Mathematical models that describe distributed parameter systems are composed of systems of partial differential and algebraic equations. The methods that solve these systems usually yield a high-order (infinite-dimensional) solution. However, for controller synthesis and practical considerations, a low-order model is preferred. This work addresses the development of model reduction through the use of multi-resolution methods that not only yield a finite low-order model but also a representation of the system's multiscale and local behavior such that scale-specific compensation can be realized. Two systems - heat transfer along a flat metal plate, and a packed-bed reactor with axial dispersion are used to demonstrate the proposed approach.