Error Estimates of Double-Averaged Flow Statistics due to Sub-Sampling in an Irregular Canopy Model

Exploration of the flow inside the roughness sublayer often suffers from sub-sampling of its complex three-dimensional and non-homogeneous flow fields. Based on detailed particle image velocimetry within a randomly-ordered canopy model, we analyze the potential differences between single-location flow statistics and their spatially-averaged values. Overall, higher variability exists inside the canopy than above it, and is two to four times higher than found inside similar, however ordered, canopy arrangements. The local mean absolute percentage error (MAPE), vertically averaged within three different regions (below, above, and at canopy height), provides a measure for quantifying and characterizing the spatial distribution of errors for various flow properties (mean velocity and stresses). We calculated the value of MAPE at predefined farthest-locations based only on geometric considerations (i.e., farther away from surrounding roughness elements), as commonly done in the field. Interestingly, most of the vertical profiles at the farthest locations lie within the interquartile range of the measured spatial variability for all studied flow and turbulent properties. Additionally, our results show that, for at least 23% of the total canopy plan area, the double-averaged streamwise velocity component and its variance inside the canopy can be reproduced from a single measured profile for which the value of MAPE does not exceed 25%. These regions also constitute most of the farthest locations. The property that exhibits the highest MAPE value inside the canopy is the Reynolds stress (up to 130 %); however, these errors are dramatically reduced in the upper half of the canopy. Furthermore, at the canopy interface and above it, the errors rarely exceed 20 %. The variability is also manifested in the computed integral length scales. The single-point velocity autocorrelation always underestimates the length scales obtained from the two-point statistics. These findings have implications for canopy flow and transport modelling inside the roughness sublayer and can help explain and evaluate the source of discrepancies between measurements and transport models.