determination of tropospheric aerosol characteristics by spectral measurements of solar radiation...

Determination of tropospheric aerosol characteristicsby spectral measurements of solar radiation using

a compact, stand-alone spectroradiometer

Naohiro Manago* and Hiroaki KuzeCenter for Environmental Remote Sensing, Chiba University, 1-33 Yayoi-cho, Inage-ku, Chiba-shi, Japan

*Corresponding author: [email protected]‑u.jp

Received 4 November 2009; revised 5 February 2010; accepted 5 February 2010;posted 19 February 2010 (Doc. ID 119524); published 9 March 2010

We developed a method for characterizing atmospheric properties from ground-based, spectral measure-ments of direct and scattered solar radiation under clear sky conditions. A compact spectroradiometer isemployed for radiation measurement in the wavelength range between 350 and 1050nm with a resolu-tion of 10nm. Spectral matching of measured and simulated spectra yields a set of optical parametersthat describe optical characteristics of tropospheric aerosols. We utilize the radiative transfer codeMODTRAN4 for constructing realistic atmospheric models. Details of the system calibration, analysisprocedure, and the results of its performance test are described. © 2010 Optical Society of America

OCIS codes: 280.1100, 280.4788.

1. Introduction

Tropospheric aerosols show significant variationsboth spatially and temporally. The direct and indir-ect effects of aerosol particles influence the Earth’sradiation budget [1]. In urban areas, aerosols inthe atmospheric boundary layer occasionally causehealth problems [2]. Satellite observations can beuseful for monitoring aerosol distributions in wideareas, though the lack of precise knowledge on theoptical properties of local/regional aerosols oftenleads to uncertainties in the retrieved results. Thenetwork observations using sunphotometers/skyradiometers [3–6] are one of the major attempts toobtain aerosol properties from ground-based mea-surements, giving aerosol optical depth (AOD) andother optical parameters indispensable for validat-ing satellite-retrieved results.Recently a number of researchers have proposed

the use of charge-coupled-device (CCD) cameras forradiation measurements. For example, Olmo et al.[7] proposed a newmethod for retrieval of the aerosol

and cloud optical depth using a CCD camera equip-ped with a fish-eye lens. Kreuter et al. [8] presented asimple, fully automated all-sky imaging systembased on a commercial digital camera with a fish-eye lens and a rotating polarizer. Kouremeti et al.[9] described the characteristics of a CCD spectro-graph developed for direct solar irradiance and skyradiance measurements. Although the applicationof a CCD camera system is attractive for enhancingthe mobility of skylight measurements, it is ratherdifficult to obtain whole spectral features in a quan-titative manner. Development of new spectroradi-ometers for solar and diffuse radiation has alsobeen undertaken. Bassani et al. [10], for instance,assessed the performance of a FieldSpec spectroradi-ometer for retrieving AOD with some modification ofits basic configuration in order to measure directsolar irradiance at ground level. Also, Zieger et al.[11] described an airborne spectrometer system de-signed for the simultaneous measurement of the di-rect solar irradiance and the aureole radiance in twodifferent solid angles. However, such spectroradi-ometer systems are often bulky, and stand-alonemeasurements without on-site PC control cannotbe practically implemented.

0003-6935/10/081446-13$15.00/0© 2010 Optical Society of America

1446 APPLIED OPTICS / Vol. 49, No. 8 / 10 March 2010

In the present work, we propose and demonstratethe use of a compact, stand-alone spectroradiometerfor the retrieval of aerosol optical properties frommeasurements of both direct and scattered solar ra-diation under clear sky conditions. As compared withthe sunphotometer/skyradiometer methodology, thepresent method provides a complementary approachin regard to the following three aspects. First, the in-strument is battery operated with no need for PCcontrol during measurement. Thus, our method en-hances the mobility of ground observation points.Second, instead of radiation values at discrete, pre-determined spectral bands, the spectroradiometerprovides a continuous spectrum that covers the en-tire visible spectral range. Thus, the spectra result-ing from the parameter fitting can be compared withthe measured spectra in the entire spectral range.Third, any types of standard radiative transfer codescan be employed for the retrieval procedure, since theanalysis is based on the forward calculation startingfrom the assumption of initial parameters. Here weemploy the MODTRAN4 radiative transfer code [12]to reproduce the observed spectra by iterative calcu-lations, with which we optimize the aerosol parame-terization. This type of approach has the advantagethat realistic atmospheric models are easily incor-porated into the analysis, while fully exploiting thecapability of the radiative transfer code. Recent de-velopment of PC capabilities has contributed greatlyto alleviate the problem of long computation time in-herently required for the implementation of such aniterative forward calculation method.

2. Experimental Details

A portable spectroradiometer (EKO, MS-720) is usedto measure the spectra of solar radiation. This in-strument is capable of measuring both direct solarradiation (DSR) and scattered solar radiation(SSR) in the wavelength range of 350–1050nm(Table 1). A thick filter (diffuser) attached to theaperture ensures an angular response that is mostlyclose to the cosine of the incidence angle θ, and it canbe approximated as

CðθÞ ¼ ð1 − C1θ − C2θ2Þ cos θ ðθ < 30 °Þ: ð1ÞThe coefficients C1 and C2 were measured to be 6:1 ×10−4 deg−1 and 7:7 × 10−6 deg−2, respectively. (The dif-ference between CðθÞ and cos θ is 0.7% at θ ¼ 10 °.)

Since the original field of view (FOV) of 180° is toowide for the present purpose, home-made baffletubes (see Fig. 1) are used to limit the FOV to 20°(SSR) and 5° (DSR). Another baffle tube capturingthe FOV between 5° and 20° is used to measurethe aureole (AUR), the scattered light just aroundthe Sun. This AUR component is useful for the aero-sol optical characterization, since it reinforces infor-mation on the forward scattering. The inner surfaceis completely covered with a photon-absorbing sheetwith a nearly constant spectral reflectance of 1.5% inthe wavelength range of 250–2500nm. During thedesign process, Monte Carlo simulation was con-ducted to evaluate the stray light intensity insidethe baffle tubes. The result shows that the level ofstray light is less than 0.3% even in the worst case.

A. Radiative and Temperature Calibration

Measured values of irradiances are temperature cor-rected and absolutely calibrated in order to removesystematic errors. Instead of controlling the tem-perature, the spectroradiometer measures its innertemperature and corrects for the temperature depen-dence automatically, though the correction is insuffi-cient for our purpose. We measured the remainingtemperature-correction factors between −10 andþ40 °C for all the channels. Some of the factors areas large as 0:5%=K. With these factors, measured ir-radiances are converted to irradiances at the stan-dard temperature (15 °C). The irradiances are thenabsolutely calibrated using factors calculated bythe Langley method, which is often used to calibratesunphotometers [13]. The data for the calibrationwere taken on the summit of Mauna Kea in Hawaiifor three days in February 2008. In order to matchthe scale of the spectroradiometer and MODTRAN4,instead of the standard airmass [14], we used theeffective airmass defined as

meff ðθ; λÞ ¼ ln½Icalcðθ; λÞ=Icalct ðλÞ�= ln½Icalcð0; λÞ=Icalct ðλÞ�:ð2Þ

Here, Icalcðθ; λÞ and Icalcð0; λÞ are solar irradiance forzenith angle θ and 0, respectively, calculated byMODTRAN4 with the same atmospheric model thatreproduces the measured irradiance; Icalct ðλÞ is the so-lar irradiance at the top of the atmosphere calculatedfrom the literature [15] and also used by MOD-TRAN4. Considering the optical resolution of thespectroradiometer properly, this method is applic-able even at wavelengths of weak molecular absorp-tion bands. The deviations of the absolute-calibrationfactors estimated with 6 Langley plots were about0.5% in the visible range.

B. Radiation Measurement and Related Corrections

All the measurements were conducted at Chiba Uni-versity (35:62°N, 140:10°E) under clear sky condi-tions. The SSR measurements were made in 24directions (north, east, south, and west directions,each with six elevation angles of 15°, 30°, 45°, 60°,

Table 1. Specifications of MS-720

Parameter Value

Dimension 100mm× 165mm× 60mmWeight (including battery) 700gNumber of channels 256Practical range 350–1050nmOptical resolution (FWHM) 10nmSampling interval 3nmField of view (full angle) 180°Exposure 5ms–5 sTypical battery life 18 h (1000 spectra)

10 March 2010 / Vol. 49, No. 8 / APPLIED OPTICS 1447

75°, and 90°). The DSR and AUR components weremeasured before and after the SSR measurements.Dark values were automatically evaluated and sub-tracted after each measurement. The total time re-quired to complete a set of DSR, AUR, and SSRmeasurements was 30–40 min.Nonuniformity of the intensity distribution of the

scattered radiation must be considered to accuratelyevaluate the SSR and AUR components, since theFOV of the baffle tube is relatively wide (20°). Simi-larly the contribution of scattered light (background)in the FOV (5°) must be corrected for the evaluationof DSR. These correction factors are estimated by si-mulating scattered radiation at several points withinthe FOV as follows.The spectral irradiance measured by the instru-

ment can be given as

IðλÞ ¼Z

Lðλ; θ;ϕÞCðθÞGðθÞdΩ; ð3Þ

where Lðλ; θ;ϕÞ stands for the scattered radiancewith wavelength λ, zenith angle θ, and azimuth angleϕ. The factor CðθÞ is the intrinsic incidence angle de-pendence of the spectroradiometer, and GðθÞ is thegeometrical factor that describes the unshaded frac-tion of the aperture area when one of the baffle tubesis attached. The incidence angle dependence of thedetection efficiency of the spectroradiometer itselfand that of the spectroradiometer with the baffletubes are shown in Fig. 2(a). The value of IðλÞ inEq. (3) is evaluated by dividing the FOV into 4 ×16 subsections as illustrated in Figs. 2(b)–2(d). By re-placing the integration with summation, we obtain

Fig. 1. (a) Baffle tube connected with a spectroradiometer MS-720. Baffle tubes are for (b) SSR, (c) AUR, and (d) DSR measurements.Units are in mm.


IðλÞ ¼Xi

LiðλÞΩ0i; ð4Þ

Ω0i ¼

ZCðθÞGðθÞdΩi: ð5Þ

Here, the spectral radiance LiðλÞ must be recal-culated for each correction procedure, while the so-lid-angle factor Ω0

i can be tabulated beforehand.For nonuniformity correction, the correction factorscan be determined by comparing the average spec-tral radiance (IðλÞ divided by the FOV solid angle)with the corresponding value at representativepoints (at which the correction factor is expected tobe ∼1, i.e., the center of FOV for SSR, and the inter-mediate point of the ring for AUR, see Fig. 2). Thecorrection factors for the background can be deter-mined by comparing IðλÞ with simulated spectralirradiance of DSR.

C. Correction of Simulated Spectra

Measured spectra are reproduced by the radiativetransfer code MODTRAN4 (see Appendix A for de-tails). The code gives simulated DSR, SSR, and

AUR spectra, which must further be corrected foreffects of spectral resolution and multiple scattering.

The optical resolution of MODTRAN4 calculationis 2, 10, or 30 cm−1, much narrower than that of thespectroradiometer (10nm). Therefore, it is necessaryto convolute a simulated spectrum with a Gaussianprofile having the instrumental resolution before it iscompared with the measured spectrum. The convolu-tion process can be included in the optimizationiteration of DSR, since the simulation can be imple-mented with short computation time. In the case ofSSR and AUR, on the other hand, limitation on thecomputation time hinders the full implementation ofthe process. Thus, the Gaussian convolution is re-placed with a calculation at four wavelength points,with the help of a lookup table that converts the four-point averaging spectra into Gaussian spectra. More-over, the scattered radiation is calculated only at thewavelengths for which this conversion factors showrelatively minor dependence on the aerosol param-eters chosen.

To evaluate the multiple scattering effects on SSR,two types of algorithms, DISORT [16] and Isaacs[17], are implemented in the MODTRAN4 code.

Fig. 2. (a) Detection efficiency of the spectroradiometer (with no baffles) and the whole instrument (with the baffle tubes for DSR/AUR/SSR measurements) as a function of the incidence angle. (b)–(d) Division of the radial and azimuthal directions into 4 and 16 subsectionsfor radiative corrections to (b) SSR, (c) AUR, and (d) DSR. The circles stand for the representative points, and the scales stand for theradiance (mW=m2=nm=sr).


Although the DISORT algorithm generally givesmore accurate results, it requires more time andonly the Isaacs algorithm can be used during theoptimization process. We calculate SSR spectrumwith Isaacs algorithm first, then we convert it to aDISORT(16 streams)-equivalent spectrum using cor-rection factors previously calculated for each mea-surement with the best-fit parameters at the time.

3. Spectrum-Matching Method

The aerosol parameters that should be optimizedthrough the fitting of the measured spectra are(i) theAOD τ550 atwavelength550nm, (ii) wavelengthdependence of the aerosol extinction coefficient αextðλÞ(normalized against the value at 550nm), (iii) wave-length dependence of the aerosol scattering coef-ficient αscaðλÞ (normalized against the extinction coef-ficient at550nm), and (iv) the phase function f ðλ; χÞasa function of wavelength λ and scattering angle χ.Auxiliary parameters such as the single-scatteringalbedoωðλÞ and asymmetry parameter gðλÞ can be cal-culated from these parameters. Additionally, (v) thewater vapor column amount should be optimizedsince it has a large impact on the measured spectradirectly at the absorption bands and indirectly bymodifying characteristics of aerosols.

A. Water Vapor Column Amount and Aerosol OpticalDepth

Water vapor exhibits absorption bands with signi-ficant intensity in the measurement range of thespectroradiometer. Figure 3 shows an example ofmeasured and simulated DSR spectra around725nm. In the simulation, water vapor columnamount can be adjusted by modifying the water scalefactor (WSF) Sw to scale the default column amount(2:92231 g=cm2 for the midlatitude summer model,and 0:85170 g= cm2 for the midlatitude winter mod-el). The value of Sw can be optimized by fitting simu-lated DSR spectra to the measured ones. In advanceof the fitting, simulated spectra are scaled to matchwith the measured ones at both ends of the absorp-tion band. In this process, differences of the linearslopes due to, for example, disagreement of theaerosol model are removed. Note that optical resolu-

tion of the spectroradiometer must be correctlyincorporated.

TheDSRspectra at550nmdependprimarily on theAOD at 550nm (τ550). Thus the value of τ550 can be op-timized by fitting simulated DSR spectra to the mea-sured ones at 550nm. To reduce the influence ofstatistical errors in the measured spectra, not onlythe channel nearest to 550nm but also the channelsbetween 535nm and 562nm are used for the fitting.

B. TCAM Parametrization

Other parameters, αextðλÞ, αscaðλÞ, and f ðλ; χÞ, are op-timized using all the measured spectra (DSR, SSR,and AUR). In order to reproduce all the observedspectra with sufficient accuracy, the appropriatechoice of aerosol parameter set is of critical impor-tance. Obviously too few parameters cannot dealwith real situations with variable aerosol compo-nents, whereas too many parameters lead to fre-quent failure of convergence during the fittingprocedure. Here we introduce the three-componentaerosol model (TCAM), which is composed of threetypes of aerosol species with own complex refractiveindexes dependent on wavelength and own monomo-dal log-normal size distribution. (The spectrum-matching program can include up to 10 components,but only the first three components can be opti-mized.) In the present work, the three species corre-sponding to water soluble (component 1), sea salt(component 2), and soot (component 3) shown inFig. 4(a) are chosen from the aerosol database com-piled by Levoni et al. [18]. It is noted that the similarchoice of aerosol species has been adopted in both theaerosol database of the World Meteorological Oega-nization [19] and the air-pollution transport simula-tion SPRINTARS [20], though the present modeldoes not include the dust particles. This is becauseat our observation location (Chiba University, about30km south of central Tokyo), dust is of relativelyminor importance [21] except for the outbreak ofheavy Asian dust events [22]. Thus, TCAM forms a“quasi-complete” basis for aerosol parametrization,i.e., optical parameters of most aerosols can be repro-duced by linear combinations of the basis. Figure 4(b)shows the possible range of optical parameterscovered by the TCAM parametrization.

Optical parameters of each component assumed tobe spherical are calculated with the Mie scatteringcode developed by Wiscombe [23]. Or, they are calcu-lated assuming a randomly oriented spheroid with afixed aspect ratio (for example, 1.7 for dust particles[24]) using the code developed by Dubovik et al. [5] inwhich the T-matrix method [25] is used for smallerparticles, while the approximate geometrical opticsintegral equation method [26] is employed for largerparticles. (Hereafter, r denotes equal-surface-area-sphere radius for spheroids.) Optical parameters ofthe total mixture are calculated assuming externalmixing.

The TCAMparametrization can be described usingnumber mixing ratio ni, mode radius ri, and width

Fig. 3. Variation of spectral irradiance around 725nm water ab-sorption band for various values of the water scale factor Sw. Solidand dashed lines represent observed and simulated spectra, re-spectively. The 12 channels marked with filled circles were usedfor the analysis.


of log-normal distribution wi ði ¼ 1; 2; 3Þ (seeAppendix B for details). The number of independentparameters is eight, since there is a normalizationcondition among number mixing ratios.In the fitting procedure, the ratio of contribution to

the spectral intensity can be treated easier than thenumber mixing ratio. Hence, we introduce mixingratio of extinction cross-section defined as

mi ¼ Cmni�σexti ðλ550Þ; ð6Þ

where �σexti ðλ550Þ is the mean extinction cross sectionat wavelength 550nm averaged over the entire sizedistribution of the ith component. The factor Cm isdefined so that mi satisfies the normalization condi-tion Σimi ¼ 1. Considering the fact that the value ofmi=m1 may change by a few orders of magnitude, thevalue of

Mi ¼ log�mi

m1

�; i ¼ 2; 3; ð7Þ

will be optimized in the fitting procedure.

As for the mode radius ri and the width wi, theycannot be optimized independently, since a largervalue of wi inevitably leads to a larger value of effec-tive radius. Here, we define effective radius reffi ðλÞ asthe radius r at which extinction cross section σexti ðr; λÞequals the mean extinction cross section �σexti ðλÞ, i.e.,

σexti ðreffi ðλÞ; λÞ ¼ �σexti ðλÞ: ð8Þ

Fig. 5. Aerosol extinction cross section as a function of particleradius r. The dashed line shows the smoothed function used inthe TCAM analysis.

Fig. 4. Aerosol models assumed in the scheme of the three-component aerosol model (TCAM). (a) Real part and (b) imaginary part of thecomplex refractive indices as a function of wavelength: component 1 (water soluble, solid line), component 2 (oceanic, dashed line), andcomponent 3 (soot, dotted line). (c)–(e) Possible range of aerosol optical parameters calculated from each component of the TCAM (grayarea, component 1; 45° lines, component 2; 135° lines, component 3), assuming that the particle size changes between 10−2:5 and 10þ1:5 μm.(c) Extinction coefficient normalized at 550nm, (d) single-scattering albedo, and (e) asymmetry parameter.


From this definition, effective radius may not bedefined uniquely if the radius r is comparable tothe wavelength λ, and σexti ðr; λÞ exhibits oscillatingbehavior that breaks the one-to-one relationship be-tween r and σexti ðr; λÞ. In this case, instead of σexti ðr; λÞ,appropriately smoothed function ~σexti ðr; λÞ is used asshown in Fig. 5 so that the one-to-one relationship isretained. The relationship between reffi ðλÞ and ri isalso one-to-one when wi is fixed. Figure 6(a) showsthe relationship between reffi ðλÞ andwi under the con-dition that ri is fixed. The wavelengths chosen for theplot is 550nm (solid line), 350nm (dashed line), and1050nm (dotted line). Parameter values in the par-entheses stand for the common logarithm of the fixedvalues of ri (μm). When wi is small, reffi ðλÞ is nearlyequal to ri, whereas for larger wi, the value ofreffi ðλÞ becomes larger than ri. Figure 6(b), on theother hand, shows the same relationship betweenreffi ðλÞ and wi, except that the effective radius at550nm, i.e., reffi ðλ550Þ is fixed instead of ri. Althoughthe value of reffi ðλÞ is still dependent onwi, the depen-dence is much more limited than in the case of Fig. 6(a). This result indicates that in the determination ofTCAM parameters, it is reasonable to optimize thevalue of reffi ðλ550Þ instead of ri. As a result, the num-ber of parameters can be reduced, with virtuallyeliminating the influence of wi. Since reffi ðλ550Þ canvary in a range of several magnitudes, practicallythe following parameter Ri is used for the optimiza-tion procedure:

Ri ¼ log½reffi ðλ550Þ�; i ¼ 1; 2; 3: ð9Þ

Fig. 6. Relation between effective radius reffi ðλÞ and the width parameter wi of the log-normal size distribution. The solid line is forwavelength λ ¼ 550nm, the dashed line for λ ¼ 350nm, and the dotted line for λ ¼ 1050nm. Parameter values in the parentheses standfor the fixed values (a) common logarithm of the mode radius ri and (b) effective radius reffi ðλ550Þ.

Fig. 7. Flow chart of the parameter optimization based on theTCAM method.


C. Optimization of TCAM Parameters

The optimization of aerosol parameters is achievedby minimizing the following function:

f ðpÞ ¼ 1NiNj

Xi

Xj

½Iiðλj; pÞ − I0iðλjÞ�2e2ij

: ð10Þ

Here I0iðλjÞ and Iiðλj; pÞ denote the measured and si-mulated spectra, with suffixes i and j denoting datanumber and wavelength number, respectivelyðNi ≡ Σi;Nj ≡ ΣjÞ. The parameter p is a vector com-posed of the parameters to be optimized: p ¼ðSw; τ550;M2;M3;R1;R2;R3Þ. The factor eij deter-mines the weight of the spectrum, and thus it influ-ences the resultant difference between measuredand simulated spectra. We defined here as eij ¼0:05I0iðλ0Þ, so that wavelength dependence of the dif-ference spectra will be small, and the intensityreflects on the weight to some extent. (The normal-ization of eij has no influence on the result exceptfor the DSR. The minimization function for DSR,fDSRðpÞ, will be compared with unity as explainedlater.) To minimize the function f ðpÞ, we use MIN-UIT, a tool used to find the minimum value of a mul-tiparameter function [27].The two basic parameters, WSF (Sw) and AOD

(τ550), are optimized independently using DSR onlyas explained in Subsection 3.A. Since DSR dependson these parameters linearly, the minimizationfunction with the only one variable has a uniqueminimum. Other parameters ðM2;M3;R1;R2;R3Þ, es-sential parts of the TCAM parameterization, are de-termined by employing all of the DSR, AUR, and SSRsimultaneously. Practically, this is implementedby minimizing the product of functions fDSRðpÞ,f AURðpÞ, and f SSRðpÞ. Instead of the summation, weuse the product so that the normalization of eachfunction has no influence. Since this minimization

function may have multiple local minima, MINUITmay end up choosing the wrong local minima. In or-der to avoid this situation, initial parameters areestimated by a grid search.

The DSR spectrum primarily depends on theextinction coefficient, which is the sum of the absorp-tion coefficient and the scattering coefficient. If onlyDSR were available, one could not distinguish differ-ent aerosol compositions with the same extinctioncoefficients but different absorption/scattering coeffi-cients, nor with the same scattering coefficients butdifferent phase functions. On the other hand, SSRand AUR depend on scattering coefficients and phasefunctions. Since both SSR and AUR are measured indifferent directions, the combined data enable se-paration between the scattering coefficient and thephase function. In particular, AUR is valuable for re-trieving the phase function, since the forward scat-tering is critically governed by the aerosol sizedistribution. For this reason, only SSR and AURare used during the optimization of the TCAM pa-rameters as long as DSR is reproduced with a certainlevel of accuracy. This is realized by replacing fDSRðpÞwith unity, if the original value is smaller than unity.

Figure 7 shows the flowchart of the spectrum-matching procedure. Normally, the procedure is exe-cuted twice to change the aerosol model required insteps 2 and 3. In the first run, one of the default aero-sol models in MODTRAN4 that reproduces the mea-sured spectra best is used at the early stage. Thenthe custom aerosol model optimized through the firstrun is used in the second run.

4. Results and Discussion

Here we show the optical parameters of aerosols de-rived by applying the spectral matching methodusing the TCAM to the data taken at the Centerfor Environmental Remote Sensing (CEReS), ChibaUniversity, from 12:25 to 12:58 JST on 30 December

Fig. 8. Spectral matching for the spectra observed at 12:30 on 30 December 2008: (a) DSR, (b) SSR, and (c) AUR. The channels markedwith circles were used for the analysis.


2008. The temperature, air pressure, relative humid-ity, wind speed, and wind direction were 13:7°C,1002:6hPa, 47%, 1:3m=s, and westerly, respectively,according to the meteorological data taken at the ob-servation site. The elevation angle (30:4° to 28:6°)and azimuthal angle (191:4° to 199:9°) of the appar-ent solar position were calculated for each spectrumfrom the time stamp recorded by the spectroradi-ometer’s built-in clock (which, in advance, was syn-chronized with a network time protocol server). Weused the aerosol vertical profile obtained by the lidarequipment near the site maintained by CEReS andthe National Institute for Environmental Studies(NIES), and we used the ground surface albedo mea-sured by the Moderate Resolution Imaging Spectro-radiometer (MODIS) on-board the Terra/Aquasatellites [28]. In addition we used the ozone columnamount (288 DU) around the site measured by theOzone Monitoring Instrument (OMI) on-board theAura satellite [29]. It is noted, however, that theseancillary parameters are not significantly differentfrom normally assumed values. Thus, even if stan-dard values were used in the analysis, the resultingchanges in the aerosol parameters are relativelysmall. Spectrum matching without the lidar profile,for example, has led to a decrease in the values ofSSA and asymmetry parameter by about 0.01 and0.005, respectively (see Fig. 9, shown below).Figure 8 shows the spectral matching between the

observed and simulated spectra. We measured theAOD and water vapor column amount to be0:190� 0:001, 0:80� 0:04 g=cm2, respectively. The

other aerosol optical parameters are shown in Fig. 9and Table 2. The errors of the fitting parameters arebased on the fitting uncertainties estimated by MIN-UIT, and some of the propagated errors are esti-mated by Monte Carlo calculations.

The AOD obtained here is considerably larger thanthe typical value of the site in winter (about 0.14).The fact that the water vapor column amount is twiceas large as the typical value suggests the occurrence

Fig. 9. Aerosol optical parameters derived from the DSR, SSR, and AUR observations on 30 December 2008: (a) extinction coefficientnormalized at 550nm, (b) single-scattering albedo, (c) asymmetry parameter, and (d) phase function at 550nm. Error bars indicate onestandard deviation. (Meteorological data at the observation site: temperature 13:7 °C, relative humidity 47%, atmospheric pressure1002:6hPa, and wind speed 1:3m=s.)

Table 2. Parameters Derived from the Spectrum Matching(12:30 JST on 30 December 30 2008)

Parameter Best-Fit Value Errora

AOD 0.190 0.001Water column (g=cm2) 0.80 0.04Ångström parameter 1.3 0.1m1 0.84 0.05m2 2:6 × 10−3 0:7 × 10−3

m3 0.16 0.05n1 0.9 0.1n2 0.1 0.1n3 7 × 10−5 7 × 10−5

reff1 ðμmÞ 0.087 0.007reff2 ðμmÞ 0.06 0.01reff3 ðμmÞ 1.7 0.5r1ðμmÞ 0.030 0.003r2ðμmÞ 0.016 0.005r3ðμmÞ 0.9 0.3w1 0.31 Fixedw2 0.33 Fixedw3 0.34 Fixed

aErrors correspond to one standard deviation.


of humidity growth of aerosol particles. The smallvalue of the Ångström parameter (see Table 2) alsoindicate the predominance of relatively largeparticles.As explained in Section 2, radiative and tempera-

ture calibration of the instrument (Subsection 2.A)and various corrections applied on the spectra (Sub-section 2.C) have both contributed to reducing sys-tematic errors. As a result, it is expected thatsystematic errors remaining in the measured spectraare around 1% in total. In addition to the systematicerrors, the measured spectra contain ∼1% of statis-tical errors. To evaluate the effects of these errors, wesimulated DSR/SSR spectra with a set of aerosol op-tical parameters (true values), then added uniformerrors or random errors (corresponding to the sys-

tematic errors and statistical errors, respectively)to the spectra and retrieved aerosol optical proper-ties from the “contaminated” spectra. Here, as abasis, we employ the aerosol optical parameters re-trieved from the sample spectra in the previous sec-tion. Since the impacts of aerosol optical parameterson DSR/SSR spectra depend on the amount of aero-sols, we investigated the turbid case with τ550 ¼ 0:37(equivalent optical visibility V550 ∼ 20km) and theclear case with τ550 ¼ 0:10ðV550 ∼ 80kmÞ. The re-sults are shown in Fig. 10. In almost all cases the dif-ferences between the true and retrieved values ofSSA and the asymmetry parameter are equal to orless than 0.01. However, larger SSA differences(∼0:04) are observed in the cases with τ550 ¼ 0:10and 1% of uniform/random errors on theDSR spectra.

Fig. 10. Sensitivity analysis of the TCAM approach. Aerosol optical parameters, namely the normalized extinction coefficient, single-scattering albedo, and asymmetry parameter, are plotted as functions of wavelength for the following three cases: (a) 1% systematic error isassumed in DSR, (b) 1% systematic error is assumed in SSR/AUR, and (c) 1% statistical (random) error is assumed in DSR/SSR/AUR. Thesolid lines represent the originally postulated values, while the dotted and dashed lines are for the turbid (τ550 ¼ 0:37) and clear(τ550 ¼ 0:10) case, respectively.


5. Conclusion

We have developed a method of retrieving aerosoloptical parameters from direct and scattered solar ra-diation spectra measured by a compact spectroradi-ometer. The MODTRAN4 code has been used toimplement radiative transfer calculations based onrealistic atmospheric models, including the three-component aerosol model that provides a quasi-complete basis for reproducing actually encounteredaerosol optical properties. Some of the input param-eters of MODTRAN4, such as ozone column amount,ground surface albedo, and vertical aerosol profile,are assumed tohavevalues estimated fromother datasources. Careful considerations on instrumental de-sign, calibration, and data correction have all contrib-uted to reducing the systematic errors to less than1%.In addition to the application to the real data, the ac-curacy and reliability of our method have beenchecked by a simulation estimating the effects of bothsystematic and statistical errors. In particular, thesingle-scattering albedo can be determined with aprecision of approximately 0.01 when the AOD is0.37 (equivalent to a ground visibility of 20km).Although we have assumed clear sky conditions inthe present analysis, it would be possible to takethe effects of cirrus clouds into account by utilizingMODTRAN4 with ancillary information from satel-lites such as Aura/MLS [30]. Another form of possibleextension of the present method is the incorporationof the polarization effect [31] by means of a polarizedversion of MODTRAN currently under development.

Appendix A: Radiative Transfer Simulation

The radiative transfer code MODTRAN4 is usedto reproduce the measured spectra. The code isdesigned to accept a variety of input options to imple-ment realistic simulations. Here we briefly summar-ize how the input data were adjusted in the actualfitting procedure.

1. Observation GeometryParameters describing the observation geometry

(altitude of the observer, apparent position ofthe Sun, and directions of the line-of-sight forSSR) are read from the input file called tape5. Sincethe apparent position of the Sun moves during theobservation period of 30–40 min, they are calculatedfor each measurement using the NOVAS-C func-tions [32].2. Molecular ModelIn the radiative transfer simulation, MODTRAN4

uses vertical profiles of pressure, temperature, 12common molecular species (H2O, CO2, O3, O2, etc.),and 13 heavy molecular species (CCl3F, etc.). Thereare 6 default molecular models (tropical atmosphere,midlatitude summer/winter, subarctic summer/winter, and 1976 U.S. standard atmosphere). Userscan choose one of themodels or use their custommod-els. We use the midlatitude summer model betweenMay and October, and the midlatitude winter modelduring the other season. The water vapor column

amount is adjusted in accordance with the measuredDSR spectra. The ozone column amount is given bythe OMI on-board the Aura satellite [29]. The verticalprofiles of pressure, temperature, and oxygen mole-cules are scaled according to the ground values.The default values are used for other parameters.

3. Aerosol ModelThe MODTRAN4 code can handle as many as four

different aerosol species with their own optical para-meters and vertical profiles. By default, aerosol 1 isassigned to the boundary-layer aerosol (0–3km),aerosol 2 to the free-tropospheric aerosol (2–11km),aerosol 3 to the stratospheric aerosol (10–35km),and aerosol 4 to the mesospheric aerosol (30–100km), although they can be distributed anywherewithin the range of 0–100km if custom profiles aregiven. The vertical profiles of default aerosols areaffected by the ground visibility (aerosol 1 and 2),season (aerosol 2 and 3), and volcanic activity (aerosol3 and 4). MODTRAN4 provides default aerosol mod-els such as rural, maritime, and urban models for theboundary layer. During the procedure of spectralmatching, aerosol optical parameters are optimizedonly in the boundary layer,while parameters for otherlayers are fixed at the default values.When lidar dataare available, the lidar profile of aerosol extinctioncoefficient at 532nm is employed in the troposphere(including the boundary layer) up to 10km. The mix-ing fraction of the boundary-layer aerosol is assumedto be 100% below 2km, linearly decreasing to 0% at3km. Absolute values of the profile are scaled inaccordance with the optical depth.

4. Ground Surface ModelScattered radiances are calculated with ground

surfaces parameterized by various bidirectional re-flectance distribution function [33] models. We as-sume the simplest Lambertian model, and theirwavelength-dependent albedo values are estimatedusing the Band 1–4 data of the Moderate ResolutionImaging Spectroradiometer (MODIS) on board theTerra/Aqua satellites [28], obtained under clear skyconditions. Different ground surface models may beinput for each measurement, and we input the aver-age albedo within a sector of 20° full angle aroundeach line-of-site direction (projected on the ground,i.e., north, east, south, and west). Here, a weightingfunction expð−αrÞ (where α is the extinction coeffi-cient and r is the distance from the site) is used tocalculate the average. It turns out that the spectralalbedos in the north, east, and south regions are si-milar to the spectral albedo of the Urban model inMODTRAN4, while the west region exhibits a spec-tral albedo similar to the Ocean Water model.

Appendix B. Aerosol Optical Parameters

Aerosol optical parameters are calculated from theTCAM parameters as follows: For each componenti, extinction cross section σexti ðr; λÞ and scatteringcross section σscai ðr; λÞ, each being a function of parti-cle radius r and wavelength λ, are related to the ex-tinction efficiency factor Qext

i ðr; λÞ and scattering


efficiency factor Qscai ðr; λÞ obtained from the Mie

calculation as

σext;scai ðr; λÞ ¼ πr2Qext;scai ðr; λÞ: ðB1Þ

It is assumed that each aerosol component has amonomodal, log-normal size distribution:

dni

d log r¼ niffiffiffiffiffiffi

2πp

wi

exp�−

ðlog r − log riÞ22w2

i

�: ðB2Þ

Here, we define mean extinction cross section �σexti ðλÞand mean scattering cross section �σscai ðλÞ as cross sec-tions averaged over the size distribution:

�σext;scai ðλÞ ¼Z

σext;scai ðr; λÞ�

dni

d log r

�d log rni

: ðB3Þ

Similarly, the mean phase function of perpendicu-larly polarized light �f si ðλ; χÞ and that of horizontallypolarized light �f pi ðλ; χÞ are calculated as

�f s;pi ðλ; χÞ ¼Z

f s;pi ðr; λ; χÞ�

dni

d log r

�d log rni

; ðB4Þ

where f si ðr; λ; χÞ and f pi ðr; λ; χÞ are phase functions ob-tained from the Mie calculation as a function of par-ticle radius r, wavelength λ, and scattering angle χ.Then, the mean phase function of natural light�f ni ðλ; χÞ can be given as

�f ni ðλ; χÞ ¼ ½�f si ðλ; χÞ þ �f pi ðλ; χÞ�=Z

½�f si ðλ; χÞ þ �f pi ðλ; χÞ�dΩ:ðB5Þ

Assuming external mixing and using the numbermixing ratio, ni, the optical parameters of the mix-ture (extinction cross section σextðλÞ, scattering crosssection σscaðλÞ, and phase function f nðλ; χÞ) are calcu-lated as

σext;scaðλÞ ¼X3i¼1

ni�σext;scai ðλÞ=X3i¼1

ni; ðB6Þ

f nðλ; χÞ ¼X3i¼1

ni�σscai ðλÞ�f ni ðλ; χÞ=X3i¼1

ni�σscai ðλÞ: ðB7Þ

Finally, normalized values of extinction coefficientαextðλÞ, scattering coefficient αscaðλÞ, and phase func-tion f ðλ; χÞ are given by

αext;scaðλÞ ¼ σext;scaðλÞσextðλ550Þ

; ðB8Þ

f ðλ; χÞ ¼ f nðλ; χÞRf nðλ; χÞdΩ : ðB9Þ

We would like to thank Dr. M. Yabuki for fruitfuldiscussion on aerosol optical properties, Dr. R. Guzzi

for providing their aerosol database, and Drs. O.Dubovik and L. Tatsiana for providing their programto calculate optical properties for nonspherical aero-sols. Also, we would like to thank the NIES commu-nity members and Drs. Takamura and Takano for thepermission to use the lidar data taken with the NIESlidar network.

References1. Intergovernmental Panel on Climate Change, Climate

Change 2007: The Physical Science Basis (Cambridge Univer-sity Press, 2007).

2. R. M. Harrison and J. Yin, “Particulate matter in theatmosphere: which particle properties are important for itseffects on health?,” Sci. Total Environ. 249(1–3), 85–101(2000).

3. T. Nakajima, G. Tonna, R. Rao, P. Boi, Y. Kaufman, andB. Holben, “Use of sky brightness measurements from groundfor remote sensing of particulate polydispersions,” Appl. Opt.35, 2672–2686 (1996).

4. B. N. Holben, T. F. Eck, I. Slutsker, D. Tanré, J. P. Buis, A.Setzer, E. Vermote, J. A. Reagan, Y. J. Kaufman, T. Nakajima,F. Lavenu, I. Jankowiak, and A. Smirnov, “AERONET—afederated instrument network and data archive for aerosolcharacterization,” Remote Sens. Environ. 66, 1–16 (1998).

5. O. Dubovik, A. Sinyuk, T. Lapyonok, B. N. Holben,M. Mishchenko, P. Yang, T. F. Eck, H. Volten, O. Munoz,B. Veihelmann, W. J. van der Zande, J.-F. Leon, M. Sorokin,and I. Slutsker, “Application of spheroid models to accountfor aerosol particle nonsphericity in remote sensing of desertdust,” J. Geophys. Res. 111, D11208 (2006).

6. T. Takamura and T. Nakajima, “Overview of SKYNET and itsactivities,” Opt. Pura Apl. 37, 3303–3308 (2004).

7. F. J. Olmo, A. Cazorla, L. Alados-Arboledas, M. A. López-Álvarez, J. Hernández-Andrés, and J. Romero, “Retrieval ofthe optical depth using an all-sky CCD camera,” Appl. Opt.47, H182–H189 (2008).

8. A. Kreuter, M. Zangerl, M. Schwarzmann, and M. Blumthaler,“All-sky imaging: a simple, versatile system for atmosphericresearch,” Appl. Opt. 48, 1091–1097 (2009).

9. N. Kouremeti, A. Bais, S. Kazadzis, M. Blumthaler, andR. Schmitt, “Charge-coupled device spectrograph for direct so-lar irradiance and sky radiance measurements,” Appl. Opt.47, 1594–1607 (2008).

10. C. Bassani, V. Estellés, M. Campanelli, R. M. Cavalli, andJ. A. Martínez-Lozano, “Performance of a FieldSpec spectrora-diometer for aerosol optical depth retrieval: method and pre-liminary results,” Appl. Opt. 48, 1969–1978 (2009).

11. P. Zieger, T. Ruhtz, R. Preusker, and J. Fischer, “Dual-aureoleand Sun spectrometer system for airborne measurements ofaerosol optical properties,” Appl. Opt. 46, 8542–8552 (2007).

12. G. P. Anderson, A. Berk, P. K. Acharya, M. W. Matthew,L. S. Bernstein, J. H. Chetwynd, H. Dothe, S. M. Adler-Golden,A. J. Ratkowski, G. W. Felde, J. A. Gardner, M. L. Hoke,S. C. Richtsmeier, and L. S. Jeong, “MODTRAN4 version 2:Radiative transfer modeling,” Proc. SPIE 4381, 455–459(2001).

13. B. Schmid and C. Wehrli, “Comparison of Sun photometer ca-libration by use of the Langley technique and the standardlamp,” Appl. Opt. 34, 4500–4512 (1995).

14. F. Kasten and A. T. Young, “Revised optical air mass tablesand approximation formula,”Appl. Opt. 28, 4735–4738 (1989).

15. R. L. Kurucz, “The solar irradiance by computation,” in Pro-ceedings of the 17th Annual Conference on Atmospheric Trans-mission Models, G. P. Anderson, R. H. Picard, and J. H.Chetwind, eds. (1995), pp. 333–334.


16. K. Stamnes, S.-C. Tsay, W. Wiscombe, and K. Jayaweera,“Numerically stable algorithm for discrete-ordinate-methodradiative transfer in multiple scattering and emitting layeredmedia,” Appl. Opt. 27, 2502–2509 (1988).

17. R. G. Isaacs, W.-C. Wang, R. D. Worsham, and S. Goldenberg,“Multiple scattering LOWTRAN and FASCODE models,”Appl. Opt. 26, 1272–1281 (1987).

18. C. Levoni, M. Cervino, R. Guzzi, and F. Torricella, “Atmo-spheric aerosol optical properties: a database of radiativecharacteristics for different components and classes,” Appl.Opt. 36, 8031–8041 (1997).

19. World Meteorological Organization, A Preliminary CloudlessStandard Atmosphere for Radiation Computation, WCP-112,WMO/TD-24 (1986).

20. T. Takemura, T. Nakajima, O. Dubovik, B. N. Holben, and S.Kinne, “Single-scattering albedo and radiative forcing of var-ious aerosol species with a global three-dimensional model,” J.Clim. 15, 333–352 (2002).

21. S. Fukagawa, H. Kuze, G. Bagtasa, S. Naito, M. Yabuki, T.Takamura, and N. Takeuchi, “Characterization of seasonalvariation of tropospheric aerosols in Chiba, Japan,” Atmos.Environ. 40, 2160–2168 (2006).

22. T. Murayama, N. Sugimoto, I. Uno, K. Kinoshita, K. Aoki, N.Hagiwara, Z. Liu, I. Matsui, T. Sakai, T. Shibata, K. Arao, B.-J.Sohn, J.-G. Won, S.-C. Yoon, T. Li, J. Zhou, H. Hu, M. Abo, K.Iokibe, R. Koga, and Y. Iwasaka, “Ground-based networkobservation of Asian dust events of April 1998 in east Asia,”J. Geophys. Res. 106, 18345–18359 (2001).

23. W. J. Wiscombe, “Improved Mie scattering algorithms,” Appl.Opt. 19, 1505–1509 (1980).

24. P. Yang, Q. Feng, G. Hong, G. W. Kattawar, W. J. Wiscombe,M. I. Mishchenko, O. Dubovik, I. Laszlo, and I. N. Sokolik,“Modeling of the scattering and radiative properties of non-spherical dust-like aerosols,” J. Aerosol Sci. 38, 995–1014(2007).

25. M. I. Mishchenko, L. D. Travis, and A. A. Lacis, Scattering,Absorption, and Emission of Light by Small Particles(Cambridge University Press, 2002).

26. P. Yang and K. N. Liou, “Geometric-optics—integral-equationmethod for light scattering by nonspherical ice crystals,” Appl.Opt. 35, 6568–6584 (1996).

27. F. James,MINUIT—Function Minimization and Error Analy-sis, CERN Program Library Long Writeup D506(CERN, 1994).

28. E. G. Moody, M. D. King, S. Platnick, C. B. Schaaf, andG. Feng, “Spatially complete global spectral surface albedos:Value-added datasets derived from terra modis land pro-ducts,” IEEE Trans. Geosci. Remote Sens. 43, 144–158(2005).

29. P. F. Levelt, G. H. J. van den Oord, M. R. Dobber,A. Malkki, H. Visser, J. de Vries, P. Stammes,J. O. V. Lundell, and H. Saari, “The Ozone Monitoring Instru-ment,” IEEE Trans. Geosci. Remote Sens. 44, 1093–1101(2006).

30. D. L. Wu, R. T. Austin, M. Deng, S. L. Durden, A. J.Heymsfield, J. H. Jiang, A. Lambert, J.-L. Li, N. J. Livesey,G. M. McFarquhar, J. V. Pittman, G. L. Stephens, S. Tanelli,D. G. Vane, and D. E. Waliser, “Comparisons of global cloud icefrom MLS, CloudSat, and correlative data sets,” J. Geophys.Res. 114 (2009).

31. S. Y. Kotchenova, E. F. Vermote, R. Levy, and A. Lyapustin,“Radiative transfer codes for atmospheric correction andaerosol retrieval: intercomparison study,” Appl. Opt. 47,2215–2226 (2008).

32. G. H. Kaplan, “NOVAS,” Bull. Am. Astron. Soc. 22, 930–931(1990).

33. W. Lucht, C. B. Schaaf, and A. H. Strahler, “An algorithm forthe retrieval of albedo from space using semiempirical BRDFmodels,” IEEE Trans. Geosci. Remote Sens. 38, 977–998(2000).


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