Arctic Amplification (AA), the amplified surface warming in the Arctic relative to the globe, is a salient feature of climate change. While the basic physical picture of AA has been depicted, how its degree is determined has not been clearly understood. Here, by deciphering atmospheric heat transport (AHT), we build a two-box energy-balance model of AA and derive that the degree of AA is a simple nonlinear function of five key parameters, including the Arctic and global feedbacks, the meridional heterogeneity in radiative forcing, and the partial sensitivities of AHT to global mean and meridional gradient of warming.

The formula captures the varying AA in climate models and attributes the spread/outlier to models’ climate feedbacks and AHT physics, which can be further targeted by modeling centers. The formula clearly illustrates how essential physics mutually determine the degree of AA and limits its range within 1.5-3.5. The formula articulates the intricate, fundamental role of AHT in AA. AHT is both forcing and feedback to AA. Its existence forms a baseline AA of ~1.6 that exists even with uniform feedbacks, and its fundamental role in AA is represented by its partial sensitivities to warming instead of its total change. The lapse-rate feedback has been widely recognized as a major contributor to AA but our results show that its effect is fully, if not overly, offset by the water-vapor feedback.

Overall, our results suggest that the degree of AA, despite governed by effects of multiple feedbacks and intricate interactions among feedbacks and AHT, can be analytically understood. The analytic theory works beyond the existing diagnostic framework of AA. It also explains some puzzling results of previous numerical experiments with idealized forcing and feedbacks.