  This work introduces a new, distributed implementation of the Ensemble Kalman
Filter (EnKF) that allows for non-sequential assimilation of large datasets in
high-dimensional problems. The traditional EnKF algorithm is computationally
intensive and exhibits difficulties in applications requiring interaction with
the background covariance matrix, prompting the use of methods like sequential
assimilation which can introduce unwanted consequences, such as dependency on
observation ordering. Our implementation leverages recent advancements in
distributed computing to enable the construction and use of the full model
error covariance matrix in distributed memory, allowing for single-batch
assimilation of all observations and eliminating order dependencies.
Comparative performance assessments, involving both synthetic and real-world
paleoclimatic reconstruction applications, indicate that the new,
non-sequential implementation outperforms the traditional, sequential one.
