24. The Force-ND Hypothesis
In this post we consider an alternative hypothesis to the force X hypothesis of the last post. Let’s entertain the idea of two indirect warming influences: “force N” causes notching, while “force D” explains the delay, the indirect solar sensitivity (ISS), and the externally-driven albedo (EDA) finding.
The force X hypothesis is based on the assumption that the four strong influences listed near the beginning of the last post are all manifestations of the same influence, namely force X. There are (at least) two possible drawbacks to this.
The first is that the cloudiness fraction, available from 1983, shows no peaking during the TSI peaks of 1990 and 2001, and if anything shows a decrease in cloud fraction around 2001. Low-altitude cloud cover underwent a distinct trough around 1990, but there was no particular feature in 2001 (Fig. 2-12 of Lockwood et. al.’s Earthshine Mission case from 2004, and Climate and Clouds). But force X acts by albedo modulation and produces a cooling peak to counteract the TSI peak at the sunspot maxima, suggesting it creates an increase in cloud cover around sunspot maxima.
However the increase in cloud cover fraction required to counteract the extra TSI at a sunspot maximum is ~0.05%, too small to detect. (0.8 W m−2 of extra TSI at 1 AU is 0.8×(1–0.3)/4 or 0.14 W m−2 of extra absorbed solar radiation (ASR), which is countered by an increase in cloud fraction of 0.14/239 or 0.05% because the average ASR is 239 W m−2.)
So either force X is affecting albedo by something other than clouds, or the small countervailing increase in cloud fraction goes undetected among noise and larger moves.
The second potential drawback is that the increase in TSI during a sunspot maximum implies increased force X one sunspot cycle later, which may well be during the next sunspot maximum, just when force X decreases in order to counteract the direct heating by the extra TSI. This could be explained by the changes in TSI that foretell changes in force X ~11 years later needing to be changes in underlying or trend TSI, while the temporary changes in force X at sunspot maxima are likely due instead to the reversal of the Sun’s magnetic field. (Each step response in Fig. 1 of post 22 is slightly complicated; obviously there exists a step response corresponding to any empirical transfer function for the solar-only system, so a single force X explanation is possible.)
Another explanation is that there are two separate influences, one that manifests itself around sunspot maxima and causes notching, and another that changes in delayed response to changes in underlying TSI and is responsible for the delay, the ISS, and the EDA finding.
Let us go to the next simplest alternative after the one-influence assumption of force X, and assume there are two influences. We call them “force N”, which causes notching, and “force D”, the delayed force, which acts about one sunspot cycle after being signaled by a change in smoothed TSI and is the same as force X except not responsible for the notching. We assume both are warming influences. Schematically,
We often make statements that apply under either notch-delay hypothesis: “force X/D” means “force X or force D”.
Force N and Force D
If there are indeed two separate significant influences on the climate, beyond those currently considered by the IPCC, then it makes the climate puzzle much harder to solve than if there was only one.
Force N doesn’t necessarily work through albedo modulation, though it could. It could even work by cloud modulation that is too small to be detected. It causes notching so it is synchronized to the Sun.
Force D is also synchronized to the Sun, because (a) the correlation between temperature and the length of the previous sunspot cycle (post 22) is synchronized to the Sun, and (b) it is not simply propagation of heat, as discussed in post 22. It works by externally-driven albedo modulation.
Interestingly, the force D transfer function (which is for the system whose input is TSI and output is surface warming), which is the transfer function of force X in the empirical transfer function (Fig. 2 of post 21) but without the notch, looks like the transfer function of a simple accumulator or first order low pass filter, shown in Fig. 1.
(An example of a first order low pass filter is a capacitor fed through a resistor, which charges or discharges depending on the voltage applied across the combination of resistor and capacitor and the charge in the capacitor.)
The fall-off in amplitude for frequencies above one cycle per 3 or 4 years suggested by the empirical transfer function implies a low pass filter with a break frequency of ~5 years, which indeed is what we get by curve fitting such a model to the data (in a later post).
Figure 1: Transfer function of a low pass filter. A low pass filter “passes” sinusoids with frequencies well below fB but “blocks” those well above fB (and the higher the frequency, the more it is attenuated).
Note that, as shown by the indirect solar sensitivity (ISS) in Post 21, force D operates with a large amplification factor over the direct heating effect of TSI, so while force D is proportional to the accumulation of TSI it is not due to the cumulative effect of the direct heating of TSI.
A simple integral of TSI over time is an accumulator of TSI, so the time-integral of TSI is similar to force D. The transfer function of an integrator depends on its details (no integrator goes back forever in time), but all are characterized by the downward sloping amplitude line on the right of Fig. 1. For example, a simple integrator circuit implemented with an op-amp is a low pass filter exactly as per Fig. 1. It has been widely observed that time-integrals of TSI roughly fit the shape of the surface warming over the last few centuries.
Researchers who have found a high sensitivity of temperature to TSI may have found a high sensitivity to force X/D. For example:
- Shaviv (2008, ) looked at three independent ocean records (net heat flux, sea level changes from tide gauges, and sea surface temperatures) and found forcings associated with solar cycle variations that are 5 to 7 times that associated with TSI variations in the current climate models.
- Douglass and Clader (2002, ) found that the sensitivity to TSI is twice that of the no-feedback Stefan-Boltzmann radiation model balance, from satellite observations of TSI and temperature.
- Scafetta & West (2009, ) argue for high sensitivity to TSI and cite paleolithic temperature reconstructions (Moberg 2005) and glacial epochs induced by Milankovitch astronomical cycles, in response to Duffy, Santer, and Wigley (2009, ) who argue that solar variability does not explain late-20th-century warming.
[1^] Shaviv, N. J. (2008). Using the Oceans as a Calorimeter to Quantify the Solar Radiative Forcing. Journal of Geophysical Research, 113:A11.
[2^] Douglass, D. H., & Clader, D. B. (2002). Climate sensitivity of the Earth to solar irradiance. Geophysical Research Letters, Vol. 29, No. 16, 10.1029.
[3^] Scafetta, N., & West, B. J. (2009). Interpretations of climate-change data. Physics Today, 62 (11), 8 (2009).
[4^] Duffy, P. B., Santer, B. D., & Wigley, T. W. (2009). Solar variability does not explain late-20th-century warming. Physics Today.