Vincent T. Cooper 

Historical observations of Earth's climate underpin our knowledge and predictions of climate variability and change. However, historical datasets are often inconsistent due to sparse, error-prone instrumental data, which limits understanding of climate dynamics. Combining linear inverse models (LIMs) with coupled data assimilation presents an opportunity to reconstruct and quantify uncertainty in globally resolved sea-surface temperature (SST), near-surface air temperature (T), sea-level pressure (SLP), and sea-ice concentration (SIC), with dynamical constraints. Here, we present a monthly resolved reconstruction using coupled data assimilation with LIMs from 1850–2023. We train LIMs on eight CMIP6 models to forecast the climate state and its error covariance, and we assimilate observations of SST, land T, marine SLP, and satellite-era SIC using the classic Kalman filter. We quantify uncertainty in model physics, observations, and bias corrections with 1600 ensemble members, and we validate the method by reconstructing an out-of-sample climate model. Key findings in the Tropics include post-1980 trends in the Walker circulation and zonal-Pacific SST gradient that are consistent with past variability, whereas the tropical SST contrast (the difference between warmer and colder SSTs) shows a consistent strengthening since 1975. ENSO amplitude exhibits substantial low-frequency variability and a local maximum in variance from 1875–1910. In polar regions, we find a muted cooling trend in the Southern Ocean post-1980 and substantial uncertainty. Changes in Antarctic sea ice are relatively small between 1850 and 2000, while Arctic sea ice declines by $0.5\pm0.1 \ (1\sigma)$ million km\textsuperscript{2} during the 1920s.