Sea surface height continuous expression and reconstruction method and system for sparse satellite orbit observation

Abstract

The invention discloses a sea surface height continuous expression and reconstruction method and system for sparse satellite orbit observation, and the method comprises the steps: forming an input-output data pair according to three-dimensional time-space coordinates of an observation point of a satellite altimeter and an original along-orbit sea surface height observation value of the satellite altimeter; the three-dimensional time-space coordinates are converted into meshless continuous input coordinates; constructing a space-time continuous expression model based on implicit neural representation on the basis of a network structure of a sine cycle activation function, introducing gradient field consistency constraint and total variation regularization, and constructing comprehensive loss; and according to global sea surface height estimation output by the model, reconstructing a regular grid, calculating a sea surface height gradient, gradient change, local curvature and power agent quantity, completing continuous expression and reconstruction of the sea surface height, and realizing synchronous and high-quality reconstruction of a fine structure and an overall scene of a sea surface height field. And the defects of non-uniform sampling, high-gradient recovery and micro-analysis capability in the prior art can be effectively overcome.

Description

Technical Field

[0001] This invention relates to the field of intelligent remote sensing data processing and spatiotemporal information reconstruction technology, and in particular to a method and system for continuous expression and reconstruction of sea surface height for sparse satellite orbit observations. Background Technology

[0002] Multi-satellite altimeter observations are typically characterized by sparse sampling, uneven coverage, and significant temporal variations, often with spatial discontinuities or large sampling intervals between orbits. Under these conditions, the most widely used approach is interpolation methods based on statistical covariance, such as the optimal interpolation technique commonly employed in operational systems. These methods grid the trajectory data using a spatial covariance model, exhibiting good smoothness and stability at large scales. However, they inherently assume a relatively stationary statistical structure in the ocean field. In real ocean environments, high-gradient regions such as fronts, vortex boundaries, and estuaries exhibit strong non-stationarity, leading to significant limitations in the recovery of detailed structures. Furthermore, reconstruction errors increase significantly when trajectories are sparse or sampling is severely uneven. To improve physical consistency, some techniques use simplified ocean dynamic models to impose constraints on interpolation, such as forward and inverse relaxation using quasi-geostrophic equations, or constructing a dynamic interpolation framework using multi-scale propagation structures. These methods can improve the ability to capture vortex or frontal structures to some extent, but they rely on strong dynamic assumptions, have insufficient adaptability, are highly sensitive to parameter adjustment and model settings, and have a large computational load, which is not conducive to real-time operation and stable deployment in engineering scenarios.

[0003] With the development of deep learning, neural networks have begun to be used for interpolation tasks of ocean observation data. Some methods utilize convolutional networks, recurrent networks, or variational neural networks to build end-to-end reconstruction models, performing well in large-scale smooth regions. However, these methods are generally based on discrete grid output formats, making them highly sensitive to high gradients and irregular sampling. They also struggle to maintain stable performance in fine grids, edge regions, and areas with significant dynamic processes. Furthermore, they cannot provide continuous, differentiable ocean field representations and cannot directly calculate physical quantities such as gradients and divergences, which limits their usability in subsequent dynamic analysis and scientific applications. Summary of the Invention

[0004] Purpose of the invention: The purpose of this invention is to provide a sea surface height reconstruction method for sparse satellite orbit observations that can accurately express local abrupt changes and dynamic boundary characteristics, and has continuous expression and high gradient preservation capabilities; another purpose of this invention is to provide a continuous expression and reconstruction system for sea surface height for sparse satellite orbit observations.

[0005] Technical solution: The method for continuous representation and reconstruction of sea surface height based on sparse satellite orbit observations described in this invention includes...

[0006] (1) Based on the three-dimensional time-space coordinates of the satellite altimeter observation point and the original sea surface height observation value along the satellite altimeter, an input-output data pair is formed;

[0007] (2) Convert the three-dimensional time-space coordinates of the input-output data pair into gridless continuous input coordinates to obtain a three-dimensional continuous coordinate-height sample set;

[0008] (3) Based on the network structure of sinusoidal periodic activation function, a spatial-temporal continuous expression model based on implicit neural representation is constructed. Gradient field consistency constraint and total variation regularization are introduced to construct a comprehensive loss. The spatial-temporal continuous expression model is trained using a three-dimensional continuous coordinate-height sample set.

[0009] (4) The trained space-time continuous representation model outputs a global sea surface height estimate, reconstructs a regular grid, calculates the sea surface height gradient, slope change, local curvature and dynamic surrogate quantity, and completes the continuous representation and reconstruction of sea surface height.

[0010] Furthermore, step (1) is as follows:

[0011] For each satellite altimeter observation point, its spatial longitude, latitude, and observation time are read to obtain a three-dimensional time-space coordinate vector; the corresponding sea surface height observation value along the orbit is read to form an input-output data pair.

[0012] Based on the quality indicators provided by the observation system, input-output data pairs corresponding to observation points marked as low confidence, invalid, or disturbed are removed.

[0013] Based on the set physical threshold, delete outliers that clearly do not conform to the reasonable sea surface height range;

[0014] Statistical detection methods are used to identify and remove isolated spike noise points, jump points, or numerical abrupt changes.

[0015] The geographic coordinates, time references, and sea surface height references are standardized.

[0016] Furthermore, the benchmark consistency process includes the standardization of time formats, latitude and longitude formats, and the standardization and adjustment of sea level height benchmarks.

[0017] Furthermore, in step (2), the three-dimensional time-space coordinates of the input-output data pair are converted into meshless continuous input coordinates, as follows:

[0018] By employing linear normalization and scale-adaptive mapping, the longitude, latitude, and time in the three-dimensional time-space coordinates are scaled to standard intervals, and after normalization, three-dimensional continuous coordinates are obtained.

[0019] Furthermore, in step (3), the comprehensive loss L is

[0020]

[0021] in, For data fitting loss, For gradient consistency constraint loss, The loss is the regularization loss of the total variation. and For regularization weights.

[0022] Furthermore, gradient consistency constraint loss for

[0023]

[0024]

[0025] Where M is the total number of sample points. This is the gradient vector of the model at the corresponding sample point, representing the continuous expression.

[0026] Furthermore, the total variation regularization loss for

[0027]

[0028] Where M is the total number of sample points. and Let represent the first-order partial derivatives of the continuous expression model along the longitude and latitude directions at the corresponding sample points, respectively. This is the error term.

[0029] Furthermore, the method for continuous expression and reconstruction of sea surface height for sparse satellite orbit observations described in this invention also includes evaluating the effect of continuous expression and reconstruction of sea surface height through point value error, normalization accuracy index and spatiotemporal spectral resolution.

[0030] The sea surface height continuous representation and reconstruction system for sparse satellite orbit observations described in this invention includes:

[0031] The ocean observation data preprocessing module is used to form input-output data pairs based on the three-dimensional time-space coordinates of the satellite altimeter observation points and the original sea surface height observations along the satellite altimeter's orbit.

[0032] The spatial-temporal coordinate continuous encoding module is used to convert the three-dimensional temporal-spatial coordinates in the input-output data pair into gridless continuous input coordinates to obtain a three-dimensional continuous coordinate-height sample set.

[0033] The continuous expression network model construction module constructs a spatial-temporal continuous expression model based on a network structure with a sinusoidal periodic activation function. It introduces gradient field consistency constraints and total variation regularization to construct a comprehensive loss and trains the spatial-temporal continuous expression model using a three-dimensional continuous coordinate-height sample set.

[0034] The reconstruction output module is used to output a global sea surface height estimate from the trained space-time continuous representation model, reconstruct a regular grid, calculate the sea surface height gradient, slope change, local curvature, and dynamic surrogate, and complete the continuous representation and reconstruction of sea surface height.

[0035] Beneficial Effects: Compared with existing technologies, the significant advantages of this invention are: 1. This invention does not rely on grids and directly models based on original observation points using a continuous expression mechanism, improving stability and detail recovery capabilities under sparse coverage and trajectory discontinuity conditions, and solving the problem of significantly reduced reconstruction accuracy when observation density decreases or trajectory distribution is uneven; 2. By introducing structured gradient constraints, this invention enables the reconstruction results to accurately express local abrupt changes and dynamic boundary features while maintaining overall consistency, solving the problem of maintaining structural sharpness and easily causing excessive smoothing of details in high-gradient regions such as fronts and vortices; 3. By constructing a continuous function expression that can be directly evaluated across the entire domain and combining it with a structured gradient constraint mechanism, this invention achieves synchronous and high-quality reconstruction of the fine structure of the sea surface height field and the overall scene, thereby significantly improving the detail recovery capability and overall reconstruction level in complex marine environments, and effectively overcoming the shortcomings of existing technologies in non-uniform sampling, high gradient recovery, and differentiability analysis capabilities. Attached Figure Description

[0036] Figure 1 This is a flowchart of the present invention;

[0037] Figure 2 This is a high-reconstruction rendering of the sea surface. Detailed Implementation

[0038] The method for continuous representation and reconstruction of sea surface height based on sparse satellite orbit observations described in this invention includes...

[0039] (1) Based on the three-dimensional time-space coordinates of the satellite altimeter observation point and the original sea surface height observation value along the satellite altimeter, an input-output data pair is formed.

[0040] For each satellite altimeter observation point, its spatial longitude, latitude, and observation time are read to obtain a three-dimensional time-space coordinate vector; the corresponding sea surface height observation value along the orbit is read to form an input-output data pair.

[0041] Based on the quality indicators provided by the observation system, input-output data pairs corresponding to observation points marked as low confidence, invalid, or disturbed are removed.

[0042] Based on the set physical threshold, delete outliers that clearly do not conform to the reasonable sea surface height range;

[0043] Statistical detection methods are used to identify and remove isolated spike noise points, jump points, or numerical abrupt changes.

[0044] The geographic coordinates, time references, and sea surface height references are standardized.

[0045] Furthermore, the benchmark consistency process includes the standardization of time formats, latitude and longitude formats, and the standardization and adjustment of sea level height benchmarks.

[0046] (2) The three-dimensional time-space coordinates of the input-output data pair are converted into gridless continuous input coordinates to obtain a three-dimensional continuous coordinate-height sample set. Linear normalization and scale-adaptive mapping are used to scale the longitude, latitude and time in the three-dimensional time-space coordinates to the standard interval, and after normalization, the three-dimensional continuous coordinates are obtained.

[0047] (3) Based on the network structure of sinusoidal periodic activation function, a spatial-temporal continuous expression model based on implicit neural representation is constructed. Gradient field consistency constraint and total variation regularization are introduced to construct a comprehensive loss. The spatial-temporal continuous expression model is trained using a three-dimensional continuous coordinate-height sample set.

[0048] The overall loss L is

[0049]

[0050] in, For data fitting loss, For gradient consistency constraint loss, The loss is the regularization loss of the total variation. and For regularization weights.

[0051] Gradient consistency constraint loss for

[0052]

[0053]

[0054] Where M is the total number of sample points. This is the gradient vector of the model at the corresponding sample point, representing the continuous expression.

[0055] Total variation regularization loss for

[0056]

[0057] Where M is the total number of sample points. and Let represent the first-order partial derivatives of the continuous expression model along the longitude and latitude directions at the corresponding sample points, respectively. This is the error term.

[0058] (4) The trained space-time continuous representation model outputs a global sea surface height estimate, reconstructs a regular grid, calculates the sea surface height gradient, slope change, local curvature and dynamic surrogate quantity, and completes the continuous representation and reconstruction of sea surface height.

[0059] (5) The effect of continuous expression and reconstruction of sea surface height is evaluated by point value error, normalization accuracy index and spatiotemporal spectrum resolution.

[0060] The sea surface height continuous representation and reconstruction system for sparse satellite orbit observations described in this invention includes:

[0061] The ocean observation data preprocessing module is used to form input-output data pairs based on the three-dimensional time-space coordinates of the satellite altimeter observation points and the original sea surface height observations along the satellite altimeter's orbit.

[0062] The spatial-temporal coordinate continuous encoding module is used to convert the three-dimensional temporal-spatial coordinates in the input-output data pair into gridless continuous input coordinates to obtain a three-dimensional continuous coordinate-height sample set.

[0063] The continuous expression network model construction module constructs a spatial-temporal continuous expression model based on a network structure with a sinusoidal periodic activation function. It introduces gradient field consistency constraints and total variation regularization to construct a comprehensive loss and trains the spatial-temporal continuous expression model using a three-dimensional continuous coordinate-height sample set.

[0064] The reconstruction output module is used to output a global sea surface height estimate from the trained space-time continuous representation model, reconstruct a regular grid, calculate the sea surface height gradient, slope change, local curvature, and dynamic surrogate, and complete the continuous representation and reconstruction of sea surface height.

[0065] A certain sea area was selected as the experimental area. This area has abundant fishery and shipping activities, as well as a large number of mesoscale and sub-mesoscale vortex structures. It is a typical highly dynamic area and is suitable as the test object of this invention.

[0066] Step 1: Preprocessing of marine observation data

[0067] Step 1.1 Experimental Area and Data Sources

[0068] Regarding observational data, this embodiment uses along-orbit SSH measurements from multiple operational altimeter satellites, including new orbit data from Haiyang-2B, Jason-3, Sentinel-3A, Sentinel-3B, and CryoSat-2. The observational data from Haiyang-2B, Jason-3, Sentinel-3A, and Sentinel-3B are used for model training; the CryoSat-2 new orbit data is not used for training and is exclusively used for model performance evaluation, ensuring that the evaluation results reflect the model's true interpolation capability under unknown orbital conditions. The experimental period is from January 1, 2021 to March 31, 2021. To avoid bias caused by time overlap between the training and test sets, this embodiment uses multi-constellation observations from the first half of January and the second half of March as training data, while using CryoSat-2 new orbit observations from January 15 to March 15 as an independent test set. This partitioning method ensures that the model cannot obtain any temporal or spatial information about new orbits during the testing phase, thus providing a rigorous test of the model's generalization ability. The data preprocessing module includes the following steps:

[0069] Step 1.2 Data Cleaning and Quality Control

[0070] In this invention, all satellite observation points are represented as three-dimensional time-space coordinate vectors:

[0071]

[0072] in Longitude Latitude For time. The corresponding sea surface height observation along the track is recorded as:

[0073]

[0074] The raw SSH data along the orbit of each satellite was filtered as follows:

[0075] Based on the quality flag filter, read the official quality flag field and remove areas with poor signal quality, abnormal reflection waveforms, unstable instrument status, and high risk of ground interference (such as near the coast < 10 km).

[0076] Remove samples with physically unreasonable values ​​that meet the following conditions:

[0077] or

[0078] Beyond the area Or peaks that are 3 times the MAD (median absolute deviation), outliers with consecutive jumps exceeding 30 cm on a single track, and observations that exceed the physical range (such as exceeding ±3 m) should be deleted.

[0079] Unified data format: Multi-constellation observations are unified to the WGS-84 geographic coordinate system, the sea surface height system in meters (m), and the same time base (2021-01-01 00:00) to ensure consistency between different satellite data.

[0080] Step 2: Spatial-Temporal Coordinate Continuous Encoding Module

[0081] This step maps physical coordinates to a numerically stable normalized coordinate space, enabling the model to perform direct calculations at any coordinate point without the need for meshing.

[0082] 2.1 Define the boundary constants of the region

[0083]

[0084]

[0085] (sky)

[0086] 2.2 Continuous Coordinate Normalization

[0087] To enable the continuous expression model to accept input at arbitrary sampling points, this invention performs linear normalization on each input coordinate, resulting in:

[0088]

[0089]

[0090]

[0091] 2.3 Model Input Vector

[0092]

[0093] The model only needs to take this vector as input; no mesh needs to be built.

[0094] Step 3: Continuous Expression Model Module Based on Periodic Activation Function

[0095] This module enables the modeling of sea surface height as a three-dimensional continuous function.

[0096] 3.1 Network Symbol System

[0097] network:

[0098] Parameter set:

[0099] Hidden layer output:

[0100] 3.2 Model Structure

[0101]

[0102] Each floor:

[0103] Final output:

[0104] 3.3 Data Fitting Loss

[0105]

[0106] Step 4: Gradient Field Constraints and Total Variation (TV) Regularization Module

[0107] 4.1 Analytical Differentiation Ability

[0108] Because this invention uses a continuous expression model, the output function can be directly processed. Taking the coordinate derivative, the first-order partial derivative is as follows:

[0109]

[0110] Obtain the gradient vector:

[0111]

[0112] 4.2 Gradient Consistency Constraint (Suppressing Oversmoothing)

[0113]

[0114] 4.3 TV Regularization (Suppressing Oscillations)

[0115]

[0116] 4.4 Total Losses

[0117]

[0118] in , For regularized weights, this method is more accurate than the traditional differential TV operator and does not introduce mesh noise.

[0119] Step 5: Reconstruction Result Output Module

[0120] Once the model is trained, the following outputs can be provided to the user:

[0121] 5.1 Sea Surface Height Estimation at Arbitrary Spatiotemporal Points

[0122] enter Normalization yields:

[0123]

[0124] 5.2 Custom Mesh Generation

[0125] Configurable settings:

[0126] Target time resolution (e.g., 1-hour interval, daily);

[0127] Target spatial resolution (0.1°, 0.05° or finer).

[0128] This will generate interpolation (track recovery) on any trajectory.

[0129] 5.3 First and Second Derivative Output (Dynamic Diagnosis)

[0130] Gradient intensity (frontal index):

[0131]

[0132] Second derivatives (curvature, Laplace, etc.) are calculated directly by automatic differentiation without the need for difference.

[0133] Step 6: Comparison and Evaluation Module

[0134] This module is used to verify the effectiveness, stability, and superiority of the method of the present invention under real ocean satellite observation conditions. To ensure the reliability of the evaluation results, this module includes an experimental environment description, data sources and construction, model parameter settings, evaluation index system, comparison method design, and result analysis process. Those skilled in the art can reproduce the experimental process on any equivalent computing platform according to the following description.

[0135] 6.1 Experimental Environment

[0136] The evaluation of this invention was conducted on a high-performance workstation equipped with an NVIDIA GeForce RTX 4080 GPU, featuring 16 GB of video memory, 64 GB of system memory, and a 12th-generation Intel i9 processor. The deep learning environment was built using Python 3.9 and PyTorch 2.1. Numerical computations were performed using NumPy 1.25 and SciPy 1.11, and all plotting and diagnostics were performed using Matplotlib, xarray, and xESMF. To ensure the stability of model training, a random seed of 1234 was used, making all training and validation processes reproducible. During the experiments, all training sessions took approximately 1–2 hours on a single GPU; the actual runtime varied slightly depending on the amount of input data and the TV regularization coefficient. The above experimental environment can be reproduced on different hardware platforms (such as NVIDIA A100, V100, and 3090), as long as at least 12 GB of video memory is maintained to complete all training.

[0137] 6.2 Model Parameter Settings

[0138] The core model of this invention is a continuous representation neural network with total variation (TV) gradient constraints. Its main parameter configurations are as follows:

[0139] (1) **Network structure:** 3 hidden layers, 256 neurons per layer; input dimensions are three (longitude, latitude, time), and output is a single-value SSH.

[0140] (2) **Activation function:** The sine function sin(·) is used, and a high-frequency weight initialization method is used to enable the network to capture the rapidly changing structure of SSH, such as fronts and vortex edges.

[0141] (3) **Frequency coefficient:** First-level frequency factor Used to accurately capture high-frequency variations; deep frequency factor It is used to stabilize low-frequency changes.

[0142] (4) **Optimizer:** Adam is used, with an initial learning rate set to It automatically drops to [a certain level] in the later stages of training. .

[0143] (5) **Batch size and number of iterations:** The batch size is set to 1024 and the iterations are 200 rounds, which can ensure model convergence and avoid overfitting.

[0144] (6) **Loss Function:** Includes a data consistency term and a continuous TV term, and its overall form is:

[0145]

[0146] The TV term comes directly from the model's automatic differentiation.

[0147]

[0148] , The value is adjusted in the range of 0.1–1.0 to balance detail preservation and noise suppression.

[0149] 6.3 Evaluation Index System

[0150] To fully verify the performance of the method of this invention, three complementary evaluation systems were constructed: point value error, normalized accuracy index, and spatiotemporal spectral resolution.

[0151] Point Value RMSE Indicator

[0152]

[0153] Used to measure the model's ability to accurately reconstruct local SSH values.

[0154] RMSE-based metrics

[0155] To standardize the error magnitude across different time periods and dynamic intensities, this invention introduces a normalized error score:

[0156]

[0157] This represents the root mean square of the observed true value; the closer this score is to 1, the higher the reconstruction accuracy.

[0158] This invention pays particular attention to the model's analytical capability for dynamic structures such as vortices and fronts, therefore, it introduces spectral domain evaluation:

[0159]

[0160] Based on the intersection of the curve and the 0.5 intercept, we can define:

[0161] --Minimum analyzable spatial scale

[0162] --Minimum resolvable time scale

[0163] This metric reflects the model’s true dynamic capture capability, not just point value error.

[0164] 6.4 Comparison Methods and Specific Procedures

[0165] To verify the robustness and universality of the method of this invention under different observation densities, complex dynamic backgrounds, and multi-satellite joint sampling conditions, this embodiment selects several representative advanced interpolation and assimilation methods in the current sea surface height (SSH) reconstruction field as comparative benchmarks. The comparative methods cover traditional covariance interpolation, dynamic equation-constrained methods, multi-scale interpolation methods, and deep learning-variable fusion methods, specifically including:

[0166] Covariance Optimal Interpolation Method (DUACS / BASELINE OI): This method uses a classic optimal interpolation framework based on empirical covariance matrices to estimate the missing regions by constructing spatial correlation functions. It is currently the standard technical approach for commercial SSH products.

[0167] The Back-and-Forth Dynamic Constraint Method (BFN-QG) is based on the quasi-geostrophic dynamic equations (QG dynamic framework). It first performs forward simulation, then uses observational data for backward correction, gradually approximating the observations through multiple iterations of "forward-backward" processes. This method maintains dynamic consistency but is highly sensitive to the approximation capability of the model equations.

[0168] BFN-QG method with coastal boundary conditions: Based on the standard BFN-QG, boundary constraints at the coastline are further introduced to make the dynamic solution more consistent with the physical characteristics of the real coastline, and it is suitable for nearshore areas with strong topographic relief.

[0169] Wavelet domain reconstruction method (WaveVar): By decomposing the sea surface height signal within a multi-scale wavelet framework and reconstructing missing values ​​at different scales, it can capture local strong gradient structures and fine-scale variability better.

[0170] The comparison process is as follows:

[0171] The method of this invention is systematically compared with the aforementioned methods under the same dataset and experimental configuration to comprehensively evaluate its advantages in terms of global error, fine-scale resolution, stability, and dynamic structure reconstruction. The comparison process is as follows:

[0172] (1) Uniform input data: All methods use only the observations along the track corresponding to the training set and do not use the test set information.

[0173] (2) Rebuild SSH field: All methods output a uniform grid (0.1°×0.1°) and a uniform time step (daily).

[0174] (3) Extract test set point values: Map the CryoSat–2 new orbit observations to the reconstruction fields of all methods to unify time and space alignment.

[0175] (4) Calculation error and spectral distribution: RMSE is calculated for each method. , .

[0176] 6.5 Interpretation of Evaluation Results:

[0177] The experimental results of this invention and the methods described above are shown in Table 1. The experiments show that different methods exhibit significant differences in global accuracy and fine-scale resolution: on the one hand, the WaveVar method performs best in terms of global RMSE normalization score, indicating its advantage in capturing large-scale background changes in the reconstructed field; on the other hand, the method of this invention performs best in terms of fine-scale resolution (shortest resolvable spatial wavelength λ). x The invention achieved state-of-the-art results, significantly improving upon similar methods from 148–118 km to approximately 106 km. This result demonstrates that the invention can reconstruct more detailed local sea surface height structures, including high-gradient regions such as eddy boundaries and fronts, while maintaining overall error stability. Comprehensive analysis reveals that traditional covariance OI methods rely heavily on empirical correlation scales, making it difficult to recover high-frequency local structures; the BFN-QG method is limited by model dynamic assumptions, limiting its adaptability to complex dynamic processes; and while WaveVar has advantages in multi-scale processing, its gradient structure remains susceptible to noise propagation. In contrast, the continuous expression model of this invention can form a smooth and consistent function mapping across the entire spatial domain, while total variation regularization further limits the aberrant amplification of local gradients, achieving a better balance between large-scale consistency and fine-scale fidelity.

[0178] Experiments show that the method of the present invention has high stability, wide applicability and fine-scale reconstruction capability in real satellite data scenarios, and can provide higher resolution and more dynamic sea surface height reconstruction results for marine monitoring operations, which has significant engineering application value.

[0179] Table 1: Comparison of the effects of different methods

[0180] method BASELINE OI 0.674136 148 BFN_QG 0.720857 125 BFNQG_coast 0.724554 125 WaveVar 0.759956 118 INR 0.747545 106

[0181] like Figure 2As shown in the figure, the data along the track at a random time point, the corresponding reconstructed sea surface height, and the calculated sea surface height gradient value are presented. It can be seen from the figure that although the track observations exhibit a clearly irregular striped distribution in space, and there are large unobserved areas between the tracks, the model of this invention can still generate a spatially continuous and structurally complete sea surface height field throughout the entire study domain. The reconstruction results not only maintain consistency with the observations at track intersections but also exhibit a smooth and physically reasonable transition in areas far from the observation locations. This indicates that the continuous representation model of this invention can effectively learn the spatial variation patterns of sea surface height at multiple scales without relying on regular grids or dense observations. The sea surface height gradient calculated based on the reconstructed field further demonstrates the advantages of this invention. High-rate-of-change regions such as fronts and vortex edges can be clearly distinguished in the gradient field, and their spatial structure is consistent with the dynamic characteristics of the sea surface, showing that this invention can directly obtain high-precision analytical gradient information from the model output without using numerical difference grids.

Claims

1. A method for continuous representation and reconstruction of sea surface height based on sparse satellite orbit observations, characterized in that, include (1) Based on the three-dimensional time-space coordinates of the satellite altimeter observation point and the original sea surface height observation value along the satellite altimeter, an input-output data pair is formed; (2) Convert the three-dimensional time-space coordinates of the input-output data pair into gridless continuous input coordinates to obtain a three-dimensional continuous coordinate-height sample set; (3) Based on the network structure of sinusoidal periodic activation function, a spatial-temporal continuous expression model based on implicit neural representation is constructed. Gradient field consistency constraint and total variation regularization are introduced to construct a comprehensive loss. The spatial-temporal continuous expression model is trained using a three-dimensional continuous coordinate-height sample set. (4) The trained space-time continuous representation model outputs a global sea surface height estimate, reconstructs a regular grid, calculates the sea surface height gradient, slope change, local curvature and dynamic surrogate quantity, and completes the continuous representation and reconstruction of sea surface height.

2. The method for continuous representation and reconstruction of sea surface height for sparse satellite orbit observations according to claim 1, characterized in that, Step (1) is as follows: For each satellite altimeter observation point, its spatial longitude, latitude, and observation time are read to obtain a three-dimensional time-space coordinate vector; the corresponding sea surface height observation value along the orbit is read to form an input-output data pair. Based on the quality indicators provided by the observation system, input-output data pairs corresponding to observation points marked as low confidence, invalid, or disturbed are removed. Based on the set physical threshold, delete outliers that clearly do not conform to the reasonable sea surface height range; Statistical detection methods are used to identify and remove isolated spike noise points, jump points, or numerical abrupt changes. The geographic coordinates, time references, and sea surface height references are standardized.

3. The method for continuous representation and reconstruction of sea surface height for sparse satellite orbit observations according to claim 2, characterized in that, The standardization process includes standardizing the time format, the latitude and longitude format, and the sea level height standard.

4. The method for continuous representation and reconstruction of sea surface height for sparse satellite orbit observations according to claim 1, characterized in that, In step (2), the three-dimensional time-space coordinates of the input-output data pair are converted into meshless continuous input coordinates, as follows: By employing linear normalization and scale-adaptive mapping, the longitude, latitude, and time in the three-dimensional time-space coordinates are scaled to standard intervals, and after normalization, three-dimensional continuous coordinates are obtained.

5. The method for continuous representation and reconstruction of sea surface height for sparse satellite orbit observations according to claim 1, characterized in that, In step (3), the overall loss L is in, For data fitting loss, For gradient consistency constraint loss, The loss is the regularization loss of the total variation. and For regularization weights.

6. The method for continuous representation and reconstruction of sea surface height for sparse satellite orbit observations according to claim 1, characterized in that, Gradient consistency constraint loss for Where M is the total number of sample points. This is the gradient vector of the model at the corresponding sample point, representing the continuous expression.

7. The method for continuous representation and reconstruction of sea surface height for sparse satellite orbit observations according to claim 1, characterized in that, Total variation regularization loss for Where M is the total number of sample points. and Let represent the first-order partial derivatives of the continuous expression model along the longitude and latitude directions at the corresponding sample points, respectively. This is the error term.

8. The method for continuous representation and reconstruction of sea surface height for sparse satellite orbit observations according to claim 1, characterized in that, It also includes assessing the effectiveness of continuous expression and reconstruction of sea surface height through point value error, normalization accuracy index, and spatiotemporal spectral resolution.

9. A system for continuous expression and reconstruction of sea surface altitude for sparse satellite orbit observations, characterized in that, include The ocean observation data preprocessing module is used to form input-output data pairs based on the three-dimensional time-space coordinates of the satellite altimeter observation points and the original sea surface height observations along the satellite altimeter's orbit. The spatial-temporal coordinate continuous encoding module is used to convert the three-dimensional temporal-spatial coordinates in the input-output data pair into gridless continuous input coordinates to obtain a three-dimensional continuous coordinate-height sample set. The continuous expression network model construction module constructs a spatial-temporal continuous expression model based on a network structure with a sinusoidal periodic activation function. It introduces gradient field consistency constraints and total variation regularization to construct a comprehensive loss and trains the spatial-temporal continuous expression model using a three-dimensional continuous coordinate-height sample set. The reconstruction output module is used to output a global sea surface height estimate from the trained space-time continuous representation model, reconstruct a regular grid, calculate the sea surface height gradient, slope change, local curvature, and dynamic surrogate, and complete the continuous representation and reconstruction of sea surface height.

Images