertian law is effectively followed bywater vapor absorption in the most transparent regionsof the visible spectrum, and the absolute values of theattenuation coefficients themselves show variations thatcannot be explained solely in terms of experimentalerrors (which are in general not sufficiently defined).This uncertainty is also reflected in the computer codeLOWTRAN. 1 2 In all versions of this computer code,which is widely used in transmission and emissionmodeling, water vapor absorption is reported as beinginsignificant over visible and near-infrared windowregions.

Guzzi et al. 13,14 computed solar spectral irradianceat the ground using the absorption coefficients takenfrom Tomasi et al. 7 and Fraser8 and compared it toexperimental values. They found that the model un-derestimates the measured data and that the mainreason was due to the incorrect parametrization of theaerosol extinction properties, which were accounted forby using the Angstrom formulation.

Rizzi et al.,15 extensively using inversion techniquesto determine aerosol size spectra, found that the aerosoloptical depth must be computed with a standard de-viation of <7% to obtain reliable size distributions.

These and other findings show that the correct esti-mation of water vapor window absorption in the visibleand near infrared is important when dealing with re-mote measurements both from the ground and fromspace not only in atmospheric attenuation studies butalso in all satellite applications where adequate atmo-spheric corrections are needed.

This paper concerns the reduction of the data mea-sured by Guzzi, Tomasi, and Vittori in the visible andnear-infrared regions, some of which have not yet beenprocessed. Our main concerns are to verify whether aLambertian absorption law is applicable to the mosttransparent regions and to check the dependence ofoptical thickness on precipitable water when going from

1000

Rcy a(I-*o)A5o 0.8(H20) QaTH 2 )

Z 500 D

C0.70 080 090 1pO

Fig. 1. Example of strip-chart recording giving deflection of therecorded D (arbitrary units) versus wavelength in microns on 24 Aug.1971. At the beginning of the reading air mass is 1.73, relative hu-midity is 43, screen temperature is 24aC, ground pressure is 1015mbar, and precipitable water is 14-mm (STP). The curve labeled Do

is the extra atmospheric deflection of the instrument.

windows to more strongly absorbing regions. Aspointed out by several authors, problems are encoun-tered when estimating the aerosol optical thickness. Anautomatic method is proposed to eliminate the re-cordings in which modification of the aerosol opticalproperties not monitored would seriously influence thedetermination of those of water vapor. Particular careis taken in evaluating the errors associated with themeasured data to correctly assess the error limits of thederived quantities.

II. Data Set and ReductionData presented in this paper were measured from 22

Sept. to 9 Oct. 1971 at Buda in the Po Valley by Guzzi,Tomasi, and Vittori and partially reported in Refs. 5-7.The computations are made at wavelengths in whichevident relative maxima and minima in the deflectioncurve of the original recordings are found. Althoughthe experimental apparatus was assembled to obtain aresolution of better than 4.7 cm-1 in the spectral rangeconsidered,5 the actual angular velocity of the prismused in the set of measurements presented in this paperallowed us to detect only broad features in the absorp-tion bands. It follows that the computations in thoseregions are done mainly to check the consistency of theresults compared with other reductions.

In Fig. 1 a recording of the solar spectrum between0.65 and 1.10 m is shown as an example of those ana-lyzed in this paper. Since the readings were made ona strip-chart recorder, the first step has been to digitizeall the analog data at our disposal. Simultaneousmeasurements of precipitable water vapor (pwv), per-formed with an infrared hygrometer (Tomasi andGuzzi16 ), are associated with each recording.

Reduction of the data to obtain the total optical pathat wavelength X is made using the Bouger-Lambertlaw

1854 APPLIED OPTICS / Vol. 23, No. 11 / 1 June 1984

l l | | l x T -

DQ() = R(X)Fo(X) exp[-a(Q)]TR(X)Tmg (X)To3 (X),

where D(X) is the recorded deflection; o(X) is the sumof particulate matter (pm) extinction optical path andwater vapor (wv) absorption optical path; TR(X),Tmg(X), and To3(X) are, respectively, the known spectraltransmittances due to molecular scattering, mixedgases, and ozone absorption; FO(X) is the extra atmo-spheric solar irradiance; and R (X) is the electrical re-sponse of the instrumental set.

Do(A) = R(X)Fo(X) has been computed by the Lang-ley plot method, by extrapolating to zero air mass thelogarithm of the deflection D (X) with respect to the airmass. The computation was performed in the mosttransparent regions using a subset of data taken in thefirst hours of the morning, to avoid the effect of in-creasing atmospheric turbidity, for days with a visualrange >20 km. The technique has been described ina previous paper.5 The results obtained for severalclear days have been averaged and the standard devia-tion associated with each Do(X) is found to be ade-quately described by the relation /

1Do = 0.07 Do. In Fig.

1 the curve Do(A) is also drawn.Once the Do are computed the pm and wv optical

path can be determined by (the dependence on wave-length will be omitted from now on for convenience)

aX) = n DoTRToaTmg (1)D

The transmittance functions appearing in Eq. (1)were computed with the computer code LOWTRAN 5using the average value of vertical ozone content mea-sured at Vigna di Valle for the days the measurementswere taken.

A general law describes the optical path of wv as givenby Goody1 7 :

a = ifMW1 + I) 1 (2)

where S is the average line intensity in the spectral in-terval centered at X, a is the mean halfwidth, is themean line spacing, w is the pwv along the vertical, andmw is the air mass computed for a given water vaporvertical distribution.

Equation (2) can be approximated in the cases ofabsorption bands (strong absorption) and absorptionin the windows (weak absorption) by

w = al(MWW)1/2 SwMW >> 1,7ra

as. = a(m.w)Swms

<< 1,7ra

where a, and a2 are absorption coefficients. Theserelations have been used by Gates and Harrop18 tocompute the absorption of water vapor in the near andfar infrared.

Moskalenko10 proposed a more general approxima-tion based on the following power law:

aw = a(wmw)b. (3)

It contains the weak- and strong-line limits and is also

apt for describing cases of intermediate absorption (0.5b < 1).Strictly speaking, the parameters a and b are also a

function of the pwv optical path. In fact a and b areusually determined using a set of data taken on days inwhich the measured pwv lie in a certain range. Thewater vapor transmittance computed using Eqs. (2) and(3) are, in the stated pwv range, in very good agreement.However Eq. (3) does not describe the natural variationof the absorption law from, for example, weak to inter-mediate or from intermediate to strong which is em-bedded in Eq. (2) as pwv content along the path varies.Therefore, the use of the power law is based on theconsideration that in the actual atmosphere and in agiven spectral range the naturally occurring variationsof pwv do not require the use of a water vapor depen-dence of the parameters a and b. Another differencebetween transmittances computed by Eqs. (2) and (3)is that, while the weak- and strong-line limits are con-tained in Goody's formulation, they must be fixed apriori by limiting the value of b when using Eq. (3). AX2 fit performed on some sets of data using Eq. (3) asdistribution to be fitted may lead to values of b outsidethe permissible range. A x2 fit of the same set of datausing the Goody absorption law would not produce suchan evident result although the value of the determinedX2 would induce caution when analyzing the results.This final consideration has led us to use the power-lawdependence to analyze the data to be able at a givenwavelength to eliminate from the set of available re-cordings a subset that eventually would clearly exhibitphysical mechanisms other than water vapor absorp-tion.

The optical path af is therefore written as

= a(wmw)b + Tama, (4)

where ma is the air mass for pm.The aerosol term in Eq. (4) is usually greater than the

wv term in regions of weak absorption and of the sameorder of magnitude in strongly absorbing regions. Aleast-squares fit of the measured data to obtain a, b, andra would almost certainly lead to incorrect results, dueto the great natural variability of the pm optical prop-erties. More information is necessary to eliminate ornormalize the aerosol optical thickness term. In ourcase measurements of the visual range R were alsomade.

Visual range measurements can be used to estimatethe horizontal aerosol extinction coefficient at 0.55 umusing Koschmieder's formula:

/3H(O.55) = 3.912 0.55),R

(5)

where 13m is the extinction coefficient due to molecularscattering. H (0.55) can also be computed:

1H(O.55) = Cn(r)irr2 Qe(0.55)dr = C3N(O.55), (6)

where Qe is the efficiency factor for extinction, n (r) isthe normalized differential aerosol size distribution atradius r, and C is the pm concentration along the path.Therefore ON is the normalized extinction coefficient.


From Eqs. (5) and (6) it is possible to express C as

H(0.55)C = - * (7)/3 N(O.55 )

The optical thickness along a vertical path can becomputed by

TV(X) = f n(r,h) f 7rr2Qedrdh, (8)

where n(r,h) is the height-dependent pm size distri-bution function. Assuming that the size distributionis independent of height, Eq. (8) can be approxi-mated:

T,( ) = CH f n(r)7rr2 Qedr = CHON(X), (9)

where H is the scale height for pm.Inspection of Eqs. (7) and (9) allows us to write

i(XR) H/3H(0.55)N(X)lN(O.55)

The applicability of the preceding relation is certainlylinked to the validity of the simplifying assumptions onthe pm vertical distribution and, above all, on the va-lidity of Eq. (5). Assuming that the Koschmiederrelation holds and that the normalized size distributionand scale height remain unchanged between two vi-sual-range estimations R and R0 we can write the ratioF(R,RO) as

'rvGN,R) O3HF(RR.) r(,R 0) =-

Tv (,Ro,) A (10)

[where A = (3.912/R0) - Om (0.55)] which is indepen-dent of wavelength. When Eq. (10) is verified, at leastpartially, by the experimental data, the measured visualrange can profitably be used to normalize the measuredpm optical thicknesses to some standard conditionsdefined by a reference visual range R,

The following procedure was used to evaluate theapplicability of Eq. (10) to our data set. A set ofwavelengths is defined in which weak or null wv ab-sorption is expected.

The quantity ro(X) = TV(XR0 ) is computed using anunweighted least-squares fit of the measured Ta (X)belonging to all recordings to the curve

G= To(, A RiA o (11)

where Ri is the measured visual range during the ithrecording. The reference visual range R0 = 10 km isselected because it has a value close to the visual rangeduring the experimental period. The set of values T0 (X)constitutes a set of optical information relative to amean pm size distribution. Tm is the molecular opticalthickness.

The dispersion in the window wavelengths of the datapoints around the curve [Eq. (11)] would constitute ameasure of the applicability of the Koschmieder for-mula to our set of data, if the visual range estimationswere free of error (which is certainly not the case).However, the comparative behavior at several wave-lengths allows us also to examine the validity of theassumptions regarding the pm size distribution. Sev-eral cases can be found:

(1) The data points of some recordings are in gen-erally good agreement with the curve [Eq. (11)], thatis,(a) the percentage deviation

iJTa (j)for the ith recording has a mean value Pi of <0.04,computed using all wavelengths;(b) the absolute value Pmaxi of the maximum of thepercentage deviation at all wavelength is <0.15. Theserecordings are retained.

(2) Some recordings show a different behavior: atsome wavelengths Pij > Pmaxi while at others Pij <-Pmaxi. These recordings are rejected since the sizedistributions were certainly inhomogeneous with themean.

(3) In some cases the deviation Pi. is significant(greater in absolute value than Pmaxi) but either sys-tematically positive or negative at all wavelengths. Thevisual-range value for the latter recording is modifiedto agree with the average spectral properties using

1 MRavi jRi

where

3.912

A [+ Ta (XJ)]A To(X)

here M is the number of selected wavelengths used tocompute Ravi'

The latter recordings are then examined for accep-tance according to the procedure already outlined incases (1) and (2) above. Out of forty-six available re-cordings the procedure outlined rejected about half ofthe data at each wavelength.

The final visual-range value associated with eachaccepted recording (which will be referred to as the ef-fective visual range Re) is either the measured value forrecordings belonging to case (1) or the arithmetic meancomputed using M specified window wavelengths forrecordings belonging to case (3).

Inspection of our data Ta (Xi) shows that it is notstrictly true that the function F(Re,R0 ) is independentof wavelength. Therefore, two procedures wereadopted to select the window wavelengths to be used tocompute the effective visual range Re for each acceptedrecording: the first (P1) uses all windows to estimateRe; the second (P2) defines three regions in the spectralinterval under consideration, centered around the mainabsorption bands, and three values of Re are computedfor each recording using all windows belonging to eachregion.

Both procedures have been used to check the sensi-tivity of the retrieved parameters and their errors withthe choice of the window wavelengths. Once the ef-fective visual range(s) is (are) computed, the pm opticalthickness can be scaled according to Eq. (10).

Equation (4) can finally be written for any wave-length:


(12) IV. Results and Discussion

here mw is the relative air mass for wm computed usinga mid-latitude winter vertical distribution, ma is therelative air mass for pm computed using a rural plustropospheric aerosol model giving a visual range at theground of 10 km. Parameters a, b, and c are to becomputed using a minimizing technique. The retrievedvalue of c represents the spectral optical thickness of amean pm size distribution leading a visual range of 10km.

111. Minimization Technique

The observations o-i are treated as statistically in-dependent and the expression for x2 takes the form, ateach wavelength,

X2 = i (a- -ai)2

(13)1 2i

where i is the standard deviation associated with eachoi. The i are computed according to the Gaussianformula applied to Eq. (1):

2+1 2+1 1 12 AO =A28 +TR + Y 83+ -2 .m + D2 D,

where u0, A1R, 03, 1,mg, and D are standard deviationsassociated, respectively, with the determination of Do,TR, To,, Tg, D. AO increases quasi-linearly with Do;the errors in transmittance computations are assumedto be equal to 0.005 (i.e., they affect the third significantdigit) while the estimated error in the deflection D is 5mm.

To determine the spectral parameters a, b, and c, thequantity x2 is minimized. The software package usedfor the minimization belongs to the CERN ComputerLibrary.19 Only a brief description will be given of thevarious methods adopted.

The process is started using a Monte Carlo technique.The method by Nelder and Mead follows which is rea-sonably fast when far from the minimum; it also esti-mates the diagonal elements of the covariance matrix(the parameter errors). The algorithm used to find thetrue minimum is Fletcher's switching method based onDavidon, and the Fletcher and Powell algorithm. Thelatter method is extremely fast and stable near theminimum; it estimates the full covariance matrix whichis used as the starting point to compute true positiveand negative errors for each parameter separately tak-ing into account the actual shape of the x2 curve nearthe minimum.

If the function x2 is correctly normalized, that is, theAi are standard deviations, the computed parametererrors are one standard deviation error for the param-eters one by one. When the A? cannot be interpretedas true variances but simply as relative weights, theparameter errors resulting from such a fit are propor-tional to the unknown overall normalization factor.

On the basis of previous discussions the steps re-quired to determine the absorption parameters are:

(a) Preprocessing. P1 or P2 is used to compute Refor all accepted recordings. Trial minimizations areattempted at a few window wavelengths to checkwhether parameter b is within physical bounds (0.5 <b < 1). When b lies outside the range by more than onestandard deviation the minimization is attempted aftereliminating the recordings one by one, starting with onetaken at the lowest visual range until b is within per-missible bounds.

(b) Processing. P1 or P2 is used to determine Reand minimization is performed at all wavelengths.

During preprocessing, all the data recorded at visualranges <7 km were rejected. The result is not depen-dent on the previous Re computation since it was ob-tained using both P1 and P2.

The final processing of the data was performed sev-eral times to investigate the effect of different hypoth-eses on the final results. In particular, attention waspaid to the aerosol normalization in the 10-km visualrange procedure and to the effect of different error es-timates on parameter value and derived parameter er-rors.

Some features were common to all the derived solu-tions. Regions of null absorption are clearly foundquite independently from the determination of Re.Absorption coefficients in strongly absorbing regionsare only slightly affected by the aforementioned choice.Some variations are observed in the value of the b pa-rameter when P1 or P2 is used. In all cases, however,the results are compatible since they are within onestandard deviation of the final results. The latter areobtained using P2. The window wavelengths used forthe determination of Re are [the wavelength number(wn) of Table I is used to identify the wavelengths]

(1) a band: 1 <wn < 10; window wn: 1,3,4,5,11,12.

(2) 0.8 um band: 11 <wn < 25; window wn: 11,12,26, 27, 28, 29, 30.

(3) poT band: 26 <wn <46; window wn: 26,27,28,*29, 30, 42, 43, 44, 45, 46.

In some computations, previously determined wvabsorption coefficients in the windows were used toimprove the values of Ta (X) from Eq. (4). These lattervalues were used to compute a new set of effective vi-sual-range values, using the procedure already outlined.The new minimization performed at all wavelengthsproduced wv absorption coefficients that lie within theerror limits specified in Table I where a complete set ofresults is shown. The parameter a is expressed in unitsof cm-b. The parameter errors Aa and Ab are thelargest of the reduced positive and negative errorscomputed at each wavelength. The statistical approachused in computing the latter quantities is outlined in theAppendix.

In Figs. 2-4 transmittance computed using presentdata and LOWTRAN 5 are compared. The equivalentsea-level absorber amount is 2.76 cm (a slant path from


,Y,�i = a(WiMwi)b + cF(R,,iR.)m.i;

Table 1. Parameters a and b and the Associated Errors are Written with a Number of Digits Which Exceeds by One the Number of Significant Digits

wn M(m) v(cm-') a Aa b Ab

123456789

10111213141516171819202122232425262728293031323334353637383940414243444546

0.68210.69740.70100.70620.71250.71940.72070.72330.72890.74470.74570.75610.77340.77760.78250.79180.80000.80710.81630.82200.82300.82610.82920.84180.84890.85030.87640.88070.88570.89050.90010.90380.90740.91120.91370.92000.93500.93980.94430.96900.97370.97801.0051.0301.0431.048

1466114340142651416014035139001387513825137201363013410132251293012860127801263012500123901225012165121501210512060118801178011760114101135511290112301111011065110201097510945108701065010640105901032010270102259950971095909540

0.0370.0240.0340.01910-4

0.1830.0310.1070.083

l0-40.0020.0020.0160.0410.0340.0410.0380.0770.2410.1710.2530.1420.1800.0980.0640.0090.0030.00050.00210-4

0.1560.0920.1970.1830.2180.0990.8260.5220.6540.1750.22010-410-410-4l0-4

0.002

0.0120.0100.0070.0060.0060.0320.0100.0160.0160.0050.0140.0100.0100.0110.0110.0140.0100.0140.0170.0150.0130.0120.0140.0220.0100.0110.0090.0090.0090.0180.0340.0160.0200.0160.0380.0170.0490.0160.0280.0420.0440.0050.0060.0050.0040.006

0.891.00.8661.0

0.501.000.720.90

1.001.001.001.001.001.001.000.670.6250.5820.5340.6010.5220.470.501.01.01.01.0

0.650.690.6150.6700.490.670.5000.6840.5350.500.50

1.0

0.160.130.0830.088

0.200.150.130.17

0.370.210.260.230.220.240.190.170.0630.0820.0470.0890.0740.200.130.210.210.160.15

0.180.160.0820.0720.150.140.0110.0250.0390.140.11

0.18

ground to space at a zenith angle of 65° using a mid-latitude winter wv model).

The agreement between the plotted data is quitesatisfactory in the and poT bands, once account istaken of the difference in spectral resolution betweenthe two sets of data. Transmittances in the 0.8-Mmband computed with our coefficients are consistentlysmaller than LOWTRAN'S.

Regions of complete transparency to wv are found atwn = 5, 10, and 42-45. At some spectral ranges (wn =11, 12, 26-29, and 46) the absorption coefficient a isclose to zero and the associated error is greater than theparameter value itself so that these regions can be re-garded as completely transparent. Absorption in thewindow is evident at wn = 1-4 and 13-17, and differ-ences between our results and those of Tomasi et al. 7and Tomasi9 are within the error limits. The increasein the coefficients around 0.70 Am is similar to that

observed in Tomasi et al. 7 The value of b is close to 1except at wn = 3 in which a slight departure from theLambertian law is found.

The variation of the parameter b is evident goingfrom regions of weak to strong absorption.

As noted in Sec. I, Moskalenko 1 0 has found, in therange of our interest, a value of b = 0.53 and Koepke andQuenzel"l have determined their absorption coefficientsusing the same value of b. This means that a graphicalcomparison between our data and those of Koepke andQuenzel would need a different set of transmittancecomputations at varying optical depths to be made andplotted. The information content of such plots is cer-tainly less than a direct inspection of Table I of theKoepke and Quenzel paper.

The main differences are found around 0.735,4m inwhich no absorption is evident in our recordings, in theregion from 0.77 to 0.79 Am at which absorption is found


100

(%1

008 0 A (YM

14000 13000v(cn-'

Fig. 2. Water vapor transmittivity in percent vs wave number v(aband). Precipitable water is 50-mm (STP). The dashed line is thetransmittivity computed using the data in Table I. For comparison

transmissivity computed using LOWTRAN 5 is drawn.

Fig. 3. Same as Fig. 2 for the 0.8 H2 0 band.

50

11000 10000v (crrf')

Fig. 4. Same as Fig. 2 for the par H2 0 band.

in our data, and at wavelengths around 0.980 Am whichis transparent in our computation.

The retrieved values of c are drawn in Fig. 5. Thevalues used to normalize the aerosol contribution areshown in the same figure. The two sets of values com-puted with different procedures are in good agreement.A weighted least-squares fit has been applied to the cvalues, assuming the relationship c = fX-a to find 3 anda. The values obtained are = 0.26 and a = 0.76.

The x2 minimization using all accepted recordingshas been performed, with Goody's model as the fittingfunction, at wavelengths wn = 32 and 35, which arecharacterized, respectively, by medium and strong ab-sorption:

Fig. 5. Retrieved values of c (dots) as a function of wavelengths Xand associated one standard deviation. Mean (relative to 10-km vi-sual range) particulate-matter optical thickness To is also drawn

(triangles).

005

0.0

0.15

0.1 1 10w(cm STP)

Fig. 6. Relative transmissivity T as a function of water vaporcontent at wn = 32 and 35.

2 [a- Plimwi (I + p2Wimwj)-" 2 ]2i 2

where p1 and P2 are defined by inspection of Eq. (2). InFig. 6 the quantity

T Tm (X) - Tg(X)Tg (X)

is plotted, where Tg and Tm are transmissivities com-puted with the optical path given by Eqs. (2) and (3).Since the wv optical path in our recordings ranges be-tween a minimum of 0.9 and a maximum of 4.7 cm, thevalue of Tp in that region is smaller than 0.015. Withinthe interval from 1 to 15 cm, which covers most valuesnormally encountered-in the atmosphere (Fig. 6), themaximum value of Tp for the strong region is 0.035; in


. I . I . . . . . I II--

- ' -1;--I X '--

I . . I I I . . , 1, I , . . , . . .

0.4

TO

0.3

0.21-

I I I I I_0.1 5000 13000 11000 v(cm')

,..,i�, I

0,7

I I I . I 1 111 . . ...... ...... .. . .

0,70

the region of intermediate absorption the discrepancybetween Tm and Tg increases reaching a value of Tp =-0.09 with an optical path of 15 cm [Tg (15 cm) =0.603].

We wish to add some information on unexpectedabsorption which is clearly evident in all the recordingsin the ranges 11,770-11,680 and 11,550-11,470 cm-.No dependence on wv is found in the two regions but,as seen in Fig. 3, the absorption is relevant and cannotbe attributed to liquid water absorption since it is alsoevident in recordings taken at the visual range >20km.

The data at our disposal do not allow us to assesswhether the weak absorption in the windows is a con-tinuum caused by accumulated contribution by distantstrong absorption lines. However, the region of nearlycomplete transparency found at wn = 5-10 indicatesthat the eventual continuum may not extend at wave-lengths smaller than 0.74 m (nothing can be said aboutthe wavelength range smaller than 0.68 m). The com-puted value for wn = 30 is affected by a large error andno conclusions can be drawn in this respect.

V. Conclusions

A set of measurements of spectral extinction of solarradiation is analyzed to determine the magnitude andassociated error of the water vapor absorption coeffi-cients in the range from 0.68 to 1.05 Am.

A power-law relationship describes the dependenceof the optical path on water vapor content along thepath.

The role of particulate matter in extinguishing solarradiation is relevant. Instead of trying to eliminate,from the measured optical paths, the contribution dueto aerosol, the latter is described in terms of mean par-ticulate matter conditions. In this way, recordings areeliminated in which the aerosol optical properties aresensibly different from the means and would seriouslyinfluence the determination of those of water vapor.

The water vapor absorption coefficients, the meanaerosol optical depth, and associated estimated trueerrors are computed using a weighted least-squaresfit.

The procedure adopted to determine mean opticalproperties has been found to be quite successful; alsothe retrieved parameters show weak dependence onaerosol normalization. The proposed methodologyappears to be applicable to any spectral measurementin real atmospheres.

Appendix

If Eq. (12) in the text is a good description of thephenomena under study and if the error estimates areclose to the real values, the computed minimum valueof X2 at any wavelength must be close to the number ofdegrees of freedom v, which can be computed once thenumber of experimental points and the type of functionto be minimized are known.

It is found that the value of the reduced x2,

Xv = X2/v,

ranges from a minimum of 0.80 to a maximum of 1.30.In general there is a decrease of x2 as X increases.Taking S as the variance of the fit and Mi as variancesassociated with the data, the reduced x2 can be ex-pressed by

2=eX = ,xv -,

1

1 E 1

The M are characteristic of the dispersion of the dataaround the parent distribution and are not descriptiveof the fit. The estimated variance of the fit S2 , however,is characteristic of both the spread of the data pointsand the accuracy of the fit. Since the fitting functionis considered a good approximation to the parentfunction, the values of x2 can be interpreted as beingcaused mainly by the somewhat incomplete specifica-tion of the errors entering into the computation of Mi.

Therefore, it is possible to obtain an estimate of awavelength-dependent overall normalization factor fjfor the experimental error at any wavelength which isfound to be

1-i = Jgi, f = aXj

at any wavelength. The term fj ranges, therefore, be-tween a maximum value of 1.14 and a minimum of0.89.

The final parameter errors, which will be called re-duced errors, are obtained by multiplying by fj thosecomputed during the fit. The correctness of this pro-cedure depends on the assumption that the fittingfunction is a good approximation to the parent one.This hypothesis can be tested by doing a minimizationusing the normalized data error estimates M'. Thesetests showed that the parameter values agree (as ex-pected) to three significant digits with that computedusing the original variance estimates; there is also a twosignificant digit agreement between the reduced pa-rameter errors (from the first fit) and the parametererrors coming put of the fit using the normalized errors

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3. F. E. Fowle, "The Transparency of Aqueous Vapour," Astrophys.J. 42, 394 (1915).

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5. R. Guzzi, C. Tomasi, and 0. Vittori, "Evidence of ParticolateExtinction in the Near Infrared Spectrum of the Sun," J. Atmos.Sci. 29, 517 (1972).

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7. C. Tomasi, R. Guzzi, and 0. Vittori, "A Search for the e-effect inthe Atmospheric Water Vapor Continuum," J. Atmos. Sci. 31,255(1974).


8. R. S. Fraser, "Degree of Interdependence among AtmosphericOptical Thicknesses in Spectral Bands between 0.36-2.4 ,um,"J. Appl. Meteorol. 14, 1187 (1975).

9. C. Tomasi, "Non Selective Absorption by Atmospheric WaterVapour at Visible and Near Infrared Wavelengths," Q. J. R.Meteorol. Soc. 105, 1027 (1979).

10. N. L. Moskalenko, "The Spectral Transmission Function in theBands of Water Vapor, 03, N20 and N2 Atmospheric Compo-nents," Izv. Akad. Nauk SSSR Fiz. Atmos. Okeana 5, 678 (1969),english edition.

11. P. Koepke and H. Quenzel, "Water Vapor: Spectral Transmis-sion at Wavelengths Between 0.7 gm and 1 gm," Appl. Opt. 17,2114 (1978).

*12. F. X. Kneizys, E. P. Shettle, W. 0. Gallery, J. H. Chetwind, L. W.Abrew, J. E. A. Selby, R. W. Fenn, and R. A. McClatchey, "At-mospheric Transmittance/Radiance: Computer Code LOWTRAN5," AFGL-TR-80-0067 (1980).

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16. C. Tomasi and R. Guzzi, "High Precision Atmospheric Hy-grometry using the Solar Infrared Spectrum," J. Phys. E 7, 647(1974).

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19. F. James and M. Ross, MINUIT, CERN Computer Center, DataHandling Division, Geneve (1977).

20-25 Los Angeles Tech. Symp., Los Angeles SPIE, P.O. Box10, Bellingham, Wash. 98227

22-30 Telecineradiotechniques '85, Moscow Telecineradi-otechniques, Expocentr, Sokolnicheski val 1-a, Mos-cow, 107113, USSR

February

4-6 Microphysics of Surfaces, Beams, & Adsorbates, OSATop. Mtg., Santa Fe OSA, Mtgs. Dept., 1816 Jeffer-son Pl., N. W., Wash., D.C. 20036

11-13 Optical Fiber Communication, OSA Top. Mtg., SanDiego OSA, 1816 Jefferson P1., N. W., Wash., D.C.20036

March

? NSF Regional Conf.: Mathematical Ecology, U. Calif.,Davis NSF, Math. Sciences, Wash., D.C. 20550

4-8 Southwest Conf. on Optics, Los Alamos S. Stotlar, P.O.Box 573, Los Alamos, New Mexico 87544

10-15 Microlithography Santa Clara Conf., Santa Clara SPIE,P.O. Box 10, Bellingham, Wash. 98227

18-20 Optical Computing, OSA Top. Mtg., Lake TahoeOSA, Mtgs. Dept., 1816 Jefferson Pl., N.W., Wash.,D.C. 20036

18-22 WINTER '85 Tech. Mtg., Lake Tahoe OSA, Mtgs.Dept., 1816 Jefferson P., N.W., Wash., D.C. 20036

19-20 Non-Invasive Assessment of Visual Function, OSATop. Mtg., Lake Tahoe OSA, Mtgs. Dept., 1816 Jef-ferson Pl., N. W., Wash., D.C. 20036

20-22 Machine Vision, OSA Top. Mtg., Lake Tahoe OSA,Mtgs. Dept., 1816 Jefferson P., N. W. Wash., D.C.20036

April

8-12 Optical & Electro-Optical Eng. Symp., Arlington SPIE,P.O. Box 10, Bellingham, Wash. 98227

15-18 Materials Res. Soc. Spring Mtg., San Francisco Mate-rials Res. Soc., 9800 McKnight Rd., Suite 327, Pitts-burgh, Pa. 15237

Meetings Calendar continued from page 1843

1985

January

7-11 NSF Regional Conf.: Multivariate Estimation: ASynthesis of Bayesian & Frequentist Approaches, U.Florida, Gainesville NSF, Math. Sciences, Wash.,D.C. 20550

15-18 Optical Remote Sensing of the Atmosphere, OSATop. Mtg., Lake Tahoe OSA, Mtgs. Dept., 1816 Jef-ferson P., N. W., Wash., D.C. 20036

15-19 2nd European Conf. on Atomic & Molecular Physics,Amsterdam L. Roos, FOM Inst. for Atomic & Mo-lecular Physics, Kruislaan 407, NL-1098 SJ Amster-dam, The Netherlands

May

21-24 OSA/IEEE Lasers & Electro-Optics Conf., BaltimoreMtgs. Dir., OSA, 1816 Jefferson P., N. W., Wash., D. C.20036

continued on page 1880


water vapor absorption in the visible and near infrared

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