The challenges of estimating the distribution of flight heights from telemetry or altimetry data

Abstract Background Global positioning systems (GPS) and altimeters are increasingly used to monitor vertical space use by aerial species, a key aspect of their ecological niche, that we need to know to manage our own use of the airspace, and to protect those species. However, there are various sources of error in flight height data (“height” above ground, as opposed to “altitude” above a reference like the sea level). First the altitude is measured with a vertical error from the devices themselves. Then there is error in the ground elevation below the tracked animals, which translates into error in flight height computed as the difference between altitude and ground elevation. Finally, there is error in the horizontal position of the animals, which translates into error in the predicted ground elevation below the animals. We used controlled field trials, simulations, and the reanalysis of raptor case studies with state-space models to illustrate the effect of improper error management. Results Errors of a magnitude of 20 m appear in benign conditions for barometric altimeters and GPS vertical positioning (expected to be larger in more challenging context). These errors distort the shape of the distribution of flight heights, inflate the variance in flight height, bias behavioural state assignments, correlations with environmental covariates, and airspace management recommendations. Improper data filters such as removing all negative flight height records introduce several biases in the remaining dataset, and preclude the opportunity to leverage unambiguous errors to help with model fitting. Analyses that ignore the variance around the mean flight height, e.g., those based on linear models of flight height, and those that ignore the variance inflation caused by telemetry errors, lead to incorrect inferences. Conclusion The state-space modelling framework, now in widespread use by ecologists and increasingly often automatically implemented within on-board GPS data processing algorithms, makes it possible to fit flight models directly to the output of GPS devices, with minimal data pre-selection, and to analyse the full distribution of flight heights, not just the mean. In addition to basic research about aerial niches, behaviour quantification, and environmental interactions, we highlight the applied relevance of our recommendations for airspace management and the conservation of aerial wildlife.