A method for predicting Arctic ocean waves based on automatic sea ice concentration fusion

Abstract

The application provides an Arctic sea wave prediction method based on automatic fusion of sea ice density, and belongs to the technical field of weather prediction. The wind field data automatic acquisition system is established to ensure the continuity of the wind field driving data. The sea ice wave interaction optimization model is applied to dynamically adjust the IC4M2 sea ice wave parameterization scheme. The open boundary line is set in the high latitude sea area of the North Atlantic, and the radiation boundary condition algorithm is combined with the sponge layer absorption technology to process the boundary wave propagation. The WAVEWATCH III sea wave numerical model is started, the fourth-order precision finite difference discrete format is combined with the adaptive artificial viscosity control algorithm to calculate the Arctic sea wave field, and the sea wave prediction product business processing system is established, so that the technical problem of low accuracy of the Arctic sea wave prediction caused by the insufficient parameterization precision of the sea ice wave interaction is solved.

Description

Technical Field

[0001] This invention belongs to the field of meteorological forecasting technology, and specifically relates to an Arctic wave forecasting method based on automatic fusion of sea ice concentration. Background Technology

[0002] Arctic wave forecasting, as a crucial component of polar marine environmental prediction, plays a vital role in polar shipping route development, marine engineering construction, and climate change research. Traditional numerical wave models, such as WAVEWATCH III, simulate wave generation, propagation, and dissipation processes by solving wave action balance equations and are widely used in global and regional operational wave forecasting. However, in the complex sea ice environment of the Arctic Ocean, the sea ice-wave interaction parameterization schemes of traditional numerical wave models have significant shortcomings. Existing parameterization schemes often use fixed parameter combinations to describe wave energy attenuation processes under different sea ice concentration conditions, lacking the ability to dynamically adapt to the spatial heterogeneity and time-varying characteristics of sea ice distribution. This leads to inaccurate descriptions of wave energy propagation processes in sea ice margins and sea ice-covered areas. Due to limitations in the spatiotemporal resolution of sea ice concentration data and insufficient understanding of sea ice-wave interaction mechanisms, traditional parameterization schemes struggle to accurately capture the complex attenuation effects of sea ice on wave energy, especially in marginal areas where sea ice concentration frequently changes. Fixed parameterization schemes cannot effectively reflect the impact of dynamic changes in sea ice distribution on wave propagation characteristics, resulting in significant discrepancies between Arctic wave forecasts and actual observations. In other words, existing technologies suffer from insufficient precision in the parameterization of sea ice-wave interactions, leading to low accuracy in Arctic wave forecasts. Summary of the Invention

[0003] In view of this, the present invention provides an Arctic wave forecasting method based on automatic fusion of sea ice concentration, which can solve the technical problem of low accuracy of Arctic wave forecasting due to insufficient parameterization accuracy of sea ice wave interaction in the prior art.

[0004] This invention is implemented as follows: It provides an Arctic wave forecasting method based on automatic sea ice concentration fusion. An Arctic orthogonal curve grid system is constructed using the ETOPO2 global water depth and topography database. A multi-source automatic sea ice concentration fusion system is established using University of Bremen AMSR2 orbital brightness temperature data to acquire sea ice concentration data and convert it into a NetCDF format sea ice concentration input file. An ECMWF (European Centre for Medium-Range Weather Forecasts) wind field data acquisition system is established to download wind field forecast data. A sea ice-wave interaction optimization model is applied to dynamically adjust the parameters of the IC4M2 sea ice wave parameterization scheme. The wave energy index attenuation coefficient is calculated based on the sea ice concentration distribution characteristics and wave spectrum bandwidth characteristics in the NetCDF format sea ice concentration input file. An open boundary line is set in the high-latitude waters of the North Atlantic, and a radiation boundary condition algorithm combined with sponge layer absorption technology is used to process boundary wave propagation. The WAVEWATCH function is then initiated. The III wave numerical model is used to calculate the Arctic wave field. A fourth-order precision finite difference discretization scheme is combined with an adaptive artificial viscosity control algorithm to establish an operational post-processing system for wave forecast products, generating spatial distribution data of effective wave height, spectral peak period, and main wave direction.

[0005] Specifically, the steps for constructing the Arctic orthogonal curve grid system involve selecting four vertex coordinates under polar coordinate projection: 54°N, -45°E; 54°N, 45°E; 54°N, 135°E; and 54°N, -135°E, forming a square calculation area around the North Pole. The area north of 88°N is designated as the land boundary. A 20km resolution grid cell is generated through coordinate transformation from geographic coordinates to projected coordinates, and the grid longitude data file, grid latitude data file, and water depth data file are output.

[0006] Specifically, the multi-source sea ice concentration automatic fusion system acquires daily Arctic sea ice concentration raw data with a spatial resolution of 6.25 km, performs coordinate transformation, time standardization, and bilinear spatial interpolation on the raw sea ice concentration data, and converts the processed sea ice concentration data into a NetCDF format sea ice concentration input file for WAVEWATCH III wave numerical pattern recognition.

[0007] Specifically, the ECMWF European Centre for Medium-Range Weather Forecasts wind field data automatic acquisition system downloads forecast data containing 10m height wind speed and wind direction components. When the wind field data quality assessment coefficient Q∈[0, 0.85), the backup NCEP global forecast system data source acquisition mechanism is activated to ensure the continuity of wind field driven data and output standardized wind field input files for use by ocean wave numerical models.

[0008] Specifically, the sea ice wave interaction optimization model uses a strong attenuation parameter combination when the sea ice concentration C∈[0.7, 1.0], a medium attenuation parameter combination when the sea ice concentration C∈[0.3, 0.7), and a weak attenuation parameter combination when the sea ice concentration C∈[0, 0.3].

[0009] Specifically, the setting of open boundary lines refers to the first open boundary line from Newfoundland to Greenland and the second open boundary line from Iceland to Norway. Boundary wave spectral density data are provided through the ww3_ounp boundary condition output command of the WAVEWATCH III global wave model.

[0010] Specifically, the sponge layer absorption technology involves setting up a sponge layer absorption area within 20km of the first and second open boundary lines, and adjusting the distribution of the artificial viscosity coefficient within the sponge layer absorption area using an exponential decay function.

[0011] Specifically, the adaptive artificial viscosity control algorithm adjusts the time integration step size to 0.5 times the original step size when the spatial gradient change rate of wave height in the computational domain is ≥ 0.05 m / km, and adjusts the time integration step size to 1.5 times the original step size when ∇H < 0.01 m / km, thus ensuring the stability of numerical calculation.

[0012] Specifically, the operational post-processing system for the sea wave forecast product triggers an automatic mode parameter optimization program to recalibrate the attenuation coefficient in the IC4M2 sea ice wave parameterization scheme when the root mean square error (RMSE) between the forecast significant wave height and the Sentinel-3A satellite altimeter observation data is ≥0.8m.

[0013] The optimized model for sea ice wave interaction is structured as a multilayer perceptron neural network, comprising an input layer, three hidden layers, and an output layer. The number of neurons in the three hidden layers are 128, 64, and 32, respectively, and it employs the ReLU activation function and Dropout regularization mechanism.

[0014] The sea ice wave interaction optimization model employs a multi-head attention mechanism, where the number of heads N is based on the variance of sea ice concentration. Wave spectrum bandwidth and grid complexity coefficient Using the formula N=max(4, min(16, int() Confirmed. Alternatively, an empirical count of 8 heads can be used.

[0015] The training dataset for the optimized sea ice wave interaction model includes collecting AMSR2 sea ice concentration observation data, NDBC buoy wave parameter data, and WAVEWATCH III numerical simulation results from the Arctic Ocean between 2015 and 2022, and constructing a complete training dataset containing 100,000 training samples and 20,000 validation samples.

[0016] The formula for calculating the fluctuation energy exponential decay coefficient is expressed as follows: .

[0017] Furthermore, when the Pearson correlation coefficient R between the wave spectrum shape in the sea ice edge region and the standard reference JONSWAP wave spectrum is ≥0.9, the preset standard wave propagation calculation mode is directly used for subsequent wave field analysis.

[0018] Furthermore, when the coefficient of variation (CV) of the spatial distribution of sea ice concentration is in the range of [0, 0.15), a unified parameter centralized processing mode is adopted to improve computational efficiency. When the coefficient of variation (CV) is greater than or equal to 0.4, a regional adaptive distributed processing mode is adopted.

[0019] The present invention also provides an Arctic wave forecasting system based on automatic sea ice concentration fusion, which is implemented by a computer. The computer is equipped with a readable storage medium, which stores program instructions. When the program instructions are run in the computer, they are used to execute the Arctic wave forecasting method based on automatic sea ice concentration fusion as described in any one of claims 1 to 15.

[0020] This invention acquires high-precision sea ice distribution information by constructing a multi-source sea ice concentration automatic fusion system. Combined with a sea ice-wave interaction optimization model, it dynamically adjusts the IC4M2 sea ice wave parameterization scheme, achieving a precise description of the sea ice-wave interaction process and overcoming the technical deficiency of traditional fixed parameterization schemes that cannot adapt to the spatiotemporal changes in sea ice distribution. The sea ice-wave interaction optimization model constructed using a deep neural network can learn the nonlinear relationship between sea ice distribution patterns and wave propagation characteristics. Through a multilayer perceptron architecture and a multi-head attention mechanism, it intelligently adjusts the wave energy attenuation coefficient under different sea ice concentration conditions, significantly improving the numerical simulation accuracy of wave energy propagation processes in sea ice-covered areas and effectively enhancing the accuracy of Arctic wave forecasting. In summary, this invention solves the technical problem mentioned in the background art where insufficient precision in sea ice-wave interaction parameterization leads to low accuracy in Arctic wave forecasting. Attached Figure Description

[0021] Figure 1 This is a flowchart of the method of the present invention.

[0022] Figure 2 This is a schematic diagram of the projected grid.

[0023] Figure 3 To compare the simulated effective wave height (Hs), peak period (Tp), and peak direction (Dp) with the measured data, and to illustrate the corresponding correlation coefficient (cc), root mean square error (rmse), and average error (bias), the following subplots are included: Subplot a shows the effective wave height Hs under the IC3 scheme, with the horizontal axis representing buoy observation results and the vertical axis representing numerical simulation results, in meters; Subplot b shows the peak period Tp under the IC3 scheme, with the horizontal axis representing buoy observation results and the vertical axis representing numerical simulation results, in seconds; Subplot c shows the peak direction Dp under the IC3 scheme, with the horizontal axis representing buoy observation results and the vertical axis representing numerical simulation results, in degrees; Subplot d shows the effective wave height Hs under the IC4M2 scheme, with the horizontal axis representing buoy observation results and the vertical axis representing numerical simulation results, in degrees; Subplot e shows the spectral peak period Tp under the IC4M2 scheme, with the horizontal axis representing buoy observations and the vertical axis representing numerical simulation results, in seconds; subplot f shows the spectral peak wave direction Dp under the IC4M2 scheme, with the horizontal axis representing buoy observations and the vertical axis representing numerical simulation results; subplot g shows the significant wave height Hs under the IC5 scheme, with the horizontal axis representing buoy observations and the vertical axis representing numerical simulation results, in meters; subplot h shows the spectral peak period Tp under the IC5 scheme, with the horizontal axis representing buoy observations and the vertical axis representing numerical simulation results, in seconds; subplot i shows the spectral peak wave direction Dp under the IC5 scheme, with the horizontal axis representing buoy observations and the vertical axis representing numerical simulation results, in degrees.

[0024] Figure 4 This is a diagram showing the forecast results for effective wave height and direction.

[0025] Figure 5 This is a graph showing the results of the periodic forecast.

[0026] Figure 6 The plot shows the root mean square error (RMSE) of the January model observations.

[0027] Figure 7 The February model-observation root mean square error (RMSE) plot.

[0028] Figure 8 The March model-observation root mean square error (RMSE) plot.

[0029] Figure 9 The RMSE plot is for the April model-observation root mean square error.

[0030] Figure 10 The RMSE plot is for the May model-observation root mean square error.

[0031] Figure 11 The June model-observation root mean square error (RMSE) plot.

[0032] Figure 12 The July model-observation root mean square error (RMSE) plot.

[0033] Figure 13 The RMSE plot is for the August model-observation root mean square error.

[0034] Figure 14 The September model-observation root mean square error (RMSE) plot.

[0035] Figure 15 The RMSE plot is for the October model-observation root mean square error.

[0036] Figure 16 The plot shows the root mean square error (RMSE) of the November model-observations.

[0037] Figure 17 The plot shows the root mean square error (RMSE) of the December model observations. Detailed Implementation

[0038] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings.

[0039] like Figure 1 The diagram shown is a flowchart of an Arctic wave forecasting method based on automatic sea ice concentration fusion provided by this invention. The method includes the following steps:

[0040] S01. Based on the ETOPO2 global water depth topography database, construct an orthogonal curve grid system for the Arctic. Under polar coordinate projection, select four vertex coordinates as 54°N, -45°E, 54°N, 45°E, 54°N, 135°E, and 54°N, -135°E to form a square calculation area around the North Pole. Set the area north of 88°N as the land boundary. A 20km resolution grid cell is generated through coordinate transformation from geographic coordinates to projected coordinates. Output the grid longitude data file lon.dat, the grid latitude data file lat.dat, and the water depth data file dep.dat.

[0041] S02. An automatic fusion system for multi-source sea ice concentration was established using University of Bremen AMSR2 orbital brightness temperature data to acquire daily Arctic sea ice concentration raw data with a spatial resolution of 6.25 km. The raw sea ice concentration data was subjected to coordinate transformation, time standardization, and bilinear spatial interpolation. The processed sea ice concentration data was then converted into a NetCDF format sea ice concentration input file for WAVEWATCH III wave numerical pattern recognition.

[0042] S03. Establish an automatic wind field data acquisition system for the European Centre for Medium-Range Weather Forecasts (ECMWF), download forecast data containing wind speed and direction components at 10m height, and activate the backup NCEP global forecast system data source acquisition mechanism when the wind field data quality assessment coefficient Q∈[0, 0.85) to ensure the continuity of wind field-driven data and output standardized wind field input files for use by ocean wave numerical models.

[0043] S04. Apply the sea ice wave interaction optimization model to dynamically adjust the parameters of the IC4M2 sea ice wave parameterization scheme. Calculate the wave energy exponential attenuation coefficient based on the sea ice concentration distribution characteristics and wave spectrum bandwidth characteristics in the NetCDF format sea ice concentration input file. When the sea ice concentration C∈[0.7, 1.0], a strong attenuation parameter combination is used; when the sea ice concentration C∈[0.3, 0.7), a medium attenuation parameter combination is used; and when the sea ice concentration C∈[0, 0.3), a weak attenuation parameter combination is used.

[0044] S05. Establish a first open boundary line from Newfoundland to Greenland and a second open boundary line from Iceland to Norway in the high latitude waters of the North Atlantic. Provide boundary wave spectral density data through the ww3_ounp boundary condition output command of the WAVEWATCH III global wave model. Use a radiation boundary condition algorithm combined with sponge layer absorption technology to set up a sponge layer absorption region within 20km inside the first and second open boundary lines. Adjust the distribution of artificial viscosity coefficient within the sponge layer absorption region through an exponential decay function.

[0045] S06. Start the WAVEWATCH III version 6.07 wave numerical model to calculate the Arctic wave field. Use a fourth-order precision finite difference discretization scheme combined with an adaptive artificial viscosity control algorithm. When the wave height spatial gradient change rate ∇H in the computational domain is ≥ 0.05 m / km, adjust the time integration step size to 0.5 times the original step size. When ∇H < 0.01 m / km, adjust the time integration step size to 1.5 times the original step size to ensure the stability of the numerical calculation.

[0046] S07. Establish an operational post-processing system for ocean wave forecast products. Based on the calculation output of the ocean wave numerical model, generate spatial distribution data of significant wave height, spatial distribution data of spectral peak period, and spatial distribution data of main wave direction. When the root mean square error (RMSE) between the predicted significant wave height and the Sentinel-3A satellite altimeter observation data is ≥0.8m, trigger the automatic optimization program of model parameters to recalibrate the attenuation coefficient in the IC4M2 sea ice wave parameterization scheme.

[0047] Among them, the ETOPO2 global depth and topography database is a digital elevation model of global seabed and land topography released by the U.S. National Geophysical Data Center. It has a spatial resolution of 2 arcminutes and contains water depth information and land elevation information for global sea areas.

[0048] Among them, the University of Bremen AMSR2 orbital brightness temperature data is a sea ice parameter product obtained by the University of Bremen in Germany based on microwave brightness temperature data observed by the Japanese Advanced Microwave Scanning Radiometer Type 2 sensor. Sea ice concentration information is extracted from the brightness temperature data through the polarization ratio algorithm.

[0049] Among them, the WAVEWATCH III numerical wave model is a third-generation numerical wave prediction model developed by the National Oceanic and Atmospheric Administration (NOAA). It uses wave action balance equations to describe the generation, propagation, and dissipation of waves.

[0050] Among them, the ww3_ounp boundary condition output command is a program module in the WAVEWATCH III wave numerical model used to output wave spectral density information at a specified boundary location, providing boundary forcing conditions for nested modes.

[0051] Among them, the IC4M2 sea ice wave parameterization scheme is the second sub-scheme of the fourth type of sea ice interaction scheme in the WAVEWATCH III wave numerical model, which uses empirical formulas to describe the attenuation effect of sea ice on wave energy.

[0052] Among them, the Arctic Orthogonal Curve Grid System is a numerical computing grid designed for polar regions. It achieves accurate geometric representation of complex polar coastlines and sea ice boundaries through an orthogonal curve coordinate system, avoiding the singularity problem of traditional rectangular grids near the poles.

[0053] Among them, the multi-source sea ice concentration automatic fusion system is a data processing platform that integrates multiple satellite remote sensing sea ice products. It achieves automatic fusion processing of different sea ice data sources through spatiotemporal matching algorithms and data quality control mechanisms, thereby improving the spatiotemporal continuity and accuracy of sea ice concentration data.

[0054] The sea ice wave interaction optimization model is a tool for optimizing sea ice wave parameterization schemes based on deep neural networks. It intelligently adjusts the parameters of the IC4M2 sea ice wave parameterization scheme by learning the nonlinear relationship between sea ice distribution patterns and wave propagation characteristics. The optimization model employs a multilayer perceptron neural network architecture, including an input layer, three hidden layers, and an output layer. The three hidden layers have 128, 64, and 32 neurons, respectively, and utilize ReLU activation and Dropout regularization. The number of heads N in the multi-head attention mechanism is determined based on the variance of sea ice concentration. Wave spectrum bandwidth and grid complexity coefficient Using the formula N=max(4, min(16, int() ))) Determined, among which , and These are reference values ​​for sea ice concentration variance, wave spectral bandwidth, and grid complexity coefficient, respectively. The training dataset for the sea ice-wave interaction optimization model was established by collecting AMSR2 sea ice concentration observation data from the Arctic Ocean from 2015 to 2022, wave parameter data measured by NDBC buoys, and WAVEWATCH III numerical simulation results. Through Z-score normalization and data cleaning, a complete training dataset containing 100,000 training samples and 20,000 validation samples was constructed. The training process of the sea ice wave interaction optimization model includes optimizing network parameters using the Adam gradient descent optimizer with a learning rate of 0.001, a batch size of 128, and 500 training epochs. The optimal combination of network parameters is determined using a 5-fold cross-validation method. The scale-invariant learning mechanism based on multi-resolution training is used to enhance the model's adaptability to different spatial scales through joint training with three different input resolutions: 6.25km, 12.5km, and 25km. An end-to-end optimization mechanism based on differentiable data augmentation incorporates data augmentation strategies such as random rotation, scale transformation, and noise addition into the network parameter optimization process.

[0055] The European Centre for Medium-Range Weather Forecasts (ECMWF) is an international weather forecasting agency located in the UK, providing high-resolution numerical weather forecast products worldwide, including forecast data for a variety of meteorological elements.

[0056] The NCEP Global Forecasting System is a global numerical weather prediction system operated by the U.S. National Center for Environmental Prediction, used as a backup data source for ECMWF forecast data.

[0057] The NetCDF format sea ice concentration input file is a sea ice concentration data file stored in a common network data format, containing sea ice concentration numerical information in three dimensions: time, longitude, and latitude.

[0058] Among them, the wave energy index attenuation coefficient is a key parameter in the IC4M2 sea ice wave parameterization scheme that describes the intensity of wave energy attenuation in sea ice-covered areas. Its calculation formula is as follows: In the formula The dimensionless wave energy attenuation coefficient. The dimensionless sea ice concentration. To represent dimensionless water depth, The dimensionless thickness of sea ice. to These are dimensionless undetermined coefficients. , , , , to These are the reference standardized values ​​for sea ice concentration, circular frequency, water depth, sea ice thickness, and various undetermined coefficients.

[0059] Among them, the radiation boundary condition algorithm is a numerical calculation method for handling wave propagation in open boundaries. It determines the wave propagation direction by analyzing wave phase velocity and group velocity, applies zero gradient boundary conditions to the outward propagating wave components, and applies specified spectral density forcing conditions to the inward propagating wave components.

[0060] Among them, the sponge layer absorption technology is a numerical wave energy absorption method set near the boundary of the computational domain. It achieves smooth absorption of wave energy near the boundary by gradually increasing the artificial damping coefficient within the sponge layer absorption region. The artificial damping coefficient... According to the relative position of the distance from the boundary Through formula Distribute, where The thickness of the sponge layer, This is a reference value for the damping coefficient. This is the maximum damping coefficient.

[0061] Among them, the fourth-order precision finite difference discretization scheme is a high-precision numerical method that uses the information of the target grid point and its two neighboring grid points before and after it, a total of five grid points, to construct the spatial derivative approximation. Compared with the second-order precision scheme, it has smaller numerical diffusion error and dispersion error.

[0062] Among them, the adaptive artificial viscosity control algorithm is a numerical stabilization method that dynamically adjusts the magnitude of the artificial viscosity coefficient based on the degree of change in the numerical solution gradient. The artificial viscosity coefficient... Based on the wave height gradient modulus Through formula Perform calculations, where This is a reference value for the viscosity coefficient. Based on the basic viscosity coefficient, The gradient-dependent viscosity coefficient, This is a reference value for the wave height gradient modulus.

[0063] Among them, the Sentinel-3A satellite altimeter is a synthetic aperture radar altimeter carried by the European Space Agency's Sentinel-3A satellite, which inverts sea wave parameters such as effective wave height by measuring changes in sea surface height.

[0064] When the Pearson correlation coefficient R between the wave spectrum shape of the sea ice edge region and the standard reference JONSWAP wave spectrum is ≥0.9, the preset standard wave propagation calculation mode is directly used for subsequent wave field analysis to avoid unnecessary consumption of computational resources.

[0065] When the coefficient of variation (CV) of the spatial distribution of sea ice concentration is in the range of [0, 0.15), a unified parameter centralized processing mode is adopted to improve computational efficiency. When the coefficient of variation (CV) is greater than or equal to 0.4, a regional adaptive distributed processing mode is adopted to deal with the spatial heterogeneity of sea ice distribution.

[0066] Optionally, the present invention is also implemented by a computer to form an Arctic wave forecasting system based on automatic sea ice concentration fusion. The computer is equipped with a readable storage medium, which stores program instructions. When the program instructions are run in the computer, they are used to execute the above-mentioned Arctic wave forecasting method based on automatic sea ice concentration fusion.

[0067] The specific implementation methods of the above steps are described in detail below.

[0068] Step S01 involves constructing an orthogonal curve grid system suitable for numerical computation in the Arctic region based on the ETOPO2 global water depth and topography database released by the U.S. National Geophysical Data Center. First, water depth and topographic information for the Arctic region are extracted from the ETOPO2 database, which provides digital elevation models of global seabed and land topography with a spatial resolution of 2 arcminutes. Next, the coordinates of the four vertices of the computational region are determined under a polar coordinate projection system: 54°N -45°E, 54°N 45°E, 54°N 135°E, and 54°N -135°E, forming a square computational region around the North Pole. Then, the area north of 88°N is set as a land boundary condition to avoid numerical computation singularities near the poles. A coordinate transformation algorithm from the geographic coordinate system to the polar coordinate projection system is used to convert latitude and longitude coordinates to projection plane coordinates, generating regular grid cells with a resolution of 20km. Finally, three key data files are output: lon.dat (stores grid longitude information), lat.dat (stores grid latitude information), and dep.dat (stores water depth information for each grid point). This step provides high-precision topographic boundary conditions and a computational grid foundation for subsequent numerical simulations of ocean waves.

[0069] Step S02 is implemented using an automatic multi-source sea ice concentration fusion system established by the University of Bremen, Germany, based on observation data from the Advanced Microwave Scanning Radiometer Type II sensor from Japan. First, sea ice concentration information is extracted from the AMSR2 orbital brightness temperature data using a polarization ratio algorithm, obtaining daily Arctic sea ice concentration raw data with a spatial resolution of 6.25 km. Then, three preprocessing operations are performed on the acquired raw sea ice concentration data: coordinate transformation to convert the data from the geographic coordinate system to a polar coordinate projection system, time normalization to ensure the consistency of the data's time reference, and bilinear spatial interpolation to interpolate the 6.25 km resolution data onto a 20 km resolution computational grid. Next, the processed sea ice concentration data is converted into a NetCDF format input file that can be recognized and read by the WAVEWATCH III wave numerical model, using a common network data format standard. This input file contains sea ice concentration numerical information in three dimensions: time, longitude, and latitude. The purpose of this step is to provide high-quality sea ice distribution forcing conditions for the wave numerical model, ensuring accurate simulation of the impact of sea ice on wave propagation.

[0070] Step S03 involves establishing an automatic wind field acquisition system based on data from the European Centre for Medium-Range Weather Forecasts (ECMWF) and configuring the NCEP Global Forecasting System as a backup data source. First, forecast data containing 10m height wind speed and direction components is automatically downloaded from the ECMWF data server. This data provides high-resolution numerical weather prediction products globally. Then, the downloaded wind field data undergoes a quality assessment, and a wind field data quality assessment coefficient Q is calculated. When this coefficient falls between 0 and 0.85, the ECMWF data quality is deemed unsatisfactory, and the backup data acquisition mechanism is automatically activated. The backup mechanism acquires wind field data for the corresponding time period from the NCEP Global Forecasting System operated by the National Center for Environmental Prediction (NCEP) in the United States, ensuring the continuity and reliability of wind field driving data. Finally, the acquired wind field data is standardized to output a standardized wind field input file for use by the WAVEWATCHIII wave numerical model. The purpose of this step is to provide stable and reliable wind field forcing conditions for wave numerical simulation, as wind field is a major driving factor for wave generation and development. The quality assessment coefficient threshold of 0.85 is an optimal value determined based on years of operational experience.

[0071] Step S04 involves applying a sea ice-wave interaction optimization model based on a deep neural network to intelligently and dynamically adjust the parameters of the IC4M2 sea ice wave parameterization scheme. First, based on the NetCDF format sea ice concentration input file generated in step S02, the distribution characteristics of sea ice concentration and the corresponding wave spectrum bandwidth characteristics are analyzed. Then, the wave energy exponential attenuation coefficient is calculated using the sea ice-wave interaction optimization model. This coefficient describes the attenuation intensity of wave energy in different sea ice coverage areas. Different combinations of attenuation parameters are used according to different ranges of sea ice concentration values. When the sea ice concentration C is in the range of 0.7 to 1.0, the sea ice coverage density is high, and the wave energy attenuation is strong, so a strong attenuation parameter combination is used. When the sea ice concentration C is in the range of 0.3 to 0.7, the sea ice coverage density is moderate, so a moderate attenuation parameter combination is used. When the sea ice concentration C is in the range of 0 to 0.3, the sea ice coverage is sparse, and wave propagation is less obstructed, so a weak attenuation parameter combination is used. The purpose of this step is to dynamically optimize the parameters affecting sea ice wave propagation based on real-time sea ice distribution, thereby improving the accuracy and adaptability of wave forecasting.

[0072] Step S05 involves setting open boundary conditions and using a sponge layer absorption technique in the high-latitude North Atlantic. First, two open boundary lines are established at the boundary of the computational domain: the first extends from Newfoundland to Greenland, and the second extends from Iceland to Norway. These boundary lines provide wave energy input from the North Atlantic to the Arctic wave computational domain. Then, the wave spectral density data at these boundary locations is obtained using the ww3_ounp boundary condition output command of the WAVEWATCH III global wave model. This data serves as the boundary forcing condition for the nested mode. Next, a radiation boundary condition algorithm is used to process wave propagation at the open boundary. This algorithm determines the wave propagation direction by analyzing wave phase velocity and group velocity, applying a zero-gradient boundary condition to the outward-propagating wave components and a spectral density forcing condition to the inward-propagating wave components. Finally, combined with sponge layer absorption technology, a sponge layer absorption region is established within 20 km inside the two open boundary lines. An exponential decay function is used to adjust the distribution of the artificial viscosity coefficient within this region, achieving smooth absorption of wave energy near the boundary and avoiding the influence of boundary reflection on the computational results. The purpose of this step is to provide accurate boundary conditions for Arctic wave calculations, ensuring the correct simulation of wave energy exchange inside and outside the computational domain.

[0073] Step S06 involves launching the WAVEWATCH III version 6.07 wave numerical model to perform numerical calculations of the Arctic wave field. First, a fourth-order precision finite difference discretization scheme is used to spatially discretize the wave action balance equations. This scheme uses information from five grid points—the target grid point and its two nearest neighbors—to construct a spatial derivative approximation, resulting in smaller numerical diffusion and dispersion errors compared to the second-order precision scheme. Then, an adaptive artificial viscosity control algorithm is used to ensure the stability of the numerical calculations. This algorithm dynamically adjusts the artificial viscosity coefficient based on the gradient change of the numerical solution. When the rate of change of the wave height spatial gradient within the computational domain is greater than or equal to 0.05 m / km, it indicates a drastic change in the wave field; in this case, the time integration step is adjusted to 0.5 times the original step size to improve computational accuracy. When the rate of change of the wave height spatial gradient is less than 0.01 m / km, it indicates a gentle change in the wave field; in this case, the time integration step is adjusted to 1.5 times the original step size to improve computational efficiency. The purpose of this step is to solve the wave action balance equations describing the wave generation, propagation, and dissipation processes using high-precision numerical methods, thereby obtaining detailed wave field information for the Arctic Ocean. The gradient rate of change thresholds of 0.05 m / km and 0.01 m / km are optimal reference values ​​determined based on numerical stability analysis and computational efficiency optimization.

[0074] Step S07 involves establishing an operational post-processing system for ocean wave forecast products, generating standardized forecast products based on the numerical simulation results from step S06. First, key wave parameters, including significant wave height, spectral peak period, and main wave direction, are extracted from the calculation output of the WAVEWATCH III ocean wave numerical model. Then, spatial and temporal interpolation is performed on these parameters to generate spatial distribution data for significant wave height, spectral peak period, and main wave direction. Next, a real-time quality control mechanism for the forecast results is established, comparing and verifying the forecast significant wave height with Sentinel-3A satellite altimeter observation data, and calculating the root mean square error (RMSE). When the RMSE is greater than or equal to 0.8m, it indicates that the forecast accuracy does not meet operational requirements, automatically triggering a model parameter optimization program. This optimization program recalibrates the attenuation coefficient of the IC4M2 sea ice wave parameterization scheme from step S04, improving forecast accuracy through iterative optimization. The purpose of this step is to convert the numerical simulation results into standardized ocean wave forecast products for users and ensure the reliability of the forecast results through real-time quality control. The root mean square error threshold of 0.8m was determined based on international wave forecasting service standards and user needs analysis.

[0075] Further explanation is needed regarding the sea ice-wave interaction optimization model, which employs a multilayer perceptron neural network architecture, comprising an input layer, three hidden layers, and an output layer. The input layer receives multidimensional feature vectors, including sea ice concentration distribution, wave spectrum information, water depth data, and grid geometry information. The number of neurons in the three hidden layers is set to 128, 64, and 32, respectively, forming a progressively decreasing network structure, which facilitates hierarchical feature extraction and abstraction. Each hidden layer uses the ReLU activation function to achieve nonlinear transformation and is configured with a Dropout regularization mechanism to prevent overfitting, with a Dropout ratio set to 0.3. The network also introduces a multi-head attention mechanism to enhance the recognition of key features. The number of attention heads N is dynamically calculated based on the sea ice concentration variance, wave spectrum bandwidth, and grid complexity coefficient, ranging from 4 to 16. The output layer generates the attenuation coefficient parameters required for the IC4M2 sea ice-wave parameterization scheme.

[0076] The creation of the training dataset involved several key steps. The data collection phase, spanning eight years from 2015 to 2022, involved collecting AMSR2 sea ice concentration observation data from the Arctic Ocean, wave parameter data measured by NDBC buoys from the National Data Buoy Center (NDBC), and data from WAVEWATCH III numerical simulations. The data preprocessing phase employed Z-score normalization to normalize all input features, eliminating the influence of different dimensions and numerical ranges between physical quantities. Simultaneously, data cleaning was performed to remove outliers and missing values, ensuring the quality of the training data. The dataset partitioning phase divided the cleaned data into training and validation sets at a 5:1 ratio, ultimately constructing a complete dataset containing 100,000 training samples and 20,000 validation samples.

[0077] The model training process employed the Adam gradient descent optimizer for adaptive optimization of network parameters, with an initial learning rate of 0.001, a batch size of 128, and a total of 500 training epochs. Five-fold cross-validation was used to evaluate the model's generalization performance during training, and grid search was employed to determine the optimal combination of network parameters. To enhance the model's adaptability to different spatial scales, a scale-invariant learning mechanism based on multi-resolution training was implemented. Joint training with three different input resolutions (6.25km, 12.5km, and 25km) enabled the model to handle multi-scale sea ice distribution characteristics. Simultaneously, an end-to-end optimization mechanism based on differentiable data augmentation was adopted, directly incorporating data augmentation strategies such as random rotation, scale transformation, and noise addition into the network parameter optimization process, further improving the model's robustness and generalization ability.

[0078] It should be noted that the key technical ideas and advantages of this invention are analyzed as follows.

[0079] The first key technological approach is an optimization model for sea ice-wave interaction based on deep neural networks. This model intelligently improves traditional empirical parameterization schemes by learning the complex nonlinear relationship between sea ice distribution patterns and wave propagation characteristics. Compared to fixed parameter settings in traditional methods, this model can dynamically adjust wave attenuation parameters based on real-time sea ice distribution, significantly improving wave forecasting accuracy in sea ice margins and areas of seasonal sea ice change. Traditional parameterization schemes, based on limited observational data and simplified physical assumptions, struggle to accurately describe the complex physical processes of sea ice-wave interaction, while deep learning models, trained on large datasets, can capture these complex nonlinear relationships.

[0080] The second key technological approach is the multi-source sea ice concentration automatic fusion system. This system integrates multiple satellite remote sensing sea ice products and achieves automatic fusion processing of different data sources through spatiotemporal matching algorithms and data quality control mechanisms. Compared to a single data source, multi-source fusion significantly improves the spatiotemporal continuity and accuracy of sea ice concentration data, especially in terms of data availability under cloud cover and polar night conditions. Traditional methods often rely on single satellite products and are easily affected by sensor failures, orbital gaps, and weather conditions, leading to data loss and decreased accuracy. Multi-source fusion effectively solves these problems through data redundancy and complementarity.

[0081] The third key technical approach is the adaptive time step control algorithm. This algorithm dynamically adjusts the numerical integration time step based on the rate of change of the wave height spatial gradient, optimizing computational efficiency while ensuring computational accuracy. When the wave field changes drastically, the time step is automatically reduced to improve accuracy; when the wave field changes gently, the time step is appropriately increased to improve efficiency. Traditional fixed time step methods either lead to numerical instability due to excessively large step sizes or waste computational resources due to excessively small step sizes, while the adaptive algorithm achieves the optimal balance between accuracy and efficiency.

[0082] The synergistic effect of these three key technological approaches has yielded significant comprehensive advantages. The sea ice wave interaction optimization model provides intelligent parameter adjustment capabilities for the entire forecasting system, the multi-source sea ice concentration fusion system provides high-quality input data for this optimization model, and the adaptive time step control algorithm ensures the stability and efficiency of numerical computation. These three elements form a complete technological chain from data input and parameter optimization to numerical computation, achieving significant improvements in forecast accuracy, data reliability, and computational efficiency compared to traditional sea ice forecasting methods, particularly demonstrating a clear technological advantage in sea ice-covered Arctic waters.

[0083] It should be noted that this invention also solves the following technical problems: First, this invention solves the problem of decreased computational accuracy caused by grid singularity in polar ocean numerical computation. Traditional rectangular grid systems suffer from grid convergence and coordinate singularity near the poles, leading to numerical computation instability and accuracy loss. This invention constructs an orthogonal curved grid system for the Arctic, uses polar coordinate projection to form a square computational region around the Arctic, and achieves uniform grid cell generation through coordinate transformation from geographic coordinates to projected coordinates, effectively avoiding grid singularity problems near the poles and ensuring the stability and accuracy of numerical computation. Second, this invention solves the problem of boundary reflection interference caused by improper open boundary handling in ocean numerical models. In wave numerical simulations within a finite computational domain, the choice of open boundary handling method directly affects the accuracy of the wave field within the computational domain. Improper boundary handling can generate artificial reflection waves, leading to distorted computational results. This invention establishes multiple open boundary lines in the high-latitude waters of the North Atlantic, employs a radiation boundary condition algorithm combined with sponge layer absorption technology, applies zero-gradient boundary conditions to outward-propagating wave components, applies specified spectral density forcing conditions to inward-propagating wave components, and simultaneously sets up a sponge layer absorption region inside the boundary to adjust the distribution of artificial viscosity coefficient through an exponential decay function. This achieves smooth absorption of wave energy near the boundary, effectively eliminating the influence of boundary reflection interference on the wave field inside the computational domain.

[0084] Specifically, the principle of this invention is as follows: This invention solves the technical problem of insufficient precision in the parameterization of sea ice-wave interaction. Its fundamental principle lies in achieving precise quantification and dynamic adjustment of the sea ice-wave interaction process through a technical approach combining multi-source data fusion and artificial intelligence optimization. First, the multi-source sea ice concentration automatic fusion system integrates multiple satellite remote sensing sea ice products, such as the University of Bremen AMSR2, and obtains high-precision sea ice distribution information through spatiotemporal matching algorithms and data quality control mechanisms. This provides accurate input conditions for the parameterization of sea ice-wave interaction, solving the problem of insufficient sea ice data precision in traditional methods. Second, the sea ice-wave interaction optimization model is built on a deep neural network architecture. It learns the complex nonlinear relationship between sea ice distribution characteristics and wave propagation laws through a multi-layer perceptron network. Utilizing a multi-head attention mechanism, it dynamically determines the number of attention heads based on sea ice concentration variance, wave spectral bandwidth, and grid complexity coefficient, achieving adaptive response to different sea ice environmental conditions. This overcomes the technical limitation of fixed parameterization schemes being unable to adapt to spatiotemporal changes in sea ice distribution. Furthermore, by dynamically adjusting the wave energy attenuation coefficient in the IC4M2 sea ice wave parameterization scheme and employing different combinations of attenuation parameters based on the sea ice concentration distribution characteristics, a precise description of the wave energy attenuation effect of sea ice was achieved, significantly improving the accuracy of numerical simulation of wave propagation processes in sea ice-covered areas. In addition, the combined application of an adaptive artificial viscous control algorithm and a fourth-order precision finite difference discretization scheme ensured the stability and accuracy of the numerical calculations, providing a reliable numerical calculation platform for the parameterization optimization of sea ice-wave interactions and ensuring the effective implementation of the technical solution.

[0085] The following provides a specific embodiment 1 of the present invention, and the specific implementation of each step in this embodiment 1 is described in detail below.

[0086] The specific implementation of step S01 is to construct a polar orthogonal curve grid system based on the polar coordinate projection coordinate transformation algorithm. The coordinate transformation formula is expressed as follows:

[0087] ;

[0088] ;

[0089] In the formula, This is the x-coordinate in the projected coordinate system, in meters. This is the y-coordinate in the projected coordinate system, in meters. The characteristic length is a reference value, taken as 20000m; The radius of the Earth is taken as 6,371,000 m. Geographic latitude, in radians; This refers to geographical longitude, expressed in radians. This is a latitude reference value, and the value is [value to be filled in]. radian; This is a longitude reference value, and the value is taken from... Radius. Among them, and Obtained from latitude and longitude coordinates in the ETOPO2 database. is a geophysical constant.

[0090] The specific implementation of step S02 involves performing bilinear spatial interpolation on the sea ice concentration data. The interpolation algorithm formula is expressed as follows:

[0091] ;

[0092] ;

[0093] In the formula, The interpolated sea ice concentration is in dimensionless form. This is a reference value for sea ice concentration, with a value of 1. is the weight coefficient of the k-th neighboring grid point, in dimensionless form; This is the total weighting coefficient, in dimensionless form. Let be the sea ice concentration at the kth neighboring grid point, in dimensionless form; This is the distance from the target point to the kth nearest neighbor grid point, in meters. This is a reference distance value, taken as 6250m. Obtained by inversion of AMSR2 orbital brightness temperature data Obtained through mesh geometry calculations.

[0094] The specific implementation of step S03 is to establish a wind field data quality assessment coefficient calculation, and the quality assessment formula is expressed as follows:

[0095] ;

[0096] In the formula, This is the wind field data quality assessment coefficient, in dimensionless form. This is a reference value for the quality assessment coefficient, and its value is 1. For wind speed measurement, the unit is m / s; The wind speed is the model wind speed, in m / s. The wind speed is a reference value, taken as 10 m / s; The correlation coefficient between observed and model wind speeds is dimensionless. The correlation coefficient is a reference value, taken as 1. Acquired through satellite remote sensing observations, Acquired through ECMWF forecast data Statistical analysis shows that the value ranges from -1 to 1.

[0097] The specific implementation of step S04 involves applying the sea ice wave interaction optimization model to calculate the wave energy exponential decay coefficient. The formula for the decay coefficient is as follows:

[0098] ;

[0099] In the formula, This is the fluctuation energy attenuation coefficient, in units of... ; The attenuation coefficient reference value is set to [value]. ; The angular frequency of the wave, in units of ; The reference value for the angular frequency is 1. ; to The coefficients are undetermined, and their units are dimensionless. to These are the reference standardized values ​​for each undetermined coefficient, all in dimensionless units and all taking the value 1; Sea ice concentration, in dimensionless units; This is a reference value for sea ice concentration, with a value of 1. Water depth, in meters (m). This is a reference value for water depth, taken as 100m; Sea ice thickness, in meters (m). This is a reference value for sea ice thickness, taken as 1m. Among them, Obtained through step S02. Obtained from the ETOPO2 database. Obtained through satellite remote sensing inversion to The results were obtained through an optimized model of sea ice wave interaction.

[0100] The formula for calculating the number of heads in a multi-head attention mechanism is as follows:

[0101] ;

[0102] In the formula, The number of attention heads is dimensionless. The reference value for the number of heads is 8; The variance of sea ice concentration is dimensionless. This is a reference value for the variance of sea ice concentration, with a value of 0.01. The wave spectrum bandwidth is expressed in Hz. This is a reference value for the spectral bandwidth, taken as 0.1Hz; This represents the grid complexity coefficient, in dimensionless form. This is a reference value for the grid complexity coefficient, taking the value 1. Wherein, The specific calculation formula is as follows, based on statistical analysis: In the formula The sample size is dimensionless and ranges from 100 to 10000. Let be the sea ice concentration of the j-th sample, in dimensionless form; This represents the average sea ice concentration, in dimensionless units. Obtained through spectral analysis; The calculation is performed through mesh geometric analysis, and the formula is as follows: In the formula and This refers to the grid spacing, in meters (m). and The reference grid spacing is in meters, and the value is 20000m.

[0103] The specific implementation of step S05 involves setting the artificial damping coefficient distribution of the sponge layer absorption technology. The formula for the damping coefficient distribution is as follows:

[0104] ;

[0105] In the formula, This is the artificial damping coefficient, in units of... ; The damping coefficient is a reference value, and the value is taken as follows. ; This is the maximum damping coefficient, in units of... Values ; This is the distance from the boundary, in meters (m). The thickness of the sponge layer is 20000 μm. The value is obtained through geometric calculation and ranges from 0 to 20000m.

[0106] The specific implementation of step S06 is to use an adaptive artificial viscosity control algorithm. The formula for calculating the artificial viscosity coefficient is as follows:

[0107] ;

[0108] In the formula, This is the artificial viscosity coefficient, in units of... ; This is a reference value for the viscosity coefficient, and the value is taken as follows. ; The basic viscosity coefficient, in units of... Values ; This is the gradient-dependent viscosity coefficient, in units of... Values ; The wave height gradient modulus, in units of ; The reference value for the wave height gradient modulus is [value to be filled in]. .in, Obtained through numerical calculation.

[0109] The specific implementation of step S07 involves establishing a root mean square error calculation for forecast result quality control, which also includes the coefficient of variation of sea ice concentration spatial distribution and spectral correlation determination. The formula for calculating the coefficient of variation of sea ice concentration spatial distribution is as follows:

[0110] ;

[0111] In the formula, , where is the coefficient of variation of the spatial distribution of sea ice concentration, in dimensionless units; The coefficient of variation is a reference value, with a value of 1. The spatial standard deviation of sea ice concentration is given in dimensionless form. This is the reference value for the spatial standard deviation, with a value of 0.1. This represents the spatial average of sea ice concentration, in dimensionless units. This is a spatial average reference value, taken as 0.5. Wherein, Calculations based on spatial statistical analysis Obtained through regional average calculation.

[0112] The formula for calculating the Pearson correlation coefficient between the spectral shape and the JONSWAP spectrum is as follows:

[0113] ;

[0114] In the formula, Pearson correlation coefficient for spectral shape, in dimensionless units; The correlation coefficient is set to a reference value of 1. The number of frequency points, in dimensionless units, with a value range of 50 to 200; The observed spectral density at the k-th frequency point is given by . ; The JONSWAP standard spectral density at the k-th frequency point is given by [value]. ; The spectral density reference value is [value to be filled in]. ; The average value of the observed spectral density is expressed in units of 1000 ppm. ; This represents the average JONSWAP spectral density, in units of... .in, Obtained through spectral analysis and calculation. Calculated using the JONSWAP theoretical spectral formula.

[0115] The formula for calculating the root mean square error is as follows:

[0116] ;

[0117] In the formula, This is the root mean square error, in meters (m). The wave height reference value is 1m. The sample size is dimensionless and ranges from 100 to 10000. The height of the i-th predicted significant wave is in meters (m). Let be the effective wave height of the i-th observation, in meters (m). Obtained through calculation using WAVEWATCH III mode. Acquired through observations using the Sentinel-3A satellite altimeter.

[0118] The formula's principle and effect analysis are as follows. The polar coordinate projection coordinate transformation formula is based on the principles of spherical geometry, using trigonometric function transformations to map geographic coordinates to planar coordinates. This formula avoids the singularity problem of traditional rectangular grids near poles, significantly improving the geometric accuracy and numerical stability of grid generation in polar regions compared to existing technologies. The bilinear spatial interpolation formula uses the inverse distance weighting principle, with weight calculation employing the inverse distance normalization method.

[0119] ;

[0120] This formula achieves spatial interpolation by weighted averaging of information from four neighboring grid points. Compared with the traditional nearest neighbor interpolation method, it can maintain the spatial continuity and gradient characteristics of the sea ice concentration field and effectively avoid data jumps and discontinuities.

[0121] The formula for assessing wind field data quality comprehensively considers three evaluation indicators: observed wind speed, model wind speed, and correlation, and adopts a weighted sum of squares form:

[0122] ;

[0123] This formula achieves quantitative assessment of data quality through a multivariate evaluation system. Compared with single-indicator evaluation methods, it can comprehensively reflect the reliability of wind field data and improve the accuracy of data source switching decisions.

[0124] The formula for the wave energy exponential decay coefficient is based on the physical properties of sea ice and wave propagation theory, and adopts a multi-parameter linear combination form:

[0125] ;

[0126] This formula uses the sea ice concentration term Describes the direct attenuation effect of sea ice cover on wave energy, using the squared frequency term. The depth term reflects the rapid attenuation characteristics of high-frequency waves in sea ice. Considering the effect of shallow water on wave propagation, the sea ice thickness term This formula reflects the impeding effect of thick ice on waves. By making both sides dimensionless, it can accurately characterize the combined effects of multiple factors on wave attenuation. Compared with the traditional linear parameterization scheme, it significantly improves the physical accuracy of wave forecasting in the sea ice edge region.

[0127] The formula for calculating the number of heads in a multi-head attention mechanism dynamically determines the number of attention heads based on three key features, including the variance term of sea ice concentration. Reflecting the spatial heterogeneity of sea ice distribution:

[0128] ;

[0129] Wave spectrum bandwidth term The frequency distribution range characterizing wave energy, and the mesh complexity term. Quantify the geometric complexity of the computational grid:

[0130] ;

[0131] This formula enables adaptive configuration of the neural network attention mechanism. Compared with a fixed number of heads, it can optimize feature extraction capabilities according to different sea ice distribution patterns, thus improving the intelligence level of the parameterization scheme.

[0132] The formula for the distribution of artificial damping coefficient uses the square of distance to achieve a smooth transition of the damping coefficient within the sponge layer:

[0133] ;

[0134] This formula avoids numerical reflection at the boundary through gradual energy absorption, which significantly improves the numerical stability and calculation accuracy of open boundary conditions compared to step damping.

[0135] The adaptive artificial viscosity coefficient formula is based on the quadratic response principle of wave height gradient, with the gradient term... Achieve dynamic matching between viscosity coefficient and the degree of change in solution gradient:

[0136] ;

[0137] This formula minimizes the impact of artificial viscosity on the physical properties while ensuring numerical stability, achieving an optimal balance between computational accuracy and stability compared to the fixed viscosity coefficient method.

[0138] The formula for the coefficient of variation of the spatial distribution of sea ice concentration quantifies the relative variability of the spatial distribution by using the ratio of the standard deviation to the mean:

[0139] ;

[0140] This formula provides a quantitative basis for sea ice distribution pattern recognition and processing strategy selection, improving the objectivity and accuracy of algorithm selection compared to subjective judgment methods.

[0141] The Pearson correlation coefficient formula calculates the similarity between the observed spectrum and the JONSWAP theoretical spectrum using standardized covariance:

[0142] ;

[0143] This formula can quantitatively assess the standardization of the spectral shape in the sea ice marginal zone, providing an objective mathematical basis for selecting wave propagation calculation models compared to qualitative methods. The root mean square error calculation formula uses the arithmetic mean square root of the squared error, providing a statistically quantifiable indicator of forecast accuracy. This formula eliminates the influence of magnitude through dimensionless processing, and compared to absolute error indicators, it more objectively reflects the overall performance level of the forecast system.

[0144] To better understand and implement this invention, the following is a specific application scenario of this invention, Example 2:

[0145] The technical team needed to establish a precise operational system for ocean wave forecasting in the Arctic region to support the navigation safety of polar research vessels. The team adopted an Arctic ocean wave forecasting method based on automatic sea ice concentration fusion to establish a high-precision numerical forecasting system for ocean waves covering the entire Arctic Ocean.

[0146] The technical team first constructed an orthogonal curve grid system for the Arctic based on the ETOPO2 global depth and topography database. Under polar coordinate projection, the engineers selected four key vertices to form a square computational region surrounding the North Pole, defining the area north of 88°N as the land boundary. Through precise conversion from geographic coordinates to projected coordinates, a 20km resolution grid cell was generated, ultimately outputting a computational grid containing 72,500 valid grid points. The grid system construction process is as follows: Figure 2 As shown, projected meshes can effectively avoid the singularity problem near poles of traditional rectangular meshes.

[0147] Sea ice concentration data acquisition utilizes University of Bremen AMSR2 orbital brightness temperature data to establish an automatic multi-source sea ice concentration fusion system. The system automatically downloads daily raw Arctic sea ice concentration data with a spatial resolution of 6.25 km, and performs coordinate transformation, time standardization, and bilinear spatial interpolation on the data. The processed sea ice concentration data is converted into a NetCDF format input file for WAVEWATCH III wave numerical model recognition. The data file size is approximately 145 MB, containing complete sea ice concentration information in three dimensions: time, longitude, and latitude.

[0148] The wind field data acquisition system uses the European Centre for Medium-Range Weather Forecasts (ECMWF) as its primary data source, downloading forecast data that includes 10m height wind speed and direction components. When the system detects that the wind field data quality assessment coefficient Q reaches 0.82, it automatically activates the backup NCEP global forecast system data source acquisition mechanism to ensure the continuity of wind field-driven data. The wind field data has a temporal resolution of 3 hours and a spatial resolution of 0.25°, covering the entire Arctic computational domain.

[0149] The technical team applied a sea ice wave interaction optimization model to dynamically adjust the parameterization scheme of the IC4M2 sea ice wave. This optimization model employs a multilayer perceptron neural network architecture, including an input layer, three hidden layers (with 128, 64, and 32 neurons respectively), and an output layer, using the ReLU activation function and Dropout regularization mechanism. The wave energy exponential decay coefficient was calculated based on the sea ice concentration distribution characteristics. When the sea ice concentration C value is 0.85, a strong decay parameter combination is adopted, and the corresponding dimensionless undetermined coefficients are shown in Table 1.

[0150] Table 1 Combinations of wave energy attenuation parameters under different sea ice concentration conditions

[0151]

[0152] Regarding boundary condition settings, the technical team established two open boundary lines in the high-latitude waters of the North Atlantic: the first open boundary line covers the Labrador Sea and the Denmark Strait region, with a total length of approximately 1850 km; the second open boundary line runs through the Norwegian Sea and the Greenland Sea, with a total length of approximately 2100 km. Boundary wave spectral density data were provided using the ww3_ounp boundary condition output command of the WAVEWATCH III global wave model. A radiation boundary condition algorithm combined with sponge layer absorption technology was employed to establish a sponge layer absorption region within 20 km of the open boundary line.

[0153] The technical team launched the WAVEWATCH III version 6.07 numerical wave model to calculate the Arctic wave field, employing a fourth-order precision finite difference discretization scheme combined with an adaptive artificial viscosity control algorithm. The calculation was successful when the rate of change of the spatial gradient of wave height ∇H in the computational domain reached 0.062. When this happens, the system automatically adjusts the time integration step size to 0.5 times the original step size, that is, from the standard 450 seconds to 225 seconds. When ∇H is less than 0.008... At that time, the time integration step size was adjusted to 1.5 times the original step size, reaching 675 seconds, to ensure the stability and efficiency of numerical calculation.

[0154] The operational post-processing system for ocean wave forecast products generates three core products based on the calculation output of ocean wave numerical models: spatial distribution data of significant wave height, spatial distribution data of spectral peak period, and spatial distribution data of main wave direction. The system generates approximately 2.8 GB of raw output data daily, which is then post-processed and compressed into a standard 350 MB forecast product file. When the root mean square error (RMSE) between the predicted significant wave height and the Sentinel-3A satellite altimeter observation data reaches 0.75 m, the system automatically triggers a model parameter optimization program to recalibrate the attenuation coefficients in the IC4M2 sea ice wave parameterization scheme.

[0155] During actual operation, the technical team conducted a 120-day operational forecasting experiment for the rapid melting period of Arctic sea ice in 2023 (June to September). The coefficient of variation (CV) of the spatial distribution of sea ice concentration showed significant differences at different time periods during the system's operation, as shown in Table 2.

[0156] Table 2. Statistics on the coefficient of variation of spatial distribution of sea ice concentration in different months

[0157]

[0158] In the wave spectrum shape analysis of the sea ice marginal zone, when the Pearson correlation coefficient R between the wave spectrum and the standard reference JONSWAP wave spectrum reaches 0.93, the system directly adopts the preset standard wave propagation calculation mode. This adaptive processing mechanism improves the system's computational efficiency by 15% while maintaining forecast accuracy.

[0159] By comparing and verifying the data with observations from the R / V Sikuliaq probe in the Beaufort Sea ice margin region in 2015, the results of the system's predicted significant wave height, spectral peak period, and main wave direction with the observed data are as follows: Figure 3As shown, cc represents the correlation coefficient, bias represents the mean error, and rmse represents the root mean square error. The correlation coefficient for the significant wave height reaches 0.89, the root mean square error is 0.52m, and the mean error is -0.08m; the correlation coefficient for the spectral peak period is 0.85, the root mean square error is 1.3s, and the mean error is 0.2s; the correlation coefficient for the main wave direction is 0.78, and the root mean square error is 18.5°.

[0160] The wave forecast products generated by the system include significant wave height and wave direction forecasts. Figure 4 ) and periodic forecast results ( Figure 5 This provides crucial sea state information support for polar research vessels. Monthly validation results show that the model-observation root mean square error (RMSE) from January to December is as follows: Figures 6 to 17 As shown, the annual average RMSE remains below 0.65m, meeting the requirements of operational forecasting.

[0161] The technical team established a training dataset for their optimized sea ice-wave interaction model, containing complete observational data from the Arctic Ocean from 2015 to 2022, with 100,000 training samples and 20,000 validation samples. The model was trained using the Adam gradient descent optimizer with a learning rate of 0.001 and a batch size of 128, converging after 500 training iterations. The optimal network parameter combination, determined through 5-fold cross-validation, improved the model's prediction accuracy under different sea ice conditions by 12% compared to traditional methods.

[0162] The number of heads N in the multi-head attention mechanism is dynamically adjusted based on the sea ice concentration variance, wave spectral bandwidth, and grid complexity coefficient. During the experiment, when the sea ice concentration variance... for Wave spectrum bandwidth 2.1Hz, mesh complexity coefficient When the value is 1.8, the calculated number of attention heads N is 8, and the corresponding computational resource consumption is 1.3 times that of the standard configuration.

[0163] The system employs an end-to-end optimization mechanism based on differentiable data augmentation. Through joint training with three different input resolutions (6.25km, 12.5km, and 25km), the model's adaptability to different spatial scales is significantly enhanced. After multi-resolution training, the model's forecast bias when processing sea ice data at different resolutions is reduced by 8%, improving the system's robustness.

[0164] It should be noted that the variables involved in this invention are explained in detail in Tables 3 and 4 below.

[0165] Table 3. Variable Explanation Table (Part 1)

[0166]

[0167] Table 4. Variable Explanation Table (Part Two)

[0168]

[0169] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any changes or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for predicting Arctic sea waves based on the automatic fusion of sea ice density, characterized in that, The ETOPO2 global water depth topography database is used to construct a polar orthogonal curve grid system, the University of Bremen AMSR2 orbital brightness temperature data is used to establish a multi-source sea ice concentration automatic fusion system to obtain sea ice concentration data and convert them into a NetCDF format sea ice concentration input file, an ECMWF European Centre for Medium-Range Weather Forecasts wind field data automatic acquisition system is established to download wind field prediction data, and a sea ice wave interaction optimization model is applied to dynamically adjust the IC4M2 sea ice wave parameterization scheme. According to the sea ice concentration distribution characteristics and wave spectrum bandwidth characteristics in the NetCDF format sea ice concentration input file, the wave energy index attenuation coefficient is calculated, the open boundary line is set in the high latitude sea area of the North Atlantic, the boundary wave propagation is processed by using the radiation boundary condition algorithm combined with the sponge layer absorption technology, the WAVEWATCH III wave numerical model is started to calculate the Arctic wave field, and a fourth-order accuracy finite difference discrete format combined with an adaptive artificial viscosity control algorithm is used to establish a sea wave prediction product business processing system to generate effective wave height spatial distribution data, spectral peak period spatial distribution data and principal wave direction spatial distribution data. The attenuation coefficient formula is as follows: ； wherein is a wave energy decay coefficient, is a decay coefficient reference value, is a wave circular frequency, is a circular frequency reference value, to is a pending coefficient, to are reference normalized values for each pending coefficient, respectively, is a sea ice concentration, is a sea ice concentration reference value, is a water depth, is a water depth reference value is a sea ice thickness, is a sea ice thickness reference value; The multi-head attention mechanism is used in the sea ice wave interaction optimization model, and the number of heads is calculated according to the following formula: ； wherein is the number of attention heads, is the number of head reference values, is the sea ice concentration variance, is the sea ice concentration variance reference value, is the wave spectrum bandwidth, is the spectrum bandwidth reference value, is the mesh complexity coefficient, is the mesh complexity coefficient reference value.

2. The Arctic sea wave forecasting method based on the automatic fusion of sea ice concentration density according to claim 1, characterized in that, The steps of constructing the polar orthogonal curve grid system are as follows: four vertex coordinates are selected as 54°N, -45°E, 54°N, 45°E, 54°N, 135°E and 54°N, -135°E to form a square calculation area around the North Pole, the area north of 88°N is set as a land boundary, the grid elements with a resolution of 20km are generated through the coordinate conversion from geographical coordinates to projection coordinates, and the grid longitude data file, the grid latitude data file and the water depth data file are output.

3. The Arctic sea wave forecasting method based on the automatic fusion of sea ice concentration density according to claim 2, characterized in that, The multi-source sea ice concentration automatic fusion system specifically acquires daily sea ice concentration data of the Arctic with a spatial resolution of 6.25km, processes the sea ice concentration data through coordinate conversion, time standardization and bilinear spatial interpolation, and converts the processed sea ice concentration data into a NetCDF format sea ice concentration input file recognized by the WAVEWATCH III wave numerical model.

4. The Arctic sea wave forecasting method based on the automatic fusion of sea ice concentration density according to claim 3, characterized in that, The ECMWF European Centre for Medium-Range Weather Forecasts wind field data automatic acquisition system specifically downloads prediction data containing 10m height wind speed components and wind direction components, starts a backup NCEP global prediction system data source acquisition mechanism when the wind field data quality evaluation coefficient Q is in the range of [0, 0.85), ensures the continuity of the wind field driving data, and outputs a standardized wind field input file for the wave numerical model.

5. The Arctic sea wave forecasting method based on the automatic fusion of sea ice concentration density according to claim 4, characterized in that, The sea ice wave interaction optimization model specifically adopts a strong attenuation parameter combination when the sea ice concentration C is in the range of [0.7, 1.0], adopts a moderate attenuation parameter combination when the sea ice concentration C is in the range of [0.3, 0.7), and adopts a weak attenuation parameter combination when the sea ice concentration C is in the range of [0, 0.3).

6. The Arctic sea wave forecasting method based on the automatic fusion of sea ice concentration density according to claim 5, characterized in that, The open boundary lines are set, specifically a first open boundary line from Newfoundland to Greenland and a second open boundary line from Iceland to Norway, and the boundary wave spectrum density data is provided by the ww3_ounp boundary condition output command of the WAVEWATCH III global wave model.

7. The Arctic sea wave forecasting method based on the automatic fusion of sea ice concentration according to claim 6, characterized in that, The sponge layer absorption technology is specifically to set a sponge layer absorption area within 20 km from the inside of the first open boundary line and the second open boundary line, and the distribution of the artificial viscosity coefficient in the sponge layer absorption area is adjusted by an exponential decay function.

8. The Arctic sea wave forecasting method based on the automatic fusion of sea ice concentration density according to claim 7, characterized in that, The adaptive artificial viscosity control algorithm is specifically to adjust the time integration step to 0.5 times of the original step when the spatial gradient change rate of the wave height in the calculation domain ∇H is greater than or equal to 0.05 m / km, and to adjust the time integration step to 1.5 times of the original step when ∇H is less than 0.01 m / km, so as to ensure the stability of the numerical calculation.

9. The Arctic sea wave forecasting method based on the automatic fusion of sea ice concentration density according to claim 8, characterized in that, The sea wave forecast product commercial post-processing system is specifically to trigger the automatic optimization program of the model parameters to re-calibrate the attenuation coefficient in the IC4M2 sea ice wave parameterization scheme when the root mean square error RMSE between the predicted significant wave height and the Sentinel-3A satellite altimeter observation data is greater than or equal to 0.8 m.

10. The Arctic sea wave forecasting method based on the automatic fusion of sea ice concentration density according to claim 9, characterized in that, The structure of the sea ice wave interaction optimization model is a multi-layer perceptron neural network architecture, which includes an input layer, three hidden layers and an output layer, the number of neurons in the three hidden layers is 128, 64 and 32 respectively, and the ReLU activation function and the Dropout regularization mechanism are adopted.

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