Precision and bias in estimating detection distances for beaked whale echolocation clicks using a two-element vertical hydrophone array

Detection distances are critical for cetacean density and abundance estimation using distance sampling methods. Data from a drifting buoy system consisting of an autonomous recorder and a two-element vertical hydrophone array at ∼100-m depth are used to evaluate three methods for estimating the horizontal distance (range) to beaked whales making echolocation clicks. The precision in estimating time-differences-of-arrival (TDOA) for direct- and surface-reflected-path clicks is estimated empirically using repeated measures over short time periods. A Teager-Kaiser energy detector is used to improve estimates of TDOA for surface-reflected signals. Simulations show that array tilt in the direction of the source cannot be reliably estimated given this array geometry and these measurements of TDOA error, which means that range cannot be reliably estimated. If array tilt can be reduced to less than 0.5°, range can be reliably estimated up to ∼3000 m. If array depth is increased to 200 m and array tilt is less than 1°, range can be reliably estimated up to ∼5000 m. Prior information on the depth of vocalizing beaked whales and estimates of declination angle can be used to precisely estimate range, but different analytical methods are required to avoid bias and to treat distributions of depth probabilistically.