The effects on the Convective Boundary Layer (CBL) of surface heterogeneities produced by various topographical features and sensible heat waves with different means, amplitudes, and wavelengths, were investigated with a Large-Eddy Simulation (LES) model. A wavelet analysis was performed on the model outputs to identify the scales of response of the CBL to these various forcing. The major objective of this study was to evaluate at which scale surface heterogeneity starts to significantly affect the heat and momentum fluxes in the CBL. We find that the impact of amplitude and wavelength of the surface heterogeneity is nonlinearly dependent upon the mean heating rate. The circulations (or rolls) resulting from surface heterogeneity are relatively strong when the amplitude and the wavelength of the surface heterogeneity are relatively large, especially at low mean heating rate. In that case the profiles of horizontally-averaged variables are quite strongly modified in the CBL. The potential temperature is not constant with elevation, and the sensible heat flux considerably departs from the linear variation with height obtained in a typical CBL that develop over an homogeneous domain. The mean turbulence kinetic energy (TKE) 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. In a dry atmosphere, a relatively weak background wind of 2.5 ms-1 is strong enough to considerably reduce the impact of ground surface heterogeneity on the CBL. A moderate background wind of 5 m/s virtually eliminates all impacts that could potentially be produced in realistic landscapes. From this study, it can be concluded that as long as the "patchiness" of the landscape has a characteristic length scale smaller than about 5-10 km (even without background wind), the "mosaic of tiles" type of land-surface scheme suggested by Avissar and Pielke (1989) can be applied to represent the land surface in atmospheric models. At larger scales, the impact of landscape heterogeneity may be significant, especially when the atmosphere is humid. Therefore, this study supports previous estimates, which were based on theoretical analyses