  We commonly refer to state-estimation theory in geosciences as data
assimilation. This term encompasses the entire sequence of operations that,
starting from the observations of a system, and from additional statistical and
dynamical information (such as a dynamical evolution model), provides an
estimate of its state. Data assimilation is standard practice in numerical
weather prediction, but its application is becoming widespread in many other
areas of climate, atmosphere, ocean and environment modeling; in all
circumstances where one intends to estimate the state of a large dynamical
system based on limited information. While the complexity of data assimilation,
and of the methods thereof, stands on its interdisciplinary nature across
statistics, dynamical systems and numerical optimization, when applied to
geosciences an additional difficulty arises by the continually increasing
sophistication of the environmental models. Thus, in spite of data assimilation
being nowadays ubiquitous in geosciences, it has so far remained a topic mostly
reserved to experts. We aim this overview article at geoscientists with a
background in mathematical and physical modeling, who are interested in the
rapid development of data assimilation and its growing domains of application
in environmental science, but so far have not delved into its conceptual and
methodological complexities.
