Available online at www.sciencedirect.com Advances in Space Research 45 (2010) 1393–1406 www.elsevier.com/locate/asr Total solar irradiance absolute level from DIARAD/SOVIM on the International Space Station Sabri Mekaoui a,b,*, Steven Dewitte a, Christian Conscience a, André Chevalier a a Royal Meteorological Institute of Belgium, Ringlaan 3, 1180 Brussel, Belgium b 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 m2. This difference is higher than the sum of the claimed individual absolute uncertainties of the instruments. In this context, the SOLAR payload on the International Space Station embarks the SOVIM package. We give the results 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 area and electrical power measurements. The measured TSI value from the left channel of DIARAD/SOVIM during three days of June 2008 is 1364.50 ± 1.38 W m2 (Total) or ±0.49 W m2 (if we combine the individual contributions in quadrature). The right channel gives 1364.75 W m2 with the same uncertainties. These values are about 1.2 W m2 lower than DIARAD/VIRGO and about 4 W m2 higher than TIM/SORCE. The difference between the left and right channels measurements is as low as 0.25 W m2 which is within the improved uncertainty limits. Ó 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 Irradiance (TSI) were suffering from a high level of noise and, more problematically, from poor absolute accuracy. With time, improvements in instrumentation allowed to converge towards the 1365 W m2 value (Crommelynck et al., 1995). The efforts were then concentrated on the long-term TSI stability (Willson, 1999; Fröhlich, 2003; Dewitte et al., 2004) and periodicities (Crommelynck and Dewitte, 1997; Willson and Mordvinov, 1999). For the determination of the Earth Radiation Budget (ERB), efforts have then been focused on the measurements of * Corresponding author. Address: Royal Meteorological Institute of Belgium, Ringlaan 3, 1180 Brussel, Belgium. Tel.: +32 23730607. E-mail address: sabri.mekaoui@oma.be (S. Mekaoui). URL: http://remotesensing.oma.be/TSI/ (S. Mekaoui). 0273-1177/$36.00 Ó 2010 Published by Elsevier Ltd. on behalf of COSPAR. doi:10.1016/j.asr.2010.02.014 the outgoing energy (reflected solar and emitted thermal). Recently, the quantification of the increase of ocean heat storage indicated a theoretical global imbalance of the ERB of 0.85 ± 0.15 W m2 (Hansen et al., 2005). However, observation of the ERB with the Clouds and Earth Radiant Energy System (CERES) (Wielicki et al., 1996) edition 2 data by Loeb et al. (2008) indicates an imbalance of 6.5 W m2 which is larger than the 0.85 W m2 theoretical value. This initiated discussions on whether CERES outgoing energies have been underestimated and/or the 1365 W m2 TSI absolute level has been overestimated. The last assumption has been triggered by the recent TIM/SORCE observations (Kopp et al., 2005) which are 4.5 W m2 lower than the commonly measured value. This new TSI value reduces the imbalance by 1.125 W m2 (taking into account the geometrical factor of four for the sphericity of the Earth). This renews the interest for accurate TSI measurements from space. The SOVIM package 1394 S. Mekaoui et al. / Advances in Space Research 45 (2010) 1393–1406 onboard the International Space Station (ISS) has been recently launched to address this question. Inside SOVIM, a Differential Absolute Radiometer (DIARAD) has been integrated. In this paper, we describe the DIARAD/ SOVIM TSI results and their associated uncertainties. We describe the instrument in Section 2. The orbit and attitude of the ISS constraints the observation strategy (Section 3). Therefore, a new observation sequence is adopted: the extended open sequence (Section 4). Different steps of data processing (Section 5) are used to identify the parameters determining the absolute accuracy. The electrical calibrations (Section 6) allow the determination of the electrical powers in different configurations of the instrument (Section 7). These powers are the main component of the instrument equation. Their uncertainties are discussed and verified by a check of the heating resistor values (Section 8). The final TSI equation (Section 9) combines the measured powers with onground measured instrumental parameters. Results are described and comparisons with TIM/SORCE are made in Section 10. 2. Description The SOVIM package is composed of three PMO6 absolute radiometers, two sunphotometers, one pointing sensor (TASS) and one DIARAD radiometer. SOVIM is mounted in 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 DIARAD instrument is developed at the Royal Meteorological Institute of Belgium. DIARAD is composed of two cylindrical cavities coated inside with diffuse black paint and mounted next to each other on the same heat sink (Fig. 1 top). The flat bottoms of the cavities are in fact heat flux transducers on which heating resistors have been mounted. Every heating resistor has been mounted in series with a current measuring resistor (Fig. 1 bottom). The voltage over the four resistors is digitized through four independent electrical measurement channels. Two other channels are dedicated to temperature measurements. Each of the measuring channels is composed of a multiplexer, an amplifier, a voltage to frequency converter (VFC) and a counter. The data from the VFC’s are integrated in frames of 10 s. A packet of data are composed of nine frames. 3. Solar periods The SOLAR orbital period is around 90 min. Only some orbits are dedicated to Solar observations. They are scheduled when the Beta angle (the angle between the plane of the ISS’s orbit and the line connecting the centers of the Earth and the Sun) is within ±23°. During solar observations the SOLAR payload tracks the Sun during 45 min. Once in Sun acquisition mode, DIARAD/SOVIM uses the data from a two-axis Sun sensor (TASS) to apply a pointing correction. This correction takes into account the offpointing of DIARAD with regards to the satellite- Fig. 1. DIARAD detectors description and the four main measuring channels (the multiplexers are not represented). The left and right heating  resistors Rheating are mounted in series with measuring resistors ðRmeas Þ. Channels 1 and 2 (V/F1 and V/F 2) are dedicated to current measurements while channels 3 and 4 are dedicated to voltage measurements. Two other channels (channels 5 and 6) acquire the temperature in different part of the instrument. These channels are not represented. Sun direction. The classical working principle of DIARAD/SOVIM allows to have one acquisition every 3 min. Therefore, 15 measurements are possible if the Sun is tracked during the 45 min of solar visibility. To increase the number of acquisitions per orbit a new working principle of DIARAD is used: the extended open mode. This principle is described in the following section. 4. Measurement sequence 4.1. Classical sequence In its classical working principle, DIARAD is operated using successive open and closed states (Crommelynck, 1982; Mekaoui et al., 2004). Fig. 2 introduces the principle using the left channel of DIARAD/VIRGO on SOHO. During the first closed state both shutters are closed. The servo system dissipates a power P left;closed in the left cavity equal to the power dissipated in the right cavity by a reference voltage. Ninety seconds are necessary to have thermal equilibrium between the two cavities. Only the last acquisition made at second 90 is used. During the next state only the left shutter opens. A part proportional to the Solar radiation (SI) is absorbed by the left cavity. The  servo reduces the dissipated power in the left cavity P left;open to maintain equilibrium between the cavities. Only the last acquisition at second 90 is used. The comparison between S. Mekaoui et al. / Advances in Space Research 45 (2010) 1393–1406 1395 Fig. 2. Three consecutive states of DIARAD/VIRGO during a left side measurement cycle. Every state lasts 90 s during which the servo system regulates the 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 power P 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 the dissipated 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 of the 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. the regulated powers of both states gives a rough approximation of the Solar Irradiance (SI) each 3 min (90 s for the open states and 90 s for the closed state) according to: A  SIleft ðtÞ  P left;closed ðtÞ  P left;open ðtÞ ð1Þ where A is the area of the precision aperture of the active channel. The detailed equation is discussed in Section 9. Since both the open and closed states do not occur simultaneously,  P left;closed ðtÞ  in Eq. (1) is replaced by the average powers P left;closed ðtÞ of the two closed states surrounding the open state (see Fig. 2 bottom). During each of the closed and open states, nine acquisitions are made. Only five of them are dedicated to powers’ acquisitions. These acquisitions are made at seconds 20, 50, 60, 80 and 90. The four other acquisitions are associated to reference voltages and temperature measurements. The evolution of the five acquired powers during a nominal sequence of measurements is represented in Fig. 2 (bottom). 4.2. Extended open measurement sequence The extended open sequence is used to increase the number of acquisition points. In this sequence, the active channel has its shutter closed for 90 s. It is maintained afterwards opened during 270 (3  90) s instead of 90 s. This corresponds to a succession of one closed state and three open states. This sequence is illustrated in Fig. 3. During the first open state following a closed state, the servo system reduces the regulated power to reach the equilibrium as during the classical operating mode. During the following two open states, the servo system starts from an equilibrium state. As a consequence all the power acquisitions made at seconds 20, 50, 60, 80 and 90 of the second and third open states can be exploited as equilibrium measurement points. In total the succession of extended sequences during Solar measurements gives 11 acquisitions of the TSI every 6 min (the last acquisition of the first open 1396 S. Mekaoui et al. / Advances in Space Research 45 (2010) 1393–1406 Fig. 3. Top: the extended open sequence is composed of one closed state and three open states. The localizations of the acquired temperatures are also displayed. Bottom: the ‘’ are the acquired dissipated power in the regulated cavity (left) during the different states. The data are linearly interpolated for a better 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 two open states). Compared to the classical operating mode, this multiplies by a factor of 5.5 the number of acquisitions during an orbit. In the next Section, we describe the applied data processing to obtain the TSI and we discuss the associated uncertainties. 5. Data processing The general processing is represented in Fig. 4. In the demultiplexing step, the measured counts from each channel are attributed to a measured parameter. These counts are then transformed in physical units during the calibration process. The power and their associated uncertainties are calculated in the next step. The TSI calculation is finally applied using the instrument parameters. The power and TSI calculations as well as their associated uncertainties are detailed in what follows. 6. Electrical calibrations The calibration process aims at determining the count to voltage relation for each channel. Two sets of reference voltages are used. The current channels (channels 1 and 2) are calibrated using six level of a highly accurate temper- Fig. 4. The main steps in the TSI data processing. 1397 S. Mekaoui et al. / Advances in Space Research 45 (2010) 1393–1406 ature-stabilized reference voltage. Six other levels are used for the calibration of the voltage channels (channels 3 and 4). These reference voltages have been measured on ground in air and in vacuum. They showed no significant dependence to temperature variations (Conscience, 2005). The calibration process is made every 90 s. A second-order least square fit is then calculated using the six measurements of counts and their corresponding reference voltages. tor Rmeasurement (Fig. 1). We have Rmeasurement left ¼ Rmeasurement right ¼ 100:001 X. These resistors are measured with 70 ppm uncertainty (Conscience, 2002). The calibration error is at maximum 40 ppm for currents in open radiometric states and 5 ppm for currents in closed radiometric states (Fig. 6). The uncertainty of the current measurements is obtained by summing the calibration error, the uncertainty of the reference voltages measurements (15 ppm) and the uncertainty of the measurement of the measuring resistor. This gives 125 ppm for currents in open radiometric states and 90 ppm for currents in closed radiometric states. 6.1. Voltage measurements accuracy The fitted calibration functions of the voltages channels during a day of measurements are represented in Fig. 5 (top). Depending on the measured voltage, the residual error is at maximum 15 ppm if the shutter is open and 7 ppm if closed (Fig. 5 bottom). The error on the voltage measurements is obtained by summing the fitting errors and the accuracy of the voltmeters used to obtain the reference voltages. The reference voltages are measured with 15 ppm uncertainty. As a consequence, the voltages corresponding to open states are measured with 30 ppm uncertainty and the voltages corresponding to closed states are measured with 22 ppm uncertainty. 6.3. Temperature measurements Eight temperatures are acquired: five in the radiometer (T1–T5) and three in the electronics (T6–T8). T1 and T5 are located under the left and right shutters, T2 and T4 measure the temperature of the precision apertures while T3 acquire the temperature of the heat sink (see Fig. 3). The temperature T6 is acquired on the amplifier of channel 4, T7 on the multiplexer of channel 1 and T8 on the VFC of channel 6. The location of T6, T7 and T8 is intended to give a good spatial coverage of the temperature in the electronic. Fig. 7 displays the temperature evolution of DIARAD/SOVIM during six orbits. During the first three orbits DIARAD/SOVIM is in standby mode. In this mode, the instrument keep its shutters closed while the regulated 6.2. Current measurements accuracy Volts To find the currents, the voltage measurements of channels 1 and 2 are divided by the value of the measuring resis9 8.5 8 7.5 7 6.5 6 5.5 5 4.5 4 3.5 3 Left voltage Right voltage 1e+06 1.5e+06 2e+06 2.5e+06 (V meas - V ref ) / V ref Counts 5e-06 0 -5e-06 -1e-05 -1.5e-05 -2e-05 3 3.5 4 4.5 5 5.5 6 Volts 6.5 7 7.5 8 8.5 9 Fig. 5. Top: black “+”: daily measured counts corresponding to the reference voltages (V1–V6) from the left channel. Red “”: counts from the right channels. Curves: estimated second-order calibration functions for the voltages channels (red: right, black: left) during a day of measurements. Two bands (red and green) indicate the operational working voltages for DIARAD/SOVIM: when one of the cavities has an open shutter, less power has to be applied to cavity to maintain the equilibrium (see Section 3). The corresponding voltage is indicated by the horizontal green band. The red band indicates the voltage level for a cavity with a closed shutter. Bottom: black “+”: relative error on the reference voltages for the left channel. Red “”: relative error on the reference voltages for the right channel. The relative error due to the use of the calibration functions can be deduced by comparing the vertical bands and the neighborhood residual errors on the reference voltages. This error is of the order of 15 ppm for a cavity with an open shutter (green band) and 7 ppm for a cavity with a closed shutter (red band). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this paper.) 1398 Volts S. Mekaoui et al. / Advances in Space Research 45 (2010) 1393–1406 2.4 2.2 2 1.8 1.6 1.4 1.2 1 0.8 Left current Right current 1e+06 1.5e+06 2e+06 2.5e+06 (V meas - V ref ) / V ref Counts 4e-05 2e-05 0 -2e-05 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 Volts 1.7 1.8 1.9 2 2.1 2.2 2.3 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. During the last three orbits, the Sun is acquired by the left channel. plays the right and left powers during six orbits. During the last three orbits, DIARAD is measuring with its left cavity. The right power is the reference power and the left power is the regulated one. 7. Power calculation 7.1. Reference power The instrument’s working principle is based on the comparison of heat fluxes. For each of the cavities, the powers are calculated using the equation (in the case of the right power):   Rc þRd Rc þRd is the , where Rheating P right ¼ V right  I right  1 þ Rheating right right parasitic effect due to the heating resistor wires (Conscience, 2002).1 The error due to calibration can be estimated by summing the calibration errors on the current 6.1 measurements, voltage measurements  (see Sections  Rc þRd and 6.2) and the 15 ppm of the term 1 þ Rheating induced right by the parasitic resistor determination. In addition to the calibration errors, 50 ppm is added due to the noise level of the servo system in the case of the regulated powers. In total, the regulated open powers are measured with 220 ppm uncertainty. The regulated closed powers are measured with 177 ppm uncertainty and the reference powers are measured with 127 ppm uncertainty (Table 1). These uncertainties reduce to 139 ppm, 106 ppm and 94 ppm if we compute the root of the sum of squares.2 The different powers as well as their dynamic range and periodicities are shown from Fig. 8 to Fig. 12. Fig. 8 dis1 The power is determined by simultaneous measurements of the heater current and voltage. Nevertheless, the connecting wires of the heating resistor contributes to some parasitic effect due to their small resistance values Rc and Rd . 2 We further use the acronym (RSS) to designate the root of the sum of squares. A constant reference power is dissipated in the right cavity through its heating resistor according to P ref ¼ V 2 =Rheating . The heating resistor value Rheating is linearly dependent of the heat sink temperature. As a consequence the evolution of the reference power is in phase opposition with the heating resistor temperature variations. The reference power during three orbits is displayed in Fig. 9. The reference power varies in opposition with the temperature of the heat sink (T3). 7.2. Regulated power The left power (Fig. 8) depends on the status of the shutter (open or closed). When there is no solar pointing (Fig. 10), the difference between the powers in closed and open states is due to the internal thermal emission of the shutter. When the instrument points to the Sun, less electrical power is dissipated in the left cavity if its shutter is open. Fig. 11 shows three sequences of the regulated open power for each of the three orbits with solar acquisitions. They all display an upward trend due to the increase of the instrument’s temperature during the day part of the orbit. A magnification of the regulated open power during the triple open sequence is shown in Fig. 12. All acquisition points follow the upward trend except the acquisition made at time t = 10 s where equilibrium has not been reached yet. 1399 S. Mekaoui et al. / Advances in Space Research 45 (2010) 1393–1406 Celcius 66 T8 65 64 Celcius 58 96.5 96.56 2 96.62 5 96.68 8 96.75 57 T6 T7 56 55 17 Celcius 96.43 8 96.43 8 96.5 96.56 2 96.62 5 96.68 8 96.75 T1 T2 T3 T4 T5 16 15 14 96.43 8 96.5 96.56 2 96.62 5 96.68 8 96.75 Time (days of 2008) Fig. 7. Temperature evolutions during six orbits. The vertical lines separate the orbits. The instrument is in standby mode during the first three orbits and in 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 T5 display the highest variation resulting from the day/night cycle. The difference between T1 and T5 is due to the lack of absolute calibration of the temperature 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 first three 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 when the shutter is closed. These oscillations are also observed with a lower amplitude in the right aperture temperature T4. The heat sink temperature (T3) is correlated with the day/night cycle. The amplifier, multiplexer and voltage to frequency converter temperatures (T6, T7 and T8): T8 is used as reference temperature point for the reference voltages. T6 and T7 are correlated with the day/night cycle. During Solar acquisition in orbits 4, 5 and 6, the temperature (T7) of the multiplexer acquiring the left current shows some anomalies. These anomalies are due to grounding issues. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this paper.) Table 1 Electrical power measurement uncertainties. The uncertainties are obtained by adding the individual contributions (Total), or by performing the root of the sum of their squares (RSS). Regulated open state (ppm) Regulated closed state (ppm) Reference power Error on current Error on voltage Error on parasitic effect Servo noise 125 30 90 22 90 22 15 15 15 50 50 0 Total (ppm) RSS (ppm) 220 139 177 106 127 94 8. Heating resistor check The four main measuring channels (Fig. 1) allow to have independent measurements of the current and voltage for each cavity. It is therefore possible to calculate the value of the heating resistor in space according to (for the right heating resistor): Rheating right ¼ V right =I right ð2Þ These values are compared to a model determined on ground (Conscience, 1999). The model describes the evolution of the resistor value as a function of the temperature of the heat sink (T3). The comparison of the modeled and cal- culated values is indicative of the absolute accuracy of the power measurements. Figs. 13 and 14 display the calculated and modeled value for each of the left and right resistors. The model is corrected for an offset of 170 ppm. This systematic uncertainty is within the limit of the accuracy of the ground measurements of the resistor. Differences are observed between the modeled and measured values when the shutter is open compared to the period when the shutter is closed. When the shutter is opened less power is dissipated 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 the voltage and current values in open states compared to the calibration errors in closed states. The heating resistor value is therefore affected by the systematic calibration errors. The variations on the heating resistors are of the order of 20 ppm; which is within the limit of the noise and fitting errors (Sections 6.1 and 6.2). 9. TSI calculation The TSI is calculated using two closed states occurring at time t = 0 s and t = 360 s (state 1 and state 2) surrounding three open states (Section 4.2). For each of the open states 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: 1400 S. Mekaoui et al. / Advances in Space Research 45 (2010) 1393–1406 0.18 0.16 W 0.14 2 1 4 3 6 5 0.12 0.1 0.08 0.06 96.43 8 96.5 96.56 2 96.62 5 96.68 8 96.75 17 Celcius 16.5 16 T1 T5 T2 T3 T4 15.5 15 14.5 14 96.43 8 96.5 96.56 2 Days of 2008 96.62 5 96.68 8 96.75 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, the instrument is in standby mode. During this sequence both shutters are closed. The reference power is dissipated in the right cavity while the servo regulates the 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. The left 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 in Fig. 9. The higher dashed square highlights the regulated power levels when the shutter is closed. These powers are magnified for the last three orbits in Fig. 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 to the web version of this paper.) 0.1776 0.177599 4 5 6 W 0.177598 0.177597 0.177596 0.177595 0.177594 96.562 96.625 96.688 96.75 17 Celcius 16.5 16 T1 T5 T2 T3 T4 15.5 15 14.5 14 96.562 96.625 96.688 96.75 Days of 2008 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 solar pointing. Bottom: the temperatures are represented to show the correlation with the reference power. The reference power varies in opposition with the evolution 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 this paper.) DP open ðtÞ ¼ P right ðtÞ  P left open ðtÞ ð3Þ DP open is measured with ±25 lW uncertainty (Total3) and ±19 lW (RSS4). 3 4 We add the individual absolute uncertainties. We compute the root sum of squares of the individual uncertainties. The difference DP open is compared to the linear interpolation DP closed ðtÞ of DP closed 1 ðtÞ and DP closed 2 ðtÞ where: DP closed 1 ðtÞ ¼ P right 1 ðtÞ  P left closed 1 ðtÞ ð4Þ DP closed 2 ðtÞ ¼ P right 2 ðtÞ  P left closed 2 ðtÞ ð5Þ 1401 S. Mekaoui et al. / Advances in Space Research 45 (2010) 1393–1406 0.173 4 5 6 Closed power with Sun W 0.1729 Open power without Sun 0.1728 0.1727 0.1726 Closed power without Sun 0.1725 96.562 96.625 96.688 96.75 17 Celcius 16.5 16 T1 T5 T2 T3 T4 15.5 15 14.5 14 96.562 96.625 96.688 96.75 Days of 2008 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 Solar pointing (green hatched zone). The difference of power levels between the open and closed states in the absence of solar pointing is due to the shutter internal thermal emission. During Solar pointing, the regulated power in open states of the instrument is much lower than for the closed states. This power is 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 with the 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.) 0.0648 W 0.0646 6 5 4 0.0644 0.0642 96.562 96.625 96.688 96.75 17 Celcius 16.5 16 T1 T5 T2 T3 T4 15.5 15 14.5 14 96.562 96.625 96.688 96.75 Days of 2008 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 average increase of the instrument’s temperature. The dashed square shows the powers for the three successive open states. These powers are magnified in Fig. 12. where P right 1 ðtÞ and P right 2 ðtÞ are the reference powers during the two closed states. P right ðtÞ is the reference power during 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 ¼ DP open ðtÞDP closed ðtÞ ðaabs ath servocst Þ 0 ðA  ð1:0 þ R þ R þ dÞ  cos hÞ þ Dshutter ð6Þ The different parameters of Eq. (6) are described in what follows. Their uncertainties are summarized in Table 2. Details can be found in Crommelynck (1982). The SI is finally normalized to 1 AU and corrected for velocity effects according to:    r 2  dr c : 1þ2 TSI ¼ SI 1 AU dt ð7Þ 9.1. Geometrical corrections  Precision aperture (A) at temperature T = 20 °C: The precision apertures have been measured at NIST5 and NPL6; we use the average of the NIST and NPL measurements. We have Aleft ¼ 0:0000794094 m2 and Aright ¼ 0:0000794533 m2 with 150 ppm uncertainty. 5 6 National Institute of Standards and Technology. National Physical Laboratory. 1402 S. Mekaoui et al. / Advances in Space Research 45 (2010) 1393–1406 Ohm 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 its equilibrium. All the following points have a slight increasing trend corresponding to the overall increase of the temperatures during the solar pointing. 349.058 349.057 349.056 349.055 349.054 349.053 349.052 349.051 349.05 349.049 96.438 96.5 96.562 6 5 4 3 2 1 96.625 96.688 96.75 17 Celcius 16.5 16 T1 T5 T2 T3 T4 15.5 15 14.5 14 96.438 96.5 96.562 96.625 Days of 2008 96.688 96.75 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 the last three orbits during the solar pointing periods. These differences are due to the systematic errors of the electrical calibration. 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 of this paper.) The precision apertures are made of Invar. This material has a very low coefficient of thermal expansion (CTE of the order of 1:5  106 K1 ). Therefore, the thermal dilatation of the precision aperture due to the opening and closing of the shutter is considered to be negligible.  Distance, velocity and pointing corrections: The distance r between the radiometer and the center of the of the satellite relatively to Sun, the radial velocity dr dt the Sun and the angle between the direction of the Sun and the radiometer (h) are used to finally compute the TSI according to Eq. (7). 9.2. Optical corrections  The absorption coefficient of the cavity aabs : This coefficient corresponds to the amount of light trapped by the radiometric cavity. For DIARAD/SOVIM we have aabs ¼ 0:999748 for both the left and right cavity with a 45 ppm uncertainty. This coefficient is calculated on the basis of the geometric dimension of the cavity and the measured hemispheric absorptivity of the black paint. This paint absorptivity is measured on the ground using a synchronous detection setup. It is of the order of 0.972 ± 0.003 (Mekaoui, 2008). This value is measured at 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 surface of the precision apertures. Part of the radiation entering from the front aperture (when the shutter is open) is therefore reflected by the precision aperture (see Fig. 1). This reflected radiation is partly reflected back by the limiting volume between the shutter and the precision aperture. R is the ratio between this backscattered radiation falling in the active cavity after multiple reflec- 1403 Ohm S. Mekaoui et al. / Advances in Space Research 45 (2010) 1393–1406 349.058 349.057 349.056 349.055 349.054 349.053 349.052 349.051 349.05 349.049 96.438 96.5 96.562 6 5 4 3 2 1 96.625 96.688 96.75 17 Celcius 16.5 16 T1 T5 T2 T3 T4 15.5 15 14.5 14 96.438 96.5 96.562 Days of 2008 96.625 96.688 96.75 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 is observed 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 of this paper.) Table 2 Instrument parameters measurement accuracies. The uncertainty on the pointing correction (cos h) is negligible. The values, the absolute uncertainties as well 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 aabs left, aabs right ath left, ath right R R0 d Aright Aleft servocst 0.999748, 0.999748 0.998490, 0.998930 0.75e5 4.5e5 0.0005 0.0000794533 m2 0.0000794094 m2 1.000000 ±45 ppm ±120 ppm ±0.013 ±0.012 ±0.2 ±150 ppm ±150 ppm ±15 ppm Uncertainty on the terms of Eq. (6) 1 þ R þ R0 þ d 1.000552 DP open  DP closed 0.108000 W Dshutter 1.24 W m2 1361.68 W m2 ±100 ppm ±100 ppm ±289 ppm ±562 ppm ±0.024 ±364 ppm ±992 ppm DP open DP closed aabs ath servocst Acos hð1:0þRþR0 þdÞ ±0.01e5 ±0.1e5 ±0.0001 (RSS) (Total) (RSS) (Total) (RSS) (Total) Uncertainty on SI RSS Total tions and the radiative power directly going into the cavity (SI  A). We have R ¼ 0:75  105 . This value is estimated from DIARAD/VIRGO characterization.  The scattering of radiation by the front aperture (R0 ): R0 is the ratio between the scattered radiation by the front aperture which enters the active cavity and SI  A. R0 is also estimated from DIARAD/VIRGO characterization. We have R0 ¼ 4:5  105 .  The diffraction of radiation (d = 0.0005): d is the ratio between the diffracted radiation by the front aperture of the active channel which falls into the active cavity and SI  A. d is of the order of 0.0005 (NIST estimated value). Absolute uncertainty ±0.0001 (RSS) ±0.0001 (Total) ±0.000031 W (RSS) ±0.000060 W (Total) ±0.030 W m2 ±0.495 W m2 (RSS) ±1.35 W m2 (Total) ±0.496 W m2 (RSS) ±1.38 W m2(Total) 9.3. Thermal corrections  The thermal efficiency or effective absorptivity of the cavity ðath Þ: From the part of the absorbed radiation in the cavity only a proportion is effectively detected by the heat flux sensor. The other part is dissipated by the external wall of the cavity. The efficiency of the cavity sensor system7 is determined in air and vacuum. We have for DIARAD/SOVIM: 7 The system is composed of a heat flux transducer, a heating resistor and a cylindrical cavity. 1404 S. Mekaoui et al. / Advances in Space Research 45 (2010) 1393–1406 0¼   DP open ðtÞDP closed ðtÞ ðaabs ath servocst Þ 0 ðA  ð1:0 þ R þ R þ dÞ  cos hÞ 1370 Solar Irradiance (W/m²) ath left ¼ 0:998490 and ath right ¼ 0:998930 in vacuum with 120 ppm uncertainty. In air, ath left ¼ 0:995863 and ath right ¼ 0:995842.  The shutter correction ðDshutter Þ: This correction takes into account the contribution of the internal thermal emission of the active shutter. This contribution is removed when the shutter is open. For DIARAD/ SOVIM the shutter correction is determined during deep space pointing just after the solar period. During this phase, the temperature of the shutter does not change significantly. Eq. (6) becomes: 1360 1350 1340 1330 100 þ Dshutter ð8Þ It is therefore possible to derive Dshutter . Fig. 10 illustrates the contribution of the internal thermal emission of the left shutter during the deep space pointing. The contribution is of the order of 1.24 ± 0.05 W m2. 9.4. Electrical corrections  The parasitic wire heating: This effect has been discussed in 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 (servocst): During the first open sequence following a closed sequence, the open powers acquired at seconds: 20, 50, 60 and 80 do not correspond to an equilibrium state. It is possible to introduce a factor (servocst) to estimate the asymptotic value of each acquisition. For DIARAD/ SOVIM the triple open sequence guarantee that equilibrium is reached during the third open state. This asymptotic value is used to compute the correction factor for each of the previous state. We have chosen to apply a factor equal to 1 after 90 s and not to use the measurements up to 90 s. 10. Uncertainty and TSI results 150 200 Days of 2008 250 Fig. 15. SI measurements (Eq. (7)) during the 6 months of mission for DIARAD/SOVIM left channel. The SI decreases and then increases as the Earth moves around the Sun. The effect of the distance is corrected in Fig. 16. The outliers are caused by some reflections on the ISS. We present the two approaches with their associated calculations in Table 2. We write Eq. (6) as: SI ¼ ab þe cd with a ¼ DP open ðtÞ; b ¼ DP closed ðtÞ; c ¼ ð1:0 þ R þ R0 þ dÞ; d ¼ aabs  ath  servocst  A  cos h and e ¼ Dshutter . ¼ 562  Dða  bÞ ¼ Da þ Db ¼ 60 lW. Therefore, DðabÞ ab ppm.Alternatively, we can consider (a  b) as the difference of two independent Gaussian distributions with estimated standard deviations sa and sb .8 Therefore, pffiffiffiffiffiffiffiffiffiffiffiffiffi ffi sðabÞ ¼ s2a þ s2b which gives an uncertainty of 31 lW. sðabÞ ¼ 289 ppm. As a consequence, ab ¼ 100 ppm (Total) and  Similarly, Dc ¼ 0:0001 and Dc c also 100 ppm (RSS). Since the terms of Eq. (9) are independent,9 we have: sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi sab s2a s2 s2ab s2 s2a s2 cd þ c2 þ 2abs þ 2th þ servocst2 þ A2 ¼ ab 2 c aabs ath servocst A ða  bÞ cd ¼ 364 ppm 10.1. Uncertainty The accuracy of each channel is determined by the TSI equation (Eqs. (6) and (7)). These equations are based on power and instruments parameters determination. The power relative uncertainty is of the order of 139 ppm in open states (see Table 1). Instruments parameters are determined on ground (in air and vacuum) during the characterization phase. Two approaches can be used to compute the uncertainty of Solar Irradiance measurements, either by adding the individual relative uncertainties or by computing the Root of the Sum of Squares (RSS). The uncertainty is of the order of 1.38 W m2 (Total) and 0.496 W m2 (RSS) (see Table 2). ð9Þ Alternatively, we can add the individual uncertainties:   D ab Dða  bÞ Dc Dd cd þ þ ¼ 992 ppm ¼ ab ab c d cd ð10Þ relative ð11Þ Finally, the uncertainty on the SI given by: sSI ¼ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi s2ab þ s2e , is equal to 0.496 W m2. cd 8 We use the absolute uncertainties as estimations of the standard deviations. 9 The uncertainty on h being very small, we neglect the uncertainty on the pointing correction. S. Mekaoui et al. / Advances in Space Research 45 (2010) 1393–1406 1405 1365.3 DIARAD/VIRGO left no ageing DIARAD/SOVIM orbit means of left channel DIARAD/SOVIM orbit means of right channel 1365.2 TSI (W/m²) 1365.1 1365 1364.9 1364.8 1364.7 2454600 2454650 Julian day 2454700 Fig. 16. TSI orbital means from DIARAD/SOVIM left (red dots) and right (blues crosses) channels. The dispersion of measurements is of the order of 0.13 W m2. The measurements during each orbit are presented for three days of observations in Fig. 17. For comparison, DIARAD/ VIRGO 3-min left channel measurements are also displayed. These data are not corrected for the ageing effects which are of the order of 1.2 W m2 over 13 years. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this paper.)  When adding the absolute uncertainties DSI ¼ D ab þ cd DeÞ the value becomes 1.38 W m2. Fig. 15 shows the SI measurements during the entire mission. These measurements are then corrected for the distance, velocity and pointing effects in Fig. 16. 10.2. TSI results Both the left and right channels measurements are presented. DIARAD/SOVIM is nominally operating with its left cavity. The right cavity is used for ageing monitoring. The dispersion of DIARAD/SOVIM is of the order of 0.13 W m2. The difference between the channels is of the order of 0.25 W m2. This difference is within the individual channel 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 m2 offset due to the long-term ageing corrections. Some disagreement between DIARAD/SOVIM and DIARAD/VIRGO appears after Julian date 2454700. After that date, DIARAD/VIRGO increases faster due to a transient effect following a swith off. This effect is currently under investigation. Fig. 17 shows the left and right channels measurements for three days of the mission (13, 14 and 15 of June 2008). All the measurements of an orbit are represented. For this period, the TSI level from DIARAD/ SOVIM was 1364.50 ± 1.38 W m2 (Total) for the left channel and 1364.75 ± 1.38 W m2 (Total) for the right channel. On the other hand, DIARAD/VIRGO has an absolute uncertainty of the order of 1.06 W m2 (Mekaoui et al., 2004). Therefore, the 1.2 W m2 difference between DIARAD/VIRGO and DIARAD/SOVIM is within the instruments absolute uncertainties. Compared to TIM/SORCE measurements, DIARAD/ Fig. 17. TSI measurements from DIARAD/SOVIM left (black) and right (red) channels during each orbit for three days (13, 14 and 15) of June 2008. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this paper.) SOVIM is 4 W m2 higher (see Fig. 18). It is worth noticing that the integration of DIARAD/SOVIM has been undertaken in 2005. Therefore, it was not possible to follow the community recommendations issued during the TSI accuracy workshop held at NIST (Butler et al., 2008). In particular, it was not possible to validate DIARAD with end-to-end optical power or irradiance tests having SI traceability to national standards laboratories. 11. Conclusion This paper gives a rigorous description of the DIARAD/SOVIM TSI data processing and the related uncertainty analysis. A new extended open sequence has been introduced to increase the TSI sampling rate. Compared to previous versions of the DIARAD instruments efforts have been done to improve the absolute uncertainty of the electrical power measurements and the precision aperture determination. The uncertainty of the electrical power measurements is 220 ppm. Concerning the acquired data, the TSI value from DIARAD/SOVIM for three days of measurements (13, 14 and 15 of June 2008) was 1364.50 ± 1.38 W m2 for the left channel and 1364.75 ± 1.38 W m2 for the right channel. The uncertainty of ±1.38 W m2 is obtained when the individual contributions of the instrument equation are added. If they are combined in quadrature, the uncertainty is around ±0.497 W m2. The difference between the independent left and right channel measurements is as low as 0.25 W m2, which is within the absolute uncertainty limit of ±1.38 W m2 (Total) and ±0.497 W m2 (RSS). Although DIARAD/SOVIM TSI measurements are 1.2 W m2 lower than DIARAD/ VIRGO TSI value, it is still 4 W m2 higher than TIM/ SORCE TSI measurements. 1406 S. Mekaoui et al. / Advances in Space Research 45 (2010) 1393–1406 TSI measurements from individual instruments 1375 1374 1373 1372 1371 1370 1369 TSI ( W/m²) 1368 1367 1366 1365 1364 1363 1362 1361 1360 1359 ACRIM 1, 2 and 3 SOVA 1 ERB SOVA 2 DIARAD /VIRGO TIM DIARAD /SOVIM ERBS PMO6 V /VIRGO NOAA 9 NOAA 10 SOLCON 1358 1357 1978 1980 1982 1984 1986 1988 1990 1992 1994 1996 1998 2000 2002 2004 2006 2008 2010 Years Fig. 18. TSI measurements on their native scale, DIARAD/SOVIM measurements (dark blue +) differ from TIM/SORCE by +4 W m2. 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