Rough Sea Surface Research Articles

Statistical Analysis of Local Extrema in Rough Sea Surfaces Based on Computer Simulation

Introduction. Generalized extreme value (GEV) distributions represent a universal description of the limiting distribution of the normalized local maxima statistics for independent and identically distributed data series. Extreme value distributions are commonly classified into three different types representing different functional forms and thus varying in shape, also known as types I, II, and III. Thus, attribution of some observational data series to a particular type of its local maxima distribution, as well as fitting of the distribution parameters, provides certain information about the laws governing the underlying natural or technogenic process. Radar-based remote sensing techniques represent a ubiquitous tool for analyzing large patterns of the sea surface and determining the parameters of the waves. In turn, understanding the laws governing the extreme values in the rough sea surface obtained from their radar images followed by evaluation of their distribution parameters, depending on the wind speed and direction, as well as the presence of surface currents and swells, can be useful for predicting wave height. Aim. Analysis of the functional forms governing the local extreme value distributions in a rough sea surface for the given wind and swell parameters based on computer simulations. Materials and methods. For the rough sea surface simulated by an additive harmonic synthesis procedure, the local extreme value distribution was fitted using the least-mean-squares technique. The fitted parameters were then used for their classification according to the three predetermined types. Results. Computer simulations of a rough sea surface with combined wind and swell waves were performed. It is shown that the distribution of local maxima in the absence of swell waves could be well approximated by theWeibull (type III GEV) distribution, with the parameters explicitly depending on the wind speed. At the same time, no significant dependence on the sea depth was observed. On the contrary, in the presence of additional swell waves, the distribution of local extrema could be rather attributed to the Fréchet (type II GEV) distribution, with the parameters additionally depending on the angle between the wind and swell waves. Conclusion. The laws governing the distributions of local wave extrema in rough seas are in a good agreement with the theoretical GEV approximations, with the distribution parameters being deductible from the key features of the waves. This indicates the predictability of wave height extrema from sea surface measurements, which can be performed based on remote radar observations.

Acoustic backscattering at a tidal intrusion front

Strong spatial gradients and rapidly evolving, three-dimensional structure make estuarine fronts difficult to sample. Echosounders can be used near fronts to provide nearly synoptic images of water column processes and, with sufficient bandwidth, can provide quantitative information about dynamical variables derived from forward and inverse methods using acoustic backscattering measurements. This manuscript discusses measurements using broadband (50-420 kHz) echosounders from the James River (Virginia, USA) tidal intrusion front. The dominant backscattering mechanisms observed at the site include bubbles, turbulent microstructure, interfaces associated with stratification, suspended sediment, and biota. Existing analytical models are used to interpret contributions from these sources with acoustic inversions providing quantitative information about the physical structure and processes that compare favorably with conventional, in situ measurements. Supporting data sets for this analysis include measurements of temperature, salinity, velocity, and turbidity; X-band radar images of sea surface roughness; aerial optical imagery; Lagrangian measurements of waves, turbulence, and velocity structure; and Regional Ocean Modeling System circulation model simulations. A notable advantage of acoustic remote sensing is the ability to resolve processes at considerably higher spatial resolution (< 1 m horizontal; < 5 cm vertical) than other in situ sampling approaches.

Verification and Modeling of the Maritime Channel for Maritime Communications and Navigation Networks

This paper presents a geometric stochastic channel model designed for analyzing maritime communication and navigation services between moving ships using the C-band or sub-6 GHz spectrum, which aligns with the focus of emerging 5G networks on land. The channel model is validated through channel measurements conducted both on the sea and land. A software tool has been developed to integrate and analyze these measurements, which is included with this publication. The main challenge in developing the channel model for maritime services lies in the dynamic nature of the sea surface, leading to constantly changing reflection conditions due to varying reflectors and scatterers on the water. Additionally, the motion conditions of the transmitter and receiver on ships change in all three dimensions, depending on the sea state. To address these complexities, data from several measurement campaigns in diverse areas were collected. The analysis involved examining the propagation conditions over the sea with variations in sea surface roughness, antenna heights, and used bandwidths. Moreover, additional propagation conditions over nearby land were also taken into account. The study demonstrates that the changing antenna height on the ship, influenced by sea conditions, significantly affects the reflection and scattering conditions. The research aims to develop reliable, high-data rate, and broadband marine communication systems. Therefore, a measurement bandwidth of 120MHz was employed to derive the propagation model. This model not only offers absolute timing information but can also be used for time-based ranging or positioning systems. The proposed geometric stochastic channel model provides valuable insights into the complex maritime communication and navigation environment. By accounting for the continuously evolving sea surface and its impact on antenna height, the model offers a robust framework for studying and optimizing marine communication systems. The availability of a software tool integrating real-world measurements further enhances the usability and practicality of the channel model for future maritime communication research and deployment.

Evaluation of sea surface roughness parameterization in meso-to-micro scale simulation of the offshore wind field

Accurate parameterization of the wind-induced effects on the Marine Atmospheric Boundary Layer (MABL) is of fundamental importance for many applications including weather forecasting and offshore wind energy. Roughness parameterizations derived from different datasets are widely used but their performance is not sufficiently assessed under realistic marine environmental conditions. To this end, a multi-scale atmosphere–wave coupled model is constructed for the first time and used in the simulation of the MABL flow over the North Sea. Results show that our model is able to capture the large-scale variation of the mean wind meanwhile reproducing the appropriate turbulence energy cascade in the frequency domain. The performance of different roughness parameterizations is evaluated in comparison with the measurement data from the FINO1 platform. The Taylor-Yelland method outperforms the others on statistics of the mean wind while yielding the highest bias of the Turbulence Kinetic Energy (TKE) from the observations. However, we find that the discrepancy between our simulation and observation mainly depends on the meso-scale model. The magnitude of the differences caused by roughness parameterizations is negligible, especially in low wind speed conditions. The micro-scale simulation is demonstrated as not sensible to the roughness input in the considered wind–wave condition.

A novel and computationally efficient subgrid technique for modeling scattering and Doppler effects of rough dynamic sea surfaces using the finite-difference time-domain method

Over the last decade, the improvements in computational performance that multiprocessing, solid-state hard drives, and fast memories have brought to desktop workstations have made modeling and simulation methods that were previously inaccessible into the office workspace. These methods were previously restricted to large servers or computer clusters because of their demanding computation and large memory requirements when applied to underwater acoustic simulation scenarios. One such method is the Finite-difference Time-domain (FDTD) technique. The FDTD method is a discrete numeric model that provides the full pressure wave solution solved directly in the time domain. This makes it an ideal model for investigating scattering and Doppler effects of boundaries with complex geometries and motion. A fully developed sea surface generated using the Pierson–Moskowitz wavenumber spectra meets these criteria. A novel subgrid technique has been developed to improve the accuracy of signals scattered from fully developed sea surfaces. This method remains computationally efficient because the subgrid is applied only along the rough sea surface as it varies over time. The FDTD subgrid method has been applied to simulations that investigate the “frozen” sea surface assumption that is utilized by other traditional models that incorporate boundary motion.

A simple formula for coherent specular reflection loss of underwater sound from rough ocean surfaces

The interaction of underwater sound with rough sea surfaces affects its propagation. The interaction may involve several coupled mechanisms: (1) a rough air-sea interface scatters and spreads the incident sound energy over a range of angles, (2) entrapped sub-surface air bubbles absorb and scatter sound energy, and (3) medium of bubble clouds refract sound energy upwards. In this paper, we ignore the effect of bubbles and consider the effect of rough air-sea interface only. We further limit our consideration to the coherent component in the specular direction. Two simple closed-form formulas are often used to model the coherent reflection loss from rough ocean surfaces. One is derived from perturbation approximation and suitable for smaller grazing angles. The other is from Kirchhoff approximation and suitable for larger grazing angles. More accurate approximations over a wide-range of grazing angles require numerical evaluation of integrals or complex special functions. In this work, we simplify and adapt earlier results by other authors to obtain a simple expression that transits from the perturbation to the Kirchhoff formulas as grazing angle increases. The new simple analytical formula is easy to use and compares well with results from complex numerical methods.

The SSR Brightness Temperature Increment Model Based on a Deep Neural Network

The SSS (sea surface salinity) is an important factor affecting global climate changes, sea dynamic environments, global water cycles, marine ecological environments, and ocean carbon cycles. Satellite remote sensing is a practical way to observe SSS from space, and the key to retrieving SSS satellite products is to establish an accurate sea surface brightness temperature forward model. However, the calculation results of different forward models, which are composed of different relative permittivity models and SSR (sea surface roughness) brightness temperature increment models, are different, and the impact of this calculation difference has exceeded the accuracy requirement of the SSS inversion, and the existing SSR brightness temperature increment models, which primarily include empirical models and theoretical models, cannot match all the relative permittivity models. In order to address this problem, this paper proposes a universal DNN (deep neural network) model architecture and corresponding training scheme, and provides different SSR brightness temperature increment models for different relative permittivity models utilizing DNN based on offshore experiment data, and compares them with the existing models. The results show that the DNN models perform significantly better than the existing models, and that their calculation accuracy is close to the detection accuracy of a radiometer. Therefore, this study effectively solves the problem of SSR brightness temperature correction under different relative permittivity models, and provides a theoretical support for high-precision SSS inversion research.

On the development of a generalized atmospheric boundary layer velocity profile for offshore engineering applications considering wind–wave interaction

Within industrial standards, effects due to wind–wave interaction on the marine atmospheric boundary layer (ABL) may be included via the Charnock sea-surface roughness parameter for open-sea and near-coastal waters. This roughness parameter does not accommodate the wide variety of wave states possible, nor does it modify the ABL to include speed-up effects resulting from an undulating wave profile. In an attempt to provide an updated definition of the general ABL profile for offshore wind engineering applications, an experimental and numerical study is performed to assess the interaction of the ABL on a fixed wave geometry. By extracting the mean velocity field during the wind–wave interaction, bespoke values of the velocity profile power exponent and wind risk factor can be obtained. A range of wave heights and wave lengths are considered from which a Kriging surrogate model is trained to supply the relevant wind profile parameters depending on the wave state. These newly garnered parameters enable the practitioner to define a reference wind velocity, and then adjust the velocity profile characteristics to contain the influence of the wave. This approach provides a new inlet velocity condition that can be used within computational wind engineering investigations without the need to explicitly model the wave surface, as well as flexibility in specifying the underlying wave conditions. Application of the re-calibrated velocity profile shows that wind forces are significantly greater throughout an offshore wind turbine (OWT) swept blade area when large (H= 15 m) and small (H= 1.5 m) wave heights are compared.

Satellite Observations and a Numerical Study of Recurring Atmospheric Gravity Waves Along the South China Sea Coast

AbstractSeveral groups of diurnal recurring atmospheric gravity waves (AGWs) were observed on an Environmental Satellite advanced synthetic aperture radar image and six Moderate Resolution Imaging Spectroradiometer (MODIS) images acquired along the South China Sea coast for 4 days from 3 to 6 March 2010. The unique observations are that the previously observed AGWs seldom recurred in a region for multiple days. Each cycle of these observed AGWs had undergone three stages: generation, propagation, and dissipation daily. Both SAR‐imaged sea surface roughness patterns and MODIS‐observed cloud imprints show that the AGWs were a group of transverse waves along the coast. We implemented the Weather Research and Forecasting (WRF) model to understand the physical characteristics and dynamical mechanisms of these AGWs. The WRF simulated results indicated that the AGWs were upstream waves triggered by the interaction of the southerly wind and topography and dissipated by the diurnal warming. We applied the spectral analysis to the model‐simulated vertical wind field and explored that the leading wave crest length and crest‐to‐crest wavelength are 156.25 and 7.14 km, respectively. The wave period and phase speed of the upstream AGWs within the vital observation of SAR are 1.81 hr and 1.26 m/s, respectively. The fifth‐generation European Centre for Medium‐Range Weather Forecasts reanalysis hourly data was used to explore the rarity of the recurring AGWs and proved that the stable air‐sea temperature difference was the main reason for the rarity of this event. And sufficient cloud content (&gt;50%) was necessary for the MODIS to capture the AGWs' imprints.

Search algorithm for the reflected signal of a satellite radio altimeter

Satellite altimeters are installed on spacecraft designed to solve problems of Earth exploration, and in addition to altitude, they are able to measure the degree of sea surface roughness and some other parameters. A rough determination of the delay time of the probing signal of the altimeter is the signal search procedure, the quality of which in real conditions can be degraded by the presence of an unknown rate of change in the height of the spacecraft. The need for a search procedure arises every time the altimeter loses the reflected signal, for example, after the satellite crosses the border of the land with the water surface. The presence of the rate of change in the height of the apparatus during the search leads to a slip of the signal relative to the time scale of the altimeter, reducing the efficiency of the search. The decrease in the influence of this factor is facilitated by a reduction in the duration of coherent signal accumulation. The aim of the work is to develop an algorithm for searching for the echo signal of a space-based altimeter, less sensitive to possible changes in the height of the spacecraft while reducing the duration of the search. The paper analyzes and compares the characteristics of two echo signal search algorithms. The first algorithm is the usual one-step procedure that checks the time uncertainty zone step by step using a bank of correlators of a given size. As an alternative, a two-stage search is proposed, the first stage of which selects the points of the uncertainty zone in which the presence of a signal is suspected. At the second stage, the results of the first are retested in order to identify a single point that should be recognized as containing a signal, while the coherent accumulation time is determined by the longest stage. It is shown that the two-stage algorithm is less sensitive to changes in the altitude of the spacecraft, provides a reduction in the duration of the search with the same probability of its correct outcome, and can be recommended for use in a space radio altimeter.

Sea Surface Roughness Determination from Grazing Angle GPS Ocean Observations and Scatterometry Simulations

Measurements of grazing angle GNSS-R ocean reflections combined with meteorological troposphere data are used for retrieval of ocean wave heights and surface roughness parameters. The observational results are compared to multiphase screen simulations for the same atmosphere conditions. The retrieved data from observations and simulations give equal results within the error bounds of the methods. The obtained ocean mean wave-heights are almost proportional to the square of the wind speed when applying a first-order approximation model to the high-wave-number part of the measured GNSS-R power spectra. The spectral variances from the measurements link directly to the ocean surface roughness, which is also verified by the performed multiple phase-screen wave propagation simulations. Thus, grazing angle GNSS-R techniques are an efficient method for determining the ocean state and the conditions in the boundary layer of the troposphere.

A Comparative Study of Rough Sea Surface and Evaporation Duct Models on Radio Wave Propagation

Microwave and millimeter-wave propagations near the sea surface are greatly affected by the vertical atmospheric refractivity profile and the sea surface. To accurately simulate or predict the performance of ship radar systems, the evaporation duct model and rough sea surface models are usually incorporated into the parabolic equation to model electromagnetic wave propagation. The Paulus-Jeske (PJ) model and Naval Postgraduate School (NPS) model are the most widely used to make the vertical atmospheric refractivity profile, and the roughness sea surface is modeled with the effective reflection coefficient of the rough surface or the generation of the rough sea surface. There are four widely used rough sea surface approximations called Ament, Miller-Brown, Shadowed, and Hybrid for rough sea surface modeling. In this study, numerical simulation is first used to compare the different rough sea surface modeling methods. Then, evaporation duct measurement data and C-band propagation experimental data are used to compare the evaporation duct models and the four rough sea surface models that are combined with evaporation duct models for propagation loss prediction. The simulation results show that the shadowing of radio waves by the rough sea surface and sea surface structure are important factors affecting the transmission of radio waves in evaporation ducts, and the difference in the path loss predicted by different rough sea surface approximations may exceed 10 dB at the same location. In particular, the frequency and wind speed will increase. In addition, the experimental data show that the evaporation duct can be better diagnosed using different evaporation duct models at different atmospheric stabilities. When the air-sea temperature difference is positive, the PJ evaporation duct is recommended; otherwise, the NPS model is better, and the results of the Shadowed and Hybrid rough sea surface models are in better agreement with the observations.

General features of multi-parameter anomalies of six moderate earthquakes occurred near Zhangbei-Bohai fault in China during the past decades

The great Zhangbei-Bohai fault (ZBF) is an important seismic active zone in Northeastern China, which intersects with another great fault, namely Tancheng-Lujiang fault (TLF), in the Central Bohai Sea. Most of the previous studies only investigated the earthquakes (EQs) happened in the west section of ZBF and anomalies appeared in the land area, but few researchers focused on the EQs happened in the east section of ZBF and studied the anomalies appeared above the Bohai Sea. Recently, we have investigated the disturbances on and above the Bohai Sea associated with the Zhangbei Mb5.6 EQ in 1998, whose epicenter located in the west section of ZBF, and found that there was seismicity induced gas release from submarine TLF. To study further the multi-parameter anomalies of EQs near ZBF during past decades and their relationship with ZBF and TLF, a scrutiny strategy for seismic anomaly in the sea area was proposed in this study. After comprehensive screening of EQs occurred near ZBF from 1998 to 2022 using multi-source remote sensing data, potential seismic anomalies including the anomalies of microwave brightness temperature and sea surface roughness on Bohai Sea were found correlated with 6 of the 23 investigated EQs, and there were commonly anomalies of CO and CH4 concentration in the atmosphere. All these seismic anomalies were found developing mainly along the TLF in Bohai Sea, and started usually before shocking, appeared co-seismically and in the next few days. Regional inconsistencies among the distribution of CO and CH4 anomalies could be owning to the specific underwater reservoir in the Bohai Bay Basin. Though analyzing the focal mechanism solutions of the selected EQ cases, we found that the seismic anomaly existed only when the TLF was in a stress state of tensile relaxation.

Waves in SKRIPS: WAVEWATCH III coupling implementation and a case study of Tropical Cyclone Mekunu

Abstract. In this work, we integrated the WAVEWATCH III model into the regional coupled model SKRIPS (Scripps–KAUST Regional Integrated Prediction System). The WAVEWATCH III model is implemented with flexibility, meaning the coupled system can run with or without the wave component. In our implementations, we considered the effect of Stokes drift, Langmuir turbulence, sea surface roughness, and wave-induced momentum fluxes. To demonstrate the impact of coupling we performed a case study using a series of coupled and uncoupled simulations of Tropical Cyclone Mekunu, which occurred in the Arabian Sea in May 2018. We examined the model skill in these simulations and further investigated the impact of Langmuir turbulence in the coupled system. Because of the chaotic nature of the atmosphere, we ran an ensemble of 20 members for each coupled and uncoupled experiment. We found that the characteristics of the tropical cyclone are not significantly different due to the effect of surface waves when using different parameterizations, but the coupled models better capture the minimum pressure and maximum wind speed compared with the benchmark stand-alone Weather Research and Forecasting (WRF) model. Moreover, in the region of the cold wake, when Langmuir turbulence is considered in the coupled system, the sea surface temperature is about 0.5 ∘C colder, and the mixed layer is about 20 m deeper. This indicates the ocean model is sensitive to the parameterization of Langmuir turbulence in the coupled simulations.

Non-line-of-sight multiple reflection underwater wireless optical communications channel model based on a capillary waves rough sea surface.

In a non-line-of sight reflective underwater wireless optical communications (UWOC) link, the transmitted beam relies on reflections from the sea surface to propagate to the underwater receiver. Most previous research on reflective channels has sufficiently considered single reflections from a smooth or rough surface, while ignoring the effect of multiple reflections. In fact, a rough sea surface may cause the reflected photons to hit the sea surface again, which is referred as a multiple reflection process. To make up for deficiencies in the existing literature, we first construct a capillary waves rough sea surface model, and then present a multiple reflection channel model with the help of the Monte Carlo ray tracing approach. The path loss and channel impulse response (CIR) were further evaluated based on the model for different communications scenarios. Numerical results suggest that multiple reflections increase the path loss by more than about 5dB, and reduce the CIR amplitude to less than one-third compared to a single reflection. The work done in this paper aims to provide theoretical support for UWOC system design.

Physics-statistics-based hybrid simulation scheme of coupled nonstationary hurricane wind and wave fields for long-span floating bridges

Abstract Long-span bridges with floating towers have recently drawn great attention from the engineering community. Due to their sensitivity to the aerodynamic and hydrodynamic loads during extreme storms, accurate and efficient simulation tools for hurricane winds and waves are needed for improved understanding of the complex dynamics of the fully coupled wind–wave–structure interaction system. Conventional simulation schemes usually generate winds and waves separately, and hence cannot capture the intense wind–wave interactions under hurricanes. In this study, a physics-statistics-based hybrid simulation scheme of nonstationary hurricane wind and wave fields is presented, where the winds and waves are coupled in both large and small scales. To simulate the large-scale winds and waves, a height-resolving hurricane wind model is coupled with a parametric hurricane wave model through a dependence between sea surface roughness and surface wind speed. In the small-scale simulations, the nonstationary wind fluctuations are statistically obtained by a Hilbert-wavelet-based scheme in which the target parameters (e.g. fluctuation intensity) are estimated based on the local sea state, while the nonstationary sea surface elevations are physically acquired by solving the governing equation of the nonlinear wave evolution under the action of winds. The simulation fidelity of the proposed physics-statistics-based hybrid scheme is demonstrated by generating the coupled nonstationary wind and wave fields approaching to a hypothetical long-span bridge with floating towers under a hurricane event.

Study on Atmospheric Stability and Wake Attenuation Constant of Large Offshore Wind Farm in Yellow Sea

Power generation estimation is one of the key steps in wind farm micro-sitting, and its accuracy is related to the wake decay constant in the wake model. Considering the influence of wind resource distribution in different regions, this study carried out interval optimization for the wake decay constant of offshore wind farms in the Yellow Sea region of China. Given the very small length of the sea surface roughness, atmospheric stability is a critical factor influencing the wake extent and recovery speed of offshore wind farms. WAsP 10 (Wind Atlas Analysis and Application software) simulates the wake of various scenarios, and the selection range of wake attenuation constant is investigated by combining the cases of two offshore wind farms in the Yellow Sea region. The study found that the higher the atmospheric stability, the larger the wake and the lower the wake attenuation coefficient. The Yellow Sea wind farm’s wake error system is between 0.03 and 0.04, and the forecast error can be controlled to within 3%. When simulating the wind farm at Yellow Sea offshore for improving power generation and economic evaluation, it is critical to select the correct value range of wake decay constant.

Simulations of sea surface reflection for V-band O2 differential absorption radar barometry

This study simulates V-band sea surface reflectance and normalized radar cross-section (NRCS) for sea surface air pressure barometry using a differential absorption radar operating at three spectrally even spaced close frequency bands (65.5, 67.75 and 70.0 GHz) with ± 15° cross-track scanning angle. The reflectance ratios of two neighboring frequency pairs and the ratio of the two ratios or three-channel approach are the focus of this study. Impacts of major sea surface geophysical variables such as sea surface temperature, wind, salinity, whitecap, and incidence angle on these reflection properties are analyzed. The reflection simulation is essentially based on geometric optics of rough sea surface. Simulation shows that NRCS values are sufficiently strong within the scanning angle and sea surface salinity would only introduce minimal variations in the surface reflection. The impact of sea surface reflection variations with sea surface temperature, wind, and whitecaps on sea surface barometry are mitigated when the ratios of frequency-paired radar signals are used. Furthermore, the ratios of a three-channel approach are very close to unity and calibration or compensation for the reflectance ratios may not be needed for sea level pressure retrievals. These results improve our understanding of sea surface reflection variations and would help the system design and development.

Trade Wind Boundary Layer Turbulence and Shallow Precipitating Convection: New Insights Combining SAR Images, Satellite Brightness Temperature, and Airborne In Situ Measurements

AbstractThe imprint of marine atmospheric boundary layer (MABL) dynamical structures on sea surface roughness, as seen from Sentinel‐1 synthetic aperture radar (SAR) acquisitions, is investigated. We focus on 13 February 2020, a case study of the elucidating the role of clouds‐circulation coupling in climate field campaign. For suppressed conditions, convective rolls imprint on sea surface roughness is confirmed through the intercomparison with MABL turbulent organization deduced from airborne measurements. A discretization of the SAR wide swath into 25 × 25 km2 tiles then allows us to capture the spatial variability of the turbulence organization varying from rolls to cells. Second, we objectively detect cold pools within the SAR image and combine them with geostationary brightness temperature. The geometrical or physically‐based metrics of cold pools are correlated to cloud properties. This provides a promising methodology to analyze the dynamics of convective systems as seen from below and above.

Modeling seismic waves in ocean with the presence of irregular seabed and rough sea surface

Abstract For the simulation of seismic wavefields in the ocean, it is very important to consider the influences of the irregular seabed and the rough sea surface. To numerically model seismic waves in the ocean, the fluid seawater and the solid seabed must be treated separately, and the air–fluid and fluid–solid boundary conditions must be considered simultaneously. A fluid–solid configuration is created with the influences of a rough sea surface and an irregular seabed to carry out wavefield simulation. Based on the boundary conformal grids, the 2D acoustic wave equations (in the fluid media), the 2D elastic wave equations (in the solid media) and two boundary conditions (at the interface between air and fluid and the interface between fluid and solid) are converted from the Cartesian coordinate system into a curvilinear coordinate system. In curvilinear coordinates, the seismic wave equations and boundary conditions are discretized with finite-difference operators. At the left, right and bottom boundaries of the model, the convolutional perfectly matched layer boundary condition is used to absorb artificial reflections. The numerical simulation results show that the snapshots and shot gathers of the rough sea surface model are more complex and contain stronger reflections than those of the flat model. The rough sea surface and the pattern of the irregular seabed have a great influence on the propagation of seismic waves in the ocean.