How constant is the “solar constant?”

How constant is the “solar constant?”

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By Andy May

The IPCC lowered their estimate of the impact of solar variability on the Earth’s climate from the already low value of 0.12 W/m2 (Watts per square-meter) given in their fourth report (AR4), to a still lower value of 0.05 W/m2 in the 2013 fifth report (AR5), the new value is illustrated in Figure 1. These are long term values, estimated for the 261-year period 1750-2011 and they apply to the “baseline” of the Schwabe ~11-year solar (or sunspot) cycle, which we will simply call the “solar cycle” in this post. The baseline of the solar cycle is the issue since the peaks are known to vary. The Sun’s output (total solar irradiance or “TSI”) is known to vary at all time scales (Kopp 2016), the question is by how much. The magnitude of short-term changes, less than 11 years, in solar output are known relatively accurately, to better than ±0.1 W/m2. But, the magnitude of solar variability over longer periods of time is poorly understood. Yet, small changes in solar output over long periods of time can affect the Earth’s climate in significant ways (Eddy 1976) and (Eddy 2009). In John Eddy’s classic 1976 paper on the Maunder Minimum, he writes:

“The reality of the Maunder Minimum and its implications of basic solar change may be but one more defeat in our long and losing battle to keep the sun perfect, or, if not perfect, constant, and if inconstant, regular. Why we think the sun should be any of these when other stars are not is more a question for social than for physical science.” (Eddy 1976)

Using recent satellite data, it has been determined that the Sun puts out ~1361 W/m2, measured at 1AU, the average distance of the Earth’s orbit from the Sun. Half of the Earth’s surface is always in the dark and the sunlight hits most latitudes at an angle, so to get the average absorbed or reflected we divide by 4, to get ~340 W/m2. Then after subtracting the energy reflected by the atmosphere and the surface, we find the average radiation absorbed is about 240 W/m2.

The Earth warms when more energy is added to the climate system, the added energy is called a climate “forcing” by the IPCC. The total anthropogenic forcing over the industrial era (1750 to 2011, 261 years), according to the IPCC (IPCC 2013, 661), is about 2.3 (1.1-3.3) W/m2 or about 1.0% of 240. Also, on page 661, the IPCC estimates the total forcing due to greenhouse gases in 2011 to be 2.83 (2.54-3.12) W/m2. The forcing for CO2 alone is 1.82 (1.63-2.01) W/m2. They further estimate that the growth rate of CO2 caused forcing, from 2001 to 2011 is 0.27 W/m2 or 0.027 W/m2/year using the same methods. These are a lot of numbers, so we’ve summarized them in Table 1 below.

IPCC Anthropogenic Forcing Estimates (AR5, page 661)

Time period Cause Years Total Forcing Forcing per year Percent of 240
      W/m2 W/m2/yr W/m2
1750-2011 Humans

261

2.3

0.0088

0.96%

1750-2011 CO2

261

1.82

0.0070

0.76%

2001-2011 CO2

10

0.27

0.0270

0.11%

Table 1. Anthropogenic forcing as estimated by (IPCC 2013, 661).

The IPCC’s assumed list of radiative forcing agents and their total forcing from 1750 to 2011 are shown in Figure 1. Next to the IPCC table, I’ve shown the Central England temperature (CET) record, which is the only complete instrumental temperature record that goes back that far in time. The CET is mostly flat until the end of the Little Ice Age and then, after a dip around the time of the Krakatoa volcanic eruption in 1883, it shows warming to modern times.

Figure 1. On the left is the IPCC list of radiative forcing agents from page 697 of AR5 WG1 (IPCC 2013). Notice they assume that solar irradiance is very small, in this post we examine this assumption. On the right is the Central England temperature record (CET), the only instrumental temperature record that goes back to 1750. The CET data source is the UK MET office.

If the Sun were to supply all 2.3 W/m2 of the forcing described in Figure 1, but as a steady change over 261 years, the change each year would have to average ~0.0088 W/m2/year. So, assuming constant albedo (reflectivity) the change in solar output would have to be 4×0.0088 on average or 0.035 W/m2/year. As noted above, we multiply by four because the Earth is a sphere and half of it is in the dark. This is a total increase in solar output of 9.2 W/m2 over 261 years (1750-2011), a change of 0.7%. Some might say we should start at 1951, since that is the agreed date when CO2 emissions became significant (IPCC 2013, 698-700). But, I started at 1750 to cover the “industrial era” as defined by the IPCC, the choice is somewhat arbitrary as long as we go back far enough to precede any significant human CO2 emissions. The year 1750 is also useful because it is near the end of the worst part of the Little Ice Age, the coldest period in the last 11,700 years (the Holocene). Do we know the solar output, over the past 261 years, accurately enough to say the Sun could not have changed 9.2 W/m2 or some large portion that amount? In other words, is the IPCC assumption that solar variability has a very small influence on climate valid?

How accurate are our measurements of Solar output?

The solar cycle variation of TSI is about 1.5 W/m2 or 0.1% from peak to trough (~5-7 years) or 0.25 W/m2/year and 0.02%/year. These changes are much larger than the longer-term changes of 0.0088 W/m2/year computed above. So, simply because we can see the ~11-year solar cycle does not necessarily mean we can see a longer-term trend that could have caused current warming. Satellite TSI measurement instruments deteriorate under the intense sunlight they measure and they lose accuracy with time. We have satellite measurements of varying quality over much of the last four solar cycles. The raw data are plotted in Figure 2 and the critical ACRIM gap is highlighted in yellow. Because the Nimbus7/ERB (Earth Radiation Budget) and ERBS/ERBE instruments are much less precise and accurate than the ACRIM (Active Cavity Radiometer Irradiance Monitor) instruments, filling this gap is the most important problem in making a long-term TSI composite (Scafetta and Willson 2014).

Figure 2. Raw satellite total solar irradiance (TSI) measurements. The ACRIM gap is identified in yellow. The trend of the NIMBUS7/ERB instrument in the ACRIM gap is emphasized with a red line. Source: (Soon, Connolly and Connolly 2015).

As Figure 2 makes clear, calibration problems have caused the satellites to measure widely different values of TSI, the solar cycle minima range from 1371 W/m2 to 1360.5 W/m2. Currently, the correct minimum is thought to be around 1360.5, but just a few years ago it was thought to be ~1364 W/m2 (Haigh 2011). After calibration corrections have been applied, each satellite produces an internally consistent record, but the records are not consistent with one another and no single record covers two or more complete solar cycles. This makes the determination of long-term trends problematic.

There have been three serious attempts to build single composite TSI records from the raw data displayed in Figure 1. They are shown in Figure 3.

Figure 3. Three common composites of the data shown in Figure 1. The ACRIM gap is identified in yellow. The PMOD composite is by P.M.O.D. (Frohlich 2006) also the source of the figure (pmodwrc.ch), the ACRIM composite is from the ACRIM team (Scafetta and Willson 2014), the IRMB composite is from the Royal Meteorological Institute of Belgium (Dewitte, et al. 2004).

The ACRIM and IRMB composites show an increasing trend during the ACRIM gap and the PMOD composite shows a declining trend. This figure was made several years ago by the PMOD team when the baseline of the TSI trend was more uncertain, so the IRMB and PMOD composites are shown with a ~1365 W/m2 base and the ACRIM composite is shown with a ~1360.5 W/m2 baseline, which is currently preferred. The important point, shown in Figure 3, is that the long-term PMOD trend is down, the ACRIM trend is up to the cycle 22-23 minimum (~1996) and then down to the cycle 23-24 minimum (~2009), and the IRMB trend is up. Thus, the direction of the long-term trend is unclear. Figure 4 shows the details of the PMOD and ACRIM trends, this is from (Scafetta and Willson 2014).

Figure 4. The ACRIM and PMOD composites showing opposing slopes in the solar minima and in the ACRIM gap, highlighted in yellow. Source: (Scafetta and Willson 2014).

In Figure 4 we see the differences more clearly. The ACRIM TSI trend from the solar cycle low between 21 and 22 to 22-23 is +0.5 W/m2 in 10 years or 0.05 W/m2 per year, then the trend is down to the cycle 23-24 minimum. The PMOD composite is steadily down about 0.14 W/m2 in 22 years (1987-2009) or 0.006 W/m2/year. The difference in these trends is 0.056 W/m2/year. If this is extrapolated linearly for 261 years, the difference is 14.6 W/m2, more than the 9.2 W/m2 required to cause the recent warming.

NOAA believe the SORCE satellite TIM (Total Irradiance Monitor) instrument is accurate and accepts the ~1360.5 TSI baseline it establishes. They have normalized the three composites discussed above to this baseline. After normalizing, they averaged the three composites to produce the record shown in Figure 5. The SORCE/TIM record starts in February 2003, so the average after that is replaced by the SORCE/TIM record. Averaging three records with differing trends creates a meaningless trend, so this TSI record is of little use for our purposes, but they also construct an uncertainty function (something notably missing for the individual composites) using the differences between the composites and the estimated instrument error. The NOAA composite is shown in Figure 5 and their computed uncertainty is shown in Figure 6, both figures show the raw data and a 100-day running average.

Figure 5. The NOAA/NCEI composite. It is the average of the three composites shown above, with the data after Feb. 2003 replaced by the SORCE/TIM data The ACRIM gap is indicated in yellow. The low points between solar cycles 21-23 and 22-23 are marked on the plot. Data source: NOAA/NCEI.

In the NOAA composite (Figure 5) the increase in the solar minimum value from the solar cycle 21-22 minimum to the solar cycle 22-23 minimum appears, just as it does in the IRMB and the ACRIM composites. The solar cycle 23-24 minimum drops down to the level of the 21-22 minimum, but this is a forgone conclusion since the earlier records are normalized to this value in the SORCE/TIM record. In fact, given that everything is normalized to TIM, we only have two points in this whole composite that we can try and use to determine a long-term trend, the 21-22 minimum and the 22-23 minimum, the peaks cannot be used since they are known to be variable (Kopp 2016). Thus, we don’t know very much.

Figure 6. NOAA TSI uncertainty, computed from the difference between the ACRIM and PMOD values, after normalization to the SORCE/TIM values, plus an assumed 0.5 W/m2 uncertainty in the SORCE/TIM absolute scale until the TIM data and uncertainties are available after Feb. 2003. A rapid increase in the computed TIM error occurs late in 2012. The ACRIM gap is highlighted in yellow. The low points between solar cycles 21-23 and 22-23 are marked on the plot. Data source: NOAA/NCEI.

Greg Kopp has calculated that in order to observe a long-term change in solar output of 1.4 W/m2 per century, or about 3.5 W/m2 since 1750, which is 38% of the total 9.2 W/m2 required to explain modern warming; non-overlapping instruments would need an accuracy of ±0.136 W/m2 and 10 years of measurements to even see the change (Kopp 2016). As Figure 6 makes clear, the SORCE/TIM instrument, the best instrument in orbit today, has an uncertainty at least 3.5 times the required level to detect such a trend and it decayed rapidly after 10 years.

Discussion

The estimated uncertainty in the NOAA satellite composite is well over 0.5 W/m2 and it increases as a function of time before 2003. The three original composites come with no estimated uncertainty, their accuracy, or lack of it, is unknown. NOAA simply used the differences in the composites to estimate the uncertainty. This makes estimating a trend from the satellite data problematic (Haigh 2011). To look at the longer term, we must rely on solar proxies, such as sunspot counts and proxies of the strength of the solar magnetic field. The relationship of the proxies to solar output is not known and can only be estimated by correlating the proxies to satellite data. Professor Joanna Haigh summarizes this in the following way:

“To assess the potential influence of the Sun on the climate on longer timescales it is necessary to know TSI further back into the past than is available from the satellite data … The proxy indicators of solar variability discussed above have therefore been used to produce an estimate of its temporal variation over the past centuries. There are several different approaches taken to ‘reconstructing’ the TSI, all employing a substantial degree of empiricism and in all of which the proxy data (such as sunspot number) are calibrated against the recent satellite TSI measurements, despite the problems with this data outlined above.” (Haigh 2011)

The uncertainty in these proxy estimates cannot be quantified, but it must be greater than the potential error (uncertainty) in the satellite data, which varies from 0.48 W/m2 to over 0.8 W/m2. Let’s return to the slopes discussed above and illustrated in Figure 4. If we combine the opposing slopes of the ACRIM and PMOD composites, the difference is 0.056 W/m2/year. The NOAA estimated uncertainty (Figure 6) in the cycle 21-22 minimum is over 0.7 W/m2 and in the 22-23 minimum it is over 0.6 W/m2. If this uncertainty is considered, the extrapolated long-term linear trend could be as high as 0.13 W/m2 to 0.18 W/m2/year. Over 261 years, these values could add up to 34 to 47 W/m2. Both values are much higher than the 9.2 W/m2required to account for the roughly one-degree of warming observed over the past 261 years (see Figure 1 and the discussion).

Given the way the composites have been generated, we only have two points to work with in determining a long-term solar trend, the points are the lows of solar cycles 21-22 and 22-23. Everything has been adjusted to the low of solar cycle 23-24, so it isn’t usable. With two points all you get is a line and a linear change is unlikely for a dynamo. Basically, the satellite data is not enough.

We have no opinion on the relative merits of the three composite TSI records discussed. There are, for the most part, logical reasons for all the corrections made in each composite. The problem is, they are all different and have opposing trends. Each composite selects different portions of the available satellite records to use and applies different corrections. The resulting, different long-term trends are simply a reflection of the component instrument instabilities (Kopp 2016). For discussions of the merits of the ACRIM composite see (Scafetta and Willson 2014), for the PMOD composite see (Frohlich 2006), for the IRMB composite see (Dewitte, et al. 2004). There are arguments for and against each composite. There are also numerous papers discussing how to extend the TSI record into the past using solar proxies. For a discussion of some of the most commonly used TSI reconstructions of the past 200 years see (Soon, Connolly and Connolly 2015). The problem with the proxies is that the precise relationship they have with TSI or solar output in general is unknown and must be based on correlations with the, unfortunately, flawed satellite records.

Whether one matches a proxy to the ACRIM or PMOD composite can make a great deal of difference in the resulting long term TSI record as discussed in (Herrera, Mendoza and Herrera 2015). As the paper makes clear, reasonable proxy correlations to the ACRIM and PMOD composites can result in computed values of TSI, in the 1700s, that are more than two W/m2 different. Kopp discusses this problem in more detail in his 2016 Journal of Space Weather and Space Climate article:

“TSI variability on secular timescales is currently not definitively known from the space-borne measurements because this record does not span the desired multi-decadal to centennial time range with the needed absolute accuracies, and composites based on the measurements are ambiguous over the time range they do cover due to high stability-uncertainties of the contributing instruments.” (Kopp 2016)

Kopp also provides us with the following plot (Figure 7) comparing different historical TSI reconstructions. The red NRLTSI2 reconstruction is the one that will be used for the upcoming IPCC report and in CMIP6 (Coupled Model Inter-comparison Project Phase 6). The TSI reconstructions plotted in Figure 7 are all empirical and make use of various proxies of solar activity (but mainly sunspot counts) and their assumed relationship to total solar output. Figure 7 illustrates some of the uncertainty in these assumptions.

Figure 7. Various recent published TSI reconstructions. The NRLTSI2 reconstruction will be used for the upcoming IPCC report and CMIP6. There is a great deal of spread during the Maunder Minimum, over 2 W/m2 and the long-term trends are very different. The figure is modified after one in (Kopp 2016).

In answer to the question posed at the beginning of the post, no we have not measured the solar output accurately enough, over a long enough period, to definitively say solar variability could not have caused all or a significant portion of the warming observed over the past 261 years. The most extreme reconstruction in Figure 7 (Lean, 2000), suggests the Sun could have caused 25% of the warming and this is without considering the considerable uncertainty in the TSI estimate. There are even larger published TSI differences from the modern day, up to 5 W/m2 (Shapiro, et al. 2011), (Soon, Connolly and Connolly 2015) and (Schmidt, et al. 2012). We certainly have not proven that solar variability is the cause of all or even a large portion of the warming, only that we cannot exclude it as a possible cause, as the IPCC appears to have done.

Works Cited

Dewitte, S., D. Crommelynck, S. Mekaoui, and A. Joukoff. 2004. “Measurement and Uncertainty of the Long-Term Total Solar Irradiance Trend.” Solar Physics 224 (1-2): 209-216. doi:https://doi.org/10.1007/s11207-005-5698-7 .

Eddy, John. 1976. “The Maunder Minimum.” Science 192 (4245). https://www.jstor.org/stable/1742583?seq=1#page_scan_tab_contents.

—. 2009. The Sun, the Earth and near-Earth space: a guide to the Sun-Earth system. Books express. https://www.amazon.com/Sun-Earth-Near-Earth-Space-Sun-Earth/dp/1782662960/ref=sr_1_2?ie=UTF8&qid=1537190646&sr=8-2&keywords=The+Sun%2C+the+Earth+and+near-Earth+space%3A+a+guide+to+the+Sun-Earth+system.

Fox, Peter. 2004. “Solar Activity and Irradiance Variations.” Geophysical Monograph (American Geophysical Union) 141. https://www.researchgate.net/profile/Richard_Willson3/publication/23908159_Solar_irradiance_variations_and_solar_activity/links/00b4951b20336363f2000000.pdf.

Frohlich, C. 2006. Solar Irradiance Variability since 1978. Vol. 23, in Solar Variability and Planetary Climates. Space Sciences Series of ISSI, by Calisesi Y., Bonnet R.M., Langen J. Gray L. and Lockwood M. New York, New York: Springer. https://link.springer.com/chapter/10.1007/978-0-387-48341-2_5.

Haigh, Joanna. 2011. Solar Influences on Climate. Imperial College, London. https://www.imperial.ac.uk/media/imperial-college/grantham-institute/public/publications/briefing-papers/Solar-Influences-on-Climate—Grantham-BP-5.pdf.

Herrera, V. M. Velasco, B. Mendoza, and G. Velasco Herrera. 2015. “Reconstruction and prediction of the total solar irradiance: From the Medieval Warm Period to the 21st century.” New Astronomy 34: 221-233. https://www.sciencedirect.com/science/article/pii/S1384107614001080.

IPCC. 2013. In Climate Change 2013: The Physical Science Basis. Contribution of Working Group I to the Fifth Assessment Report of the Intergovernmental Panel on Climate Change, by T. Stocker, D. Qin, G.-K. Plattner, M. Tignor, S.K. Allen, J. Boschung, A. Nauels, Y. Xia, V. Bex and P.M. Midgley. Cambridge: Cambridge University Press. https://www.ipcc.ch/pdf/assessment-report/ar5/wg1/WG1AR5_SPM_FINAL.pdf.

Kopp, Greg. 2016. “Magnitudes and timescales of total solar irradiance variability.” J. Space Weather and Space Climate 6 (A30). https://www.swsc-journal.org/articles/swsc/abs/2016/01/swsc160010/swsc160010.html.

Scafetta, Nicola, and Richard Willson. 2014. “ACRIM total solar irradiance satellite composite validation versus TSI proxy models.” Astrophysics and Space Science 350 (2): 421-442. https://link.springer.com/article/10.1007/s10509-013-1775-9.

Schmidt, G.A., J.H. Jungclaus, C.M. Ammann, E., Braconnot, P. Bard, and T. J. Crowley. 2012. “Climate forcing reconstructions for use in PMIP simulations of the last millennium.” Geosci. Model Dev. 5 185-191. http://pubman.mpdl.mpg.de/pubman/faces/viewItemOverviewPage.jsp?itemId=escidoc:1407662.

Shapiro, A., W. Schmutz, E. Rozanov, M. Schoell, M. Haberreiter, A. V. Shapiro, and S. Nyeki. 2011. “A new approach to the long-term reconstruction of the solar irradiance leads to large historical solar forcing.” Astronomy and Astrophysics 529 (A67). https://www.aanda.org/articles/aa/pdf/2011/05/aa16173-10.pdf.

Soon, Willie, Ronan Connolly, and Michael Connolly. 2015. “Re-evaluating the role of solar variability on Northern Hemisphere temperature trends since the 19th century.” Earth Science Reviews 150: 409-452. https://www.sciencedirect.com/science/article/pii/S0012825215300349.

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