The climate variability at multi-decadal and centennial scale over Antarctica is closely linked to the stability of regional glaciers, the whole ice sheet mass balance, and thus the estimation of future sea-level rise. However, the short instrumental data limit our ability to fully estimate such low-frequency variability. The main objective of this thesis is to reconstruct the centennial variability reproduced by low-and high-frequency records and climate models and to understand the related physical processes. Our reconstructions display the long-term cooling over the past millennium over West Antarctica, which has been captured by the current simulations with climate models. The centennial variability of surface air temperature could be primarily linked to external forcings, for instance, the volcanism, over the past millennium. In contrast, over the first millennium, naturally internal variability in the climate system plays a dominant role in these low-frequency changes. Our work also highlights that data assimilation is able to achieve the combination of the low-resolution proxy records with the high frequency ones based on climate model results without assuming a stationary relationship between proxy records and the target reconstruction. The corresponding reconstruction confirms the compatible information among various sources and provides the estimation for multiple climate variables which could help us understand the relevant mechanisms that might be responsible for the origin of the proxy records.