Distance measurements using binoculars from ships at sea: accuracy, precision and effects of refraction

Abstract

The distances to 1,576 targets between 0.3 and 10.4km from two ships were measured using the reticle scale in 253 binoculars during cetacean surveys in the eastern tropical Pacific Ocean. Distances were measured under a range of conditions representing the environmental variability in three years of field surveys. Alternative formulae for calculating distance from optical devices were applied to the reticle measurements and compared to distances measured by radar. Reticles in 253 binoculars provided unbiased measurements to about a third of the way to the horizon, or from 0-4km for the 10.5m platform heights used for the study. Between 4 and 8km (approximately one-third to two-thirds of the distance to the horizon), distances tended to be slightly underestimated, reaching a maximum bias at the most distant targets of 6% for one ship and 16% for the other. Distances beyond about two-thirds of the way to the horizon were not measurable because the angles were too small. The negative bias in measurements of distances from 4-8km was due to refraction of light and other factors. Refraction had less of an effect than expected for a temperature gradient based on a standard atmosphere, suggesting a mean gradient for the eastern tropical Pacific of –0.02°C m–1 in the first 10m above the sea surface rather than the standard value of –0.0065°C m–1. Correcting the measurements for refraction improved their accuracy, eliminating the bias for one ship and reducing it for the other. Adjusting for refraction should improve measurements of distance using theodolites or photographic/video imaging as well as measurements using binoculars. An additional regression-based correction suggested that the remaining negative bias for one ship was a complex interaction of Beaufort Sea state, swell height and wind speed. Precision of distance measurements decreased multiplicatively with target distance. Including errors due to bias, the multiplicative standard error was 12%, or a 95% confidence interval from 0.8-1.2km for a target at 1km and from 6.5-9.9km for a target at 8km. Compared with other methods of measuring distance to marine mammals at sea, measurements using binocular reticles are more precise than distances estimated by eye, less precise than distances measured with photographic imaging, and useful over a larger range.