When using the mean wind direction in Reynolds-averaged Navier-Stokes (RANS) simulations of atmospheric dispersion, it is well documented that peak concentration levels are often overestimated, and lateral spreading underestimated. A number of studies report that if the variability of wind directions observed in experiments is included in the boundary conditions, peak levels improve, but lateral spreading is overestimated. In the current work, we argue that fluctuations in wind directions observed in experiments are partly accounted for by the modeled turbulence in RANS simulations; and hence, the effective variability that should be used as a boundary condition to the simulations, needs to be lower than experimentally measured. A simple approach is proposed that reduces the variability based on turbulence levels predicted in the RANS turbulence model. We test the approach by performing a series of dispersion simulations of the well-documented Prairie Grass experiments, and demonstrate that simulations improve significantly.