Fisheries Acoustics — From Ping to Biomass

01

The Echosounder Sends a Ping

Sound pulses travel down through water, hit fish and the seabed, and bounce back

Survey Parameters

Frequency

38 kHz

Pulse length

1 ms

Sound speed

1500 m/s

Ping rate

1/s

1 / sec

Vessel speed

~3 kn

~1.5 m/ping

How the pulse works

Travel time = 2 × depth / c
// 2× because sound goes DOWN and UP

At 80m depth:
t = 2 × 80 / 1500 = 0.107 seconds

            The echosounder records echo strength at every millisecond of the return trip → this becomes depth-resolved Sv data
          

Water Column Zones

0–10m ⚠ Vessel noise zone — excluded

10–60m 🐟 Fish integration layer

60–75m Sparse / near-bottom water

75–79m ⚠ Acoustic dead zone

79–80m 🪨 Seabed — excluded

Step 1 of 7

02

Raw Echo Data — The Echogram

Thousands of pings stacked side by side form a 2D acoustic image of the water column

Raw Sv Data Table — First 3 Pings

DEPTH	PING 1 (Sv dB)	PING 2 (Sv dB)	PING 3 (Sv dB)	WHAT IT IS
5 m	−45	−80	−78	VESSEL NOISE
20 m	−75	−74	−76	empty water
35 m	−78	−77	−79	empty water
50 m	−55	−53	−56	🐟 FISH SCHOOL
60 m	−72	−70	−71	empty water
80 m	−34	−33	−35	🪨 SEABED

Echogram Visualization

 −80 dB
          
 −20 dB

Color Scale (Sv in dB)

🔵 −80 dB → near noise floor, empty water
🟢 −65 dB → sparse zooplankton
🟡 −55 dB → fish aggregation
🟠 −45 dB → dense school
🔴 −34 dB → seabed / very dense

Step 2 of 7

03

Noise Removal & Data Cleaning

Remove vessel noise, impulse spikes, attenuated pings, and set exclusion boundaries

Types of Noise Detected

🚢

Vessel / Cavitation Noise

Top 0–10 m → fully excluded

EXCL

⚡

Impulse Spikes

Single-sample outliers flagged by median filter

FLAG

📉

Background Noise

Electronic noise subtracted via Ryan method

CORR

🪨

Seabed + Dead Zone

Bottom 1 m above seabed excluded

EXCL

Impulse Spike Detection — Example

PING	DEPTH 20m Sv (dB)	STATUS
Ping 1	−76	OK
Ping 2	−75	OK
Ping 3	−74	OK
Ping 4	−20 ⚡	SPIKE!
Ping 5	−75	OK

Median of neighbors = −75 dB
Spike value = −20 dB
Deviation = 55 dB > threshold (10 dB)
→ FLAGGED → set to NaN

Background Noise Correction

Sv_corr = 10·log₁₀(10^(Sv/10) − 10^(Pn/10))

// Example at 50m depth:
Sv = −55 dB → linear = 3.16×10⁻⁶
Pn = −115 dB → linear = 3.16×10⁻¹²
Sv_corr ≈ −55.00 dB (barely changed)

// At 400m where signal is weak:
Sv = −78 dB, noise matters much more!

Before vs After Cleaning

DEPTH	RAW Sv	CLEANED Sv	ACTION
0–10 m	−45 dB	NaN	VESSEL NOISE EXCLUDED
20 m	−75 dB	−75 dB	CLEAN
50 m	−55 dB	−55 dB	FISH SIGNAL OK
79–80 m	−34 dB	NaN	DEAD ZONE EXCLUDED
80 m	−34 dB	NaN	SEABED EXCLUDED

Step 3 of 7

04

Bottom Detection

Find the seabed in each ping to define the lower boundary of fish integration

Algorithm — Ping by Ping Scan

Scan downward from min depth (e.g. 20 m)

Find first depth where Sv exceeds −50 dB threshold

Apply median smoothing across 5–10 pings to remove jumps

Apply backstep = 0.5 m upward from detected bottom

Exclude bottom 1 m (dead zone) from integration: integration stops at 79 m

Ping 1 Scan Result

DEPTH	Sv (dB)	vs −50 dB	RESULT
20 m	−75	BELOW	—
40 m	−73	BELOW	—
50 m	−55	BELOW	—
60 m	−72	BELOW	—
80 m	−34	ABOVE ✓	BOTTOM!

Water Column with Boundaries

Step 4 of 7

05

Echo Integration — Computing NASC

Full arithmetic: from raw Sv values to NASC = 1500 m² nmi⁻², every number shown

Survey Setup (inputs to this calculation)

38 kHz
frequency
0.5 m
Δz sample thickness
1.5 m
Δx ping spacing
1235
pings per nmi

① Convert Sv (dB) → sv (linear) · formula: sv = 10^(Sv ÷ 10)

        Sv in dB is logarithmic — you cannot do arithmetic on it directly. Convert to linear first.
        Every 10 dB difference = 10× difference in linear power.
      

DEPTH	Sv (dB)	CALCULATION	sv (linear, m⁻¹)	RELATIVE
20 m	−75 dB	10^(−75 ÷ 10) = 10^(−7.5)	3.16 × 10⁻⁸	1×
50 m	−55 dB	10^(−55 ÷ 10) = 10^(−5.5)	3.16 × 10⁻⁶	100× stronger!
60 m	−72 dB	10^(−72 ÷ 10) = 10^(−7.2)	6.31 × 10⁻⁸	2×

Why 100× stronger? Because −55 dB − (−75 dB) = 20 dB
10^(20/10) = 10^2 = 100 — that's what 20 dB means in linear scale

② Multiply Each sv by Sample Cell Volume · cell contribution = sv × Δz × Δx

        Each sample cell is a thin horizontal slab: 0.5 m deep × 1.5 m wide (one ping width).
        Multiply sv by the cell dimensions to get its acoustic contribution.
      

DEPTH	sv (linear)	× Δz (0.5 m)	× Δx (1.5 m)	CELL CONTRIBUTION
20 m	3.16×10⁻⁸	× 0.5	× 1.5	2.37 × 10⁻⁸
50 m	3.16×10⁻⁶	× 0.5	× 1.5	2.37 × 10⁻⁶ 🐟
60 m	6.31×10⁻⁸	× 0.5	× 1.5	4.73 × 10⁻⁸

③ Multiply by Number of Pings in 1 nmi · 1 nmi = 1852 m ÷ 1.5 m/ping = 1235 pings

        Each depth layer repeats across all 1235 pings as the vessel moves 1 nautical mile forward.
      

DEPTH	CELL CONTRIBUTION	× 1235 PINGS	LAYER TOTAL	% OF SIGNAL
20 m	2.37×10⁻⁸	× 1235	2.93 × 10⁻⁵	~1%
50 m 🐟	2.37×10⁻⁶	× 1235	2.93 × 10⁻³	~98%
60 m	4.73×10⁻⁸	× 1235	5.84 × 10⁻⁵	~2%

④ Sum All Depth Layers

Total = 2.93×10⁻⁵ ← 20m layer (empty water)
+ 2.93×10⁻³ ← 50m layer (FISH SCHOOL — dominates!)
+ 5.84×10⁻⁵ ← 60m layer (empty water)
───────────────────
Total ≈ 2.93 × 10⁻³ ← fish school is 98% of everything

        ⚡ Key insight: in linear space, 2.93×10⁻³ vs 2.93×10⁻⁵ means the fish school is
        100× bigger than the empty water contribution.
        Empty water is essentially invisible.
      

⑤ Apply 4π Correction and Normalize to 1 nmi² → Final NASC

        The 4π factor comes from the standard NASC convention (MacLennan et al. 2002).
        It accounts for the spherical geometry of acoustic backscattering — sound radiates in all directions,
        but we only capture the back-reflected portion. Normalizing to 1 nmi² (= 1852² m²) makes NASC
        comparable across surveys regardless of transect length.
      

s_A = Total × 4π × 1852²

s_A = 2.93×10⁻³ × 4π × (1852)²

// 4π = 12.566
// 1852² = 3,430,000 m²

s_A = 2.93×10⁻³ × 12.566 × 3,430,000

s_A = 2.93×10⁻³ × 43,100,000

s_A = ≈ 1500 m² nmi⁻²

Full Arithmetic Chain

📥

Input: Sv at 50m

Raw echosounder measurement

−55 dB

🔢

dB → linear

10^(−55/10)

3.16×10⁻⁶

📦

× cell size

× 0.5 m × 1.5 m

2.37×10⁻⁶

🔁

× all pings

× 1235 pings / nmi

2.93×10⁻³

➕

+ all depths

sum all layers

≈2.93×10⁻³

🎯

× 4π × 1852²

spherical correction + normalize

≈ 1500

Contribution by Depth Layer

1500

m² nmi⁻² · NASC

            = total effective "mirror area" of all fish
in this 1 nmi survey strip
          

Step 5 of 7

06

Convert NASC to Fish Density

Full arithmetic: from NASC = 1500 → ρ = 2,354,000 fish/nmi², every number shown

What we carry in from Step 5

1500
NASC (m² nmi⁻²)
28 cm
avg herring length (trawl)
120 g
avg herring weight (trawl)

① Trawl Sampling — Why We Need It

        Acoustics only measures how much echo — it cannot tell you which species or how big the fish are.
        A trawl net is deployed alongside the acoustic transect to physically catch fish and measure them.
        The trawl gives us the length distribution needed to calculate mean TS.
      

TRAWL MEASUREMENT	VALUE	USED FOR
Species identified	Atlantic Herring	Select correct TS equation
Number of fish measured	350 fish	Statistical confidence
Average total length (L)	28 cm	Input to TS–length formula
Average weight (w)	120 g = 0.12 kg	Biomass calculation in Step 7

② Calculate Mean Target Strength (TS) · formula: TS = 20·log₁₀(L) + b₂₀

        Target Strength (TS) is how strongly one average fish reflects sound back to the transducer.
        The 20·log₁₀(L) term means TS scales with the square of fish length
        (because the swim bladder area ∝ L²). The intercept b₂₀ = −71.9 dB is species-specific for herring (Foote 1987).
      

TS = 20 · log₁₀(L) + b₂₀ // Foote 1987, Atlantic Herring

// Step by step with L = 28 cm:

log₁₀(28) = 1.4472 // because 10^1.4472 = 28

20 × 1.4472 = 28.944

TS = 28.944 + (−71.9)

TS = −42.96 dB

        What does −42.96 dB mean physically? A 28 cm herring reflects back only
        0.005% of the incident sound energy — the rest passes through or scatters elsewhere.
      

③ Convert TS (dB) → σ_bs (linear m²) · formula: σ_bs = 10^(TS ÷ 10)

        Just like Sv must be converted from dB to linear before math,
        TS must also be converted. σ_bs (backscattering cross-section) is the
        effective mirror area of one fish in m².
      

σ_bs = 10^(TS ÷ 10)

σ_bs = 10^(−42.96 ÷ 10)

σ_bs = 10^(−4.296)

σ_bs = 5.07 × 10⁻⁵ m²

// = 0.0000507 m² — about the area of a postage stamp
// This is the "acoustic mirror size" of one 28 cm herring

FISH LENGTH	TS (dB)	σ_bs (m²)	RELATIVE SIZE
20 cm (small)	−45.9 dB	2.57×10⁻⁵	0.5×
28 cm (our fish)	−42.96 dB	5.07×10⁻⁵	1× baseline
40 cm (large)	−39.9 dB	10.2×10⁻⁵	2× bigger

          ⚡ Doubling fish length increases σ_bs by 4× (because area ∝ length²)
        

④ Calculate Fish Density · formula: ρ = s_A ÷ (4π × σ_bs)

        Now divide the total acoustic signal (NASC) by the signal one fish produces (σ_bs).
        The 4π again appears because NASC and σ_bs use the same spherical geometry convention — they cancel correctly to give fish per nmi².
      

ρ = s_A ÷ (4π × σ_bs)

// plug in our numbers:

ρ = 1500 ÷ (4π × 5.07×10⁻⁵)

// compute denominator first:
4π × 5.07×10⁻⁵ = 12.566 × 5.07×10⁻⁵ = 6.37×10⁻⁴

ρ = 1500 ÷ 6.37×10⁻⁴

ρ = 1500 ÷ 0.000637

ρ = 2,354,000 fish per nmi²

⑤ TS Sensitivity — Why Getting TS Right is Critical

        A 3 dB error in TS = 2× error in σ_bs = 2× error in fish density.
        This is the biggest source of uncertainty in any acoustic survey.
      

SCENARIO	TS USED	σ_bs	ρ (fish/nmi²)	ERROR
Correct	−42.96 dB	5.07×10⁻⁵	2,354,000 ✓	0%
Fish too big (trawl bias)	−39.96 dB (+3dB)	10.1×10⁻⁵	1,177,000	÷2 (−50%)
Fish too small (trawl bias)	−45.96 dB (−3dB)	2.54×10⁻⁵	4,708,000	×2 (+100%)
Wrong species used	−36.96 dB (+6dB)	20.2×10⁻⁵	588,500	÷4 (−75%)

Full Arithmetic Chain — Step 6

🎣

Trawl sample

measure fish on board

L = 28 cm

📐

TS–length formula

20·log₁₀(28) − 71.9

−42.96 dB

🔢

dB → linear σ_bs

10^(−42.96/10)

5.07×10⁻⁵ m²

➗

NASC ÷ (4π·σ_bs)

1500 ÷ 0.000637

2,354,000

🐟

Fish density ρ

per square nautical mile

2.35M / nmi²

Step 6 of 7

07

Scale Up to Total Biomass

Full arithmetic: from ρ = 2,354,000 fish/nmi² → 56,500 tonnes, every number shown

What we carry in from Step 6

2,354,000
ρ fish / nmi²
200 nmi²
survey area
0.12 kg
mean fish weight
1000 kg
= 1 tonne

① Survey Area — How Transects Cover the Bay

        The vessel doesn't cover every square metre — it follows a set of parallel transects
        spaced evenly across the survey area. Each 1 nmi segment gives one NASC value.
        The average NASC across all segments is used to represent the whole area.
      

TRANSECT	LENGTH (nmi)	NASC (m² nmi⁻²)	NOTES
T-01	14	1820	dense school area
T-02	14	1540	typical
T-03	14	1390	typical
T-04	14	1200	sparser
T-05	14	1050	edge of distribution
Mean across all transects		≈ 1500 m² nmi⁻²	our working value

Total survey area = 5 transects × 14 nmi × ~2.9 nmi spacing
≈ 200 nmi² // the bay we are surveying

② Total Fish Abundance (N) · formula: N = ρ × Area

        Multiply the fish density per nmi² by the total survey area to get the absolute number of fish in the entire bay.
      

N = ρ × Area

N = 2,354,000 fish/nmi² × 200 nmi²

N = 470,800,000 fish

// ≈ 471 million herring in this bay

        To put this in perspective: 471 million fish stacked nose-to-tail at 28 cm each would stretch
        131,880 km — more than 3× around the Earth.
      

③ Mean Fish Weight — From Trawl to Length–Weight Relationship

        Fish weight is measured directly from the trawl catch, or estimated from a
        length–weight relationship: W = a · Lᵇ (species-specific constants).
        For herring: a ≈ 0.0057, b ≈ 3.04
      

W = a × L^b // length-weight relationship

W = 0.0057 × 28^3.04

28^3.04 ≈ 28³ × 28^0.04 ≈ 21952 × 1.138 ≈ 24,982

W = 0.0057 × 24,982 ≈ 142 g // predicted from formula

// Trawl directly measured: 120 g (we use this as it's more reliable)
Mean weight used = 0.12 kg per fish

④ Total Biomass (B) · formula: B = N × mean weight ÷ 1000

B = N × w

B = 470,800,000 fish × 0.12 kg/fish

B = 56,496,000 kg

// convert kg → tonnes (÷ 1000):

B = 56,496,000 ÷ 1000

B = 56,496 tonnes ≈ 56,500 tonnes

Final Results

471M

total herring in the bay

56,500

tonnes of biomass

            56,500 tonnes = weight of ~375 fully loaded Boeing 747s
          

Full End-to-End Chain

🔊

Sv at fish school

echosounder ping

−55 dB

📊

NASC

echo integration

1500 m²/nmi²

🎣

TS from trawl

28 cm herring

−42.96 dB

🐟

Fish density ρ

NASC ÷ (4π·σ_bs)

2.35M/nmi²

✖️

× survey area

200 nmi²

471M fish

⚖️

× mean weight

× 0.12 kg ÷ 1000

56,500 t

⑤ Uncertainty Budget — Where Errors Propagate From

        Every step introduces uncertainty. These errors multiply together through the chain —
        so a 50% error in TS combined with a 30% spatial coverage error gives roughly a 65% total error in biomass.
      

ERROR SOURCE	TYPICAL SIZE	EFFECT ON BIOMASS	RISK
TS uncertainty (wrong length or species)	±3 dB	×2 or ÷2 (±100%)	HIGH
Species misclassification in echogram	variable	wrong σ_bs used entirely	HIGH
Spatial coverage (transect spacing)	±20–30%	under/overestimate area	MED
Fish availability (below survey depth)	±10–25%	missed fish = underestimate	MED
Acoustic dead zone (near seabed)	±5–15%	demersal fish missed	LOW–MED
Background noise correction	±2–5%	correctable with good data	LOW

// Combined uncertainty (if independent errors):
CV_total ≈ √(CV_TS² + CV_spatial² + CV_availability²)
≈ √(0.5² + 0.25² + 0.15²) ≈ ±58% on biomass

// This is why fisheries acoustic surveys report confidence intervals,
// not just single numbers — 56,500 t ± 33,000 t is the honest answer.

Step 7 of 8

08

Spatial Biomass Prediction

Kriging, Random Forest/XGBoost, and CNN-based mapping from transect points to full-lake biomass hotspots

Step 8 of 8