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How would you classify someone such as Kilifarska? She looked at ozone levels in the lower stratosphere since 1926 and found that changes in total ozone explain 75% of global temperature changes. The strongest driver for changes in total ozone variability is the multi-decadal variation of galactic cosmic rays. Looking at the next decade, a prediction is made for a cooling of 0.05–0.25°C (depending on the ozone model).

The link you posted to Kilifarska's earlier paper no longer works.

Regardless, ozone in the Earth's atmosphere is not produced by cosmic rays but by solar ultraviolet radiation. Ozone production correlates with the cosmic ray background because solar UV flux increases with solar activity (i.e., with a more sunspots), but this correlation does not imply causation. Cosmic rays do not form an appreciable amount of ozone. Instead, higher solar activity increases the solar magnetic field which deflects more cosmic rays away from the inner solar system, thereby decreasing the cosmic ray background. So, more ozone production occurs at times of low cosmic ray background, but this relationship is not causal.

I get Arrhenius and greenhouse gases. My questions have to do with what happens down the line. The current state of the art is not firm enough for my liking.

The role of greenhouse gases and carbon dioxide in particular on climate is the fundamental issue. People denying that CO2 affects climate are those I consider "deniers" because ignoring this relation means denying so much established science that the consequences are untenable.

The question of current model predictions, as DB2 points out is quite another matter. There are all manner of deficiencies in climate codes. Processes occurring in small spatial scales are not well-modeled because of limitations on the size of the numerical grids involved. Consequently, the physics of processes occurring on scales smaller than that of the grid (such as condensation) must be parametrized. Neither is the growth and decay of ice sheets included, because of the very different timescales between ice sheet growth and that of atmospheric dynamics. So, no-one claims climate models are perfect, but they can still be used to approximate future climate regimes. Numerical codes in physics are always imprecise approximations of reality. However, to claim that climate models have no relevance at all, as some do, is to enter the realm of "denial". Numerical modeling is widely used in physics and engineering, and there is no evidence that this approach is methodologically flawed. With regard to climate science, models, although flawed, provide the best current estimate of future climate regimes given the realities of present-day computation.

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