Bayesian approach for predicting photogrammetric uncertainty in morphometric measurements derived from drones

Increasingly, drone-based photogrammetry has been used to measure size and body condition changes in marine megafauna. A broad range of platforms, sensors, and altimeters are being applied for these purposes, but there is no unified way to predict photogrammetric uncertainty across this methodological spectrum. As such, it is difficult to make robust comparisons across studies, disrupting collaborations amongst researchers using platforms with varying levels of measurement accuracy. Here we built off previous studies quantifying uncertainty and used an experimental approach to train a Bayesian statistical model using a known-sized object floating at the water's surface to quantify how measurement error scales with altitude for several different drones equipped with different cameras, focal length lenses, and altimeters. We then applied the fitted model to predict the length distributions and estimate age classes of unknown-sized humpback whales Megaptera novaeangliae, as well as to predict the population-level morphological relationship between rostrum to blowhole distance and total body length of Antarctic minke whales Balaenoptera bonaerensis. This statistical framework jointly estimates errors from altitude and length measurements from multiple observations and accounts for altitudes measured with both barometers and laser altimeters while incorporating errors specific to each. This Bayesian model outputs a posterior predictive distribution of measurement uncertainty around length measurements and allows for the construction of highest posterior density intervals to define measurement uncertainty, which allows one to make probabilistic statements and stronger inferences pertaining to morphometric features critical for understanding life history patterns and potential impacts from anthropogenically altered habitats.