Special problems in the estimation of power-law spectra as applied to topographical modeling

An increasing number of topographical studies find that natural surfaces possess power-law roughness spectra. Power-law spectra introduce unique difficulties in the spectral estimation process. The authors describe how an improper window choice allows leakage that yields a spectral estimate that is insensitive to the spectral slope. In addition, the commonly used Fourier-based spectral estimates have higher variances than other available estimators. Higher variance is particularly problematic when data records are short, as is often the case in remote sensing studies. The authors show that Capon´s spectral estimator has less variance than Fourier-based estimators and measures the spectral slope more accurately. The authors also show how estimates of a 2D roughness spectrum can be obtained from estimates of the 1D spectrum for the isotropic power-law case