Addendum Two Methane

The contribution from methane to the total Greenhouse effect is:

Most of the variability observed comes from changes in temperatures (lower and mid Troposphere and lower Stratosphere).

For Methane, the effective emission altitude for the saturation zone is determined by the Cardinaal Model to be near the lower Stratosphere.

For Methane's broadening/overlap zone the effective emission altitude averages between 3- and 4-kilometres altitude.

By looking at annual averages (thereby averaging out seasonal effects) and adjusting for temperature variations, the progression of methane’s contribution to the total Greenhouse effect may be plotted against ground-level methane concentration.

The green line is of the form proposed by Arrhenius and is the form used as the foundation relationship for Anointed Modellers.

The best fit to Cardinal model calculated data is: WM-2 = 0.214 * ln(methane ppb)

The blue line follows a combination of an Arrhenius form and a proposed empirical relationship based on the author’s experience studying reflection, refraction, transmission and absorption of far-infrared and microwave radiation in his late-1960s laboratory:

Greenhouse effect = a * tanh(b * Methane concentration in ppb)
Where: a = 1.539  and b = 1.858

Note hyperbolic tangent (tanh) is a mathematical function that describes various physical processes involving radiation interaction with matter - see further Addendum three.

The Arrhenius form that dominates at low concentrations, is already 'flattening out' to the tanh() form at pre-industrial levels of methane (0.72 ppb),

The tanh form begins to dominate at high concentrations seen more recently (1.8 to 1.9 ppm)

Note: the blue line shown above is a best-fit empirical relationship and the parameter values giving the best-fit are not underpinned by theoretical calculations.

The value for ‘tripling’ from 0.77 to 2.31 ppm (c.f. current levels of 1.95 ppm) is 0.094 WM-2 derived from this empirical curve.

The Arrhenius form model derives estimates for ‘tripling’ nearly double the best fit empirical curve.