  We propose reduced order methods as a suitable approach to face parametrized
optimal control problems governed by partial differential equations, with
applications in en- vironmental marine sciences and engineering. Environmental
parametrized optimal control problems are usually studied for different
configurations described by several physical and/or geometrical parameters
representing different phenomena and structures. The solution of parametrized
problems requires a demanding computational effort. In order to save com-
putational time, we rely on reduced basis techniques as a reliable and rapid
tool to solve parametrized problems. We introduce general parametrized linear
quadratic optimal control problems, and the saddle-point structure of their
optimality system. Then, we propose a POD-Galerkin reduction of the optimality
system. Finally, we test the resulting method on two environmental
applications: a pollutant control in the Gulf of Trieste, Italy and a solution
tracking governed by quasi-geostrophic equations, in its linear and nonlinear
version, describing North Atlantic Ocean dynamic. The two experiments underline
how reduced order methods are a reliable and convenient tool to manage several
environmental optimal control problems, for different mathematical models,
geographical scale as well as physical meaning.
