TÉCNICAS E INSTRUMENTOS 43

As the DTAG does not contain a speed sensor, speed was estimated by merging analyses of kinematic measurements and flow noise, recorded simultaneously and continuously with the DTAG. Flow noise is combined with sensor data since speed estimation from kinematics is only accurate during ascents and descents, when the whale has high body pitch angles. The greater the body pitch angle, the closer speed through the water can be estimated using the rate of change of depth.

Speed was derived from the sound pressure levels (SPL’s) of the recorded low-frequency flow noise, as done previously by other authors (Goldbogen et al., 2006; Simon et al., 2009; Goldbogen et al., 2012; Simon et al., 2012), per individual whale to account for tag placement, and per tag period to account for tag movements. Acoustic data were uploaded and sub- sampled from 96 kHz to 1 kHz to reduce the size of the data for analyses. A 4th order Butterworth low-pass filter was implemented to create a sharp frequency cut-off and have a flat frequency response. The frequency of the low-pass filter varied from 200 to 350 Hz between individuals and was specified per tag record so that the fluctuations in flow noise, within individual records, were captured most effectively. Root mean squared (RMS) levels, with an averaging window of 50 ms, were computed from the squared band-pass filtered

pressures using the “filtfilt”-function in MATLAB® to eliminate a phase shift. These were ultimately converted into SPL’s in µPa, which had the same sampling rate as the sensor data (50 Hz).

Speed through the water was estimated kinematically for all entire tag records by using the “vertical”-function in MATLAB® (Johnson, unpublished data) to calculate the rate of depth change. The depth change rate over 1s intervals was divided by the sine of the body pitch angle:

(dt – dt-1) / sin αt, (3)

Where dt is the depth at second t, dt-1 is the depth at the preceding second, and αt is the body

pitch angle at second t.

The SPL’s from the flow noise and the kinematic speed estimates from the sensor data were synchronized over 1s intervals. A pitch angle threshold was introduced which varied per individual and per tag period depending on data quantity and pitch angle occurrence and distribution. The lowest minimal pitch angle used was + 45°/ - 45°, which seemed realistic compared to previous studies (Miller et al., 2004; Ware et al., 2011). The highest minimal pitch angle used was + 65°/ - 65°, equal to the one used by Goldbogen et al. (2006). As surfacings produced high flow noise levels as well, unrelated to swimming speed, a depth threshold of 10 m was implemented to eliminate intervals at the surface.

After eliminating surfacing intervals and intervals with small body pitch angles an exponential least-squares fit between the flow noise SPL’s and speed through water was established per tag record and tag period within records using regression analyses, using the following equation:

U = a * exp (b * SPL), (4)

Where, U is the speed through water in m·s-1, a and b are estimated coefficients, and SPL is the sound pressure level in dB re 1 µPa calculated from the flow noise. Other authors which conducted studies on speed estimations from flow noise foregoing this study mostly chose for

a polynomial function (Goldbogen et al., 2006; Goldbogen et al., 2008; Simon et al., 2012). However, during this study an exponential function was chosen as regression between SPL and speed through water particularly since a polynomial curve would result in an unrealistic increase in speed estimation for SPL values lower than the SPL value that gives the lowest speed estimation. The parameters for this exponential function were determined per individual whale and per tag period within individuals. To define valuable correlations there had to be a considerable amount of data points (depending on spreading) covering a range of at least 10 dB. In the occurrence of a gradual tag movement, an average correlation was determined from the previous and following tag period. When for one of these periods it was not feasible to determine a speed-SPL correlation, the gradual movement period was handles as a normal tag period if feasible. For tag periods for which it was not feasible to determine the speed-SPL correlation, the correlation of the preceding period was maintained. These established relationships were then used to calculate the continuous speed through the water from the recorded flow noise level per one-second intervals for the entire tag records.

To take into account speed overestimation by the increase of the SPL caused by breaking the surface, it was investigated whether it was more sensible to take either a time criterion around a breathing event or a depth criterion; it appeared that the time criterion was more accurate in accounting for SPL difference caused by surfacing. Accordingly, the speed measurements of the three last seconds before the breath and at time of the breath were replaced by the measurement of the fourth second before the breath. The three succeeding measurements after the breathing event were replaced with the speed value of the fourth second after the breathing event.

Consequently, time series data of speed for all individual whales were investigated for outliers through evaluating the difference between consecutive 1s measurements. The difference threshold was set at 2.8 m·s-1 after which the number of observations showing a greater deviation than this decreased substantially. When a speed measurement showed a greater deviation from the previous or succeeding measurement than this criterion, the measurement was considered an outlier and replaced by the mean speed of that entire tag record. One female (06_327s) and three males (06_327t, 09_144a and 09_144b) showed outliers, with a minimum of one (06_327s, 06_327t, and 09_144b) and a maximum of four (09_144a) per tagging record.

For one male no audio was recorded, while for one female there were insufficient periods with sufficient pitch angles to derive kinematic speed. Both of these individuals were excluded from speed analyses.