Quantifying the Terrestrial Carbon Feedback to Anthropogenic Carbon Emission

The surface warming response to carbon emission is dependent on feedbacks operating in both the physical climate and carbon cycle systems, with physical climate feedbacks quantified via linearly combinable climate feedback terms, lambda(climate) in watt per square meter per kelvin. However, land carbon feedbacks are often quantified using a two-parameter description, with separate cumulative carbon uptake responses to surface warming, gamma(L) in petagram of carbon per kelvin, and rising atmospheric CO2 concentration, beta(L) in petagram of carbon per parts per million. Converting the gamma(L) and beta(L) responses to an overall terrestrial carbon feedback parameter, lambda(carbon) in watt per square meter per kelvin, has remained problematic, with lambda(carbon) affected by significant nonlinear interactions between carbon-climate and carbon-concentration responses and a nonlinear relation between atmospheric CO2 and subsequent radiative forcing. This study presents new relationships quantifying how the overall steady state terrestrial carbon feedback to anthropogenic emission, lambda(carbon), is dependent on the terrestrial carbon responses to rising CO2 and temperature, beta(L), and gamma(L), and the physical climate feedback, lambda(climate). Nonlinear interactions between beta(L) and gamma(L) responses to carbon emission are quantified via a three-parameter description of the land carbon sensitivities to rising CO2 and temperature. Numerical vegetation model output supports the new relationships, revealing an emerging sensitivity of land carbon feedback to climate feedback of partial differential lambda(carbon)/ partial differential lambda(climate) 0.3. The results highlight that terrestrial carbon feedback and physical climate feedback cannot be considered in isolation: Additional surface warming from stronger climate feedback is automatically compounded by reduced cooling from terrestrial carbon feedback, meanwhile around half the uncertainty in terrestrial carbon feedback originates from uncertainty in the physical climate feedback.