In a dynamical system the singular vector SV indicates which perturbation will exhibit maximal growth after a time interval . We show that in systems with spatiotemporal chaos the SV exponentially localizes in space. Under a suitable transformation, the SV can be described in terms of the Kardar-Parisi-Zhang equation with periodic noise. A scaling argument allows us to deduce a universal power law − for the localization of the SV. Moreover the same exponent characterizes the finite- deviation of the Lyapunov exponent in excellent agreement with simulations. Our results may help improve existing forecasting techniques.
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