# Another study on solar influence

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 ‘Z_{eq}‘ in their Equation 4. They assume a linear relationship between the response and the forcing Z_{eq}=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, T^{4} (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 T^{4}, where ‘s’ here is the Boltzmann constant (~5.67 x 10^{-8} J/s m^{2}K^{4}).

(**‘=’ moved after Scafetta pointed out this error. **)

S&W’s sun-climate sensitivity (Z_{eq} =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 Z_{eq}, 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.

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