Solar Physics (2004) 224: 237–246 C© Springer 2005

ABSOLUTE ACCURACY AND REPEATABILITY OF THE RMIBRADIOMETERS FOR TSI MEASUREMENTS

SABRI MEKAOUI, STEVEN DEWITTE, DOMINIQUE CROMMELYNCK,ANDRE CHEVALIER, CHRISTIAN CONSCIENCE and ALEXANDRE JOUKOFF

The Royal Meteorological Institute of Belgium, Ringlaan 3, B 1180 Brussel, Belgium(e-mail: sabri.mekaoui@oma.be)

(Received 2 September 2004; accepted 15 October 2004)

Abstract. Radiometers for the measurement of the total solar irradiance from space have been de-veloped by D. Crommelynck at the Royal Meteorological Institute of Belgium (RMIB) since 1970.These radiometers, also used in the set of instruments defining the “World Radiometric Reference”,have successively flown on SPACELAB 1, ATLAS 1, EURECA, ATLAS 2, ATLAS 3, SOHO andHITCHHIKER, among them the SOLCON radiometer on the last STS107 flight. Other radiometersare under construction or integration for the upcoming missions: one as part of the SOVIM experimenton the International Space Station and SOVAP on the PICARD micro satellite. These radiometershave a symmetrical side by side cavity design. They are operated using the differential active cavityradiometric principle. In order to construct a long time series and to detect any variation between twocycles, it is important to know all the instrument parameters and make a clear distinction between whatwill lead to uncertainty on an absolute level and what guarantees the repeatability of the measure-ments. The purpose of this paper is to review these parameters; after a description of its principle, theinstrumental equation will be established. The electrical parameters and the determination of remain-ing instrumental parameters are done during the characterisation phase at the RMIB. The results fromthe DIARAD/VIRGO radiometer on SOHO are presented. The repeatability of the measurements isfound to be of the order of 100 ppm after correction of the in-flight aging. The accuracy on an absolutelevel is about 1.06 W m−2 for DIARAD left cavity. This accuracy is limited by the characterisationaccuracy with a dominant role of the precision aperture area determination. The understanding of thebehaviour of the DIARAD type instrument allows improving the design of the new radiometers onthe upcoming missions.

1. Introduction

To derive the most accurate total solar irradiance (TSI) measurements it is importantto understand the error sources of the measuring instrument in order to try toapply appropriate corrections and to quantify the remaining uncertainty from thebasic electrical power measurements. These corrections are used to deliver the finalscientific TSI data set. Any misunderstanding or neglecting of an error source couldlead to a trend or even a discontinuity in the TSI time series.

In the present paper we proceed as follows: in Section 2 we describe the radiome-ters built at the Royal Meteorological Institute of Belgium (RMIB), in Section 3 weexplain the measurement principle. In Section 4 we estimate the absolute accuracyfrom the instrumental equation whereas in Section 5 the repeatability is treated as

238 S. MEKAOUI ET AL.

a separate point. Finally we give the value of the accuracy and repeatability of theTSI data.

2. Description of the Radiometers

The DIARAD/SOLCON type radiometers (Crommelynck, 1973, 1975, 1982;Crommelynck and Domingo, 1984; Crommelynck and Dewitte, 1999) is a dif-ferential absolute solar radiometer developed at the Royal Meteorological Instituteof Belgium (RMIB). It is the first absolute radiometer operated in space which isbased on a full symmetrical metrological design (two side by side cavities) andoperation (successive opened and closed state of the measurement cavity). Theseradiometers are also the first to be completely characterized for operation at theground in air. The RMIB maintains a set of these instruments for periodic compar-isons at the ground as its “reference scale”. The instrument can be described bythree parts: the detectors, the electrical measurement chains with their referencevoltages and the servo loop system.

– The detectors: the detectors are formed by two blackened cylindrical cavitiesmounted side by side on a common heat sink. Between each cavity and theheat sink a heat flux transducer and a heating resistor are mounted. Bothcavity channels are equipped with a shutter in front to block or admit lightto the cavity through a precision and a limiting aperture. Finally an opticalbaffle separates both channels from the other channel aperture, both channelssee the same common angular limiting volume or baffle. It is imperative thatthe whole system be insulated from the outside and absolutely symmetric(Figure 1).

– The electrical chains: every heating resistor is mounted in series with a cur-rent measuring resistor. The voltage over the four resistors is digitized throughfour electrical measurement chains. Every electrical chain is composed of a

Figure 1. Main features of the DIARAD radiometers.

ABSOLUTE ACCURACY AND REPEATABILITY OF THE RMIB RADIOMETERS 239

Figure 2. The electrical chains measurement for DIARAD/VIRGO, the counters are not represented.

differential amplifier, a voltage to frequency converter and a counter, see Fig-ure 2. For the calibration of these electrical chains, DIARAD radiometers usehighly accurate reference voltages derived with a precision resistor ladder fedby a highly accurate temperature-stabilized reference voltage. For the SOVIM(solar variability and irradiance monitoring) and SOVAP (solar variability onPicard) case, DIARAD uses six levels of the reference voltage and six for thecurrent for the in-flight measurement of the function that relates digital countto voltage.

– The servo loop system: equilibrium between the two cavity heat fluxes ismaintained by regulating the electrical power in one of the two cavities usingan analog proportional–integrator servo system.

3. Measurement Principle

DIARAD operates similarly as a “household scale” and thus different radiometricstates can be used. They enable to verify the coherence of the instrument. In thedefault measurement sequence a constant electrical power is fed into one cavity,the “reference” cavity, while its shutter remains closed. The electrical power in theother cavity, the “measurement” cavity, is regulated continuously, while its shuttersequentially opens and closes (both open and closed states take 90 s). When the in-strument is pointed to the Sun, the equilibrium electrical power in the measurement

240 S. MEKAOUI ET AL.

Figure 3. Schematic representation of the different powers involved during the opened (right) andclosed state (left).

cavity drops proportionally to the absorbed solar power when going from the closedto the open state.

– Closed state: both shutters are closed, a reference power Pref is dissipatedthrough the heating resistor of the reference cavity. Pref = V I , where V is theapplied voltage and I is the current across the heating resistor. A heat flux isdetected by the sensor. As a consequence, the servo loop system dissipatesa power Pclosed in the measuring cavity (right) through its heating resistor.This state is represented in Figure 3 left. The servo system brings Pclosed toequilibrium with Pref with a systematic error �Peq,

�Peq + Pref = Pclosed. (1)

– Open state: the active shutter opens. If we suppose the cavity perfectly blackand without any thermal loss, an absorbed solar power A · SI is detected bythe heat flux sensor where SI is the solar irradiance and A the surface of theprecision aperture. The optical baffle prevents scattered light from falling intothe reference cavity. The servo system takes 90 s to reduce the dissipatedelectrical power in the active cavity Popen and to bring it to equilibrium withthe reference power Pref,

�Peq + Pref = Popen + A × SI. (2)

From the opened and closed state we have, if we assume the stability of Pref and�Peq, a first approximation of the value of the solar irradiance, depending on theeffective sensitivity of the exposed channel:

SI ≈ (Pclosed − Popen)/A. (3)

The equilibrium error �Peq can be subject to changes. On the other hand the closedand opened state do not occur at the same time. It is therefore necessary to have an

ABSOLUTE ACCURACY AND REPEATABILITY OF THE RMIB RADIOMETERS 241

estimation of Pclosed during the open state. This is done by averaging the power oftwo closed states occurring before and after the open state.

4. Absolute Accuracy

Equation (4) is modified to take the remaining instrumental parameters into account:

SI = 1

kαabsαth A(Pclosed − Popen + �P)/ cos θ. (4)

These parameters and their estimation are described in the following:– A: the precision aperture area in front of the shutter. The area should be chosen

as large as possible in order to be able to measure it with a high relativeaccuracy. For DIARAD left, the mean measured diameter of the precisionaperture area is 8.00325 mm with a 95% level uncertainty of 0.5µm, and with adeparture from roundness1 of 0.6 µm (Chevalier, Conscience, and Lombaerts,1995). Thus the resulting total absolute uncertainty on the diameter is 1.7 µm.Therefore the resulting relative uncertainty of A is 425 ppm.

– αabs: the absorption factor of the cavity covered with diffusive black paint.From the measured black paint absorptivity, taking into account the knowngeometry of the cavity, we can calculate αabs = 0.999809 with an uncertaintyof 40 ppm. αabs is systematicaly measured for each channel as well as αth thatis measured in air and vacuum.

– αth: the thermal efficiency factor of the cavity. αth is defined as the fractionof the total heat dissipated in the cavity that flows trough the heat flux sensorat the bottom of the cavity related to the incident radiation. The remainingpart escapes trough the side walls of the cavity. This remaining part is propor-tional to the part of the incoming radiation that is reflected on the side walls,and hence with the reflection factor of the black paint. For the DIARADleft cavity, in vacuum, the measured αth = 0.997338 (Chevalier, Conscience,and Lombaerts, 1995; Crommelynck, Fichot, and Bauwens, 1995). For theDIARAD right cavity, in vacuum, the measured αth = 0.995918. Differentvalues are used when operating instruments in air. The uncertainty of αth isdominated by the uncertainty of the black paint absorption factor. The latteris equal to 0.970 with an uncertainty of 0.005, leading to an uncertainty of150 ppm of αth.

– �P: the internal thermal emission of the shutter. When the shutter is closed itirradiates some energy into the cavity. When the shutter is opened this energyis removed. �P is the term which takes this effect into account. The relativemagnitude of �P is around 600 ppm for DIARAD/VIRGO but reduces to 60ppm for DIARAD/SOVIM due to a low thermal emission coating. Moreover,

1The departure from roundness is defined as the difference in radii of two coplanar concentric circles,the annular space between which just contains the profile of the surface measured.

242 S. MEKAOUI ET AL.

the value of �P is measured during deep space calibrations. During thisphase, Equation (5) becomes:

0 = 1

kαabsαth A(Pclosed − Popen + �P)/ cos θ. (5)

We deduce �P from the electrical power determination according toEquation (5).

– k: total correction factor for remaining effects. These effects are: the diffrac-tion and scattering around the two apertures in front of the cavity and the preci-sion of the servo system. The servo system does not reach its equilibrium valueafter 90 s. A systematic correction �Peq is applied with an uncertainty of theorder of 30 ppm. The experimental determination of the diffraction and scatter-ing errors around the apertures is difficult because these effects are relativelysmall (Crommelynck, 1982). For the DIARAD left cavity, k = 0.998502. Forthe DIARAD right cavity, k = 0.998594 (Fichot, 1993). The uncertainty onk is at least 30 ppm without taking into account the diffraction and scatteringeffects.

– θ is the solar pointing angle. When θ = 0, the sunlight enters straight into thecavity. For θ �= 0, the radiation received in the cavity varies as cos θ .

– Electrical power determination: accurate electrical power measurements areobtained by separate measurement of the voltage over and the current throughboth cavity heating resistors. The current I through the heating resistor is de-rived from the voltage measurement UI thanks to an accurate measurementresistor, Rmeasurement placed in series with the heating resistor. As a conse-quence, I = UI /Rmeasurement. The two voltages over the heating resistors UV ,and the two voltages over the measurement resistors UI , are measured simul-taneously with four electrical measurement chains, see Figure 2. Therefore,the electrical power is P = UV UI /Rmeasurement. The heating resistor wirescontribute to some parasitic electrical power dissipation detected by the heatflux detectors which could give rise to some systematic error (Crommelynck,1982). The uncertainty of P is then reduced to an uncertainty of two voltagemeasurements (UV , UI ), one measuring resistor determination (Rmeasurement)and the uncertainty of the resistor wires effect. These values are detailed inthe following.

– Electrical calibration: every three minutes, the electrical measurement chainsare calibrated using a temperature-stabilized, high-accuracy reference voltagesource. The electrical calibration allows the determination of the functionthat relates the counts to the voltages. This function is estimated with three(DIARAD/VIRGO) or six levels (SOVIM) of the reference voltages using aleast squares fit. The residual error between the estimated function and themeasurements is of the order of 60 ppm peak-to-peak for DIARAD/VIRGO.The resulting uncertainty of the electrical power is up to 131 ppm (60 ppm

ABSOLUTE ACCURACY AND REPEATABILITY OF THE RMIB RADIOMETERS 243

for UV an UI , 5 ppm for Rmeasurement and 6 ppm due to the heating wireeffect.)

The ‘solar constant’ or total solar irradiance (TSI) is defined as the solar irradi-ance at the mean Earth–Sun distance, i.e., 1 Astronomical Unit (A.U.). It is givenby

TSI = SI( r

1 A.U.

)2(

1 + 2dr

dt

/c

), (6)

where r is the distance between the satellite and the Sun and c the speed of light.The factor 1

(1− drdt /c)2 ≈ 1 + 2 dr

dt /c corrects for the Doppler-shift effect due to the

moving satellite (Frohlich et al., 1997).The different parameters of Equation (4) are determined during the character-

isation phase at the Royal Meteorological Institute of Belgium with a dominantuncertainty for the determination of the precision aperture. The resulting relativeuncertainty of the TSI measurement is of the order of 776 ppm when adding thedifferent contributions detailed previously and 471 ppm RMS. It corresponds to anabsolute uncertainty of the irradiance of the order of 1.06 and 0.64 Wm−2 RMS fora nominal value of 1368 Wm−2 and without taking into account the diffraction andscattering uncertainties.

5. Repeatability of the Measurements

The repeatability of the measurement is better than the absolute uncertainty. Therepeatability is limited by two main elements : the stability of the reference voltagefor the calibration of the electrical measuring chains and the correct monitoring ofthe in-flight aging effect.

5.1. STABILITY OF THE REFERENCE VOLTAGE

Throughout the mission the ratio between the two references of VIRGO has re-mained stable within the measurement resolution of 24 ppm. For additional veri-fication, 10 references of the same fabrication have been measured on the groundregularly since 1993. The largest measured peak to peak difference is 165 ppm over8 years. The repeatability over that time period of the electrical measurements isthen of the order of 100 ppm. Figure 4 represents the relative error that wouldbe made on the measurement of the solar irradiance in the case that one would as-sume that the gains and offsets of the DIARAD/VIRGO amplifiers (i.e. the functionrelating the counts to the voltages) would remain equal to their initial value andwithout electrical calibration. In fact DIARAD is continuously corrected for thiseffect (160 ppm over 8 years). On the other hand, the separate measurement ofthe current and voltage allows the calculation of the heating resistor. This value

244 S. MEKAOUI ET AL.

Figure 4. Relative error on left channel irradiance without electrical calibrations.

Figure 5. The time variation of the daily mean value of the heating resistor of the DIARAD/VIRGOleft cavity for left-side measurement days: “resistor.left.close”: resistor measured in closed state,corresponding to voltage level of 3.5 V; “resistor.left.open”: resistor measured in open state, corres-ponding to voltage level of 2 V. “resistor.left.model”; resistor modelled as a function of temperature,according to preflight measurements.

compared to a pre-flight model is used as quality control. This feature is repre-sented in Figure 5. Moreover, a continuous measurement of resistors values afterevery SOLCON flight provides confidence in regard to an unlikely drift of resistorsvalues.

ABSOLUTE ACCURACY AND REPEATABILITY OF THE RMIB RADIOMETERS 245

Figure 6. The total solar irradiance measured by the DIARAD right channel minus the one measuredby the left channel. The difference is set to zero at the beginning of the mission. An unexplaineddifference of the order of 4 Wm−2 exists between both channels (Dewitte and Crommelynck, 2004).

5.2. AGING EFFECT

DIARAD routinely measures the solar irradiance with its left channel. Exposureto the Sun may cause an aging of the black paint and affects the thermal efficiencyof the cavity. To verify and correct this trend on the left cavity, measurementswith the right cavity are made from time to time. As the exposure of the rightcavity is lower, its solar induced aging is very small but at long duration a simi-lar correction is applied. Figure 6 compares the right and left channel measure-ments of DIARAD/VIRGO. Without aging monitoring, a trend of 0.5 Wm−2 over 8years would have occurred on the TSI measurements (Dewitte and Crommelynck,2004).

6. Conclusion

In this article we have presented the RMIB radiometer design. After a detailed analy-sis of the different uncertainties and their quantification, it is found that accurate TSIobservations must be accompanied with accurate electrical power measurementsand crosschecking capabilities. For DIARAD/VIRGO, the relative uncertainties ofthe electrical power are of the order of 131 ppm. For DIARAD, the absolute accu-racy of the TSI measurements is of the order of 1.06 and 0.64 Wm−2 RMS without

246 S. MEKAOUI ET AL.

taking into account the diffraction and scattering uncertainties. The repeatabilityof the measurement is of the order of 100 ppm. The stability of the reference volt-ages is the main hypothesis. The aging effect is corrected by comparison betweenthe channels of the radiometers. These values represent our current knowledge ofthe DIARAD type radiometer. Better achievement is foreseen for the upcomingmissions.

Acknowledgements

This work was supported in the beginning by the “Fonds de la Recherche Fonda-mentale d’initiative Ministerielle” followed by the support of the Belgian SciencePolicy office (DWTC-SSTC) through the ESA PRODEX program.

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