Simple electrical circuit analogies have also been used by other papers to demonstrate that radiative-convective equilibrium in the troposphere is "short-circuited" by convection dominating over the radiative forcing from greenhouse gases, and thus implying minimal impact from changes of CO2 concentrations on surface temperatures.
|Illustration of an electrical circuit analogy to radiative-convective equilibrium in a planetary atmosphere. Pressure and heat capacity set the resistance [opacity] to infrared transmission illustrated as the resistor Rc above. GHGs set the resistance [opacity] to infrared transmission illustrated as the resistor Rt above. As noted, "Resistance Rc corresponds to convection "shorting out" the radiative resistance Rt, allowing more current [analogous to heat in the atmosphere] to escape. If the resistance [IR opacity] of Rt increases due to adding more greenhouse gases, the resistance [IR opacity] of Rc will automatically drop to re-establish balance and thus the current through the circuit remains the same, and analogously, the temperature of the surface of the planet remains the same and self-regulates. Source|
Dr. Abdussamatov's more sophisticated circuit analogy includes the additional "components" of surface and atmospheric "capacitors" analogous to the thermal inertia of atmosphere, land, and oceans. The paper finds Earth's "thermal inertia constant" to be ~8.5 years, and that perturbations in energy balance require about 3 thermal inertia values ~3*8.5 = 25.5 years to reach a new steady-state condition.
Analysis of the circuit using differential and simultaneous equations finds that for typical values corresponding to the present climate system, "a decrease of atmospheric transparency (for example, as result of the growing of the greenhouse gases concentration) causes increasing of the heat power emitted by the atmosphere to space, and this heat power increases faster than the heat power absorbed by the atmosphere from the surface radiation." i.e. increasing greenhouse gas concentrations at the present levels in the atmosphere causes increased cooling, not warming, of the surface.
"Dependencies of derivatives Ns= dTs/dγ and Na= dTa/dγ on the radiative heat flux from the surface to the space through the atmospheric window were investigated. We found that the decreasing of atmospheric transparency causes the decreasing of Ti when qs < 50 Wm2 , because in the range of value 0 < qs < 50 Wm2 the derivatives are positive. For such conditions it is found that decrease of atmospheric transparency (for example, as result of the growing of the greenhouse gases concentration) causes increasing of the heat power emitted by the atmosphere to space, and this heat power increases faster than the heat power absorbed by the atmosphere from the surface radiation. Note, that this result corresponds to conclusion from  obtained using the other approach."This is also consistent with increased greenhouse gases increasing the radiative surface area to space, analogous to a larger heat sink on your microprocessor causing increased cooling via enhanced convection and radiative heat losses. The finding that increased greenhouse gases cause "increasing of the heat power emitted by the atmosphere to space" is also consistent with observations of an increase over the past 62 years of outgoing longwave infrared radiation [OLR] to space, opposite to the predictions of climate models and AGW theory.
Modeling of the Earth’s Planetary Heat Balance with Electrical Circuit Analogy
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Habibullo I. Abdussamatov, Alexander I. Bogoyavlenskii, Sergey I. Khankov, Yevgeniy V. Lapovok
The integral heat model for the system of the Earth’s surface—the atmosphere—the open space based on the electrical circuit analogy is presented. Mathematical models of the heat balance for this system are proposed. Heat circuit which is analog of the electrical circuit for investigating the temperature dependencies on the key parameters in the clear form is presented.