Angström turbidity parameters and aerosol optical thickness: A study over 500 solar beam spectra

JOURNAL OF GEOPHYSICAL

RESEARCH, VOL. 102, NO. D18, PAGES 21,905-21,914, SEPTEMBER 27, 1997

Angstr6m turbidity parameters and aerosol optical thickness: A study over 500 solar beam spectra A. I. Bokoye,A. de La Casini•re,andT. Cabot Equipede RechercheInteractions Rayonnement SolaireAtmosphere (IRSA), Universit•JosephFourier,Grenoble, France

Abstract. Thereexistsin the literaturemanymethodsof determiningthe Angstr6mparameters for themeasurement of theopticalthickness of aerosols. Thisthickness is requiredin casessuch aswhenthespectral beamsolarirradiance at groundlevelhasto beassessed. Thepresent work studiesthedifferences betweensomeof thesemethodsandestablishes the relationships between theirresults.A systenmtic studyinvestigating 509 directsolarirradiancespectrawasundertaken. As a result,a newwavelength pair for filtermeasurements is proposed to calculatetheAngstr6m parameters with the Voltz technic,namely,thepair (0.400 gm,0.750gm). Thisnewpair is the onewhich bestdescribes the solarbeamattenuationin the atmospherictransmittance models.For theconsidered atmospheric conditions (continental tubanaerosols), themeanvalueof the Angstr6mparameter c•is foundto be 1.0+ 0.3, whichis relativelycloseto theconventional 0t= 1.3if takingintoaccount thevariance. Thewavelength rangeexploredis from0.290gm to 0.900 lain,whichconcerns manyapplications in bioscience.

1. Introduction

The changesof the spectralcompositionof solar radiations due to atmosphericturbidityconstitutea sourceof information on the optical properties of the atmosphereand provide indices for characterizing the air pollution level. The knowledgeof suchindicesis particularlyinvaluablein cases such as when the performanceof solar energy systemson a given site has to be assessed.During the past few decades, several atmospheric turbidity coefficients have been proposed.The mostpopularare the Linke turbidity factor TL

[Linke, 1922], the Angstr6mturbidity parameters• and [5 [AngstrOm,1929,1930],the SchiieppcoefficientB0.5defined at ?•= 0.5 •tm [Schiiepp,1949], and the horizontalvisibility V [McClatcheyand Selby, 1972]. The presentwork deals with Angstr6m coefficientsbecausethey are the most commonly usedatmospheric pollutionindices;furthermore,evaluationof the opticalthicknessof aerosolsis simple.The latter is used to describethe attenuationof solarbeamsby suspendedliquid or solidparticles.It is well known that suchattenuationis due to scatteringand absorptionphenomena.For calculatingthe aerosol optical thickness,Angstr6m suggestedtaking these two phenomena into account by means of the following expression:

Various authors [AngstrOm, 1929, 1930; Voltz, 1974; Dogniaux,1976; Cachorroand Casanova,1987;Loucheet al., 1987;Cachorro et al., 1987; Gueymard,1993a; Grenier et al., 1994] have proposedor contributedto the developmentof methodswhich determinethe AngstrOmturbidity parameters. The World MeteorologicalOrganization(WMO) has produced severalreportsand recommendations dealingwith t• and [• measurements, through monitoring of environmental pollution and research programs like the Background Air Pollution Monitoring Network {BAPMoN ). Also, during the last two decades, theoretical and experimental studies concerning these coefficients were carried out. These include

the study of the dependenceof a on wavelength [Nicholls, 1984], the study of the influence of (a,i•) values on calculated direct spectralirradiances[Cachorro eta!., 1985, 1987, 1989; Cachorro and Casanova, 19871, and the study of the relationshipsbeween aerosolssize distributionand • values [Cachorro et al., 1993]. These studies conclude that, for

identical atmospheric conditions, the (a,f•) pairs obtained stronglydependon the methodusedto derivethem. This paper will therefore attempt to relate the various AngstrOmparametersobtained from the different methodsin the literature,and to find the methodwhich permitsthe best modeling of the direct solar spectral irradiance from these parameters.

where X is in microns.

The parameterI• is a dimensionless h•dexof the opacityof a vertical column of atmosphere.It may range from 0.0 to 0.5 and is called the AngstrOm turbidity coefficient. The wavelength exponent • is an index for aerosol size distribution which ranges from 0.5 to 2.5. For normal atmospheres the value of 1.3 is commonlyadopted. Copyright1997by theAmericanGeophysical Union. Papernumber97JD01393. 0148-0227/97/97JD-01393 $09.00

Except for the amount of ozone, all experimental data involved in this studywere measuredin the town of Grenoble (45012' N, 5043' E and 210 m altitude), which is located in an industrial urban valley of the French Alps and omen suffers from strongepisodesof atmosphericpollution.

2. Available

Methods

Five representativemethods of calculating the AngstrOm coefficientsare detailedin this section.Three of them require only total irradiancemeasurements, while for the othertwo the knowledge of spectral irradiances at one or two distinct 21,905

21,906

BOKOYE ET AL.' ANGSTROM TURBIDITY AND AEROSOL OPTICAL THICKNESS 3

wavelengths is necessary. In an attempt to avoid possible confusions,subscripts are usedto relate e and [3valuesto the methodin question.

2.1.

4

TLAM2 =E [Eaij(,na) j] (TL) i

Louche Coefficients(eL,BL)

(7)

The equationsbelow were proposedby Loucheet al. [ 1987]. They were deducedfrom Bird and HulstrOtn's[1983] model of

1

the total direct solar irradiance, obtained from the LOWTRAN

3

BI =E [Ebij(w)J] (TLAM2) i

code: -1

BL= (ma D)

ln[C/(A - B')]

(2)

where

A = In/0.975EoIoro rwrg rr

(3)

B' = 0.12445 e L - 0.0162

(4)

C = 1.003 - 0.125 eL

(5)

D = 1.089 eL + 0.5123

(6)

where TLAM2 is a standardizedLinke turbidity factor at air massrna = 2, which is nearly independentof solar elevation and may be obtained, via TL, from I n measurements.The

precipitable water wisingcm-2.Thecoefficients aijandbij are given in Table 1, the latterbeing calculatedfor lo = 0.3 cm NTP of ozone,and assumingthat ei = 1.3.

In is thenormaltotalsolarirradiance (W m-2),whichcanbe

2.3.

measureddirectly by means of a pyrheliometeror indirectly using a pyranometerand a diffusometer.Eo is the earth's rna is the relative optical air mass at local conditions.

Parameters foX,rwx,rgX,andTr•, arethetotaltrans•nittances of

2.2. IRSA

Coefficients (el, gl)

This method was developed by the IRSA research team [Grenier et al., 1994] from a definitionof the Linke turbidity factor TL based on spectral solar beam irradiances. The Angstr6m turbidity coefficient is then given by the following polynomials:

Coefficients

Dogniaux [1976] established the following relationship (reportedby Page [1986]) from numerousi• valuesobtainedby pyrheliometersfitted with color filters as standardOG1, RG2

excentricity factor,1o is the solarconstant (1367W m-2),and ozone, water vapor, uniformly mixed gases, and Rayleigh scattering, respectively. Bird and Hulstr6m's model is summarized by lqbal [1983] as parameterizationmodel C. Assuming that e L = 1.3 for most atmospheres,•L can be determined from (2) by using measured values of I n and assessedvalues of the atmosphericprecipitablewater vapor thicknessw and of the vertical ozone layer thickness1o (see Appendix A).

Dogniaux

and RG8:

fid = {TL- 0.1 - (¾+85)/ [39.5exp(-w) + 47.41}

X(16+ 0.22w )-1 (8) where ¾is the solaraltitudeanglein degrees.

2.4.

Usual

Coefficients

(ev, Bv)

By this method, the Angstr6m parameters are obtained using the so-called Voltz technic, which permits determinationof the spectralaerosol optical thickness.This latter is inferred from direct spectral solar irradiance measurementsmade at two wavelengthswhere the molecular absorptionis negligible. The usually chosenpair is at Xl = 0.380 pm and X2 = 0.500 gm, where only a weak absorption

Table1.Polynomial Coefficients aij andbij forCalculation of Standard Linke TurbibityFactorTLAM2andof Angstr6mParameter 111 Value

j =0

j=1

j =2

j =3

j =4

of/

aijCoefl•cients forfi > 0.010and0.5< w< 2cm 0 1 2 3

-1.6010 1.6582 -0.050727 0.00081967

1.4986 -0.59102 0.045026 -0.0010673

-0.47879 0.17870 -0.013305 0.00045071

0.073617 -0.027070 0.0019667 -6.9064^-05

-0.0042818 0.0015660 -0.00011265 3.9632^-06

aijCoeffiients forfi > 0.010and1.6< w< 4 cm 0 1 2 3

-2.0477 1.6870 -0.048754 0.00070327

1.9361 -0.62050 0.043599 -0.00095804

-0.62668 0.18918 -0.013011 0.00041325

0.096814 -0.028740 0.0019250 -6.2191^-05

bijCoefficients 0 1

-0.10545 0.073554

-0.020050 -0.0029011

0.0050689 0.00075553

-0.00052020 -7.8281^-05

-0.0056447 0.0016650 -0.00011021 3.5204^-06

BOKOYE ET AL.: ANGSTROM TURBIDITY AND AEROSOL OPTICAL THICKNESS

by ozone is observed;the spectralaerosoloptical thicknessis then given by

ba• = [(lima) ln(EoIox/l•] - (br•+ bo•)

Table 2. Angstrtm ParameterctG as a Functionof Relative HumidityandArea Relativehumidity,%

(9) 0

where I;• and Io• are the direct spectralsolar irradianceon the groundand outsideof the atmosphere,respectively[FrOhlich and Wehrli, 1981], while 5rx and 5oX are the optical thicknesses of Rayleigh scattering and ozone absorption, respectively(see Appendix B). Therefore,accordingto Voltz and following (1),

21,907

50

70

90

99

Rural

0.933 0.932 0.928 0.844 0.659 1.444 1.441 1.428 1.377 1.134 Urban

0.822 1.167

0.827 1.171

0.838 1.186

0.779 1.256

0.492 1.127

0.468 0.626

0.449 0.598

0.378 0.508

0.232 0.246

0.107 0.053

1.008 2.379

1.005 2.357

0.911 2.130

0.797 1.962

Maritime

(•U = ln(SaMISa•2)/ln()•l/)•2)

(10)

atI •t2

Troposphere

and

[3U-- 5aX1 •.1aU

(i 1)

•t 1 1.010 •2 2.389

However, if one assumesthat ct = 1.3, the parameter• can be obtainedby using a single-wavelengthsunphotometer.It :an also be inferred frowna measure•nentat X = 1 gm, where ct has no effect. For turbidity measurements, the WMO recommendedthe following four wavelengths:0.368, 0.500, 0.778, and 0.862 gm [Webnan, 1978]; a fifth value, 0.675 gm, was added later. Since these wavelengths concern conventional measurements,they are rarely used in solar

nm bandpass),which is automaticallyshadedby meansof the motorizedrotating disk for diffuse irradiancemeasurements. 2. The inner part comprises a Bentham double monochromator with holographicgratings(1200 lines/mm), which is driven by steppingmotors.The slit widths are 0.900 mm at the inlet and 0.915 mm at the outlet; the focal is 150

spectralengineeringand thereforenot consideredin this

mm long, and the device dispersion is about 2.5 nm. The detector used is a Hamamatsu photomultipliertube (R636) poweredby a high tensionvoltage supply (optimal value 758 2.5. Gueymard Coefficients (cta,13c,) V). The wavelengthaccuracyis +0.3 nm. All the devicesand Consideringthe wavelengthdependenceof the parameterct the data logging are controlledby means of a PC with Turbo (pointedout by Nicholls [1984] and appliedby Bird [1984] in Pascalas the programminglanguage. The outer and inner parts are linked by a 3 m long his model), Gueymard[1993] developeda new model for solar beam spectral irradiance. This model uses two possible ct UV/visible fiber optic bundle, usedto transmitthe solar fluxes values:Ctl for X < 0.5 gm and ct2elsewhere.The [• parameter collectedby the diffuserto the monochromatorslit inlet. The whole spectroradiometric system is calibrated in takenis independent of the wavelengthand is derivedfrom the wavelength as well as in irradiance. The wavelength following relation:

study,except0.500 gm.

•G= 0.5a2 55

(12)

calibrationis cardedoutby usingspectrallinesof mercuryand sodiumlamps.The accuracyof 0.5 nm obtainedis satisfactory

in comparison with the 5 nm step chosen for the spectral scanning;this large stepvalue was adoptedin order to reduce by about 7.5 min the lapse of time between the two framing global irradiancemeasurements. The coefficientof calibration of irradiance at normal incidence, notated as k(0, X), was determined initially by using a 200 W Oriel Standard certificatelamp (model issue63355; spectralrange 250 - 2500 3. Experimental Processesand Devices nm), which was calibratedby emissionsof a sourcetraceable The processused for determininga direct solar spectral to National Institute of Standard and Technology (NIST) irradianceconsistsof two measurements of global irradiance standards.In orderto preservethis standardsource,whoselife that frame an intermediate diffuse irradiance measurement. The spanis short(200 hours),several250 W quartz-halogenlamps diffusemeasurementis carriedout by meansof a rotatingdisk, were calibratedas secondarystandardswhich were used to which shadesthe diffuserwith a 5.7ø half-angle cone (as the controlperiodicallythe values of k(0,X); when this coefficient was determinedtwice consecutivelyat the same temperature, apertureof currentpyrheliometers). The direct horizontal spectral irradiance signal Vx(¾)is one found a mean standard deviation of about 2%. For the obtainedby taking the differencebetween the mean value of calibratingprocess,the lamps were positionedat 0.5 m in' the two framing global signals and the diffuse signal (the front of the diffuser. To account for the marked influence on the detection device, relativedifferencebetweenthe two globaloutputswas foundto of the temperatureof the room where the inner part of the be lessthan 0.5% over the 509 spectra). measurement system was located, the following corrective The spectroradiometric measuringsystemusedfor recordhag algorithmwas applied: solarbeam spectrais composedof two main parts

where 55 is the aerosol optical thickness at 0.5 gm; consequently,only a singlemeasurementof the beam spectral irradianceat this wavelengthis necessary.The GtI and ct2 valuesproposedby Gueymardare given haTable 2 as functions of relative humidityand originsof the aerosols.

1. The outer part consistsof a horizontal flat plate UV diffuser (type OPAL from Oriel Company, with a 200 - 1100

k(0,X)= A(t)k(O,X)ref+ B(t)

(13)

21,908

BOKOYE ET AL.: ANGSTROM TURBIDITY AND AEROSOL OPTICAL THICKNESS

wherek(O,X)ref is a fixedreference. A(t) andB(t) areboth commonlyused are not the most suitablefor determiningthe linear functionsof temperature,which were determinedfrom a previous systematicstudy of the variations of k(0,X). Between 20øC and 30øCthis correctionis on average0.8% per øC. The spectroradiometer was calibrated twice in wavelength and seven times in irradiance, with measurementstaken over a period of 1 year. No significantaging effect was observedover this period. The cosineresponseof a diffuseris never ideal, with errors that may alter the absolute measurement of irradiances, especially at low y. A correction factor, namely, the relative cosine response c(¾,X) [La Casinigre et al., 1995], must consequentlybe applied to the direct spectral irradiance measurements:for the diffuser used, the correction varies from

0% at ¾= 80ø to 12% at 3'= 30ø (X = 500 nm). The irradiance calibration

device

described

above

served as a test bench to

determinethe c(y,X) values. The relative cosineresponsewas measuredfor 123 wavelengthsranging from 290 to 900 nm, and for 16 angles of incidence between 0 ø and 80ø with an accuracyof 0.1ø. To assessthe stability in time of the cosine response,four seriesof c(¾,X) measurementswere taken over 2 years;the mean discrepancyobservedbetweenthesetestswas 1% with a maximum of 2%.

Finally, the direct horizontal spectral irradiance is expressedas lh x = k(0,X) Vx(y)/c(y,X )

(14)

Two Kipp and Zonen model CM 11 pyranometerswere also used to determine

the total

solar beam

irradiance

which

is

neededto calculateIlL, Ill, or BD. The I n valueswere inferred from

simultaneous

measurements

of

the

total

horizontal

aerosoloptical thicknessesnecessaryto accuratelymodel the solar beam spectralirradiance(see Appendix B). In order to find the best (Xl,X2) pair from this viewpoint, a systematic study was undertakenusing the following method: for each measuredsolarbeam spectrum,the ln(15aX) valuesinferredfrom (9) were plotted againstIn(X); the two parametersas and Ils were then obtained from

ln(15ax)= - as ln(X) + ln([•s)

(15)

by usinga linear least squaresfit. The (X1,x2)pair considered as optimalis thusthe one which gives from (10) and (11), the au and 13uvaluesthe closestto as and Ils the mostfrequently.The subscripts denotesthe fact that such coefficients

are obtained

from the whole

measured

spectrum and, consequently, are the most appropriate to

describeit. Obviously,the as and IIs values dependon the spectral solar beam model considered, that is, on the algorithms chosen for calculating the various optical

thicknesses brX,boX,•wX,and 4.2.

Practical

Results

The wavelengths considered for the determinationof the optimalpair are thoserangingfrom 350 nm to 800 nm with a step of 50 nm. They were chosenbecausethe corresponding optical filters are readily available; however, the aerosol scattering is quite significant over this wavelength range. Consequently,45 distinctpairs are considered. The suitable (Xl,X2) pairs were selected by using the following criterion

global irradianceand of the total horizontaldiffuse irradiance, d = {(as- art)2+ [(Ils-Ilu)as/[•s]2}1/2< 0.2 (16) the latter being obtainedby meansof a shadowring. The two pyranometerswere checkedtwice, duringclear sky conditions, where d is the distancebetween the two points (as,•s) and against a reference pyranometer which was previously (au,l•u ) in the (a,[•) space.The factoras/[•s wasintroduced in calibrated

in a radiometric

station

of the French

National

Meteorology Service. The accuracy of the calibration was approximately 1%. The sky radiance anisotropywas taken into account in the shadowring correction,following Battles et al. [1995], and a cosineerror correctionwas appliedto the pyranometers,following Michalsky et al. [1995]. Algorithmsrecommendedby Gueyrnard[1993b] were used to assessthe precipitablewater vapor from surfaceambient temperatureand relative humidity. The amountof ozone was obtainedfrom Dobson'sspectrometermeasurements made at the Haute-Provence Observatory(OHP), locatedabout 140 km from the Grenoble site. A systematiccomparisonwas made betweenmeandaily total ozoneabundancederivedfromthe UV spectral irradiance measured at Grenoble and the values obtained

from OHP.

A mean relative

difference

of 8% was

observed,which may be explainedby differentatmospherical conditions, by differences in the values of extraterrestrial irradiancesand of ozone absorptioncoefficientsused,and by the well-known

difficulties

with calibration

and detection

in

the UV band.

4. Search of an Optimal Wavelength Pair 4.1.

General

Procedure

According to Cachorro and Casanova [1987], a and [}

valuesobtainedfrom the Voltz technicdependsignificantly on the choice of the two wavelengthsXl and X2 defined in section2. Furthermore,it is likely that the wavelengthpairs

orderto give to (13 s - [Su)equalweightwith (as- au). Sucha Table 3. Valuesof au, [•u, andd ObtainedWhen Usingthe Respective 45 Wavelength Pairson a GivenSpectrum (%5= 0.712 and [3s = 0.092) Pair,lam (0.35,0.40) (0.35,0.50) (0.35,0.60) (0.35,0.70) (0.35,0.80) (0.40,0.50) (0.40,0.60) (0.40,0.70) (0.40,0.80) (0.45,0.55) (0.45,0.65) (0.45,0.75) (0.50,0.55) (0.50,0.65) (0.50,0.75) (0.55,0.60) (0.55,0.70)

aU 0.90 2.39 1.62 0.79 1.07 3.28 1.86 0.77 1.10 1.19 0.43 0.78 •1.93 -1.00 -0.06 2.37 •0.50

15U d 0.10 0.02 0.05 0.11 0.08 0.01 0.04 0.11 0.08 0.06 0.11 0.09 0.40 0.21 0.11 0.03 0.17

0.19 1.77 0.98 0.14 0.37 2.65 1.22 0.14 0.40 0.53 0.33 0.09 3.54 1.94 0.78 1.73 1.35

Pair,lum

Otu

[SU d

(0.35,0.45) (0.35,0.55) (0.35,0.65) (0.35,0.75) (0.40,0.45) (0.40,0.55) (0.40,0.65) (0.40,0.75) (0.45,0.50) (0.45,0.60) (0.45,0.70) (0.45,0.80) (0.50,0.60) (0.50,0.70) (0.50,0.80) (0.55,0.65) (0.55,0.75)

1.71 0.04 1.48 0.05 0.95 0.09 1.09 0.08 2.64 0.02 1.72 0.05 0.97 0.09 1.13 0.08 4.01 0.01 1.55 0.05 0.27 0.13 0.79 0.09 0.12 0.10 -0.90 0.20 0.07 0.10 -0.48 0.17 0.52 0.09

1.08 0.83 0.24 0.39 2.01 1.07 0.25 0.43 3.36 0.91 0.52 0.10 0.59 1.80 0.65 1.32 0.19

(0.55,0.80) 0.58 0.09 0.14

(0.60,0.65) -3.58 0.63 5.99

(0.60,0.70) (0.60,0.80) (0.65,0.75) (0.70,0.75) (0.75,0.80)

(0.60,0.75) (0.65,0.70) (0.65,0.80) (0.70,0.80)

-2.12 0.03 1.68 4.06 0.86

0.30 0.10 0.07 0.00 0.08

3.26 0.68 0.99 3.38 0.16

-0.21 0.11 -0.54 0.17 1.43 0.07 2.51 0.06

0.93 1.39 0.73 1.82

BOKOYE ET AL.: ANGSTROM TURBIDITY AND AEROSOL OPTICAL THICKNESS

criterionensuresthat Ices-c•O < 0.2 and that 115s - [StA< 0.02, sincees/•s is generally> 10. When theselast two conditions are met, the mean relative difference between beam irradiances

calculatedfrom (O•u, Bu) and from ((•s,•s) is then2%. Table 3 shows,for example,for a given beam spectrum,the set of c•U, 13 U, and d values obtainedfrom the respective45 pairs of wavelengthswhich were selected.As was previously observed by Cachorro et al. [1987], the dependence of Angstr6m coefficients on the selected wavelength pair is significant.The negativevalues of au which are observedare generally due to the unsuitabilityof the correspondingpair. If o•s is also negative,the presenceof very large sized particles in the atmospherecan be suspected. Table 4 gives in terms of percentage, for each of the 45 pairs of wavelengths considered, the number of the 509 spectra which follow relation (16). The best results are observed for the three pairs (0.350 [tm,0.750 [tm), (0.400 [tm,0.750 [tm), and (0.400 [tm,0.800 gin), where over 20% of the spectra follow relation (16). Although the (0.400 gm,0.800 [tm) pair achievesthe highestpercentage,0.400 and 0.750 [tm is consideredas the optimal pair becausethem is

no selectiveabsorptionby atmosphericgasesat 0.400 [tm and only a slight absorption by water vapor at 0.750 [tm; furthermorethese wavelengthsare located in the visible band. The Angstr6mparametersobtainedfrom this last pair are then notedas 0•oand [50(subscripto for optimal). For the wavelength pairs proposed by Cachorro and Casanova [1987], fewer than 10% of the spectra follow relation (16), as shown in Table 5. With regard to the usual (0.38 [tm,0.5 [tm) pair, no spectra were found to follow relation (16).

In order to assessa possible influence of the atmospheric turbidity and the solaraltitudeangle on the precedentresults, the 509 recorded spectra were divided into 24 classes of various TLAM2 and ¾values, as shown in Table 6. Figure 1 givesfor each (TLAM2,¾)classso defined,the sumN of the 45 numbersof spectra(corresponding to the 45 wavelengthpairs tested)which follow relation (16). From this figure, one can conclude that there are very few wavelength pairssuitable for an accuratemodeling of solar beam irmdiancesat low solar altitude,whereasat very high ¾values,suchmodelingappears to be more efficient at strongturbidity conditions.

Table 4. Percentages p of the 509 RecordedSpectraWhich Meet the Criteriond < 0.2 for EachWavelengthPair Pair, lum

p, %

(0.35,0.40) 4.71 (0.35,0.55) 11.60 (0.35,0.70) 1.75 (0.40,0.45) 0.00 (0.40,0.60) 0.98 (0.40,0.75) 22.98 (0.45,0.55) i2.80 (0.45,0.70) 0.20 (0.50,0.55) 0.00 (0.50,0.70) 0.00 (0.55,0.60) 0.39 (0.55,0.75) 3.73 (0.60,0.70]) 0.00 (0.65,0.70) 5.30 (0.70,0.75) 0.98

Pair, gm (0.35,0.45) (0.35,0.60) (0.35,0.75) (0.40,0.50) (0.40,0.65) (0.40,0.80) (0.45,0.60) (0.45,0.75) (0.50,0.60) (0.50,0.75) (0.55,0.65) ('0.55,0.80) (0.60,0.75) (0.65,0.75) (0.70,0.80)

p, %

Pair, lum

6.88 8.25 20.23 0.00 7.07 23.96 10.2i 8.40 1.76 0.00 0.00 2.75 0.00 5.69 1.18

(0.35,0.50) (0.35,0.65) (0.35,0.80) (0.40,0.55) (0.40,0.70) (0.45,0.50) (0.45,0.65) (0.45,0.80) (0.50,0.65) (0.50,0.80) (0.55,0.70) (0.60,0.65) (0.60,0.80) (0.65,0.80) (0.75,0.80)

p, % 0.59 3.53 19.40 4.51 5.10 0.00 5.90 6.68 0.00 0.59 0.00 0.00 5.89 12.57 3.92

21,909

Table 5. Percentages p of the 509 RecordedSpectraWhich Meet the Criteriond < 0.2 for EachWavelengthPair as Proposedby Cachorroand Casanova[1987] ,

Pair, lum

p, %

Pair, lum

p, %

(0.44,0.50) (0.44,0.66) (0.50,0.64) (0.50,0.85) (0.64,0.85)

0.00 8.25 0.59 1.18 7.66

(0.44,0.64) (0.44,0.85) (0.50,0.66) (0.64,0.66) (0.66,0.44)

9.82 6.68 0.39 !.I 8 8.25

5. Comparison of Various AngstrOmParameters 5.1. Parameter

In an attemptto link the Angstr6m15coefficientsobtained from the five methods presented, these parameters were

comparedto referenceparameter155.The polynomial fitting method was applied in order to assessthe magnitudeof such comparisons.The correspondingcorrelationswhich permit us to infer the relYrenee13sfrom the other [• valueswere expressed in polynomial form as •$ = mo + ml [• + rn2 fi2 (17) The resultsof thesecorrelationsare given in Figure 2. The

coefficient13o,which is calculatedfrom the optimal wavelength pair, expectedly gives the best coefficient of correlation(r = 0.981), while [•D gives the worst (r = 0.859). On the other hand, the coefficient obtained for the usual

wavelengthpair, is surprisinglygood (r = 0.932). The methodsof determinationof parameterssuchas [•L,[•I, or •D are the •nostsimpleand the leastexpensivebecausethey implementclassicalpyranometers(broadbandirmdiances)and require only, as input data, the precipitablewater vapor w and the amountof ozone lo. As a result, second-orderpolynomials of the type of (17) were establishedbetweeniSLtaken as a measuredvariableand the other 15parameters.Figure 3 shows the various r coefficientsobtainedand the correspondingsets

of m coefficients whichpermitcorrelations between15 L andthe valuesof 13I,•D, •U, •G, •O to be inferred.The coefficientof the correlation between 131and [•L is strong because,even though determinedby meansof broadbandinstruments,these parametersare both defined from direct spectral irradiance models.The scatteringobservedfrom the correlationswith [Su, 13G,and Bo is mainly due to the variationsof the a parameter (assumed to be constantfor [•I or 15L).

Table 6. Numbersof RecordedSpectrain the Respective Classesand CorrespondingMean Solar Altitude TLAM2

¾, deg

2.0-3.0

3.0-4.0

4.0-5.0

10-20 20-30 30-40 40-50 50-60 60-70

24 (17.6) 77 (25.3) 39 (34.4) 23 (45.6) 16 (53.1) 0

!3 (17.1) 22 (24.7) 49 (35.4) 36 (45.5) 34 (54.5) 26 (64.9)

0 8 (27.1) 8 (36.i) 18 (44.7) 29 (54.6) 38 (64.6)

5.0-6.0

0 0 10 (36.3) 11 (45.6) 9 (55.6) 19 (64.5)

Values in parantheses are mean solaraltitudein degrees.

21,910

BOKOYE ET AL.' ANGSTROMTURBIDITY AND AEROSOLOPTICALTHICKNESS 5.2.

It is possibleto determinethe a value simultaneouslywith the • valueonlyif directirradiance at two or morewavelengths is known (as in the three methods U, O, and S). Since Gueymard'sone wavelengthmethodrequirestwo a valuesfor each spectra(given in Table 2 as functionsof atmospheric humidity,for four typical conditions),a comparisonwas made betweenau, ao, and as only. As shownin Figure 4, a strong correlationis observedwhen as is comparedwith a o (r = 0.910), while as exhibitsa weak correlationwith au. It is interesting to note that as can be expressed as a linear functionof TLAM2, but the validity of sucha relationshipis

250

200

.....

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• 4