What does the Cardinal Model tell us?

The values of the empirical parameters that minimised variance did so that the model calculation matched every estimate of total Greenhouse effect to within 0.01WM-2 or less for each of the 447 months.

The range of total Greenhouse effect is about 14WM-2 (over 1,000 times larger) so this is close to a perfect fit.

Water is the main contributor to the total at 71.2%.

Note that Greenhouse effect warming directly heats the atmosphere of Earth and has only an indirect effect on surface temperatures.

By attributing all enhanced Greenhouse effect to surface warming the Cardinal model output can be empirically related to surface warming.

This is found to be – on a ‘best fit’ basis – to approximate more to a tanh (hyperbolic tangent) curve than a ln (logarithmic) curve as proposed by Arrhenius (and asserted by Anointed modellers).

Only at low concentrations of any particular Greenhouse gas is there evidence of a more Arrhenius form contributionion.

For carbon dioxide which was already at a high concentration pre-industrialisation (277 ppm or 0.03%v/v) the ‘best fit’ curve is almost entirely a tanh (hyperbolic tangent) form.

Some Specific results:

Carbon Dioxide ‘doubling’: an extra 0.366 WM-2 since pre-industrial times

Methane ‘tripling’: 0.094 WM-2 since pre-industrial times

Other Greenhouse gas ‘doublings’ <0.311 WM-2 since pre-industrial times

Total ‘doubling’/’tripling’: <0.771 WM-2 since pre-industrial times

Total from pre-industrial times to 2025: <0.653 WM-2.

Total from 2025 to ‘doubling’/’tripling’ ~ 0.118 WM-2.

Converting these to surface warming in degrees centigrade using the equivalence factor 1⁰C = 4.71 WM-2 gives an estimate of the contribution of all increased concentrations of Greenhouse gases (except water) to surface warming from pre-industrial times to 2025 of 0.14⁰C and to ‘doubling’ (‘tripling in the case of methane) of a further 0.02⁰C.