Atmospheric stabilization and the timing of carbon mitigation

Stabilization of atmospheric CO₂ concentrations below a pre-industrial doubling (~550 ppm) is a commonly cited target in climate policy assessment. When the rate at which future emissions can fall is assumed to be fixed, the peak atmospheric concentration - or the stabilization "frontier" - is an increasing and convex function of the length of postponement. Here we find that a decline in emissions of 1% year^-1 beginning today would place the frontier near 475 ppm and that when mitigation is postponed, options disappear (on average) at the rate of ∼9 ppm year ^-1, meaning that delays of more than a decade will likely preclude stabilization below a doubling. When constraints on the future decline rate of emissions are relaxed, a particular atmospheric target can be realized in many ways, with scenarios that allow longer postponement of emissions reductions requiring greater increases in the intensity of future mitigation. However, the marginal rate of substitution between future mitigation and present delay becomes prohibitively large when the balance is shifted too far toward the future, meaning that some amount of postponement cannot be fully offset by simply increasing the intensity of future mitigation. Consequently, these results suggest that a practical transition path to a given stabilization target in the most commonly cited range can allow, at most, one or two decades of delay.