Nonlinear Sea Surface Research Articles

Deep learning with autoencoders and LSTM for ENSO forecasting

El Niño Southern Oscillation (ENSO) is the prominent recurrent climatic pattern in the tropical Pacific Ocean with global impacts on regional climates. This study utilizes deep learning to predict the Niño 3.4 index by encoding non-linear sea surface temperature patterns in the tropical Pacific using an autoencoder neural network. The resulting encoded patterns identify crucial centers of action in the Pacific that serve as predictors of the ENSO mode. These patterns are utilized as predictors for forecasting the Niño 3.4 index with a lead time of at least 6 months using the Long Short-Term Memory (LSTM) deep learning model. The analysis uncovers multiple non-linear dipole patterns in the tropical Pacific, with anomalies that are both regionalized and latitudinally oriented that should support a single inter-tropical convergence zone for modeling efforts. Leveraging these encoded patterns as predictors, the LSTM - trained on monthly data from 1950 to 2007 and tested from 2008 to 2022 - shows fidelity in predicting the Niño 3.4 index. The encoded patterns captured the annual cycle of ENSO with a 0.94 correlation between the actual and predicted Niño 3.4 index for lag 12 and 0.91 for lags 6 and 18. Additionally, the 6-month lag predictions excel in detecting extreme ENSO events, achieving an 85% hit rate, outperforming the 70% hit rate at lag 12 and 55% hit rate at lag 18. The prediction accuracy peaks from November to March, with correlations ranging from 0.94 to 0.96. The average correlations in the boreal spring were as large as 0.84, indicating the method has the capability to decrease the spring predictability barrier.

Investigating electromagnetic scattering characteristics based on a nonlinear sea surface

Investigating electromagnetic scattering characteristics based on a nonlinear sea surface

Thermal Discharge Temperature Retrieval and Monitoring of NPPs Based on SDGSAT-1 Images

High-accuracy sea surface temperature (SST) retrieval near nuclear power plants (NPPs) is one of the most significant indicators for evaluating marine ecological environment quality, monitoring the real-time situation of thermal discharge, and supporting planning decisions. However, complex computations, the inaccessible real-time vertical profile of the atmosphere, and the uncertainty of atmospheric profile data increase the error of SST retrieval. Additionally, influenced by their low spatial resolution, the widely used AVHRR/MODIS remote sensing images (RSIs) are unable to retrieve the detailed distribution of SST in small scale regions such as coastal NPPs. In this paper, we propose a simplified split-window-based temperature retrieval method (the SW method) suitable for SDGSAT-1 30 m thermal infrared spectrometer (TIS) RSIs. Specially, this method only needs atmospheric transmittance and surface emissivity by counteracting the average atmospheric temperature to monitor the thermal discharge of offshore NPPs. First, the geometric and radiometric calibrated thermal infrared and multi-spectral cloudless data of the target regions are selected to obtain the corresponding apparent radiance of the RSIs. Second, in accordance with the red and near-infrared (NIR) bands of multi-spectral RSIs, the surface emissivity is calculated to distinguish water from land. Next, we determine the atmospheric profile parameters from the weather conditions of the target region at the imaging time. Finally, according to the theory of surface-atmosphere radiative transfer, the SST of target regions is retrieved with the proposed SW method, and the results are compared with those of the conventional radiative transfer equation (RTE), mono-window (MW), and the nonlinear sea surface temperature (NLSST) algorithms. The experimental results indicate that the SST retrieved from the split-window algorithms (i.e., SW and NLSST) are generally higher than those of the single-channel algorithms (i.e., RTE and MW). The SST difference between the SW algorithm and the NLSST algorithm is within 0.5 °C. In addition, SDGSAT-1 can monitor the seasonal detailed variation of the thermal discharge near coastal NPPs. This article is the first to attempt to quantitative small-scale SST retrieval based on thermal infrared and multi-spectral images obtained from the SDGSAT-1 TIS and a multispectral imager (MII), and therefore, provide an effective reference for marine environment monitoring.

Relative Merits of Optimal Estimation and Non-Linear Retrievals of Sea-Surface Temperature from MODIS

We compared the results of an Optimal Estimation (OE) based approach for the retrieval of the skin sea surface temperature (SSTskin) with those of the traditional non-linear sea surface temperature (NLSST) algorithm. The retrievals were from radiance measurements in two infrared channels of the Moderate Resolution Imaging Spectroradiometer (MODIS) on the NASA satellite Aqua. The OE used a reduced state vector of SST and total column water vapor (TCWV). The SST and atmospheric profiles of temperature and humidity from ERA5 provided prior knowledge, and we made reasonable assumptions about the variance of these fields. An atmospheric radiative transfer model was used as the forward model to simulate the MODIS measurements. The performances of the retrieval approaches were assessed by comparison with in situ measurements. We found that the OESST reduces the satellite–in situ bias, but mostly for retrievals with an already small bias between in situ and the prior SST. The OE approach generally fails to improve the SST retrieval when that difference is large. In such cases, the NLSST often provides a better estimate of the SST than the OE. The OESST also underperforms NLSST in areas that include large horizontal SST gradients.

Simulation and Calculation of Sea State Bias Based on the Electromagnetic Backscattering from the Simulated Nonlinear Rough Sea Surface

Abstract Due to the improvement of satellite orbit determination technology, sea state bias(SSB) has become the main source of altimeter height measurement error. In this paper, the physical mechanism and causes of SSB are simulated and analyzed by electromagnetic scattering, and the SSB correction method and model are given. Firstly, this paper simulates and studies four kinds of nonlinear rough sea surface and their electromagnetic scattering characteristics for the first time, calculates SSB from the physical mechanism of SSB, and analyzes the physical mechanism and process causes of SSB from the electromagnetic scattering characteristics. Secondly, a fitting model to correct SSB is proposed in terms of the electromagnetic simulation. Finally, the paper compares the “true value of SSB” of HY-2B satellite radar altimeter in China’s offshore waters with SSB calculated by the simulating model. The comparison results show that they are consistent with a weak bias, indicating that it is an effective method to correct SSB by simulating nonlinear rough sea surface and its electromagnetic scattering. It is expected to improve the accuracy of SSB correction by the new way of simulating the physical mechanism and causes of SSB.

Analysis of microwave backscattering from nonlinear sea surface with currents: doppler spectrum and SAR images

AbstractElectromagnetic scattering from the sea surface is of great significance in radar detection, target recognition, ocean remote sensing, etc. By introducing the action spectrum, the modified spatio-temporal variation wave spectrum is used to establish a nonlinear sea surface with currents in this paper. Traditional capillary wave modification facet scattering model (CWMFSM) can only calculate the backscattering from the wind-driven sea surface. By using the new spatio-temporal variation wave spectrum to modify the scattering amplitude of every facet, the new CWMFSM can be used to calculate the nonlinear sea surface scattering with surface currents. Therefore, the model simultaneously considers the modulation of sea surface wind and currents to the radar back echo. The dependence of backscattering coefficient from nonlinear sea surface on the incident angle and the polarization are discussed. The results verify that the nonlinear model is more consistent with the measurement data. This paper also investigates the Doppler spectrum characteristics of the sea with currents. It is found that the effect of wave–current interaction on Doppler spectra is weaker than that of wave–wave interaction. The SAR images of nonlinear sea surfaces are also simulated and different bands, polarizations, and baseline length effects on sea current detection performance of along-track interference SAR are analyzed.

Doppler spectra of electromagnetic wave scattered from an object flying above time-varying nonlinear sea surfaces

ABSTRACTDoppler spectra of electromagnetic wave scattered from an object flying above time-varying nonlinear sea surfaces are investigated by utilizing a hybrid algorithm combining method of moments (MoM) and Kirchhoff approximation (KA). The “choppy wave” model is employed for describing nonlinear hydrodynamic interactions between ocean waves. Doppler spectra of scattered wave are simulated and analyzed for different incidence angles, target velocities, target heights, sea states as well as sea surface models, and an obvious broadening of Doppler spectrum is observed due to the coupling scattering between the flying target and rough sea surfaces. In comparison with the normalized radar cross section, Doppler spectra of scattered wave have the advantage of extracting information regarding target flying above dynamic sea surfaces. This study is of great value for the analysis of coupling scattering between flying target and rough sea surface as well as for the detection low-flying target in sea clutter environment.

Numerical computational modeling of random rough sea surface based on JONSWAP spectrum and Donelan directional function

SummaryIn this paper, 51 sets of directional spectrum measured data collected from the Bohai offshore site were applied to study the comparative characteristics of Wen's direction spectrum and Donelan direction function. Firstly, the optimal frequency value of direction spectrum is analyzed from two aspects: the direction cumulative distribution and the direction distribution function fitting quality. Secondly, combined with the experimental results, the distribution characteristics of different direction functions are compared from the maximum and standard deviation of the distribution function. The experiments prove that Donelan function contains all the states of the wind and wave growth stage, which can fully measure the influence of the wave age on wind frequency spectrum. Then, this paper analyzes the classical Monte Carlo method and the Las Vegas method from the perspective of the computational complexity and direction distribution difference of simulation step. Based on the classical Monte Carlo method, this paper proposes a two‐dimensional random rough sea surface numerical calculation model suitable for different water depths and different wind wave growth stages. Finally, by analyzing the characteristics of the nonlinear sea surface, this paper studies the effects of wind speed, wind direction, and fetch on sea surface wave height and growth state.

Climate model configurations of the ECMWF Integrated Forecasting System (ECMWF-IFS cycle 43r1) for HighResMIP

Abstract. This paper presents atmosphere-only and coupled climate model configurations of the European Centre for Medium-Range Weather Forecasts Integrated Forecasting System (ECMWF-IFS) for different combinations of ocean and atmosphere resolution. These configurations are used to perform multi-decadal ensemble experiments following the protocols of the High Resolution Model Intercomparison Project (HighResMIP) and phase 6 of the Coupled Model Intercomparison Project (CMIP6). These experiments are used to evaluate the sensitivity of major biases in the atmosphere, ocean, and cryosphere to changes in atmosphere and ocean resolution. All configurations successfully reproduce the observed long-term trends in global mean surface temperature. Furthermore, following an adjustment to account for drift in the subsurface ocean, coupled configurations of ECMWF-IFS realistically reproduce observation-based estimates of ocean heat content change since 1950. Climatological surface biases in ECMWF-IFS are relatively insensitive to an increase in atmospheric resolution from ∼ 50 to ∼ 25 km. However, increasing the horizontal resolution of the atmosphere while maintaining the same vertical resolution enhances the magnitude of a cold bias in the lower stratosphere. In coupled configurations, there is a strong sensitivity to an increase in ocean model resolution from 1 to 0.25°. However, this sensitivity to ocean resolution takes many years to fully manifest and is less apparent in the first year of integration. This result has implications for the ECMWF coupled model development strategy that typically relies on the analysis of biases in short ( < 1 year) ensemble (re)forecast data sets. The impacts of increased ocean resolution are particularly evident in the North Atlantic and Arctic, where they are associated with an improved Atlantic meridional overturning circulation, increased meridional ocean heat transport, and more realistic sea-ice cover. In the tropical Pacific, increased ocean resolution is associated with improvements to the magnitude and asymmetry of El Niño–Southern Oscillation (ENSO) variability and better representation of non-linear sea surface temperature (SST)–radiation feedbacks during warm events. However, increased ocean model resolution also increases the magnitude of a warm bias in the Southern Ocean. Finally, there is tentative evidence that both ocean coupling and increased atmospheric resolution can improve teleconnections between tropical Pacific rainfall and geopotential height anomalies in the North Atlantic.

Influence of Breaking Waves and Wake Bubbles on Surface-Ship Wake Scattering at Low Grazing Angles**Supported by the National Natural Science Foundation of China under Grant No 61571355.

A surface-ship wake model is proposed for calculating the scattering of ship wake from a nonlinear sea surface at a high sea state. Ship waves are simulated based on the Kelvin wave model by the point-source method. A Creamer II sea surface based on the Elfouhaily sea spectrum is generated, and breaking waves and foam layer effects are taken into account for the background sea scattering at slight, moderate and high wind speeds. Turbulent bubbles scattering from the ship, which is different from wind-driven bubble breaking, is taken into account with a different concentration distribution using a polynomial fitting function combined with measured data. The surface-ship wake scattering is presented for different wind speeds. Numerical simulations show that ship wake scattering results will be higher when wake bubbles are taken into account. The ship beam is a key parameter that influences the width of the turbulent wake, and results in different scattering characteristics on the scattering image. The wind-induced surface in the presence of breaking waves and whitecaps results in scattering enhancement. This will cause the ship wake signal to be submerged in the back-ground of sea noise, leading to false alarms.

Scattering and Doppler analysis for electrically large nonlinear sea surfaces: a field-based semi-deterministic model

ABSTRACTThis paper presents a semi-deterministic facet model based on the combination of the two-scale theory and the small slope approximation (SSA). Based on the model, normalized radar cross section (NRCS) and the Doppler spectra from electrically large nonlinear ocean scenes are analysed at moderate and large incidence angles. The analytic scattering amplitude of small-scale capillary waves based on the local configuration angles is conducted. Different from the conventional two-scale model (TSM), the model is a field-based rather than RCS-based model, which considerably widens its potential applications. In order to take into account the influence of nonlinear hydrodynamics on echo characteristics, the choppy wave model (CWM) is adopted to simulate nonlinear surfaces. Several examples of bistatic NRCS and Doppler spectra are given with comparison and analysis, which validate the rationality of the model at moderate and large incidence angles. In addition, the running time and memory consumption comparisons can indicate the model is more efficient than the SSA.

Polarimetric Doppler spectrum of backscattered echoes from nonlinear sea surface damped by natural slicks

Based on the Lombardini et al. model that can predict the hydrodynamic damping of rough sea surfaces in the presence of monomolecular slicks and the “choppy wave” model (CWM) that can describe the nonlinear interactions between ocean waves, the modeling of time-varying nonlinear sea surfaces damped by natural or organic sea slicks is presented in this paper. The polarimetric scattering model of second-order small-slope approximation (SSA-II) with tapered wave incidence is utilized for evaluating co- and cross-polarized backscattered echoes from clean and contaminated CWM nonlinear sea surfaces. The influence of natural sea slicks on Doppler shift and spectral bandwidth of radar sea echoes is investigated in detail by comparing the polarimetric Doppler spectra of contaminated sea surfaces with those of clean sea surfaces. A narrowing of Doppler spectra in the presence of oil slicks is observed for both co- and cross-polarization, which is qualitatively consistent with wave-tank measurements. Simulation results also show that the Doppler shifts in slicks can increase or decrease, depending on incidence angles and polarizations.

Rogue events in spatiotemporal numerical simulations of unidirectional waves in basins of different depth

The evolution of unidirectional nonlinear sea surface waves is calculated numerically by means of solutions of the Euler equations. The wave dynamics corresponds to quasi-equilibrium states characterized by JONSWAP spectra. The spatio-temporal data are collected and processed providing information about the wave height probability and typical appearance of abnormally high waves (rogue waves). The waves are considered at different water depths ranging from deep to relatively shallow cases ($k_p h > 0.8$, where $k_p$ is the peak wavenumber, and $h$ is the local depth). The asymmetry between front and rear rogue wave slopes is identified; it becomes apparent for sufficiently high waves in rough sea states at all considered depths. The lifetimes of rogue events may reach up to 30-60 wave periods depending on the water depth. The maximum observed wave has height of about 3 significant wave heights. A few randomly chosen in-situ time series from the Baltic Sea are in agreement with the general picture of the numerical simulations.

Doppler spectrum of polarimetric scattering field from two-dimensional time-varying nonlinear sea surfaces

Polarimetric scattering model of second-order small-slope approxi-mation combined with “choppy wave" model (CWM) for describing nonlinear hydrodynamic interactions between ocean waves is utilized in this paper to investigate the influence of sea surface nonlinearities on backscattering coefficient as well as Doppler spectrum signatures including Doppler shift and spectral bandwidth. Simulation results show that at moderate to large incidence angles the Doppler shift and spectral bandwidth of the CWM nonlinear sea surfaces are significantly larger than those of linear sea surfaces, in particular at low grazing angles. In addition, Doppler signatures show distinct polarization dependence, and most importantly the cross-polarized Doppler signatures significantly differ from the co-polarized ones. It is also indicated that co-polarized Doppler shift increases obviously with wind speed increasing, whereas the cross-polarized Doppler shift looks less sensitive to wind speed variations. The difference of Doppler signatures between co- and cross-polarization is potentially valuable for ocean remote sensing applications, especially for observing very high winds.

Electromagnetic scattering and Doppler spectrum simulation of time-varying oil-covered nonlinear sea surface

Based on the model of Lombardini et al. [J. Atmos. Ocean. Technol.6(6), 882–890 (1989)], which can predict the hydrodynamic damping of rough sea surfaces in the presence of oil films, the influence of sea slicks on the sea surface roughness spectrum and sea surface geometrical structure is examined briefly in the present study. On this basis, the influence of sea slicks on the angular distribution of the bistatic scattering coefficient of sea surfaces and the Doppler spectrum signature of backscattered radar sea-echo is investigated in detail based on a frequency-domain numerical method of the parallel fast multiple method. Simulation results show that Doppler spectrum signatures including Doppler shift and spectral bandwidth of radar sea-echo are significantly affected by sea slicks, which are qualitatively consistent with wave-tank or open sea measurements. Moreover, simulation results indicate that the Doppler spectrum signature is a promising technique for remote sensing of oil films floating on sea surfaces.

An analytical model for the description of the full‐polarimetric sea surface Doppler signature

AbstractThis paper describes an analytical model of the full‐polarimetric sea surface scattering and Doppler signature. The model combines the small‐slope‐approximation theory (at the second order) with a weak nonlinear sea surface representation. Such a model is used to examine the variation of the Doppler central frequency/bandwidth and of the normalized radar cross section as function of wind speed and direction. The results suggest that the model can be a valuable tool for the accurate observation of sea surface currents.

Study on Doppler spectra of two-dimensional skewed sea surfaces

This paper deals with the effects of horizontal skewness on Doppler spectra. A.K. Fung et al. pointed out that the crests of the sea waves are tilted towards the wind direction, which is referred to as horizontal skewness. Although the nonlinear sea surface is more realistic than the linear one, it cannot embody the statistical front-back asymmetry of real sea waves due to the influence of the wind. Thus, the impact of horizontal skewness must be considered. The first-order modified Lagrange model for asymmetric ocean waves is combined with Monte Carlo method to produce the two-dimensional (2-D) time-varying skewed sea surfaces which are nonlinear and skewed simultaneously. Moreover, the second-order small-slope approximation method is used to calculate the scattering field and study the Doppler spectral characteristics from skewed sea surfaces. Horizontal skewness makes Doppler spectra broader in upwind case, but narrower in downwind case. In addition, the impact of horizontal skewness on Doppler spectra is dependent on wind direction and incident elevation angle.

Composite scattering of an electrically large ship on a two-dimensional time-evolved sea surface

A time-varying composite scattering of a moving ship on a two-dimensional non-linear sea surface is modelled with the help of the Doppler spectrum in high-frequency bands. A non-linear sea surface is simulated to approximate a real sea environment with high-order terms of the solution to hydrodynamic equations. Numerical simulations are based on the principle of a quasi-stationary algorithm (QSA), which solves time domain problems with frequency domain methods. A four-path model is modified to calculate the composite scattering field, which is utilized for the analysis of the Doppler spectrum. With depth-buffer technology, self-shadowing of the complex physical model is eliminated. Correspondence of the numerical results with experimental data proves that the inclusion of the non-linear interaction term and wind-speed influence is reasonable. The simulated Doppler spectrum of the composite scattering shows a functional dependence of time-evolved scattering components on incidence direction and sea state.

SCATTERING ANALYSIS FOR SHIP KELVIN WAKES ON TWO-DIMENSIONAL LINEAR AND NONLINEAR SEA SURFACES

The ship Kelvin-wake models on two-dimensional (2-D) linear and nonlinear sea surfaces are combined with the second-order small-slope approximation method (SSA-II) to comparatively study the corresponding electromagnetic (EM) scattering characteristics. The nonlinear sea-surface models include the Choppy Wave Model (CWM) and the second-order Creamer model (Creamer (2)). Considering the limitations of using the ideal plane EM wave incident upon a rough sea surface of the limited size, the modifled tapered wave is utilized as the incident wave to derive the scattering waves. Due to the fact that the nonlinear efiects of Creamer (2) surfaces is obviously stronger than those of CWM surfaces, the bistatic normalized radar cross section (NRCS) calculated from Creamer (2) surfaces is signiflcantly greater than that of its linear and CWM surfaces for scattering angles departing from the specular direction, and the backscattering coe-cients from Creamer (2) surfaces are also the greatest except within quasi-specular (near vertical incidence) region. Moreover, for the linear and nonlinear sea surfaces, the in∞uences of difierent wind speeds and directions on scattering characteristics are also calculated and analyzed in detail. However, taking the ship Kelvin wakes into account, the corresponding scattering features are obviously distinct from those of the single linear and nonlinear sea surfaces. This helps to provide a basis to extract the related ship information through the scattering characteristics of ship Kelvin wakes. Also it shows that the small-slope approximation method is a very efiective analysis method to deal with the EM scattering from the rough sea surface.

Scattering and Doppler Spectral Analysis for Two-Dimensional Linear and Nonlinear Sea Surfaces

Two-dimensional linear and second-order Creamer [Creamer (2)] nonlinear sea-surface models are combined with the second-order small-slope approximation method to comparatively study the electromagnetic scattering and the Doppler spectral characteristics from sea surfaces. Due to nonlinear hydrodynamics, the bistatic normalized radar cross section (NRCS) calculated from Creamer (2) surfaces is slightly larger than its linear surface counterpart for scattering angles departing from the specular direction, and the Creamer (2) surface backscattering coefficient increases as well for wind direction angles around upwind and downwind, whereas, for the crosswind direction, it is interesting to note that the observations are contrary. However, as was pointed out by Toporkov in a 1-D surface case, the effect of the nonlinear surface model on the average NRCS is minute. In particular, the Doppler spectra of the backscattered echoes are compared for the linear and Creamer (2) surfaces at various incident angles. It is seen, as expected, that the Doppler shifts and spectral widths of 2-D Creamer (2) surfaces exhibit different features compared with those of the linear surfaces, agreeing with the 1-D cases. However, for larger incident angles, the Doppler spectral broadening for Creamer (2) surfaces is not as severe as was reported in previous 1-D studies that used full Creamer model. The reason for this discrepancy appears to be the reduced nature of the Creamer (2) approximation. Moreover, studies of the Doppler characteristics for different wind directions demonstrate that nonlinear effects become weaker as the wind direction varies from upwind to crosswind.