Threshold effects of CO₂ on Sea-Ice Volume:Empirical Evidence with Data from Global Circulation Models of the Arctic and Antarctic

The year 2024 marked a critical milestone in global warming, with global mean temperatures exceeding pre-industrial levels by 1.55 °C. Polar ice loss, largely driven by anthropogenic CO₂ emissions, exhibits highly nonlinear dynamics that challenge conventional linear modeling approaches. This paper investigates the nonlinear effects of CO₂ on Arctic and Antarctic sea-ice volumes using regime-switching econometric models defined for both accumulated concentration levels and annual changes in CO₂. Specifically, we estimate reduced-form Smooth Transition Autoregressive (STAR) and Threshold Autoregressive (TAR) specifications using data generated from General Circulation Models (GCMs). We consider the identification of CO₂ thresholds and the evaluation of sea-ice dynamics under alternative CO₂ emissions trajectories, such as the IPCC’s Shared Socioeconomic Pathways (SSPs). Our results reveal important threshold effects across hemispheres. For the Arctic, a single CO₂ threshold is identified at approximately 330 ppm (or 𝛥𝐶𝑂2 = 1.16 ppm), while for the Antarctic, two thresholds emerge at 285 ppm (or 𝛥𝐶𝑂2 = 0.13 ppm) and 321 ppm (or 𝛥𝐶𝑂2 = 0.56). Beyond these points, the decline in sea-ice volume accelerates sharply. Forecasts under business-asusual (BAU) scenarios suggest that the Arctic could become ice-free around 2060 [2045, 2078], while Antarctic sea-ice loss may extend well beyond 2100. Under an intermediate emissions path, such as SSP2-4.5, recovery of sea-ice volume remains feasible if global CO₂ growth begins to decline after 2035 by an average of 3.2 ppm every year, with projected reversion to historical levels around 2075 for both hemispheres.