“…Furthermore, a linear inverse model of coupled atmosphere-ocean dynamics was applied for online PDA, and the reconstructed annual-resolution atmosphere and ocean fields demonstrated the added value of dynamical memory for the proxy data and physical constraints from the atmosphere-ocean interaction (Perkins & Hakim, 2021). Based on an intermediate complexity general circulation model, Okazaki et al (2021) showed that the online PDA could outperform the offline PDA when the length of predictability is longer than the averaging time of observations, and the ocean plays an important role to extend predictability that is helpful for online PDA. Although online PDA is feasible with a simplified model or a linear inverse model (e.g., Jebri & Khodri, 2023;Perkins & Hakim, 2017), online PDA could require intensive computational cost for the paleoclimate simulations with a realistic and complex model, due to the length of simulations.…”