Using UAS to Assess Impact of Terrain Heterogeneity on Measured Profile Uncertainty within the Atmospheric Boundary Layer

Recent advances in small uncrewed aerial system (sUAS) meteorological sensing capability have raised interest in, and demonstrated the potential for, assimilating data from sUAS into operational weather forecasting. These systems present an opportunity for low-cost, high-resolution profiling within the planetary boundary layer, thereby increasing fidelity of forecasts in a region of the boundary layer utilized for urban air mobility operations. The most practical configuration for autonomous, or semi-autonomous, UAS meteorological measurements is that of a rotorcraft UAS conducting periodic profiling at a fixed location.

As many contemporary approaches to data assimilation employ ensemble Kalman filtering to assimilate observations into forecasts, a priori knowledge of the measurement uncertainty is necessary to ensure effective assimilation of the sUAS data into the numerical weather prediction. Although much effort has been made to identify and minimize measurement uncertainty of the sUAS, there has been much less attention devoted to the impact of spatial heterogeneity on the representativeness of near-surface thermodynamic and kinematic profiles. The influence of this spatial heterogeneity can be expected to be dependent on the temporal and spatial resolution of the numerical weather prediction.

To evaluate the uncertainty corresponding to such spatial heterogeneity, we conducted several measurements employing multiple fixed-wing sUAS simultaneously measuring over different terrain to obtain an estimate of the statistical variation of key properties. These measurements of temperature, relative humidity and wind speed and direction, were made by the aircraft flying in rectangular flight patterns at a constant pressure altitude to allow statistical evaluation of both temporal and spatial dependencies of the measured properties. Measurements were also made with a profiling rotorcraft and ground reference to provide comparison and validation data, although these measurements have not yet been incorporated into the analysis.

We examined spatial dependency of the statistics along the longitudinal axis of the flight pattern, which was divided into statistical ensembles of varying length, Δx, allowing quantification of the spatial dependence of the statistics on Δx. Temporal dependence was determined by treating each pass along the longitudinal axis as a separate transect. Statistics were then calculated over a varying timescale corresponding to Δt = nδt, where n is the number of transects included in the calculation and δt is the average time between transects. In this way the dependence of, for example, a statistical average can be found as a function of Δx and Δt, which act as analogues to a numerical mesh size and time step. As the objective of the analysis was to examine the variability of measured variables relative to a single profile of scale Δx→0 and Δt→0, a variance calculation was conducted which treated each segment of a particular Δx and Δt combination as a separate sample, with the variance thereby providing a measure of variability in the statistical values calculated over a span of Δx and Δt. By normalizing by the value measured at Δx→0 and Δt→0, an uncertainty estimate is thereby provided. Results show the uncertainty of assuming a single profile measurement of wind velocity magnitude represents the mean value of a mesh scale and time step of Δx and Δt, can reach values up to 50% over a 25 minute time step and 500 m numerical cell.

The form of the uncertainty dependence on spatial and temporal step size also suggests that a model can be developed by assuming the variability arises due to the turbulent velocity fluctuations within the numerical mesh. By using a simple spectral model of turbulence, this structure can be recreated. Although there are some differences in the magnitude of the uncertainty, the statistical distributions are similar enough to suggest that there is merit in the approach. Furthermore, the results suggest that uncertainty estimates can be reproduced using only an estimate of the turbulence dissipation rate and integral scale. The influence of topography is then contained within the modification of these two parameters, allowing an uncertainty estimate of the sUAS measurement to be obtained from the numerical weather prediction itself.

Work is currently ongoing to extend this analysis for temperature and moisture content, as well as to examine the influence of boundary layer stability, and height above ground level using recently acquired measurements. We also intend to compare this approach to additional uncertainty estimate determination schemes currently in development.