A primer on upscaling tools for porous media

Over the last few decades a number of powerful approaches have been developed to intelligently reduce the number of degrees of freedom in very complex heterogeneous environs, e.g. mathematical homogenization, mixture and hybrid mixture theory, spatial averaging, moment methods, central limit or Martingale methods, stochastic-convective approaches, various other Eulerian and Lagrangian perturbation schemes, projection operators, renormalization group techniques, variational approaches, space transformational methods, continuous time random walks, and etc. In this article we briefly review many of these approaches as applied to specific examples in the hydrologic sciences.