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Equation 4 · How Earth Systems and Climate Dynamics Actually Work

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α\alpha

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the empirically constrained coefficient (commonly near 5. Read the equation part by part below; each part has a contextual explanation and a link to its mathematical background.

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α\alpha

Symbol α

the empirically constrained coefficient (commonly near 5.

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is the standard simplified radiative-forcing relation for CO2, where C0C_0 is a reference concentration, C the current concentration, and α\alpha an empirically constrained coefficient (commonly near 5.35 W m⁻² in widely used formulations). Its logarithmic form is itself an empirical and physical result: it reflects the fact that CO2’s absorption bands are already partially saturated at pre-industrial concentrations, so each additional increment of concentration adds progressively less forcing than the last increment did. This is why forcing does not scale linearly with emissions, and why halving emissions growth does not halve the added forcing — it is a statement about band saturation, not a…
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is the standard simplified radiative-forcing relation for CO2, where C0C_0 is a reference concentration, C the current concentration, and α\alpha an empirically constrained coefficient (commonly near 5.35 W m⁻² in widely used formulations). Its logarithmic form is itself an empirical and physical result: it reflects the fact that CO2’s absorption bands are already partially saturated at pre-industrial concentrations, so each additional increment of concentration adds progressively less forcing than the last increment did. This is why forcing does not scale linearly with emissions, and why halving emissions growth does not halve the added forcing — it is a statement about band saturation, not a policy assumption.

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