total solar irradiance absolute level from diarad/sovim on the international space station

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Advances in Space Research 45 (2010) 1393–1406

Total solar irradiance absolute level from DIARAD/SOVIMon the International Space Station

Sabri Mekaoui a,b,*, Steven Dewitte a, Christian Conscience a, Andre Chevalier a

a Royal Meteorological Institute of Belgium, Ringlaan 3, 1180 Brussel, Belgiumb Vrije Universiteit Brussel, Pleinlaan 2, 1050 Brussel, Belgium

Received 27 February 2009; received in revised form 8 February 2010; accepted 10 February 2010

Abstract

Current measurements from DIARAD/VIRGO, PMO6V/VIRGO and ACRIM3 radiometers are of the same order of magnitude,but differ from TIM/SORCE by about 4.5 W m�2. This difference is higher than the sum of the claimed individual absolute uncertaintiesof the instruments. In this context, the SOLAR payload on the International Space Station embarks the SOVIM package. We give theresults of the differential absolute radiometer DIARAD/SOVIM and discuss its associated uncertainties. Compared to DIARAD/VIRGO, all possible efforts have been made to improve the absolute accuracy. Substantial progress has been made in the aperture areaand electrical power measurements. The measured TSI value from the left channel of DIARAD/SOVIM during three days of June 2008is 1364.50 ± 1.38 W m�2 (Total) or ±0.49 W m�2 (if we combine the individual contributions in quadrature). The right channel gives1364.75 W m�2 with the same uncertainties. These values are about 1.2 W m�2 lower than DIARAD/VIRGO and about 4 W m�2 higherthan TIM/SORCE. The difference between the left and right channels measurements is as low as 0.25 W m�2 which is within theimproved uncertainty limits.� 2010 Published by Elsevier Ltd. on behalf of COSPAR.

Keywords: Total solar irradiance; Absolute level; Instrumentation; TSI accuracy

1. Introduction

The early spaceborne measurements of Total Solar Irra-diance (TSI) were suffering from a high level of noise and,more problematically, from poor absolute accuracy. Withtime, improvements in instrumentation allowed to con-verge towards the 1365 W m�2 value (Crommelyncket al., 1995). The efforts were then concentrated on thelong-term TSI stability (Willson, 1999; Frohlich, 2003;Dewitte et al., 2004) and periodicities (Crommelynck andDewitte, 1997; Willson and Mordvinov, 1999). For thedetermination of the Earth Radiation Budget (ERB),efforts have then been focused on the measurements of

0273-1177/$36.00 � 2010 Published by Elsevier Ltd. on behalf of COSPAR.

doi:10.1016/j.asr.2010.02.014

* Corresponding author. Address: Royal Meteorological Institute ofBelgium, Ringlaan 3, 1180 Brussel, Belgium. Tel.: +32 23730607.

E-mail address: [email protected] (S. Mekaoui).URL: http://remotesensing.oma.be/TSI/ (S. Mekaoui).

the outgoing energy (reflected solar and emitted thermal).Recently, the quantification of the increase of ocean heatstorage indicated a theoretical global imbalance of theERB of 0.85 ± 0.15 W m�2 (Hansen et al., 2005). However,observation of the ERB with the Clouds and Earth Radi-ant Energy System (CERES) (Wielicki et al., 1996) edition2 data by Loeb et al. (2008) indicates an imbalance of6.5 W m�2 which is larger than the 0.85 W m�2 theoreticalvalue. This initiated discussions on whether CERES outgo-ing energies have been underestimated and/or the1365 W m�2 TSI absolute level has been overestimated.The last assumption has been triggered by the recentTIM/SORCE observations (Kopp et al., 2005) which are4.5 W m�2 lower than the commonly measured value. Thisnew TSI value reduces the imbalance by 1.125 W m�2 (tak-ing into account the geometrical factor of four for the sphe-ricity of the Earth). This renews the interest for accurateTSI measurements from space. The SOVIM package

http://dx.doi.org/10.1016/j.asr.2010.02.014

mailto:[email protected]

http://remotesensing.oma.be/TSI/

Fig. 1. DIARAD detectors description and the four main measuringchannels (the multiplexers are not represented). The left and right heatingresistors Rheating

� �are mounted in series with measuring resistors Rmeasð Þ.

Channels 1 and 2 (V/F1 and V/F 2) are dedicated to current measurementswhile channels 3 and 4 are dedicated to voltage measurements. Two otherchannels (channels 5 and 6) acquire the temperature in different part of theinstrument. These channels are not represented.

1394 S. Mekaoui et al. / Advances in Space Research 45 (2010) 1393–1406

onboard the International Space Station (ISS) has beenrecently launched to address this question. Inside SOVIM,a Differential Absolute Radiometer (DIARAD) has beenintegrated. In this paper, we describe the DIARAD/SOVIM TSI results and their associated uncertainties.We describe the instrument in Section 2. The orbit andattitude of the ISS constraints the observation strategy(Section 3). Therefore, a new observation sequence isadopted: the extended open sequence (Section 4). Differentsteps of data processing (Section 5) are used to identify theparameters determining the absolute accuracy. The electri-cal calibrations (Section 6) allow the determination of theelectrical powers in different configurations of the instru-ment (Section 7). These powers are the main componentof the instrument equation. Their uncertainties are dis-cussed and verified by a check of the heating resistor values(Section 8). The final TSI equation (Section 9) combinesthe measured powers with onground measured instrumen-tal parameters. Results are described and comparisons withTIM/SORCE are made in Section 10.

2. Description

The SOVIM package is composed of three PMO6 abso-lute radiometers, two sunphotometers, one pointing sensor(TASS) and one DIARAD radiometer. SOVIM is mountedin the SOLAR payload of the International Space Station(ISS) together with the SOLSPEC (Thuillier et al., 2008)and SOLACE (Brunner et al., 2008) instruments. The DIA-RAD instrument is developed at the Royal MeteorologicalInstitute of Belgium. DIARAD is composed of two cylin-drical cavities coated inside with diffuse black paint andmounted next to each other on the same heat sink (Fig. 1top). The flat bottoms of the cavities are in fact heat fluxtransducers on which heating resistors have been mounted.Every heating resistor has been mounted in series with acurrent measuring resistor (Fig. 1 bottom). The voltageover the four resistors is digitized through four indepen-dent electrical measurement channels. Two other channelsare dedicated to temperature measurements. Each of themeasuring channels is composed of a multiplexer, anamplifier, a voltage to frequency converter (VFC) and acounter. The data from the VFC’s are integrated in framesof 10 s. A packet of data are composed of nine frames.

3. Solar periods

The SOLAR orbital period is around 90 min. Only someorbits are dedicated to Solar observations. They are sched-uled when the Beta angle (the angle between the plane ofthe ISS’s orbit and the line connecting the centers of theEarth and the Sun) is within ±23�. During solar observa-tions the SOLAR payload tracks the Sun during 45 min.Once in Sun acquisition mode, DIARAD/SOVIM usesthe data from a two-axis Sun sensor (TASS) to apply apointing correction. This correction takes into accountthe offpointing of DIARAD with regards to the satellite-

Sun direction. The classical working principle of DIA-RAD/SOVIM allows to have one acquisition every3 min. Therefore, 15 measurements are possible if the Sunis tracked during the 45 min of solar visibility. To increasethe number of acquisitions per orbit a new working princi-ple of DIARAD is used: the extended open mode. This prin-ciple is described in the following section.

4. Measurement sequence

4.1. Classical sequence

In its classical working principle, DIARAD is operatedusing successive open and closed states (Crommelynck,1982; Mekaoui et al., 2004). Fig. 2 introduces the principleusing the left channel of DIARAD/VIRGO on SOHO.During the first closed state both shutters are closed. Theservo system dissipates a power P left;closed in the left cavityequal to the power dissipated in the right cavity by a refer-ence voltage. Ninety seconds are necessary to have thermalequilibrium between the two cavities. Only the last acquisi-tion made at second 90 is used. During the next state onlythe left shutter opens. A part proportional to the Solarradiation (SI) is absorbed by the left cavity. The servoreduces the dissipated power in the left cavity P left;open

� �to maintain equilibrium between the cavities. Only the lastacquisition at second 90 is used. The comparison between

Fig. 2. Three consecutive states of DIARAD/VIRGO during a left side measurement cycle. Every state lasts 90 s during which the servo system regulatesthe left power until it reaches the level of the right power. Top left, the left shutter is closed from time t � 90 s to t. The servo system dissipates a powerP left;closed until it reaches the level of P right;ref . Equilibrium is reached at second 90. Top middle, the left shutter closes from t to t + 90 s. The servo lowers thedissipated power P left;open since the radiative power from the Sun is added to equal P right;ref . Top right: a closed state is repeated. Bottom: time evolution ofthe different powers. Data are integrated every 10 s. For each cycle of 90 s, acquisition is made at seconds: 20, 50, 60, 80 and 90. For a better visualization,the acquired data are linearly interpolated and an arbitrary offset is applied to the powers of the second closed state.

S. Mekaoui et al. / Advances in Space Research 45 (2010) 1393–1406 1395

the regulated powers of both states gives a rough approxi-mation of the Solar Irradiance (SI) each 3 min (90 s for theopen states and 90 s for the closed state) according to:

A � SIleftðtÞ � P left;closedðtÞ � P left;openðtÞ ð1Þwhere A is the area of the precision aperture of the activechannel. The detailed equation is discussed in Section 9.Since both the open and closed states do not occur simul-taneously, P left;closedðtÞ in Eq. (1) is replaced by the averagepowers P left;closedðtÞ

� �of the two closed states surrounding

the open state (see Fig. 2 bottom). During each of theclosed and open states, nine acquisitions are made. Onlyfive of them are dedicated to powers’ acquisitions. Theseacquisitions are made at seconds 20, 50, 60, 80 and 90.The four other acquisitions are associated to reference volt-ages and temperature measurements. The evolution of thefive acquired powers during a nominal sequence of mea-surements is represented in Fig. 2 (bottom).

4.2. Extended open measurement sequence

The extended open sequence is used to increase the num-ber of acquisition points. In this sequence, the active chan-nel has its shutter closed for 90 s. It is maintainedafterwards opened during 270 (3 � 90) s instead of 90 s.This corresponds to a succession of one closed state andthree open states. This sequence is illustrated in Fig. 3.During the first open state following a closed state, theservo system reduces the regulated power to reach the equi-librium as during the classical operating mode. During thefollowing two open states, the servo system starts from anequilibrium state. As a consequence all the power acquisi-tions made at seconds 20, 50, 60, 80 and 90 of the secondand third open states can be exploited as equilibrium mea-surement points. In total the succession of extendedsequences during Solar measurements gives 11 acquisitionsof the TSI every 6 min (the last acquisition of the first open

Fig. 3. Top: the extended open sequence is composed of one closed state and three open states. The localizations of the acquired temperatures are alsodisplayed. Bottom: the ‘�’ are the acquired dissipated power in the regulated cavity (left) during the different states. The data are linearly interpolated for abetter visualization. The ‘+’ are the weighted average of the regulated power of the two closed states surrounding the three open states.


state and each of the five acquisitions of the following twoopen states). Compared to the classical operating mode,this multiplies by a factor of 5.5 the number of acquisitionsduring an orbit. In the next Section, we describe the applieddata processing to obtain the TSI and we discuss the asso-ciated uncertainties.

5. Data processing

The general processing is represented in Fig. 4. In thedemultiplexing step, the measured counts from each chan-nel are attributed to a measured parameter. These countsare then transformed in physical units during the calibra-tion process. The power and their associated uncertaintiesare calculated in the next step. The TSI calculation is finallyapplied using the instrument parameters. The power andTSI calculations as well as their associated uncertaintiesare detailed in what follows.

Fig. 4. The main steps in the TSI data processing.

6. Electrical calibrations

The calibration process aims at determining the count tovoltage relation for each channel. Two sets of referencevoltages are used. The current channels (channels 1 and2) are calibrated using six level of a highly accurate temper-


ature-stabilized reference voltage. Six other levels are usedfor the calibration of the voltage channels (channels 3 and4). These reference voltages have been measured on groundin air and in vacuum. They showed no significant depen-dence to temperature variations (Conscience, 2005). Thecalibration process is made every 90 s. A second-order leastsquare fit is then calculated using the six measurements ofcounts and their corresponding reference voltages.

6.1. Voltage measurements accuracy

The fitted calibration functions of the voltages channelsduring a day of measurements are represented in Fig. 5(top). Depending on the measured voltage, the residualerror is at maximum 15 ppm if the shutter is open and7 ppm if closed (Fig. 5 bottom). The error on the voltagemeasurements is obtained by summing the fitting errorsand the accuracy of the voltmeters used to obtain the refer-ence voltages. The reference voltages are measured with15 ppm uncertainty. As a consequence, the voltages corre-sponding to open states are measured with 30 ppm uncer-tainty and the voltages corresponding to closed states aremeasured with 22 ppm uncertainty.

6.2. Current measurements accuracy

To find the currents, the voltage measurements of chan-nels 1 and 2 are divided by the value of the measuring resis-

1e+06 1.5e+063

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eas

- V

ref

) /

V r

ef

Fig. 5. Top: black “+”: daily measured counts corresponding to the referencechannels. Curves: estimated second-order calibration functions for the voltages(red and green) indicate the operational working voltages for DIARAD/SOVIMto cavity to maintain the equilibrium (see Section 3). The corresponding voltavoltage level for a cavity with a closed shutter. Bottom: black “+”: relative errothe reference voltages for the right channel. The relative error due to the use ofand the neighborhood residual errors on the reference voltages. This error is o7 ppm for a cavity with a closed shutter (red band). (For interpretation of theversion of this paper.)

tor Rmeasurement (Fig. 1). We have Rmeasurement left ¼Rmeasurement right ¼ 100:001 X. These resistors are measuredwith 70 ppm uncertainty (Conscience, 2002). The calibra-tion error is at maximum 40 ppm for currents in openradiometric states and 5 ppm for currents in closed radio-metric states (Fig. 6). The uncertainty of the current mea-surements is obtained by summing the calibration error,the uncertainty of the reference voltages measurements(15 ppm) and the uncertainty of the measurement of themeasuring resistor. This gives 125 ppm for currents in openradiometric states and 90 ppm for currents in closed radio-metric states.

6.3. Temperature measurements

Eight temperatures are acquired: five in the radiometer(T1–T5) and three in the electronics (T6–T8). T1 and T5are located under the left and right shutters, T2 and T4measure the temperature of the precision apertures whileT3 acquire the temperature of the heat sink (see Fig. 3).The temperature T6 is acquired on the amplifier of channel4, T7 on the multiplexer of channel 1 and T8 on the VFC ofchannel 6. The location of T6, T7 and T8 is intended togive a good spatial coverage of the temperature in the elec-tronic. Fig. 7 displays the temperature evolution of DIA-RAD/SOVIM during six orbits. During the first threeorbits DIARAD/SOVIM is in standby mode. In this mode,the instrument keep its shutters closed while the regulated

2e+06 2.5e+06Counts

Left voltageRight voltage

6 6.5 7 7.5 8 8.5 9Volts

voltages (V1–V6) from the left channel. Red “�”: counts from the rightchannels (red: right, black: left) during a day of measurements. Two bands: when one of the cavities has an open shutter, less power has to be appliedge is indicated by the horizontal green band. The red band indicates ther on the reference voltages for the left channel. Red “�”: relative error onthe calibration functions can be deduced by comparing the vertical bandsf the order of 15 ppm for a cavity with an open shutter (green band) andreferences to color in this figure legend, the reader is referred to the web

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-2e-05

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4e-05

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eas

- V

ref

) /

V r

ef

Fig. 6. Calibration functions (top) and residual errors (bottom) for the current channels (see also legend of Fig. 5).


and reference powers are inverted every 180 s. Duringthe last three orbits, the Sun is acquired by the leftchannel.

7. Power calculation

The instrument’s working principle is based on the com-parison of heat fluxes. For each of the cavities, the powersare calculated using the equation (in the case of the rightpower):

P right ¼ V right � I right � 1þ RcþRd

Rheating right

� �, where RcþRd

Rheating rightis the

parasitic effect due to the heating resistor wires (Con-science, 2002).1 The error due to calibration can be esti-mated by summing the calibration errors on the currentmeasurements, voltage measurements (see Sections 6.1

and 6.2) and the 15 ppm of the term 1þ RcþRd

Rheating right

� �induced

by the parasitic resistor determination. In addition to thecalibration errors, 50 ppm is added due to the noise levelof the servo system in the case of the regulated powers.In total, the regulated open powers are measured with220 ppm uncertainty. The regulated closed powers are mea-sured with 177 ppm uncertainty and the reference powersare measured with 127 ppm uncertainty (Table 1). Theseuncertainties reduce to 139 ppm, 106 ppm and 94 ppm ifwe compute the root of the sum of squares.2

The different powers as well as their dynamic range andperiodicities are shown from Fig. 8 to Fig. 12. Fig. 8 dis-

1 The power is determined by simultaneous measurements of the heatercurrent and voltage. Nevertheless, the connecting wires of the heatingresistor contributes to some parasitic effect due to their small resistancevalues Rc and Rd.

2 We further use the acronym (RSS) to designate the root of the sum ofsquares.

plays the right and left powers during six orbits. Duringthe last three orbits, DIARAD is measuring with its leftcavity. The right power is the reference power and the leftpower is the regulated one.

7.1. Reference power

A constant reference power is dissipated in the rightcavity through its heating resistor according toP ref ¼ V 2=Rheating. The heating resistor value Rheating is line-arly dependent of the heat sink temperature. As a conse-quence the evolution of the reference power is in phaseopposition with the heating resistor temperature variations.The reference power during three orbits is displayed inFig. 9. The reference power varies in opposition with thetemperature of the heat sink (T3).

7.2. Regulated power

The left power (Fig. 8) depends on the status of theshutter (open or closed). When there is no solar pointing(Fig. 10), the difference between the powers in closed andopen states is due to the internal thermal emission of theshutter. When the instrument points to the Sun, less elec-trical power is dissipated in the left cavity if its shutter isopen. Fig. 11 shows three sequences of the regulatedopen power for each of the three orbits with solar acqui-sitions. They all display an upward trend due to theincrease of the instrument’s temperature during the daypart of the orbit. A magnification of the regulated openpower during the triple open sequence is shown inFig. 12. All acquisition points follow the upward trendexcept the acquisition made at time t = 10 s where equi-librium has not been reached yet.

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65

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Time (days of 2008)

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T1T2T3T4T5

Fig. 7. Temperature evolutions during six orbits. The vertical lines separate the orbits. The instrument is in standby mode during the first three orbits andin Solar acquisition for the last three. The red hatch-marked zone on the top indicates the periods of Solar pointing. The front face temperatures T1 and T5display the highest variation resulting from the day/night cycle. The difference between T1 and T5 is due to the lack of absolute calibration of thetemperature sensors. The unusual shape of their curve is due to the switch on and off of the thermal regulation of SOVIM’s heat shield. During the firstthree orbits, the temperatures T2 and T4 of the precision apertures have the same variations. During the last three orbits, the left aperture temperature (T2)displays some oscillation during the solar periods. These oscillations are due to the heating by the Sun when the shutter is open and due to cooling whenthe shutter is closed. These oscillations are also observed with a lower amplitude in the right aperture temperature T4. The heat sink temperature (T3) iscorrelated with the day/night cycle. The amplifier, multiplexer and voltage to frequency converter temperatures (T6, T7 and T8): T8 is used as referencetemperature point for the reference voltages. T6 and T7 are correlated with the day/night cycle. During Solar acquisition in orbits 4, 5 and 6, thetemperature (T7) of the multiplexer acquiring the left current shows some anomalies. These anomalies are due to grounding issues. (For interpretation ofthe references to color in this figure legend, the reader is referred to the web version of this paper.)

Table 1Electrical power measurement uncertainties. The uncertainties areobtained by adding the individual contributions (Total), or by performingthe root of the sum of their squares (RSS).

Regulated openstate (ppm)

Regulated closedstate (ppm)

Referencepower

Error on current 125 90 90Error on

voltage30 22 22

Error onparasiticeffect

15 15 15

Servo noise 50 50 0

Total (ppm) 220 177 127RSS (ppm) 139 106 94


8. Heating resistor check

The four main measuring channels (Fig. 1) allow to haveindependent measurements of the current and voltage foreach cavity. It is therefore possible to calculate the valueof the heating resistor in space according to (for the rightheating resistor):

Rheating right ¼ V right=I right ð2Þ

These values are compared to a model determined onground (Conscience, 1999). The model describes the evolu-tion of the resistor value as a function of the temperature ofthe heat sink (T3). The comparison of the modeled and cal-

culated values is indicative of the absolute accuracy of thepower measurements. Figs. 13 and 14 display the calcu-lated and modeled value for each of the left and right resis-tors. The model is corrected for an offset of 170 ppm. Thissystematic uncertainty is within the limit of the accuracy ofthe ground measurements of the resistor. Differences areobserved between the modeled and measured values whenthe shutter is open compared to the period when the shutteris closed. When the shutter is opened less power is dissi-pated in the cavity compared to when the shutter is closed.Eq. (2) is then used for two value levels of I right. From Figs.5 and 6, we see that the calibration errors are larger for thevoltage and current values in open states compared to thecalibration errors in closed states. The heating resistor va-lue is therefore affected by the systematic calibration errors.The variations on the heating resistors are of the order of20 ppm; which is within the limit of the noise and fitting er-rors (Sections 6.1 and 6.2).

9. TSI calculation

The TSI is calculated using two closed states occurringat time t = 0 s and t = 360 s (state 1 and state 2) surround-ing three open states (Section 4.2). For each of the openstates starting at time t = 90 s, t = 180 s and t = 270 s,the difference between the reference (right) and regulated(left) powers is computed according to:

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Fig. 8. Top: left power (black curve) and right power (red curve) during six orbits. The data are linearly interpolated. During the first three orbits, theinstrument is in standby mode. During this sequence both shutters are closed. The reference power is dissipated in the right cavity while the servo regulatesthe left cavity for 180 s. The process is then inverted for an other 180 s. During the last three orbits the instrument acquires the Sun with its left cavity. Theleft power is regulated and the right power is the reference power. The vertical lines indicate the duration of an orbit. The reference power is magnified inFig. 9. The higher dashed square highlights the regulated power levels when the shutter is closed. These powers are magnified for the last three orbits inFig. 10. The lower dashed square highlights the level of the powers when the shutter is open during Solar acquisition. Theses powers are magnified in Figs.11 and 12. Bottom: temperature evolution during the six orbits. (For interpretation of the references to color in this figure legend, the reader is referred tothe web version of this paper.)

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Fig. 9. Top: reference power in the right cavity during the last three orbits with solar acquisition. The red hatched zone indicates the periods of solarpointing. Bottom: the temperatures are represented to show the correlation with the reference power. The reference power varies in opposition with theevolution of the temperature of the base. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of thispaper.)


DP openðtÞ ¼ P rightðtÞ � P left openðtÞ ð3ÞDP open is measured with ±25 lW uncertainty (Total3) and±19 lW (RSS4).

3 We add the individual absolute uncertainties.4 We compute the root sum of squares of the individual uncertainties.

The difference DP open is compared to the linear interpo-lation DP closedðtÞ of DP closed 1ðtÞ and DP closed 2ðtÞ where:

DP closed 1ðtÞ ¼ P right 1ðtÞ � P left closed 1ðtÞ ð4ÞDP closed 2ðtÞ ¼ P right 2ðtÞ � P left closed 2ðtÞ ð5Þ

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Closed power

without Sun

with Sun

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Open powerwithout Sun

Fig. 10. Top: the regulated power in the left cavity when the shutter is open and closed, in the case of Solar pointing (red hatched zone) and without Solarpointing (green hatched zone). The difference of power levels between the open and closed states in the absence of solar pointing is due to the shutterinternal thermal emission. During Solar pointing, the regulated power in open states of the instrument is much lower than for the closed states. This poweris out of the range of the figure. It is represented in Fig. 11. Bottom: temperature evolution during the three orbits. The regulated power is correlated withthe evolution of T3 (blue curve). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this paper.)

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Fig. 11. Regulated open power during the solar pointing for the three orbits of solar acquisition. The upward trend in each of the orbits is due to averageincrease of the instrument’s temperature. The dashed square shows the powers for the three successive open states. These powers are magnified in Fig. 12.

5 National Institute of Standards and Technology.6 National Physical Laboratory.


where P right 1ðtÞ and P right 2ðtÞ are the reference powers dur-ing the two closed states. P rightðtÞ is the reference powerduring the open states.

DP closed is measured with an uncertainty of ±35 lW(Total) and ±24 lW (RSS).

The Solar Irradiance (SI) is computed according to:

SI ¼DP openðtÞ�DP closedðtÞ

aabs�ath�servocstð Þ

� �ðA � 1:0þ Rþ R0 þ dð Þ � cos hÞ þ Dshutter ð6Þ

The different parameters of Eq. (6) are described in whatfollows. Their uncertainties are summarized in Table 2. De-tails can be found in Crommelynck (1982). The SI is finallynormalized to 1 AU and corrected for velocity effectsaccording to:

TSI ¼ SIr

1 AU

� �2

1þ 2drdt

�c

� �: ð7Þ

9.1. Geometrical corrections

� Precision aperture (A) at temperature T = 20 �C: Theprecision apertures have been measured at NIST5 andNPL6; we use the average of the NIST and NPL mea-surements. We have Aleft ¼ 0:0000794094 m2 andAright ¼ 0:0000794533 m2 with 150 ppm uncertainty.

Fig. 12. Regulated open power for the three successive open states. An acquisition point at time t = 10 s is made when the servo did not reach itsequilibrium. All the following points have a slight increasing trend corresponding to the overall increase of the temperatures during the solar pointing.

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Ohm

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T5T2T3T4

1 2 3 4 5 6

Fig. 13. Top: calculated left resistor value when the left shutter is closed (red dots) and open (green dots) for the six orbits. A difference is observed for thelast three orbits during the solar pointing periods. These differences are due to the systematic errors of the electrical calibration. The curve in blackrepresents the modeled resistor value. Bottom: temperature evolution during the six orbits. (For interpretation of the references to color in this figurelegend, the reader is referred to the web version of this paper.)


The precision apertures are made of Invar. This materialhas a very low coefficient of thermal expansion (CTE ofthe order of 1:5� 10�6 K�1). Therefore, the thermaldilatation of the precision aperture due to the openingand closing of the shutter is considered to be negligible.� Distance, velocity and pointing corrections: The dis-

tance r between the radiometer and the center of theSun, the radial velocity dr

dt of the satellite relatively tothe Sun and the angle between the direction of the Sunand the radiometer (h) are used to finally compute theTSI according to Eq. (7).

9.2. Optical corrections

� The absorption coefficient of the cavity aabs: This coeffi-cient corresponds to the amount of light trapped by theradiometric cavity. For DIARAD/SOVIM we have

aabs ¼ 0:999748 for both the left and right cavity witha 45 ppm uncertainty. This coefficient is calculated onthe basis of the geometric dimension of the cavity andthe measured hemispheric absorptivity of the blackpaint. This paint absorptivity is measured on the groundusing a synchronous detection setup. It is of the order of0.972 ± 0.003 (Mekaoui, 2008). This value is measuredat only one wavelength (512 nm).� The effect of backscattered radiation within the view

limiting volume (R): The openings below the shutters(the front apertures) are actually larger than the surfaceof the precision apertures. Part of the radiation enteringfrom the front aperture (when the shutter is open) istherefore reflected by the precision aperture (seeFig. 1). This reflected radiation is partly reflected backby the limiting volume between the shutter and the pre-cision aperture. R is the ratio between this backscatteredradiation falling in the active cavity after multiple reflec-

96.438 96.5 96.562 96.625 96.688 96.75349.049349.05

349.051349.052349.053349.054349.055349.056349.057349.058

Ohm

96.438 96.5 96.562 96.625 96.688 96.75Days of 2008

14

14.5

15

15.5

16

16.5

17C

elci

us T1T5T2T3T4

1 2 3 4 5 6

Fig. 14. Top: calculated right resistor value when the left shutter is closed (red dots) and open (green dots) for the six orbits. No significative difference isobserved due to systematic electrical calibration since the right shutter remains closed. The curve in black represents the modeled resistor value. Bottom:temperature evolution during the six orbits. (For interpretation of the references to color in this figure legend, the reader is referred to the web version ofthis paper.)

Table 2Instrument parameters measurement accuracies. The uncertainty on the pointing correction (cosh) is negligible. The values, the absolute uncertainties aswell as the relative uncertainties (when needed) are provided both by adding the individual contributions in quadrature (RSS) and by computing the sum.The uncertainty on the multiplicative terms of Eq. (6) are also provided.

Instrument parameters Value Relative uncertainty Absolute uncertainty

aabs left, aabs right 0.999748, 0.999748 ±45 ppmath left, ath right 0.998490, 0.998930 ±120 ppmR 0.75e�5 ±0.013 ±0.01e�5R0 4.5e�5 ±0.012 ±0.1e�5d 0.0005 ±0.2 ±0.0001Aright 0.0000794533 m2 ±150 ppmAleft 0.0000794094 m2 ±150 ppmservocst 1.000000 ±15 ppm

Uncertainty on the terms of Eq. (6)

1þ Rþ R0 þ d 1.000552 ±100 ppm (RSS) ±0.0001 (RSS)±100 ppm (Total) ±0.0001 (Total)

DP open � DP closed 0.108000 W ±289 ppm (RSS) ±0.000031 W (RSS)±562 ppm (Total) ±0.000060 W (Total)

Dshutter 1.24 W m�2 ±0.024 ±0.030 W m�2

DP open�DP closed

aabs �ath �servocst �A�cos h� 1:0þRþR0þdð Þ 1361.68 W m�2 ±364 ppm (RSS) ±0.495 W m�2 (RSS)±992 ppm (Total) ±1.35 W m�2 (Total)

Uncertainty on SI

RSS ±0.496 W m�2 (RSS)Total ±1.38 W m�2(Total)

7 The system is composed of a heat flux transducer, a heating resistorand a cylindrical cavity.


tions and the radiative power directly going into the cav-ity (SI � A). We have R ¼ 0:75� 10�5. This value is esti-mated from DIARAD/VIRGO characterization.� The scattering of radiation by the front aperture (R0): R0

is the ratio between the scattered radiation by the frontaperture which enters the active cavity and SI � A. R0 isalso estimated from DIARAD/VIRGO characteriza-tion. We have R0 ¼ 4:5� 10�5.� The diffraction of radiation (d = 0.0005): d is the ratio

between the diffracted radiation by the front apertureof the active channel which falls into the active cavityand SI � A. d is of the order of 0.0005 (NIST estimatedvalue).

9.3. Thermal corrections

� The thermal efficiency or effective absorptivity ofthe cavity athð Þ: From the part of the absorbed radia-tion in the cavity only a proportion is effectivelydetected by the heat flux sensor. The other part isdissipated by the external wall of the cavity. Theefficiency of the cavity sensor system7 is determined inair and vacuum. We have for DIARAD/SOVIM:

1330

1340

1350

1360

1370

Sola

r Irr

adia

nce

(W/m

²)


ath left ¼ 0:998490 and ath right ¼ 0:998930 in vacuumwith 120 ppm uncertainty. In air, ath left ¼ 0:995863and ath right ¼ 0:995842.� The shutter correction Dshutterð Þ: This correction takes

into account the contribution of the internal thermalemission of the active shutter. This contribution isremoved when the shutter is open. For DIARAD/SOVIM the shutter correction is determined during deepspace pointing just after the solar period. During thisphase, the temperature of the shutter does not changesignificantly. Eq. (6) becomes:

100 150 200 250Days of 2008

Fig. 15. SI measurements (Eq. (7)) during the 6 months of mission forDIARAD/SOVIM left channel. The SI decreases and then increases as theEarth moves around the Sun. The effect of the distance is corrected inFig. 16. The outliers are caused by some reflections on the ISS.

0 ¼DP openðtÞ�DP closedðtÞ

aabs�ath�servocstð Þ

� �ðA � 1:0þ Rþ R0 þ dð Þ � cos hÞ þ Dshutter ð8Þ

It is therefore possible to derive Dshutter. Fig. 10 illustratesthe contribution of the internal thermal emission of the leftshutter during the deep space pointing. The contribution isof the order of 1.24 ± 0.05 W m�2.

9.4. Electrical corrections

� The parasitic wire heating: This effect has been discussedin Section 7.� The value of the resistor used to measure the heating

currents: This effect is described in Section 6.2.� The correction for the time constant of the system (ser-

vocst): During the first open sequence following a closedsequence, the open powers acquired at seconds: 20, 50,60 and 80 do not correspond to an equilibrium state. Itis possible to introduce a factor (servocst) to estimate theasymptotic value of each acquisition. For DIARAD/SOVIM the triple open sequence guarantee that equilib-rium is reached during the third open state. This asymp-totic value is used to compute the correction factor foreach of the previous state. We have chosen to apply a fac-tor equal to 1 after 90 s and not to use the measurementsup to 90 s.

8 We use the absolute uncertainties as estimations of the standarddeviations.

9 The uncertainty on h being very small, we neglect the uncertainty onthe pointing correction.

10. Uncertainty and TSI results

10.1. Uncertainty

The accuracy of each channel is determined by the TSIequation (Eqs. (6) and (7)). These equations are based onpower and instruments parameters determination. Thepower relative uncertainty is of the order of 139 ppm inopen states (see Table 1). Instruments parameters are deter-mined on ground (in air and vacuum) during the character-ization phase. Two approaches can be used to compute theuncertainty of Solar Irradiance measurements, either byadding the individual relative uncertainties or by comput-ing the Root of the Sum of Squares (RSS). The uncertaintyis of the order of 1.38 W m�2 (Total) and 0.496 W m�2

(RSS) (see Table 2).

We present the two approaches with their associated cal-culations in Table 2.

We write Eq. (6) as:

SI ¼ a� bc � d þ e ð9Þ

with a ¼ DP openðtÞ; b ¼ DP closedðtÞ; c ¼ 1:0þ Rþ R0 þ dð Þ;d ¼ aabs � ath � servocst � A � cos h and e ¼ Dshutter.

� Dða� bÞ ¼ Daþ Db ¼ 60 lW. Therefore, Dða�bÞa�b ¼ 562

ppm.Alternatively, we can consider (a � b) as the differ-ence of two independent Gaussian distributions withestimated standard deviations sa and sb.8 Therefore,sða�bÞ ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffis2

a þ s2b

pwhich gives an uncertainty of 31 lW.

As a consequence,sða�bÞa�b ¼ 289 ppm.

� Similarly, Dc ¼ 0:0001 and Dcc ¼ 100 ppm (Total) and

also 100 ppm (RSS).

Since the terms of Eq. (9) are independent,9 we have:

sa�bc�d

a�bc�d¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffis2

a�b

ða� bÞ2þ s2

c

c2þ

s2aabs

a2abs

þs2ath

a2th

þs2

servocst

servo2cst

þ s2A

A2

s

¼ 364 ppm ð10Þ

Alternatively, we can add the individual relativeuncertainties:

D a�bc�d� �a�bc�d

¼ Dða� bÞa� b

þ Dccþ Dd

d¼ 992 ppm ð11Þ

Finally, the uncertainty on the SI given by: sSI ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffis2

a�bc�dþ s2

e

q, is equal to 0.496 W m�2.

2454600 2454650 2454700Julian day

1364.7

1364.8

1364.9

1365

1365.1

1365.2

1365.3

TSI

(W/m

²)

DIARAD/VIRGO left no ageingDIARAD/SOVIM orbit means of left channelDIARAD/SOVIM orbit means of right channel

Fig. 16. TSI orbital means from DIARAD/SOVIM left (red dots) andright (blues crosses) channels. The dispersion of measurements is of theorder of 0.13 W m�2. The measurements during each orbit are presentedfor three days of observations in Fig. 17. For comparison, DIARAD/VIRGO 3-min left channel measurements are also displayed. These dataare not corrected for the ageing effects which are of the order of 1.2 W m�2

over 13 years. (For interpretation of the references to color in this figurelegend, the reader is referred to the web version of this paper.)

Fig. 17. TSI measurements from DIARAD/SOVIM left (black) and right(red) channels during each orbit for three days (13, 14 and 15) of June2008. (For interpretation of the references to color in this figure legend, thereader is referred to the web version of this paper.)


When adding the absolute uncertainties DSI ¼ D a�bc�d þ

�DeÞ the value becomes 1.38 W m�2. Fig. 15 shows the SImeasurements during the entire mission. These measure-ments are then corrected for the distance, velocity and point-ing effects in Fig. 16.

10.2. TSI results

Both the left and right channels measurements are pre-sented. DIARAD/SOVIM is nominally operating with itsleft cavity. The right cavity is used for ageing monitoring.The dispersion of DIARAD/SOVIM is of the order of0.13 W m�2. The difference between the channels is of theorder of 0.25 W m�2. This difference is within the individualchannel absolute uncertainties. For comparison DIARAD/VIRGO measurements on SOHO are displayed in Fig. 16.These data do not take into account the 1.2 W m�2 offsetdue to the long-term ageing corrections. Some disagree-ment between DIARAD/SOVIM and DIARAD/VIRGOappears after Julian date 2454700. After that date, DIA-RAD/VIRGO increases faster due to a transient effectfollowing a swith off. This effect is currently underinvestigation.

Fig. 17 shows the left and right channels measure-ments for three days of the mission (13, 14 and 15 ofJune 2008). All the measurements of an orbit are repre-sented. For this period, the TSI level from DIARAD/SOVIM was 1364.50 ± 1.38 W m�2 (Total) for the leftchannel and 1364.75 ± 1.38 W m�2 (Total) for the rightchannel. On the other hand, DIARAD/VIRGO has anabsolute uncertainty of the order of 1.06 W m�2

(Mekaoui et al., 2004). Therefore, the 1.2 W m�2 differ-ence between DIARAD/VIRGO and DIARAD/SOVIMis within the instruments absolute uncertainties.Compared to TIM/SORCE measurements, DIARAD/

SOVIM is 4 W m�2 higher (see Fig. 18). It is worthnoticing that the integration of DIARAD/SOVIM hasbeen undertaken in 2005. Therefore, it was notpossible to follow the community recommendationsissued during the TSI accuracy workshop held at NIST(Butler et al., 2008). In particular, it was not possibleto validate DIARAD with end-to-end optical power orirradiance tests having SI traceability to national stan-dards laboratories.

11. Conclusion

This paper gives a rigorous description of the DIA-RAD/SOVIM TSI data processing and the related uncer-tainty analysis. A new extended open sequence has beenintroduced to increase the TSI sampling rate. Comparedto previous versions of the DIARAD instruments effortshave been done to improve the absolute uncertainty ofthe electrical power measurements and the precision aper-ture determination. The uncertainty of the electrical powermeasurements is 220 ppm.

Concerning the acquired data, the TSI value fromDIARAD/SOVIM for three days of measurements (13,14 and 15 of June 2008) was 1364.50 ± 1.38 W m�2 forthe left channel and 1364.75 ± 1.38 W m�2 for the rightchannel. The uncertainty of ±1.38 W m�2 is obtainedwhen the individual contributions of the instrument equa-tion are added. If they are combined in quadrature, theuncertainty is around ±0.497 W m�2. The differencebetween the independent left and right channel measure-ments is as low as 0.25 W m�2, which is within the abso-lute uncertainty limit of ±1.38 W m�2 (Total) and±0.497 W m�2 (RSS). Although DIARAD/SOVIM TSImeasurements are 1.2 W m�2 lower than DIARAD/VIRGO TSI value, it is still 4 W m�2 higher than TIM/SORCE TSI measurements.

1978 1980 1982 1984 1986 1988 1990 1992 1994 1996 1998 2000 2002 2004 2006 2008 2010Years

1357

1358

1359

1360

1361

1362

1363

1364

1365

1366

1367

1368

1369

1370

1371

1372

1373

1374

1375

TS

I (

W/m

²)

ACRIM 1, 2 and 3

SOVA 1ERBSOVA 2DIARAD /VIRGOTIMDIARAD /SOVIMERBSPMO6 V /VIRGONOAA 9

NOAA 10SOLCON

TSI measurements from individual instruments

Fig. 18. TSI measurements on their native scale, DIARAD/SOVIM measurements (dark blue +) differ from TIM/SORCE by +4 W m�2. (Forinterpretation of the references to color in this figure legend, the reader is referred to the web version of this paper.)


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