Assessment of the acoustic telemetry positioning system

The performance of the acoustic telemetry system was assessed by determining positions

of three beacon tags. The beacon tags were associated with two acoustic receivers located

above intakes 1 and 5, and another one about 275 m from the powerhouse (Figure 1b in

the main article). The position estimates for the beacon tags were computed with the

software ALPS (Lotek Wireless Inc., Newmarket, Canada), using detections recorded in

15 randomly selected days when the receivers also detected tagged bull trout.

The number of positions obtained for each beacon tag per hour was divided by the

number of positions expected (i.e., 120) based on their burst rate of 30 seconds. The

resulting proportions were multiplied by 100 and the values were used as a measure of

positioning efficiency.

Overall, median positioning efficiency was highest in the spring and lowest in the

fall (Figures 1a, 1c, 1e). There was substantial variation in positioning efficiency among

beacon tags, with those located on the powerhouse wall having the lowest values in each

season (Figures 1a, 1c, 1e). Positioning efficiency for the beacon tags located on the

powerhouse wall decreased with increases in operational discharge (Figures 1b and 1d).

For the beacon tag located about 275 m from the powerhouse, positioning efficiency

decreased with operational discharge changing from low to intermediate values and then

increased with higher discharge (Figure 1f). The reasons for this unlikely relationship

with discharge are unclear and indicate that other factors (e.g. wind, precipitation) not

evaluated here might also have been responsible for variation in positioning efficiency of

that beacon tag.

1

The easting and northing components of the position estimates were subtracted

from the corresponding components of the fixed known locations of the beacon tags to

compute positioning errors. Positioning errors were classified according to the quality

class of each position as determined by their reliability number. Reliability number is a

variable computed by ALPS that represents the effective number of receivers

participating in the computation of a position estimate, with smaller errors occurring with

increasing reliability number [1]. In our study, reliability number ranged from 0 to 7 and

accordingly we categorized each positioning error into one of seven possible classes.

Approximately 90% of the positions had absolute errors under 50 m on both the

easting and northing components. Positions with absolute errors under 10 m on the

easting and northing components comprised, respectively, 63% and 43% of the data

(Figures 2a–b). As expected, error in the position estimates decreased in magnitude and

variability with increasing reliability number (Figures 2c–d).

We estimated the parameters of a t-distribution (using the “fitdistr” function in the

R package “MASS”; [2]) fitted to the errors in the easting and northing components of

positions in each reliability number class (Table 1). We used the estimates to fix the

parameters of the t-distribution describing the positioning error in the observation

equation (Eq. 2 in Additional file 2) of the DCRWS state-space model.

References

1. Niezgoda G, Benfield M, Sisak M, Anson P: Tracking acoustic transmitters by code

division multiple access (CDMA)-based telemetry. Hydrobiologia 2002, 483:275–

286.

2

2. Venables WN, Ripley BD: Modern Applied Statistics with S. 4th edition. New York:

Springer; 2002.

3

Table 1 Maximum likelihood estimates of t-distribution parameters fitted to

positional error data on the easting and northing components

Parameter

RN class μ τ ν

Easting

1 177.52 748.94 99.68

2 15.69 24.10 0.80

3 3.71 13.67 1.38

4 2.05 6.01 1.74

5 −1.62 4.25 1.79

6 −3.94 4.62 4.50

7 −1.83 0.90 2.22

Northing

1 — — —

2 23.78 24.64 0.69

3 −10.59 19.21 1.64

4 −11.57 15.63 4.39

5 −6.78 9.92 7.31

6 −3.20 0.92 0.88

7 −3.77 0.38 1.41

The location and scale parameters are denoted, respectively, by μ and τ , and ν denotes

degrees of freedom. RN stands for reliability number and is a measure of position quality.

It was not possible to estimate the parameters for RN class 1 in the northing component.

4

Therefore, in the DCRWS state-space model, parameter values for RN class 1 in the

northing component were fixed to the values estimated for RN class 1 in the easting

component. The units for the location and scale parameters are meters.

5

Figure 1 Efficiency of the acoustic telemetry system in positioning beacon tags by

season (a, c, e) and hourly mean total operational discharge (b, d, f). (a, b) Beacon

6

tag on receiver above intake 1. (c, d) Beacon tag on receiver above intake 5; (e, f) Beacon

tag on a receiver located about 275 m from the powerhouse. See Figure 1b in the main

article for the location of the receivers and beacon tags. The lines in (b, d, f) denote a

LOESS smoother identifying the trend in the data.

7

Figure 2 Error in the position estimates of three beacon tags (data were pooled).

Cumulative empirical distribution function of the absolute error in the (a) easting and (b)

northing components of the beacon tags position estimates. Relationship between

reliability number (RN) and positioning error in the (c) easting and (d) northing

components.

8