“…The adjoint method has been applied to the coupled ocean and sea ice system for adjoint sensitivities studies (Heimbach et al, 2010;Kauker et al, 2009;Koldunov et al, 2013) and Arctic synthesis (Fenty and Heimbach, 2013;Koldunov et al, 2017;Lyu et al, 2021b;Nguyen et al, 2021). However, due to the persistence of numerically instability issues, the adjoint of sea ice dynamics is omitted (Forget et al, 2015;Nguyen et al, 2021;Fenty and Heimbach, 2013;Mazloff et al, 2010) or simplified to a free-drift sea ice model (Koldunov et al, 2017;Lyu et al, 2021a;Lyu et al, 2021b). Toyoda et al (2019) described stabilizing the adjoint of full elastic-viscous-plastic sea-ice dynamics and noted much weaker evolution of sensitivity to sea-ice velocity by O (10 2 ) in the central Arctic Ocean than the adjoint of free-drift sea ice dynamic.…”