JASA 
https:/doi.org/10.1121/10.0043324 
Measured-Scaled Median and Mean RNL 
N 
— A Median RNL 
— A Mean RNL 
generic speed effect is inherently limited. The negative corre- 
lation between RNL and distance, increasing with frequency, 
indicates that a residual distance dependence remains in the 
data. Since a negative correlation means that RNLs decrease 
with increasing distance, this pattern implies that, particularly 
at higher frequencies, more distant vessels are associated with 
systematically lower RNLs. 
While the bivariate analyses provide useful first-order 
insights, they do not capture potential interactions between 
vessel properties and operational parameters. To address 
this, we applied GAM and RF regressions per frequency 
band to assess the relative importance of each parameter. 
GAMs and RFs were computed across eight different com- 
binations of the following predictors: speed, length, dis- 
tance, propulsion type, and individual vessel [Maritime 
Mobile Service Identity (MMSI)]. Three different propul- 
sion types were found for the investigated CTVs: controlla- 
ble pitch propellers (CPPs), fixed pitch propellers (FPPs), 
and APs. Model performance was evaluated using the 
adjusted coefficient of determination (adjusted R?), which 
accounts for differences in model complexity and allows a 
fair comparison between models with different numbers of 
predictors. All GAMSs were statistically significant (F tests, 
p < 0.05 across frequency bands), confirming that the evalu- 
ated predictor sets explain a non-random fraction of the 
observed RNL variability. For the RF models, statistical sig- 
nificance in the classical sense cannot be assessed via p val- 
ues. Model performance is therefore evaluated 
comparatively, based on explained variance (adjusted R?). 
The frequency-dependent effects and relative impor- 
tance of the individual predictors inferred from the GAMs 
and RF models are illustrated in Fig. S5 in the supplemen- 
tary material, providing insight into how the explanatory 
power of the multivariate models is distributed across pre- 
dictors and frequency bands. 
Overall model performance is summarized in Table III. 
which reports mean adjusted R* values averaged over all 37 
Me 
= 
| * 
410- 
103 10% 
Frequency (Hz) 
10% 
FIG. 6. Differences between J-E scaled and unscaled RNL spectra (mean 
and median), illustrating the limited effect of J-E speed and length scaling 
on the observed RNL variability. 
vessel speed, length, and DCPA (see Fig. 7). The resulting 
relationships between RNL, speed, and length are frequency 
dependent. While speed primarily influences sound levels at 
40 and 8SOHz, there is a noticeable trend suggesting that lev- 
e]s above 1kHz tend to increase with vessel length. 
However, the maximum correlation of approximately 0.5 is 
relatively weak, indicating that these bivariate relationships 
between RNL and individual predictors explain only a lim- 
ited fraction of the observed variability when considered in 
isolation. 
It is also important to note that ship-specific correlations 
‘gray lines in Fig. 7) differ significantly from the overall cor- 
relation for speed. Additionally, the observed trend with ves- 
sel length is based on only 13 vessels with a limited range of 
lengths and is therefore not conclusive. Given the relatively 
narrow speed distributions in our dataset (10-25 kn) (Table 
[I; see Fig. 9, right panel, below), statistical power to isolate a 
RNL vs. Speed 
RNL vs. Length 
RNL vs. Distance 
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vet 
daft 
103 104 107 10? 10? 10% 2201 a 
Frequency (Hz) Frequency (Hz) 
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A 
a PAS 
ha He 
Vi 1,8 Ba 
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FIG. 7. Spearman correlation coefficients of the RNLs with speed, length, and distance. Gray lines represent correlations with individual vessels. 
J. Acoust. Soc. Am. 159 (4), April 2026 
Basan et al. 341‘