Journal of Atmospheric and Solar-Terrestrial Physics 77 (2012) 132–143

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Journal of Atmospheric and Solar-Terrestrial Physics

1364-68

doi:10.1

n Corr

E-m

journal homepage: www.elsevier.com/locate/jastp

An absolute cavity pyrgeometer to measure the absolute outdoor longwaveirradiance with traceability to international system of units, SI

Ibrahim Reda a,n, Jinan Zeng b, Jonathan Scheuch c, Leonard Hanssen b, Boris Wilthan b,Daryl Myers a, Tom Stoffel a

a National Renewable Energy Laboratory, 1617 Cole Blvd., Golden, CO 80401-3305, USAb National Institute of Standards and Technology, USAc Labsphere, USA

a r t i c l e i n f o

Article history:

Received 6 April 2011

Received in revised form

12 December 2011

Accepted 14 December 2011Available online 27 December 2011

Keywords:

Pyrgeometer

Irradiance

Longwave

Infrared

Measurement equation

WISG

ACP

26/$ - see front matter & 2012 Elsevier Ltd. A

016/j.jastp.2011.12.011

esponding author. Tel.: þ1 303 384 6385; fax

ail address: Ibrahim.reda@nrel.gov (I. Reda).

a b s t r a c t

This article describes a method of measuring the absolute outdoor longwave irradiance using an

absolute cavity pyrgeometer (ACP), U.S. Patent application no. 13/049, 275. The ACP consists of

domeless thermopile pyrgeometer, gold-plated concentrator, temperature controller, and data acquisi-

tion. The dome was removed from the pyrgeometer to remove errors associated with dome

transmittance and the dome correction factor. To avoid thermal convection and wind effect errors

resulting from using a domeless thermopile, the gold-plated concentrator was placed above the

thermopile. The concentrator is a dual compound parabolic concentrator (CPC) with 1801 view angle to

measure the outdoor incoming longwave irradiance from the atmosphere. The incoming irradiance is

reflected from the specular gold surface of the CPC and concentrated on the 11 mm diameter of the

pyrgeometer’s blackened thermopile. The CPC’s interior surface design and the resulting cavitation

result in a throughput value that was characterized by the National Institute of Standards and

Technology. The ACP was installed horizontally outdoor on an aluminum plate connected to the

temperature controller to control the pyrgeometer’s case temperature. The responsivity of the

pyrgeometer’s thermopile detector was determined by lowering the case temperature and calculating

the rate of change of the thermopile output voltage versus the changing net irradiance. The responsivity

is then used to calculate the absolute atmospheric longwave irradiance with an uncertainty estimate

(U95) of 73.96 W m�2 with traceability to the International System of Units, SI. The measured

irradiance was compared with the irradiance measured by two pyrgeometers calibrated by the World

Radiation Center with traceability to the Interim World Infrared Standard Group, WISG. A total of 408

readings were collected over three different nights. The calculated irradiance measured by the ACP was

1.5 W/m2 lower than that measured by the two pyrgeometers that are traceable to WISG, with a

standard deviation of 70.7 W m�2. These results suggest that the ACP design might be used for

addressing the need to improve the international reference for broadband outdoor longwave irradiance

measurements.

& 2012 Elsevier Ltd. All rights reserved.

1. Introduction

Accurate measurements of broadband outdoor longwave(infrared) irradiance are important for renewable energy applica-tions and the study of the atmosphere and climate change. Priorto the introduction of the Interim World Infrared Standard Group(WISG) by the Physikalisch-Meteorologische ObservatoriumDavos (PMOD) in 2007, calibration of pyrgeometers was limitedto artificial blackbody measurements conducted in a laboratory or

ll rights reserved.

: þ1 303 384 6391.

manufacturer’s facility. The WISG was established through theInternational Pyrgeometer and Absolute Sky-scanning RadiometerComparisons, IPASRC-I (Philipona et al., 2001) and IPASRC-II (Martyet al., 2003). The two comparisons were held in Oklahoma and Alaska,USA, consecutively. The Absolute Sky-scanning Radiometer (ASR) wasused to establish the absolute reference irradiance during the twocomparisons (Philipona, 2001).

The participating pyrgeometers during IPASRC-I&II were firstcalibrated using 11 different blackbody sources (BB) to derivetheir indoor calibration coefficients, then they were deployedoutdoor with the ASR. The reference irradiance measured by theASR was then used to adjust the BB calibration coefficients foreach pyrgeometer. The calibration results of the two comparisons

I. Reda et al. / Journal of Atmospheric and Solar-Terrestrial Physics 77 (2012) 132–143 133

showed a bias of at least 3 W m�2 for clear sky conditions (Redaet al., 2008a,b,c). Since the ASR has a chopper and its responsivityis calculated using its built-in BB (Philipona, 2001), this biasmight be attributed to errors in measuring the chopper tempera-ture, spectral mismatch between the clear sky and the built-in BB,and condensation on the BB surface during clear sky conditions.Condensation occurs because the temperature of the built-in BB isadjusted below the dew point to match the clear sky temperature(i.e. less than �30 1C). As a result of IPASRC-I&II bias and othersources of system uncertainty, the traceability of WISG to SI unitshas not been established, and its estimated uncertainty mightexceed 74 W m�2 (private communication Julian Grobner fromPMOD/WRC, 2011).

Since IPASRC-I&II there have been two attempts to measurethe absolute irradiance to calibrate pyrgeometers with traceabil-ity to SI units. One method was developed by Reda et al., 2006; insummary, a standard pyrgeometer with dome that was charac-terized in a BB to calculate its calibration coefficients, wasinstalled on a temperature-controlled aluminum plate to lowerits case temperature until the outgoing irradiance matches theincoming atmospheric irradiance, i.e. the thermopile voltage ofthe pyrgeometer is close to zero. Then, by calculating the out-going irradiance using the calibration coefficients from the BBcalibration, the incoming atmospheric irradiance was calculated.The results of this method agreed with WISG to within73 W m�2 (Reda et al., 2006). At the time, when a claimwas made that this method yields an absolute measurementfor the atmospheric longwave irradiance, it was faced withresistance from the article’s reviewers. Rightfully, it was notconsidered absolute because of the inconsistent calibration coef-ficient of the dome, and the sky and blackbody spectral non-equivalence.

Thermal Ma

Fig. 1. Simplified diagram for abso

Another method was developed by Grobner and Los in 2007 tocalibrate pyrgeometers. The method was based on a BB calibra-tion, combined with calculated atmospheric longwave spectrausing a model to convert Planck radiation spectra to atmosphericlongwave spectra. The results of this method agreed with WISG towithin 71%, i.e. approximately 73 W m�2 Grobner and Los(2007).

The methods described above were attempts to establish aninternationally recognized absolute reference traceable to SIunits; this reference would then be used to calibrate pyrge-ometers. To properly calibrate a test pyrgeometer, it is calibratedin BB first, and then deployed outdoor with a reference pyrge-ometer for an extended period so that cloudy and clear skyconditions occur. The reference pyrgeometer is calibrated withtraceability to an International reference. The BB coefficients arethen re-adjusted so that the irradiance measured by the testpyrgeometer agrees with that measured by the reference pyrge-ometer. The blackbody coefficients are adjusted at two conditionsonly, cloudy and clear sky conditions (Philipona et al., 2001 andReda et al., 2002). From many pyrgeometer calibrations at NRELand PMOD, this method agreed with WISG to within 72 W m�2

for all environmental conditions, including cloudy, partiallycloudy, and clear sky conditions.

From many pyrgeometer calibrations performed at NREL andPMOD using WISG as a reference, the blackbody calibration yieldsoutdoor irradiance measurement to within 72 W m�2 for cloudysky conditions. This is attributed to the fact that during cloudy skyconditions the pyrgeometer’s thermopile-output-voltage is negli-gible (close to zero). Therefore, the only contribution to theuncertainty of measuring the longwave irradiance with trace-ability to SI units, during cloudy sky conditions, would be fromthe uncertainty of measuring the temperature of the case and

ss

lute cavity pyrgeometer, ACP.

I. Reda et al. / Journal of Atmospheric and Solar-Terrestrial Physics 77 (2012) 132–143134

dome of the pyrgeometer. Thermistors with larger than 70.1 1Cuncertainty are typically used to measure such temperature, thismight introduce larger than 3 W m�2 error in the irradiancemeasurement. This error is reduced by the blackbody calibrationor by calibrating the thermistors with lower uncertainty. Yet forclear sky conditions, using the blackbody calibration coefficientsfor many pyrgeometers calibrations yields a bias that exceeds12 W m�2 (Reda et al., 2008a,b,c). Therefore, measuring theatmospheric longwave irradiance under clear sky conditions isthe main obstacle in establishing an absolute reference forcalibrating pyrgeometers.

Since the traceability to SI units under clear sky conditions isnot established for WISG, this article is presented as a contribu-tion to establishing such traceability. In the article we introducean absolute cavity pyrgeometer (ACP), shown in Fig. 1, U.S. Patentapplication no. 13/049, 275. Then we describe a method using theACP that accounts for the environmental conditions, including theatmospheric longwave spectra, to measure the absolute outdoorlongwave irradiance under clear sky conditions.

2. Absolute cavity pyrgeometer

The ACP consists of a thermopile detector with its receivingjunctions (receiver) painted black to absorb the broadbandspectrum from the incoming longwave irradiance, gold-plateddual compound parabolic concentrator (CPC), and temperaturecontroller with temperature range from �40 1C to 40 1C; Fig. 1 isa simplified diagram of the ACP. To validate the concept, anEppley PIR pyrgeometer was used as the thermopile detector. Thedome was removed from the PIR to eliminate errors associatedwith the dome transmittance and the dome correction factor. Inthe future, other thermopile detectors designed specifically forsuch ACP might be used.

As shown in Fig. 1, the thermopile reference junctions of thedomeless PIR are thermally conductive to a thermal mass with itstemperature controlled by the temperature controller. To avoidthermal convection and wind effect errors resulting from usingthe domeless thermopile pyrgeometer, the CPC was placed abovethe thermopile, see Fig. 1. The CPC, manufactured by Labsphere(Jablonski and Carr, 1995), was modified to accommodate theACP’s design and functionality.

The dual CPC has 1801 view angle to measure the incominglongwave irradiance from the hemispherical sky outdoors (atmo-sphere). The incoming irradiance is reflected from the speculargold surface of the CPC and concentrated onto the 11 mmdiameter of the domeless pyrgeometer’s thermopile receiver.When the ACP is installed outdoor, the CPC’s upper port faceszenith and the lower port is above the thermopile. The thermopileis thermally insulated from the CPC to eliminate thermal conduc-tion between the CPC and pyrgeometer’s case. This allows thereceiver’s temperature, Tr, to be changed or controlled withoutaffecting the temperature of the CPC. Tr is measured by athermistor in thermal contact with the thermopile’s referencejunctions. The CPC’s temperature, Tc, is measured by six thermis-tors that are installed in the walls of the CPC; three thermistorsare installed in each of its lower and upper halves with a 1201angular distance on the perimeter, see Fig. 1. The thermistorsinstalled in the pyrgeometer and the CPC walls are calibrated withtraceability to SI to within a standard uncertainty of 70.03 K.

2.1. ACP measurement equation

The measurement equation is derived from the energy budgetat any thermopile receiving junctions, i.e. receiver (Reda and

Stoffel, 2010),

Wnet ¼W incoming�Woutgoing ð1Þ

where,

–

Wnet is the net irradiance at the thermopile receiver, inW m�2.

–

Wincoming is the incoming irradiance incident on the thermo-pile receiver, in W m�2.

–

Woutgoing is the outgoing irradiance from the thermopilereceiver, in W m�2.

To derive the measurement equation using the ACP, the threeirradiance values in Eq. (1) are derived as follows (see Fig. 1 forthe ACP irradiance sources).

2.1.1. The net irradiance, Wnet,

Wnet ¼ K1 � V tp ð2Þ

where,

–

K1 is the reciprocal of the ACP responsivity, in W m�2 uV�1

–

Vtp is the thermopile output voltage, in uV.

2.1.2. The incoming irradiance, Wincoming, at the thermopile receiver

consists of:

a)

An incident portion of the atmospheric longwave irradiance onthe thermopile receiver, Win: the unknown atmospheric irra-diance, Watm, is received at the top port of the CPC and is thenreflected from the CPC’s inside surface and concentrated at thereceiver’s surface,

W in ¼ t�Watm ð3Þ

where t is the ACP’s throughput, characterized at NIST.

b) An emitted portion of the CPC’s irradiance, dWc: the irradiance

resulting from the CPC’s temperature is emitted from the CPC’sinside surface, and then incident on the thermopile’s receiver,

dWc ¼ eg � s� T4c ¼ egWc ð4Þ

where,– eg is the gold emissivity, measured by NIST and equal to

0.0225 at wavelength of 10 um.– s is Stefan–Boltzmann constant¼5.6704�10�8 W m�2 K�4.– Tc is calculated as the average temperature (in Kelvin)

measured by the calibrated thermistors installed in theCPC’s wall.

– Wc is the CPC’s irradiance.

c) The emitted portion of the receiver irradiance, dWr: the

receiver irradiance (Wr) will be reflected on the CPC’s insidesurface and out to the atmosphere. The portion of Wr that isnot reflected will be absorbed at the gold surface, then emittedback and incident on the thermopile’s receiver surface,

dWr ¼ egK2Wr ð5Þ

where,– K2 is a constant that includes the emissivity of the black-

ened receiver and the error of measuring the receivertemperature.

– Wr is the emitted receiver irradiance, in W m�2,

Wr ¼ sT4r ð6Þ

I. Reda et al. / Journal of Atmospheric and Solar-Terrestrial Physics 77 (2012) 132–143 135

where Tr is the pyrgeometer’s receiver temperature, in K,

Tr ¼ TcaseþK4 � V tp ð7Þ

where,– Tcase is the temperature measured by the thermistor

installed in the pyrgeometer’s case (body), at the refer-ence junctions of the thermopile detector.

– K4 is the PIR’s thermopile efficiency factor¼0.0007044 K uV�1 (Reda et al., 2002).

d) A differential irradiance, dWd: this irradiance is a resultof the difference between the internal thermal energyinside the cavity (i.e. the enclosed air inside the CPC)and that of the thermopile receiver. Since the ACP isused when the environmental conditions are stable, andsince its top port is exposed to the outside air tempera-ture, then the temperature inside the cavity equals thatof the CPC; therefore,

dWd ¼ ec a v �Wc�K2 �Wr ð8Þ

where ecav is the emissivity of the enclosed volume. ecav

is assumed to equal one because of the CPC cavitation.The cavitation is a result of the highly reflective surfaceinside the CPC. The uncertainty of assuming ecav equalsone is included in the expanded uncertainty of the ACP.

The incoming irradiance is then calculated by addingEqs. (3),(4),(5), and (8),

W incoming ¼ t�WatmþðecavþegÞ �Wc�ð1�egÞ � K2 �Wr: ð9Þ

2.1.3. The outgoing irradiance from the thermopile receiver,

Woutgoing,

Woutgoing ¼ K2Wr ð10Þ

The three irradiances calculated by Eqs. (2),(9), and (10) arethen substituted in Eq. (1), thus,

K1V tp ¼ t�WatmþðecavþegÞ �Wc�ð2�egÞ � K2 �W r: ð11Þ

Then, the ACP’s Measurement Equation to measure the atmo-spheric longwave irradiance, Watm, is:

Watm ¼K1 � V tpþð2�egÞ � K2 �Wr�ðecavþegÞ �Wc

t : ð12Þ

2.2. ACP operation

The ACP might be operated using two methods, defined hereas steady-state method and transient-state method. The steady-state method is when the ACP is installed outdoor with notemperature controller, i.e. the receiver temperature is not con-trolled. The transient-state is when the receiver temperature ischanging using the temperature controller at the time of measur-ing the atmospheric longwave irradiance.

2.2.1. Steady-state method

When the ACP is installed outdoor at steady state with notemperature controller, the atmospheric longwave irradiance,Watm, is calculated using the Measurement Equation, Eq. (12).The variables in the right hand side of Eq. (12) are measured andcalculated with traceability to SI units, except for the unknown K1

and t. These two unknown variables are dependent on theenvironmental conditions, e.g. ambient temperature, relativehumidity, barometric pressure, wind speed, and the atmosphericlongwave spectral distribution at the time of measurement.Therefore, a full characterization of the ACP as a system is needed.This characterization must be at variable environmental condi-tions that would be a good representation to outdoor conditions.

A system for such characterization needs to be developed, and atpresent might be technologically challenging and cost prohibitive.Therefore this method is not used in this article.

2.2.2. Transient-state method

This method is used to calculate the magnitude of K1 (i.e. thereciprocal of responsivity) using thermal substitution method tosubstitute for the atmospheric longwave irradiance incident on theACP’s thermopile receiver. The thermal substitution method issimilar to the electrical substitution method used in the AbsoluteCavity Radiometer (ACR) to calculate its responsivity at the time ofmeasuring the solar irradiance (Caroli et al., 1983). The thermal orelectrical substitution method is used to account for the environ-mental conditions at the time of measuring the atmosphericlongwave or solar irradiance. The responsivity in both cases willchange as the environmental conditions change. Therefore, theresponsivity of the ACR or the ACP must be recalculated at the timeof measurement and as frequent as the environmental conditionschange, e.g. for stable clear sky conditions, the responsivity mightbe calculated every 20 min for ACR and 10 min for ACP.

For the ACR, the traceability to SI units is established frommeasuring traceable electrical power and optical characterization,e.g. model AHF manufactured by Eppley Laboratories and PMO-6manufacture by PMOD (for the PMO-6 temperature traceability isincluded). Similarly, the traceability for the ACP is establishedthrough measuring temperature, voltage, and NIST’s opticalcharacterization.

The thermal substitution method, or transient-state method, isperformed by decreasing the thermopile receiver temperaturewhen the ACP is installed outdoor to measure the atmosphericlongwave irradiance, Watm. It is fundamental to this transient-state method that the thermopile receiver cooling period isperformed under stable environmental conditions, includingstable Watm to within one W m�2 from the average irradianceduring the cooling cycle. While cooling the thermopile receiver,the rate of change of the net irradiance (Wnet) versus the rate ofchange of the output thermopile voltage (Vtp) is then used tocalculate K1. Once K1 is calculated, then t is calculated using afunction of K1 that was developed from the ACP characterizationat NIST; and then Watm is calculated using Eq. (12).

a)

To calculate K1, the ACP is installed outdoors as shown inFig. 1, at night when there is no shortwave irradiance. Thestability of the longwave irradiance is monitored by anyatmospheric longwave detector. Since the detector is used tomonitor relative stability of Watm, it does not need to becalibrated. In this experiment, two collocated pyrgeometerswith domes were used to monitor the stability, defined asstability pyrgeometers. When a clear and stable atmosphericcondition occurs, the temperature controller is adjusted tocool down the thermopile receiver of the ACP to approximately5 1C lower than the stable ambient temperature, or as cool aspossible till the temperature is above the dew point toavoid condensation on the thermopile receiver surface. Whilethe ACP’s receiver temperature is decreasing, all outputsignals from the ACP and the stability pyrgeometers aremeasured every 10 s. The output signals include, Vtp, Tr, andTc from the ACP. The signals from the two collocated pyrge-ometers, i.e. thermopile voltage, case temperature, and dometemperature, are also measured at the same time. The averageirradiance measured by the stability pyrgeometers is thencalculated and used to monitor the atmospheric longwavestability.Since Watm is constant, K1 is calculated during the coolingprocess by differentiating Eq. (11) with respect to time,

I. Reda et al. / Journal of Atmospheric and Solar-Terrestrial Physics 77 (2012) 132–143136

therefore,

K1 ¼ðecavþegÞ �DWc�ð2�egÞ � K2 �DWr

DV tpð13Þ

where,– DWc, DWr, and DVtp are the differences between the

measured values of Wc, Wr, and Vtp at the start and endtimes of the cooling process.

– K2 is assumed to equal one because the thermistors arecalibrated, and the emissivity of the black receiver isassumed to equal one. The uncertainty of such assumptionis included in the expanded uncertainty of the ACP.Since ecav equals one, and eg is known from NIST’s char-acterization, then K1 is calculated.Here, instead of calculating the differences in Eq. (13), K1 iscalculated by plotting the changing irradiance versus thechanging thermopile output voltage. Since tWatm is con-stant and K2 equals one, the changing net irradiance portionin Eq. (11) equals W00net,

W ’’net ¼ ðecavþegÞ �Wc�ð2�egÞ �Wr: ð14Þ

When W00net is plotted versus Vtp; the slope (a) of the

straight line fit of the data set (e.g., y¼axþb) would equalK1. From Eq. (11), the intercept (b) with the W00net axis(y-axis) would equal the constant �tWatm (see Figs. 6–10).

b)

To calculate t, the ACP was characterized at NIST using theComplete Hemispheric Infrared Laser-Based Reflectometer(CHILR) at a wavelength equal to 10.16 um. The details of thecharacterization is beyond the scope of this article, but can bereviewed in detail in Jinan et al., 2010. In summary, the ACP wascharacterized using a Lambertian source as a standard, to simulatethe night time clear sky conditions, with its output directed to theACP top port. A reference detector was used to measure therelative irradiance. The throughput, t, is then calculated bydividing the irradiance measured at the receiver of the ACP withthe CPC installed by that without the CPC installed:

t¼ ðK1nVc t pþK2nWc rÞnV r e f

ðK1nV t pþK2nWrÞnVc r e fð15Þ

where,

– Vctp and Vtp are the thermopile output voltage with and

without the CPC installed, in uV

285

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Atm

osph

eric

Lon

gwav

e Irr

adia

nce

(W/m

2 )

Mountain

September 15, 2010 Septem

Fig. 2. Atmospheric longwave irradiance stability

–

3:38

3:40

Sta

ber 1

dur

Wcr and Wr are the thermopile receiver irradiance with andwithout the CPC installed, in W m�2

–

Vcref and Vref are the output voltage of the reference detectorwith and without the CPC installed, in uV.

Since all variables in Eq. (15) are measured at NIST except forthe unknown t and K1, then Eq. (15) is expressed so that t is afunction of K1,

t¼ 0:004903� K1þ0:004419

0:007548� K1þ0:004242: ð16Þ

By substituting the derived K1 from step (a) in Eq. (16) tocalculate t, the atmospheric longwave irradiance, Watm, is calcu-lated,

Watm ¼�b

tð17Þ

where b is the intercept of the line fit in step (a) above.In summary, using the transient-state method, the irradiance

is measured when stable clear sky conditions occur with windspeed less than 5 m/s to minimize convection effects. The irra-diance is then measured by the ACP during the cooling cycle only,and might also be measured few minutes before the cooling startsif the irradiance is stable. After the cooling cycle is completed, theACP has to reach equilibrium with the ambient conditions beforeanother cooling cycle starts. The waiting period between coolingcycles might be from 1 min to 30 min; varies depending on thethermal mass of the thermopile and the thermal capacity andresponse time of the temperature controller.

2.3. Outdoor measurement results and comparison to WISG

Outdoor measurements were taken at the National RenewableEnergy Laboratory (NREL) in Golden, Colorado, on September, 15,16, and 17, 2010, starting at 3 AM and ending at 4:30 AM eachday. The sky was clear for these three days, with stable longwaveirradiance during the period of time when the measurementstook place (Fig. 2). The average wind speeds were 2 m/s, 1 m/s,and 5 m/s for September 15, 16, and 17, respectively (Fig. 3). Theoutdoor ambient temperature varied from 12 1C to 20 1C (Fig. 4).The total atmospheric water vapor varied from 0.3 cm to 1.3 cm

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ndard Time

6, 2010 September 17, 2010

ing the five cooling events on three days.

0

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Win

d Sp

eed

(m/s

)

Mountain Standard Time

September 15, 2010 September 16, 2010 September 17, 2010

Fig. 3. Wind speed during the five cooling events on three days.

8

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Am

bien

t Tem

pera

ture

(°C

)

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September 15, 2010 September 16, 2010 September 17, 2010

Fig. 4. Ambient temperature during the five cooling events on three days.

I. Reda et al. / Journal of Atmospheric and Solar-Terrestrial Physics 77 (2012) 132–143 137

(Fig. 5). Figs. 6–10 show W00net versus Vtp, including the slope andintercept of the line fit for five cooling events during the threeclear days.

For the five cooling events, two on each of the 15th and 16thand one on the 17th, the figures show the strong correlationbetween W00net and Vtp, i.e. the goodness of the fit (R2) is 40.99with a calculated standard error less than 0.22 W m�2. Table 1lists the K1, intercept (Win), R2, standard error of the line fit, andthe calculated t. Table 1 also shows that K1 variation is within72% from the RMS value of the five events. This variation is aresult of the changes in the environmental conditions at eachcooling event. Using Eq. (16), the variation in t is within 70.1%from the average value of the five events.

Fig. 11 shows the difference between the irradiance measuredby the ACP and the average irradiance measured by twopyrgeometers that have traceability to WISG. The two traceablepyrgeometers were also used as the stability pyrgeometers.The average difference for the five events over the threedays was �1.5 W/m2 with a standard deviation of 0.7 W/m2.It is noteworthy that the figure shows that the average differenceis �1.8 W/m2 for September 15 and 16 when it was less windy,and �1 W/m2 for September 17 when it was windier. Theeffect of wind speed is not conclusive because some ofthe difference could be attributed to the non-ideal spectraltransmittance of the domes of the two pyrgeometers thatare traceable to WISG. Future comparison of ACP results against

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Tota

l Wat

er V

apor

(cm

)

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September 15, 2010 September 17, 2010September 16, 2010

Fig. 5. Total atmospheric water vapor during the five cooling events on three days.

y1 (September 15, 2010)= 0.0784x -295.5R2 = 0.9959

-390

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Wne

t" (W

/m2 )

Vtp (uV)-900 -700 -500 -300 -100

Fig. 6. Changing net irradiance versus the thermopile voltage during the first cooling event of the ACP.

I. Reda et al. / Journal of Atmospheric and Solar-Terrestrial Physics 77 (2012) 132–143138

other absolute instruments might help in resolving the windeffect.

2.3.1. Validation of measurement equation for steady and transient

states

To confirm that the ACP’s measurement equation is valid whenused for the steady and transient state methods, data from theACP with no cooling (i.e. steady-state period) and the twopyrgeometers traceable to WSIG, was collected for a period of21 min before the cooling cycle on September 17. K1 and t werecalculated from the cooling cycle (i.e. transient-state method).Then using the measurement equation, Eq. (12), the irradiancewas calculated for the 21 min prior to the cooling cycle (i.e.steady-state period). Fig. 12 shows the irradiance measured by

the ACP and the average irradiance measured by the two WISGpyrgeometers during the steady state period. From the figure, theACP irradiance has larger spikes than the WISG pyrgeometers.This is attributed to the fact that the ACP is an open cavitywith a faster response than that of the WISG pyrgeometers (frommanufacturer’s specification, time constant o1 s for thermopileversus 42 s for pyrgeometer with dome).

Fig. 13 shows the difference between the irradiance measuredby the ACP and the average WISG irradiance during the 21 minsteady-state period. From the figure, the average differencebetween the irradiance measured by the ACP and the WISGpyrgeometers is negligible (0.04 W m�2); the calculated standarddeviation equals 0.52 W m�2. Fig. 11 shows that during thetransient-state method, the average difference between the irra-diance measured by the ACP and the WISG pyrgeometers on

y2 (September 15, 2010) = 0.0823x -294.23R2 = 0.9986

-390

-380

-370

-360

-350

-340

-330

-320

-310

-300

-290-1100

Wne

t" (W

/m2 )

Vtp (uV)

-900 -700 -500 -300 -100

Fig. 7. Changing net irradiance versus the thermopile voltage during the second cooling event of the ACP.

y1 (September 16, 2010) = 0.0797x -289.49R2 = 0.9996

-390

-380

-370

-360

-350

-340

-330

-320

-310

-300

-290-1100

Wne

t" (W

/m2 )

Vtp (uV)

-900 -700 -500 -300 -100

Fig. 8. Changing net irradiance versus the thermopile voltage during the third cooling event of the ACP.

I. Reda et al. / Journal of Atmospheric and Solar-Terrestrial Physics 77 (2012) 132–143 139

September 17 was approximately �1 W m�2. Therefore, thedifference between the steady and transient state methods equals0.04þ1¼1.04 W m�2.

Part of this difference in results might be attributed to the factthat during the transient-state, the ACP’s thermopile is cooled bythe temperature controller at the reference-junctions (i.e. bottomof the detector), while during steady-state the receiving-junctions(top of the detector) are cooled by the radiative exchange with thecold sky. This results in a difference in the temperature gradientof the thermopile.

Most of such gradient difference is taken into account becausethe energy balance is calculated at the receiver using Eq. (7), yetspectral effects and errors in K4 might contribute to the differentresults between transient and steady state methods. In thisarticle, this difference is named thermal non-equivalence. Thisnon-equivalence is added to the expanded uncertainty of the ACPas a random component (Type-A) because its magnitude willchange based on the environmental conditions at the time ofmeasurement. Future comparisons against other absolute

instruments might evaluate the magnitude of non-equivalenceand its uncertainty.

Nevertheless, a 1.04 W m�2 difference between steady andtransient state methods is within the overall uncertainty of theACP as will be shown in the uncertainty section. This is aconfirmation that the measurement equation can be used forthe transient and steady state methods to within the stateduncertainty of the ACP.

To further clarify the ACP’s operation and the contribution ofeach irradiance source to the measured Watm, Table 2 lists anexample from September 17th data set. The table includes Vtp,dWa, dWr, dWd, and Wr when the ACP is installed outdoor duringthe steady and transient states.

3. Uncertainty estimate

This section summarizes the relevant uncertainty estimate formeasuring the atmospheric longwave irradiance using ACP. It is

y2 (September 16, 2010)= 0.0819x -284.8R2 = 0.9993

-390

-380

-370

-360

-350

-340

-330

-320

-310

-300

-290-1100

Wne

t" (W

/m2 )

Vtp (uV)

-900 -700 -500 -300 -100

Fig. 9. Changing net irradiance versus the thermopile voltage during the fourth cooling event of the ACP.

y (September 17, 2010) = 0.0819x -296.54R2 = 0.9897

-390

-380

-370

-360

-350

-340

-330

-320

-310

-300

-290-1100

Wne

t" (W

/m2 )

Vtp (uV)

-900 -700 -500 -300 -100

Fig. 10. Changing net irradiance versus the thermopile voltage during the fifth cooling event of the ACP.

Table 1Summary of outdoor data with line fit and throughput results.

Outdoor Cooling Events

Sep. 15 (1) Sep. 15 (2) Sep. 16 (1) Sep. 16 (2) Sep. 17 (1)

K1¼a¼Slope (W m�2 mV�1) 0.0784 0.0823 0.0797 0.0819 0.0819

Win¼b¼t*Watm (W m�2) 295.50 294.23 289.49 284.8 296.54

R2 0.9959 0.9986 0.9996 0.9993 0.9897

Standard error (W m�2) 0.15 0.15 0.04 0.04 0.22

t 0.9937 0.9916 0.9930 00.9919 0.9919

I. Reda et al. / Journal of Atmospheric and Solar-Terrestrial Physics 77 (2012) 132–143140

consistent with the current Evaluation of measurementdata—Guide to the expression of uncertainty in measurement(GUM) (JCGM 1995). For details with numerical examples aboutusing the GUM guidelines to calculate uncertainty in radiometry,see Reda et al. (2008a,b,c). All uncertainty estimates are traceableto SI and are based on practical experience in measuring theatmospheric longwave irradiance using pyrgeometers of differentmodels and manufacturers.

Since GUM is beyond the scope of this article, only the relevantvalues to the final uncertainty estimate for measuring theabsolute atmospheric irradiance are listed in Tables 3 and 4.Table 3 is a list of the standard uncertainty (u), sensitivitycoefficient (c), the contribution of each variable to the combineduncertainty (cnu), and the combined standard uncertainty forderiving K1 and t. Table 4 is a list of u, c, cnu for the relevantvariables, and the combined Type-B standard uncertainty (uB),

-3.5

-3

-2.5

-2

-1.5

-1

-0.5

0

3:18

3:21

3:23

4:33

4:35

4:38

4:41

4:46

3:30

3:33

3:36

3:39

3:41

3:44

4:41

4:44

3:21

3:24

3:27

3:30

3:32

3:35

3:38

3:41

WA

CP-W

WIS

G (W

/m2)

Mountain Standard Time

September 17, 2010September 16, 2010September 15, 2010

Fig. 11. Difference between measured irradiance by ACP and WISG at night time for three days.

299

299.5

300

300.5

301

301.5

302

302.5

303

2:55

2:56

2:57

2:58

2:59

3:00

3:01

3:02

3:03

3:04

3:05

3:06

3:07

3:08

3:09

3:10

3:11

3:12

3:13

3:14

3:15

3:16

Wat

m (W

/m2 )

Mountain Standard Time

Average WISG Irradiance ACP Irradiance

Fig. 12. Measured irradiance using ACP and WISG pyrgeometers when the ACP is at steady state on September 17, 2010.

I. Reda et al. / Journal of Atmospheric and Solar-Terrestrial Physics 77 (2012) 132–143 141

Type-A standard uncertainty from line fit (uAf), Type-A standarduncertainty from non-equivalence (uAne), combined standarduncertainty of Watm (uatm), coverage factor (k), and the finalExpanded Uncertainty (U95, atm). The Type-A standard uncertaintyof the line fit in Table 4 is calculated from the residuals of the fiveline fits in Figs. 6–10, which would account for data acquisitionnoise and the unavoidable changes in the environmental condi-tions during the cooling process. From Table 4, the expandeduncertainty of Watm, with a 95% confidence level (k¼1.96) equals73.96 W m�2 with respect to SI.

In the last column of Table 4, the percentage contribution tothe total uncertainty of each variable is listed. From the list, it isevident that the largest contributions are from the uncertainty inK2, then from t. Therefore, characterizing the emissivity ofthe thermopile receiver and t with lower uncertainty wouldimprove the overall uncertainty. This might be accomplished bydeveloping a system that simulates the outdoor environmentalconditions, including the spectral distribution, to characterizethe ACP.

4. Conclusion and future work

We designed, built, characterized, and evaluated an AbsoluteCavity Pyrgeometer. The absolute longwave irradiance was mea-sured during three nighttime periods with cloudless sky condi-tions using the ACP with an expanded uncertainty of73.96 W m�2 and a coverage factor of 1.96 with respect to SI.To achieve such uncertainty, all measuring instruments arecalibrated with traceability to SI; this includes the temperatureprobes, data acquisition, and the characterization at NIST. Thecomparison between the ACP and two pyrgeometers that aretraceable to WISG, showed that the average difference betweenthe ACP and WISG instruments for the three days was�1.5 W m�2 with a standard deviation of 0.7 W m�2. Thisdifference is within the uncertainty of both the ACP and theWISG; estimated UWISGZ74 W m�2. The ACP measurementswere 1.8 W/m�2 lower than that simultaneously measured byWISG instruments on September 15 and 16 when it was lesswindy, and about 1 W/m2 lower on September 17 when it was

-1

-0.5

0

0.5

1

1.5

2

2:55

2:56

2:57

2:58

2:58

2:59

3:00

3:01

3:02

3:03

3:03

3:04

3:05

3:06

3:07

3:08

3:08

3:09

3:10

3:11

3:12

3:13

3:13

3:14

3:15

3:16

WA

CP-

WW

ISG

(W/m

2 )

Mountain Standard Time

Fig. 13. Difference between irradiance measured by ACP and WISG when the ACP is at steady state on September 17, 2010.

Table 2

Example of Vtp, dWa, dWr, dWd, Wr, and Watm on September 17, 2010.

Variable Steady state(at one data point)

Transient state(cooling cycle period)

Vtp (uV) �1021 �1014 to �207

Wc (W m�2) 413.6 414.1–410.1

Wr (W m�2) 406.5 406.7–371.1

K2 1 1

eg 0.0225 0.0225

dWc¼egn Wc (W m�2) 9.3 9.3–9.2

dWr¼egn Wr (W m�2) 9.1 9.1–8.3

ecav 1 1

dWd¼ecavn Wc�K2

n Wr

(W m�2)

7.1 7.4–39.0

K1 (W m�2 uV�1 )n 0.0819n 0.0819

sn 0.9919n 0.9919

WACP¼Watm (W m�2) 299.7 299.0

n Calculated using the transient state method (i.e. cooling method).

Table 3Standard uncertainty of the variables in the measurement equation.

Variable Value u c cnu

1. K1’s standard uncertainty from the outdoor measurement

DWc 6.2 0.02 -0.0014 -0.00003

DWr 34.3 0.09 0.0026 0.0003

DVtp �748 �2.16 0.0001 �0.00024

eg 0.0225 0.00004 �0.0541 �0.000002

ecav 1 0.0006 0.0083 0.000005

K2 1 0.0017 0.0907 0.0003

Calculated K1 using Eq. (13) 0.0822

Combined standard uncertainty for K1 0.0004

2. s’s standard uncertainty from NIST measurementK1 0.0822 0.0004 �0.5092 �0.00024

Vtp 481 0.1079 0.0002 0.00002

K2 1 0.0017 0.0442 0.00008

Wrc 432 0.3389 0.0021 0.00072

Vref 102430 295.7 0.00001 0.00287

Vtp 773 0.1093 �0.0002 �0.00002

Wr 431 0.3393 �0.0019 �0.00068

Vrefc 98174 283.4 �0.00001 �0.00287

Calculated s using Equation 16 0.99169

Combined standard uncertainty for s 0.00418

Table 4Sensitivity coefficients, combined standard uncertainty, and expanded uncertainty

in atmospheric longwave irradiance.

Variable Value u c cnu Percentagecontribution

K1 0.0822 0.00044 �818.24 �0.366 9.4

Vtp �825 �2.38 0.083 �0.198 5.1

eg 0.0225 0.00004 �783.23 �0.031 0.8

ecav 1 0.0006 �394.53 �0.228 5.9

Wr 385.5 0.1835 1.994 0.366 9.4

Wc 391.3 0.1061 1.031 0.109 2.8

s 0.99169 0.00418 �299.32 �1.250 32.2

K2 1 0.00173 768.65 1.331 34.3

Type-B Combined standard uncertainty¼uB 1.93 (W m�2)Type-A standard uncertainty from line fit¼uAf 0.15 (W m�2)Type-A standard uncertainty from non-equivalence¼uAne 0.60 (W m�2)Combined standard uncertainty of Watm¼uatm 2.02 (W m�2)Effective degrees of freedom 290239407

Student’s ‘‘t’’¼k 1.96

Expanded uncertainty¼knuatm¼U95, atm 3.96 (W m�2)Percentage expanded uncertainty¼U95, atm 1.3%

I. Reda et al. / Journal of Atmospheric and Solar-Terrestrial Physics 77 (2012) 132–143142

windier. This might be attributed to the wind effect and/or to thefact that WISG instruments have domes, which will have morespectral dependence than that of the domeless ACP. The derivedACP’s measurement equation is used for steady and transientstate methods. This was validated to within the stated uncer-tainty of the ACP. The two methods yielded a difference of1.04 W m�2. This difference might be attributed to the thermalnon-equivalence during the cooling cycle, or to the dome trans-mittance of the two WISG pyrgeometers. Future comparisonsagainst other absolute instruments might resolve this difference.Future angular response characterization of the ACP and devel-opment of a fast sky scanner to measure the angular distributionof the sky IR-irradiance at the time of measurement, mightimprove the uncertainty of using the ACP, especially when usedunder partially cloudy conditions. The uncertainty might also belowered by developing new systems that simulates the outdoorconditions to characterize the ACP, e.g. K1 and t versus differentenvironmental conditions and spectral distributions.

I. Reda et al. / Journal of Atmospheric and Solar-Terrestrial Physics 77 (2012) 132–143 143

Acknowledgments

We thank the National Renewable Energy Laboratory’s Photo-voltaic and Metrology programs, DOE-Atmospheric System ResearchProgram, and Optical Technology Division, Physical MeasurementLab, NIST, DOC for providing the funds for this effort. We also thankBev Kay and Preston Morse for their administrative help andinstrument setup for the outdoor measurement.

References

Caroli, Alton R.; Hickey, John R.; Frieden, Roger G. 1983. Self calibrating cavityradiometers at the Eppley Labortory: Capabilities and applications. Proceed-ings of the International Society for Optical Engineering. vol. 416, DPIE,Dillingham, WA, USA; pp. 43–50.

Grobner, J., Los, A. 2007. Laboratory calibration of pyrgeometers with knownspectral responsivities, Journal of Optical Society of America. vol. 46, no. 30/Applied Optics, October 2007; pp. 7419–7425.

Jablonski, J.W.; Carr, K.F. 1995. Highly efficient collection optical system forproviding light detectors such as photodetectors and the like with hemisphe-rical field of view. Labsphere, Inc., Patent number: 5479009, Dec. 26, 1995.

Jinan, Z.; Hanssen, L.; Reda, I.; Scheuch, J. 2010. Preliminary Characterization Studyof a Gold-Coated Concentrator for Hemispherical Longwave Irradiance Mea-surements. Paper no. 77920Z. Gu, Z.H., Hanssen, L.M., (eds.); Reflection,Scattering, and Diffraction from Surfaces II: Proceedings of SPIE Conference,3–5 August 2010, San Diego, California. Proceedings of SPIE - The InternationalSociety for Optical Engineering, volume 7792. Bellingham, WA: SPIE—TheInternational Society for Optical Engineering, 12 pp.

Marty, C., Philipona, R., Delamere, J., Dutton, Ellsworth G., Michalsky, J., Stamnes,K., Storvold, R., Stoffel, T., Clough, Shepard A., Mlawer, Eli J., 2003. Downward

longwave uncertainty under arctic atmospheres: measurement and modeling.Journal of Geophysical Research 108 (D12)., pp. ACL 4-1.

Philipona, R., 2001. Sky-scanning radiometer for absolute measurements ofatmospheric long-wave radiation. Journal of Applied Optics 40 (15),2376–2383. May 2001.

Philipona, R., Dutton, Ellsworth G., Stoffel, T., Michalsky, J., Reda, I., Stifter, A.,Wendling, P., Wood, N., Clough, Shepard A., Mlawer, Eli J., Anderson, G.,Revercomb, Henry E., Shippert, Timothy R., 2001. Atmospheric longwaveirradiance uncertainty: pyrgeometers compared to an absolute sky-scanningradiometer, atmospheric emitted radiance interferometer, and radiativetransfer model calculations. Journal of Geophysical Research 106,28129–28141. D22, 2001.

Reda, I., Hickey, J.R., Stoffel, T., Myers, D., 2002. Pyrgeometer calibration at theNational Renewable Energy Laboratory (NREL). Journal of Atmospheric andSolar-Terrestrial Physics 64 (15), 1623–1629.

Reda, I., Hickey, J.R., Grobner, J., Andreas, A., Stoffel, T., 2006. Calibratingpyrgeometers outdoors independent from the reference value of the atmo-spheric longwave irradiance. Journal of Atmospheric and Solar-TerrestrialPhysics 68 (12), 1416–1424.

Reda, I.; Grobner, J.; Stoffel, T.; Myers, D.; Forgan, B. 2008a. Improvements in theBlackbody Calibration of Pyrgeometers (Presentation). Annual science teammeeting, Atmospheric Radiation Measurement Program, ARM. 14 pp.; NRELReport no. PR-560-45868.

Reda, I., Myers, D., Stoffel, T., 2008b. Uncertainty estimate for the outdoorcalibration of solar pyranometers: a metrologist perspective. Measure (NCSLIJournal of Measurement Science 3 (4), 58–66.

Reda, I.; Grobner, J.; Stoffel, T.; Myers, D.; Forgan, B. 2008c. Improvements in theBlackbody Calibration of Pyrgeometers (Presented at the Eighteenth Atmo-spheric Radiation Measurement (ARM) Program Science Team Meeting). 14pp.; NREL Report no. PR-560-45868.

Reda, I.; Stoffel, T. 2010. Pyrgeometer Calibration for DOE-Atmospheric SystemResearch Program Using NREL Method (Presentation). 9 pp.; NREL Report no.PR-3B0-47756. Golden, Colorado: National Renewable Energy Laboratory.