The scale factors produced by make_scale_factors are calculating a 'true' RMS of the data. Literally just np.sqrt(np.mean(y ** 2.0)). These values are not equivalent to the published Sheppard RMS and Theta Bar slope probability distributions calculated by slope_dist(). The slope probability distribution of the output DEM of make_zsurf can be modeled well using a least squares routine with slope_dist() as the objective function and equivalent Sheppard RMS and Theta Bar scale factors can be computed. However, this only seems to works well at low (~<30) RMS values. At higher RMS the probability distributions simply don't match well in overall shape and magnitude. I have been working on varying the make_zsurf parameters (Hurst Exponent and qr PSD rolloff wavevector) to see which parameters best match the traditional Sheppard RMS and Theta Bar values. This may take some time to figure out. In the short term, new scale factors can be generated for low RMS that better approximate Sheppard RMS and Theta Bar so that we know we are making solid comparisons for lower roughness surfaces like the Moon and Mars.
The scale factors produced by make_scale_factors are calculating a 'true' RMS of the data. Literally just np.sqrt(np.mean(y ** 2.0)). These values are not equivalent to the published Sheppard RMS and Theta Bar slope probability distributions calculated by slope_dist(). The slope probability distribution of the output DEM of make_zsurf can be modeled well using a least squares routine with slope_dist() as the objective function and equivalent Sheppard RMS and Theta Bar scale factors can be computed. However, this only seems to works well at low (~<30) RMS values. At higher RMS the probability distributions simply don't match well in overall shape and magnitude. I have been working on varying the make_zsurf parameters (Hurst Exponent and qr PSD rolloff wavevector) to see which parameters best match the traditional Sheppard RMS and Theta Bar values. This may take some time to figure out. In the short term, new scale factors can be generated for low RMS that better approximate Sheppard RMS and Theta Bar so that we know we are making solid comparisons for lower roughness surfaces like the Moon and Mars.