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- Hindawi Publishing Corporation
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- Copyright © 2019 Nicola Scafetta and Richard C. Willson. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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- 1687-7977
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- 10.1155/2019/1214896
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Abstract
Hindawi Advances in Astronomy Volume 2019, Article ID 1214896, 14 pages https://doi.org/10.1155/2019/1214896 Research Article Comparison of Decadal Trends among Total Solar Irradiance Composites of Satellite Observations 1 2 Nicola Scafetta and Richard C. Willson Department of Earth Sciences, Environment and Georesources, University of Naples Federico II, Via Cinthia 21, 80126 Naples, Italy Active Cavity Radiometer Irradiance Monitor (ACRIM), Coronado, CA 92118, USA Correspondence should be addressed to Nicola Scafetta; nicola.scafetta@unina.it and Richard C. Willson; rwillson@acrim.com Received 1 December 2018; Accepted 31 January 2019; Published 10 March 2019 Academic Editor: Elmetwally Elabbasy Copyright © 2019 Nicola Scafetta and Richard C. Willson. is Th is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. We present a new analysis of the two-decade-old controversy over interpretation of satellite observations of total solar irradiance (TSI) since 1978 and the implications of our findings for TSI as a driver of climate change. Our approach compares the methods of constructing the two most commonly referenced TSI composites (ACRIM and PMOD) that relate successive observational databases and two others recently constructed using a novel statistical approach. Our primary focus is on the disparate decadal trending results of the ACRIM and PMOD TSI composite time series, namely, whether they indicate an increasing trend from 1980 to 2000 and a decreasing trend thereaer ft (ACRIM) or a continuously decreasing trend since 1980 (PMOD). Construction of the four-decade observational TSI composites from 1978 to the present requires the use of results from two less precise Earth Radiation Budget experiments (Nimbus7/ERB and ERBS/ERBE) during the so-called ACRIM-Gap (1989.5–1991.8), between the end of the ACRIM1 and the beginning of the ACRIM2 experiments. eTh ACRIM and PMOD composites used the ERB and ERBE results, respectively, to bridge the gap. The well-established paradigm of positive correlation between Solar Magnetic Field Strength (SMFS) and TSI supports the validity of the upward trend in the ERB results and the corresponding decadal upward trend of the ACRIM composite during solar cycles 21 and 22. eTh ERBE results have a sensor degradation caused downward gap trend, contrary to the SMFS/TSI paradigm, that biased the PMOD composite decadal trend downward during solar cycles 21 and 22. eTh dier ff ent choice of gap bridging data is clearly the cause of the ACRIM and PMOD TSI trending difference, agreeing closely in both magnitude and direction. We also analyze two recently proposed statistical TSI composites. Unfortunately their methodology cannot account for the gap degradation of the ERBE experiment and their resulting uncertainties are too large to uniquely distinguish between the trending of the ACRIM and PMOD composites. Our analysis supports the ACRIM TSI increasing trend during the 1980 to 2000 period, followed by a long-term decreasing trend since. 1. Introduction cycle-to-cycle trending that provides valuable information for evaluating solar models and investigating the relative Satellite total solar irradiance (TSI) composite databases, significance of natural and anthropogenic forcing of climate using observations from different satellites covering different change [7, 10–12]. The two mostly frequently cited TSI segments of time since November 1978, have been con- composites, compiled by the ACRIM [3, 7] and PMOD [2, structed by several research teams (e.g., [1–9]). TSI com- 13, 14] science teams, are shown in Figure 1. posites are important for investigating both solar physics and the effects of TSI variations on the earth’s climate. 1.1. ACRIM and PMOD Composites. ACRIM combines the The currently accepted mean TSI value for last complete published and archived NASA records collected and pro- solar cycle 23 (1996–2009) is near 1361 W/m [7]. The most cessed by the ACRIM science teams responsible for the important feature of a TSI composite for earth climate studies Solar Maximum Mission/ACRIM1 (1980–1989), the Upper on decadal to multidecadal timescales is the solar magnetic Atmosphere Research Satellite/ACRIM2 (1991–2001), and the 2 Advances in Astronomy ACRIM ACRIM1 ACRIM2 ACRIM3 1980 1984 1988 1992 1996 2000 2004 2008 2012 2016 year TSI minimum in 1986: 1360.62 W/m (a) PMOD 1980 1984 1988 1992 1996 2000 2004 2008 2012 2016 year TSI minimum in 1986: 1360.59 W/m (b) Figure 1: (a) ACRIM TSI composite. (b) PMOD (v. 1702) TSI composite [7, 14]. Components of each composite are ACRIM123 (blue), Nimbus7/ERB (brown), and VIRGO (orange). Table 1: Mean values of the TSI composite solar cycle activity during ACRIMSAT/ACRIM3 (1999–2013) mission, together with the year of their minima. The error bar of the annual mean values is the original ERB science team results from the Nimbus7/ERB less than𝜎 =0.01 W/m . (1978–1993) experiment prior to the launch of ACRIM1 (1878–1980) and during the about 2-year gap between 1986 1996 2009 2 2 2 ACRIM1 and ACRIM2 results (the so-called ACRIM-Gap (W/m ) (W/m ) (W/m ) from 1989.5 to 1991.8). ACRIM 1360.62 1361.08 1360.78 The PMOD composite uses their model-modified ver- PMOD (v. 1702) 1360.59 1360.54 1360.40 sions of the ACRIM1, ACRIM2, Nimbus7/ERB and Earth de Wit - Unmodified 1360.32 1360.66 1360.54 Radiation Budget Satellite/ERBE (1984–2003) records from late 1978 to 1996, together with the Solar and Heliospheric de Wit - Modified 1360.52 1360.68 1360.54 Observatory/VIRGO observational record (1996 to present). Satire-T2 1365.63 1365.50 missing Other TSI composites have been proposed. The RMIB Satire-S 1360.98 1360.75 1360.55 [4, 8] is based on daily averaged TSI data from all available instruments once they are rfi st put on a common absolute scale. Scafetta [6] proposed three alternative composites based onanoptimal merging of the TSIrecords where the followed by a decrease of 0.30 W/m between 1996 and 2009. ACRIM-Gap was resolved either by Nimbus7/ERB results, by PMOD shows a continuous, increasing downward trend with ERBS/ERBE results, or by their average. The most significant difference between the ACRIM and a 1986 to 1996 decrease of 0.05 W/m followed by a decrease PMOD composites is their multidecadal trending during of 0.14 W/m between 1996 and 2009. The RMIB composite solar cycles 21-24. This can be seen clearly in Table 1 where agrees qualitatively with the ACRIM trend by increasing the solar cycle minima in 1986, 1996, and 2009 are compared. between the 1986 and 1996 minima and decreasing slightly ACRIM shows a 0.46 W/m increase between 1986 and 1996 between 1996 and 2009. TSI @ 1 AU (W/m ) TSI @ 1 AU (W/m ) Advances in Astronomy 3 The dieff rent methodologies and components of the TSI decreasing trend similar to that in the PMOD composite records used to construct the ACRIM and PMOD compos- (e.g.,[2,15,16, 21–25]).However,the proxydata used by ites cause subtle but important differences between them. these models are derived from observations of the solar The most significant of these, the opposite trends in TSI active regions, sunspots, and faculae, which nearly disappear minima between 1986 and 1996, is caused by their different during solar cycle minima and are therefore poorly suited for approaches to bridging the ACRIM-Gap (1989.5–1991.8): modeling quiet solar brightness variability. Regarding the Nimbus7/ERB data modification imple- (1) The ACRIM composite uses the original overlapping mented by PMOD during the ACRIM-Gap, it is important Nimbus7/ERB results to link ACRIM1 and ACRIM2 results. to stress that Dr. Hoyt, who was the director of the (2) The PMOD has produced several composites (cf.: Nimbus7/ERB mission, disregarded Frohlich ¨ ’s claims from [2, 13, 14, 17, 18]) using different models of the available TSI an experimental perspective (see the supplement lfi es data during the gap. It bases the results during the gap on published in[26]). Inthat occasion Hoyt stated: “Concerning the Nimbus7/ERB data sampling frequency but “conformed” the supposed increase in Nimbus7 sensitivity at the end of to the lower TSI level and negative trend slope of the September 1989 and other matters as proposed by Frohlich’s ERBS/ERBE results, essentially recalibrating and altering the PMOD TSI composite: (1) There is no known physical change trend in the ERB data to agree with the magnitude and trend in the electrically calibrated Nimbus7 radiometer or its of the sparse ERBE results and of some TSI proxy models. electronics that could have caused it to become more sensitive. This approach is followed mostly by Lee III et al. [19] claiming At least neither Lee Kyle nor I could never imagine how such that during the ACRIM-Gap period Nimbus7/ERB sensitivity a thing could happen and no one else has ever come up with increased anomalously. Their proposed evidence supporting a physical theory for the instrument that could cause it to this claim was that the Nimbus7/ERB record diverged from become more sensitive. (2) eTh Nimbus7 radiometer was a simple TSI proxy model based upon the 10.7-cm solar calibrated electrically every 12 days. eTh calibrations before radio ux fl (F10) and the photometric sunspot index (PSI). and after the September shutdown gave no indication of any u Th s, PMOD used overlapping comparisons of ACRIM1 change in the sensitivity of the radiometer. u Th s, when Bob and ACRIM2 with ERBE observations and proxy models Lee of the ERBS team originally claimed there was a change to construct their first composite. Other PMOD composites in Nimbus7 sensitivity, we examined the issue and concluded [17, 18] used different models of the ERBE-ACRIM-Gap there was no internal evidence in the Nimbus7 records to degradation. The result of these various modifications during warrant the correction that he was proposing. Since the result the ACRIM-Gap was that PMOD introduced a downward was a null one, no publication was thought necessary. (3) trend in the Nimbus7/ERB TSI data that decreased results by Thus, Frohlich’s PMOD TSI composite is not consistent with 0.8 to 0.9 W/m (cf. [18, 20]). the internal data or physics of the Nimbus7 cavity radiometer” The PMOD rationale for using models to alter the (https://agupubs.onlinelibrary.wiley.com/action/download- Nimbus7/ERB data was to compensate for the sparsity of the Supplement?doi=10.1029%2F2008GL036307&le=grl2 fi 5417- ERBS/ERBE data and conform their gap results more closely sup-0002-txts01.txt). to the proxy predictions of solar emission line models of The consistent downward trending of the PMOD TSI TSI behavior. In fact, the ERBS/ERBE record is too sparse composite is negatively correlated with the global mean tem- and aeff cted by uncalibrated degradation to provide a useful perature anomaly during 1980–2000. This has been viewed bridge of the gap between the ACRIM1 and ACRIM2 records with favor by those supporting the CO anthropogenic global using only its observational data. warming (CAGW) hypothesis since it would minimize TSI The trending difference between the two composites has variation as a competitive climate change driver to CO , been the subject of a lengthy controversy. ACRIM contends the featured driver of the hypothesis during the period (cf.: the following: [10, 11, 24]). (1) PMOD’s modifications of the published ACRIM and ACRIM composite trending is well correlated with the ERB TSI records are questionable because they are based record of global mean temperature anomaly over the entire on conforming satellite observational data to proxy model range of satellite observations (1980–2018) [12]. The climate predictions rather than an original analysis of the ACRIM, warming hiatus observed since 2000 is inconsistent with CO ERB, and ERBE data [3, 20]. anthropogenic global warming (CAGW) climate models [27, (2) The PMOD trend during 1986 to 1996 is biased 28]. This points to a signicfi ant percentage of the observed downward by scaling ERB results to the rapidly degrading 1980–2000 warmingbeing drivenby TSIvariation[6,7,12].A ERBE results during the ACRIM-Gap using the questionable number of other studies have pointed out that climate change justicfi ation of agreement with some TSI proxy predictions and TSI variability are strongly correlated throughout the first proposed by Lee III et al. [19] (cf.: [3]). Holocene including the recent decades (e.g., [12, 20, 27, 29– (3) PMOD misinterpreted and erroneously corrected 36]). ERB results for an instrument power down event (Sep. 25- The paradigm of positive correlation between Solar Mag- 28, 1989) as an instrument “glitch” and sensitivity change and netic Field Strength (SMFS) and TSI, rfi st established by for a presumed drift (cf.: [13, 20]). ACRIM1observations[1,3,20,37–41],supportsthevalidityof (4) The fabrication and endorsement of the PMOD the upward trend in the ERB results during the ACRIM-Gap and the corresponding decadal upward trend of the ACRIM composite by some might have been influenced by the fact that TSI proxy models popular at the time predicted a TSI composite during solar cycles 21 and 22. 4 Advances in Astronomy The above empirically based studies provide a strong made of 4 points, the statistical error of the merging would be indication that TSI variability resulting from solar magnetic just s/2, where 2 is the root of 4. activity variation is the main driver of the earth’s climate. Dudok de Wit et al. [9] claim that the uncertainty in the TSIrecordsappearstobesolargethatitwould notbepossible Proxy TSI results, derived from the SMFS/TSI paradigm, correlate with the global mean temperature anomaly both to discriminate between the ACRIM and PMOD composites during and prior to the satellite TSI observations [7, 20]. actually discovered by Scafetta twelve years earlier, in 2005 [42]. Scafetta compared ACRIM and PMOD total solar It has been shown that the solar cycle amplitude from 1980 to 1989 and the trending from 1992 to 2002 of a irradiance satellite composites during solar cycles 21-23 and proxy model represented as supporting the PMOD TSI assumed only random uncertainties of the TSI satellite data composite[22]wereactually contradicted by the unmodiefi d sets. The TSI record overlapping comparisons assumed the TSI satellite data in these periods (see Figures 8 and 9 maximum statistical error derived from a point to point comparison. In this way, Scafetta determined the maximum published in [20]). When the proxy model was empirically adjusted to tfi the original TSI data, it conformed much more statistical uncertainty of two simple satellite composites, closely to the multidecadal ACRIM trending than that of which were statistically equivalent to ACRIM and PMOD composites. The evaluated uncertainty was just slightly larger the PMOD. Similar conclusions were implied by alternative magnetic field strength measurements ([20], Figures 7, 10, 11 than those evaluated in Dudok de Wit et al. [9]. It was found and 13). that the secular upward trend of +0.047%/decade between the minima of solar cycles 21-22 and 22-23 presented by the 1.2. Alternative Statistical Composites. More recently, a novel ACRIM satellite composite is statistically equivalent to the -0.009%/decade trend between the same minima presented TSI composite has been constructed using a wavelet trans- form algorithm that simultaneously uses all available TSI by the PMOD composite. However, this happens only if records [9]. This methodology is statistically based, which the merging among the various TSI records is made using very short overlapping intervals, which is what the wavelet means that the differences between the TSI values reported by the various TSI satellite databases are assumed to have methodology by Dudok de Wit et al. [9] does. However, when a solely statistical rather than a physical origin. The authors alloverlapping data areused atonceand onedistinguishes between Nimbus7/ERB and ERB/ERBE, the uncertainty is claim that their proposed composite is “in closer agreement with the trending of the PMOD than the ACRIM or RMIB.” greatly reduced since it scales with the root of the number N of overlapping points between each couple of records: see Yet, herein we show the opposite to be the case. Their novel approach produced average TSI composites that agree more the detailed discussion in Scafetta [6]. However, the optimum closely with the ACRIM TSI composite trending during solar approach is the use of observational analysis to test data versus models as discussed in Scafetta and Willson [20]. cycles 21- 24 [1] than with the PMOD. Composing a TSI database using a solely statistical In the following we provide a detailed analysis of the methodology has a fatal flaw in that it fails to account for the alternative TSI composites recently proposed by Dudok de Wit et al. [9] by taking into consideration the discussion physical limitations of observation, such as degradation of the TSI sensors. Such composites will have uncertainties so containedinScafettaandWillson[20].Itshouldbenotedthat large that they have limited ability to uniquely discrimi- de Wit et al. [9] ignored the arguments presented by Scafetta and Willson [20]. nate between the ACRIM and PMOD TSI composites. The methodology proposed by Dudok de Wit et al. [9] cannot improve our knowledge regarding the TSI trending difference 2. Comparisons of TSI Reconstructions between ACRIM and PMOD. The RMIB composite by Mekaoui and Dewitte [5] used a more simplistic statistical 2.1. Observational Data Based Composites. The ACRIM and model than Dudok de Wit et al. [9] but was afflicted by the PMOD composites shown in Figure 1 display two alter- the same problem, namely, a failure to account for possible native TSI trending patterns during solar cycles 21-24 as observational flaws of the original TSI records. discussed above. The values of the irradiance at the solar Moreover, it is important to clarify that the uncertainty minima are marked. The data are depicted with dieff rent produced by the TSI composites proposed by Dudok de Wit colors to indicate the satellite experiment results used for et al. [9] is further stressed by the fact that a wavelet merging dieff rent composite segments. methodology uses short overlapping periods which poorly The cause of the primary difference in trending between take into account the statistics of the overall records. It is the ACRIM and PMOD during solar cycles 21–23 is shown well known that to cross-calibrate two records one needs to in Figure 2. The results from the ACRIM1, ACRIM2, Nim- compare their average values during their overlapping period. bus7/ERB, ERBS/ERBE TSI experiments and Kitt Peak Solar The statistical error of this procedure scales with the root of Magnetic Field Strength (SMFS) are plotted before, during the number of the overlapping points. For example, if the and after the approximately two-year gap between the end of statistical error associated with a single measure is𝜎 and there the ACRIM1 and beginning of ACRIM 2 experiments. are 100 overlapping points, then the statistical error associated The TSI results and Solar Magnetic Field Strengths are with the merging between two such records would be𝜎 /10, all correlated except for the ACRIM-Gap where the ERBE where 10 is the root of 100. However, by using a wavelet results trend downward while the others trend up. This occurs methodology the statistical error associated with the merging during the increasing phase of solar magnetic activity leading would be signicfi antly larger. For example, if the wavelets are to the peak of solar cycle 22 during 1990–1992. The most likely Advances in Astronomy 5 0.1 0.1 0.1 0.1 ACRIM2 ACRIM1 ACRIM1 ACRIM GAP 0.05 0.05 0.05 0.05 0 0 0 0 −0.05 −0.05 −0.05 −0.05 Slope: -0.000 Slope: +0.022 No Data Slope: -0.010 −0.1 −0.1 −0.1 −0.1 1985 1986 1987 1986 1988 1990 1990 1992 1992 1993 0.1 0.1 0.1 0.1 Nimbus7/ERB 0.05 0.05 0.05 0.05 0 0 0 0 −0.05 −0.05 −0.05 −0.05 Slope: -0.004 Slope: +0.017 Slope: +0.011 Slope: -0.003 −0.1 −0.1 −0.1 −0.1 1985 1986 1987 1986 1988 1990 1990 1992 1992 1993 0.1 0.1 0.1 0.1 ERBS/ERBE 0.05 0.05 0.05 0.05 0 0 0 0 −0.05 −0.05 −0.05 −0.05 Slope: -0.012 Slope: -0.004 Slope: +0.020 Slope: -0.007 −0.1 −0.1 −0.1 −0.1 1985 1986 1987 1986 1988 1990 1990 1992 1992 1993 100 100 100 100 SMF３ 50 50 50 50 0 0 0 0 −50 −50 −50 −50 Slope: -1.180 Slope: +36.425 Slope: +9.109 Slope: -12.777 −100 −100 −100 −100 1986 1988 1990 1990 1992 1992 1993 1985 1986 1987 Figure 2: Comparison of the TSI results from the ACRIM1, Nimbus7/ERB, ERBS/ERBE experiments and the NSO/Kitt Peak Solar Magnetic Field Strength (SMFS) during the solar cycle 21-22 minimum and the upward trend to and through solar cycle 22 maximum. eTh eeff ct of degradation for the ERBE sensors during the 1989–1992 maximum is seen in the downward trend of its results relative to the trends of the ERB results and the SMFS that is anticorrelated with the SMFS–TSI paradigm. explanation is that the ERBE solar TSI detectors degraded experiment. The ratios of the observations by sensor C from “bleaching” of their absorptive sensor coatings by the (primary reference sensor) to sensors B (secondary reference higher levels of short wavelength radiation and particle ux fl sensor) and A (continuously observing sensor) are shown. that occur during peaks of solar activity maxima. This eeff ct The reference sensors are exposed to the sun infrequently and had been observed in the ACRIM1 experiment during the the constancy of the C/B ratio is a measure of the precision high but descending SMFS phase of solar cycle 21 from of the calibration of sensor A’s degradation. The C/A ratio its peak and was self-calibrated precisely using ACRIM1’s changes rapidly during the initial exposure of the sensor multisensor approach [43]. to the solar maximum levels of solar flux before saturating Sensor degradation caused by mission exposure to high and settling into a more slowly varying, more linear slope SMFS solar ux fl es has been observed in the performances throughout the mission. of all satellite TSI experiments to date. Rapid detector The ERB experiment exhibited rapid sensor degradation degradation occurs during exposure to the enhanced solar during the peak of solar cycle 21 but responded in corre- short wavelengths and ionized particulate during peak levels lation with the SMFS and, hence, the SMFS-TSI paradigm of solar activity and reaches a saturation level, an asymp- during the gap. This would be expected from the ACRIM1 totic limit or a more slowly varying, more linear rate of degradation experience, since its initial sensor “saturation” degradation thereaer ft . The timing and shape of the degra- degradation had occurred during the peak of solar cycle 21 dation curve depends on the details of the solar sensor and its subsequent rate of degradation would be slower. On surfaces, geometries, and exposure rates [3]. Characteristic the contrary, a rapid degradation of the ERBE observations sensor degradation can be seen in Figure 3 for the ACRIM3 during the ACRIM-Gap was likely caused by the highly % Variation % Variation % Variation % Variation 6 Advances in Astronomy ACRIMSAT/ACRIM3 Degradation Calibration 600 Sensor A: Polynomial Fit Order: 6 Sensor B: Polynomial Fit Order: 6 −200 2000 2002 2004 2006 2008 2010 2012 year Figure 3: Degradation of the ACRIMSAT/ACRIM3 sensors over the mission. TSI unmodified 1980 1984 1988 1992 1996 2000 2004 2008 2012 2016 year TSI minimum in 1986: 1360.32 W/m (a) TSI modified 1980 1984 1988 1992 1996 2000 2004 2008 2012 2016 year TSI minimum in 1986: 1360.52 W/m (b) Figure 4: TSI composites proposed by Dudok de Wit et al. [9]. (a) Using the original published TSI satellite data. (b) Using the TSI satellite data modified by PMOD. Daily values (blue), monthly mean (black). energetic solar maximum ux fl es it experienced for the rfi st records, while in (b) the PMOD-modified TSI records are time during the gap since it was launched during the initial used. In both cases trends qualitatively similar to those of the rising phase of SMFS for solar cycle 22. ACRIM composite are found among the TSI minima in 1986, 1996, and 2009 (see Table 1). Both the original and modified 2.2. Statistically Derived Composites. Figure 4 shows the two TSI composites show an upward trend during 1980–2000 and downward trend thereafter similar to ACRIM trend- TSI composites proposed by Dudok de Wit et al. [9]. In (a) the compositeis madeusing theoriginal unmodiefi d TSIsatellite ing. 2 2 Sensor C Ratios (ppm) TSI @ 1 AU (W/m ) TSI @ 1 AU (W/m ) Advances in Astronomy 7 SATIRE-T2 1980 1984 1988 1992 1996 2000 2004 2008 2012 2016 year TSI minimum in 1986: 1365.63 W/m (a) SATIRE-S 1980 1984 1988 1992 1996 2000 2004 2008 2012 2016 year TSI minimum in 1986: 1360.98 W/m (b) Figure 5: (a) SATIRE-T2 TSI proxy reconstruction [15]. (b) SATIRE-S TSI proxy reconstruction [16]. Daily values (blue), monthly mean (black). The composite in Figure 4(a) shows a high degree of simi- composites agree better with PMOD. However, this conclu- larity to the ACRIM composite. The composite in Figure 4(b) sion was not based on analysis but on a visual inspection of shows a smaller upward trend between the minima of 1986 their Figure 3. Here these authors appear to have misinter- and 1996, followed by a downward trend to the minimum preted the fact that ACRIM and PMOD are characterized by in 2009, making it positively correlated with the ACRIM slightly different scales because ACRIM3 and VIRGO (the composite during this period but with smaller amplitudes. bases of the two composites) were independently recalibrated Both composites in Figure 4 are negatively correlated with the against the TSI cryogenic radiometer facility of the Labo- PMOD composite trend between the 1986 and 1996 minima. ratory for Atmospheric and Space Physics (LASP) and it is Figure 5 depicts two additional, recently developed TSI unclear whether later VIRGO was empirically recalibrated proxy models: (a) the SATIRE-T2 TSI reconstruction [15] and to agree better with the TIM/SORCE scale. In fact, Frohlich ¨ (b) the SATIRE-S TSI reconstruction [16]. In both models [44] claimed that the new absolute value of VIRGO record there is a consistent downward trend among TSI minima was 0.86 W/m lower than TIM/SORCE during the period in 1986, 1996, and 2009. During these three solar cycle 2008/09/20–2009/05/05. us, Th the better agreement between minima the TSI values are as shown in Table 1 for SATIRE- PMOD and the TSI composites proposed by Dudok de Wit T2 and SATIRE-S. The continuous downward trending makes et al. [9] refers to their absolute scales which might have been SATIRE-T2 and SATIRE-S incompatible not only with the coincidental. However, such a slight difference in TSI scales ACRIM composite, but also with both TSI models proposed is irrelevant because the important issue is how well the TSI by Dudok de Wit et al. [9]. decadal trends agree among the various records. This analysis In Figure 6 and Table 2 we analyze and compare the is proposed below. deviation of the ACRIM, PMOD, and SATIRE-S model from Figure 6(a) depicts monthly time scale functions of the the two TSI composites proposed by Dudok de Wit et al. difference between the ACRIM TSI composite and the [9]. The purpose of this analysis is to determine which of the unmodified and PMOD-modified TSI by Dudok de Wit et al. former three records agrees better with the latter composites. [9] from 1980 to 2013. Figures 6(b) and 6(c) depict the same Dudok de Wit et al. [9] claim that their proposed TSI but using the PMOD TSI composite and the SATIRE-S TSI TSI @ 1 AU (W/m ) TSI @ 1 AU (W/m ) 8 Advances in Astronomy Table 2: Mean and standard deviation of the curves depicted in Figure 4 in the reported time intervals. ACRIM PMOD SATIRE-S 2 2 2 (W/m ) (W/m ) (W/m ) Original Unmodified TSI Results 1980-2013 0.38± 0.13 −0.01± 0.24 0.21± 0.31 1980-1990 0.40± 0.15 0.31± 0.18 0.01± 0.10 1992-2013 0.37± 0.12 −0.16± 0.05 0.01± 0.10 PMOD Modified TSI Results 1980-2013 0.33± 0.19 −0.07± 0.12 0.15± 0.21 1980-1990 0.16± 0.16 0.07± 0.06 0.38± 0.14 1992-2013 0.38± 0.13 −0.15± 0.04 0.02± 0.11 0.8 0.6 0.4 0.2 −0.2 1980 1985 1990 1995 2000 2005 2010 year ACRIM - TSI modified ACRIM - TSI unmodified (a) 0.6 0.4 0.2 −0.2 −0.4 1980 1985 1990 1995 2000 2005 2010 year PMOD - TSI modified PMOD - TSI unmodified (b) 0.8 0.6 0.4 0.2 −0.2 1980 1985 1990 1995 2000 2005 2010 year SATIRE S - TSI modified SATIRE S - TSI unmodified (c) Figure 6: (a) Variation between the ACRIM TSI composite and the unmodified and modified TSI by Dudok de Wit et al. [9] from 1980 to 2013. (b) and (c) The same using the PMOD TSI composite and the SATIRE TSI proxy model. Plots are based on monthly means. 2 2 2 ７/Ｇ ７/Ｇ ７/Ｇ Advances in Astronomy 9 Table 3: e Th TSI composite data. ACRIM http://acrim.com/RESULTS/data/composite/acrim composite 131130 hdr.txt PMOD p ft ://ftp.pmodwrc.ch/pub/data/irradiance/virgo/TSI/virgo tsi d v6 005 1702.dat SORCE https://spot.colorado.edu/∼koppg/TSI/iTh erry TSI composite.txt SATIRE-S http://www2.mps.mpg.de/projects/sun-climate/data/SATIRE-T SATIRE-S TSI 1850 20160802.txt SATIRE-T2 http://www2.mps.mpg.de/projects/sun-climate/data/TSI SATIRE-T2 1878-2008.dat model, respectively. Table 2 reports the mean values in the activity cycle-to-cycle trending of the ACRIM and PMOD intervals 1980-2013, 1980-1990, and 1992-2013. composites. ACRIM contends that the original data from satellite measurements, as processed and published by the The level of agreement between two records is measured original science teams, are the best representation of the by the standard deviation 𝜎 of their mutual difference on experimental results and demonstrate that the TSI increased a given time interval: smaller𝜎 means a better agreement from 1980 to 2000 and decreased aer ft wards. PMOD modifies between the two chosen records. This choice makes the slight the original science teams’ satellite results using proxy models different absolute scales among the TSI composites irrelevant. causing the TSI to gradually decrease since 1980. Resolving The relative standard deviation of the deviation functions this controversy has important implications for understand- for the periods shown in Table 2 indicates the ACRIM ing climate change and assessing the usefulness of TSI proxy composite agreement with the unmodiefi d TSI composite models. is nearly identical to the PMOD composite agreement with 2 We have shown that the average value of the statistical the modified TSI composite: 𝜎 = 0.13 W/m versus𝜎 =0.12 TSI composite models proposed by Dudok de Wit et al. W/m , respectively. However, during the 1980-2003 period, [9] actually demonstrates better agreement with the ACRIM the ACRIM composite agreement with the modified TSI composite than with the PMOD from 1980 to 2013. Their large composite is 25% superior to that of the PMOD with the error bars are irrelevant because it is the TSI mean values on unmodified TSI composite: 𝜎 = 0.19 W/m versus𝜎 = 0.24 2 scales of 1-year or larger which need to be taken into account. W/m , respectively. The variations of the SATIRE-S model When this is done their error bars are reduced by a factor of and both Dudok de Wit et al. [9] composites are signicfi antly 20 or more. This is in direct disagreement with the Dudok 2 2 larger:𝜎 = 0.31 W/m versus𝜎 = 0.21 W/m , respectively. de Witetal.’s assessment that their composite mostclosely Comparing the intervals 1980-1990 and 1992-2003 using agrees with the PMOD composite. We contend that the Table 2, ACRIM is essentially balanced with the unmodified Dudok de Wit et al.’s conclusion was not based on technical TSI composite because the two mean values of the difference arguments but on a qualitative impression derived from their are compatible (Figure 6(a), blue curve): 0.40± 0.15 W/m Figure 3 where a larger divergence of the ACRIM composite and 0.37± 0.12 W/m , respectively. Conversely, PMOD is is observed. This conclusion is incorrect, however, because not balanced with the modified TSI composite because the they failed to recognize that the larger ACRIM divergence two mean values of the difference are incompatible, showing is caused by ACRIM having a larger mean value than a clear downward trend (Figure 6(b), red curve): 0.07 ± PMOD because its absolute scale was based on the ACRIM3 2 2 0.06 W/m and -0.15± 0.04 W/m . Therefore PMOD would measurements. appear to be erroneously composed. The large divergence of the SATIRE TSI proxy models Regarding the large error bars reported for the TSI suggests they are inadequate to reproduce the cycle-by-cycle composites proposed by Dudok de Wit et al. [9], it is decadal TSI trending with useful precision, as discussed in a important to stress that they are nearly irrelevant for the previous paper by Scafetta and Willson [20]. above discussion. In fact, we have compared means covering It is important to consider whether the satellite records 1-year and longer periods. When the means are considered, require corrections not made by the original experiment the original statistical error reported by these authors, which teams. We label the second TSI composite proposed by refers to the single daily measure, needs to be reduced at Dudok de Wit et al. [9] as “PMOD modified” whereas they least by a factor of about 20 (the root of 365 is about 19). label it “corrected”. The “corrected” label is misleading since That is, because their largest reported error is less than 0.7 the modifications proposed by Fr o¨hlich discussed above are W/m , the relative annual and multiannual means would be proxy model based and have not been validated by an in- aec ff ted by an error equal to or less than about 0.035 W/m , depth reanalysis of the satellite experiment data. In particular, which are significantly smaller than the observed mean value regarding the claims that Nimbus7/ERB sensors drastically differences reported in the Tables 1 and 2. The TSI composite increased their sensitivity at the end of September 1989, Dr. data are available at the websites listed in Table 3. Hoyt, the scientist responsible for the ERB instrument and data processing, examined those claims from an experimen- tal point of view and disregarded them ([26], supplement). 3. Discussion The dangers of utilizing ex-post-facto corrections by those Today there exists general agreement among various science who did not participate in the original science teams of teams that the mean TSI during solar cycle 23 is near 1361 satellite experiments are that(1) erroneous interpretations of W/m but differences have persisted about the decadal solar the data can occur because of a lack of detailed knowledge of 10 Advances in Astronomy the experiment and(2) unwarranted manipulation of the data by their sensors. The latter deficiencies are physical rather can bemadebased on adesire tosupport a particular solar than statistical and therefore cannot be addressed by Bayesian model or some other nonempirical bias. We contend that the statistics as in the approach proposed by Dudok de Wit et al. [9]. PMOD TSI composite construction is compromised in both these ways. The difference between Nimbus7/ERB and ERBS/ERBE Analysis has disproved the validity of most of Frohlich ¨ ’s during the ACRIM-Gap is too large to be due to statistical modifications to the satellite TSI records published by the fluctuation and so at least one of the two records erroneously original ACRIM and Nimbus7/ERB science teams he used in represents the TSI variation trends during the ACRIM-Gap. constructing the PMOD composite [20]. The rfi st and most In such a situation it is required to determine which of important one for trending was Frohlich ¨ ’s modification of the two records is the most reliable (compare the various arguments proposed in [3, 13, 18, 20]). Ignoring such a ERB results during the ACRIM-Gap by -0.47 W/m ,based fundamental issue has only the consequence of producing a on a misinterpretation of a three-day ERB instrument power TSI composite with an anomalously large uncertainty. This cycle event. Here Frohlich ¨ corrected for what we now know is clearly demonstrated by the central panel of Figure 3 in was a nonexistent “step function increase” of instrument Dudok deWit et al.[9]. Thestandard deviation error oftheir sensitivity ([20], Figure 5). A second important erroneous composites reaches the value of ± 0.45 W/m during the modification derives from Fr ohlich ¨ ’s claim that the TSI 1980-1989 ACRIM1 interval while during thesameperiod the instrumental sensitivity of Nimbus7/ERB gradually increased ACRIM composite has on average a precision of less than± 0.1 during theACRIM-Gap, inanapparent eoff rt tojustify the relative decrease in the ERBE results ([20], Figure 4). W/m . Such a large uncertainty appears to make the Dudok These modicfi ations are not supportable by the original TSI de Witetal. [9]TSIcomposite inclusive of both ACRIMand experiment results and are responsible for the most important PMOD TSI composites and, therefore, it is unable to provide cycle-by-cycle differences between the ACRIM and PMOD any insight on, or solution to, the ACRIM-PMOD contention. TSI composites: the 1986 to 1996 trend divergence. The In any case, as explained above, any comparison must involve analysis and TSI composite of Dudok de Wit et al. [9] did some moving average curve of the data whose statistical error not consider the PMOD “correction” errors documented in will be scaled down with the root of the smoothing algorithm our 2014 paper [20] which negates the usefulness of their order. results. The statistical issue of the variability of TSI composites The use of unverified modified data has fundamentally resulting from the choice of the Nimbus7/ERB or ERBS/ flawed the PMOD TSI satellite composite construction. Com- ERBE during the ACRIM-Gap was discussed in Scafetta posite TSI time series would have greater scientific credibility [6]. The proposed composites were built in such a way to if the most afl wed records, such as the Nimbus7/ERB before approximately force a merging continuity among the various 1980 (cf. [20]) or the ERBE data during the ACRIM-Gap [3], TSI records based on a 91-day smooth curve. The com- were ignored. This is the plausibility argument used in Table 2 posites were made using ACRIM1, ACRIM2,and ACRIM3 to limit our statistical analysis to the period 1980-2013. while the ACRIM-Gap was bridged using (A) the unaltered Nimbus7/ERB record or (B) the Nimbus7/ERB altered in There is another important issue regarding the appropri- such a way to exactly reproduce the ERBS/ERBE trending ateness of the algorithm proposed by Dudok de Wit et al. during the ACRIM-Gap. The two alternative composites [9]. It treats all TSI records as physically reliable although a provide the maximum range of uncertainty related to the statistical instrument weighting assumption was taken into availableTSIdatabaseasproduced by thedivergencebetween account. This methodology would only be appropriate when Nimbus7/ERB and ERBS/ERBE during the ACRIM-Gap. processing stationary TSI records from stable experiments whose results differ from each other only because of statistical Figure 7 shows these two composites updated to 2018 by errors of measure. extending the most recent ACRIM3 data with the VIRGO record aeft r 2013 and then with SORCE/TIM record. Note In general, modifying high quality records with those of that VIRGO and TIM are quite similar aer ft 2013, but the lesser quality will not provide the most accurate represen- SORCE/TIM record suffers of a serious gap lasting several tation of the data in particular when the low quality of a months in 2013 and 2014 caused by spacecraft battery prob- dataset has a physical rather than a statistical origin. This is lems. certainly a concern with the TSI satellite databases. ACRIM These composites show a slight decrease between the TSI 1, 2 & 3 made up to 720 30-second averaged, self-calibrated, minima in 1996 and 2009 as do the ACRIM and PMOD. shuttered measurements per day [3]. Nimbus7/ERB observed However, their variation between the 1986 and 1996 TSI min- for a few minutes during each of an average of 14 orbits ima depend on the specific record used to bridge ACRIM1 perday,three days out ofevery four, mostofits lifetime and ACRIM2 during the ACRIM-Gap period. As Table 1 [45]. ERBS/ERBE was limited to one shuttered observation shows, this variation varies between +0.67± 0.1 W/m (using on an average of every 14 days [19]. Moreover, the quality of Nimbus7/ERB) and -0.11± 0.1 W/m (using ERBS/ERBE). the ERB and ERBE observations was further constrained by (1) a lack of degradation self-calibration capability and (2) a Since the discrepancy between the two results is 0.78 W/m lack of independent solar pointing in which measurements which is significantly larger than their statistical error, then, were made while the sun moved through their fields of view, during the ACRIM-Gap, at least either Nimbus7/ERB or degrading knowledge of the average cavity absorptance of TSI ERBS/ERBE is proven to be physically afl wed. us, Th it is Advances in Astronomy 11 1980 1984 1988 1992 1996 2000 2004 2008 2012 2016 2020 year minima in 1986: 1360.28 W/m (a) 1980 1984 1988 1992 1996 2000 2004 2008 2012 2016 2020 year minima in 1986: 1361.06 W/m (b) Figure 7: Updates of the TSI composites proposed in Willson and Mordvinov [3], Scafetta [6], and Willson [7]. (a) Unaltered Nimbus7/ERB data are used during the ACRIM-Gap; (b) Nimbus7/ERB data are altered to agree with the ERBS/ERBE trending during the same period. Data from Nimbus7/ERB (brown), ACRIM1 (green), ACRIM2 (cyan), ACRIM3 (orange), VIRGO (yellow), and TIM (blue). inappropriate to adopt solely a statistical methodology using The downward trending of PMOD between 1986 and 1996 both Nimbus7/ERB and ERBS/ERBE results as proposed by would be acceptable only if it were experimentally demon- strated that ERBS/ERBE trending during the ACRIM-Gap RMIB [4, 8] and more recently by Dudok de Wit et al. [9]. was highly accurate. However, as Willson and Mordvinov [3] If the physical issue is not solved first, it is only possible to noted, this scenario would be experimentally unlikely since conclude that between 1986 and 1996 TSI varied between the the ERBE sensor degraded significantly during the ACRIM- two above estimates. Gap as its sensor first experienced the enhanced short The full maximum range of possible TSI composites sug- 2 wavelength solar radiation which is known to excessively gests that the TSI minimum in 1996 was about 0.3± 0.4 W/m degrade the coatings of TSI sensors. Moreover, Scafetta and higher than that in 1986. u Th s, once all available TSI records Willson ([20], Figure 5B) showed that the Solar Magnetic are used, the ACRIM upward 1986-1996 trending (0.46± 0.02 Field Strength increased during the ACRIM-Gap. This fact W/m ) is statistically favored above the downward trending clearly supports the greater reliability of the Nimbus7/ERB of PMOD (-0.05 ± 0.02 W/m )even if the ACRIM-Gap record showing upward trending between 1989 and 1991 dur- Nimbus7/ERB increased its sensitivity for some amount, e.g., ing the ACRIM-Gap further emphasizing the ERBS/ERBE for about 0.2 W/m . The latter value falls within the observed downward trend during the same period: see Figure 2. divergence between Nimbus7/ERB and ACRIM1 between 1981 and 1989 on an annual time scale ([6], Figure 3), which is 4. Conclusion likely due to Nimbus7/ERB’s lack of solar pointing and sensor degradation self-calibration as well as other instrumental The Dudok de Wit et al. [9] approach failed to make the best instabilities. Note that the measured mean range increase of use of the satellite TSI database by not including the quality TSI between 1986 and 1996 (0.38 ± 0.41 W/m )isnearly and sampling rates of each experiment in their evaluation. identical to thatobtained by Dudok de Wit etal. [9] when Moreover, the different trending and sampling rates of ERB the original TSI satellite database is used (0.34± 0.05 W/m ). and ERBE records during the ACRIM-Gap were not just 2 2 TSI @ 1 AU (W/m ) TSI @ 1 AU (W/m ) 12 Advances in Astronomy statistical but physical. Therefore, it cannot be properly On the contrary, a TSI increase between 1986 and 1996 would handled using data-driven estimates of the uncertainties, as be supported by the following: in the approach of Dudok deWit et al.[9].More precise (1) The solar cycle length model (e.g., [46–48]) which results would require a detailed analysis of the local trends predicts that short solar cycles correlate with with a preference for the higher quality records, as proposed increased TSI (in fact, solar cycle 22 (1986-1996) in Scafetta [6]. Because of known uncorrected degradation was only 9.9-years long and was shorter than both issues, it would be preferable to ignore ERB results before 1980 solar cycle 21 (1976-1986, 10.5 year) and solar cycle 23 and ERBE results during and before the ACRIM-Gap. Failure (1996-2008, 12.3 year). to take into account the detailed physical characteristics of the various data sets will only have the effect of considerably (2) A model of solar variability driven by planetary tidal increasing the uncertainty of a TSI composite time series. harmonics [49, 50]. Therefore, we contend that using a purely statistical (3) The global surface temperature of the Earth increased methodology to compose TSI records that could contain from 1970 to 2000 and remained nearly stable from a physically unreliable one is improper. Such an approach 2000 and 2018. This pattern is not reproduced by neither produces a more authentic composite nor improves CO AGW climate models but correlates with a TSI our knowledge regarding a given phenomenon: it can only evolution with the trending characteristics of the produce a composite aeff cted by an anomalously large uncer- ACRIM TSI composite as explained in Scafetta [6, 12, tainty that encloses all possibilities. 27] and Willson [7]. Improvement of the physical knowledge of TSI behav- ior since 1978 requires the determination of which of the Nimbus7/ERB and ERB/ERBE experiment results were least Data Availability defective during the ACRIM-Gap (1989.5-1991.8). Then, our All data can be downloaded from the websites listed in scientific knowledge could be improved by excluding the Table 3. more afl wedrecordfrom the composite. This was the logic applied by the ACRIM team. In point of fact PMOD failed to do this, instead selecting the ERBE results that were known Conflicts of Interest to be degraded and sparse, because that made the solar cycle 21–22 trend agrees with TSI proxy models and the CAGW The authors do not have any conflicts of interest to declare. explanation of CO as the driver of the global warming trend of thelate20thcentury. Acknowledgments We note that the considerable evidence discussed by Scafetta and Willson [20] which clearly favors the TSI The National Aeronautics and Space Administration sup- composites proposed by Willson and Mordvinov [3], Scafetta ported Richard C. Willson under contracts 1405003 at [6] and Willson [7] is not challenged by the statistical the Jet Propulsion Laboratory and ROSES 2016 Contract approach of Dudok deWit et al.[9].The large errors of NNH15C0020. their composites are an artifact of their adoption of a wavelet merging methodology and of their simultaneous adoption of References the ERB and ERBS records during the ACRIM-Gap when they diverge significantly. In any case, such large uncertainty [1] R.C.Willson,“Total solar irradiance trend duringsolar cycles is significantly attenuated by a factor of 20 or more when 21 and 22,” Science, vol.277, no.5334,pp.1963–1965, 1997. annual or longer averages are adopted. This smoothing makes [2] C. Frohlich ¨ and J. 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