JASA

https:/doi.org/10.1121/10.0043324

estimation (ISO, 2025). However, no international standard
currently exists for opportunistic underwater radiated noise
measurements from transiting vessels. In this study, ISO
17208-3 was used as a methodological framework for
apportunistic shallow water ship-noise measurements.
All validated CTV passages were processed as
described in the following. A data window period (DWP)
was defined around each manually validated TCPA. The
DWP corresponds to the time during which the vessel
remained within a +30° sector centered around the CPA.
The length of this data window (DWL) is defined as
Ipw = 2 tan(30°)dcpa.
Consequently, the DWP is given by
Iipw = IDw

where v is the speed of the passing vessel. All 103 passages
with DWPSs shorter than 10s were excluded from further
analysis. Mean-square SPLs were calculated for all passages
aver their respective DWPs. The background noise level
during each passage was defined as the 5th percentile of the
SPLs over a period of 60 min around the TCPA. The corresponding
 background noise levels per frequency band were
subtracted from the measured signal within the DWP. Only
passages where the signal exceeded the background noise
level by at least 3 dB across all frequency bands were considered
 for further analysis, resulting in a total of 529 passages
 included in the final dataset. In practice, more than
35% of passages exceeded the background by > 6dB in all
bands, indicating that background-noise bias is negligible.
To calculate SLs from these background-noise-corrected
 SPLs, L„, the propagation loss Npr needs to be added,
Ls(fe) = Lp(fe, dera) + Nrı(fe, dera), 3)

where f. is the center frequency of the respective decidecade
frequency band. According to the ISO 17208-3 standard, the
recommended method to determine Npr_ in shallow water is
:he SSCI method (ISO, 2025). SSCI combines coherent contributions
 from the direct path and the first reflections from
‘he sea surface and seafloor with an incoherent sum of conributions
 from multiple reflected paths.
However, the SSCI formulation neglects frequencydependent
 absorption, x(f), and is derived under the
assumption that absorption losses over DCPA are negligible
compared to geometric spreading (Yubero ef al., 2025).
Accordingly, ISO 17208-3 and Yubero ef al. (2025) recommend
 applying SSCI only within specific applicability limits,
 namely, for frequencies up to 20kHz and DCPAs not
exceeding 5 x the local water depth.
Because several passages in our dataset exceed the recommended
 range limits (DCPA >5 x water depth) and fre-Juencies
 up to 40kHz were analyzed, absorption cannot be
neglected. Following the recommendation of Yubero ef al.
(2025), the SSCI was extended by adding an absorption term,

J. Acoust. Soc. Am. 159 (4), April 2026

Npu (fo, dera) = Nsscılfe, depa) + o(fo) depa, (4)
where Nsscı is the SSCI propagation loss estimate and «(f,)
is the absorption coefficient in decibels per meter. x(f£) was
computed using the Thorp parameterization for seawater
absorption (Urick, 1983),
0.10 140 4275 x 107*f? 40.003
1+f? 4100+f?
HP) =———— 9 — am

(5)

where f is the frequency in kHz. The influence of this
absorption correction on SSCIT is illustrated in Figs. S2 and
S$3 in the supplementary material, which quantify the SSCI
propagation-loss error relative to the image source model
‚Urick, 1983) as a function of frequency and range. The figures
 show that absorption has little influence below approximately
 10KkHz, but neglecting it at higher frequencies leads
to a systematic underestimation of propagation loss. Using
the SSCI-plus-absorption formulation, we obtained SLs for
each CTV passage.
Some applications (e.g., quiet ship certification) refer to
deep water RNLs rather than SLs. RNL is a standardized.
depth-independent noise metric that corrects for sourcedepth-dependent
 interference effects and thereby enables
consistent comparison across vessels and with literature values.
 The SSCI-derived SLs were converted to RNLs using
the ISO 17208-2 formulation (ISO, 2019)
14(kd)* + 2(kd)*
Lrn = Ls + 10108 19 ( 7 2(kdY T 2) dB, (6)

where k = 2uf./cw is the acoustic wavenumber, c„ is the
sound speed in water, and d is the source depth in meters. c„
was measured by a nearby BSH measurement frame and
extracted for each passage. The source depth was set at 0.7
x the draught of each CTV, which was given in the AIS
data and verified from detailed specification sheets per vessel
 (see Table II).
To contextualize the CTV measurements, we compare
the resulting RNL spectra to those of a representative commercial
 vessel operating in the North Sea—a 200m bulk
carrier travelling at 14 kn. The bulker reference SL spectrum
was derived from the empirical J-E SL parameterization
(MacGillivray and de Jong, 2021).
E. Statistical analysis

For each passage, AIS provides metadata such as speed
over ground (SOG) and vessel length. The J-E model
(MacGillivray and de Jong, 2021) predicts SLs as a function
of speed and length using the relationship
Ls,y-E(f, 0,1) = Ls;o(f) +60 10g ‚o(v/vc) dB
+2010g 10(7//0) dB, 7)

where Ls..o(f) is a baseline spectrum for each vessel class, v
is the vessel speed, and vr is the reference speed for that

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