Surface fluxes are commonly inferred from vertical fluxes measured by micrometeorological techniques such as eddy covariance, in which horizontally homogeneous conditions are usually assumed so that the effect of advection and horizontal turbulent flux divergence can be ignored. These micrometeorological criteria are not easy to satisfy in practice. Surface flux inhomogeneities may lead to errors in estimates of surface fluxes based on point eddy-covariance measurements. Tower flux sites include multiple-scale surface heterogeneities that alter the flux measurements, and this influence depends on the height of the flux measurement. Scaling arguments show qualitatively that the effects of small-scale heterogeneity decay with height faster than large-scale effects. In this study, a three-dimensional turbulent scalar flux conservation equation is solved via second-order closure to quantify how surface heterogeneity affects fluxes at different heights. Two cases of surface heterogeneities, a single intermediate (3 km, 300m), and a random distribution across spatial scales up to 200km, are examined in the quasi-steady boundary layer. The meteorological fields are assumed initially to be horizontally homogeneous. The simulation shows that the effects of surface heterogeneity in general decays exponentially with the height, but at scales greater than a certain critical scale depending on the wind and turbulence fields, the perturbations caused by surface heterogeneity exist throughout the boundary layer. The simulations also indicate that the effects of scales larger than approximately 10km exist throughout the boundary layer. These results are qualitatively consistent with aircraft observations. The simulations will be used to estimate the influence of advection and horizontal flux divergence on surface fluxes inferred fluxes from single-point eddy-covariance measurements.