Light absorption measurements: new techniques

Gofried Hanel, Reinhold Busen, Christel Hillenbrand, and Regine Schloss

A new radiometer is described which simplifies measurement of the radiation supply of solar wavelengths.Two methods of measuring the radiant energy absorbed by aerosol particles are described: A photometrictechnique is used for particles collected on filters, and a calorimetric technique is used for in situ measure-ments. Data collected with the radiometer and the light absorption techniques yield the heating rate of theatmosphere due to light absorption by the particles. Sample measurements show substantial atmospherictemperature increases due to absorption, especially in industrial regions.

1. IntroductionThe global radiation budget in the multiannual mean

is fairly well known considering the top of the atmo-sphere, the surface of the earth, and the total absorptionin the atmosphere. However, the amounts of shortwaveradiation (0.29-3.5-Am wavelength) absorbed in thecloud-free atmosphere and in clouds given by differentauthors scatter considerably. The relevant numbersare 8-20% of the incoming solar radiation for the firsteffect and 3-11% for the second one. Because of theseuncertainties in situ measurements of the absorptionof shortwave radiation by gases and particles are de-sired. In the following measurement techniques aredescribed allowing in situ measurements of the amountof shortwave radiation absorbed by aerosol and cloudparticles.

II. TheoryThe aim of our work is to measure in situ the time

rate Cap of electromagnetic energy, which is trans-formed into internal energy by absorption of shortwaveradiation in aerosol or cloud particles. To get Qap, theenergy budget of radiation processes in a small volumeV of air has to be combined with the equation of radia-tive transfer yielding

0ap = Vap f-J N(w)do, (1)

The authors are with Johann Wolfgang Goethe Universitdit, Institutfur Meteorologie und Geophysik, 6000 Frankfurt a.M.-1, FederalRepublic of Germany.

Received 13 July 1981.0003-6935/82/030382-05$01.00/0.© 1982 Optical Society of Anierica.

where ap = mean absorption coefficient of the parti-cles for shortwave radiation;

N(w) = radiance of shortwave radiation; andX = solid angle ( 1 = unit solid angle).

Equation (1) is valid when the energy density ofshortwave radiation in the volume remains constant inthe time interval considered. For illustration Qa isexpressed as the heating rate of the air (dT/dt)ap causedby absorption of shortwave radiation in particlesyielding

(dtap ap frul(2)

where T = temperature,t = time,6 = density of air, and

cp = specific heat of air at constant pressure.In general the absorbed radiative energy first causes

a rise in the internal energy of the particles. Then thisenergy is used partly to heat the atmosphere and partlyto evaporate water from the particles. Thus (dT/dt)apis the real heating rate of the atmosphere due to ab-sorption of shortwave radiation within the particles onlywhen the water in the particles is in equilibrium withthe water vapor in the atmosphere.

Thus the method of determining in situ Qap or(dT/dt)ap is to measure the mean absorption coefficientCap of the particles in the shortwave region and theshortwave radiation supply

iN(w)d o,

i.e., the total shortwave radiation flowing from all di-rections toward the point of measurement.

111. Measuring Techniques

A. Shortwave Radiation SupplyThe perfect way to measure the shortwave radiation

supply would be to point a photometer successively in

382 APPLIED OPTICS / Vol. 21, No. 3 / 1 February 1982

Support

Fig. 1. Schematic diagram of the integrating radiometer.

all directions and integrate the readout of N. However,this technique is too time-consuming and expensive forsimultaneous measurements at different places on aroutine basis. Therefore, we have developed a simpli-fied measuring technique applicable to routine mea-surements. With this instrument the flux densities ofshortwave radiation coming from six equal ranges of thesolid angle are measured separately by thermopilescovered with a quartz disk (Fig. 1). The sum of thesesix ranges of the solid angle is equal to 4r sr. The sixflux densities measured are corrected

(a) for the error (about -3.5%) arising from the factthat radiation flowing from an edge of a funnel to oneof the sensors can be determined partly also by thesensor detecting the neighboring range of the solidangle; and

(b) for the error (about 25 5%) coming from thecosine response of the sensors for that part of incomingradiation not arriving perpendicularly with respect tothe planes of the sensors.

To avoid large cosine errors during sunshine the solarradiant flux density is measured separately with anangstrom pyrheliometer, and the output of the instru-ment is corrected accordingly. The calibration errorsare i1% for the pyrheliometer and 2% for the inte-grating radiometer. The maximum error by which theshortwave radiation supply can be measured is smallerthan 7.2% during sunshine when the shortwave albedo

of the ground aG = 0.4; it is smaller than 16.1% duringsunshine and when aG = 0.2 and smaller than 8.6%when there is no sunshine and aG = 0.2. These errorshave been computed considering the calibration errorsof the instruments and the distributions of the short-wave sky radiation and the reflected shortwave radia-tion from walls and from the ground according to theliterature and our own model calculations of diffuse skyradiation (de Bary and Eschelbach, 1973; Koepke andKriebel, 1978). At present, the integrating radiometeris modified slightly to reduce considerably the cosineerror.

B. Absorption Measurements

1. Photometric Method for Samples of Particles onFilters

For photometric absorption measurement, particlesfrom the atmosphere are collected on a filter. In theapparatus the particle loaded filter is placed in front ofa light diffuser, and the particles are directly irradiatedwith shortwave radiation from a lamp emitting radia-tion close to the spectrum of solar radiation (Fig. 2).The flux density of the incoming radiation and the an-gular dependence of the radiation scattered by thesystem particles-filter-light diffuser is measured witha thermopile covered with a quartz plate. For com-parison purposes this measurement is repeated for thesystem filter-light diffuser alone. (a) Using energybudget equations for both systems, i.e., the sum of for-ward scattered, back scattered, and absorbed energiesequals the energy input, and (b) considering multiplereflections of radiation between the particles and thesystem filter-light diffuser regarded as a unit, we getthat part of the flux density of the incoming parallel

Paricls

aC '_ c

F c

/ of

F

Filter OiffuserI II i'

/

p

I

I

. N.\- Photometer

Fig. 2. Schematic diagram of the photometric absorptionmeasurement.

1 February 1982 / Vol. 21, No. 3 / APPLIED OPTICS 383

Rbsorber * dry air Dry air

Fig. 3. Schematic diagram of calorimetric absorptionmeasurement.

radiation being absorbed by the particles to be equalto

F0p. FRFvs + FoFv (3)F. FRsFV + FoFvs

where Fapo = flux density of that part of incomingparallel radiation absorbed by the par-ticles;

F, = flux density of incoming parallel radia-tion;

FV,FR = flux density of the forward scattered andback scattered radiation by the systemparticle-filter-diffuser; and

FVSFRS = flux density of the forward scattered andback scattered radiation by the systemfilter-diffuser.

According to Chin-I. Lin et al. (1973) the absorptionof radiation by the particles on the filter is equalized tothe absorption of radiation by the same particles in theairborne state according to

1 Fp = exp F-ap X(4)F.

where V is the volume of air sucked through the filterand F is the particle loaded area of the filter. When thesystem filter-diffuser absorbs most of the incident ra-diation, FR FVS << FFV and FVFRS << FoFvs andconsequently 1 - Fapo/Fo = FVIFvs. When in additionthe forward scattered radiation is in both cases directlyproportional to the radiance N(0) in the forward di-rection we get

1 - Fap./Fo = Nv(O)/Nvs(0). (5)

This is the formulation of 1 - Fapo/Fo by Chin-I. Lin etal. (1973). It is one goal of this work to study experi-mentally the conditions for which Eqs. (3) and (5) givethe same results.

After the mean absorption coefficient of the particlesis obtained according to Eqs. (3) and (4) it has to becorrected, because the wavelength dependences of theshortwave radiation emitted -by the lamp and of theshortwave circum-global radiation in real atmosphericconditions are slightly different:

Fnp (atmosphere) = (0.955 O.OlO)Fap (lamp). (6)

2. Calorimetric Method for Airborne ParticlesThe experimental setup for the calorimetric method

mainly consists of two closed chambers connected bya differential pressure meter of high sensitivity (Fig. 3).Into one of these chambers (the measuring chamber),

trap an absorber and dry air are sucked; into the second (thecomparison chamber) dry air only is sucked. Whenthese chambers are illuminated at the same time byparallel shortwave radiation, electromagnetic energyis transformed into internal energy within the absorber.When this energy is transferred to the surrounding dryair a pressure increase in the measuring chamber takesplace. This pressure increase is directly proportionalto the absorbed flux density. The relevant formulareads

1 _ Fapo = _ CVApa, = ep(-Sas),F RE

(7)

where V = 524 cm3 (volume) and = 18 cm (length) ofthe measuring chamber, cv = specific heat of the air, R= specific gas constant of the air, APap = pressure in-crease in the measuring chamber due to the absorptionof shortwave radiation within the particles. When amean absorption coefficient for the airborne particleswithin the chamber has been obtained according to Eq.(7), it has to be corrected for real atmospheric conditionsaccording to Eq. (6). At present only too small short-wave absorption coefficients are measured at airborneaerosol particles with the calorimetric method. Thisis due to difficulties mostly caused by evaporation ofvery small amounts of water from the particles after theabsorption of radiation has taken place. The energyused for the evaporation is of the order of the energyabsorbed and cannot be detected with the instrument.Therefore, results from the calorimetric measurementare not presented.

IV. Results of MeasurementsIn Fig. 4 some measurements of the shortwave ra-

diation supply are compiled. These measurementshave been taken in the City of Frankfurt and atopKleiner Feldberg (-800 m above MSL) in the Taunusmountains near Frankfurt. Results show that theshortwave radiation supply may be much larger in a citythan in a natural environment. This is due to reflectionof light from bright walls. Second, it is common for theshortwave radiation supply to be of the order of the solarconstant. The maximum values measured in Frankfurtare -50% larger than the solar constant. Above snowand between clouds one should expect even much largervalues than these maximum values.

Mean shortwave absorption coefficients in the Cityof Frankfurt together with the appertaining heatingrates at the shortwave radiation supply of 1000 and 2000W cm2 are compiled in Table I. The absorption coef-ficients have been measured with the photometric

384 APPLIED OPTICS / Vol. 21, No. 3 / 1 February 1982

1800 1800

6.00 7.00 8oo 9.00 10.00 11.00 12 00 1300

(a)

Fig. 4. Shortwave radiation sup-ply S4-w1 Ndw in W/m 2 : solarconstant = 1380 W/m 2 ; solid line,S4-1 Ndw; dotted line, flux den-

sity of direct solar radiation.

[ZW/t I AlddnS uoJ4e'peH [Zw/M I AiddnS uof4elpe8

1 February 1982 / Vol. 21, No. 3 / APPLIED OPTICS 385

1600t

C4JE 1400

1200

C 8 00

.2

, 600'

400

200

Frankfurt / Main17. 7.1980

Tme [WI

1600

1400

1200

1000

800

603

400

* 200

1B00 t 1800

Table 1. Mean Shortwave Absorption Coefficients asp and Corresponding Heating Rates of the Atmosphere In Frankfurt/Main; V/F = Equivalent Lengthof Absorption Path In the Atmosphere

Heating rates in K/hV/F Crap for shortwave radiation supply of

Date/time (km) (cm-') 1000 W/m2

2000 W/m 2

13.2.1980/1500-1700 1.96 1.98 X 10-7 + 16% 0.058 0.127.11.1980/1000-1400 3.89 7.91 X 10-7 + 9% 0.23 0.467.11.1980/1410-1805 2.98 1.34 X 10-7 + 17% 0.039 0.078

10.11.1980/1450-2215 5.30 1.67 X 10-7 4 10% 0.049 0.098

method. Their values range between -10-7 and 10-6 Literaturecm-'. The corresponding heating rates at 1000 W/m2 M. B. Baker, Atmos. Environ. 10, 241 (1976).range between 0.94 and 5.53 K/day. They can be re- Chin-I Lin, M. Baker, and R. J. Charlson, App. Opt. 12, 1356garded as approximate mean values during the day for (1973).

situations with clear sky and scattered cloud . Th R. M. Goody, Atmospheric Radiation. Vol 1: Theoretical Basissituations with clear sky and scattered cloudiness. Thne (Clarendon, Oxford, 1964).heating rates at 2000 W/M2 are maximum values during (Caedn Oxod'16)heating rates at 2000 ,/m. are maximum values during G. Kortfim, Reflexionsspektroskopie (Springer, Heidelberg, 1969).clear sky situations. These results show that the ab- G. W. Paltridge and C. M. R. Platt, Radiative Processes in Meteo-

sorption of solar radiation in aerosol particles is a pro- rology and Climatology (Elsevier, Amsterdam, 1976).cess of high climatological importance especially in in- E. de Bary and G. Eschelbach, Tellus 26, 682 (1974).dustrial regions. P. Koepke and K. T. Kriebel, Appl. Opt. 17, 260 (1978).

A. Korpel of the University of Iowa photographed by Milton Birnbaum (Aerospace Corp.) during theGabor Tribute Symposium at the OSA 1981 Annual Meeting in Kissimmee, Fla.

386 APPLIED OPTICS / Vol. 21, No. 3 / 1 February 1982