  This tutorial provides a broad introduction to Bayesian data assimilation
that will be useful to practitioners, in interpreting algorithms and results,
and for theoretical studies developing novel schemes with an understanding of
the rich history of geophysical data assimilation and its current directions.
The simple case of data assimilation in a 'perfect' model is primarily
discussed for pedagogical purposes. Some mathematical results are derived at a
high-level in order to illustrate key ideas about different estimators.
However, the focus of this work is on the intuition behind these methods, where
more formal and detailed treatments of the data assimilation problem can be
found in the various references. In surveying a variety of widely used data
assimilation schemes, the key message of this tutorial is how the Bayesian
analysis provides a consistent framework for the estimation problem and how
this allows one to formulate its solution in a variety of ways to exploit the
operational challenges in the geosciences.
