<p>The streamwise and vertical wind speed fluctuations predicted by a multi-scale wind speed fluctuation prediction model were introduced into a one-dimensional windblown sand model to simulate windblown sand under different friction velocities and particle sizes. And the scaling relation of major physical statistics was studied. Our results show that the mean and standard deviation of sand transport rate and average saltation velocity are proportional to <i>u</i>_*³/<i>g</i>. The mean and standard deviation of average saltation length are proportional to<i> u</i>_*²/<i>g</i>. The mean and standard deviation of speed and angle distribution of lift-off sand particles over time also need to consider friction velocity (<i>u</i>_*) and particle size. Here, <i>g</i> represents the gravitational acceleration. Empirical representations of mean and standard deviation of these five statistics were obtained based on the scaling relation, and the variations of coefficients with dimensionless particle size were mainly considered. Empirical representations provide a basis for simulating windblown sand over a large spatial range and introducing turbulent motions in the study of aeolian landforms.</p> Graphical abstract <p></p>