Coupled Seasonal Data Assimilation of Sea Ice, Ocean, and Atmospheric Dynamics over the Last Millennium

``Online" data assimilation (DA) is used to generate a new seasonal-resolution reanalysis dataset over the last millennium by combining forecasts from an ocean--atmosphere--sea-ice coupled linear inverse model with climate proxy records. Instrumental verification reveals that this reconstruction achieves the highest correlation skill, while using fewer proxies, in surface temperature reconstructions compared to other paleo-DA products, particularly during boreal winter when proxy data are scarce. Reconstructed ocean and sea-ice variables also have high correlation with instrumental and satellite datasets. Verification against independent proxy records shows that reconstruction skill is robust throughout the last millennium. Analysis of the results reveals that the method effectively captures the seasonal evolution and amplitude of El Ni\~{n}o events. Reconstructed seasonal temperature variations are consistent with trends in orbital forcing over the last millennium.