Hysteresis and irreversibility in permafrost physical response to increase and decrease of CO₂ emissions

Abstract. Boreal permafrost over the Northern Hemisphere high latitudes, defined as areas where the ground temperature is below 0 °C for two or more years, stores more than twice as much carbon as the atmosphere. Therefore, thawing of the permafrost, an important tipping element, due to global warming may lead to additional carbon emissions and accelerate the warming. To investigate the permafrost response to increase and decrease of CO₂ emissions, we conducted a series of numerical experiments using an emission-driven Earth System Model, MIROC-ES2L, and adopting idealized overshooting scenarios in which a prescribed CO₂ emission of 10 PgC is given until the global warming level reaches different values between 2 and 8 °C followed by the negative emission until the cumulative emission becomes zero.

We found that the response of permafrost area to surface warming and cooling is reversible but has hysteresis for all the emission scenarios. Furthermore, the permafrost property was shown to have irreversibility in the deep soil layer; part of the frozen area in the initial condition was replaced by a mixed water-ice area in the final state despite ground temperature turned almost to the initial condition. Sensitivity experiments reveal that the hysteresis and irreversibility are attributed to the delay of the soil freezing and melting associated with the soil heat conductivity and specific heat of water phase change. This result indicates that once permafrost thaws with warming it will continue for decades after warming diminishes and the delay in the permafrost recovery is larger at global warming levels greater than 2 °C. An offline calculation shows that the additional CO₂ emission during the permafrost hysteresis cycle accounts for about 0.6–41 % of the prescribed cumulative carbon emission.