Abstract
The transport of material through the atmosphere is an issue with wide ranging implications for fields as diverse as agriculture, aviation, and human health. Due to the unsteady nature of the atmosphere, predicting how material will be transported via the Earth’s wind field is challenging. Lagrangian diagnostics, such as Lagrangian coherent structures (LCSs), have been used to discover the most significant regions of material collection or dispersion. However, Lagrangian diagnostics can be time-consuming to calculate and often rely on weather forecasts that may not be completely accurate. Recently, Eulerian diagnostics have been developed which can provide indications of LCS and have computational advantages over their Lagrangian counterparts. In this paper, a methodology is developed for estimating local Eulerian diagnostics from wind velocity data measured by a single fixed-wing unmanned aircraft system (UAS) flying in a circular arc. Using a simulation environment, driven by realistic atmospheric velocity data from the North American Mesoscale (NAM) model, it is shown that the Eulerian diagnostic estimates from UAS measurements approximate the true local Eulerian diagnostics and also predict the passage of LCSs. This methodology requires only a single flying UAS, making it easier and more affordable to implement in the field than existing alternatives, such as multiple UASs and Dopler LiDAR measurements. Our method is general enough to be applied to calculate the gradient of any scalar field.
Highlights
The transport of material in the atmosphere is a problem with important implications for agriculture [1,2,3,4], aviation [5,6], and human health [7,8]
Using realistic atmospheric velocity data from the North American Mesoscale (NAM) 3 km model, this algorithm was applied to circular trajectories restricted to a 2D isosurface and simulated unmanned aircraft system (UAS) flights in 3D, with radii ranging from 2 km to 15 km
The approximations were very good for the smaller radii that were looked at, but even the larger radii approximations were able to pick up the trend of the trajectory divergence rate and attraction rate, though they underestimated the magnitude
Summary
The transport of material in the atmosphere is a problem with important implications for agriculture [1,2,3,4], aviation [5,6], and human health [7,8]. The study of atmospheric transport from a dynamical systems perspective has long focused on the study of large-scale phenomena [1,2,3,4,5,9,10,11,12] This has been largely due to the larger-scale grid spacing of readily available atmospheric model data and the lack of high-resolution atmospheric measurements on a scale large enough to calculate Lagrangian data. This field of study has been largely relegated to numerical simulations. In [6,13], the authors used wind velocity measurements from a Doppler light detection and ranging (LiDAR) to detect LCS which had passed near Hong Kong
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