Measurement of the integrated water vapor content in theatmosphere by a radiometric method

E. Raz, Adam D. Devir, A. Ben-Shalom, Uri P. Oppenheim, and Stephen G. Lipson

An improved version of a two-wavelength radiometric method is described by which the total water vaporamount along an optical path may be determined by the use of a radiometer and a source at the two ends of theoptical path. The method requires two transmission measurements: one at 1.14 m (at the center of anabsorption band) and another at 1.06 gm (an atmospheric window). The spectral transmittance is calculatedusing the FASCODE computer code, convolved with the source, filter, and detector response curves of thetransmissometer. Good agreement (1-7%) is obtained with experimental observations of this quantity as afunction of total water vapor amount. The method was verified for horizontal paths of up to 10 km.

I. Introduction

The amount of water vapor in the atmosphere is animportant parameter in determining atmospherictransmittance in the infrared region. The absorptionof radiation in the 8-14-gm spectral window by watervapor is of special importance, since water vapor is themain absorber of radiation in this region. Knowledgeof the exact amount of water vapor, integrated alongthe optical path, is crucial for calculations of atmo-spheric transmittance. The concentration of watervapor in the atmosphere varies from point to point, sothat measuring the local water vapor density at theends of an optical path does not necessarily representits value along the entire path.

The radiometric method for measuring the integrat-ed water vapor content is based on measuring the ratioof the spectral absorption at two adjacent wavelengths,one of which is located at the center of an absorptionband and the other outside it. Measurements by thismethod were carried out previously by our group atthe Technionl using a wide filter centered at the1.14-gim absorption band and a narrow filter at 1.06 gtmoutside the band. A radiation source was placed atone end of the optical path and a filter radiometer wasplaced at the other end. Results and a discussion ofthis "transmissometer" were published in detail in

The authors are with Technion-Israel Institute of Technology,Physics Department, Haifa 32000, Israel.

Received 18 June 1986.0003-6935/87/122436-05$02.00/0.© 1987 Optical Society of America.

1981.' Later work done on this subject by other au-thors was based mostly on measurements of scatteredradiation using lidar techniques.2 3 The results pre-sented in these works were obtained from measure-ments made at optical paths of 7-8 km, but at absolutehumidities of -2 g/m3. The results presented herewere made at almost similar optical paths, but at abso-lute humidities of 15-19 g/m3.

This paper reports a continuation and an improve-ment of the method described in our earlier work.'The changes were necessary because the prediction ofthe Goody and LOWTRAN-4 models4 for water vaporabsorption in the 1.14-Am band, on which the methodwas based, did not agree with the measurements. Thefollowing improvements were therefore carried out.

(a) A line-by-line calculation was made to predictthe spectral transmittance of the atmosphere andthese results were convolved with filters centered at1.14 and 1.06 gim. Use was made of the FASCODEcomputer program. This computer code is far moreaccurate than the Goody or LOWTRAN models used inour previous work.' It is important to use this theoret-ical model, and not the predictions of a band model, toget results of high accuracy which can match that ofthe conventional wet and dry bulb measurementsmade at the two ends of the optical path (assuminghomogeneous water vapor content).

(b) A new method of measurement was established,which made the short distance calibration measure-ment obsolete. This new method of measurementincreases the accuracy of the experimental results to ahigher level, which can be matched to the accuracy ofthe theoretical prediction [see (a)]. Moreover, in theprevious method the calibration was dependent on ameasurement of the atmospheric transmittance along

2436 APPLIED OPTICS / Vol. 26, No. 12 / 15 June 1987

an optical path of -0.5-1 km, and in addition integrat-ed water vapor content in this path had to be known.

(c) Automatization of the measuring system en-abled the operator to average out the results and toobtain the integrated water vapor amount while mea-suring.

With the above improvements quantities of watervapor up to a range of 10 km were measured and theresults of the integrated water vapor quantities dif-fered only by 1-7% from those obtained by wet-dryhygrometers situated at the end of the optical path.To check the reliability of the method a comparisonwith a wet-dry hygrometer was made in conditions ofconstant temperature, relative humidity, and pressureand in an area of homogeneous path. The method isapplicable also for a nonhomogeneous path.

11. Method of Measurement

At one end of the optical path of the transmissome-ter we placed an infrared source (usually a blackbody)that emitted radiation chopped at -400 Hz. At theother end of the path we measured the transmittedradiation with a radiometer using filters centered at1.14 and 1.06 gim.

The signal measured by the detector was given bythe expression

S(L,w) = " A f J(v,T) *F(v) *D(v) *T(v,w)dv, (1)

where the integration is carried out over the spectralwidth of the filter AP.

In Eq. (1) the symbols have the following meaning:S(L,w) signal obtained by the radiometer (volt),J(v,T) spectral intensity of the source

[watt/(sr cm-')],r(v) spectral tramsmittance of the atmosphere,F(v) spectral transmittance of the filter centered

at vo,D(v) relative responsivity of the detector,

v wavenumber (cm-1),vo central wavenumber of the filter (cm-'),T temperature (K),L optical path (km),A entrance aperture of the radiometer (cm2),a conversion factor (volt/watt),w integrated water vapor amount (g cm2).

We now define the equivalent transmittance ofwater vapor by

= [J(vT)/J(v 0,T)] . F(v) D(v) - r(v,w)dv (2)

Twv~vosw = fX [J(vT)/J(v 0 ,T)] F(v) D(v)dv

Both numerator and denominator contain the expres-sion f(r,vo) = [J(vT)/J(voT)] - F(v) D(v), which doesnot depend on the absorber amount and is therefore aunique function of v for any combination of source,filter, and detector. The calculation of r' j(vo,w) issimplified by the use of f(v,vo) for each filter.

The expression for r' now reduces to

Wr',(vopw) = f( ,vo) -r(v)dv/f f(vv 0 )dv.

We also define

C(P0 ,T) = S f(v,v 0 )dv, (3)

which, like f(vvo), does not depend on the absorberamount and is a constant for each filter. Consequent-ly, the signal obtained by the radiometer over a dis-tance L is given by

S(L,w) = A J(vPoT) -T(POw)

Tae(voL) C(v0,T)/L 2 . (4)

In this expression we have introduced the transmit-tance of the aerosols at vo, denoted by irae(v0,L). Hereit is assumed that aerosol transmittance is constantover the frequency interval Av in which the filter istransparent. Over very long ranges and in bad visibili-ty conditions this assumption is not valid, and isae(roL)must remain under the integral sign as part of f(v,vo).

In the following discussion the subscript 1 will indi-cate the filter, which is centered at 1.14 gim (8772cm-'), and subscript 2 the filter centered at 1.06 gim(9433 cm-'). The ratio of the signals obtained by thetwo filters over a distance L is given by

S2(Lw) J(v2,T) * Cl(T) - 720 (vj,w) T,(v 2,L)

S2(LXw) J(V2MT *C2(T) * TW,(V2,W) * ra,(V2,L)

Repeating this operation over a distance L = 0, onenotes that rsw(vO) = rae(v,O) = 1. Therefore

(6)R(L,w) rw' ) * T(v (Vw L)

Ro Tw,(V2,W) * a,(V2L)

We now define

rWV,(W) = TWV(VlW)/r'WV(V2,w)

and set E(L,v) = Tae(Vl,L)/Tae(V2,L). It has been shownthat the dependence of E(L,v) on visibility for rural orurban aerosols is approximated by' E(L,v) = exp[5.5 X10-3 (24.743/V - 0.076) L], where V is the visualrange (or the visibility) measured in kilometers. Thisallows Eq. (6) to be written as

r"(w) = R(Lw)I[Ro * E(L,v)]. (8)

It follows that r"(w) may be found experimentallyby making the following measurements: the ratio ofthe signals obtained through the two filters over adistance L, the same ratio at L = 0, the visibility, andthe distance L.

The important advantage of the present methodover the previous one' is that -r"(w) is obtained withouta calibration measurement of the water vapor contentat a shorter distance. The need for this measurementis eliminated by the calibration of the experimentalsystem obtained through the measurement of R0,which is a constant of the instrument for a given pair offilters and is established by a single measurement atthe beginning of the experiment (see Sec. III). Theo-retically, r"(w) is a single-valued function of w andmay be calculated using the FASCODE program. Oncethis theoretical curve is established for a certain pair offilters the experimental value of -r1 (w) may be used toread the integrated amount of water vapor (w) off thecurve. In the present study we first calculated thetheoretical curve of r"(w) and plotted it against w.

15 June 1987 / Vol. 26, No. 12 / APPLIED OPTICS 2437

(7)

WAVELENGTH (MICROMETER)1.110 1.100 1.090 1.080

oZ

2 0.6U,U,

20I-

0.2

08960 9040 9120 9200 9280

WAVENUMBER (cm-')

Fig. 1. Spectral transmittance of part of the 1.14-pm band of H 20vapor; calculated by the FASCODE-1C computer code, for a horizontalpath through the atmosphere. Amount of water vapor, 10 g CM2;

temperature, 300 K; total pressure, 1013 mbar; range, 8 km.

This curve was then compared with a plot of experi-mental values of r(w) against values of w obtainedwith a wet-dry hygrometer. The agreement betweenthe two curves was regarded as proof of the validity ofthe present method. The effect of inhomogeneity ofthe temperature profile along the optical path on thepredicted (theoretical) results is discussed later.

Calculation of r(w) was achieved by taking intoaccount the contributions of all the absorption lines inthe band through the FASCODE program.5 The pro-gram enabled the calculation of spectral transmittancewith essentially infinite resolution. It was run on anIBM 3081 computer, using as input parameters therelevant atmospheric parameters (temperature, totalpressure, relative humidity) and the optical pathlength. A Voigt profile was used for the line shape.The water vapor continuum was taken into account,but aerosols were not included in the calculation. Theprogram allowed convolution of the spectrum withvarious slit functions. For the present study we ranthe program both without convolution (infinite resolu-tion) as well as with a triangular slit function of 5-cm-'HWHM [the spectral transmittance curve of the filterswe used is smooth and yields negligible changes inincrements of 5 cm-' in wavelength, hence the changesin r"(w) as a result of using this slit function are alsonegligible]. The amounts of water vapor varied from0.5 to 40 g cm 2, corresponding to ranges of 0.4-32 kmat 300 K, 1013 mbar, and 48% relative humidity.

Figure 1 shows an example of such a spectrum (with-out convolution) for part of the 1.14-gim water vaporband (other gases contributed negligibly small absorp-tion in this region). It is seen that many individuallines are fully saturated and give 100% absorption.Figure 2, on the other hand, shows the same spectralregion convolved with a triangular scanning func-tion with 5-cm-1 HWHM. The program was run for10 g cm-2 of water vapor, a temperature of 300 K, anda relative humidity of 48%. This corresponds to a pathlength of 8 km.

WAVELENGTH (MICROMETER)1.110 1.100 1.090

z0

2

I-

.0 9120 9200WAVENUMBER (cm-')

1.080

9280

Fig. 2. Spectral transmittance of part of the 1.14 gim band of H 20vapor, calculated by the FASCODE-1C computer code, using a slitfunction of 5 cm-1 . All the other parameters are the same as in Fig.

1.

wU-zi-~I-U,zI-

0 9000WAVENUMBER (cm-')

Fig. 3. Spectral transmittance of the entire 1.14-um H20 vaporband, calculated by the FASCODE-1C computer code using a slitfunction of 5 cm-1 . Temperature, 300 K; total pressure, 1013 mbar;relative humidity, 48%; amounts of water vapor: a, 0.2 g CM-2,

b, 3 g cm- 2 , c, 10 g cm- 2 , and d, 40 g cm- 2 .

Figure 3 shows the entire band with a resolution of 5cm-' for various amounts of water vapor. It is seenthat the selection of the appropriate filter depends onthe water vapor quantities we want to measure, sincethe function -r"(w) depends on the spectral transmit-tance curve of the filter. For small vapor quantities itis recommended to use a narrow filter, Av = 100-200cm-', to obtain high sensitivity located at the center ofthe band, while for large quantities we have two alter-natives: (a) if the large water vapor content is due tohigher absolute humidities, this narrow filter can bemoved into the weaker absorbing part of the watervapor absorption band; (b) however, if this larger watervapor content is due to the larger optical path, use of awider filter is recommended, which includes the entireband (Av - 1300 cm-'), to keep the SNR of the experi-mental system as high as possible. The location of thefilter outside the band (1.06 ,gm) is not critical in bothcases. Figure 4 presents the spectral transmittancefunction v) of a wide filter having its center at 1.14 mwithin the water band and another filter which has its

2438 APPLIED OPTICS / Vol. 26, No. 12 / 15 June 1987

@ e l el w-

C-) 0.8

0- 2 ~

0

0 8500 9000 9500WAVENUMBER (cm-')

Fig. 4. Spectral transmittance of the entire 1.14-,um band of H2 0vapor, calculated by the FASCODE-1C computer code, using theparameters of curve c in Fig. 3 (curve 1); spectral transmittance f(v)

of a filter centered at 1.14 um (curve 2) and of another filter at 1.06um (curve 3). The ordinates of f(v) are in arbitrary units.

center at 1.06 gm outside the band. The function f(r)is presented in arbitrary units. The figure also showsthe spectral transmittance of 10 g cm- 2 of watervapor.

The theoretical transmittance curve of r" (w) vs w fordifferent filters and the present experimental resultsfor r"(w) are shown in Fig. 5. The top curve refers to awide filter used for measuring water vapor quantitiesat large distances (-10 km) whose spectral transmit-tance was shown in Fig. 4, and the lower curve repre-sents a more recently acquired narrow filter with atransmittance of 52% at the center of the spectraltransmittance curve at 8630 cm'1 and a HWHM of 75cm'.Ill. Experimental

A schematic diagram of the experimental transmis-someter system is described in Fig. 6. It is composedof a radiation source (top left), which is usually ablackbody at 21000C with a parabolic mirror 64 cm indiameter developed at the Technion,6 a filter radiome-ter (top right), and a computerized control system.Another source used by us is based on a quartz halogenlamp operating at 3000 K. This source emits a narrowbeam of 3 mrad through a Newtonian optics withf# = 5 and an aperture of 15-cm diameter. Theradiation emitted from the source is chopped at afrequency of -400 Hz. The chopper produces an elec-trical reference signal, which is in phase, with thechopped optical beam. The reference signal is trans-mitted by means of a radio transmitter to the radiome-ter (an optical reference signal is not reliable as itcontains too much noise). The radiation from thesource is collected by a parabolic mirror in the radiom-eter and focused on a germanium detector after goingthrough a 1.14- or 1.06-Am filter. These filters aremounted on a filter wheel. The voltage received fromthe germanium detector is transferred to a lock-inamplifier. The reference signal received by radio fromthe source provides a reference signal to the lock-inamplifier. The output voltage of the lock-in amplifierdepends linearly on the radiation intensity that

iP1

50INTEGRATED WATER VAPOR CONTENT (gr cm-

21)

Fig. 5. Plot of the calculated transmittance function r"(w) as afunction of w for two pairs of filters. The upper curve is for filtersshown in Fig. 4. Experimental results are also shown, with squaresrepresenting data obtained at a range of 10.3 km (1984), circles at7.35 km (1983), and triangles at 8.6 km (1984). The lower curve iscalculated for a different set of filters with crosses representing themost recent experimental results obtained at ranges of 0.6, 1.5, 2.8,

and 3.4 km (representing increasing values of w).

SOURCE RADIOMETER

I,,-- ~ ~~~~~~~~~~~~~~~~~~~ -FILTERSCHOPPER -- 1 DETECTORS a t

,~ TRANSMITTER RECEIVER LOCK IN AMR

Fig. 6. Schematic diagram of the transmissometer system.

reaches the detector. The output signal is convertedinto a digital signal by an analog-to-digital converter.The digital signal is transferred to a personal computerwhere it is averaged (primary averaging takes place atthe lock-in amplifier by a proper selection of the timeconstant). The computer controls the rotation of thefilter wheel and translates the ratio of the signals ob-tained through the filters at 1.14 and 1.06 gim intointegrated water vapor quantities through use of thefunction r"(w).

Ro is measured in the laboratory. A simple trans-mittance measurement at L = 0 is impossible, as thesignal would saturate the detector of the radiometer.Instead the radiometer is pointed at a strip of metal,coated with BaSO4, obtained from Kodak under thetrade name of Eastman White Reflectance Coating,catalog No. 6080. The strip is illuminated by a beamfrom the source and scattered light from the stripenters the radiometer. Since the reflectance of BaSO4is very nearly constant in the 1.06-1.14-gm region,7 it ispossible to obtain Ro from the ratio of the two signalsS,(0,w) and S2(0,w). Using this method Ro was estab-lished without saturating the radiometer.

15 June 1987 / Vol. 26, No. 12 / APPLIED OPTICS 2439

IV. Results and Analysis

Using the above experimental system we measuredintegrated water vapor quantities for distances be-tween 0.6 and 10.3 km in different areas of Israel dur-ing the years 1983-1985. On all occasions a measure-ment of the relative humidity was also carried out witha wet-dry hygrometer at the two ends of the opticalpath. The integrated water vapor quantity in theoptical path was calculated from the relative humiditymeasured by the wet-dry hygrometer. Figure 5 showsthe results of the experimentally obtained values ofRL/RO E and the theoretical curve r"(w) as a functionof the integrated water vapor quantities w. The re-sults presented in this figure contain a collection ofmeasurements using a number of filters for the follow-ing distances: 600, 1500, 3400, 7350, 8600, and 10,300m. We found a satisfactory agreement of 1-7% be-tween the measurements taken and the theoreticalcalculation. The experiments were carried out duringthe day as well as during the night, in summer as wellas in winter, with relative humidity in the range of45-100%.

From a theoretical examination of the dependenceof T'r(w) on meteorological conditions, it was foundthat the variations of the function were negligible andthere was no need to introduce correction factors, ex-cept for conditions of unusually high temperatures(310 K) together with values of relative humidity(90%). These results were obtained by the followingcalculations. The dependence of 1-'(v,w) at 1.14 m ontemperature and relative humidity was calculated fortemperature variations between 280 and 310 K andrelative humidity variations between 25 and 98%. Theresults showed a change of only 1-2% in '(rv,w) in themost extreme conditions. A similar check was run forthe dependence on total pressure between 800 and1050 mbar and it was found that when the transmit-tance was 65% it decreased by 2-3% when the pressureincreased through this range. The dependence of theratio E(L,v) [see Eq. (7)] on visibility is well defined,but the visibility itself is not always known to a highaccuracy. It was shown that for values of L/V > 0.6,the factor E(L,v) changed by 3-4% for a change of 20%in V. Most of our experiments were carried out duringperiods of high visibility (V > 20 km) and these correc-tions did therefore not apply.

One source of uncertainty could originate in thehygrometer measurements at both ends of the path.For long ranges the humidity may vary along the pathand this can be a source of disagreement between theradiometric and hygrometric results. It is possiblethat part of the disagreement found in our results wasdue to this cause.

It should be noted that the dependence of r"(w) onF(P) of the filter is critical. The function F(p) has to beestablished carefully on a good spectrophotometer,both inside and outside the region of interest (1.14gim)and this should be repeated frequently to verify itsconstancy. For an interference filter the transmit-tance depends on the angle of incidence and this dic-tates a lower limit to the F/No. of the radiometer. Inour radiometer the f/No. was equal to 5.2440 APPLIED OPTICS / Vol. 26, No. 12 / 15 June 1987

V. Conclusions

The method described above has proved itself effi-cient and relatively simple. It enables the measure-ment of w for distances ranging up to 10 km and may beextended to much larger distances (see Fig. 5). It alsoconfirms the validity of the calculated transmittanceof the FASCODE program.

The main advantages of the methods are summa-rized below:

(1) Water vapor may be measured over large opticalpaths, like lidar and other single-ended methods, butaccording to our results at higher absolute humidities(up to -20 g/m3).

(2) The integrated water vapor amount is obtainedas opposed to local measurements of H20 concentra-tion. Similar results can be obtained from integrationof lidar results.

(3) The method is based on the establishment ofratios of optical signals at a given range, eliminatingthe need for absolute intensity measurements. Thisfeature is particularly useful since a change in rangemeans moving the instruments from one location toanother with a possibility of upsetting the opticalalignment of the instruments.

The disadvantages are that the present system isdouble-ended, unlike lidar systems, and the slight de-pendence of the results on meteorological conditions(as discussed in Sec. IV) introduces some uncertainty.

The authors are grateful to E. Trakhovsky, S. Ariov,and Y. Moses for useful advice and technical assis-tance. This work was partly supported by U.S. ArmyAtmospheric Sciences Laboratory, Contract DAJA45-84-C-0020 through the European Research Office,London.

References1. E. Trakhovsky, A. D. Devir, and S. G. Lipson, "Integrated Water-

Vapor Density Along Long Atmospheric Paths Determined byRadiometric Methods," Infrared Phys. 21, 343 (1981).

2. D. J. Brassington, "Differential Absorption Lidar Measurementsof Atmospheric Water Vapor Using an Optical Parameter Oscil-lator Source," Appl. Opt. 21, 4411 (1982).

3. R. M. Hardesty, "Coherent DIAL Measurement of Range-Re-solved Water Vapor Concentration," Appl. Opt. 23, 2545 (1984).

4. W. L. Wolfe and G. J. Zissis, Eds. Infrared Handbook (U.S. Officeof Naval Research, 1978), Chap. 5, p. 524.

5. H. J. P. Smith, D. J. Dube, M. E. Gardner, S. A. Clough, F. X.Kneizys, and L. S. Rothman, "FASCODE-Fast Atmospheric Sig-nature Code (Spectral Transmittance and Radiance)," AFGL-TR-78-0081 (Air Force Geophysics Laboratory, Hanscom AirForce Base, MA, 1978).

6. A. Ben-Shalom, A. D. Devir, S. G. Lipson, and U. P. Oppenheim,"New Developments in Instrumentation for Long Path Trans-mittance and Radiance Measurements," Proc. Soc. Photo-Opt.Instrum. Eng. 356,98 (1982). This blackbody is used in our longrange atmospheric transmittance measurements which have beencarried out in ranges of up to 45 km.

7. F. Grum and G. W. Luckey, "Optical Sphere Paint and a Work-ing Standard of Reflectance," Appl. Opt. 7, 2289 (1968).

A