A R C H I V E S Arch. Met. Geoph. Biold., Ser. B, 30, 67-72 (1982) FOR METEOROLOGY,

GEOPHYSICS, AND B I O C L I M A T O L O G Y © by Springer-Verlag 1982

551.521.31:551.508.21

Department of Physics and Meteorology, Agricultural University of Norway, Aas, Norway

Atmospheric Monitoring Using a Solar Spectrometer Part 2: Determination of Columnar Atmospheric Water Vapor Content from Spectral Measurements of the Direct Solar Radiation

V. Hansen

With 2 Figures

Received July 2, 1981

Summary

This work represent the second of two reports concerning the information content derived by using a solar spectrometer combined with an efficient data logging and computational system in atmospheric monitoring. A description of the system and experimental procedure was given in the first report [1]. By using published values of the wavelength dependent transmission coefficients of the bands between 0.7/~m and 1/am (preferably the 0.82/ira band) and analytical representations of the transmission functions [2], the equivalent water vapor absorber amount was calculated for some selected days. The method is quick and easy to use on a routine basis and is expected to give reasonable accuracy.

Zusammenfassung

Atmosph~irische Beobachtung mit Verwendung eines Solar-Spektrometers. Teil 2: Bestimmung des Wasserdampfgehaltes einer Lufts~ule aus spektralen Messungen der direkten Sonnenstrahlung

Diese Arbeit bringt einen zweiten Informationsgehalt, der aus der Verwendung eines Solar-Spektrometers in Verbindung mit einer leistungsf~ihigen Datenerfassung und einem Computersystem ans atmosph~irischer Beobachtung abgeleitet wurde. Eine Beschreibung des Systems und des experimentellen Verfahrens wurde im ersten Bericht [ ! ] gegeben. Mit Benutzung ver6ffentlichter Werte der wellenliingenabh~ingigen Trans- missionskoeffizienten der Banden zwischen 0.7 gm und 1 tim (vorziiglich der 0.82/am- Bande) und analytischer Darstellungen der Transmissionsfunktionen [2] wurde der equivalente Betrag des absorbierenden Wasserdampfes for ausgew~ihlte Tage berechnet. Das Verfahren ist rasch und leicht routinem~ii~ig anzuwenden und l~tgt eine angemessene Genauigkeit erwarten.

5*

0066-6424/82/0030/0067/$ 01.20

68 V. Hansen

1. Introduction

Water vapor absorbs solar radiation in the vibrational-rotational bands located at 0.72, 0.82, 0.94, 1.1, 1.38, 1.87, 2.7 and 3.2 #m. This absorption plays a major role in the radiation balance of the earth and atmospheric system, and hence the surface temperature. The bands, which have been examined by several investigators [3 -7 ] , consist of many closely spaced lines whose strength varies greatly with wavenumber. The lines are smoothed by the optical system used, and what is measured is thus the transmittance averaged over the spectral width of the spectrometer, and not the monocromatic transmittance. In general, the average transmission cannot be described by a simple exponential function of water vapor path length, that is

~(g)= ~ exp[--c(v)L]du=/=exp[--U(~L], Av

(1)

where c(v) represent the monocromatic absorption coefficient and b-(u-) an average absorption coefficient. Several methods exist that can be applied for the calculation of water vapor transmittance in the wavelength range here considered (2 .6-13) . One widely used band model concept is the Lowtran [8] computer codes, based on a series of tables and charts of available laboratory transmittance data and molecular line constants. As the primary goal o f this code is to determine the transmittance between two arbitrary points in space, the code has limited value for the problem here considered, which is the determination of water vapor content from measured values of water vapor transmittance. Upon examination of the tabulated Lowtran transmission functions Gruentzel [2], however, proposed the use of an analytical function for their representation. This enables water vapor content to be determined directly from measured values of trans- mittance or fractional absorption by simple numerical methods, replacing cumbersome and less accurate manual graphical procedures.

With the spectrometer used we are able to examine the three bands located at 0.72, 0.82 and 0.94 #m. The first of these is, however, severly contami- nated by Fraunhofer absorption lines, and the last is barely measurable due to the low spectrometer efficiency at the long wavelength limit. We will therefore concentrate on the 0.82/~m band.

In principle, any part of this absorption band may be used for water vapor determination. From the Lowtran tables, or directly from the transmitted solar spectrum in Fig. 1, maximum absorption is found to occur at the Q-branch head around 823 rim. We therefore chose a region that included the main part of the Q-branch and the strong rotational line P1 at 824.3 nm.

Atmospheric Monitoring Using a Solar Spectrometer, Part 2 69

2. The Transmission Function

The general form of the transmittance of a Lorentzian-broadened spectral line through a homogeneous atmosphere is given by the expression

r = f (Sa n. W0) , (2)

where S is the average line strength, a the average halfwidth and Wo the absorber amount. If n is set equal to zero and unity, respectively, the equation reverts to the well known weak and strong line approximations common to several band models. For an inhomogeneous atmosphere the arguments must be replaced with the equivalent path-length integrals. Temperature and pressure effects are introduced through the equations

S = So (To~T) a (3)

and a = a o ( P / P o ) ( T o / T ) 1/2 , (4)

where the index "0" refers to standard conditions. Inserting eq. (3) and (4) into eq. (2) leads to the expression

r = f ( C ~ . W)

where C~ = S0a~

and W = (P /po)n (T /To) a+l/2n Wo •

(5)

(6)

(7)

In the Lowtran model the form of the function l a n d the parameters n and a were empirically determined using laboratory transmittance data and avail- able molecular line constants. Mean values of n and a were determined to be 0.9 and 0 respectively. The transmittance was first degraded in resolution to 20 cm -1 and the data points then digitized at steps of 5 cm -a , except for the ultraviolet and visible ozone bands. Upon examination of the tabulated Lowtran transmission functions Gruentzel proposed the use of the expression

¥(v-) = exp [ - -aW b 10 b#(v--) ] . (8)

A first-order least squares fit gave the values a = 0.07054 and b = 0.5523 for the bands considered. Defining the fractional absorption as

?t

f r ~ d v Z ¥~(~)dv Av 1

Ar = 1 Av ~ 1 ndu (9)

the equivalent water vapor absorber amount, defined by eq. (7), may be estimated from eqs. (8) and (9) by a simple trial and error procedure, using measured values of fractional absorption. The temperature T and pressure P in eq. (7) are then to be understood as mean values weighted according to the water vapor density versus height distribution. Profile measurements o f

70 V. Hansen

water vapor densities show that water vapor is main ly concent ra ted in the lowest few ki lometers in the a tmosphere , as a rule o f thumb the dens i ty at 10 km al t i tude is only 0.1% o f the densi ty at the surface. Al though the pressure sharply decreases with a l t i tude, the "ef fec t ive" pressure to be inserted in eq. (7) thus does not differ much from the surface pressure, rough calculat ions show tha t their rat io is of the order 0 . 8 - 0 . 9 . The t empera tu re dependancy is o f minor impor tance in pract ice compared to the pressure effect . As a conclusion, the "ef fec t ive" absorber amount as de te rmined f rom the absorp t ion measurements , will be 1 0 - 2 0 % lower than the " t r u e " absorber amoun t W 0. Also compare With Fig. 17 o f [8]. The conten t in a vertical co lumn Wz is ob ta ined through the relat ion

W = W z . m , ( 1 0 )

where m is the relative air mass.

3. Resul ts

Fig. 1 show the 0.81 #m water vapor band, measured on 9 th Sep tember 1980 (m = 2.0). The Q-branch is marked with an arrow, and the absorp t ion cal-

2-

Intensity {arb.units]

i ~ P2 P1 RI i iii ILLI P3

P5 P4 ~ ~-- > R /

Q

Fig, 1. Absorption of solar radiation by the 0.8 #m water vapor band. The spectrum was obtained on September 8th 1980 with a relative air mass m = 2.0

Atmospheric Monitoring Using a Solar Spectrometer, Part 2 71

culated using a planimeter and a simple eye-fitted construction of the synthetic solar background. A computer can of course do this much faster with more accuracy, but our approach was mainly to show the appliciability of the method. Fig. 2 shows the daily variation in effective absorber amount for the 1 st and 18th September, and 16th December. The mean values are

W(cm)

2 -

x

o o o

o o o o

~ o o o

o

o o o o

o

110 ~ ]l~ ]

W(cm)

~I Oo~ ° °° "°°

1'8 ~ime

Fig. 2. Daily variation in equivalent water vapor absorber amount; above: during September 1st (x) and 18th (o) and below: during December 16th

1.21, 1.19 and 0.71 cm respectively. The spread in the September data is surprisingly great, and may be caused by thin, barely visible, white clouds passing the sun, although the sky would be classified as clear in the meteoro- logical sense of the word.

Acknowledgements The author wishes to express his gratitude to professor G. Kvifte for his active interest in this work and valuable criticism of the manuscript. He will also thank the technical staff, especially the engineers P. Granroth and R. Markussen, for the design and con- struction work done of the solar spectrometer. This work is supported by NLVF (Norwegian Agriculture Research Council of Norway), project no. 10 009.07.

72 V. Hansen: Atmospheric Monitoring Using a Solar Spectrometer, Part 2

References

1. Hansen,V.: Atmospheric Monitoring Using a Solar Spectrometer. Part 1: Determina- tion of Aerosol Size Distribution Spectra by Inverting Solar Spectral Extinction Measurements. Arch. Met. Geoph. Biokl., Set. B 30, 45-66 (1982).

2. Gruenzel, R. R.: Mathematical Expressions for Molecular Absorption in Lowtran 3B. Appl. Opt. 17, 2591-2598 (1978).

3. Fowle, F. E.: The Spectroscopic Determination of Aqueous Vapor. Astrophys. J. 35, 149-162 (1912).

4. Fowle, F. E.: The Transparency of Aqueous Vapor. Astrophys. J. 42, 394-411 (1915).

5. Howard, J. N., Burch, D. L., Williams, D.: Near Infrared Transmission through Synthetic Atmospheres. J. Opt. Soc. Amer. 46,186-190 (1956).

6. McDonald, J. E.: Direct Absorption of Solar Radiation by Atmospheric Water Vapor. J. Met. 17, 319-328 (1960).

7. Koepke, P., Quenzel, H.: Water Vapor: Spectral Transmission at Wavelengths between 0.7/ira and 1 tim. Appl. Opt. 17, 2114-2118 (1978).

8. Selby, J. E. A., McClatchey, R. A., et al.: Atmospheric Transmittance from 0.25 to 28.5 ttm: Computer Code Lowtran 5. AFCRL Environmental Research Paper 697 (AFCRL, Hanscom AFB, Mass.), 1980.

9. Moskalenko, N. L.: Izv. Akad. Nauk SSR Fiz. Atmos. Okeana (English edition) 5, 678 (1969).

10. Smith, W. L.: A Polynomial Representation of Carbon Dioxide and Water Vapor Transmission. ESSA Technical Report NESC 47 (National Environmental Sattelite Center, Wash., D.C.), 1969.

11. Pierluissi, J. H., Tomiyama, K., Gomez, R.: Analysis of the Lowtran Transmission Functions. Appl. Opt. 18, 1607-1612 (1979).

12. Roach, W. T.: The Absorption of Solar Radiation by Water Vapor and Carbon Dioxide in a Cloudless Atmosphere. Quart. J. R. Met. Soc. 87, 364-373 (1961).

13. Yamamoto, G.: Direct Absorption of Solar Radiation by Atmospheric Water Vapor, Carbon Dioxide and Molecular Oxygen. J. Atmos. Sci. 19,182-188 (1962).

Author's address: Dr. V. Hansen, Agricultural University of Norway, Department of Physics and Meteorology, P.O. Box 19, 1432 Aas-NLH, Norway.