Defending a Hydroacoustic Biomass Estimate Before Quota Setting
A hydroacoustic monitoring programme on a 6,800 ha monomictic reservoir uses one 38 kHz split-beam transducer mounted 1.2 m below the surface of a 9 m survey boat. Transects total 96 km and are run between 09:00 and 15:00 at 10 knots. The last calibration was 11 months ago; the current calibration file shows an on-axis gain 0.8 dB above the manufacturer's nominal value, and this offset has never been applied to the data. Quality checks from the most recent survey showed that 62% of echoes were rejected by the single-target filter, the TS distribution was bimodal at −52 dB and −38 dB, very few targets were detected in the upper 3 m, and a persistent noise band appeared at the bottom from propeller wash. The resulting estimate of 410 t was used to set this year's harvest quota. The reservoir also holds dense populations of small pelagic cyprinids that are not landed commercially. The reservoir manager asks whether the 410 t figure is defensible.
1. Identify and rank the principal sources of bias in the 410 t estimate and explain the mechanism by which each one acts.
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1. Uncorrected gain offset (largest, quantifiable). The system gain is 0.8 dB high, so every measured Sv is 0.8 dB too high. Because σbs = 4π·10^(TS/10), a 0.8 dB offset inflates σbs and therefore volumetric density by a factor of 10^(0.8/10) = 1.20 - about +20% on biomass, which propagates straight into the quota.
2. Daytime-only surveying with a surface blind zone. Transducer at 1.2 m plus near-field means roughly the top 2 m is un-sampled, and the 'few targets in the upper 3 m' confirms a surface layer is being missed. Small pelagic cyprinids that shoal near the surface by day are precisely the group lost, so the community is under-represented.
3. Single-target filter rejecting 62% of echoes. At 10 knots the transducer pitches and rolls, and propeller bubbles attenuate the beam. Off-axis and bubble-distorted echoes fail the angle and pulse-width criteria, so the TS distribution used for scaling is built from a biased subset and the rejected targets are effectively discarded rather than corrected.
4. Bimodal TS with no species apportionment. Modes at −52 dB and −38 dB correspond to very different body sizes/species. Applying a single TS–length relation to a mixed assemblage misallocates density between cyprinids and the target stock, and a −60 dB threshold may clip the smallest fish entirely.
5. Noise inflation of sA. The bottom noise band from propeller wash adds spurious echo energy that is not removed by thresholding alone, biasing the integrated area upward.
2. Recommend a revised survey and analysis protocol, and quantify what the defensible biomass figure becomes if only the calibration problem is corrected.
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Quantification first. If gain bias is the only correction made, the corrected estimate is 410 ÷ 10^(0.8/10) = 410 ÷ 1.202 ≈ 341 t (about 340 t). State clearly that this removes one bias only; the remaining biases are unquantified and do not cancel, so the figure should be presented as an index with an uncertainty band (±30–50% is realistic), not as an absolute stock size.
Design changes.
- Recalibrate with a standard tungsten-carbide sphere before and after each survey, and apply the calibration file to raw data, not to post-processed Sv.
- Move transects to dusk/night, when fish disperse upward and are less vessel-avoidant; keep a small daytime stratum to preserve comparability with the historical series.
- Reduce speed to 5–6 knots and run with the transducer vertical; monitor pitch/roll and discard or correct off-vertical pings.
- Add 120 kHz alongside 38 kHz so the −38 dB and −52 dB modes can be separated by frequency response, and ground-truth with a midwater trawl to build an in-situ TS–length regression rather than importing a general equation.
- Shorten the pulse and lower the transducer (or use a towed body) to shrink the surface dead zone; apply an explicit dead-zone correction for the bottom layer.
- Set the single-target filter from measured pulse length and beam angle, and remove background noise by SVG/background subtraction before integration.
Reporting. Re-run the historical series with the same corrections so the new index is comparable, and publish the CV alongside the point estimate.
3. The regulator wants a number for next year's quota. Propose a decision rule that uses the acoustic index without over-claiming precision.
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Use the acoustic output as a relative index within a harvest control rule, not as an absolute abundance to be multiplied by a fixed harvest rate.
- Rebuild the series. Re-process all years with the calibrated, corrected pipeline so the index is internally consistent. A 340 t corrected value that is not comparable with previous years is worse than no number.
- Attach uncertainty. Estimate a CV from transect-to-transect variance (geostatistics), plus a calibration/filtering component. If the combined CV is around 30%, the 95% interval on 340 t is roughly 180–500 t - quota must not be set at the upper end.
- Precautionary buffer. Set the quota as a fixed fraction (e.g. 10–15%) of the lower confidence bound, then cap year-on-year change at ±20% to avoid destabilising the fishery when survey noise moves the estimate.
- Trigger rules. If the corrected index falls more than 20% below the three-year mean, cut the quota automatically; if it rises, allow only half the increase until confirmed by a second survey.
- Separate the bycatch species. The cyprinids that dominate the −52 dB mode are not harvested, so their acoustic contribution must be apportioned out before any harvest rate is applied; otherwise the quota is set on biomass the fishery cannot use.
Record the decision rule in advance, with the correction factors, so the next survey cannot be re-interpreted after the quota is known.