Equation 2 · How Earth Systems and Climate Dynamics Actually Work
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a reference concentration. Read the equation part by part below; each part has a contextual explanation and a link to its mathematical background.
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subscript
The lower label selects a particular version, component, or indexed member of the quantity. For example, x₀ and xₜ can be values at different positions.
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What the article says around this equation
is the standard simplified radiative-forcing relation for CO2, where is a reference concentration, C the current concentration, and 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 is a reference concentration, C the current concentration, and 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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