  The failure of roughness parameters to predict surface properties stems from
their inherent scale-dependence; in other words, the measured value depends on
the way it was measured. Here we take advantage of this scale-dependence to
develop a new framework for characterizing rough surfaces: the Scale-Dependent
Roughness Parameters (SDRP) analysis that yields slope, curvature and
higher-order derivatives of surface topography at many scales, even on a single
topography measurement. We demonstrate the relationship between SDRP and other
common statistical methods for analyzing surfaces: the height-difference
autocorrelation function (ACF), variable bandwidth methods (VBMs) and the power
spectral density (PSD). We use computer-generated and measured topographies to
demonstrate the benefits of SDRP analysis, including: novel metrics for
characterizing surfaces across scales, and the detection of measurement
artifacts. The SDRP is a generalized framework for scale-dependent analysis of
surface topography that yields metrics that are intuitively understandable.
