In a recent paper in Geophysical Research Letters, Scafetta & West (S&W) estimate that as much as 25-35% of the global warming in the 1980-2000 period can be attributed changes in the solar output. They used some crude estimates of ‘climate sensitivity’ and estimates of Total Solar Irradiance (TSI) to calculate temperature signal (in form of anomalies). They also argue that their estimate, which is based on statistical models only, has a major advantage over physically based considerations (theoretical models), because the latter would require a perfect knowledge about the underlying physical and chemical mechanisms.
In their paper, they combine Lean et al (1995) proxy data for the TSI with recent satellite TSI composites from either Willson & Mordvinov (2003) [which contains a trend] and of Fröhlich & Lean (1998) [data from the same source, but the analysis doesn't contain a trend, henceforth referred to as 'FL98']. From 1980 and afterwards, they see a warming associated with solar forcing, even when basing their calculations on the FL98 data. The fact that the FL98 data doesn’t contain any trend makes this finding seem a bit odd. Several independent indices on solar activity – which are direct modern measurement rather than estimations – indicate that there has been no trend in the level of solar activity since 1950s.
But, S&W have assumed a lagged response (which they state is tS4~4.3 years), so that the increase prior to 1980 seems to have a delayed effect on the temperature. The delayed action is a property of the climate system, which also affects greenhouse gases, and is caused by the oceans which act as a flywheel due to their great heat capacity and thermal inertia. The oceans thus cause a planetary imbalance. When the forcing levels off, the additional response is expected to taper off as a decaying function of time. In contrast, the global mean temperature, however, has increased at a fairly steady rate (Fig. 1). The big problem is to explain a lag of more than 30 years when direct measurements of quantities (galactic cosmic rays, 10.7 cm solar radio, magnetic index, level of sunspot numbers, solar cycle lengths) do not indicate any trend in the solar activity since the 1950s.
In order to shed light on these inconsistencies, we need to look more closely at the methods and results in the GRL paper. The S&W temperature signal, when closely scrutinised (their Fig. 3), starts at the 0K anomaly-level in 1900, well above the level of the observed 1900 temperature anomalies, which lie in the range -3K < T < -1K in Fig. 1. In 1940, their temperature [anomaly] reconstruction intercepts the temperature axis near 0.12K, which is slightly higher than the GISS-curve in Fig. 1 suggests. The S&W temperature peaks at 0.3K in 1960, and diverge significantly from the observations. By not plotting the curves on the same graph, the reader may easily get the wrong impression that the construction follows the observations fairly closely. The differences between the curves have not been discussed in the paper, nor the time difference for when the curves indicate maxima (global mean temperature peaks in 1945, while the estimated solar temperature signal peaks in 1960). Hence, the decrease in global temperature in the period 1945 – 1960 is inconsistent with the continued rise in the calculated solar temperature signal.
Another more serious weakness is a flawed approach to obtain their ‘climate sensitivity’, and especially so for ‘Zeq‘ in their Equation 4. They assume a linear relationship between the response and the forcing Zeq=288K/1365Wm-2. For one thing, the energy balance between radiative forcing and temperature response gives a non-linear relation between the forcing, F, and temperature to the fourth power, T4 (the Stefan-Boltzmann law). This is standard textbook climate physics as well as well-known physics. However, there is an additional shortcoming due to the fact that the equilibrium temperature is also affected by the ratio of the Earth’s geometrical cross-section to its surface area as well as how much is reflected, the planetary albedo (A). The textbook formulae for a simple radiative balance model is:
F (1-A)/4 = s T4, where ‘s’ here is the Boltzmann constant (~5.67 x 10-8 J/s m2K4).
(‘=’ moved after Scafetta pointed out this error. )
S&W’s sun-climate sensitivity (Zeq =0.21K/Wm-2), on which the given solar influence estimates predominantly depend, is thus based solely on a very crude calculation that contradicts the knowledge of climate physics. The “equilibrium” sensitivity of the global surface temperature to solar irradiance variations, which is calculated simply by dividing the absolute temperature on the earth’s surface (288K) by the solar constant (1365Wm-2), is based on the assumption that the climate response is linear in the whole temperature band starting at the zero point. This assumption is far from being true. S&W argue further that this sensitivity does not only represent the direct solar forcing, but includes all the feedback mechanisms. It is well known, that these feedbacks are highly non-linear. Let’s just mention the ice-albedo feedback, which is very different at (hypothetically) e.g. 100K surface temperature with probably ‘snowball earth’ and at 300K with no ice at all. In their formula for the calculation of the sun-related temperature change, the long-term changes are determined by Zeq, while their ‘climate transfer sensitivity to slow secular solar variations’ (ZS4) is only used to correct for a time-lag. The reason for this remains unclear.
In order to calculate the terrestrial response to more ephemeral solar variations, S&W introduce another type of ‘climate sensitivity’ which they calculate separately for each of two components representing frequency ranges 7.3-14.7 and 14.7-29.3 year ranges respectively. They take the ratios of the amplitude of band-passed filtered global temperatures to similarly band-passed filtered solar signal as the estimate for the ‘climate sensitivity’. This is a very unusual way of doing it, but S&W argue that similar approach has been used in another study. However, it’s not as simple as that calculating the climate senstivity (see here, here, here, and here). Hence, there are serious weaknesses regarding how the ‘climate sensitivities’ for the 11-year and the 22-year signals were estimated. For linear systems, different frequency bands may be associated with different forcings having different time scales, but chaotic systems and systems with convoluted response are usually characterised with broad power spectra. Furthermore, it’s easy to show that band-pass filtering of two unrelated series of random values can produce a range of different values for the ratio of their amplitudes just by chance (Fig. 2). As an aside, it is also easy to get an apparent coherence between two band-pass filtered stochastic series of finite extent which are unrelated by definition – a common weakness in many studies on solar-terrestrial climate connection. There is little doubt that the analysis involved noisy data.
The fact that there is poor correspondence between the individual amplitudes of the band-passed filtered signals (Fig. 4 in Scafetta & West, 2005) is another sign indicating that the fluctuations associated with a frequency band in temperature is not necessarily related to solar variability. In fact, the 7.3-14.7 and 14.7-29.3 frequency bands may contain contributions from El Niño Southern Oscillation (ENSO), although the time scale of ENSO is from 3-8 years. The fact that the amplitude of the events vary from time to time implies slower variations, just like modulations of the sunspot number has led to the proposition of the Gleissberg cycles (80-90 years). There is also volcanic activity, and the last major eruption in 1982 and 1991 are almost 10 years apart, and may contribute to the variance in the 7.3-14.7 year frequency range. S&W argue that their method eliminates influences of ENSO and volcanoes because their calculated sensitivity in the higher frequency band is similar to the one derived by Douglass and Clader (2002) by regression analysis (0.11 K/Wm-2). This conclusion is not valid. Having signals of different frequencies in the 7-15 years band, the amplitude of the signal in the higher band may correspond roughly to the 11-year signal by accident, but that doesn’t mean that there are no other influences.
S&W combined two different types of data, and it is well-known that such combinations in themselves may introduces spurious trends. The paper does not address this question.
From regression analysis cited by the authors (Douglass and Clader 2002, White et al. 1997), it seems possible that the sensitivity of global surface temperature to variations of total solar irradiance might be about 0.1K/Wm-2. S&W do not present any convincing result that would point to noticeably higher sensitivities to long-term variations. Their higher values are based on unrealistic assumptions. If they would use a more realistic climate transfer sensitivity of 0.11K/Wm-2, or even somewhat higher (0.12 or 0.13) for the long-term, and use trends instead of smooth curve points, they would end up with solar contributions of 10% or less for 1950-2000 and near 0% and about 10% in 1980-2000 using the PMOD and ACRIM data, respectively.
We have alread discussed the connection between solar activity (here , here, here, and here), and this new analysis does not alter our previous conclusions: that there is not much evidence pointing to the sun being responsible for the warming since the 1950s.
Thanks to Urs Neu for comments and inputs.