Laboratory and field calibrations
Ten V16P-6H acoustic transmitters with pressure sensors (from Vemco: maximum depth = 68 m, accuracy = ±3.4 m, resolution = 0.3 m) were first calibrated in a pressurized chamber at Hammond Bay Biological Station (HBBS; Millersburg, MI). Transmitters were then surgically implanted into adult Lake Trout (Salvelinus namaycush) or Walleye (Sander vitreus) that were released into Lake Huron for a period of 23–351 days before being recaptured and returned by commercial or recreational fishers. (The implantation of the transmitters in fish was incidental to this study). Returned transmitters were then calibrated via an additional laboratory calibration and two field calibrations.
Post-recapture laboratory calibrations were performed at Carleton University (Ottawa, ON) using a different pressure chamber than was used for pre-deployment calibrations at HBBS (Fig. 1). The two pressure chambers were constructed identically from 10-cm diameter, schedule-40 PVC (PolyVinyl Chloride) pipe (1.2 m long), which was sealed on the bottom end with a PVC cap. The top end of the PVC tube was capped with a 20-cm y-fitting (schedule 40 PVC) containing a Banjo cam-lever cap (Alsco Industrial Products, Inc.) for accessing the chamber, a Tel-Tru stainless steel pressure gauge (Tel-Tru Manufacturing Company; model 33: 0–30 PSI), an air-filling valve, and a release valve for controlling and monitoring pressure within the chamber. The chambers were 3/4 filled with room-temperature water, and an acoustic receiver (Vemco, model VR2W) was placed in the bottom of the chamber to record transmissions. A maximum of six transmitters were suspended near the water surface inside the chamber at one time to limit the frequency of transmitter signal collisions. The chamber was then sealed, and pressure was increased to 21 psi (equivalent to the pressure at a depth of 14.8 m in fresh water at sea level) using a 6-gallon 150-psi pancake electric air compressor. The pressure was maintained at 21 psi for 10 min, and then decreased to 16 psi for another 10 min. These steps were repeated for pressures of 11, 6, and 0 psi (i.e., 7.75, 4.23, and 0 m). A more powerful air compressor with a maximum pressure of 200 psi can be used to simulate a depth of 140 m, although appropriate safety protocols should be used to ensure safety of operators.
Field calibrations were conducted in Toronto Harbour (Toronto, ON) and Lake 373 within the Experimental Lakes Area (ELA) (Kenora, ON) with a mobile acoustic receiver (Vemco, model: VR100) and an omnidirectional hydrophone. At ELA, calibrations took place in a small (4.7 m) aluminum boat tied to a center buoy permanently anchored at the deepest part of the Lake 373 (Z
max = 21 m; see [1] for details). Calibrations in Toronto Harbour were performed similarly; however, the maximum depth was only 12 m. Individual transmitters were placed in a mesh bag and attached to a rope that was marked every meter and kept vertical by a heavy weight. The rope was lowered to a depth of 1 m for a few minutes until the reported depth was determined with the receiver (the hydrophone remained at the same depth, just below the surface of the lake). Transmitters were then lowered to increasing depths (i.e., 2, 5, 10, 15, 20 m) and reported depths were recorded at each step. Field calibrations were conducted on calm days to ensure that the rope remained vertical. Field calibrations were also conducted during the fall of 2012 when lakes were not stratified (water temperatures ranged from 7 °C at the surface to 5 °C at a depth of 20 m).
Calibration curves were constructed for each tag under each calibration scenario. Transmitted sensor values (raw values recorded by the receivers called Analog to Digital Converter; ADC) were plotted against actual (field-based) or simulated (lab-based) transmitter depths. A line of best fit was plotted for each transmitter, and the slope, intercept, and R
2 values of the relationship between depth and sensor value were calculated (using Microsoft Office Excel 2007). To determine the degree of difference from actual or simulated depth, we calculated the difference between depths estimated using the factory-derived slope and intercept, and depths estimated using researcher calibration slopes and intercepts, up to a maximum simulated depth of 68 m.
Calibrations at three different water temperatures
To evaluate the effects of temperature on sensor output, transmitters were calibrated at three different biologically relevant temperatures; cold (9 °C), cool (20 °C), and warm (34 °C). Transmitters were calibrated in the laboratory at Carleton University, following procedures described above. Slopes, intercepts, R
2 values, and the degree of difference between obtained and actual depths were calculated as above.
Quantifying error from temperature-driven changes in water density
To calculate the effect of water temperature on depth estimates derived from pressure sensor values, the following equation was used: P
total = P
atmosphere + P
fluid. P
fluid = ρgh, where P
atmosphere = atmospheric pressure (Pa), ρ = water density (kg/m3), g = gravitational acceleration (9.8 m/s2), and h = depth (m). For all evaluations of external effects on depth estimates, depths of 68 m (maximum depth of V16 transmitters) were used because errors would be most pronounced here (i.e., because changes in water density are cumulative with depth). The hydrostatic pressure of fresh water at three different water temperatures was calculated; 4 °C represents the temperature at which water has the highest water density (i.e., 999.9720 kg/m3), 20 °C represents the default water temperature used for factory calibrations, and 40 °C was chosen because most natural bodies of water do not exceed this temperature. A transmitter located at 68 m in 20 °C fresh water should sense a total pressure of 766,530.2781 Pa. To determine the maximum error associated with temperature-driven changes in water density, we calculated the corresponding depths at which the same transmitter would register 766,530.2781 Pa in both 4 and 40 °C fresh water. The difference in calculated depth among the three temperatures reflects the sensitivity of the sensor to temperature-driven changes in water density.
Quantifying error from salinity-driven changes in water density
We calculated the effect of salinity-driven changes in water density on depth estimates in the same manner as above for temperature (i.e., P
total = P
atmosphere + P
fluid). A transmitter located at a depth of 68 m in 20 °C fresh water (998.2072 kg/m3) senses a total pressure of 766,530.2781 Pa. We calculated the depth at which the same transmitter would sense 766,530.2781 Pa in full strength salt water (35 ‰ salt; 1024.8103 kg/m3). The difference in calculated depth between freshwater and sea water reflects the sensitivity of the sensor to salinity-driven changes in hydrostatic pressure.
Quantifying error from changes in atmospheric pressure
We calculated the effect of atmospheric pressure-driven changes in water density on depth estimates in the same manner as above (i.e., P
total = P
atmosphere + P
fluid). We calculated the total pressure of fresh water at three different atmospheric pressures; 87,000 Pa, representing an extremely low but observed atmospheric pressure; 101,325 Pa, representing the standard atmospheric pressure; and 108,000 Pa, representing an extremely high but observed atmospheric pressure. A transmitter located at a depth of 68 m in 20 °C fresh water senses a total pressure of 766,530.2781 Pa. To determine the maximum error associated with atmospheric pressure-driven changes in water density, we calculated the corresponding depths at which the same transmitter would register 766,530.2781 Pa in both 87,000 and 108,000 Pa atmospheric pressures. The difference in calculated depths among the three atmospheric pressures reflects the sensitivity of the sensor to changes in atmospheric pressure.
Statistical analysis
Differences among slopes, intercepts, and R
2 values from the four calibration methods (i.e., HBBS, Carleton, Toronto, and ELA) were evaluated using three separate linear mixed-effects models (LMEs). Each model included the response variable (i.e., slope, intercept, or R
2) with calibration method as a fixed factor and transmitter identification number as a random effect variable to account for the repeated measures on each transmitter. The models were fitted using restricted maximum likelihood (REML). The analysis on R
2 data included the variance structure VarIdent to take into account differences in variance among the four calibration methods (see [16]. LMEs were also used to compare differences among slopes, intercepts, and R
2 values from calibrations performed in the three different water temperatures (i.e., cold, cool, and warm). When a significant effect of calibration method or calibration temperature was found, Tukey honestly significant difference (HSD) test was employed to investigate difference among groups.
All analyses were conducted in R version 3.1.2 [13] using the “nlme” package [12]. Prior to the analyses, data explorations were applied following a protocol described by [17]. The models were validated to verify that the underlying statistical assumptions were not violated. Homogeneity of variance was assessed by plotting residual versus fitted values, normality of residuals was evaluated by plotting theoretical quantiles versus standardized residuals (Q–Q plots), and independence was examined by plotting residuals versus the explanatory variable. R
2 data were arcsine transformed prior to analysis. One transmitter was excluded from all analysis and deemed defective as it reported erroneous data. Statistical significance for all analyses was set at p < 0.05.