Scaling laws for perturbations in the ocean–atmosphere system following large CO₂ emissions

Abstract. Scaling relationships are found for perturbations to atmosphere and ocean variables from large transient CO₂ emissions. Using the Long-term Ocean-atmosphere-Sediment CArbon cycle Reservoir (LOSCAR) model (Zeebe et al., 2009; Zeebe, 2012b), we calculate perturbations to atmosphere temperature, total carbon, ocean temperature, total ocean carbon, pH, alkalinity, marine-sediment carbon, and carbon-13 isotope anomalies in the ocean and atmosphere resulting from idealized CO₂ emission events. The peak perturbations in the atmosphere and ocean variables are then fit to power law functions of the form of γ D^αE^β, where D is the event duration, E is its total carbon emission, and γ is a coefficient. Good power law fits are obtained for most system variables for E up to 50 000 PgC and D up to 100 kyr. Although all of the peak perturbations increase with emission rate E/D, we find no evidence of emission-rate-only scaling, α + β = 0. Instead, our scaling yields α + β ≃ 1 for total ocean and atmosphere carbon and 0 < α + β < 1 for most of the other system variables.