  Roughness of driven elastic interfaces in random media is typically
understood to be characterized by a single roughness exponent $\zeta$. We show
that at the depinning threshold, due to symmetry breaking caused by the
direction of the driving force, elastic interfaces with local, long-range and
mean-field elasticity exhibit asymmetric roughness. It is manifested as a
skewed distribution of the local interface heights, and can be quantified by
using detrended fluctuation analysis to compute a spectrum of local,
segment-level scaling exponents. The asymmetry is observed as approximately
linear dependence of the local scaling exponents on the difference of the
segment height from the mean interface height.
