^{1,a)}, David K. Mellinger

^{1}, Len Thomas

^{2}, Tiago A. Marques

^{3}, David Moretti

^{4}and Jessica Ward

^{4}

### Abstract

Passive acoustic methods are increasingly being used to estimate animal population density. Most density estimation methods are based on estimates of the probability of detecting calls as functions of distance. Typically these are obtained using receivers capable of localizing calls or from studies of tagged animals. However, both approaches are expensive to implement. The approach described here uses a MonteCarlo model to estimate the probability of detecting calls from single sensors. The passive sonar equation is used to predict signal-to-noise ratios (SNRs) of received clicks, which are then combined with a detector characterization that predicts probability of detection as a function of SNR. Input distributions for source level, beam pattern, and whale depth are obtained from the literature. Acoustic propagation modeling is used to estimate transmission loss. Other inputs for density estimation are call rate, obtained from the literature, and false positive rate, obtained from manual analysis of a data sample. The method is applied to estimate density of Blainville’s beaked whales over a 6-day period around a single hydrophone located in the Tongue of the Ocean, Bahamas. Results are consistent with those from previous analyses, which use additional tag data.

This research was undertaken as part of the Density Estimation for Cetaceans from passive Acoustic Fixed sensors (DECAF) project, work supported by National Oceanographic Partnership Program grant 2007-0145-002. It was also supported by Naval Postgraduate School grants N00244-08-1-0029, N00244-09-1-0079, and N00244-10-1-0047. This is NOAA/PMEL contribution No. 3648.

I. INTRODUCTION

II. BEAKED WHALES AT AUTEC

III. DENSITY ESTIMATION

IV. ESTIMATING CLICK DETECTION PROBABILITY

A. Animal location and orientation

B. Source level

C. Off-axis attenuation of source level

D. Transmission loss

E. Ambient noise levels

F. Detector characterization

G. Probability of detection: Monte Carlo simulations

V. ESTIMATION OF CLICK PRODUCTION RATE

VI. RESULTS AND DISCUSSION

### Key Topics

- Microphones
- 46.0
- Agroacoustics
- 29.0
- Acoustic sensing
- 13.0
- Data analysis
- 13.0
- Acoustic signal processing
- 9.0

## Figures

Distribution of AUTEC’s hydrophones showing the single sensor (#57) used in this paper’s analysis, and the sensors used in ambient noise measurements.

Distribution of AUTEC’s hydrophones showing the single sensor (#57) used in this paper’s analysis, and the sensors used in ambient noise measurements.

Whale orientation and respective angles. Upper diagrams show whale heading and pitch, and lower diagrams show whale heading and elevation angle with respect to the hydrophone. These angles are necessary to estimate the acoustic off-axis angle between whale and hydrophone (see text).

Whale orientation and respective angles. Upper diagrams show whale heading and pitch, and lower diagrams show whale heading and elevation angle with respect to the hydrophone. These angles are necessary to estimate the acoustic off-axis angle between whale and hydrophone (see text).

Attenuation of source level as a function of off-axis angle for Blainville’s beaked whales, estimated by using a piston model with radius of 16 cm.

Attenuation of source level as a function of off-axis angle for Blainville’s beaked whales, estimated by using a piston model with radius of 16 cm.

Sound speed as a function of depth measured in spring at the AUTEC range and used as input for the transmission loss calculations.

Sound speed as a function of depth measured in spring at the AUTEC range and used as input for the transmission loss calculations.

Transmission loss as a function of range, or distance between source and receiver, for 3 different depths: (top) 400, (middle) 800, and (bottom) 1200 m. The different curves represent results of calculations for the coherent (gray) and incoherent (solid black) acoustic fields as well as the spherical spreading law with frequency-dependent attenuation α = 8.9 dB/km (dashed).

Transmission loss as a function of range, or distance between source and receiver, for 3 different depths: (top) 400, (middle) 800, and (bottom) 1200 m. The different curves represent results of calculations for the coherent (gray) and incoherent (solid black) acoustic fields as well as the spherical spreading law with frequency-dependent attenuation α = 8.9 dB/km (dashed).

High-frequency ambient noise levels, integrated over 24–48 kHz, measured at five different hydrophones at AUTEC and used in the Monte Carlo simulations.

High-frequency ambient noise levels, integrated over 24–48 kHz, measured at five different hydrophones at AUTEC and used in the Monte Carlo simulations.

Probability of detection (*P*) as a function of signal-to-noise ratio (SNR), estimated by fitting a binary generalized additive model (GAM) to the manually annotated detections. The vertical lines on the top of the figure correspond to the manually detected clicks that were also detected by the FFT detector, and the ones at the bottom correspond to the manually detected clicks that were not detected by the FFT detector. Circles summarize the data, showing the proportion detected in 8 successive intervals, each containing 1/8 of the measured clicks; the vertical lines above and below each circle indicate 95% binomial confidence intervals for each proportion. Solid line shows estimate from the GAM, and dashed lines are 95% pointwise confidence intervals. The fall-off in detection probability at high SNR is discussed in the text.

Probability of detection (*P*) as a function of signal-to-noise ratio (SNR), estimated by fitting a binary generalized additive model (GAM) to the manually annotated detections. The vertical lines on the top of the figure correspond to the manually detected clicks that were also detected by the FFT detector, and the ones at the bottom correspond to the manually detected clicks that were not detected by the FFT detector. Circles summarize the data, showing the proportion detected in 8 successive intervals, each containing 1/8 of the measured clicks; the vertical lines above and below each circle indicate 95% binomial confidence intervals for each proportion. Solid line shows estimate from the GAM, and dashed lines are 95% pointwise confidence intervals. The fall-off in detection probability at high SNR is discussed in the text.

Estimated detection function as a function of slant distance for three angles measured from the whale’s acoustic axis: 0° (solid), 45° (dashed), and 90° (dotted).

Estimated detection function as a function of slant distance for three angles measured from the whale’s acoustic axis: 0° (solid), 45° (dashed), and 90° (dotted).

Average probability of detection from the 10 000 simulated clicks for each realization of energy flux density taken from a Gaussian distribution.

Average probability of detection from the 10 000 simulated clicks for each realization of energy flux density taken from a Gaussian distribution.

## Tables

Values used to estimate whale clicking depth *z* and pitch β for three distinct dive phases. Click proportion is an estimate of the fraction of clicks produced during each dive phase. Mean depth and standard deviation (in parentheses) are used in Gaussian distributions for sampling clicking depths. Pitch distribution indicates the distribution used for each dive phase, the pitch range, and values used for the required distribution parameters. Negative pitch is measured downwards.

Values used to estimate whale clicking depth *z* and pitch β for three distinct dive phases. Click proportion is an estimate of the fraction of clicks produced during each dive phase. Mean depth and standard deviation (in parentheses) are used in Gaussian distributions for sampling clicking depths. Pitch distribution indicates the distribution used for each dive phase, the pitch range, and values used for the required distribution parameters. Negative pitch is measured downwards.

Source levels of beaked whales, *Ziphius cavirostris* (Zc) and *Mesoplodon densirostris* (Md), available in the literature. Source levels are in dB re 1 µPa at 1 m. Note that RMS values can vary depending on the window length used.

Source levels of beaked whales, *Ziphius cavirostris* (Zc) and *Mesoplodon densirostris* (Md), available in the literature. Source levels are in dB re 1 µPa at 1 m. Note that RMS values can vary depending on the window length used.

Vocal behavior data for beaked whales, *Ziphius cavirostris* (Zc) and *Mesoplodon densirostris* (Md), available in the literature and used for estimating click production rate. The inter-click interval (ICI), mean click duration, duration of deep foraging dives, the amount of time spent clicking during each dive, the IDI (or inter-deep-dive interval), and the number of buzz clicks produced per foraging dive are derived from acoustic tag studies.

Vocal behavior data for beaked whales, *Ziphius cavirostris* (Zc) and *Mesoplodon densirostris* (Md), available in the literature and used for estimating click production rate. The inter-click interval (ICI), mean click duration, duration of deep foraging dives, the amount of time spent clicking during each dive, the IDI (or inter-deep-dive interval), and the number of buzz clicks produced per foraging dive are derived from acoustic tag studies.

Summary of the values derived for each parameter needed to estimate density of Blainville’s beaked whale at AUTEC using Eq. (1), and their associated CVs.

Summary of the values derived for each parameter needed to estimate density of Blainville’s beaked whale at AUTEC using Eq. (1), and their associated CVs.

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