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We study the synchronization of two spatially extended dynamical systemswhere the models have imperfections. We show that the synchronization erroracross space can be visualized as a rough surface governed by theKardar-Parisi-Zhang equation with both upper and lower bounding wallscorresponding to nonlinearities and model discrepancies, respectively. Twotypes of model imperfections are considered: parameter mismatch and unresolvedfast scales, finding in both cases the same qualitative results. Theconsistency between different setups and systems indicates the results aregeneric for a wide family of spatially extended systems.

Synchronizing spatio-temporal chaos with imperfect models: a stochastic surface growth picture