Atmospheric aerosols have an important effect on theEarth’s climate forcing, causing marked inhomogene-ities over space and time scales in the distribution ofthe Earth’s global radiation balance. Such discrep-ancies need to be more appropriately characterizedthrough the simultaneous use of remote sensing andground-based Sun-photometric measurements.1 Sev-eral international networks of ground-based photom-eters have been set up over the past 20 years, takingadvantage of the development of new instruments and
techniques. Two of these networks are the SKYNETnetwork2 and the AERONET network.3
SKYNET consists of more than 20 sites mainly lo-cated in Asia. Its standard sky–Sun photometer is aPREDE POM sky radiometer whose data are pro-cessed using the public domain inversion code knownas SKYRAD.4,5 AERONET is distributed mainly inNorth America and Europe and employs the CIMELCE318 sky–Sun photometer as the standard instru-ment. More than 200 units take part in the AERONETprogram, which adopts an original inversion code toanalyze the measurements.6,7 The simultaneous studyof the databases from both networks offers a globalpicture of the atmospheric aerosol properties: themore widespread these networks are on the Earth,the better the picture that will be achieved to elu-cidate the climate prognoses.
According to World Meteorological Organization(WMO) guidelines,8 only data provided by recogni-zed international networks should be used in aerosolclimatology studies, since they alone can ensure well-tracked calibration procedures and data quality stan-dards. SKYNET and AERONET are therefore bothsuitable for yielding reliable data. The AERONET cal-ibration procedure is defined by a stringent protocol.3Field instruments must be periodically sent to theNASA Goddard Space Flight Center in Maryland,USA or Lille University, France, for calibrationthrough intercomparison with reference instruments.
M. Campanelli ([email protected]) and V. Malvestuto arewith the Institute of Atmospheric Sciences and Climate, ItalianNational Research Council, Via Fosso del Cavaliere, 100, Roma TorVergata, I-00133, Italy. V. Estellés and J. A. Martínez-Lozano arewith the Departamento Termodinámica of the Facultat de Física,Universitat de València, c�Dr. Moliner, 50 46100 Burjassot, Spain.C. Tomasi is with the Institute of Atmospheric Sciences and Cli-mate, Italian National Research Council, Via Gobetti 101, Bologna,I-40129, Italy. T. Nakajima is with the Center for Climate SystemResearch, The University of Tokyo 5-1-5 Kashiwanoha, Kashiwa,Chiba 277-8568, Japan.
Received 30 August 2006; revised 18 December 2006; accepted20 December 2006; posted 10 January 2007 (Doc. ID 74604); pub-lished 23 April 2007.
The periodicity is nominally stated to be 6 months,although periods of 1 year are not unusual. The annualreturn of the equipment not only allows the calibrationbut also provides an important opportunity to main-tain the equipment, including changing filters, whenrequired. However, the calibration status is checkedonly once a year, and hence the appropriate correctionto data can only be applied a posteriori, through are-elaboration of the corrected data. An additionalproblem is that the numerous instruments participat-ing in the network imposes the need for supplemen-tary manpower, implying higher costs. Therefore thiswell-planned calibration protocol is a major activity,which considerably limits the expansion capacity ofthe network, bearing in mind that some 240 CIMELinstruments now operate officially within AERONET,while a further 250 examples are working outside ofit.9 The consequence is that a great amount of globallydistributed data are in practice not utilized to reach amore exhaustive and extended aerosol climatology as-sessment over the global scale.
Conversely, SKYNET adopts an in situ uncentral-ized calibration procedure that allows operators totrack and evaluate the calibration status on a contin-uous basis,10 keeping the periodic check mostly formaintenance reasons and offering the advantage ofreducing the overall cost. In this way, the data gapsincurred by the periodical shipments are considerablyreduced, and the likelihood of instrumental damagesattributable to transport also decreases. However, thisin situ method can thus far be correctly employed onlyon PREDE instrumentation.
The method, hereinafter referred to as SKYIL(SKYRAD Improved Langley plot), retrieves the solarcalibration constant by means of a modified version ofthe Langley plot.10 The calibration value is retrievedby fitting the natural logarithm of the direct solarirradiance versus the product of the relative opticalair mass and the total extinction optical thickness, asretrieved by the SKYRAD code, instead of only the airmass as occurs with the standard Langley plot.11 Theresults obtained applying SKYIL to PREDE fieldmeasurements have provided estimates of the preci-sion in determining the solar calibration constantranging from 1% to 2.5%, depending on wavelength.10
The aim of the present paper is to apply the SKYILmethod to a CIMEL sky–Sun photometer. A calibra-tion method independent of the AERONET systemwould be very useful for diagnosing the condition of asky radiometer, whose data analysis is very vulner-able to small errors in the measured data. Using anindependent method, the variation of the calibrationconstant owing to instrumental drift can be quicklyspotted and the appropriate corrections to data ap-plied starting exactly from the period in which thedeviation occurred.
At present, the instrument used in the presentanalysis does not belong to AERONET, although ithas recently been included in RIMA (Red Ibérica deMedida de Aerosoles), a network of CIMEL CE318sky–Sun photometers being set up in Spain. There-fore access to raw data, calibration process, and
EPROM user programming were available for thepresent study.
2. Instrument Database and Calibration
The SKYIL method was applied to the CIMEL Sun–sky radiometer, model CE318-2 (serial number 176),belonging to the Solar Radiation Group of the Univer-sity of Valencia, Spain. This model is equipped with aneight-filter wheel having peak transmission wave-lengths of 440, 670, 870, and 1020 nm. A channelcentered on a strong water vapor absorption band�940 nm� is used for the retrieval of the columnar wa-ter vapor content, and three plastic polarizers are in-stalled to take polarization measurements at 870 nm.The instrument automatically measures direct so-lar and sky diffuse irradiance following a standardschedule,3 resulting in the retrieval of 8–10 almucan-tar scenarios per day. However, up to 26 user scenar-ios can be added to retrieve more daily almucantarmeasurements. When implemented, instrument No.176 was capable of measuring a daily number of morethan 30 almucantar scenarios.
The Sun photometer was deployed in January 2002in Burjassot, Spain, and has been working at this sitealmost continuously. The site (latitude 39.508°, lon-gitude 0.418°, altitude 60 m above sea level (ASL)) ison the Spanish Mediterranean coast, located in thesuburbs of Valencia (total population of 1.5 million).Due to its proximity to Valencia (5 km northwest) andthe Mediterranean shore (10 km west), it is charac-terized by the continuous presence of local anthropo-genic and marine aerosols. Air masses from northernAfrica frequently arrive over the site, mainly in thesummer season. This renders the site clearly unsuit-able for the application of the standard Langley plotmethod for calibration purposes, since the numerousaerosol sources can increase the daily variability ofthe aerosol burden.
The data set used in the present work consists ofmeasurements taken from January 2002 to March2005, only in the almucantar geometry.12 To ensurethat measurements were not affected by clouds, acloud screening was performed according to the fol-lowing steps: (i) a symmetry test of the radiance mea-sured at several zenith angles, on both sides of thesolar disk, as described by Holben et al.3; (ii) therejection of the complete almucantar in all caseswhere none of the data points, for angles smaller than7°, respect the symmetry test of the above criterion;this step is important because this region is crucialfor an accurate inversion of the radiance data; (iii) thescreening algorithm described by Smirnov et al.,13
applied to measurements of direct solar irradiance.Applying the cloud screening procedure to measure-ments taken at the above-mentioned wavelengths, itis difficult to recognize high thin clouds or spatiallyhomogeneous stratus. Therefore the presence of suchclouds cannot be definitely excluded.13 Further de-tails on the characterization of the aerosol propertiesat this site can be found elsewhere.14,15
Throughout the period, the instrument calibrationconstants were regularly checked, for both direct anddiffuse irradiance measurements. The methods andthe results are described in the following subsections.
A. Direct Irradiance Calibration
The first set of calibration constants (11 July 2002) fordirect solar irradiance measurements was retrievedthrough intercomparison with a reference instrument,the CIMEL CE318 (serial number 307), operating dur-ing a field campaign in Sierra Nevada, Spain, at a siteabove 2300 m ASL.16 This master instrument was cal-ibrated by applying the standard Langley plot methodto such measurements performed over 16 days in July2002. Additional details of the calibration procedureare provided in other papers.12,15
The second set of calibration constants (25 Octo-ber 2004) was obtained through an intercomparisontransfer test employing another reference instru-ment, the CIMEL model CE318NE (serial number430), performing simultaneous measurements onseveral clear-sky days of October 2004, in Valencia.The reference instrument was calibrated using thestandard Langley plot, applied to a database ofmeasurements taken from 24 April to 12 July 2004at Aras de los Olmos, Spain, a mountain site locat-ed at 1300 m ASL and 100 km away from anthro-pogenic sources. The resulting calibration values�V0
exp� and their estimated percentage uncertainty��T�%�� are shown in Table 1. The parameter �T isgiven as the sum of the Langley uncertainty, evalu-ated as the standard deviation (STD) over the entiredata set of the calibration values retrieved at Arasde los Olmos, and the uncertainty obtained from thetransfer ratio itself, evaluated as the STD over thedays of simultaneous measurements. The outlierswere removed following the Chauvenet criterion.17
Compared with the nominal calibration uncertaintiesprovided by the AERONET-related literature for fieldinstruments3 (1%–2%), the values obtained here aresomewhat higher. The reason could be the differentconditions of the calibration performed for the masterinstruments. In fact, AERONET master Sun–sky ra-diometers are calibrated at Mauna Loa, Hawaii, aremote site in the middle of the Pacific Ocean, with anaccuracy of 0.2%–0.5%.3 The present master instru-ments were calibrated instead at continental sites,often strongly affected by the arrival of European andAfrican air masses. Therefore their calibration uncer-
tainty ��m�%��, given in Table 1, is rather higher thanexpected and propagates to the field instruments.
B. Lamp Calibration of Diffuse Radiance
The diffuse radiance calibration is generally obtain-ed by measuring the exit radiance of a previouslycalibrated integrating sphere. It was performed ap-proximately every six months, throughout the wholemeasurement period. A set of four lamps was em-ployed over different spectral intervals and for variousilluminance levels during the period: (i) a Li-Cor cali-brator unit with an adaptor for radiance, (ii) twoBentham integrating spheres, and (iii) an OptronicOL-455 integrating sphere. The details of the calibra-tion procedure are described by Estelles.12 The uncer-tainty of the exit radiance of each integrating sphere isobviously different for each manufacturer, although italso depends on their temporal degradation (mainlyrelated to the numbers of hours of instrumental use). Anew Bentham lamp is claimed to have a 2% radianceuncertainty from 380 to 800 nm, increasing up to 5%at 1100 nm. The CIMEL calibration session was per-formed after a few hours of use of the two lamps. TheOptronic lamp is claimed to be more accurate, but itaccumulated a great number of measurement hoursbefore the calibration session and the uncertaintywas estimated consequently to rise to roughly 5%.Therefore a propagated 5% nominal uncertainty wasassumed for the CIMEL radiance calibration. Figure1 shows the evolutionary patterns of the calibrationconstants throughout the 2003–2005 period. The cal-ibration values determined using the Optronic OLsource are given in Fig. 1, separately from those si-multaneously obtained using the two Bentham lamps(unit No. 4884 in the 2003 session and No. 7281 inthat of 2005), to check the performances of the lamps.The calibration time patterns give evidence of an an-nual decrease in the radiance calibration constant
Fig. 1. Evolutionary time patterns of the radiance calibrationconstant values throughout the 2002–2005 period. Open symbolsrefer to the calibration constants obtained using the Optronic OLlamp, and solid symbols refer to the simultaneous calibration val-ues obtained with the Bentham SRS8 lamps. The error bars definea 5% uncertainty value.
Table 1. Spectral Solar Calibration Constants as Retrieved by theStandard Langley Plot with the Estimated Uncertainty for the Master
Instruments (�m) and for the Field Instruments (�T) after theIntercomparison Transfer Test
values equal to �1.1%, �1.8%, �1.5%, and �2.0% forthe 440, 670, 870, and 1020 nm channels, respec-tively. No optical parts of the instrument were sub-stituted or renewed during the calibration periodexamined in Fig. 1.
3. Method
As mentioned above, the application of the SKYILmethod10 is based on the use of the SKYRAD code.The method retrieves the spectral values of the solarcalibration constant V0��� at various wavelengths �,through a best-fit procedure of ln V��� plotted versusm0����, based on the following:
ln V��� � ln V0��� � m0����, (1)
where V��� is the measured direct solar irradiance,m0 � 1�cos �0 is the inverse of the cosine of the solarzenith angle �0, and ���� is the total extinction opticalthickness calculated by the inversion procedure of theforward-scattering sky radiance data, performed us-ing the SKYRAD code.
In particular, the quantity used in the inversion isthe normalized radiance R��, �� defined as follows:
R��, �� �E��, ��
����V���m0�
L��, ��V���m0
, (2)
where E��, �� is the solar diffuse irradiance mea-sured by the instrument at several scattering angles�, ���� is the solid view angle of the instrumentoptics, and L��, �� � E��, ������� is the corre-sponding radiance.
This calibration method was developed for thePREDE instruments, where both direct and diffuseirradiance can be measured using the same sensor.Normalized radiance R��, �� can be calculated usingthe above quantities in measured count units, thuseliminating the need for further calibrations. When-ever the technique is applied to the CIMEL sky–Sunphotometers, it must be taken into account that V���and E��, �� are measured by two different sensors,and hence the ratio R��, �� in Eq. (2) cannot be cor-rectly defined in terms of these two quantities givenin count units. To express the above quantities inabsolute radiance units �W�m2�, it is useful to employa lamp calibration for calculating the diffuse radianceL��, �� and to express V��� in terms of the radianceunits of F��� given by
F��� �V���V0���
F0���, (3)
where F0��� �Wm�2nm�1� is the incoming solar irra-diance at the top of the atmosphere, obtained fromthe SMARTS2 model.18 This model applies some im-provements to the extraterrestrial spectrum19 andwas convoluted with the CIMEL experimental trans-missivity filter functions to retrieve a reliable irradi-ance value for each channel. To apply the SKYILmethod to CIMEL instruments, using Eqs. (2) and
(3), it is convenient to first assume a preliminaryvalue of solar calibration constant V0��� as a firstguess, retrieved, for example, by the standardLangley plot technique. Subsequently, the iterativemethod shown in Fig. 2 can be applied by first de-termining F��� in terms of Eq. (3), using a first guessfor V0���, indicated as V0
0���, and then calculatingR��, ��. From the inversion of this quantity, ���� isretrieved and inserted into Eq. (1) to derive a firstestimate of V0��� [indicated as V0
1���], which is in turnused to recalculate F��� and R��, �� and to retrieve����. Thereupon the improved Langley plot is againapplied to estimate V0���. The loop is stopped at thenth iteration, when the difference between V0
n�1���and V0
n��� is found to be lower than 2.5%, or thenumber of iterations exceeds ten. Each final retrievedvalue is adopted as a first guess for the following dayor for the calculation of the evening value of the sameday, since the method permits the determination oftwo values of V0��� each day, the former relative tothe morning, the latter to the evening. The thresholdvalue of 2.5% was chosen because it defines the ac-curacy of the method retrieved by Campanelli et al.10
4. Results
The data set was processed using as a first guess thecalibration values determined in July 2002 (Table1). The values of V0��� obtained for a SKYRAD codeinversion accuracy lower than 5% were rejected ac-cording to the selection criteria established by Cam-panelli et al.10 A quality check was also applied tothe fit of ln V0��� versus m0����, which consists of thefollowing steps: (i) only the measurements taken form0 4.5 were selected; (ii) a minimum number offour points was used, providing that they were atleast half of the total number of available points; (iii)the difference between the maximum and the mini-mum value of ln�m0����� was required to be greaterthan 0.5; and (iv) a fit was performed using only themeasurements whose vertical distance from thetrend does not exceed the corresponding residualstandard deviation.
In all cases where ��500 nm� � 0.3, V0��� was foundto have a significant dependence on the imaginarypart k of the particulate refractive index that is as-sumed in the SKYRAD code inversion.10 Since anincorrect value of k yields an unreliable value of V0���,a quality check was performed, rejecting all the val-ues of V0��� found for ��440 nm� � 0.3, measurementsnot being available at the 500 nm wavelength.
Following the procedure defined by Campanelliet al.10 to filter the outliers and short-term variationsrelated to the method itself, the Chauvenet criteri-on17 was adopted and a three-point moving averagetechnique was applied to the series of V0��� obtainedafter the rejection of all cases with high values of theoptical thickness. Figure 3 shows the results after thequality check. The accuracy of the method in termsof the internal consistency of the retrieved values ofV0��� was estimated by the dispersion of the valueswith respect to the regression line of each series.
Percentage values of accuracy are given in Table 2,where they are also compared with those retrieved byCampanelli et al.10 for the PREDE instrument usingthe same SKYIL method. Table 2 shows that an ap-preciably improved accuracy was achieved in thepresent results at all the wavelengths with respectto the previous ones.10 This improvement is sub-stantially due to (i) the rejection of the data corre-sponding to high optical thickness values, while thisselection was not made in the procedure followed byCampanelli et al.,10 and (ii) the adoption of the Chau-venet criterion17 imposing more restricted limits thanthose proposed by Campanelli et al.,10 where only thepoints lying beyond the 3� distance were discarded, �
being the standard deviation calculated over the en-tire data set. In fact, the calibration constant valueswere monitored in the present procedure on a dailybasis, and not only at the end of the analysis of theentire three-year data set, as done in Campanelliet al.10 Through this step, each calibration value pro-vided by the SKYIL method and lying far from themean by more than 3� was rejected, the values of �and the mean being calculated over the whole set ofcalibration points within a time interval of 60 days,providing that the above set included at least fivecalibration points. In this way the data set turned outto be better filtered, and the dispersion of the resultswas appreciably limited.
Fig. 2. Iterative method for the calculation of the solar calibration constant using the SKYIL method for a CIMEL instrument.
The improvement of accuracy with respect to thepreviously retrieved values10 is an important result,since the nominal uncertainty on the values of V0���given by the AERONET calibration method (of 1%–2%) and the uncertainty of the SKYIL method turnedout to be more similar in the present case, althoughthey could not be properly compared because neitherof them are absolute estimates.
A preliminary examination of the features shown inFigs. 3(a), 3(b), 3(c), and 3(d) clearly reveals the occur-rence of an oscillation of V0��� over a period of approx-imately one year, particularly marked at 1020 nm.Comparing this behavior with the temperaturetime patterns shown in Fig. 3(e) and measured by asensor placed inside the head of the instrument,where both sensor and filters are housed, the oscil-lation seemed to have the same tendency. Thus aspecific analysis of the temperature dependencewas required, considering that (i) the SKYILmethod does not include a similar study since thePREDE instrument is thermostated, and (ii) amarked influence of the external temperature of theCIMEL on the output signals and, hence, on thedetermination of the calibration constants V0���, isexpected to occur, since this CIMEL example is nothoused in a thermostated box. Therefore it is reason-able to assume that the measurements taken by thesensor are subject to marked drift effects related tothe inner temperature, which depend closely onwavelength, while the transmission peak wavelength
Fig. 3. Time patterns of the calibration constants V0��� at the four wavelengths, obtained after the quality selection: (a), (b), (c), and (d)refer to � � 440, 670, 870, and 1020 nm, respectively. Gray points with error bars give the experimental calibration values of V0
exp���. (e)Time patterns of the temperature inside the instrument. The origin of the Julian day axis is set at 1 January 2002.
Table 2. Accuracy of the SKYIL Method in Retrieving V0(�) at the FourWavelengths
Accuracy of the V0��� Retrieval(%)
Present case 440 nm 670 nm 870 nm 1020 nmBefore temperature
of each filter may be simultaneously subject to appre-ciable thermal shift effects.
A. Dependence of Diffuse Radiance on Temperature
In the CIMEL used in the present study, the depen-dence of the measured diffuse radiance on the tem-perature was investigated through laboratory testsand then corrected. In particular, the radiance exit-ing a Bentham calibration sphere was measured bythe radiometer, changing the room temperaturethroughout the range from 26 °C to 33 °C. As clearlyshown in Fig. 4, the 1020 nm wavelength was foundto be significantly affected by the temperature vari-ation, whereas a less marked dependence was de-tected at the 870 nm wavelength. No evidence wasfound of significant variations in the measured sig-nals as a function of the ambient temperature at both670 and 440 nm wavelengths.
During the period in which the present data set wasrecorded, the laboratory tests were repeated threetimes, and the temperature coefficients were calcu-lated in terms of percentage variations of the mea-sured radiance per unit temperature change. Theirvalues are shown in Table 3 for the two most sensi-tive wavelengths. At the 670 and 440 nm wave-lengths, the laboratory tests were more difficult toperform. Thus the retrieved values of the tempera-ture coefficients were not considered to be entirelyreliable. Both the radiance exiting from the lamp andthe sensitivity of the CIMEL sensor at the 440 nmwavelength assumed systematically very low values,
making it difficult to determine temperature depen-dence correctly.
Although the values in Table 3 can be affected byappreciable experimental errors owing, for example,to the inhomogeneous heating of the optical sensor,filters, and temperature detector, the temperaturecoefficient at the 1020 nm wavelength was found todecrease from 2003 to 2004. Such year-to-year vari-ations must be taken into account in the analysis ofthe V0�1020 nm� time series. In fact, the entire radi-ance data set was corrected for the temperature de-pendence, using the coefficients retrieved in 2002. Noupdate of the temperature coefficient was performedto correct the data recorded in 2003 and 2004. Suchmissed correction could have contributed to the ap-parent temperature dependence characterizing thelast data set at 1020 nm wavelength.
Fig. 4. Signal dependence on sensor temperature at the four wavelengths, defined through the comparison between uncorrected andcorrected output signals.
Table 3. Values of the Temperature Coefficients for the MeasuredDiffuse Radiance
At 870 nm wavelength, the temperature coeffi-cient was considered to be extremely small, so thediffuse radiance measured at this wavelength wasnot corrected. No corrections were applied to the ra-diances measured at 670 and 440 nm. The tempera-ture correction applied to the CIMEL radiometer inthis work, is slightly different from the standardcorrection procedure performed by AERONET to themeasurements taken by the network instrumentssimilar to the example used in the present study. Thetemperature coefficients are derived by AERONETfrom laboratory tests for (i) three different tempera-ture (T) ranges, T 21 °C, 21 °C T 32 °C, andT � 32 °C, and (ii) for measurements taken at smallangles from the lamp (6°, called geometry A) andlarge angles (�6°, called geometry K). This is becausein the above two cases the CIMEL takes measure-ments with the same sensor but using different gains.In this work the temperature coefficients, calculatedfor geometry K, were considered to be the same forboth geometries.
Comparing the values retrieved here with thoseprovided by AERONET20 in the temperature range21 °C T 32 °C (Table 3), agreement was foundwith both the geometries at the 1020 nm wavelength.The 870 nm temperature coefficients were alsofound to be comparable with the values provided byAERONET for geometry K, even though no correc-tion was applied in the present study at this wave-length. The fact that the measured radiance wascorrected by using temperature coefficients retrievedfor only one temperature range and not three tem-perature ranges, as in AERONET, could be a furtherreason for the temperature dependence found at the1020 nm wavelength in Fig. 3.
B. Dependence of Direct Solar Irradiance onTemperature
It was not possible to perform a laboratory testto investigate the dependence of the measured di-rect solar irradiance on temperature. Therefore theirradiance measurements taken at the 1020 nmwavelength were corrected using the temperaturecorrection coefficient per unit temperature variation�V�V � �0.25% �°C��1 suggested by Holben et al.3 Nocorrections were applied at the other wavelengths inagreement with the standard temperature correctionprocedure performed by AERONET.
The SKYIL method uses both the diffuse radianceand the direct solar irradiance measurements to re-trieve the values of V0��� because the normalizedradiance R��, �� defined in Eq. (2) is processed rou-tinely. Therefore it is reasonable to suppose that re-sidual uncorrected temperature effects, induced byboth the above quantities, can still be present on dataand easily recognized in the retrieved time patternsof V0���, as shown in Fig. 3. To ascertain the suitabil-ity of these assumptions, a first step was performedby calculating the correlation coefficient betweenV0��� and temperature. According to the results
shown in Table 4, a significant correlation was foundon analyzing the subsets relative to the 1020 and870 nm wavelengths, with a confidence level of 99%in both cases. At the 870 nm wavelength, an anticor-related relationship was highlighted, in agreementwith the decreasing trend of the corrected valuesof R��, �� versus the sensor temperature, as clearlyshown in Fig. 4. Similarly, a slight anticorrelation(with a confidence level equal to 95%) was also foundat the 440 nm wavelength, while that relative to the670 nm wavelength was found to be very small (seeTable 4).
As a second step, a Fourier analysis was performedon the temperature time patterns to identify not onlythe yearly frequency (long wave) due to the seasonaltemperature oscillation but also the frequency re-lated to the diurnal component (short wave), whichcould affect the calculated values of V0��� since theSKYIL method retrieves two values of the solar cal-ibration constant, one for the morning and one for theafternoon. The percentage difference between the ex-traterrestrial voltages computed using morning andafternoon selected data sets, was found to be on av-erage equal to �1 � 0.7�% at the 440 nm wavelengthand �0.4 � 0.3�% at the other wavelengths. Althoughthe average differences fall closely within the thresh-old of the uncertainty of the method, they present adiurnal variability.
Although the selected data set was characterizedby large scatter features, presenting irregularlyspaced values of V0���, with temporal gaps of as muchas 60 days in some cases, the Fourier analysis per-formed on the time series of V0���, relative to the 440,870, and 1020 nm wavelengths, gave evidence of thepresence of both the long- and short-wave frequencycomponents. The short-wave component should havebeen smoothed after the application of the three-point moving average performed during the filteringof the data. Nevertheless, it was found to exist evenafter the moving procedure, due to the occurrence ofa large number of temporal gaps. In fact, the movingaverage was applied on the data set (previously equi-spaced) by filtering only consecutive data (minimumtwo points) and without changing the isolated points.
The spectral analysis was not applied to the670 nm series because no significant correlation withtemperature was found, as shown in Table 4. In theother cases the time patterns of V0��� were assumedto consist of the following time-dependent terms:
V0�t� � V0LONG � V0SHORT � V0RES
� AL sin��Lt � �L� � AS sin��S � �S� � R�t�, (4)
where AL, �L, and �L are the amplitude, the angular
Table 4. Values of the Correlation Coefficients between the TimeSeries of V0(�) and the Sensor Temperature
frequency, and the phase of the long wave attribut-able to the seasonal oscillation, and AS, �S, and �S
are the same quantities relative to the short waveowing to the diurnal oscillation, respectively, whileR(t) is the residual term containing the other fre-quencies typical of the SKYIL method, as well as thetrend of the time patterns.
It should be noted that the seasonal and diurnalcomponents of V0 can also be related to the seasonaland diurnal variations of minor external factors, suchas NO2 and O3 absorption or daily fluctuations ofrelative humidity, which are all closely related to thetemperature variations. To clean the signal V0 fromthe V0LONG and V0SHORT terms, and then from the tem-perature and the other minor external factor effects,a generalized least-squares method was set up to (i)extract both the sinusoids from the detrended signal,(ii) calculate the weight of each oscillation term insidethe original signal, and (iii) subtract the two terms byre-adding the trend. This analysis was applied to theentire data sets relative to the 440 and 870 nm wave-lengths. At the 1020 nm wavelength, the analysiswas limited to the period from 20 March 2003, on-ward. The reason for this choice is that the temper-ature dependence cannot be clearly spotted beforethis date, and the present method was found to failwhen the two oscillation terms were extrapolatedover the entire data set. This agrees with the fact thatthe omission of the update of temperature coefficientsfor the 2003 and 2004 measurements, as statedabove, could favor the appearance of an oscillation inthe data set relative to the period after 20 March2003. The results are shown in Table 5.
At the 1020 nm wavelength, the seasonal compo-nent was found to include 58.2% of the total signal,whereas the diurnal component was evaluated to be9.4% of the signal previously cleaned by the long-wave effects. Thus 67.6% of the time variations inV0��� with wavelength � � 1020 nm were estimatedto be attributable to temperature-dependence effects,although the normalized radiance R��, �� was con-sidered to be properly corrected for both direct anddiffuse irradiance components. The reason for awrongly corrected signal may be due to (i) the ignoredupdate of the temperature coefficients for the diffuseirradiance data taken after 20 March 2003, (ii) theuse of a temperature coefficient independent of tem-perature within the measurement range, and (iii) anunrealistic correction of direct irradiance.
With regard to the latter quantity, evidence of thetemperature dependence of the aerosol optical thick-ness retrieved from only direct irradiance measure-ments was found by Campanelli et al.,21 who examinedsimultaneous measurements taken with a CIMEL anda PREDE Sun–sky radiometer, regularly thermo-stated. Evaluating the difference between the corre-lation coefficients calculated by relating each set ofaerosol optical thickness to the measured externaltemperature, the measure of the temperature depen-dence for the CIMEL was estimated. The dependencefeatures were found to be particularly marked at the440 and 870 nm wavelengths and weak at only the1020 nm wavelength, although an appropriate cor-rection procedure3 was applied at the last wave-length.
Variations in the solar calibration constants withtemperature clearly depending on wavelength werealso found by von Hoyningen-Huene22 validating sat-ellite measurements through the use of AERONETdata. Estimates of the growing coefficient K of V0���per unit increase of temperature were obtained bythis author at various wavelengths. He found thatthe temperature dependence decreases appreciablyas the wavelength increases from 440 to 870 nm, butbecomes stronger at 1020 nm, presenting values ofK � 0.01, 0.004, 0.002, and 0.004 �°C��1 at the 440,670, 870, and 1020 nm wavelengths, respectively.
Consequently, in spite of the use of the suggestedcorrection, the existence of further temperature de-pendence effects on the direct irradiance cannot beexcluded. Thus the 2002 data set relative to the1020 nm wavelength should also be submitted tospectral analysis, in order to extrapolate the long-and short-wave components. The application of theabove method allowed the retrieval and correction ofthe data for this time period, for a seasonal compo-nent that was evaluated to be 25.8% of the overallsignal, and for a diurnal component of 0.9%, which isin practice negligible.
With regard to the 870 nm wavelength, the long-wave contribution to the signal was found to be equalto 20.7%, and, hence, lower than that determined atthe 1020 nm wavelength for the 2003–2005 data set,whereas the short-wave contribution was estimatedto be 7.2% and, therefore, quite comparable with thatfound at 1020 nm. At this wavelength, approximately
Table 5. Values of the Amplitude, Phase, and Weight of the Seasonal (Long-Wave) and Diurnal (Short-Wave) Components at the Three AnalyzedWavelengths
1020 nm 870 nm 440 nm
Long Wave Short Wave Long Wave Short Wave Long Wave Short Wave
28% of the signal was evaluated to be attributable totemperature dependence effects.
As expected, the signals taken at the 440 nmwavelength were found to be even less affected bytemperature dependence effects, since the overallweight of long- and short-wave components amountsto 10.1%.
The corrected signals are plotted in Fig. 5, and theaccuracy of the method calculated after the tempera-ture correction is given in Table 2. To validate themethod proposed here, the calibration values retrievedby SKYIL can be compared with the experimental val-ues of V0
exp��� given in Table 1. The validation consistsof the two following steps: (i) comparison of the generaltrend of the calibration constant time patterns and (ii)comparison among their absolute values. With regardto the first step, the trend of V0
exp��� was estimated ateach wavelength by examining the experimental dataand then determining the slope of the line connectingtwo available points �mexp�. The uncertainty of the re-trieved trend was calculated following the method ofthe minimum and maximum slope coefficients of thefitted line, taking into account the errors affecting thevalues of V0
exp��� listed in Table 1.
The trend of V0 determined at each wavelengthusing the SKYIL method �msky� was estimated bydefining the slope of the regression line for the dataset taken only on the days from 23 July 2002 to 17October 2004, i.e., on days within the two experimen-tal calibration dates. The results are shown in Table6. The increasing trend recorded by mexp at the
Fig. 5. Time patterns of the calibration constant V0��� at the four wavelengths after the temperature correction. Data shown in (c) relativeto the 670 nm wavelength are not corrected. The solid symbols with error bars represent the experimental calibration values of V0
exp���. (e)Time patterns of the temperature inside the instrument. The origin of the Julian day axis is set at 1 January 2002.
Table 6. Trend of the Calibration Constants Obtained for theExperimental Values (mexp) and the Values Retrieved by the SKYIL
440 nm wavelength was found to be consistent withmsky, within the experimental error, and the nearlystable behavior at the 670 nm wavelength was alsowell reproduced. At the 870 nm wavelength, the neg-ative trend turns out to be defined by both mexp andmsky, but it is slightly underestimated using theSKYIL method. This seems mainly attributable tothe poor agreement between the second V0
exp calibra-tion value and the V0 SKYIL values retrieved in Oc-tober 2004 as shown in Fig. 6. Even in the case of the1020 nm wavelength, the decreasing trend is recog-nized by both mexp and msky although it again turnsout to be slightly underestimated with respect to theprevious case, because of the poor agreement betweenthe first V0
exp value and the V0 SKYIL calibrationsretrieved in July 2002 as can be seen in Fig. 6. How-ever, it must also be taken into account that theslopes of both regression lines found at this wave-length are very small and presumably not related toa real instrumental drift.
Examining the comparison between the absolutevalues of V0
exp and V0 retrieved by the SKYIL method,the agreement quality cannot be evaluated directlywithout an accurate selection, at each wavelength, ofthe values of V0��� located at approximately V0
exp���.In fact, comparing the values of V0
exp��� with the clos-est values of V0��� is not a correct procedure, princi-
Fig. 7. Time patterns of the calibration constants V0exp��� and
V0Sky��� at the four wavelengths.
Fig. 6. Time patterns of the calibration constants V0��� at the four wavelengths, obtained after the application of the temperaturecorrection to the data relative to the period limited by the two experimental calibration dates. Data pertaining to the 670 nm wavelengthwere not corrected. The gray line represents the corresponding regression line, msky. The solid symbols with error bars represent theexperimental calibration values V0
exp. The solid black line represents the corresponding regression line mexp. The origin of the Julian dayaxis is set at 1 January 2002.
pally because (i) the time patterns of V0��� providedby SKYIL do not follow a linear trend but frequentlyexhibit some short-time variations related to themethod itself, which can distort the comparison inparticular cases, and (ii) the dates of the two calibra-tion constants are only nominal, because the inter-comparison transfer test was performed using datafrom 8 July to 11 July 2002, for the first calibration(having 11 July as a nominal date) and from 27 Sep-tember to 25 October 2004, for the second calibration(with a nominal date fixed at 25 October). Thus itwas decided to compare each value of V0
exp��� with avalue of V0��� obtained as the average calculated overthe SKYIL available points determined within onemonth around the experimental date, that is, 15 daysbefore and 15 days after the experimental date. Theresults are labeled with symbols V0
Sky���. The uncer-tainty affecting the results provided by the SKYILmethod, as retrieved in Table 2 after the use of thecorrection procedure, was assumed to be the measureof the uncertainty on V0
Sky. The choice of the abovetime interval seems to be reasonable, since a signif-icant change in the solar calibration constant is un-likely within a limited time interval of only onemonth. The results are shown in Fig. 7 and Table 7.
In all cases, the values of V0exp and V0
Sky were found tobe comparable within their uncertainties, althoughgreater differences have been observed in the 2002calibration findings at all the wavelengths. The mostapparent disagreement was found at the 440 nmwavelength, equal to 3% in 2002 and 2.2% in 2004. Apossible explanation for such discrepancies could bethat this wavelength is more sensitive to the scatteringeffects produced by clouds than the others. Even if the
cloud screening performed on the present data setswas estimated to be capable of rejecting the data takenwith clouds in front of the Sun or around the Sun, thepresence of cirrus or other clouds in sky sectors farfrom the observation point of the instrument couldcorrupt the direct irradiance measurements performedat this wavelength. Moreover effects attributable tothe NO2 absorption could also be present at this wave-length.
The other marked disagreement recognizable for the2002 calibration at the 670 nm wavelength could berelated to the fact that the intercomparison transfertest for the determination of V0
exp at this wavelengthwas performed between two instruments having slight-ly different transmission peak wavelengths of 674 nmfor the master instrument No. 307 and 670 nm for thefield instrument.
5. Sensitivity Study
The first sensitivity study was carried out to demon-strate that the method does not depend on the as-sumed first guess V0
0���. For this purpose a slightlydifferent elaboration procedure was set up. As shownin Fig. 2, for each day considered in the analysis, thevalue of V0��� retrieved on the previous day was usedas a first guess, except for the first day of the data setin which the experimental calibration constants V0
exp���were used as V0
0��� inputs. The independence of thefirst guess can be carefully checked by arbitrarilychanging the first guess and then analyzing the re-trieved final values, but with this elaboration proce-dure it can be done by varying only the inputcalibration of the first day of the data set. Consideringeach day separately and processing each daily data setusing the same first guess in place of the value re-trieved from the previous day, the independence can bechecked using the entire data set. Following this cri-terion, the data set was divided into two parts, the firstfrom early January 2002 to 14 September 2003, andthe second from 15 September 2003 to March 2005.Subsequently for each day the values of V0
exp��� relativeto 2002 and 2004 and given in Table 1 were used asa first guess, respectively. The procedure was re-peated by increasing and decreasing the constantsV0
0��� by 0.1%, 10%, and 20%. All the series wereselected, as in the previous section, for an inversion
Fig. 8. Final values of the calibration constant V0�440 nm�, as retrieved on two measurement days after the application of the SKYILmethod for several first guesses obtained by increasing and decreasing the original value (0% in the legend) by 20%, 10%, and 0.1%.
Table 7. Absolute Percentage Differences between the Values ofV0
accuracy higher than 5%, for ��440 nm� 0.3, andaccording to the Chauvenet criterion.17
The results found at the 440 nm wavelength on twomeasurement days are shown in Fig. 8. It is evidentthat the method converges toward very close finalvalues, independent of the first guess. In particular,the mean percentage discrepancies among the re-trieved final values were found to be equal to 0.2%,0.05%, 0.03%, and 0.02% at the 440, 670, 870, and1020 nm wavelengths, respectively, clearly withinthe uncertainty limits of the method. Such differ-ences were calculated with respect to the final valueretrieved using the values of V0
0��� associated withnull increase. The convergence was reached at thethird loop even in the worst cases.
The second sensitivity analysis aimed to study thedependence of the retrieval procedure on the as-sumed refractive index of particulate matter. TheSKYIL method retrieves the calibration constant as-suming a fixed value of the complex refractive indexto calculate the spectral values of aerosol extinctionoptical thickness. Campanelli et al.10 demonstratedthat the method can depend closely on (i) the imagi-nary part k to an extent not exceeding 1.8% at� � 400 nm, and 0.5% at � � 1020 nm, and (ii) thereal part n to an extent within 2.2% at � � 400 nm,and 1.4% at � � 1020 nm, as can be seen in Table 8.However, these sensitivity features were determinedby using different filtering criteria, in contrast to theprocedure adopted in the present study and ex-plained in Section 3. In the present case, by adoptingmore severe selection criteria, the sensitivity was cal-culated to ascertain whether the dependence on theassumed refractive index is really consistent with themethod’s uncertainty. The sensitivity to n was stud-ied by applying the SKYIL method for an assumedvalue of k � 0.005 and several values of n equal to1.35, 1.50, and 1.65. For each day of the selected dataset, the STD relative to V0��� was retrieved for all theabove values of n, and the percentage relative errorswere calculated. A similar procedure was followed toevaluate the dependence of V0��� on the imaginarypart k, using a fixed value of n � 1.50 and severalvalues of k equal to 0, 0.005, and 0.03. The results areshown in the first two rows of Table 8. The maximumdependence on n was 2.1% at 440 nm, decreasing to0.5% at both 870 and 1020 nm, whereas the maxi-mum variability on k was found to be of 0.9% at440 nm, 0.2% at 870 nm, and 0.3% at 1020 nm. Allthese values are within the method’s uncertainty.
Therefore it can be stated that the sensitivity of theSKYIL method to the assumed refractive index is alsonegligible. Moreover, in both the analysis proce-dures followed to define the dependence features on nand k, the percentage dependence was evaluated to besmaller than the those retrieved by Campanelli et al.,10
presumably as a result of the stricter selection of thevalues of V0��� adopted in the present study.
6. Conclusions
The SKYIL method is a well-tested in situ procedurefor the daily determination of the solar calibrationconstants, specifically created for the PREDE Sun–sky radiometers. It was applied to a CIMEL instru-ment located in Valencia, Spain, not belonging to theAERONET network, taking into account the differentmechanical and electronic characteristics of the tworadiometers. For this reason, the SKYIL method wasadapted to the characteristics of the CIMEL instru-ment, bearing in mind that it is suitable for applica-tion only if the radiometer has previously beencalibrated using a standard lamp for the diffuse ra-diance. The iterative procedure for the determinationof the solar calibration constants was applied to a3-year data set, and the results were compared withthe two available sets of experimental calibrationconstants determined during this period with thestandard Langley plot method. To improve the accu-racy of the method, a more severe selection of theretrieved values of V0��� was performed, as comparedwith the qualified selection made by Campanelliet al.10 In particular, all the values retrieved duringdays characterized by high atmospheric turbidityconditions were rejected, and the method followed tofilter the short-term variations related to the SKYILfindings was appreciably improved.
A marked influence of the external temperature onthe retrieved time patterns of the calibration constantswas highlighted. Since the SKYIL method uses bothdiffuse radiance and direct solar irradiance measure-ments to retrieve the values of V0���, the temperaturedependence effects induced by both these irradiancecomponents have been clearly identified in the re-trieved time patterns of V0���. The temperature depen-dence of the diffuse radiance measured at 1020 nmwas investigated through laboratory tests and subse-quently corrected. The direct solar irradiance mea-surements taken at the same wavelength were alsocorrected following the Holben et al.3 procedure. Inspite of these corrections, the correlation coefficients
Table 8. Mean Percentage Dependence of Constant V0(�) on the Real and Imaginary Parts of Particulate Refractive Index n � ik, Obtained throughan Averaging Procedure over the Entire Data Set
440 nm 670 nm 870 nm 1020 nm
Present dataset
Dependence on n (%) 1.02 � 1.09 0.31 � 0.31 0.22 � 0.22 0.24 � 0.22Dependence on k (%) 0.46 � 0.42 0.13 � 0.13 0.12 � 0.11 0.15 � 0.15
400 nm 500 nm 870 nm 1020 nmCampanelli
et al. (Ref. 10)Dependence on n (%) 1.29 � 0.90 0.80 � 0.79 0.61 � 0.83 0.57 � 0.78Dependence on k (%) 0.85 � 0.98 0.35 � 0.38 0.29 � 0.45 0.25 � 1.95
calculated between V0��� and the measured tempera-ture showed evidence of residual temperature effectsat all the wavelengths except 670 nm. The use of aFourier analysis allowed the definition of a yearly fre-quency owing to the seasonal temperature oscillations,as well as a diurnal component, both relative to the440, 870, and 1020 nm wavelengths. Subsequently, ageneralized least-squares method was set up to re-move the two components from the values of V0���.The analysis established that percentages of approxi-mately 68%, 28%, and 10% of the total signal can beattributed to temperature dependence effects at the1020, 870, and 440 nm wavelengths, respectively.
It should be made clear that the analysis of thetemperature dependence is not a part of the SKYILmethod. During the present study, it was necessaryto perform such analysis because the results obtainedby applying the SKYIL method to the CIMEL data,without AERONET temperature corrections, werefound to be of worse quality than those obtained whenthe method was applied to a PREDE instrument,10
which does not require any temperature correction.The procedure set up in this study to correct thetemperature dependence certainly requires furtherinvestigation. Nevertheless, the SKYIL method wasevaluated to give very good results, when tested onthe AERONET database, which is accurately cor-rected for temperature dependence.
Once the temperature correction was performed, theaccuracy of the method was evaluated, finding that itis within 2.1% and 1.0%, depending on wavelength.The improvement of the accuracy with respect to thepreviously retrieved values10 is an important resultsince the nominal uncertainty affecting the values ofV0��� given by the AERONET calibration method (of1%–2%) and the uncertainty produced by the SKYILmethod turn out to be more similar in the presentcase.
The time trend of the calibration constant valuesretrieved by the SKYIL method was compared withthat calculated in the two experimental calibrations.The agreement was consistent with the experimentalerrors at the 440 and 670 nm wavelengths. At 870 nmand 1020 nm, a negative trend was defined using boththe experimental calibrations and the SKYIL method,although slightly underestimated in the latter case.
A comparison was also performed between the val-ues of the calibration constants found from the twoexperimental calibrations and the values of V0��� re-trieved following the SKYIL method, averaged over a1-month period centerd on the two experimental cal-ibration dates. At all the wavelengths, the values ofV0
exp��� and V0Sky��� were found to be comparable,
within their uncertainties.Finally, a study was performed to define the de-
pendence features of the results on the first guessV0
0��� and on the assumed refractive index. It is truethat the present analysis does not take into accountthe possible dependence on numerous input param-eters and assumptions, which are implicit in a radi-ative transfer model, such as those concerning the
surface albedo and the choice of the overall size rangeof the particle volume size distribution used in theSKYRAD code.5 However, the first guess V0
0��� andthe refractive index were considered to be the mostimportant causes of uncertainty. In both cases thevariability was found to be consistent with the un-certainty of the method.
In conclusion, the SKYIL method was found to besuitable for use to determine the solar calibrationconstants also for CIMEL instruments, providedthat the radiometer has been previously calibratedfor the diffuse radiance. A further step of thepresent investigation will be the application of themethod to a CIMEL Sun–sky radiometer belongingto the AERONET network. A calibration methodindependent of the AERONET system would bevery useful to diagnose the condition of a sky radi-ometer, whose data analysis is sensitive to smallerrors in the measured data. Using an independentmethod the variation of the calibration constantattributable to instrumental drift can be quicklyidentified, so that appropriate corrections can beapplied to data, starting exactly from the period inwhich the deviation occurred.
Before this step, several problems must be re-solved. First, the measured values of direct solar ir-radiance (not provided on the AERONET web site)need to be retrieved from the aerosol optical thick-ness values that can be downloaded directly from theweb. To perform this inversion, all the correctionsapplied following the AERONET protocol for the cal-culation of the aerosol optical depth from direct solarirradiance measurements need to be well known. Afurther problem is that the SKYIL method needs atleast eight measurements in the almucantar geome-try performed on the same day. The instrument usedin the present analysis has been implemented formore than 30 almucantar measurements per daysince it does not belong to the AERONET network,but the standard schedule for network Sun–sky ra-diometers usually leads to eight to ten almucantarmeasurements per day. This number of measure-ments can be drastically lowered after the applicationof the cloud screening, spoiling the application of theSKYIL method. Currently, the only way of overcom-ing this drawback is to use instruments located atsites where the meteorological conditions ensure aless frequent presence of clouds around the Sun.
Although limited to only one instrument, thepresent study furnished interesting results. Forthese reasons, it is worthwhile to continue investiga-tions for better application of the SKYIL method tothe AERONET database. Simultaneously, the appli-cation of the present methodology is recommendedfor CIMEL instruments involved in other networks,such as the recently created Spanish network RIMA.Furthermore these instruments should be employed,performing a greater number of experimental cali-bration tests, for both direct and diffuse solar irradi-ance, thus improving the validation of the SKYILmethod.
The authors dedicate this work to the memory oftheir colleague and friend Yoram Kaufman. He neverfailed to prove his scientific generosity, and duringhis last visit in Rome he made important suggestionsfor the development of the present work, always withhis spontaneous intellectual honesty.
The authors thank Brent Holben and Ilya Slutskerof the AERONET project for their comments, whichresulted in a substantial improvement of this work.
This research was supported by the strategic FondoIntegrativo Speciale per la Ricerca program Sustain-able Development and Climate Changes sponsored bythe Italian Ministry of University and Scientific Re-search (MIUR) and developed in the framework ofthe cooperative project between the CNR and MIUR,Study of the Direct and Indirect Effects of Aerosolsand Clouds on Climate (AEROCLOUDS).
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