Power-Budget Equations and Calibration Factors for Fish Abundance Estimation Using Scientific Echo Sounder and Sonar Systems

Per Lunde,Rolf Korneliussen

doi:10.3390/jmse4030043

Abstract

Acoustic methods used in fish abundance estimation constitute a key part of the analytic assessment that makes the basis for abundance estimation of marine resources. The methods rely on power-budget equations and calibrated systems. Different formulations of power-budget equations and calibration factors have been proposed for use in scientific echo sounder and sonar systems. There are unresolved questions and apparent inconsistencies in prior literature related to this field. A generic (instrument independent) and unifying theory is presented that attempts to explain the different power-budget and calibration factor formulations proposed and used in prior literature, and how these are mutually related. Deviations and apparent inconsistencies in this literature appear to be explained and corrected. This also includes different (instrument specific) formulations employed in important modern scientific echo sounder systems, and their relationship to the generic theory of abundance estimation. Prior literature is extended to provide more complete power-budget equations for fish abundance estimation and species identification, by accounting for echo integration, electrical termination, and the full range of electrical and acoustical echo sounder parameters. The expressions provide a consistent theoretical basis for improved understanding of conventional methods and instruments used today, also enabling improved sensitivity and error analyses, and correction possibilities.

Highlights

Acoustic methods are widely used for estimating fish abundance [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28], and constitute a key part of the analytic assessment that makes the basis for international regulations of marine resources
It is shown here that Formulation C leads to expressions for the calibration factors that are identical to those given for the EK500 echo sounder [11]. As these calibration factors cannot be derived directly from the average power budget expressions for σbs and sv given in [11], the analysis shows that the expressions for σbs and sv implemented and used in the EK500 system, cannot be those given in [11]
On the basis of an average power formulation of power-budget equations for σbs and sv known from prior literature [13,16], four new echo integration formulations for σbs and sv and associated calibration factors are derived for narrowband signals, denoted Formulations B–E

Summary

Introduction

Acoustic methods are widely used for estimating fish abundance [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28], and constitute a key part of the analytic assessment that makes the basis for international regulations of marine resources. A power-budget equation for multi-target (volume) backscattering [6,11,12,13,14,15,16] is typically used to measure volume backscattering from aggregations of fish or zooplankton. In terms of this equation, the volume backscattering coefficient sv is measured for a sequence of thin spherical shell “ping volumes”, Vp, at increasing range. The sequence of sv measurements is integrated over the range of an observation volume Vobs [6,11,16], to give the fish density in Vobs, ρa [17], in terms of an echo-integrator equation [3,6,8,10,16]

Objectives

Results

Conclusion