Abstract
Various space missions have measured the total solar irradiance (TSI) since 1978. Among them the experiments Precision Monitoring of Solar Variability (PREMOS) on the PICARD satellite (2010–2014) and the Variability of Irradiance and Gravity Oscillations (VIRGO) on the mission Solar and Heliospheric Observatory, which started in 1996 and is still operational. Like most TSI experiments, they employ a dualchannel approach with different exposure rates to track and correct the inevitable degradation of their radiometers. Until now, the process of degradation correction has been mostly a manual process based on assumed knowledge of the sensor hardware. Here we present a new datadriven process to assess and correct instrument degradation using a machinelearning and data fusion algorithm, that does not require deep knowledge of the sensor hardware. We apply the algorithm to the TSI records of PREMOS and VIRGO and compare the results to the previously published results. The data fusion part of the algorithm can also be used to combine data from different instruments and missions into a composite time series. Based on the fusion of the degradationcorrected VIRGO/PMO6 and VIRGO/DIARAD time series, we find no significant change (i.e \(0.17\pm 0.29\) W/m\(^2\)) between the TSI levels during the two most recent solar minima in 2008/09 and 2019/20. The new algorithm can be applied to any TSI experiment that employs a multichannel philosophy for degradation tracking. It does not require deep technical knowledge of the individual radiometers.
Introduction
Machine learning and data fusion are two major components of Big Data to analyse vast amount of data and to look for trends or patterns, which have found many applications especially in the industry, opening new niche markets attracting more consumers^{1}. In geosciences and solar sciences, the main goal is to process large data sets collected by satellites and/or other networks of receivers^{2}. Those various data sources can hide common patterns, longterm trends or abnormal behaviors which can be detected using machine learning and data fusion algorithms. From a data science perspective, these algorithms allow the extraction of relevant information from various data sets through the adoption of intelligent monitoring (machine learning) based on a probabilistic analysis of the data sets. This datadriven approach reduces the “human factor” which can introduce biases in the data analysis.
Total solar irradiance data sets
Total solar irradiance (TSI) measurements are important for both solar physics and climate sciences. In the Earth radiation budget, the TSI affects directly the relative significance of natural and anthropogenic contributions to the climate change^{3}. To date, the longest TSI time series have been produced by the ACRIM (JPL)^{4}, VIRGO (PMOD/WRC together with the Institute Royal de Méteéorologie Belgique, IRMB)^{5,6,7}, and the Laboratory for Atmospheric and Space Physics (LASP, University of Colorado)^{8,9} teams. The ACRIM team provides the data records collected by the Solar Maximum Mission SSM/ACRIM1 (1980–1989), the Upper Atmosphere Research Satellite UARS/ACRIM2 (1991–2001), and the ACRIMSAT/ACRIM3 (1999–2013) missions. The VIRGO team produces the TSI record from the DIARAD (IRMB) and PMO6 (PMOD/WRC) radiometers on board of the SOHO/VIRGO experiment (1996–present), the PICARD/PREMOS (2010–2014), and the NORSAT1/CLARA (2017–present)^{10}. LASP provides the TSI time series from the SORCE/TIM instrument (2003–2020), TCTE/TIM (2013–2019) and TSIS1/TIM (2018 to present).
Instrument degradation and TSI composites
Degradation of radiometers on board of satellites due to UV/EUV radiation has been a subject of research and several methods for its correction have been proposed^{5,11}. Each of the data sets listed above consist of the TSI measurements from an active (continuously operated) and at least one backup (occasionally operated) channel. The instrument degradation is then assessed by comparing the measurements of the active channel to the occasionally operated backup channel(s). The exact procedure is a matter of personal judgement by the instrument team and is often evolving over the lifetime of each experiment. Correction of degradation is particularly important when comparing and/or combining the TSI measurements from different missions into a single composite time series. During the last 3 decades, different groups have produced individual TSI composites from different TSI data sets, based on different assumptions and often using personal judgement when processing the data sets^{4,5,12}. The scientific community is debating the different solutions with respect to which of the composites should be used as reference. More recently, Ref.^{13} published a new method to combine the data from different sensors in an objective way using a maximum likelihood estimator. However, this new method still relies on the time series produced by the individual instrument teams, which often suffer from at least some level of subjectivity in the assessment and correction of instrument degradation.
Here, we present an algorithm based on machine learning and data fusion to process the TSI observations without filtering or applying any sort of data preprocessing which can be assimilated to “human refinement”. Based on the PREMOS/PMO6 data set, we demonstrate the robustness of our approach to correct for sensor degradation in TSI radiometers. We then apply the algorithm to the VIRGO/DIARAD and VIRGO/PMO6 data sets and combine them into a new VIRGO TSI composite. The VIRGO TSI composite has been the major contributor to the widely used PMOD composite, which was never updated since the demise of its maintainer and former PI of VIRGO, Dr. Claus Fröhlich (1936–2019).
Data fusion
Various data fusion techniques are already available in many engineering fields^{14}. Our algorithm to merge (fuse) the simultaneous measurements from two sensors is based on maximum likelihood and Gaussian processes in order to model the stochastic noise intrinsic to the TSI observations (e.g., Gaussian noise). The underlying (Bayesian) probabilistic framework guarantees the robustness of our approach^{15}. We use data fusion to merge the active and backup channels into the degradationcorrected time series of the respective TSI experiment. Ultimately, the data fusion algorithm can also combine the simultaneous observations from different TSI experiments in order to produce a composite based on the stochastic noise properties relative to each instrument. We demonstrate the concept by fusing the VIRGO/PMO6 and VIRGO/DIARAD time series.
Observations and methodology
The TSI observations
The TSI has been recorded by several space missions since the late 1970s. The time series from the various instruments are almost contiguous. The VIRGO experiment on the ESA/NASA SOHO Mission was launched in December 1995 and started observations in January 1996. The VIRGO experiment carries two different TSI radiometers, DIARAD, which was designed and built by IRMB, and PMO6V by PMOD/WRC. A detailed description of the instrumentation is given in Ref.^{16}. The DIARAD observations are processed at IRMB^{12}, while the PMO6V observations are processed at PMOD/WRC. We also use the observations from PICARD/PREMOS, which have also been processed at PMOD/WRC. For reference we compare our results to SORCE/TIM^{17} and ACRIMSAT/ACRIM3^{4}. Table 1 displays the instruments and the processing centers providing the observations used in this work. The data processing, including corrections for all a priori known influences such as distance from the sun (normalized to 1 AU), radial velocity to the sun, and thermal, optical, and electrical corrections, are usually implemented by each processing center, leading to level1 time series. On the other hand, the degradation of the radiometer is caused by longterm sensitivity changes of the sensor and/or drifts of the electrical characteristics. The degradation is assessed a posteriori based on the relative change of the active channel with respect to the backup channel(s). The change of sensitivity is generally related to the changes in the absorptance of the black coating of the cavity^{18}, or the loss of glossiness of specular paint. Both effects are thought to be caused by the UV and EUV radiation^{16}.
The VIRGO/PMO6V observations
On VIRGO, two PMO6V radiometers (i.e. PMO6VA and PMO6VB) of the same design and black coating (Aeroglaze Z302) are used as ’active’ and ’backup’ instruments. The backup instrument PMO6VB is operated only rarely to keep its degradation low compared to PMO6VA. PMO6VB is operated once every ten days during 39 min. Before 6 July 1996, PMO6VB was operated 3 times per day for 39 min. Further details can be found in Ref.^{16}.
The degradation function of PMO6VA has been previously determined and published online as versions PMO6v6 and v7. The assumptions vary slightly between both versions, but we recall the main three hypotheses: (a) the sensitivity decreases with exposure to solar radiation and is modelled by an exponential, (b) there is an early increase in sensitivity during the first few days modelled with an exponential, (c) a nonexposure dependent degradation of \(0.3\) ppm/mission day is found by comparing PMO6VB with the backup channel of VIRGO/DIARAD (DIARADR). It leads to correct the level1 PMO6VA observations with a sum of exponential and linear functions. The process is fully described in Refs.^{7,16}.
The VIRGO/DIARAD observations
DIARAD is the second type of radiometer on the SOHO/VIRGO experiment. It features two radiometric channels (DIARADL and DIARADR) and uses a different black coating than the PMO6V (3M Nextel VELVET Black 2010). The backup channel DIARADR is operated every 60 days during 90 min (30 min until 7 August 1996). The degradationcorrected TSI time series are produced in a process similar to PMO6V. Here, we use two degradationcorrected data products, namely the PMODv6 discussed in Ref.^{7} and the TSI composite released by IRMB^{12,19}. The former will be referred in the following as PMODv6 and the latter as the IRMB/DIARAD product. According to Ref.^{20}, the degradation correction of the IRMB/DIARAD product is based on an exponential, with various assumptions (e.g. exposure time, offsets).
The PREMOS/PMO6P observatsions
Like VIRGO, PICARD/PREMOS is also equipped with two PMO6type radiometers^{21}. These are referred to as PMO6PA (active) and PMO6PB (backup). The PICARD mission started in 2010 and ended in 2014. The degradation of the PREMOS/PMO6 radiometer was determined in Ref.^{21} and reevaluated by Ref.^{22}.
Robust TSI estimates with machine learning and data fusion
In this section, we produce degradationcorrected TSI time series using the active and backup instruments/channels for each experiment (i.e. PMO6VA and PMO6VB, DIARADL and DIARADR, PMO6PA and PMO6PB). Our first assumption is that degradation is a function of exposure time only. The exposure time is estimated via a cumulative sum of the measurements recorded by each sensor. We are aware that an effective UV/EUV dose could be used instead of the exposure time. However, in practice, it turns out that using dose does not yield a significant difference in the degradation assessment^{22}. Since the backup instruments/channels (PMO6VB, DIARADR, PMO6PB) have lower observation rates (and hence exposure times) than the active instruments/channels (PMO6VA, DIARADL, PMO6PA), they degrade less rapidly. Our second assumption is that all instruments and channels start with no degradation and the third assumption is that the degradation curve is monotonically decreasing.
The proposed new algorithm is divided in 2 steps. The first step is modelling the degradation curve and corrects the level1 observations, whereas the second step is the data fusion where the corrected measurements from the active and backup instruments (or channels) are merged in order to produce a single TSI time series. The algorithm is published in Refs.^{23,24}. In the following we give a brief summary.
Degradation modeling and correction
The three assumptions defined above can be formally be expressed in the following way for the degradation function d:
where \(e_x\) is the exposure time, and \({\partial \over \partial e_x}\) denotes the partial derivative. Note that for PMO6type radiometers the observations indicate that \({\partial \over \partial e_x}d>0\) for \(e_x \lessapprox 5\mathrm {\ days}\)^{22,25}. Because the algorithm cannot yet model such negative degradation, we still use the method described in Ref.^{22} to manually correct this socalled early increase of PMO6type radiometers based on a linear fit of the active vs. backup channels over the first five days of exposure time of the active channel. A detailed description of how the early increase is corrected is given in the appendix. A future version of the algorithm will be able to model and correct for nonmonotonic degradation.
If \(e_a\) and \(e_b\) are the respective exposure times of the active and backup sensors, s the “true” TSI signal (without degradation), and \(\varepsilon _a\) and \(\varepsilon _b\) the measurement noise, then the actual signals a and b (with degradation) which each sensor measures at time t are:
with the assumption that the noise \(\varepsilon\) is zeromean Gaussian distributed (with variance \(\sigma ^2\)) and independent for each instrument and channel. The active and backup radiometers are technically identical, therefore the degradation function is assumed to be identical for both channels.
Now, the goal is to estimate \(d(e_x)\) from the observations a(t) and b(t). Neither the true signal s(t) (i.e. without noise and degradation) nor the degradation function \(d(e_x)\) are known throughout the process. We determine d solely from the ratio of the signals \(r(t)={a(t) / b(t)}\). To estimate \(d(e_x)\) we propose an iterative process to correct the signals a(t) and b(t) as follows:
where \(a_0(t)=a(t)\), \(b_0(t)=b(t)\). As shown in^{24}, the ratio \(r_p(e_x)\) converges towards the degradation function \(d(e_x)\):
In practice, the iterative process described in Eq. (3) is performed by fitting of a function \(d_\theta (e_a(t))\) (parametrized by \(\theta\)) to \(r_p(e_a(t))\) by minimizing the objective function:
For our type of observations, we empirically established via simulations that \(d_\theta\) is best described as an isotonic function^{26}, although monotonic and smooth monotonic functions have also been tried. Once \(d_\theta\) is estimated iteratively, the measurements a(t) and b(t) can be corrected using:
The algorithm to extract the corrected measurements is displayed in the appendices together with the definition of the isotonic functions (monotonic and smooth monotonic).
Data fusion
After correcting the measurements (\(a_c(t_i), b_c(t_i)\)), the Eq. (2) becomes:
The data fusion aims at merging the corrected observations from the two channels in order to get a reliable estimate of the true signal s, knowing that the underlying process model of s is random and unknown. Therefore, we formulate two assumptions: a/the solar cycle is not a deterministic signal and its variations are random (no a priori knowledge). s is then assumed to be a Gaussian process (GP) with zero mean and a covariance function \(k_{\alpha }(.,.)\) (or kernel); b/ because we consider the noise on the measurements zero mean Gaussian distributed, then we can estimate the parameters of the model of s(t) via maximum likelihood estimator. We then formulate \(\mathbf {s} \sim GP (0, k_{{\alpha }}(.,.))\). However, the main limitation of GPs is that given n observations, the inverse of the \(n \times n\) covariance matrix must be computed. Time complexity of such operation is of the order of \(O(n^3)\), which is not scalable, especially when computational resources are limited. The VIRGO/SOHO mission has been recording observations at a high rate (i.e. 1 min sampling of PMO6VA) for a long time (since 1996), therefore we deal with large TSI data set (i.e. \(n >10^7\)). We therefore approximate the exact GP with a Sparse Gaussian Process^{24} (SPG) to construct a lower bound for the loglikelihood \(\log {p(\mathbf {y}\mathbf {x})}\). \(\mathbf {x}\) and \(\mathbf {y}\) are the concatenation of times, \(\mathbf {x} = [t_i, t_i], i=1\ldots n\), and corresponding corrected observations \(\mathbf {y} = [a_c(t_i), b_c(t_i)]\). The mathematical formula is displayed in the appendices.
It is important to emphasize that the training of \(k_{{\alpha }}\) with the socalled “inducing points” is to learn about the stochastic properties of the data, which allows to take into account shortterm correlations in the observations and a reasonable approximation of s. Thus, our simulations use 2500 inducing points which is a tradeoff between modelling well all the processes and avoiding long computing time (i.e. no more than 10h) with a regular desktop computer (i.e. 16G RAM, 4 cores). Note that the final time series has an hourly rate in order to avoid large data set (i.e. > 100 MB).
Results and discussion
Degradation correction of PREMOS/PMO6 measurements
In the previous sections, we have introduced the algorithm to estimate the degradation function based on the ratio of the raw measurements from the active and backup channel. We apply this algorithm to the PREMOS PMO6PA and PMO6PB level1 data after manually correcting the early increase (see appendix). The Fig. 1 displays the ratio of level1 observations of PMO6PA and PMO6PB as a function of time together with the degradation function determined by our algorithm using isotonic regression (red curve). To assess the validity of our new degradation function, we compare it to the previously published solution. We find that our algorithm reproduces the wellestablished degradation curve (at the level of 0.0062 W/m\(^2\)) determined for PREMOS/PMO6 in a classical approach^{22} with no appreciable relative trend between both solutions (see Fig. 2). Over the full PREMOS mission the new TSI time series agrees with previous release in absolute value \(\sim 0.12\) W/m\(^2\) RMSE (PREMOSv1, see Figure A.5).
Degradation correction of VIRGO measurements
The VIRGO experiment provides the longest TSI time series to date, covering more than two 11year solar cycles. Comparing the TSI levels during consecutive solar minima is thought to provide important information on secular changes in the radiative output of the Sun. It is crucial to accurately model and correct the degradation of the VIRGO radiometers before we can assess the variability of solar minimum levels of the TSI. Previously, the degradation of the VIRGO time series was corrected in a highly sophisticated, mostly manual procedure which has become increasingly complex as the time series grew longer and additional instrumental effects had to be considered in order to accurately model the degradation curve^{5,7,11}. We now use our machinelearning algorithm to solve the degradation issue in an automated, fully reproducible process for both VIRGO/PMO6 and VIRGO/DIARAD time series. Manual correction of the early increase was applied to the VIRGO/PMO6 time series as explained in the previous section. The degradationcorrected TSI time series of VIRGO/PMO6 is shown in Fig. 3 together with the previous solutions PMO6v6 and v7. The degradationcorrected DIARADL time series is shown in Fig. 4.
Table 2 shows how our solutions compare with previous data releases in terms of the average TSI levels during the solar minimum in 2008/2009, at the transitions from solar cycle 23 to 24. The solar minimum period (2008 September 20–2009 May 5) was chosen according to the ISSI team meetings 2012 and 2013^{8,9,27}.
In Table 2 all VIRGO data are expressed according to the “new VIRGO” scale^{25} to allow easier comparison with the data sets of SORCE/TIM and ACRIM3. The scale offset is explained by different reference scales of both data sets. SORCE/TIM is traceable to SI while SOHO/VIRGO was calibrated against the World Radiometric Reference (WRR), which is offset by \(0.34\%\) with respect to SI^{28}, resulting in an offset of \(4.6\) W/m\(^2\). During solar minimum 23/24 the previous (“classical”) PMO6v6 and v7 releases and the new (“machinelearning”) solution for VIRGO/PMO6 differ on the order of magnitude of \(\sim 0.2\) W/m\(^2\), with the “classical” TSI values being lower. This difference is just within the 1sigma interval of 0.2 W/m\(^2\), which we define as the inter quantile range (i.e. difference between the 25th and 75th percentile, see Figure A.5).
For DIARAD the machinelearning algorithm suggest a TSI level for solar minimum 23/24 which is between the “classical” solutions provided by IRMB (0.05 W/m\(^2\) lower) and PMOD/WRC (0.08 W/m\(^2\) higher).
Over the full VIRGO mission, we have found that the new TSI time series’ agree with previous releases by PMOD/WRC and IRMB in absolute value between \(\sim 0.1\) W/m\(^2\) RMSE (VIRGO/DIARAD) and \(\sim 0.25\) W/m\(^2\) RMSE (PMODv7, Figure A.5).
Data fusion and new TSI composite
We use the data fusion process not only to merge the degradationcorrected time series of the active and backup channels into a single time series for each TSI experiment, but also to produce the new VIRGO TSI composite from DIARAD and PMO6V. More generally, the fusion process can be applied to any two simultaneous time series from different TSI experiments with different noise variances to produce a TSI composite. Unfortunately, the DIARADR sensor does not record any observations since early 2018 due to a technical issue. Since then, we can no longer merge the DIARAD time series from fusing DIARADL and DIARADR. Therefore, we produce the new VIRGO TSI composie from fusing only the degradationcorrected PMO6VA and DIARADL time series instead. To produce the degradationcorrected DIARADL, we first estimate the degradation function using both sensors (DIARADL, DIARADR) for the time when they are available. We then extrapolate with a third order polynomial the degradation function in order to correct the DIARADL time series in its full length.
Before the fusion, we align the VIRGO/DIARAD composite at the same nominal TSI value as VIRGO/PMO6 corresponding to the last solar minimum (i.e. 1365.39 W/m\(^2\)). We can then produce the VIRGO TSI composite by fusing the degradationcorrected PMO6VA and DIARADL observations (Fig. 4). The mean value and the standard deviation of this new VIRGO TSI composite have similar characteristics than the ones estimated for VIRGO/DIARAD and VIRGO/PMO6.
The difference in the TSI levels during the last two solar minima are \(0.26\) W/m\(^2\) (PMO6VA) and \(0.08\) W/m\(^2\) (DIARADL), respectively (empirical uncertainties based on combined standard deviations of both time series during the solar minimum periods). For the cycle 24/25 solar minimum we chose the period from 2019 Nov 1 to 2020 May 1, during which virtually no signs of solar activity appear in neither the Solar Sunspot Number nor the TSI measurements from VIRGO/PMO6. We estimate the empirical cycletocycle stability of our new degradation algorithm by comparing the VIRGO TSI composite to the independent data set from SORCE/TIM. In 2008/09 VIRGO reads 0.27 W/m\(^2\) higher than SORCE/TIM, in 2019/20 the VIRGO reads 0.01 W/m\(^2\) lower than SORCE/TIM, resulting in a relative trend of \(0.28\) W/m\(^2\) of VIRGO with respect to SORCE/TIM (see Table 2). We take this trend as the empirical uncertainty of the longterm stability of the machinelearning and data fusion algorithm. Together with the empirical standard deviations of both time series (i.e. 0.04 W/m\(^2\) for SORCE/TIM and 0.05 W/m\(^2\) for the VIRGO composite, see Table 2) the resulting uncertainty is \(\sqrt{0.28^2+0.04^2+0.05^2)}=0.29\). From the VIRGO TSI composite, we thus find a nonsignificant minimumtominimum variation between 2008/2009 and 2019/2020 of \(0.17 \pm 0.29\) W/m\(^2\).
Note that Figure A.4 in the appendices show the comparison between all the data sets and our new TSI time series.
We note that the agreement with TIM has improved compared to previous version PMO6v7 (Fig. 5). This is however fully attributable to an improved temperature correction algorithm which we implemented in the upstream data processing pipeline for PMO6V. The updated temperature correction algorithm removes the slight sensitivity to the absolute temperature, which the original, purely empirical, algorithm was suffering from. The overall temperature of the VIRGO package had risen by several degrees in the course of the mission, causing a slight drift of the PM06V measurement. This drift has now been eliminated by switching to a correction algorithm which is based solely on the temporal derivative of the heat sink temperature to correct for measurement bias. This bias is caused by slight mismatch of the thermal time constants of the measuring and compensating cavities in each PMO6V channel. This is an apriori effect, hence not part of the degradation correction. The concept of this new algorithm was originally developed for the PREMOS/PMO6 radiometers^{27}, but never applied to the VIRGO/PMO6.
Conclusions
The classical approach for correcting TSI instrument degradation suffers from two major weaknesses. 1/ It is subject to personal judgement, and 2/ it is based on assumed physical and photochemically induced changes in the sensor hardware which cannot be verified. In this study, we propose a datadriven approach of processing TSI data using machinelearning and data fusion where a small number of objective (i.e. not specific to the instrument) assumptions are sufficient to correct for instrument degradation and to produce robust TSI estimates. The first assumption is that the degradation function depends only on exposure time. Secondly, at the first epoch we have two identical, nondegraded instruments (or channels). Thirdly, the degradation is assumed to be a decreasing function. This approach largely eliminates the “human factor” and by virtue of its datadriven nature it is detached from the actual hardware changes.
From the low RMSE (\(\sim 0.12\) W/m\(^2\)) between PREMOSv1 and the machinelearning solution for PREMOS/PMO6 together with the absence of any appreciable longterm trend between both solutions, we conclude that the machinelearning and data fusion algorithm is capable of reproducing the degradation function with similar accuracy and precision than classical approaches. The PREMOSv1 solution by Ball et al.^{22} is the best documented (and arguably the most sophisticated) of the four classical solutions (incl. PMO6v6, v7, IRMB/DIARAD) which we considered in this work. From the excellent agreement of our solution with PREMOSv1 we conclude that for the latter three, applying the machinelearning and data fusion algorithm likely constitutes an improvement over their respective classical solutions.
We composed a new VIRGO TSI composite by fusing the degradationcorrected time series of PMO6VA and DIARAD. The data fusion process requires coaligning the absolute values of both time series, therefore the absolute value of the new VIRGO TSI composite is still somewhat arbitrarily chosen to match with PMO6VA. Nevertheless, we can use the new VIRGO TSI composite to estimate drifts in TSI level between consecutive solar minima. We found no significant change (\(0.17\pm 0.29\) W/m\(^2\)) between the two most recent solar minimum periods (2019/2020 solar minimum vs. 2008/2009 solar minimum).
The data fusion part of the algorithm can also be used to fuse contemporaneous TSI time series from different instruments in order to produce composite time series. Future work will focus on refining the underlying assumptions of the machinelearning algorithm, including additional TSI experiments in order to feed them into the “community composite” approach by Ref.^{13}, and to validate the result by comparing it to a composite based on our data fusion approach.
Data availibility
The VIRGO PMO6 and VIRGO DIARAD data are accessible on the PMOD website (ftp://ftp.pmodwrc.ch/pub/data/irradiance/virgo/TSI/), whereas the IRMB DIARAD data are available on request to Dr. S. Dewitte. The data related to the monthly mean sunspot numbers are retrieved from http://www.sidc.be/silso/datafiles. The PREMOS/PICARD data can be accessed at http://idocpicard.ias.upsud.fr/sitools/clientuser/Picard/projectindex.html (It is recommended to use Data Access at the top left \(\rightarrow\) Datasets Explorer and download TSI_N2_complete). The ACRIM3 data is downloadable at http://www.acrim.com and the latest SORCE/TIM dataset is available at https://lasp.colorado.edu/home/sorce/data/tsidata. We downloaded the ACRIM data from http://www.acrim.com. But the site does indeed seem to no longer exist! Alternatively, https://www.ftp://ftp.ngdc.noaa.gov/STP/SOLAR_DATA/SOLAR_IRRADIANCE/ACRIM3/ could be used.
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Acknowledgements
We gratefully acknowledge the support of KarbacherFunds. We also acknowledge the lifelong dedication to the TSI community of the late Dr. Claus Fröhlich in memoriam as former director of PMOD/WRC, PI of SOHO/VIRGO and his invaluable contribution to the analysis of TSI observations.
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W.F., J.P.M. and W.S. conceived the study and wrote the article. W.F. and J.P.M. analyzed the data. R.S., L.K., and L.T. were responsible to develop the machine learning and data fusion algorithm. All authors reviewed the manuscript.
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Finsterle, W., Montillet, J.P., Schmutz, W. et al. The total solar irradiance during the recent solar minimum period measured by SOHO/VIRGO. Sci Rep 11, 7835 (2021). https://doi.org/10.1038/s4159802187108y
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DOI: https://doi.org/10.1038/s4159802187108y
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