The last years a new highly demanding framework has been set for
environmental sciences and applied mathematics as a result of the needs
posed by issues that are of interest not only of the scientific
community but of today’s society in general: global warming, renewable
resources of energy, natural hazards can be listed among them. Two are
the main directions that the research community follows today in order
to address the above problems: The utilization of environmental
observations obtained from in situ or remote sensing sources and the
meteorological-oceanographic simulations based on physical-mathematical
models. In particular, trying to reach credible local forecasts the two
previous data sources are combined by algorithms that are essentially
based on optimization processes. The conventional approaches in this
framework usually neglect the topological-geometrical properties of the
space of the data under study by adopting least square methods based on
classical Euclidean geometry tools. In the present work new optimization
techniques are discussed making use of methodologies from a rapidly
advancing branch of applied Mathematics, the Information Geometry. The
latter prove that the distributions of data sets are elements of
non-Euclidean structures in which the underlying geometry may differ
significantly from the classical one. Geometrical entities like
Riemannian metrics, distances, curvature and affine connections are
utilized in order to define the optimum distributions fitting to the
environmental data at specific areas and to form differential systems
that describes the optimization procedures. The methodology proposed is
clarified by an application for wind speed forecasts in the
Kefaloniaisland, Greece
