We systematically study the role of surface roughness in fluid flow through rough fractures using direct numerical simulations. Random rough fractal surfaces are generated with different relative roughness, which are then decomposed using the wavelet analysis method. Different frequencies of surface topological information is filtered in a level-by-level procedure, while the large-scale waviness remains approximately unchanged. To explore the effects of surface roughness across a spectrum of length scales, simulations are carried out for each approximation level under different flow conditions and fracture spacing. Our results reveal the impact of relative roughness and roughness details at different length scales on the non-linear flow behavior due to inertia associated with formation of eddy flows. We further propose an error index to describe the relative error in permeability induced by limited resolution in surface profile description. Our analysis shows that the relative error in permeability from surfaces under different levels of approximation and relative roughness can be well described by the proposed index for a wide range of flow conditions and fracture apertures. This study provides insights into the role of multi-scale roughness on the fluid flow through rough fractures.