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Based on an extensive wind dataset over complex terrain, the commonly used small-angle approximation σv ≈ σθV is studied and found to overestimate over all wind speeds and σθ values observed. This should be anticipated due to the assumptions necessary to derive the approximation. Overestimation (of 10%–30%) is also observed in the small σθ range. The three parameters involved are further discussed to gain better understanding of the behavior of the approximation under different conditions. The standard deviation of wind direction σθ is shown to vary inversely with wind speed not only under stable, but also under convective conditions, reaching a site-dependent constant value at high wind speeds. The dependence of the ratio of the mean longitudinal wind component to the scalar mean wind speed on wind speed and σθ is examined, as well as that of the relevant standard deviations (σu,σVa). While the former obtains small values in the high-σθ, or low-wind range, or both, estimated values of the latter...