  In a dynamical system the singular vector (SV) indicates which perturbation
will exhibit maximal growth after a time interval $\tau$. 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 $\tau^{-\gamma}$ for the localization of the
SV. Moreover the same exponent $\gamma$ characterizes the finite-$\tau$
deviation of the Lyapunov exponent in excellent agreement with simulations. Our
results may help improving existing forecasting techniques.
