© 2004 by ICES/CIEM International Council for the Exploration of the Sea/Conseil International pour l'Exploration de la Mer
The evaluation of noise- and threshold-induced bias in the integration of single-fish echoes
Federal Research Centre for Fisheries, Institute for Fishery Technology and Fish Quality Palmaille 9, 22767 Hamburg, Germany
*Correspondence to E. Bethke: tel: +49 40 38905 203; fax: +49 40 38905 264. e-mail: eckhard.bethke{at}ifh.bfa-fisch.de.
The echo integration of single-fish echoes shows that characteristically the received-signal energy of single targets is small compared with the echo energy of schooled fish. The measuring error is minimized by the application of an integration threshold. The echo energy, however, is often only slightly larger than the noise and reverberation level making the determination of the optimal integration threshold difficult. During the evaluation of data from the echo-integration surveys on redfish in the Irminger Sea it was observed that the integration value of single fish increased steadily with decreasing integration threshold. There is no way to determine the integration threshold by eye as for schooled fish.
The approach taken in all past publications for the estimation of the influence of the integration threshold on the integration result has been based on the computation of an equivalent beam angle. The influence of "environment noise" was not considered. Here a model is presented, which considers both influences on the integration result during the integration of single-fish echoes. It is assumed that the targets are distributed evenly in the observed volume and that in each pulse volume of the beam only one target is present. The starting point of the computations is the equation for signal processing implemented in the EK500. The echo signal power received is converted pixel-by-pixel into the appropriate volume-backscattering coefficients, sv and stored as echograms. These echograms are available for post-processing in the Bergen Integrator BI500. To exclude noise and reverberation from the subsequent processing a threshold was introduced.
We assume that the fish echoes are always larger than the noise and reverberation. This is a very common situation and the largest part of the energy of noise and reverberation can be eliminated in this way. When a fish echo is received outside the centre of the beam it is attenuated by the beam pattern of the transducer and may therefore lie below the threshold and could be cut off. This leads to the reduction of the measured values and a measuring error. An opposite error arises when the signal crosses the threshold. In practice the signal received always consists of noise and echo signals and has more power than it should have. The measured value is larger and this is another error of the measurement process per se.
The object of this paper is to calculate the influence of the threshold level on the result of measurement and to derive a practicable rule for the determination of the threshold level. The noise is modelled as a constant input power. The computations are carried out with model functions of the transducer beam and the received-echo pulse. General statements can be met by defining a signal-to-noise ratio and a signal-to-threshold ratio. The results of the theoretical investigations are applied on acoustic data obtained during redfish survey WH229 in the Irminger Sea and adjacent waters.
Keywords: acoustics, bias, echo integration, echosounder, EK500, equivalent beam angle, fisheries, noise, redfish, single-fish echoes, threshold
Received 17 March 2003; accepted 29 December 2003.
 |
1 Introduction |
|---|
 Top 1 Introduction 2 Materials and methods3 Results4 DiscussionAppendix 1References |
|---|
Echograms of international surveys on redfish in the Irminger Sea show that redfish, the target species, occurs as single targets in this area. The reflected echo energy of fish and the signal-to-noise ratio is very low. From the received-signal energy of redfish it is possible to calculate the fish density if the target-strength distribution is known. The measurement of the energy of the targets desired is often disturbed by "noise" e.g. propeller noise, wind-generated noise and thermal noise, and reverberation from the echo of unwanted targets, e.g. plankton. It is necessary, therefore, to suppress the measurement of the extraneous sound. This could be done by using noise-reduction software but another way is the application of an integration threshold for echo integration as suggested in this paper. This approach, applying as it does a threshold on the sv signal, is preferable for international surveys because all the participants have to have the same equipment if they are to get comparable results. Indeed the sv-threshold was part of the BI500 software in use on all research vessels participating in this survey. The object of this paper is therefore the derivation of a method for the determination of the integration threshold for echo integration on fish occurring in very low densities under the conditions of noise and reverberation. In publications to date (Aglen, 1982; Lassen, 1986; Ona, 1987; Reynisson, 1996), the estimation of the influence of the integration threshold on the integration result was based on the computation of an equivalent beam angle without any consideration of noise. Here the influence of noise is taken account of.
During the evaluation of data of the echo integration it was noted that the integration value of a single fish increases continuously with decreasing integration threshold. There is no way to determine the integration threshold by trial and error as is possible for schooled fish. The integration threshold cuts off the largest part of the interference but also parts of the fish echoes received from outside the centre of the beam. This leads to an underestimation if not accounted for. On the other hand the signals over the threshold level comprise both fish echoes and noise and this may lead to an overestimation. Since these measuring errors have opposite effects they will cancel out each other to some extent. Depending on the conditions this could lead to an underestimation or overestimation of the fish density in the actual case.
|
2 Materials and methods |
|---|
|
Top1 Introduction2 Materials and methods3 Results4 DiscussionAppendix 1References |
|---|
The equipment for measuring echo integration comprises a transducer, a scientific echosounder, EK500 (SIMRAD, 1996), and a post-processing system, BI500 (Foote et al., 1991).
2.1 Transducer
The sensitivity of a transducer depends on the effective transducer surface and the receiving direction. The overall gain G(
) is the product of the power gain in the acoustical axis G0 and the beam pattern b2(). Within the echo integration the directivity properties of a transducer are summarized in a two-way solid beam angle, 
(Urick, 1975)
|
| (1) |
is used here
|
| (2) |
. As is evident from Figure 1, the beam pattern is well described by the approximation.
|
2.2 Sounder
Scientific echosounders used for echo-integration measure the power, Pr(r), at the transducer output and compute the volume-backscattering coefficient, sv(r). The following equation is implemented in the scientific echosounder EK500 used for our measurements (SIMRAD, 1996):
|
| (3) |
Signal recording for echo-integration pulses with a constant carrier frequency and a rectangular envelope are usually used. Reflection of the signal from small targets does not change its shape. However, additional noise and reverberation are received at the same time with the reflected signal
|
| (4) |
|
| (5) |
is the distance between transducer and target and has the characteristic:
|
| (6) |
|
| (7) |
|
| (8) |
|
|
|
| (9) |
|
|
|
|
|
|
–1/2c
and r=r+1/2c. For this short range, or time interval, the approximation of a constant amplification is introduced. The error thereby is minimal, since we can assume generally that the pulse received is much shorter than the distance of the transducer to the target. Thus the noise and the signal amplification (TVG) can be regarded as constant during the echo pulse. Now we define a signal-to-noise ratio:
|
| (10) |
|
| (11) |
|
| (12) |
|
|
|
The maximum range for echo integration depends on the signal-to-noise ratio and therefore on the energy of the transmitted pulse (e.g. Wiener, 1950). To achieve a sufficient distance resolution and a large measuring range for a depth range of 500 m we should choose a long pulse length and narrow bandwidth. However, due to software bugs it is difficult to calibrate the EK500 for these settings. Therefore the following settings were used for survey WH229: frequency = 38 kHz; pulse length = medium (PL = 1 ms); bandwidth = wide (BW = 3.8 kHz); two-way beam angle = –20.6 dB; minimum TS value = –50 dB; minimum echo length = 0.8; maximum echo length = 1.8; maximum gain compensation = 6 dB; and maximum phase deviation = 2.0.
2.3 Post-processing
During post-processing for every "elementary sampling distance unit" (ESDU) a "nautical-area-scattering coefficient" (NASC), sA is computed. If the target-strength distribution of the fish is known the NASC, sA is a measure for the area-based fish density. The following equation is implemented in the post-processing system BI500
|
| (13) |
|
| (14) |
to integrate within the limits 0–
/2. For the distance r the pulse length determines the limits. To present the influences of noise and threshold as generally as possible we calculate a relative-error function, based on the true value, which would have been measured under noise-free conditions
|
| (15) |
. By inserting Equation (12) into Equation (13) we obtain:
|
| (16) |
|
| (17) |
. The calculation of the true NASC, sATrue is based on the assumption of a uniform distribution of the targets in the volume and one target within each pulse volume and differs from the known calibration equation only by the ratio of total solid angle to two-way solid beam angle of the transducer being used, 4/. Note that with only one target within the pulse volume sATrue decreases as expected with the distance squared.
The output signal of the sounder comprises signal and noise. The amplitude of the fish echo depends on the angle-dependent, directivity function, and the backscattering strength of the fish. If the targets are far outside the centre of the beam when the measurements are taken the echo amplitudes are relatively small. If, in addition, the fish echoes are small in number then the integration of the noise can cause substantial errors. To exclude noise and reverberation from the computation of the NASC on the input signal to the post-processing systems a threshold is applied. The threshold level has to be set above the noise level, as the threshold is otherwise ineffective. However, the threshold level has to be considerably below the maximum echo level, for as little as possible of the fish-energy power (see Figure 4) has to be cut off. Inserting our approximation, Equation (2) for the beam pattern into Equation (12), we get the following form for the output signal as function of and r:
|
| (18) |
The signal svOut represents the output of the EK500 and the input signal of the BI500. The first step of post-processing is the application of the integration threshold. Figure 4 corresponds to Figure 3 and, on the left, shows the normalized, threshold-output signal for a single pulse according to Equation (18) as a function of and r not influenced by noise whilst on the right there is the signal received under the "noise" condition. The parts of the signal below the threshold, svOut
svThr are cut off and do not contribute to NASC. This is the case for targets outside the centre of the beam above the angle max and the distance rmax and below rmin. Here the signal does not exceed the threshold and is cut off completely. The echo amplitude, measured under noise conditions (right), has a larger amplitude and, as is clearly evident from Figure 4, the limits (extension in distance r and angle ) for the integration of the average NASC depend on the SNR and the threshold level. For svThr=svOut and using the definition of STR (Equation (11)), inserting into Equation (18) and solving for r we get for the integration over r the following limits:
|
| (19) |
is at r=r. Inserting this into Equation (18) and rearranging to we get (where lg x = log10 x):
|
| (20) |
|
| (21) |
|
3 Results |
|---|
|
Top1 Introduction2 Materials and methods3 Results4 DiscussionAppendix 1References |
|---|
Computing the multiple integrals according to Equations (17) and (21) for practical ranges of SNR and STR we get Equation (15) for the relative error as illustrated in Figure 5. The threshold for noise reduction is only effective if the signal-to-noise ratio (SNR) is larger than the signal-to-threshold ratio (STR). It is evident that for small values of the two parameters substantial measuring errors can occur. Specifying ±10% as margin of error, we obtain Figure 6. Here only values which are below the accuracy range of
sA<±10% are plotted. It should be noted that an STR above 13 dB and a difference, SNR – STR > 4 dB always results in integration errors below ±10%.
|
|
This leads to a simple procedure to determine the threshold level and the maximum range for echo integration giving results with relative error below ±10% viz.
- Measure the maximum NASC, SvMax with the zoom function of the BI500 for the smallest-expected, single-target strength of fish of interest within the considered depth layer.
- Calculate the threshold value by subtracting 13 dB from SvMax (measured in dB).
- Obtain the maximum range for the desired measurement accuracy at the range where the noise or reverberation level is larger than the Sv threshold – 4 dB.
This is applicable to all pulse length/bandwidth combinations. The threshold, SvThr level is, like SvMax, a function of depth and pulse length. Unfortunately the BI500 provides only a constant threshold for the whole depth range. By using Equation (9) it is possible to calculate the threshold value too. We get for the threshold value measured in dB:
|
| (22) |
|
4 Discussion |
|---|
|
Top1 Introduction2 Materials and methods3 Results4 DiscussionAppendix 1References |
|---|
Figure 7shows a typical echogram measured and stored by the German FRV "Walther Herwig III" during survey WH229 on redfish in the Irminger Sea. Whilst the echogram was being recorded a trawl haul was carried out. The length distribution of caught redfish was determined and a corresponding TS distribution within the trawl depth was measured with the post-processing system BI500 and calculated, using the equation given in Reynisson (1992).
|
The measured mean-TS value and the calculated TS value were in good agreement. Figure 8shows the TS frequency distribution measured during trawl haul 719. The many very large TS values are probably TS values of multiple targets, because redfish producing these values would have a length of about 1.10 m. Double targets can produce a 6-dB larger TS value than a single target but they could also cancel each other out to varying degrees. Other explanations for the large values are also possible, e.g. jellyfish with a diameter of more than 1 m or large fish of other kinds. In this case though only small fish were caught in the trawl.
|
The smallest redfish caught had an average target strength of –41.9 dB. This value corresponds to an SvMax of –65.7 dB and a threshold value of –78.7 dB according to the rule derived above. Taking into account that there is a certain deviation from the mean we can assume TSmin = –48 dB (see Figure 8). A TS value of –48 dB corresponds to an SvMax of –71.7 dB. For those targets SvThr should have a value of –84.7 dB. Fish producing a target strength below –50 dB are assumed to be myctophids. These fish appear in the catches in different numbers and are most likely underestimated because of the large meshes in the codend. TS values of small deep-sea fish were not recorded during the survey but it is believed that these fish have target strengths of below –50 dB, with a maximum frequency at approximately –56 dB (Reynisson, 1992). The target strength of –56 dB corresponds to an SvMax of –79.7 dB for single targets and to an SvMax of –73.7 dB for large single targets and double echoes of this fish at a depth of about 220 m.
This highlights an additional problem of thresholding. Parts of the echoes of myctophids (SvMax>SvThr) are able to cross the threshold matched to the smallest redfish and can contribute to the measured NASC. In some cases a compromise has to be found. To exclude as much as possible of undesired reverberation (echo energy reflected by deep-sea fish) from the integration and to minimize the loss of signal energy of redfish it is evident that we have to choose a threshold value between –84.7 dB and –73.7 dB. A test was carried out to investigate the effect on the measured NASC of thresholding the Sv data. The data were recorded during trawl haul 719 (Figure 9). It can be seen that the NASC increases steadily by applying a decreasing threshold to the data. No appropriate threshold can be found by eye. Applying a threshold of SvThr = –84.7 dB corresponding to TSmin of redfish ensures an integration of most parts of the redfish echo energy but also reverberation. The integration result for this threshold can be considered as a maximum NASC. For the measured TS distribution of targets observed during trawl haul 719 we obtain NASCmax = 6.45m2 nmi–2.
|
The characteristic of redfish surveys in the Irminger Sea is that redfish occurs almost exclusively as single targets. Therefore it is possible to calculate an NASC based on the measured TS distribution. The method is described in Appendix 2 and presents that part of NASC explained by the TS distribution. Multiple echoes might be rejected by the single-target discrimination, therefore the calculated NASC based on this method might be lower than the true value and can be regarded as a minimum NASC. We obtain here NASCmin = 4.64m2 nmi–2. Using Equations (19)–(21) we can investigate the effect of thresholding by calculating the mean NASC for a given TS distribution of the considered number of pings.
To show the influence of noise and reverberation this was done for the measured TS distribution for a very large SNR and a low SNR (smallest SvMax = –74 dB, SvN = –90 dB). The calculations were carried out with Mathematica 4.0 (Wolfram, 1999). Both curves have almost the same shape and run parallel to the curve measured in a practical test for threshold values of 62 dB–78 dB. The calculated curves always show lower values than the measured curve (see Figure 9). This indicates that not all the redfish were recognized as single targets. Probably some multiple targets were rejected by the single-target discrimination. To estimate this part we add some large targets to the TS distribution so that for threshold values between 62 dB and 78 dB the computed curve is fitted to the measured curve. Using this correction method and comparing the results of the computations for the corrected and uncorrected TS distributions for a low threshold (e.g. –90 dB) we conclude that only 85% of the targets are recognized as single targets provided that the unrecognized targets have the same TS distribution. This suggests that the NASC probably closest to reality is sA = 5.28m2 nmi–2 which is almost the same NASC as is measured by applying a threshold of –80 dB for the depth range considered.
We have to conclude that applying only the echo-integration method leads to the accuracy of the results of redfish surveys being rather low. The threshold rules derived above provide only initial evaluation settings but unfortunately not a final solution for the problem. Existing methods for noise reduction (e.g. Korneliussen, 2000), do not help in this case because the main problem is not environmental noise but reverberation. The accuracy could be improved by combining the conventional echo-integration method with a TS-based method. Large deviations between the results of both methods show the need for the application of the correction method described above. Additional work has to be done to provide this within the post-processing software.
|
Appendix 1 |
|---|
|
Top1 Introduction2 Materials and methods3 Results4 DiscussionAppendix 1References |
|---|
- A [m2]Area
- bBeam-pattern function
- c [ms–1]Sound speed
- D [m]Diameter of the transducer
- GGain
- G0Gain at
=0
- GenvAdditional gain for correction of the influence of filtering
- kWavenumber
- J1Bessel function of first kind and first order
- Penv [W]Power of the envelope signal
- PN [W]Received noise power
- PS [W]Received signal power of target
- Pr [W]Received power
- Pt [W]Transmitted power
- r, r1, r2 [m]Distances
- rmin, rmax [m]Integration limits
- r0 [m]Standard reference distance (=1m)
- r
[m]Distance between transducer and target
- sA [m2nmi–2]Nautical-area-scattering coefficient (NASC)
- sATrue [m2nmi–2]True nautical-area-scattering coefficient, not influenced by noise
- svMax [m2nmi–2]Maximum of volume-backscattering signal
- svN [m–1]Noise signal at the EK500 output
- svOut [m–1]Output signal of the EK500
- svThr [m–1]Threshold level of the BI500
- sv [m–1]Volume-backscattering coefficient
- SNRSignal-to-noise ratio
- STRSignal-to-threshold ratio
- TS [dB re 1 m2]Target strength
[dBm–1]Attenuation constant
sARelative error of the nautical-area-scattering coefficient
[Steradian]Solid angle
[Steradian]Two-way solid beam angle (TWBA)
comp [Steradian]Solid beam angle for beam-pattern compensation
[m]Wavelength
[Rad]Angle between reference axis and a target in a spherical system
[Rad]Angle between acoustical axis and a target in a spherical system
comp [Rad]Angle, according to EK500 settings for beam-pattern compensation
max [Rad]Integration limit
[m2]Differential scattering cross-section
bs [m2]Backscattering cross-section
[m]Pulse length of the transmitted pulse
- bBeam-pattern function
Appendix 2
Based on Equation (17) we can derive an equation similar to the calibration equation (SIMRAD, 1996), allowing the calculation of the NASC for a given TS distribution:
|
| (23) |
|
|
eff represents the effective solid beam angle. The angle comp corresponds to the EK500 settings in the "TS Detection Menu" for the "Maximum Gain Compensation" and can be calculated in a similar way as Equation (1). Note that the maximum gain compensation refers to the one-way directivity of the beam pattern (SIMRAD, 1996). The signal-to-noise ratio decreases outside the centre of the beam and lowers the probability of an echo passing the single-target discrimination criteria of the EK500. Therefore the relative-area-based, target density 
()/0 is a function of the angle (Figure 10). Where the echo-integration method includes the complete signal energy, and also that of multiple echoes, the TS-based method excludes multiple echoes to a great extent. Applying Equation (23) and using the measured TS distribution (Figure 8, BI500 values) leads therefore to an estimation of the minimum NASC (see Figure 9) derived from the detected single targets.
|
|
Acknowledgements |
|---|
I thank Páll Reynisson for his useful comments and questions.
This work was supported by the redfish-research project; funded within the European Commission's Fifth Framework Programme (1998–2002), contract QLK5-CT1999-01222.
|
References |
|---|
|
Top1 Introduction2 Materials and methods3 Results4 DiscussionAppendix 1References |
|---|
-
Aglen A. (1982) Echo-integrator threshold and fish-density distribution. FAO Fisheries Report No. 300. Symposium on Fisheries Acoustics, Bergen.
Foote K.G., Knudsen H.P., Korneliusen R.J., Nordbö P.E., Röang K. (1991) Post-processing system for echosounder data. Journal of American Statistical Association 90:37–47.
Korneliussen R.J. (2000) Measurement and removal of echo-integration noise. ICES Journal of Marine Science 57:1204–1217.
Lassen H. (1986) Signal threshold in echo integration. ICES CM 1986/B: 35. 13 pp.
Lozow J. B. (1982) Integral-transform method for extracting target-strength distribution from received echo signals. Symposium on Fisheries Acoustics (Appendix A)FAO, Bergen.
MacLennan D.N., Fernandes P.G., Dalen J. (2002) A consistent approach to definitions and symbols in fisheries acoustics. ICES Journal of Marine Science 59:365–369.
Ona E. (1987) The equivalent beam angle and its effective value when applying an integrator threshold. ICES CM 1987/B: 35. 13 pp.
Reynisson P. (1992) Target-strength measurements of oceanic redfish in the Irminger Sea. ICES CM 1992/B: 8. 13 pp.
Reynisson P. (1996) Evaluation of threshold-induced bias in the integration of single-fish echoes. ICES Journal of Marine Science 53:345–350.
SIMRAD. (1996) EK500 Scientific Echosounder. Operator Manual. Base Version. Horten Norway.
Urick R.J. (1975) Principles of Underwater Sound 2nd edn (McGraw-Hill, New York).
Wiener N. (1950) Extrapolation, interpolation and smoothing of stationary time series(Wiley & Sons, New York).
Wolfram S. (1999) The Mathematica Book 4th edn (Wolfram Media/University Press, Cambridge).
CiteULike 
Connotea 
Del.icio.us What's this?
| ||||||||||||||||||||||||||||||||||||||||||||||||||||||||