A study of range dependent acoustical field based on the FVCOM model: A Case of typhoon NANMADOL

This study simulated the acoustical field in the western North Pacific (WNP) during typhoon NANMADOL, based on the FVCOM model and Range dependent Acoustic Model RAM. We implements a new approach, which helps to accurately characterize the energy distribution of acoustical field obtained by considering the range dependent ocean dynamical environment elements. The results show that, the sound speed profile in the upper-layer ocean of the sea water decreases to a certain extent on the day after the typhoon’s arrival, while the maximum decrease in the sound speed after the typhoon’s transit occurs 1∼2 days. The maximum decrease in the seawater sound speed can be up to 2-3 m/s 2 days after the typhoon’s transit. The passage of the typhoon mainly affects the far-field acoustical energy distribution when the sound source is located near the upper-layer ocean.


Introduction
The three-dimensional temperature, salinity and depth data produced by ocean models are important data for ocean acoustic applications.Generally ocean models focus on the evolution and development trend of ocean temperature, salinity and other elements of the ocean dynamic environment in the regional ocean, the open ocean and even the global ocean.Since the vertical scale of the sea area concerned by the ocean model is relatively small compared with the horizontal one, the selection of coordinates is one of the key factors which determine the adaptability of the sea area for its calculation.The coordinates selected by the ocean model mainly include σ, z, S and ρ coordinates.To more precisely fit the boundaries of various seabed topography, the ocean model typically chooses the σcoordinate for the vertical spatial discretization near the seabed.As one of the most commonly used coordinate systems in the ocean model, σ-coordinate is a terrain-following coordinate system in essence.It discretizes the vertical space of the seafloor and the water body into a number of coordinate surfaces to provide the ocean model with the lower boundary conditions and the boundary exchange conditions of the dynamical environment elements.At the horizontal scale, Its unstructured triangular grid is a more common spatial discretization in the ocean model, and this horizontal grid has an advantages of precisely delineation of continental and island boundaries [1].
Acoustic modeling and applications are important bases for acoustic performance assessment and target information perception.In the engineering practice, ocean acoustic propagation models, such as ray model [2],normal modes model [3],parabolic equation model [4], discretizes the ocean threedimensional space into N×2D mode (where N is the number of spatial azimuths), ocean acoustic application focuses on solving the spatial distribution of acoustic field energy in two-dimensional space (2D) of horizontal distance-depth.
2 According to analysis above, the spatially discrete coordinate mismatch between ocean acoustic applications and ocean models restricts the effective transfer of seawater temperature and salt depth data.Da [5]and Guo [6]focus on the influence of spatial and temporal changes of the marine environment on the acoustic environmental uncertainty, and establish an ocean-acoustic coupled numerical model, which concentrates on the numerical results of the acoustic propagation loss and its uncertainty at different depths and frequencies, but no specific technical solution is given to the ocean model and the acoustic application.However, no specific technical solution for data coordinate conversion between the ocean model and acoustic application is given, and the application of acoustic field related to horizontal distance is not considered.
Typhoons have an impact on the acoustic field through changing the ocean environment, however, there have been few investigations on this object.Newhall et al studied the process of Typhoon Morakot in 2009, and discovered that strong upwelling was caused by typhoon, which changes the stratification of the water column, and thus changes in the speed of sound; typhoons can significantly increase ambient noise levels and alter their vertical distribution [7].Chan and Chen used underwater acoustic remote sensing to collect the distant noise generated by typhoon-induced surface winds, which can be used to calculate typhoon intensity [8].Typhoon NANMADOL was generated on the ocean southeast of Kyushu Island, Japan in the early morning of September 14, 2022, and strengthened as a typhoon at 1400 UTC 15 September.It then moved northwestward and gradually increased in intensity.On the afternoon of September 16th, Typhoon NANMADOL strengthened into a super typhoon.Finally, on the afternoon of 18 September, Typhoon NANMADOL made landfall along the coast of Tsukiki City, Kyushu Island, Japan.The impact on China is extensive.The typhoon path data comes from the National Meteorological Administration (tcdata.typhoon.org.cn),Fig. 1 depicts the specific path of the typhoon.

Data
The simulated area in the WNP and East China Sea ranges from 97°E-155°E and 1°N-57°N.The calculation area includes the Philippines Islands, Taiwan Islands, and Japan Islands.Daily averaged heat flux data are taken from the National Centers for Environment Prediction (NCEP)(https://downloads.psl.noaa.gov/Datasets/ncep.reanalysis/surface_gauss/).The wind data using improved atmospheric models and a four-dimensional variational assimilation method, with wind field resolution of 0.125°×0.(http://www.ngdc.noaa.gov/mgg/global/global.html ) with a resolution of 1' × 1'.The initial temperature field and the salinity field, as well as the lateral boundary were derived from HYCOM data with a resolution of 0.08°× 0.08°.

Ocean model FVCOM
FVCOM is a triangular-grid, 3-D, primitive equation ocean model [9].As one of the popular ocean circulation models, FVCOM has been extensively applied to coastal and estuarine environments [10,11,12].The model uses the finite volume method, which combines the geometric flexibility of a finite-element method and the simple discrete calculation of the finite difference method.Irregular bottom slopes are transformed in σ coordinates and the horizontal grid includes unstructured triangular cells [13].The model has been continuously improved since its initial development with the inclusion of a wave-current coupling module, an estuarine module, an assimilation module, and so on. In

the Range dependent Acoustic Model RAM
In column coordinates, the acoustic field of a particular orientation is taken as the object of study, and it is assumed that the pressure p satisfies the following far-field governing equations over a distancedependent spatial region  is the density,   is the wave number is the  circular frequency, c is the speed of sound ,  is the attenuation in dB /  ,and , Factoring the operator in Eq. obtain as follows Where 0 0 / k c   ,and 0 c is a representative phase speed, Eq.( 2) contains the incident and outgoing wave parts, where the equation for the outgoing wave part is: The formal solution of Eq.( 4) is: where r  is the range step, Applying an n-term rational function to approximate the exponential function we obtain

Methods of spatial coordinate conversion
We obtain the distance-relevant point location is located, extract the temperature, salinity, and depth data of the indexed triangular grid of the ocean model at a fixed moment in time, and use the empirical formula of Chen & Millero's sound speed profiles [14] to convert the temperature, salinity, and depth data into the seawater sound speed profile data.
Under the unified depth stratification framework of the acoustic field, based on the sound speed profile data of the indexed triangular mesh, the three-dimensional discrete data interpolation method is used to obtain the seawater sound speed profile data of the distance-dependent points at a fixed stratified depth.The seawater sound speed profiles at the distance-related points are used as input information for the ocean acoustic propagation model, and the energy distribution of the sound field in the horizontal distance-depth two-dimensional space can be solved based on the acoustic propagation model RAM.Fig. 2 shows a schematic diagram of the above spatial coordinate transformation.( ) where i x and i y respectively represent observational values and simulated values.x and y represent the average of the observational values and simulated values, respectively.N represents the number of data point (Table 1).

Validation and analysis of temperature profiles
The numerical simulation of ocean temperature and salinity is carried out from September 14 to September 18, 2022.The ocean temperature is the most important physical quantity affecting the sound speed profile among them.In order to verify the reliability of the ocean temperature simulation, the ARGO buoy data are used for the verification and analysis of the SST.Fig. 3 shows the distribution of ARGO buoy positions in the simulation area on September 16, and the red pentagrams represent the buoy positions.ARGO buoys presented in Fig. 4 are used as validation points.The MAE , RMSE and R between the buoy of upper-layer ocean temperature and the simulated upperlayer ocean temperature on September 16 were calculated (Table 1).
We comparted the SSTs from the available Argos data with those simulated using the FVCOM during the NANMADOL typhoon Fig. 5a shows SSTs simulated on September 15 (RMSE of 0.88 •C and COR of 0.98), while Fig. 5b shows SSTs simulated on September 16 (RMSE of 1.37 •C and COR of 0.97).Therefore, it is concluded that the FVCOM model can simulate the temperature well.In general, the upper-layer ocean temperature simulated by the model is more reasonable and reliable, which provides a basis for the next analysis of the changes of the acoustic field before, during and after the passage of the typhoon.

Ocean acoustic field analysis
Based on the numerical results of the FVCOM ocean model, the spatial coordinate transformation method is used to obtain the distance-dependent sound speed of seawater, and the sound speed profiles at (134.7°E, 24.8°N) at 1200 h from 14 to 18 September are given in Fig. 6.Since this location is the center of the typhoon's path on September 16, September 14 and 15 can be considered to be before the typhoon, while September 17 and 18 are after the passage of the typhoon.
As shown in Fig. 6, the sound speed in the upper-layer ocean of the sea water decreases to a certain extent on the day after the typhoon's arrival, while the maximum decrease in the sound speed after the typhoon's arrival occurs 1~2 days after the typhoon's arrival.Comparing the seawater sound speed profiles at 12:00 on September 16 and 18, the differences in sound speed values in different depths are not the same, and the maximum decrease in the seawater sound speed can be up to 2-3 m/s 2 days after the typhoon's arrival.In order to compare and analyze the acoustical field before and after the passage of the typhoon, the acoustical field at the center of the typhoon track on September 16 (134.7°E,24.8°N) in the longitudinal section at 35°NE and 35°SW is selected (see Fig. 7), assuming that the frequency of the sound source is 50 Hz, the value of the horizontal distance step of the Range dependent Acoustic Model RAM is 25 m, and that the value of the vertical step is 5 m.The distance-dependent sound speed profile information is taken into account on the longitudinal sections (Sections 1 & 2), and the distance-dependent sound speed profile information is also considered on the vertical sections.
The acoustical field simulated by the ocean acoustical field model RAM numerical simulation at 1200 UTC September 14, 16, and 18 are given in Fig. 8, respectively, where the sound source is located 200 m underwater at (134.7°E, 24.8°N).Along Section 1, the seafloor topography has a gentle slope with an undulation of about 1700m, and there is a certain slope-climbing aggregation effect of the sound source energy in this cross-section, and the acoustical field energy continues to propagate to the far after the slope has been slowed down.Since there is a more obvious acoustic shadow area and convergence area at the far end of the field on September 18(Fig 8).Above phenomenon is closely related with the deflection of the acoustic field energy in the direction of the lower sound speed because the upper-surface sound speed decreases the most dramatically on September 18(Fig 6).In Section 2, due to the relatively flat seafloor topography, the sound source propagates in the far field to form a more periodic energy band, and the width of the convergence zone is stable at about 59 km.To sum up, it can be seen that when the sound source is located near the upper-layer ocean , the passage of the typhoon mainly affects the energy distribution of the acoustical field .

Conclusion
Based on FVCOM model, we used the the Range dependent Acoustic Model RAM to simulate acoustical field during typhoon NANMADOL.Combined with ARGO buoy data, upper-layer ocean temperature were verified.By analysis of the acoustical field during typhoon, the following conclusions were obtained: (1) This paper implements a new approach, which facilitates the modular operation of data coordinate transformation under the coupled application of ocean model and Acoustic Model, and is suitable for long distance conditions, which helps to accurately portray the energy distribution of the acoustic field obtained by considering distance-related ocean dynamical environment elements.It helps to accurately characterize the energy distribution of Acoustical field obtained by considering the distance-related ocean dynamical environment elements.
(2) The sound speed in the upper-layer ocean of the sea water decreases to a certain extent on the day after the typhoon's arrival, while the maximum decrease in the sound speed after the typhoon's arrival occurs 1~2 days after the typhoon's arrival.it can be seen that when the sound source is located

Figure 1 .
Figure 1.Map of the study area in the western North Pacific (WNP):(a) Track of Typhoon NANMADOL and(b) with color indicating water depth.

Figure 2 .
Figure 2. A schematic diagram of the above spatial coordinate transformation 3.5 Validation StrategyMean error ( MAE ), root mean square error ( RMSE ), correlation coefficient ( R ) were used to measure the accuracy of the simulation results and the expressions for the above physical quantities are as follows.

Figure 3 .Figure 4 .Figure 5 .
Figure 3. ARGO buoy position on September 16 (orange star is the typhoon position at 1200 UTC 16September and the red star is the ARGO position)

Figure 8 .
(a) acoustical field before the typhoon passes by (1200 UTC 14 September) (b) acoustical field when the typhoon passes by (1200 UTC 16 September) (c) Acoustical field after the typhoon passes by (1200 UTC 18 September) Acoustical field(Section 1&2) centered on (134.7°E,24.8°N) this experiment, an unstructured triangular horizontal grid with 26,073 nodes and 50,244 triangular grids is used.The land boundary, island boundary, and open ocean boundary are all considered.One open boundaries.Sponge boundary conditions are used on open boundaries.The model adopts σ -coordinate in the vertical direction with 40 layers.Time steps of the internal and external mode are 10 and 1 s, respectively; and the output time interval is 60 min.

Table 1 .
Error statistics of temperature simulation and ARGO buoy measurements.