  We introduce a new framework of numerical multiscale methods for
advection-dominated problems motivated by climate sciences. Current numerical
multiscale methods (MsFEM) work well on stationary elliptic problems but have
difficulties when the model involves dominant lower order terms. Our idea to
overcome the assocociated difficulties is a semi-Lagrangian based
reconstruction of subgrid variablity into a multiscale basis by solving many
local inverse problems. Globally the method looks like a Eulerian method with
multiscale stabilized basis. We show example runs in one and two dimensions and
a comparison to standard methods to support our ideas and discuss possible
extensions to other types of Galerkin methods, higher dimensions and nonlinear
problems.
