Method for the simplistic modelling of the acoustic footprint of the vessels in the shallow marine area☆

Graphical abstract

Environmental Science More specific subject area Underwater acoustics Method name Simplistic modelling of the vessels acoustic footprint in the shallow marine area

Method details
The research area and the hydro-acoustic properties Lithuanian marine area is located at the Eastern part of the Baltic Sea coast in the Gotland basin [1]. Lithuanian marine areas borders with the Russian Federation in the southern part, in the North with Latvia, and in the West with Sweden. At the centre of the Lithuanian EEZ the Nemunas Palaeo opens to the inside of the Gdansk Peninsula [2]. A Klaipeda-Ventspils Plateau gradually slopes through the Gdansk sill to the West forming the deeper areas having the depths of >60 m reaching $125 m at the West [3], where the downslope from the East to West has no any steep ridges or cliffs forming favourable sound propagation paths. The bathymetry of the Lithuanian EEZ depicted in the Fig. 1A.
For description of sound propagation conditions and determination of winter ducting period at Lithuanian EEZ the SVP's were computed using TS data for the year of 2015. The TS data were acquired from the EU Marine Environment Monitoring Service database (Baltic Sea Physics Reanalysis From SMHI 1989-2015 HIROMB model, [4]), acquired at the location 55 43 0 8.32 00 N; 20 36 0 40.31 00 E (see Fig. 1A), using the equation: Where Cw(z)depth dependant sound velocity (m/s), Ttemperature, Ssalinity, Hwater depth [5].  [6]). During the rest of the year (spring-summer-autumn seasons), the sound velocity profiles assumed to be an ISO and negatively inclined, where the sound propagation taking place in the "mode stripping" region, with extensive surface-bottom interaction of sound waves [7].
The dominating bottom sediments in the coastal Lithuanian marine area are the sandy and aleuritic substrate. Central part of the EEZ is covered mainly by coarse aleurite and western deepest part of EEZ is covered mostly with pelitic and pelitic-aleuritic mud. Still, at the Lithuanian EEZ and coastal areas the sandy bottom substrates dominate [8]. For the computations of sound transmission losses the bottom sediments assumed to be sandy and silty substrate throughout the Lithuanian marine area.

Ship source levels
To compute shipping noise levels, three entities are in generally required; density of shipping, the source level of the ships, and the transmission loss [9]. These computations inevitably will vary due to the different locations and different seasons [10]. Source levels of vessels are computed in 1 Hz frequency bands ( Fig. 2 Y & Z axes), using the Research Ambient Noise Directionality Model 3.1 algorithm (for description see [11]). The ship source levels assumed to be dipole, "surface modified" radiated noise levels [7].

Sound propagation modelling
For sound transmission loss modelling, the algorithm by Ainslie et al. [7] was used where the three propagation scenarios are modelled.
Three propagation scenarios: Spherical propagation loss, equation: Cylindrical propagation loss equation: Propagation loss in the Mode stripping area: Colour bar marks power spectral density levels in dB re 1 mPa 2 /Hz.
Where the r is a distance, r 0reference distance (1 m), kwavenumber, zsource depth, Dreceiver depth (assumed to be H/2 at any location), Hwater depth, βcritical angle, hconstant for sandy and silty substrate (0.3 Np/rad). The cylindrical and mode stripping sound transmission loss computations were implemented at 1 Hz frequency bands across the frequency range of 10 Hz -10 kHz including depth dependence "H" at each range step.
Sound transmission loss equations divided in to two values of A + B i.e. A = 25log 10 (x); B = 10log 10 (y), where TL = A + B = 25log 10 (x) + 10log 10 (y). Any case of sound propagation losses (either cylindrical or mode stripping) are summed at discrete ranges (range steps 300 m). Then computations implemented as a summation of the values of A and B, which are denoted as TL A and TL B : The TL Ar equals to: The TL Br equals to: In the summer season (January-February): In the winter season (rest of the year): The transition range between spherical sound transmission losses and the losses in the mode stripping region or cylindrical propagation regions were equated using the equation: Where r ttransition range between spherical propagation and propagation of sound waves in the entire shallow sound channel, ensonified in a cylindrical mode, Hwater depth, βthe critical grazing angle of sound propagation [12]. Critical grazing angle defined by: Where v 1sound speed in water, v 2sound speed in sediments [13]. Sound transmission losses in winter season while computed where filtered using pass-band filter, where winter ducting cut-off frequencies were defined using the equation: Where f ocut-off frequency in Hz below which sound cannot propagate in the duct [13]. Consequentially sound propagation in the spectra of the frequencies above the cut-off frequency were computed using winter transmission loss equation TL winter and the remaining frequencies of spectra using the TL summer transmission loss equation. An example of two modelled different seasonal propagation scenarios presented in the Fig. 2. In the Fig. 2B is clearly visible the sound propagation trapped in the winter duct above the 600 Hz extending to the great distance.
As well, model was programmed to account for sound leakage from the duct [13] at the shoaling bathymetry, where transmission loss values are conserved as the highest loss values, while reaching the lowest depths at the sound wave paths.
In the areas with the shoaling bottom, model was programed to filter noise spectra with a pass band filter applying the cut-off frequency equation: Where fc is the cut-off frequency in the shallow water [14]. Modelled summer sound transmission losses were compared with the Normal Mode sound propagation loss model KRAKEN [15] and sound transmission loss model was tested for depth dependence. The comparison and test results are presented in the Fig. 3.
Computed summer transmission losses were compared with the transmission losses computed using the Normal Mode model in 100 Hz frequency band at the different receiver depths above and below the thermocline (summer sound speed profile), computed with the shoaling bathymetry. The comparison presented in the Table 1.
Greater deviations of computed transmission losses from the losses computed using NM model were observable at the greater distances at both scenarios (>15 km).

Computations of the surface acoustic footprint
For the spatial noise distribution computations around the vessel, the transmission losses along uncoupled azimuthal planes of length Dr = 20 nm (distance chosen for experimental purposes), allowing the construction of an acoustic image around the noise sources was used. The vertical radials   11.25 (360 /w) at each noise source position (see [13]). Noise propagation directivity was computed as well, using the coefficients of sound propagation pattern of merchant vessel example (sailing at 8 kn speed) in the frequency band of 4 kHz, expressed as the sound pressure ratio between the highest-pressure levels radiated at the ships abeam and the rest of the noise propagation directions. Sound pressure levels around the noise source then were multiplied by obtained coefficients. Radiated acoustic energy is computed as greatest at abeam direction and noise radiated astern is weakened by bubbly wake and in forward direction reduced by ship's hull [16]. The directivity coefficients presented in the Table 2.
The sound pattern directivity of the merchant vessel radiating the broadband surface sound pressure level equal to 171.3 dB re 1 mPa 2 m 2 at the distance of 48 km from the land sailing at the 9.2 knot speed, plotted as the geographical map in the Fig. 4. Table 2 Directivity coefficients derived from data by [16].
Azimuthal mid angle, deg Acquired noise data of ships then can be integrated in to the spatial grid to build acoustic footprint in the area of interest and the soundscape surface maps can be derived using the interpolation techniques [17].