Adaptive sampling with unmanned aircraft in Rankine vortices

A comprehensive set of observing system simulation experiments (OSSEs) were designed to characterize sampling patterns for unmanned aircraft in a Rankine nature vortex. The OSSEs encompass a spectrum of ensemble vortex parameter distributions; variances for vortex intensity, radius, and position are adjusted to emphasize different modes of background uncertainty. In the simplest case where only intensity is uncertain, an ensemble Kalman filter (EnKF) can exploit the fully correlated background covariance structure to use a single arbitrarily located point observation to eliminate all uncertainty in the ensemble. Results presented in this talk demonstrate how a single radial intersecting the nature vortex's eye is sufficient to achieve a perfect state estimate regardless of how intensity, radius, and position are distributed.

The aforementioned sampling strategy is a broad result that holds for any combination of purely symmetric vortices, but its applicability is complicated by two factors. First, the feasibility of radial trajectories directly through the eye is constrained by the ratio of the peak wind speed to the aircraft cruise speed. Second, when observations are noisy, the “ideal” linear trajectory would require infinite sampling density to yield perfect information about the flow. Given a limited sampling period, trajectories with an azimuthal component can prove to be more efficient, maximizing independence between successive samples. We run an identical set of OSSEs as before, but incorporating feasibility constraints and adding noise to the observations. For each vortex parameter distribution, we find the most effective spirograph, suggesting how aircraft trajectories can be tailored to the ensemble "errors of the day."

The sampling theory developed here provides a planning component that can be readily integrated into a real-time feedback process between an ensemble forecast cycle and an unmanned aircraft fleet. Future experiments in which optimal trajectories are selected, then executed with a non-linear control algorithm, are expected to be an important application of our work.