Robust Daytime In Situ Target Strength Estimation of Pacific Hake (Merluccius productus) over a Wide Size Range

Abstract

Accurate determination of the target strength (TS) of a fish species is essential for estimating the biomass of fish stocks using acoustic technology. This study estimated the daytime in situ target strength of Pacific hake (Merluccius productus) at 38 kHz using echosounder data collected during hake biomass acoustic-trawl surveys and research cruises conducted from 2009 to 2019 by U.S. and Canadian scientists. The intercept term for the 20-log TS regression over fish length at 38 kHz, $b_{20}$ was found to be −67.9 dB re 1 m² (CI: −68.09, −67.72), closely aligning with the currently used value of −68 dB in biomass assessments. Applying the revised $b_{20}$ value of −67.9 dB in past stock assessments suggests that biomass estimates would be underestimated by less than 3%, which is well within the typical uncertainty range of fish stock assessments.

1. Introduction

Effective management of fisheries and ecosystems requires marine scientists to take on substantial responsibilities, including monitoring, assessing, and researching marine resource distributions. Pacific hake (Merluccius productus), hereafter referred to as hake, is a commercially important marine fish found off the west coast of North America [1]. Over the past decade (2014–23), coastwide annual harvests averaged 338,606 metric tons [2], with U.S. and Canadian catches averaging 275,957 metric tons and 62,648 metric tons, respectively. In 2023, the coastwide catch reached 263,981 metric tons [2]. The U.S. West Coast’s hake fishery, including non-tribal at-sea and shoreside operations, supported 4450 jobs and generated an income of USD 335 million in 2021 when considering revenue (including production values and exports) and jobs.

Beyond its commercial significance, hake is a key trophic species and the most abundant groundfish in the California Current Large Marine Ecosystem [3]. Given its prominent economic and ecological value, integrated acoustic-trawl (IAT) surveys have been conducted to assess hake’s abundance, spatial and temporal distributions, and additional biological characteristics along the west coasts of the United States and Canada [4]. These surveys began in 1977, with the Alaska Fisheries Science Center (AFSC) conducting triennial IAT surveys in U.S. and Canadian waters. In 1990, Fisheries and Oceans Canada (DFO) initiated annual IAT surveys in Canadian waters. After the 2001 survey, responsibility for the U.S. portion of the IAT survey transitioned to the Northwest Fisheries Science Center (NWFSC), and the survey frequency increased from triennial to biennial. Since 1995, the United States and Canada have collaborated on hake assessments. The triennial IAT surveys of 1995, 1998, and 2001 were conducted jointly by AFSC and DFO, while surveys since 2003 have been conducted by NWFSC and DFO. The joint hake surveys normally began at Point Conception, California (the current southern extent of the survey area) and proceeded north along the west coast of the U.S. and Canada, surveying Queen Charlotte Sound, Hecate Strait (above Port Hardy in Figure 1), Dixon Entrance (the northern extent of the survey area, straddling the Canada and Alaska border), and the west side of Haida Gwaii, which was surveyed from north to south (Figure 1, with the actual 2019 survey transects).

Acoustic-trawl surveys are widely used for assessing stocks of pelagic and semi-pelagic fish species worldwide [5]. Methods and instruments have significantly improved over the years and the technology has become a recognized tool in ecological studies and the application of the ecosystem approach to fisheries management [6,7]. Estimating the abundance or biomass of fish stocks using acoustic technology requires accurate measurements of an acoustic property known as target strength (TS). TS is directly tied to biomass estimates, which are based on echo integration theory [8]. Conceptually, TS measures the acoustic energy scattered (typically in the backward direction) from an object relative to the source intensity [9].

Three common methods are used to estimate the TS of fish: in situ field data [10,11,12,13,14], ex situ data [15,16,17], and theoretical model predictions [18,19,20,21]. The target strength currently used by NWFSC and DFO to estimate hake biomass was originally published by Traynor [22]. This value was derived from in situ hake echosounder data at 38 kHz using a widely accepted 20-log regression formula based on the theoretical relationship between the differential backscattering cross-section (${\sigma }_{bs}$) and fish length ($L$) ${\sigma }_{bs}\propto L^2$. In the case of Pacific hake, L represents the fork length. The TS is commonly expressed logarithmically as

$$TS=10 {\log }_{10} {\sigma }_{bs}=20 {\log }_{10}L +b_{20}$$

(1)

where the fish length is measured in centimeters, and the intercept term $b_{20}$ is in dB re 1 m². The b₂₀ that has been used by NWFSC/DFO for Pacific hake biomass estimates has been historically set to −68 dB based on in situ target strength values reported by Traynor [22]. However, this intercept value was questioned by Henderson and Horne [16], where a much smaller $b_{20}$ was suggested (by 4–6 dB).

To address discrepancies in $b_{20}$ estimates and evaluate the validity of the currently used b₂₀, we analyzed in situ echosounder TS data from single targets collected between 2009 and 2019 during hake biomass surveys and research cruises. In contrast to Henderson and Horne [16], who used a combination of ex situ and nighttime in situ methods (similar to Traynor [22]) to estimate target strength, this study focused on daytime in situ methods as being more representative of fish encountered during the daytime survey used for stock assessment, and also provided estimates of accuracy and robustness. Daytime estimates of TS are considered more representative since the fish would be in the same orientation, distribution, and conditions (both physiologically and behaviorally) as when they are assessed for acoustic estimates of biomass. To account for bias due to multiple target scattering and a low signal-to-noise ratio (SNR) typically encountered during daytime surveys (when fish are found in denser aggregations at greater depth), we have used a stepwise approach for selecting valid targets and further introduced a pulse energy filtering method. Our specific objectives for this study were to (1) introduce a new approach based on target pulse energy to improve the selection of single targets under high-fish-density conditions, (2) to provide in situ estimates of Pacific hake target strength over a wide range of survey conditions and fish sizes, and (3) to validate and compare the TS-L relationship obtained from these measurements to the one currently used for stock assessment purposes.

2. Materials and Methods

2.1. Data Description

Acoustic data were collected between 2009 and 2019 using Simrad EK60 split-beam echosounders manufactured by Kongsberg (Horten, Norway). This study focused on data collected at 38 kHz, the primary frequency used for hake biomass estimation and widely recognized for fish biomass assessments globally [5]. Single-fish TS estimates were collected from the vessel’s echosounder during midwater trawl verification tows conducted at an average vessel speed of approximately 3 knots (~1.5 m/s) using the NOAA Fisheries Survey Vessel (FSV) Bell M. Shimada. This ensured that the TS measurements were made on individual fish just prior to their capture from the trawl net behind the vessel. Only trawls in which hake exceeded 95% of the total catch composition (by weight) were selected for TS analysis, minimizing any misidentification. All trawls were monitored with a Simrad FS70 third wire trawl sonar equipped with a depth sensor. The path of the trawl was overlayed on the echogram to only select acoustic targets that were vertically within 50 m of the trawl path. Thus, mean fish fork lengths from each selected trawl were assigned to the selected individual acoustic targets from the same corresponding trawl event.

In addition, a Dropped Acoustic Information SYstem (DAISY), a deployable instrument, was used to collect echosounder data off the Canadian Coast Guard Ship (CCGS) W. E. Ricker (Inset in Figure 1). DAISY consisted of 38 kHz and 120 kHz split-beam EK60 echosounders connected to a power supply inside a pressure housing. The unit was equipped with 200 m of cable for deployment at depth using a relay for topside control and included a heading, pitch, and roll sensor. The CCGS W. E. Ricker drifted while the DAISY was deployed to collect data. Each deployment of DAISY was associated with midwater verification trawl. Catches of hake from these trawls comprised 80%, 82%, and 99% of the total catch for 7 September 2014, 14 September 2014, and 23 March 2016, respectively. An in-trawl camera system indicated that the other species caught in 2014 (mostly opalescent inshore squid, Dorytheutis opalescens) were in different depth layers than the hake. The geographic locations of all selected trawls used for hake in situ target strength estimation are shown in Figure 1. Echosounders from the Shimada and DAISY transmitted narrowband pulses with a duration of 1.024 ms. All echosounders were calibrated using the standard sphere method [23] prior to each survey, including the deployment of a calibration sphere at depth for DAISY measurements.

2.2. Data Analysis

To correctly obtain single-target TS data, the single-target detection algorithm of Echoview (version 13.1, Hobart, Tasmania) was used (Table 1). The single targets that fell within these parameters only served as a foundation for further analysis. Originally, we used the fish-tracking algorithm provided within Echoview (Table 2), based on the Alpha-Beta tracking algorithm described by Blackman [24], but inspections revealed a high number of erroneous tracks, which required substantial manual corrections, despite several attempts at fine-tuning the tracking parameters. To better ensure the TS samples in the selected fish tracks were from individual fish, we manually selected candidates from these fish tracks, following stringent guidelines to guarantee the quality of the samples for final TS analysis. A single analyst (co-author Steve de Blois) made the selection of candidate tracks to ensure consistency throughout the dataset. The guidelines for single targets based on initial fish track analysis were the following:

• Fish tracks were selected throughout the depth range of aggregations but primarily from the outskirts of fish aggregations away from regions of highest densities (generally the center of aggregations) to minimize potential biases from multiple targets.
• Each fish track had to contain at least five contiguous echoes.
• Following track selection, only targets that were within 2° of the acoustic beam axis were retained for further analyses.
• Sample TS values greater than −30 dB were excluded to eliminate larger, non-hake targets or potential multiple targets.

Table 1. EK60 echosounder parameters for single-target detection.

Single-Target Detection
General Parameter	Parameter Value
TS threshold (dB)	−60
Pulse length determination level (dB)	6.0
Minimum normalized pulse length	0.2
Maximum normalized pulse length	1.8
Beam compensation
Beam compensation model	Simrad LOBE
Maximum beam compensation (dB)	12.0
Exclusion
Maximum standard deviation of
Minor-axis angles (deg)	2.0
Major-axis angles (deg)	2.0

Table 1. EK60 echosounder parameters for single-target detection.

Single-Target Detection
General Parameter	Parameter Value
TS threshold (dB)	−60
Pulse length determination level (dB)	6.0
Minimum normalized pulse length	0.2
Maximum normalized pulse length	1.8
Beam compensation
Beam compensation model	Simrad LOBE
Maximum beam compensation (dB)	12.0
Exclusion
Maximum standard deviation of
Minor-axis angles (deg)	2.0
Major-axis angles (deg)	2.0

Table 2. EK60 initial target tracking parameters.

Direction on a 3D Orthogonal Frame	Major Axis	Minor Axis	Depth
A	0.7	0.7	0.7
B	0.5	0.5	0.5
Exclusion distance (m)	4.0	4.0	0.4
Weights	30	30	40
Minimum number of single targets	3
Minimum number of pings	3
Maximum gap (pings)	1

Table 2. EK60 initial target tracking parameters.

Direction on a 3D Orthogonal Frame	Major Axis	Minor Axis	Depth
A	0.7	0.7	0.7
B	0.5	0.5	0.5
Exclusion distance (m)	4.0	4.0	0.4
Weights	30	30	40
Minimum number of single targets	3
Minimum number of pings	3
Maximum gap (pings)	1

Following the selection of the TS samples satisfying these criteria, additional filtering was applied using a pulse-energy detection range on each single target. The reasoning of using this pulse-energy criterion was based on the concept that if the echoes from two targets (or multiple targets) were either in or out of phase but arrived at slightly different times, the resultant echo would be either elongated or shortened, respectively, but still within the single-target detection pulse duration window specified in Table 1. As a result, the combined and normalized pulse energy over a time window of the transmit pulse duration would likely be either greater or less than the normalized transmit pulse energy over the duration of the transmit pulse (1.024 ms in this study). The pulse energy ($E_{pulse}$) was calculated as

$$E_{pulse}={\int }_0^{T}I\left(i\right)dt$$

(2)

where $I\left(t\right)$ is the echo intensity, which is proportional to the volume backscattering coefficient, $s_v={10}^{S_v/10}$, where $S_v$ is the volume backscattering strength. Since the absolute value of $s_v$ depends on the target, we used a normalized $s_v$ and the normalized pulse energy in the actual algorithm:

$${\widehat{E}}_{pulse}= {\sum }_{i=1}^{N_p}{\widehat{s}}_v\left(i\right)$$

(3)

where $N_p$ is the number of samples in each transmitted pulse (4 in the case of Simrad EK60 system) and ${\widehat{s}}_v={\displaystyle \frac{s_v\left(i\right)}{\underset{i=1,\dots ,N_p}{\mathrm{m}\mathrm{a}\mathrm{x}}\left\{s_v\left(i\right)\right\}}}$ is the normalized $s_v$ of the pulse of interest. TS samples were retained if their pulse energy satisfied the following relation:

$${\overline{E}}_{theo}-3 {\sigma }_{st} <{\widehat{E}}_{pulse} <{\overline{E}}_{theo}+3 {\sigma }_{st}$$

(4)

where ${\overline{E}}_{theo}$ and ${\sigma }_{st}$ are the theoretical mean and the standard deviation of the normalized echo energy, respectively, and were estimated based on the recorded waveform of the EK60 transmit pulse presented in Figure 2.30 of Demer et al. [25]. Since each pulse in the EK60 has four samples, the start of a (theoretical) echo was randomized within the first 256 μs time window of the pulse (equivalent to 1/4 of a 1024 μs pulse length). We used 10,000 realizations of this randomized start time in estimating the theoretical ${\overline{E}}_{theo}$ and ${\sigma }_{st}$ with values of 3.56 and 0.14, respectively.

Biological catch data were matched with acoustic data by assigning the mean fork length from each trawl to corresponding single-fish TS samples. Only trawls in which the fork length distribution of hake was relatively unimodal and had a standard deviation of less than 5 cm were retained for analyses to ensure that each estimate of in situ target strength was representative of a relatively narrow fish size (e.g., representative of the fish length at the trawl location). Unimodality was assessed visually on each length distribution to ensure that only one clear single peak was present.

Representative echograms illustrating single-target detections are shown in Figure 2, where the trawl traces were superimposed onto the echogram (Figure 2a) and the chosen TS samples from single fish were away from the center of the fish aggregation, the region with the highest fish density. The single-fish TS were much easier to determine from the echograms collected with DAISY due to the slow vessel speed (Figure 2b). As a result, the detected single-fish TS echo traces were much longer than those collected when trawling at a ship speed of about 3 kts (~1.5 m/s). Since all of the data for these analyses were collected on natural aggregations of fish (prior to trawl sampling), we assumed that the orientation (tilt, pitch, and roll) of the retained targets was representative of the orientation and distribution of free swimming fish. The Pacific hake population is acoustically assessed during daytime acoustic-trawl surveys under the same conditions as their target strength was estimated.

2.3. Estimation of $b_{20}$

To obtain an optimized estimate of the intercept, $b_{20}$, we used the least-square fit to the TS data using Equation (1), a 20-log form of the TS-length regression relation. The mean fork length (from trawl samples) was categorized in 1 cm length bins. Since the only unknown is the intercept term $b_{20}$, it is straightforward to show that using the standard least-square approach, $b_{20}$ can be estimated by

$$b_{20}={\displaystyle \frac{\sum _{i=1}^{n_L}\sum _{j=1}^{n_{i_L}}(T{S}_{ij}-20 {\log }_{10} {L_i}_j)}{\sum _{i=1}^{n_L}{n}_{i_L}}}$$

(5)

where $n_L$ is the total number of length bins and $n_{i_L}$ is the number of length samples in each length bin (which may have included more than one trawl when their mean length was within the same 1 cm bin). $T{S}_{ij}$ and ${L_i}_j$ are the measured TS (dB) value and the corresponding hake fork length (cm) for the ith length bin and jth TS sample in the ith length bin, respectively. For comparison, the TS-length regression was also assessed empirically with a free slope parameter in the form of

$$TS=a {\log }_{10} L \left(\mathrm{c}\mathrm{m}\right)+b_a$$

(6)

where a is the slope parameter and b_a its associated intercept.

2.4. Statistical Analysis

To evaluate the variability and robustness of the $b_{20}$ estimate, three statistical methods were applied and compared. Each method provides a slightly different perspective on the sampled data and their reliability:

• Resampling: All TS data were randomly resampled with non-replacement, using 95%, 90%, and down to 5% of the original data, with 1000 realizations for each percentage bracket. This addresses the sensitivity of the data to marginally high or low TS samples (or specific to trawl hauls) by assessing significant divergence in slope estimates as the TS sample size is gradually reduced down to a small fraction of all available data. This resampling approach also helps in identifying potential bias due to outliers, or disproportionate weight to sample values that are at the tail end of the distribution (e.g., hauls with the smallest and largest mean fork lengths).
• Bootstrapping: The bootstrap method estimated the sampling distribution of $b_{20}$ by resampling the original data using all (100%) data samples with replacement [26,27], also with 1000 realizations.
• Jackknife: The jackknife cross-validation technique, a leave-one-out resampling method with replacement, was used for bias and variance estimation [28].

3. Results and Discussion

3.1. Target Strength (TS) Data Processing and Acceptance

After applying the single-target detection and tracking criteria specified in Table 1 and Table 2, the manual selection guidelines, and a pulse-energy filter, the processed TS samples were analyzed. The accepted TS samples from assumed single targets associated with the selected hauls across different years are summarized in

Table 3. Information on target strength (TS) samples from the targets associated with the chosen midwater trawl hauls. The average catch weight per haul was 377 kg and the average hake catch was 97%.

Dataset	No. of Hauls	TS Samples (Original)	TS Samples (Pulse-Energy Filtered’)
2009	8	6891	150
2011	7	4875	98
2013	12	14,103	241
2014	2	1898	6
2015	9	1915	48
2016 Winter	13	9922	218
2017 Winter	9	4158	92
2017 Summer	5	3365	61
2018	2	216	5
2019	22	16,829	481
DAISY 7 September 2014	1	3722	40
DAISY 12 September 2014	1	3788	47
DAISY 23 March 2016	1	5372	23
Sum	92	77,054	1510

. The dataset comprises a total of 92 hauls from 13 surveys conducted between 2009 and 2019, with an overall acceptance rate of single targets less than 2%. This was largely due to the pulse energy filter, which we found necessary to analyze targets at a long range in low signal-to-noise ratio conditions, because of the relatively high density of hake (and other scatterers) at depth during daytime surveys. The average biological catch per haul was approximately 380 kg, with an average hake catch composition of 98%, confirming that the samples were representative of hake-dominated areas. Exceptions were two hauls in 2014 that were associated with the DAISY data, where hake catch proportions were slightly above 80% (Appendix A,

Table A1. Detailed catch information of all hauls used in this study.

Year	Haul Number	Latitude (Deg North)	Longitude (Deg West)	Mean Fork Length (cm)	Standard Deviation of Fork Length (cm)	CV (%)	# of Length Samples	Total Catch (kg)	% of Hake by Weight
Shimada
2009	8	37.0401	122.6764	40	3.76	9.4	324	321	95
2009	22	39.0280	123.9685	40	2.58	6.5	347	1426	100
2009	39	42.7018	124.7260	38	2.34	6.2	437	4590	100
2009	56	44.2032	124.9930	42	2.12	5.0	301	1100	99
2009	57	44.3706	124.8315	41	2.5	6.1	288	446	100
2009	62	44.8783	124.4680	19	1.64	8.6	336	1749	100
2009	64	44.8796	124.8209	43	2.52	5.9	248	128	99
2009	66	45.3749	124.4020	41	2.48	6.0	339	268	100
2011	2	35.3790	121.0993	22	1.25	5.7	242	82	99
2011	4	35.7137	121.4605	23	1.13	4.9	280	941	100
2011	9	37.3658	122.9050	24	1.88	7.8	208	18	100
2011	18	39.3728	123.9755	35	2.00	5.7	276	116	100
2011	27	44.3747	124.8392	39	2.96	7.6	307	216	99
2011	40	46.8773	124.9192	37	1.83	5.0	264	259	100
2011	44	47.3707	124.8633	38	1.93	5.1	325	140	100
2013	5	35.4248	121.3085	35	1.00	2.9	118	33	99
2013	10	35.9212	121.5310	26	1.42	5.5	317	463	100
2013	13	36.5982	122.6653	37	1.56	4.2	308	181	100
2013	16	37.2632	123.0873	37	1.72	4.7	536	177	99
2013	18	37.4207	122.9600	37	1.54	4.2	333	495	100
2013	33	40.5868	124.6773	38	2.24	5.9	556	198	98
2013	38	41.5960	124.5763	37	1.56	4.2	414	369	100
2013	42	43.0928	124.8732	37	1.94	5.2	397	259	98
2013	45	43.9313	124.9667	38	2.15	5.7	345	446	100
2013	48	44.2608	124.9428	39	2.69	6.9	230	86	100
2013	56	46.2453	124.2052	40	2.97	7.4	353	318	97
2013	76	50.0928	128.0172	51	3.62	7.1	537	522	89
2014	15	43.8840	124.7910	43	3.16	7.3	237	642	100
2014	16	43.8858	124.7343	44	3.35	7.6	200	192	100
2015	9	36.4460	122.1363	23	2.22	9.7	373	49	98
2015	13	37.4495	122.9712	22	1.46	6.6	285	431	88
2015	15	38.1177	123.6143	24	1.06	4.4	375	69	94
2015	21	39.7728	124.0748	35	3.40	9.7	418	166	100
2015	39	43.4477	124.7072	24	1.36	5.7	323	1316	100
2015	42	43.7828	124.9052	42	1.56	3.7	62	34	96
2015	46	44.7827	124.6060	21	1.23	5.9	481	290	100
2015	60	47.3663	124.8485	23	2.02	8.8	237	314	99
2015	73	49.1188	126.8678	44	2.37	5.4	288	156	100
2016 Winter	2	42.1750	124.6632	29	2.74	9.4	235	35	92
2016 Winter	4	41.3485	124.4978	27	1.58	5.9	474	440	93
2016 Winter	7	41.4722	125.0988	44	2.72	6.2	195	234	96
2016 Winter	8	40.4218	125.0995	44	3.04	6.9	221	460	100
2016 Winter	9	39.8428	125.0960	44	3.02	6.9	123	61	97
2016 Winter	10	39.1192	125.2397	43	2.55	5.9	256	141	85
2016 Winter	11	39.1202	125.2287	43	2.59	6.0	256	118	99
2016 Winter	13	37.9578	123.5278	28	1.67	6.0	210	125	96
2016 Winter	18	37.2152	124.0930	42	3.01	7.2	211	237	100
2016 Winter	21	35.9870	123.8852	43	2.43	5.7	235	139	92
2016 Winter	29	37.1723	124.0630	42	2.99	7.1	231	332	98
2016 Winter	30	39.0515	125.1992	42	3.00	7.1	200	225	99
2016 Winter	32	42.5568	125.8293	44	2.75	6.3	287	143	97
2017 Summer	1	34.9915	121.0798	26	2.14	8.2	331	37	98
2017 Summer	4	36.4908	122.1897	28	2.15	7.7	415	1163	98
2017 Summer	10	38.3297	123.6627	37	2.39	6.5	395	531	98
2017 Summer	14	39.1445	124.0088	38	2.30	6.1	403	351	95
2017 Summer	16	40.8132	124.5613	40	2.90	7.3	419	316	91
2017 Summer	19	41.6540	124.4612	27	1.91	7.1	250	90	99
2017 Summer	20	41.8235	124.4860	28	1.87	6.7	242	586	100
2017 Summer	25	42.9898	125.1188	41	2.92	7.1	226	119	95
2017 Summer	31	44.1580	124.9715	39	2.76	7.1	396	202	98
2017 Winter	3	42.1720	124.5940	19	1.28	6.7	156	51	96
2017 Winter	4	37.2585	123.3062	35	2.22	6.3	201	123	93
2017 Winter	6	35.4527	123.5482	43	3.21	7.5	191	99	100
2017 Winter	7	34.4397	120.7680	21	1.07	5.1	401	100	100
2017 Winter	12	38.9510	124.0153	34	1.67	4.9	301	1080	100
2018	18	44.5778	124.6725	41	2.81	6.9	245	378	100
2018	19	44.5685	124.6752	43	2.67	6.2	236	156	97
2019	7	35.3937	121.1582	22	1.26	5.7	212	52	100
2019	8	35.5583	121.4342	23	1.69	7.3	212	104	99
2019	12	36.0648	121.7403	24	2.44	10.2	220	87	97
2019	19	37.5640	123.0483	32	2.32	7.3	356	178	100
2019	22	38.0565	123.5303	42	3.70	8.8	349	525	99
2019	24	38.5600	123.7883	38	3.01	7.9	322	121	94
2019	25	38.7320	123.8278	39	3.17	8.1	334	141	100
2019	29	39.4012	123.9842	40	2.25	5.6	326	182	92
2019	30	39.7312	124.2135	41	2.22	5.4	441	210	98
2019	33	40.3948	124.7948	41	2.07	5.0	403	413	100
2019	35	40.5643	124.7252	41	2.68	6.5	438	612	99
2019	36	40.7295	124.8352	41	2.57	6.3	468	648	100
2019	38	41.0465	124.4185	42	2.83	6.7	373	393	100
2019	45	42.7263	124.7283	42	3.23	7.7	381	1567	100
2019	46	42.8943	124.9795	42	2.99	7.1	366	576	100
2019	47	43.0708	125.0855	42	2.54	6.0	235	115	97
2019	48	43.2257	124.7650	42	2.47	5.9	343	313	100
2019	50	43.7210	125.0668	43	2.44	5.7	215	111	100
2019	54	44.0552	124.9563	41	2.73	6.7	381	701	99
2019	56	45.0540	124.7597	44	1.97	4.5	83	46	97
2019	57	45.2223	124.6620	43	2.02	4.7	276	148	97
2019	59	45.5570	124.5612	45	2.12	4.7	184	107	97
DAISY
9/7/2014	36	41.6582	124.5003	29	1.25	4.3	101	259	80
9/12/2014	41	48.9242	126.5505	48	3.41	7.1	174	161	82
3/23/2016	30	50.0170	123.9078	33	4.70	14.2	150	29	99
Mean		41.0717	124.1269	36.2	2.34	6.5	299	379	98

). Although the hake catches were lower for these DAISY data, the non-hake catches were primarily squids (no gas inclusions) and small lanternfish (~5-cm), whose TSs were believed to be much less than those of hake ($L\ge 17\mathrm{c}\mathrm{m}$). Furthermore, in-trawl camera footage indicated that these non-hake animals were caught at different depths from hake, as explained in Section 2.1.

3.2. TS Distribution and Depth Analysis

The histogram of the TS samples from detected single targets is shown in Figure 3. The TS distribution was not symmetric around the mean or mode, approximately at −37.5 dB. A small portion of the TS samples had very low TS values, indicating the TS samples were either from smaller hake individuals, from hake that had larger tilt angles, or from small non-hake targets. Although the lower limit of the single-target detection algorithm was specified at −60 dB re 1 m², the actual accepted TS samples following the filtering processes were all greater than −55 dB re 1 m².

TS samples distributed between 150 and 400 m represented about 80% of the total accepted TS values (Figure 4). There were few samples detected in very shallow water, i.e., shallower than 100 m depth, but their corresponding TS values were mostly lower than −45 dB re 1 m², significantly lower than the mean TS value of −36.8 dB re 1 m², or the median value of −36.3 dB re 1 m² (Figure 5), likely from smaller age-1 juvenile hake, or even age-0 young-of-year (YOY) hake. The left side of Figure 5 illustrates the lower target strength values observed in shallower water, associated with smaller juvenile fish that are typically found at those depths. There was no trend observed in target strength with depth beyond 175 m. Since Pacific hake are a physioclist species, where the amount of gas inside the closed swimbladder is controlled internally by the rete mirabile [29], we assumed that the volume of their swimbladder was constant since they were acclimated for the depth at which they were sampled.

3.3. Spatial Variability and Fork Length Association

Except for TS samples around lat 43.5° N, where the TS values were lower and more spread out, all TS samples had median values close to the overall median of −36.9 dB re 1 m² (Figure 6). These low TS values at lat 43.5° N possibly correspond to the smaller hake fork length at the same latitude (Figure 7), as stated in Section 3.2. Some trawls at the median length were at the higher end of the 75th percentile (lat 36.5° N, 38.5° N, 39° N, 41° N, and 43.5° N), or at the lower end of the 25th percentile (lat 37.5° N, 42° N, 42.5° N, and 44° N). At some latitudes, the 25th and 75th percentiles and the median were identical (lat 41.5° N and 45.5° N), indicating that the catches were uniform in length distribution. The smallest fork length of Pacific hake for this study was just over 16 cm. A resonance peak for these fish would be expected well below 38 kHz [18,30,31].

3.4. TS-Length Regression

One of the most important results of this study is the regression of TS versus length. The regression was performed in the logarithmic domain for TS (dB) and linear domain for the length (cm) (Section 2.3). The boxplot of the TS values of the accepted samples as a function of length is presented in Figure 8. Mean lengths from trawls were categorized in 1 cm length bins, which may include samples from more than one trawl (when their mean length was similar). The forced slope of 20 for the model provided an estimated slope of −67.9 dB (p < 0.001, with a residual standard error of 3.73). This value is only 0.1 dB larger than the value derived from Traynor et al. [22] currently used for biomass estimates of Pacific hake. The areal acoustic scattering coefficient (NASC) is used for converting the acoustic quantity to biological quantity, i.e., the number of fish,

$$N={\displaystyle \frac{NASC}{{\sigma }_{bs}}}$$

(7)

where ${\sigma }_{bs}$ is the differential scattering cross-section defined in Equation (1), or ${\sigma }_{ba}={10}^{TS/10}$. For a fixed NASC value, the difference in ${\sigma }_{bs}$ will result in a change in the number of fish, N:

$$\mathsf{\Delta }N=-{\displaystyle \frac{NASC}{{\sigma }_{bs}^2}}\mathsf{\Delta }{\sigma }_{bs}$$

(8)

A relative change in the estimated fish number is expressed as the ratio of (8) to (7):

$${\displaystyle \frac{\mathsf{\Delta }N}{N}}=-{\displaystyle \frac{\mathsf{\Delta }{\sigma }_{bs}}{{\sigma }_{bs}}}=-\mathsf{\Delta }TS{\displaystyle \frac{{\log }_{e}10}{10}}\approx -0.23\mathsf{\Delta }TS$$

(9)

As a result, a 0.1 dB increase in TS would lead to a change of less than 3% $\left({\displaystyle \raisebox{1ex}{$\mathsf{\Delta }N$}\!\left/ \!\raisebox{-1ex}{$N$}\right.}\approx -0.23<3\%\right)$ in the estimated fish number. Applying this revised value and assuming that the fish weight is proportional to the fish number, the estimated biomass would have been less than 3% higher than the acoustic biomass estimates reported from previous Joint U.S.-Canada IAT Surveys [2].

For comparison, a linear regression where slope was estimated was also performed, resulting in a slope of 17.1 and the intercept of −63.3 dB (p < 0.001, adjusted R² of 0.21). This regression curve is also shown in Figure 8 (dashed black line), which is not very different from the 20-log regression curve (solid magenta line) and well within the sample confidence interval that includes the slope of 20. This non-20-log regression relation was an empirical data fit comparison. For gadoids, which have large spheroid-shape swimbladders, the relationship is justified to follow a 20-log relationship [32]. Scattering physics reveals that the differential backscattering cross-section in the farfield (i.e., plane wave incidence) should be proportional to the squared length of the target of finite size (i.e., smaller than the first Fresnel zone) [33,34,35]. There have been debates in the literature about whether the relationship of target strength to length does not always necessarily follow a 20-log regression [36,37], perhaps due to complexity in fish body types and swimbladder morphologies.

3.5. Statistical Robustness of $b_{20}$

To assess the robustness and the variability of the value of $b_{20}$ in the TS-length regression, we performed the three statistical processes as described in Section 2.2, i.e., partial, bootstrapping, and jackknife resampling methods, all with 1000 iterations.

• Partial sampling: For the partial sampling, we resampled the whole data population with 95% down to 5% in 5% increments, and at each percentage value, we performed the resampling with replacement 1000 times or realizations. The results are tabulated in

  Table 4. Results from the partial resampling with replacement.

  Resample Percentage	Mean (dB)	Standard Deviation (dB)
  5%	−67.9	0.42
  10%	−67.9	0.29
  20%	−67.9	0.19
  30%	−67.9	0.15
  40%	−67.9	0.12
  50%	−67.9	0.10
  60%	−67.9	0.08
  70%	−67.9	0.06
  80%	−67.9	0.05
  85%	−67.9	0.04
  90%	−67.9	0.03
  95%	−67.9	0.02

  , and their graphic representation is shown in Figure 9. All distributions from the resampling can be well described by Gaussian or normal distributions. A representative example at 90% resampling is illustrated in Figure 10, where a Gaussian Probability Density Function (PDF) with a mean of −67.9 dB and standard deviation of 0.03 dB is superimposed onto the plot of the raw resampled values. Note that even with a substantially low number of selected TS samples at 5% of the original data, the estimated mean value of the in situ TS was only 0.003 dB lower than −67.9 dB.
• Bootstrapping: Bootstrapping yielded a $b_{20}$ mean of −67.9 dB with a 95% confidence interval of [−68.09, −67.72]
• Jackknife analysis also resulted in a $b_{20}$ mean of −67.9 dB with a standard deviation of 0.002 dB.

These analyses all confirm the robustness of the $b_{20}$ estimate, with minimal variability, well within the tolerance for uncertainty in the stock assessment [2]. The low variability observed in the data indicates consistency in TS measurements, likely the result of the extensive filtering of data, primarily based on the last step involving the pulse energy filter.

3.6. Comparison with Previous Studies

Although the $b_{20}$ value reported here is similar to that of Traynor [22], it was 4–6 dB higher than that reported by Henderson and Horne [16]. Several factors may explain this discrepancy:

• Data Collection Conditions: Previous studies on Pacific hake used TS data collected at night, while all of the data presented in this paper were collected during the daytime, i.e., consistent with the hake survey time from sunrise to sunset [38]. Hake TS measurements during daylight are more representative for biomass estimation as hake aggregate at depth during the day, but tend to scatter at night when there are fewer visual cues. As hake scatter and spread out through the water column at night, they could present increased tilt angles, resulting in reduced TS values.
• Length Range and Regression Consistency: Henderson and Horne’s ex situ TS data spanned a narrow fork length range (44–53 cm), with TS values spread over an 8 dB range [16], potentially reducing regression reliability and robustness.
• Backscatter Model Discrepancies: The Kirchhoff Ray-Mode (KRM) [30] backscatter model used by Henderson and Horne, with X-ray images of fish bodies and the swimbladders of live fish captured at sea, showed predictions 4–6 dB higher than their ex situ TS measurements [16], indicating inconsistencies between model predictions and the ex situ measurements, but consistent with the findings from this study. It has been shown that when the fish body and swimbladder morphology are known, the KRM model is appropriate and suitable for single fish [39].

Results from these in situ measurements are consistent with the findings of Traynor despite their relatively small dataset of target strength measurements. The intercept value of −67.9 dB is in line, but lower by ~2 dB than reported for other gadoids [22,32,40,41]. Recent broadband measurements on Atlantic cod yielded a b₂₀ of −65.6 dB, consistent with narrowband measurements and also about ~2 dB higher than for Pacific hake [42]. Interestingly, early target strength measurements reported a b₂₀ of −67.4 dB for physioclists (which include Pacific hake), which is only 0.5 dB higher than our estimate [43]. Consistency and low variability in TS measurement values observed over nine surveys (spanning 10 years) provide confidence in the use of the −68 dB intercept value currently used for Pacific hake biomass estimates obtained from acoustic surveys. This consistency and low variability were likely the result of using the same methodology over a wide range of conditions across several years. Because of the uneven distribution of samples across survey years, it was not possible to investigate the effect of interannual environmental or biological factors that might affect TS—however, the consistency of results over the span of this study indicates that these trends would likely be small compared to the natural variability observed in target strength measurements.

3.7. Limitations of the Study

Collection of Pacific hake in situ target strength data during the day is problematic because these fish tend to aggregate at high densities in relatively deep waters (often mixed with other smaller mesopelagic scatterers), making collection of ship-based data prone to multiple target bias. Collection made at shorter range, for example, using the DAISY system, partially addresses this issue, but is resource-demanding (requiring dedicated time and equipment). On the other hand, data collected during assessment and research surveys provide large volumes of data that can be mined afterward (see [32] for another example). Because of the low signal-to-noise ratio conditions encountered in relatively deep Pacific hake aggregations, selection of targets based on fish or target density metrics [44,45], even at reduced survey speeds, was not used in this study (as very little data would be preserved). Rather, a stepwise approach to the selection of targets was adopted, with the addition of a novel filter based on pulse energy used on the final dataset. The consistency of TS values obtained (especially when compared to closer measurements made with DAISY) provides further evidence for the validity of this approach. It is also important to note that ship-based target strength measurements in this study were all made during midwater trawling operations (because of the reduced vessel speed). There is evidence that trawling affects fish behavior [46]. Acoustic data collection from the centerboard of the vessel was performed prior to the trawl going through the aggregation, but increased vessel and trawling gear noise may have an impact on the orientation and swimming behavior of fish. There is, however, little evidence of a change in aggregation characteristics and depth distribution prior compared to during trawling, so we are assuming that these measurements of target strength data were made on fish representative of those encountered during routine acoustic surveys.

4. Conclusions

Single-fish TS data of Pacific hake at 38 kHz from more than ten surveys and research cruises spanning ten years were analyzed. These data were processed with a number of filters and criteria to ensure data quality so that all accepted TS samples were expected to be from individual hake. All echosounder datasets were verified by biological trawl catches with an average hake composition of more than 95% by weight to ensure the echoes were most likely from hake. The TS-length regression of 20-log linear representation, i.e., Equation (1), suggests an intercept term, $b_{20}$ of −67.9 dB, only 0.1 dB larger than the value currently used in acoustic biomass estimates. The updated $b_{20}$ aligns closely with current biomass estimation practices, ensuring an accuracy well within acceptable uncertainty limits. The results from three statistical validation methods, i.e., partial, bootstrapping, and jackknife resampling procedures, were used to assess the variability of the estimated $b_{20}$, ensuring accuracy within acceptable uncertainty limits while addressing discrepancies with earlier studies. These findings emphasize the importance of standardized sampling protocols and robust methods for advancing acoustic biomass assessment. Our methodology and new filtering of single-target data based on pulse-energy information may be useful for a wide range of pelagic and semi-pelagic species assessed using acoustic methods.