  We study the synchronization of two spatially extended dynamical systems
where the models have imperfections. We show that the synchronization error
across space can be visualized as a rough surface governed by the
Kardar-Parisi-Zhang equation with both upper and lower bounding walls
corresponding to nonlinearities and model discrepancies, respectively. Two
types of model imperfections are considered: parameter mismatch and unresolved
fast scales, finding in both cases the same qualitative results. The
consistency between different setups and systems indicates the results are
generic for a wide family of spatially extended systems.
