Visual anemometry of natural vegetation from their leaf motion

High-resolution, near-ground wind-speed data are critical for improving the accuracy of weather predictions and climate models,$^{1-3}$ supporting wildfire control efforts,$^{4-7}$ and ensuring the safe passage of airplanes during takeoff and landing maneouvers.$^{8,9}$ Quantitative wind speed anemometry generally employs on-site instrumentation for accurate single-position data or sophisticated remote techniques such as Doppler radar for quantitative field measurements. It is widely recognized that the wind-induced motion of vegetation depends in a complex manner on their structure and mechanical properties, obviating their use in quantitative anemometry.$^{10-14}$ We analyze measurements on a host of different vegetation showing that leaf motion can be decoupled from the leaf's branch and support structure, at low-to-moderate wind speed, $U_{wind}$. This wind speed range is characterized by a leaf Reynolds number, enabling the development of a remote, quantitative anemometry method based on the formula, $U_{wind}\approx740\sqrt{{\mu}U_{leaf}/{\rho}D}$, that relies only on the leaf size $D$, its measured fluctuating (RMS) speed $U_{leaf}$, the air viscosity $\mu$, and its mass density $\rho$. This formula is corroborated by a first-principles model and validated using a host of laboratory and field tests on diverse vegetation types, ranging from oak, olive, and magnolia trees through to camphor and bullgrass. The findings of this study open the door to a new paradigm in anemometry, using natural vegetation to enable remote and rapid quantitative field measurements at global locations with minimal cost.