Minimizing the Uncertainties in Empirical Estimates of the Bulk Mean Canopy Drag Associated with Non-Stationary Mean Velocity

Parameterizing the exchange of momentum between canopies of large roughness elements (e.g., plants, wind turbines, and buildings) and the atmosphere for regional and global models requires understanding of the bulk drag-wind relationship. Developing a model for the bulk mean canopy drag from first principles is non-trivial, calling for empirical estimates from experimental data. The empirical estimates of bulk mean canopy drag assumes stationary mean velocity, a requirement never perfectly satisfied in the atmospheric boundary layer. The goal of this work is to minimize the uncertainties in empirical estimates of the bulk mean canopy drag associated with non-stationary mean velocity. Data obtained within and above a walnut orchard canopy during the Canopy Horizontal Array Turbulent Study (CHATS) are analyzed. For time intervals during which the characteristics of time series remain unchanging, the reverse arrangement test provides a desirable measure of stationarity that is insensitive to the arbitrary choice of the starting point within the time series and the duration of the time interval. Given a level of significance, we can determine groups of overlapping time intervals with stationary mean velocity. For a single group of overlapping time intervals, the probability distribution of bulk mean canopy drag can be either single- or multi-modal, and the uncertainties associated with single-modal distribution are remarkably smaller than the uncertainties associated with multi-modal distribution. The time intervals involving secondary modes of the bulk mean canopy drag contain time periods to which the starting or ending points of the stationary time intervals never belong, and can be excluded from analysis. The remaining time intervals solely associated with the primary mode are analyzed to quantify the minimum temporal variability of mean velocity. The criteria for stationary mean velocity is determined using time series measured in the field, without any arbitrary assumptions about the characteristics of the turbulent flow. This approach is capable of minimizing the uncertainties in empirical estimates of the mean canopy drag associated with non-stationary mean velocity, an essential step in developing reliable models of the drag-wind relationship for canopies of large roughness elements.