  We study the time evolution of perturbations in spatially extended chaotic
systems in the presence of quenched disorder. We find that initially random
perturbations tend to exponentially localize in space around static pinning
centers that are selected by the particular configuration of disorder. The
spatial structure of typical perturbations, $\delta u(x,t)$, is analyzed in
terms of the Hopf-Cole transform, $h(x,t) \equiv\ln|\delta u(x,t)|$. Our
analysis shows that the associated surface $h(x,t)$ self-organizes into a
faceted structure with scale-invariant correlations. Scaling analysis of
critical roughening exponents reveals that there are three different
universality classes for error propagation in disordered chaotic systems that
correspond to different symmetries of the underlying disorder. Our conclusions
are based on numerical simulations of disordered lattices of coupled chaotic
elements and equations for diffusion in random potentials. We propose a
phenomenological stochastic field theory that gives some insights on the path
for a generalization of these results for a broad class of disordered extended
systems exhibiting space-time chaos.
