The scale at which topography and surface heat flux heterogeneity start to significantly affect the mean characteristics and structure of turbulence in the convective boundary layer (CBL) was evaluated with large-eddy simulations (LES). The LES option of the Regional Atmospheric Modeling System developed at Colorado State University was used for that purpose. We find that turbulence is non-linearly dependent on the scale of the topographical features and flux heterogeneity. At a horizontal length scale of less than about 4 km, topography has very little impact on the mean properties of the CBL even with hills as high as 30% the height of the CBL. However, it has a significant impact on the organization of the eddies. At larger horizontal scales, topographical features as small as about 10% the height of the CBL have some effect on the mean characteristics of the CBL. In particular, we notice a pronounced impact on the "dispersion" statistics (i.e., horizontal and vertical velocity variances and higher moments). Furthermore, the mean turbulence kinetic energy profile depicts two maxima, one near the ground surface and one near the top of the CBL, corresponding to the strong horizontal flow that develops near the ground surface and the return flow at the top of the CBL resulting from the organization of eddies into rolls. The larger the sensible heat flux fueling the CBL at the ground surface, the less important this impact is. We conclude that in a very irregular terrain, where topography presents a vertical scale of at least 200-400 m, and a horizontal scale of over 4 km, CBL parameterization of turbulence currently employed in mesoscale and large-scale atmospheric models (e.g., General Circulation Models) as well as in dispersion models, need to be improved. The impact of surface-flux heterogeneity is very similar, and a heat wave of 5-10 km is sufficient to trigger a significant impact on the CBL