A method for dynamically fusing and predicting temporal and spatial data of sediment scouring and deposition

Abstract

This invention provides a dynamic fusion and prediction method for spatiotemporal data of sediment erosion and deposition, belonging to the technical field of dynamic fusion and prediction of spatiotemporal data of sediment erosion and deposition. This invention collects multi-temporal satellite remote sensing inversion water depth data, field-measured hydrological and sediment sequence data, and output data from a three-dimensional sediment numerical model. It projects the analysis weight vector onto the manifold tangent space and performs manifold projection correction. Based on the dynamic fusion quality evaluation function, it dynamically adjusts the number of set members and the localization radius of covariance. The fusion historical time-series features are input into an artificial intelligence prediction model with the Mamba structured state-space model as its backbone. Through causal dilatational convolution multi-scale feature extraction and self-referential iterative refinement, it outputs hourly predicted fields of erosion and deposition thickness and suspended sediment concentration. This solves the technical problem of degradation in the accuracy of medium- and long-term erosion and deposition prediction caused by the lack of physical consistency constraints during the fusion of multi-source heterogeneous sediment spatiotemporal data.

Description

Technical Field

[0001] This invention belongs to the field of dynamic fusion and prediction technology of spatiotemporal data of sediment erosion and deposition. Specifically, it relates to a method for dynamic fusion and prediction of spatiotemporal data of sediment erosion and deposition. Background Technology

[0002] Sediment erosion and deposition prediction is a core technical requirement in estuarine and coastal engineering, port and waterway maintenance, and flood control and disaster reduction. Currently, the acquisition of sediment erosion and deposition status mainly relies on three types of methods: multi-temporal satellite remote sensing inversion of water depth data, field-measured hydrological and sediment sequence data, and output data from three-dimensional sediment numerical models. In practical engineering applications, these three types of data sources have been widely used for sediment state estimation, and are fused using traditional weighted averaging or Kalman filtering data assimilation methods to improve the spatial coverage and temporal continuity of sediment state estimation.

[0003] However, traditional weighted mean fusion methods are prone to pseudo-multimodal phenomena when there are significant differences in the probability distribution of each data source, and cannot preserve the physical rationality of the log-normal or heavy-tailed distribution of sediment concentration. Classical ensemble Kalman filtering leads to filter divergence in high-dimensional nonlinear sediment dynamic systems due to covariance estimation errors, and lacks constraints on the inherent nonlinear manifold structure of the sediment dynamic system. After correction, the ensemble members may deviate from the physically realizable state space.

[0004] In existing technologies, the heterogeneous distribution characteristics of multi-source sediment data and the nonlinear manifold structure of sediment dynamic systems are not effectively modeled and constrained during data fusion and aggregation, resulting in the inability to guarantee the physical consistency of the fused analysis field. Consequently, medium- and long-term scour and deposition prediction models driven by fused historical time-series characteristics exhibit systematic biases under extreme hydrological conditions, leading to a significant degradation in prediction accuracy. In other words, existing technologies suffer from a technical problem: the lack of physical consistency constraints during the fusion of multi-source heterogeneous sediment spatiotemporal data results in the degradation of medium- and long-term scour and deposition prediction accuracy. Summary of the Invention

[0005] In view of this, the present invention provides a dynamic fusion prediction method for spatiotemporal data of sediment erosion and deposition, which can solve the technical problem in the prior art where the lack of physical consistency constraints during the fusion of multi-source heterogeneous spatiotemporal data of sediment leads to the degradation of the accuracy of medium- and long-term erosion and deposition prediction.

[0006] This invention is implemented as follows: This invention provides a method for dynamic fusion and prediction of spatiotemporal data of sediment erosion and deposition, comprising the following steps:

[0007] Collect multi-temporal satellite remote sensing inversion water depth data, field measured hydrological and sediment sequence data and time-by-time output data of three-dimensional sediment numerical model, complete coordinate registration and format standardization processing according to unified spatiotemporal resolution, and construct a spatiotemporal data assimilation framework.

[0008] Based on the data from each data source in the spatiotemporal data assimilation framework, the optical detectability index of each data source is calculated. For areas where the optical detectability index is lower than the effective optical detection threshold, the data source is switched to a multibeam bathymetry data source. Based on the historical verification error statistics of each data source, a concentration-dependent adaptive observation error weight is set for each data source. The Wasserstein centroid distribution of the multi-source data is calculated, and the fusion analysis field point estimate and assimilation uncertainty are output.

[0009] Based on the fusion analysis field point estimation and assimilation uncertainty, within the framework of the physical constraint manifold embedding adaptive local ensemble transformation filtering algorithm, low-dimensional intrinsic manifold coordinates are extracted, the covariance localization radius is dynamically calculated, non-uniform localization schemes are applied to the deep trench region and the shallow shoal region respectively, the analysis weight vector is projected onto the low-dimensional intrinsic manifold tangent space, the ensemble analysis step is completed and the manifold projection correction is performed, and the corrected ensemble analysis members are output.

[0010] Based on the corrected set analysis members, the set dispersion, observational information statistics and manifold projection residuals are calculated and substituted into the scour-deposition dynamic fusion quality assessment function to obtain the scour-deposition fusion quality assessment value. The number of set members and the localization radius of covariance are adjusted according to the interval to which the scour-deposition fusion quality assessment value belongs, triggering set expansion or set reduction processing.

[0011] Based on the fusion historical time series characteristics of the adjusted and corrected set analysis members, the input is the spatial prediction model of sediment erosion and deposition state, and the output is the hourly prediction field of erosion and deposition thickness and the prediction field of suspended sediment concentration.

[0012] The spatiotemporal data assimilation framework refers to a data fusion architecture that integrates multi-temporal satellite remote sensing inversion water depth data, field measured hydrological and sediment sequence data, and hourly output data from three-dimensional sediment numerical models, after coordinate registration and format standardization using a unified spatiotemporal grid.

[0013] The optical detectability index refers to a dimensionless index calculated by combining the backscattering intensity of water in the satellite multispectral bands with the estimated suspended sediment concentration. It is used to determine whether the current optical depth of the water body meets the effective detection conditions for satellite depth inversion.

[0014] The effective optical detection threshold was determined by conducting on-site synchronous measurements and satellite overpass comparison experiments under different sediment concentration gradients, statistically analyzing the segmented inflection points of the inversion error as sediment concentration changes, and then performing regression analysis.

[0015] The concentration-dependent adaptive observation error weight refers to the diagonal elements of the observation error covariance matrix that dynamically changes with the suspended sediment concentration in the water body. The higher the suspended sediment concentration, the greater the error weight of the water depth data retrieved by satellite remote sensing. The mapping relationship between the weight and the suspended sediment concentration is determined through multiple on-site synchronous observation experiments and error statistical regression.

[0016] The calculation of the Wasserstein centroid distribution adopts the Sinkhorn iterative algorithm, which models the estimates of the same sediment state variable from multiple sources as probability distributions carrying uncertainty. The Wasserstein-2 distance is used to measure the distribution difference, the conditional mean of the Wasserstein centroid distribution is used as the fusion analysis field point estimate, and the conditional variance of the Wasserstein centroid distribution is used as the assimilation uncertainty output.

[0017] Specifically, the extraction of low-dimensional intrinsic manifold coordinates is achieved by using the diffusion mapping algorithm to perform manifold learning on the state vectors of set members. The diffusion mapping algorithm is implemented by constructing a heat kernel similarity matrix between data points and performing spectral decomposition on the normalized Laplacian matrix.

[0018] The covariance localization radius is dynamically calculated based on the product of the estimated sediment transport velocity and the assimilation time step. The ratio of the covariance localization radius of the deep trough region to that of the shallow shoal region is determined through geomorphic unit clustering experiments and assimilation error sensitivity analysis.

[0019] The calculation formula for the dynamic fusion quality evaluation function of scouring and silting is as follows: ,in This is the quality assessment value for siltation and erosion fusion. For set discreteness, To observe the new information statistics, Let the norm of the projected residuals of the manifold be denoted as . , , The weighting coefficients are satisfied. .

[0020] The interval to which the sludge-flushing fusion quality assessment value belongs corresponds to three processing strategies: when the sludge-flushing fusion quality assessment value is lower than the first quality threshold, the current number of set members and the localization radius of covariance remain unchanged; when the sludge-flushing fusion quality assessment value is between the first quality threshold and the second quality threshold, the number of set members is increased and the localization radius of covariance is expanded; when the sludge-flushing fusion quality assessment value is not lower than the second quality threshold, the set is expanded to the maximum number of set members and global manifold relearning processing is initiated.

[0021] The sediment erosion and deposition state space prediction model uses the Mamba structured state space model as its backbone. The input layer incorporates multiple causal dilatational convolution parallel branches, with the dilation rate of each branch calculated according to... The outputs of each causal dilatational convolution parallel branch are arranged in an ascending order and then fused through a learnable time-varying gating matrix before being fed into the backbone of the Mamba structured state-space model.

[0022] Among them, the discretization matrix of the state space equations of the backbone of the Mamba structured state space model. The eigenvalue range is constrained by the sediment characteristic timescale derived from Rouse's suspended sediment vertical distribution theory, and the sediment settling time. satisfy ,Will The corresponding frequency range is mapped to the discretized matrix. The spectral radius constraint interval.

[0023] The sediment erosion state space prediction model is internally designed with a self-reference iterative refinement module. The initial prediction output is injected back into the input layer and spliced ​​with the fused historical time series features. Through multiple internal iterations, the residual between the predicted value and the physical conservation constraints is gradually reduced. Each iteration assimilates the latest observation increment to correct the hidden state vector.

[0024] The modified set analysis members are compressed using low-rank sparse decomposition. Specifically, singular value decomposition is used to retain the first few major singular value modes to reconstruct the set member state vector. Combined with memory-mapped file technology, the set member state vector is asynchronously prefetched to the graphics processor memory in blocks. A mixed precision strategy is used to store it in FP16 format and calculate it in FP32 format.

[0025] Wherein, the first quality threshold is 0.6, the second quality threshold is 0.85; the localization radius of covariance in the deep channel region is 1.5 to 3.0 times that of the localization radius of covariance in the shallow shoal region; the number of main singular value modes retained by singular value decomposition is 50 to 100; the historical statistical window length of weight stability is 30 to 90 assimilation time steps; the total number of network layers of the sediment erosion and deposition state space prediction model is 12 to 24, and the dimension of the hidden state vector is 128 to 512.

[0026] This invention constructs a Wasserstein centroid distribution fusion framework based on optimal transport theory and an adaptive local ensemble transformation filtering algorithm with physical constraint manifold embedding. This eliminates the heterogeneity probability distribution differences of multi-source sediment data through geometric interpolation. At the same time, it explicitly embeds the nonlinear manifold structure of the sediment dynamic system into the ensemble integration process, so that the members of the modified ensemble analysis are always located in the neighborhood of the physically realizable state space.

[0027] The pseudo-multimodal phenomenon that occurs in traditional weighted mean fusion when the distribution patterns of various data sources differ significantly stems from the disruption of the distribution geometry caused by the linear superposition assumption. This invention replaces linear fusion with a Wasserstein centroid distribution, achieving geometric interpolation between distributions within an entropy-regularized optimal transmission framework. This fundamentally eliminates the pseudo-multimodal phenomenon, allowing the uncertainty structure of the fused analysis field to more accurately reflect the physical state of the sediment system. The filtering divergence problem caused by the classical set integration method neglecting the inherent nonlinear geometry of the sediment dynamic system is overcome by the diffusion map manifold constraint, ensuring that the set update step strictly follows the inherent nonlinear geometry of the sediment dynamic system.

[0028] In summary, this invention solves the technical problem mentioned in the background art of the degradation of medium- and long-term sedimentation prediction accuracy due to the lack of physical consistency constraints during the fusion of multi-source heterogeneous sediment spatiotemporal data. Attached Figure Description

[0029] Figure 1 This is a flowchart of the method of the present invention.

[0030] Figure 2 This is a comparison chart showing the evolution of field point estimation and assimilation uncertainty over time in a fusion analysis.

[0031] Figure 3 This is a graph showing the dynamic changes in the quality assessment value of siltation and sedimentation as a function of hydrological conditions. Detailed Implementation

[0032] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below.

[0033] like Figure 1 The diagram shown is a flowchart of a dynamic fusion and prediction method for spatiotemporal data of sediment erosion and deposition provided by this invention. This method includes the following steps:

[0034] S01. Collect multi-temporal satellite remote sensing inversion water depth data, field measured hydrological and sediment sequence data and three-dimensional sediment numerical model hourly output data, complete coordinate registration and format standardization processing according to unified spatiotemporal resolution, and construct a spatiotemporal data assimilation framework.

[0035] S02. Based on the data from each data source in the spatiotemporal data assimilation framework, calculate the optical detectability index of each data source. For areas where the optical detectability index is lower than the effective optical detection threshold, switch to a multibeam bathymetry data source. Based on the historical verification error statistics of each data source, set the concentration-dependent adaptive observation error weight for each data source, calculate the Wasserstein centroid distribution of the multi-source data, and output the fusion analysis field point estimate and assimilation uncertainty.

[0036] S03. Based on the fusion analysis field point estimation and assimilation uncertainty, within the framework of the physical constraint manifold embedding adaptive local ensemble transformation filtering algorithm, low-dimensional intrinsic manifold coordinates are extracted. The covariance localization radius is dynamically calculated based on the sediment transport velocity and the assimilation window length. Non-uniform localization schemes are applied to the deep channel region and the shallow shoal region respectively. The analysis weight vector is projected onto the low-dimensional intrinsic manifold tangent space to complete the ensemble analysis step and perform manifold projection correction. The corrected ensemble analysis members are then output.

[0037] S04. Based on the corrected set analysis members, calculate the set dispersion, observational information statistics and manifold projection residuals within the current assimilation window, substitute them into the sludge-deposition dynamic fusion quality assessment function to obtain the sludge-deposition fusion quality assessment value, adjust the number of set members and the localization radius of covariance according to the interval to which the sludge-deposition fusion quality assessment value belongs, and trigger set expansion or set reduction processing.

[0038] S05. Based on the fusion historical time series characteristics of the adjusted and corrected set analysis members, input the sediment erosion and deposition state spatial prediction model, and output the hourly erosion and deposition thickness prediction field and suspended sediment concentration prediction field.

[0039] Specifically, the extraction of low-dimensional intrinsic manifold coordinates is achieved by using the diffusion mapping algorithm to perform manifold learning on the state vectors of set members.

[0040] It needs to be explained that after inputting the sediment erosion and deposition state space prediction model, the process includes: extracting multi-scale local temporal patterns through causal dilatation convolution branches and inputting them into the structured state space backbone; gradually reducing the physical residuals through a self-reference iterative refinement module; and then outputting the prediction field.

[0041] Optionally, it also includes: injecting the latest observation data into the spatiotemporal data assimilation framework, updating the hidden state vector of the sediment erosion and deposition state space prediction model, and iteratively executing S02 to S05 to continuously correct the medium- and long-term erosion and deposition prediction results.

[0042] The Sinkhorn iterative algorithm is used to calculate the Wasserstein centroid distribution of multi-source data.

[0043] The spatiotemporal data assimilation framework refers to a data fusion architecture that integrates multi-temporal satellite remote sensing inversion water depth data, field measured hydrological and sediment sequence data, and time-by-time output data from three-dimensional sediment numerical models, after coordinate registration and format standardization using a unified spatiotemporal grid. This architecture provides standardized input for subsequent ensemble analysis steps.

[0044] Among them, the optical detectability index is a dimensionless index calculated by combining the backscattering intensity of water in the satellite multispectral band and the estimated value of suspended sediment concentration. It is used to determine whether the current optical depth of the water body meets the effective detection conditions of satellite water depth inversion. The effective optical detection threshold is determined by conducting on-site synchronous measurement and satellite overpass comparison experiments under different sediment concentration gradient conditions, statistically analyzing the segmented inflection points of the inversion error as sediment concentration changes, and performing regression analysis on 20 to 50 sets of experimental data.

[0045] Among them, the concentration-dependent adaptive observation error weight refers to the diagonal elements of the observation error covariance matrix that dynamically changes with the concentration of suspended sediment in the water body. The higher the concentration of suspended sediment, the greater the error weight of the water depth data retrieved by satellite remote sensing. The mapping relationship between the concentration-dependent adaptive observation error weight and the suspended sediment concentration is determined through multiple on-site synchronous observation experiments and error statistical regression.

[0046] Among them, the Sinkhorn iterative algorithm is a numerical algorithm that efficiently approximates the optimal transport problem through alternating normalization iteration. Its principle is to transform the solution of the optimal transport mapping into a matrix scaling iterative problem under entropy regularization constraints. In this method, the estimates of the same sediment state variable from three data sources—multi-temporal satellite remote sensing inversion water depth data, field measured hydrological and sediment sequence data, and hourly output data from a three-dimensional sediment numerical model—are modeled as probability distributions carrying uncertainty. The Wasserstein-2 distance is used to measure the differences in these distributions, and the Wasserstein centroid distributions of the three distributions are calculated using the Sinkhorn iterative algorithm. The conditional mean of the Wasserstein barycenter distribution is used as the estimated field point for fusion analysis, and the conditional variance of the Wasserstein barycenter distribution is used as the assimilation uncertainty output. The weights of the Wasserstein barycenter distribution are adaptively inverted from the historical verification error statistics of each data source. Specifically, the root mean square error sequence of each data source in the same historical period is statistically analyzed, and the inverse of the error is normalized as the initial weight value, which is updated after each assimilation window ends. The length of the historical statistical window is determined through sensitivity experiments on the stability of the weights under different window lengths, ranging from 30 to 90 assimilation time steps. The Sinkhorn iterative algorithm reduces the computational complexity from... Reduce to ,in The number of discretely distributed support points. The entropy regularization parameter is used. The technical effect of the Sinkhorn iterative algorithm is as follows: Compared with the traditional weighted mean fusion, the Wasserstein centroid distribution fusion can still maintain the physical rationality of geometric interpolation when the distribution morphology is significantly different. It has natural robustness to the log-normal distribution or heavy-tailed distribution of sediment concentration during the flood peak, avoids the pseudo-multimodal phenomenon caused by the linear superposition assumption, and makes the field point estimation of the fusion analysis more realistically reflect the uncertainty structure of the sediment system, thereby improving the reliability of subsequent rolling prediction.

[0047] The principle and implementation of the physically constrained manifold embedding adaptive local ensemble transformation filtering algorithm are as follows: Within the framework of classical local ensemble transformation Kalman filtering, the diffusion mapping algorithm is used to learn the manifold of the high-dimensional dataset composed of the state vectors of historical ensemble members. The diffusion mapping algorithm extracts the low-dimensional intrinsic manifold coordinates of the sediment system state space by constructing the heat kernel similarity matrix between data points and performing spectral decomposition on the normalized Laplacian matrix. In the ensemble analysis step, the analysis weight vector obtained by classical local ensemble transformation Kalman filtering is projected into the tangent space of the low-dimensional intrinsic manifold, so that the corrected ensemble analysis members are located in the neighborhood of the physically realizable manifold. The covariance localization radius is dynamically calculated based on the product of the estimated sediment transport velocity in the current assimilation window and the assimilation time step. Different covariance localization radii are applied to the deep channel region and the shallow shoal region according to the geomorphic unit classification results. After the ensemble analysis step is completed, the manifold projection correction step is performed to modify the manifold coordinates. The positive set analysis members are reprojected to the neighborhood of the low-dimensional intrinsic manifold, eliminating spurious expansion of the set variance and maintaining the sediment mass conservation constraint. The classification criteria and the localization radius of the regional covariance of the deep channel and shallow shoal regions are determined through geomorphic unit clustering experiments and assimilation error sensitivity analysis of historical topographic measurement data. The localization radius of the covariance of the deep channel region is 1.5 to 3.0 times that of the shallow shoal region. The technical effect of the physical constraint manifold embedding adaptive local set transformation filtering algorithm is as follows: the manifold constraint ensures that the correction of the modified set analysis members always follows the inherent nonlinear geometric structure of the sediment dynamic system, avoiding the physical irrationality caused by covariance estimation error in the Euclidean space set update. It reduces the probability of filter divergence in extreme floods or strong storm surges and other scenarios with drastic changes in observation conditions. At the same time, the non-uniform localization scheme of geomorphic zoning preserves the long-range hydrodynamic correlation of the deep channel region, improving the spatial rationality of scour and sedimentation prediction.

[0048] Among them, the Gaspari-Cohn function is a compactly supported fifth-order piecewise polynomial function used for covariance localization. Its function is to truncate the spurious covariance between distant grid points in the physical constraint manifold embedding adaptive local set transformation filtering algorithm to zero, limit the spatial propagation radius of the observation influence, and thus suppress spatial pollution caused by insufficient set members; the covariance localization radius is dynamically adjusted by the sludge fusion quality assessment value.

[0049] The calculation formula for the dynamic fusion quality evaluation function of scouring and silting is expressed as follows: ;in This is the quality assessment value for siltation and erosion fusion. The current set dispersion, As a reference set of discreteness, To observe the new information statistics, To observe the theoretical expected value of the innovation statistic, Let the norm of the projected residuals of the manifold be denoted as . For the reference manifold projection residual norm, , , The weighting coefficients are satisfied. , It is a dimensionless quantity; when When, the number of current set members and the localization radius of covariance remain unchanged; when When the number of set members is increased to 1.2 to 1.5 times the current number of set members, the covariance localization radius is also expanded; when When this happens, the set is expanded to the maximum number of members, and global manifold relearning is initiated, while the assimilation time step is shortened. , , and , , By statistically analyzing the error distribution of historical assimilation experiments under different hydrological conditions and combining the Neyman-Pearson criterion, the trade-off between the missed detection rate and the false alarm rate was determined, and the results were calibrated through 10 to 30 sets of experiments. The interval thresholds of 0.6 and 0.85 were determined through the above experimental iterative calibration process.

[0050] The specific structure of the sediment erosion and deposition state space prediction model is as follows: It uses the Mamba structured state space model as its main framework, and the input layer is designed with 4-8 channels of causal dilated convolution parallel branches. The dilation rate of each causal dilated convolution parallel branch is determined according to... ( , The outputs of each causal dilatation convolution parallel branch are arranged in ascending order from 4 to 8 and used to extract local time-series patterns at the tidal cycle scale, flood process scale, and seasonal trend scale, respectively. The outputs of each branch are fused through a learnable time-varying gating matrix and then fed into the backbone of the Mamba structured state-space model. The discretization matrix of the state-space equations of the Mamba structured state-space model backbone is used. The eigenvalue range is constrained by the sediment characteristic timescale derived from Rouse's suspended sediment vertical distribution theory, and the sediment settling time. The calculation formula is expressed as follows: ;in This refers to the sediment settling time. Because of the water depth, For sediment settling speed, Let be the Kármán constant; The corresponding frequency range is mapped to the discretized matrix. The spectral radius constraint interval makes the discretization matrix The network features a physically interpretable time-memory structure. An internal self-referenced iterative refinement module is designed to feed the initial prediction output back to the input layer and concatenate it with fused historical time-series features. Through 2-3 internal iterations, the residual between the predicted value and the physical conservation constraints is gradually reduced. Each iteration assimilates the latest observation increment to correct the hidden state vector, achieving rolling updates. The output layer outputs the hourly predicted scour and sedimentation thickness field, the predicted suspended sediment concentration field, and the prediction uncertainty estimate. The total number of network layers is 12-24, and the hidden state vector dimension is 128-512. The total number of network layers and the hidden state vector dimension were determined through grid search experiments on historical datasets. The scour and sedimentation state... The steps for establishing the training dataset for the spatial prediction model specifically include: collecting hourly hydrological and sediment observation records for no less than 5 years in the study area, hourly output data from the concurrent 3D sediment numerical model, and concurrent multi-temporal satellite remote sensing inversion water depth data. After spatiotemporal registration and quality control, the dataset is divided into training, validation, and test sets in an 8:1:1 ratio. A logarithmic transformation is performed on the suspended sediment concentration sequence to compress the dynamic range of the heavy-tailed distribution. Sample pairs are truncated using a sliding window with a length of 720–2160 time steps. The steps for training the spatial prediction model for sediment erosion and deposition specifically include: using the AdamW optimizer, with an initial learning rate set within a certain range. to The training loss function is a weighted combination of a mean squared error term and a physical conservation constraint penalty term. The weight of the physical conservation constraint penalty term linearly increases from 0 to the target value in the first 50 training rounds. The target value is determined through ablation experiments on the validation set. The training process adopts a cosine annealing learning rate scheduling strategy, with 100-300 training rounds. After each round, the root mean square error is evaluated on the validation set, and an early stopping mechanism is used to prevent overfitting. The technical effects of the sediment erosion and deposition state space prediction model are as follows: replacing the long short-term memory network with the Mamba structured state space model allows the model to maintain linear time complexity when processing hourly sediment time series over several years, avoiding the degradation of long-range dependency capture ability caused by gradient vanishing in the long short-term memory network; embedding the characteristic time scale of Rouse suspended sediment vertical distribution theory into the discretized matrix. The spectral constraints couple the evolution rhythm of the hidden state vector with the characteristic time scale of the sediment physical process, giving the model a physically interpretable time memory structure. The multi-scale causal dilatation convolution parallel branch, combined with the multiple internal iterative corrections of the self-reference iterative refinement module, achieves a balance between short-term fine response and long-term trend stability in the time-by-time scour and sedimentation thickness prediction field and suspended sediment concentration prediction field, thereby improving the prediction reliability of medium- and long-term scour and sedimentation evolution.

[0051] Specifically, low-rank sparse decomposition is used to compress the set member state vectors. This involves reconstructing the set member state vectors by retaining the first 50 to 100 main singular value modes using singular value decomposition, and asynchronously prefetching the set member state vectors to the graphics processor memory in blocks using memory-mapped file technology. A mixed-precision strategy is adopted to store the vectors in FP16 format and compute them in FP32 format to reduce memory usage and alleviate memory bandwidth bottlenecks. The number of singular value modes to retain is determined through experiments that weigh the reconstruction error against the computational cost at different truncation orders, ranging from 50 to 100.

[0052] Among them, the diffusion mapping algorithm is a nonlinear manifold learning method based on random walk theory. By constructing a local heat kernel similarity matrix between data points and performing spectral decomposition on the normalized Laplacian matrix, it embeds the high-dimensional set member state vectors into the low-dimensional intrinsic manifold coordinate space, revealing the intrinsic geometric structure of the data. In this method, the diffusion mapping algorithm is used to extract the low-dimensional intrinsic manifold coordinates of the sediment system from the historical set member state vectors, providing a geometric basis for the low-dimensional intrinsic manifold tangent space projection in the subsequent set analysis step.

[0053] Among them, the multibeam bathymetry data source refers to underwater topographic measurement data collected by a multibeam acoustic detection system, which replaces multi-temporal satellite remote sensing inversion water depth data in areas where the optical detectability index is lower than the optical effective detection threshold, and serves as the active bathymetry data input for the assimilation framework.

[0054] Optionally, the present invention also provides a computer-based method for forming a dynamic fusion prediction system for spatiotemporal data of sediment erosion and deposition. The computer is equipped with a readable storage medium, which stores program instructions. When the program instructions are run on the computer, they execute the above-mentioned dynamic fusion prediction method for spatiotemporal data of sediment erosion and deposition.

[0055] The specific implementation of step S01 is as follows. The purpose of this step is to construct a unified spatiotemporal data assimilation framework to provide standardized multi-source input for subsequent aggregated assimilation analysis. First, multi-temporal satellite remote sensing inversion water depth data, field-measured hydrological and sediment sequence data, and time-by-time output data from the three-dimensional sediment numerical model are acquired for the study area. These three types of data sources typically differ in temporal resolution, spatial resolution, and coordinate system. To address these differences, bilinear interpolation is used to resample each data source to a unified spatiotemporal grid. Geographic registration is completed using the WGS-84 coordinate system. Missing data and outliers from each data source are quality controlled and removed according to a three-standard-deviation criterion based on historical statistics. After format standardization, the three types of data sources are incorporated into a unified spatiotemporal data assimilation framework, establishing a connection using timestamps and grid indices as keys, providing structured input for multi-source fusion in step S02.

[0056] The specific implementation of step S02 is as follows. The purpose of this step is to achieve physical and reasonable fusion of multi-source data through optimal transmission theory, and output the fusion analysis field point estimate and assimilation uncertainty. First, the optical detectability index is calculated for each grid point. This index is jointly calculated by the backscattering intensity of water in the satellite multispectral band and the estimated value of suspended sediment concentration. When the optical detectability index is lower than the optical effective detection threshold, the satellite remote sensing water depth data source of that grid point is switched to a multibeam bathymetry data source. The optical effective detection threshold is determined by regression analysis after statistically analyzing the piecewise inflection points of the inversion error as a function of sediment concentration through 20 to 50 sets of field synchronous measurements and satellite overpass comparison experiments. Subsequently, based on the historical verification error statistics of each data source, a concentration-dependent adaptive observation error weight is set for each data source. That is, the reciprocal normalized of the root mean square error sequence of each data source in the same historical period is used as the initial weight value. The length of the historical statistical window is 30 to 90 assimilation time steps, and the weight is updated after each assimilation window ends. After completing the data source switching and weight setting, the estimates of the same sediment state variable from the three data sources are modeled as probability distributions carrying uncertainty. The Sinkhorn iterative algorithm is used to calculate the Wasserstein barycenter distributions of the three distributions under entropy regularization constraints. The conditional mean of the Wasserstein barycenter distribution is used as the estimated field point for fusion analysis, and the conditional variance of the Wasserstein barycenter distribution is used as the assimilation uncertainty output. The Sinkhorn iterative algorithm transforms the optimal transport problem into a matrix scaling iterative problem, reducing the computational complexity from... Reduce to ,in The number of discretely distributed support points. This is the entropy regularization parameter.

[0057] The specific implementation of step S03 is as follows. The purpose of this step is to complete the set assimilation analysis within the framework of the physically constrained manifold embedding adaptive local set transformation filtering algorithm, ensuring that the members of the corrected set analysis are located in the neighborhood of the physically realizable manifold. Using the fusion analysis field point estimate and assimilation uncertainty output from S02 as the observation input, the diffusion mapping algorithm is first used to perform manifold learning on the high-dimensional dataset composed of the state vectors of the historical set members. The diffusion mapping algorithm extracts the low-dimensional intrinsic manifold coordinates of the sediment system state space by constructing the heat kernel similarity matrix between data points and performing spectral decomposition on the normalized Laplace matrix. The covariance localization radius is dynamically calculated based on the product of the estimated sediment transport velocity within the current assimilation window and the assimilation time step. Different covariance localization radii are applied to the deep trough region and the shallow shoal region according to the geomorphic unit classification results. The covariance localization radius of the deep trough region is 1.5 to 3.0 times that of the shallow shoal region. The spurious covariance between distant grid points is truncated to zero using the Gaspari-Cohn function. In the ensemble analysis step, the analysis weight vector obtained by classical local ensemble transformation Kalman filtering is projected onto the tangent space of a low-dimensional intrinsic manifold. After completing the ensemble analysis step, a manifold projection correction step is performed, reprojecting the corrected ensemble analysis members onto the neighborhood of the low-dimensional intrinsic manifold. This eliminates spurious expansion of the ensemble variance and maintains the sediment mass conservation constraint, outputting the corrected ensemble analysis members. The ensemble member state vectors are compressed using singular value decomposition, retaining the first 50 to 100 principal singular value modes for low-rank compression. Combined with memory-mapped file technology, they are asynchronously prefetched into the graphics processor's memory in blocks, stored in FP16 format, and computed in FP32 format to reduce memory usage.

[0058] The specific implementation of step S04 is as follows. The purpose of this step is to quantitatively evaluate the current assimilation quality using the dynamic fusion quality evaluation function for sedimentation and siltation, and adaptively adjust the ensemble configuration based on the evaluation results. Based on the corrected ensemble analysis members output in S03, the ensemble dispersion within the current assimilation window is calculated. Observational Information Statistics and manifold projection residual norm Substitute into the dynamic fusion quality evaluation function of scouring and silting Obtain the quality assessment value of siltation and erosion fusion. ,in , , and reference values , , By statistically analyzing the error distribution of 10 to 30 sets of historical assimilation experiments and combining the Neyman-Pearson criterion to determine the trade-off between the false alarm rate and the missed detection rate, iterative calibration was performed. The interval thresholds of 0.6 and 0.85 were also determined through the above calibration process. When it is below 0.6, the current number of set members and the localization radius of covariance remain unchanged; when When the value is between 0.6 and 0.85, increase the number of set members to 1.2 to 1.5 times the current number and expand the covariance localization radius; when When the value is not lower than 0.85, the set is expanded to the maximum number of set members and global manifold relearning is started, while the assimilation time step is shortened.

[0059] The specific implementation of step S05 is as follows. The purpose of this step is to use fused historical time-series features to drive the sediment erosion and deposition state-space prediction model, and output the predicted fields of medium- and long-term erosion and deposition thickness and suspended sediment concentration. The fused historical time-series features composed of the modified ensemble analysis members adjusted in S04 are input into the sediment erosion and deposition state-space prediction model with the Mamba structured state-space model as the backbone. The input layer is designed with 4 to 8 causal dilated convolution parallel branches, and the dilation rate of each branch is calculated according to... ( , Using an increasing sequence of 4 to 8, local time-series patterns at tidal cycle, flood process, and seasonal trend scales are extracted. The outputs of each branch are fused using a learnable time-varying gating matrix and then fed into the backbone of the Mamba structured state-space model. State-space equation discretization matrix. The eigenvalue range is derived from Rouse's theory of suspended sediment settling time. constraint, satisfy ,Will The corresponding frequency range is mapped to the discretized matrix. The spectral radius constraint range endows the model with a physically interpretable temporal memory structure. The self-referential iterative refinement module within the network feeds back the initial prediction output to the input layer and concatenates it with fused historical time-series features. Through 2 to 3 internal iterations, the residual between the predicted value and the physical conservation constraints is gradually reduced. Each iteration assimilates the latest observation increment to correct the hidden state vector, ultimately outputting the hourly predicted fields of sediment thickness and suspended sediment concentration, along with an estimate of the prediction uncertainty. Training employs the AdamW optimizer, with an initial learning rate ranging from [value missing]. to The training loss function is a weighted combination of the mean squared error term and the physical conservation constraint penalty term. The training rounds are 100 to 300. A cosine annealing learning rate scheduling strategy is adopted, and an early stopping mechanism is used to prevent overfitting.

[0060] It should be noted that the key technologies of this invention include: a Wasserstein centroid distribution multi-source fusion technology based on the Sinkhorn iterative algorithm, which eliminates the pseudo-multimodal phenomenon caused by differences in distribution morphology in traditional linear fusion by performing geometric interpolation on the probability distribution of multi-source sediments under the optimal transmission framework, ensuring that the uncertainty structure of the fusion analysis field is consistent with the physical state of the sediment system; a physically constrained manifold embedding adaptive local ensemble transformation filtering technology, which extracts the low-dimensional intrinsic manifold coordinates of the sediment dynamic system through a diffusion mapping algorithm, strictly constraining the weight update of ensemble invariance within the manifold tangent space, avoiding physically unreasonable states caused by covariance estimation errors in Euclidean space ensemble updates; and a Mamba structured state-space prediction technology driven by Rouse theory spectral constraints, which embeds the sediment deposition characteristic timescale into the spectral constraints of the discretized matrix, coupling the latent state evolution rhythm with the sediment physical process. These three key technologies work synergistically to form a complete technical closed loop from the physical rationality of data fusion and the constraint of ensemble invariance manifold to the physical interpretability of the prediction model. Compared with the simple superposition of individual technologies, the comprehensive prediction reliability under extreme hydrological conditions is significantly improved.

[0061] It should be noted that this invention also solves the following technical problem: In existing ensemble filtering methods, the number of ensemble members and the localization radius of covariance are usually kept fixed during the assimilation process, and cannot be adaptively adjusted according to the dynamic changes in the current assimilation quality. As a result, in scenarios with drastic changes in observation conditions such as extreme floods or strong storm surges, the fixed-configuration ensemble assimilation scheme may produce serious sampling errors due to insufficient ensemble members, or may miss long-range hydrodynamic information due to an excessively small localization radius of covariance. This invention designs a dynamic fusion quality assessment function for scour and sedimentation, integrating three types of diagnostic quantities—ensemble dispersion, observational innovation statistics, and manifold projection residuals—into a unified quality assessment index. Based on the interval to which the assessment result belongs, corresponding ensemble expansion or reduction processing is triggered, realizing closed-loop adaptive adjustment of the number of ensemble members and the localization radius of covariance during the assimilation process. This enables the ensemble assimilation scheme to maintain reasonable sampling accuracy and spatial correlation structure under different hydrological conditions, solving the problem of insufficient adaptive capability of fixed ensemble configuration in dynamic hydrological scenarios.

[0062] Specifically, the principle of this invention is as follows: The core logic that enables this invention to solve the aforementioned technical problems lies in the fact that the estimation of the same sediment state variable by multi-source sediment data sources is essentially a probability distribution carrying uncertainty, rather than a deterministic value. The destruction of the distribution geometry by traditional linear fusion is the fundamental reason for the lack of physical consistency. The Wasserstein barycentric distribution performs geometric interpolation on multiple probability distributions under the Wasserstein-2 distance metric, and its result has the optimality of minimizing the weighted transmission cost in the distribution space. Therefore, it can achieve physically reasonable fusion while preserving the distribution morphology of each data source. This property is particularly important for the heavy-tailed distribution of sediment concentration during the flood peak. At the set integration level, the state space of the sediment dynamic system is not a Euclidean flat structure, but a low-dimensional nonlinear manifold embedded in a high-dimensional space. The diffusion mapping algorithm accurately extracts the eigencoordinates of the manifold by constructing a heat kernel similarity matrix and performing spectral decomposition on the normalized Laplace matrix, so that the weight projection of the set analysis step is strictly constrained within the tangent space of the manifold, thereby ensuring the physical realizability of the corrected set analysis members. The synergistic effect of the two constraints enables the fusion of historical time series features to have a physically consistent uncertainty structure, thereby providing a reliable driving input for the subsequent sediment erosion and deposition state space prediction model. This is the intrinsic reason why the present invention can improve the accuracy of medium- and long-term sediment erosion and deposition prediction from a mechanistic perspective.

[0063] 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.

[0064] The specific implementation of step S01 is as follows: collect multi-temporal satellite remote sensing inversion water depth data, field measured hydrological and sediment sequence data, and time-by-time output data of the three-dimensional sediment numerical model; perform coordinate registration and format standardization processing on each data source according to a unified spatiotemporal grid; construct a spatiotemporal data assimilation framework; and provide standardized input for subsequent ensemble analysis steps.

[0065] The specific implementation of step S02 is as follows: Based on the data from each data source in the spatiotemporal data assimilation framework, calculate the optical detectability index. Its formula is expressed as follows:

[0066] ;

[0067] In the formula, The intensity of water backscattering in the multispectral bands of the satellite, in units of The backscattering intensity is for reference under clear water conditions, and the unit is . This is an estimated value for the current suspended sediment concentration, in units of... For reference suspended sediment concentration, the unit is... It is a dimensionless quantity. and Both are dimensionless, and their ratio has the same dimension. Below the optically effective detection threshold In the area, switch to a multibeam bathymetry data source. As a dimensionless quantity, it was determined by conducting on-site synchronous measurements and satellite overpass comparison experiments under 20 to 50 different sediment concentration gradients, statistically analyzing the piecewise inflection points of the inversion error as a function of sediment concentration, and then determining them through regression analysis.

[0068] Concentration-dependent adaptive observation error weights for each data source With suspended sediment concentration The dynamic changes can be expressed by the following normalization formula:

[0069] ;

[0070] In the formula, For the first Data source for suspended sediment concentration The observation error variance is given below, in units of For the first Each data source at reference concentration The baseline observation error variance is given in units of For the first The concentration sensitivity coefficients of each data source are dimensionless and were determined through multiple on-site synchronous observation experiments and error statistical regression. The left side of the formula is the dimensionless normalized error ratio, and all terms on the right side are dimensionless.

[0071] The Wasserstein barycenter distribution of multi-source data was calculated using the Sinkhorn iterative algorithm, modeling the estimates of the same sediment state variable from the three data sources as probability distributions. ,by Distance metric distribution differences. Weights of each data source. The error is adaptively determined by historical verification error statistics, and the formula is expressed as follows:

[0072] ;

[0073] In the formula, For the first The root mean square error of each data source within the historical statistical window, in units of satisfy The weights are dimensionless; the historical statistical window length ranges from 30 to 90 assimilation time steps. Wasserstein barycentric distribution. The problem to be solved is stated as follows:

[0074] ;

[0075] In the formula, For distribution With the Data source distribution Between The square of the distance, in units of For reference Squared distance, in units of This is used for normalization to make the right side of the formula dimensionless; the Sinckhorn iterative algorithm uses entropy regularization parameters. Under constraints, the optimal transport problem is transformed into a matrix scaling iterative problem. Each iteration alternately performs normalization on rows and columns until convergence, reducing the computational complexity from... Reduce to ,in The number of discretely distributed support points. Entropy regularization parameter, dimensionless. Fusion analysis field point estimation. Pick Conditional mean, in units of Assimilation uncertainty Pick The conditional variance, in units of .

[0076] The specific implementation of step S03 is as follows: Within the framework of the physically constrained manifold embedding adaptive local set transformation filtering algorithm, the diffusion mapping algorithm is used to perform manifold learning on the high-dimensional dataset composed of the state vectors of historical set members. A heat kernel similarity matrix between data points is constructed. Its elemental formula is expressed as follows:

[0077] ;

[0078] In the formula, The first Each set contains a member state vector, with units of _ . The square of the distance between the two, in units of This is the diffusion mapping kernel width parameter, in units of... This makes the exponent dimensionless. These are the elements of the dimensionless heat kernel similarity matrix. For the angle matrix... The elements are Dimensionless. Normalized Laplace matrix. Dimensionless, for Perform spectral decomposition to obtain eigenvalues and the corresponding eigenvector matrix , for The 1 eigenvalue, dimensionless, superscript Used in conjunction with other places Symbol differentiation; selection before The eigenvectors corresponding to the largest nontrivial eigenvalues ​​constitute a low-dimensional eigenmanifold coordinate matrix. , For the first 1 eigenvector For the number of members in the set, Let be the dimension of the manifold, with an empirical value of 5 to 20.

[0079] In the set analysis step, the analysis weight vector is analyzed within the classical local set transformation Kalman filter framework. The solution formula is expressed as follows:

[0080] ;

[0081] In the formula, The set of observation perturbation matrices is normalized to unify the dimensions of all terms. The observation error covariance matrix, in units of It is an identity matrix, dimensionless. To observe the innovation vector, the unit is... For the observation dimension The dimension of the state vector is used for normalization to unify the dimensions of each quantity. The weight vector is dimensionless for analysis. Covariance localization is achieved using the Gauss-Cohen function. Element-wise weighting of the covariance matrix, The distance between grid points and the localization radius The ratio, Dimensionless, Gauss-Cohen function in The time cutoff is zero, limiting the spatial propagation range of the observational impact.

[0082] Covariance localization radius Based on the current sediment transport rate within the assimilation window With assimilation time step The product is dynamically calculated, and the formula is expressed as follows:

[0083] ;

[0084] In the formula, For reference localization radius, the unit is This is an estimated value of sediment transport velocity within the current assimilation window, in units of... For reference purposes, the unit is . This represents the current assimilation time step, in units of For reference, the assimilation time step is in units of Both sides of the formula are dimensionless ratios. For deep trench regions, the localization radius is taken as... Take action in the shallow water area ,and The range is 1.5 to 3.0.

[0085] Analyze the weight vector Projected onto the tangent space of a low-dimensional intrinsic manifold After completing the ensemble analysis step, manifold projection correction is performed. The corrected ensemble analysis members are reprojected onto the neighborhood of the low-dimensional intrinsic manifold, eliminating spurious expansion of ensemble variance and maintaining the sediment mass conservation constraint. The corrected ensemble analysis members are then output. .

[0086] The specific implementation of step S04 is as follows: Based on the corrected set analysis members, calculate the set dispersion within the current assimilation window. Observational Information Statistics and manifold projection residual norm Observational Information Statistics The calculation formula is expressed as follows:

[0087] ;

[0088] In the formula, The observation operator matrix is ​​dimensionless. The set is the background error covariance matrix, in units of The unit is The dimensions on both sides cancel each other out. These are dimensionless quantities. Substituting the above three statistics into the dynamic fusion quality assessment function for sedimentation and scouring, the formula is as follows:

[0089] ;

[0090] In the formula, This is a dimensionless value for assessing the quality of siltation and erosion fusion. The current set's discreteness is dimensionless. The discreteness of the reference set is dimensionless. The theoretical expectation of the observation statistic is dimensionless; the empirical value is the observation dimension. Let be the norm of the projected residuals of the manifold, which is dimensionless. The reference manifold projection residual norm is dimensionless. For the weighting coefficients, satisfying The parameters are dimensionless; the above parameters were determined by statistically analyzing the error distribution of historical assimilation experiments under different hydrological conditions, combined with the Neiman-Pearson criterion, to find the trade-off between the missed detection rate and the false alarm rate, and were calibrated through 10 to 30 sets of experiments. At the same time, maintain the current number of members in the set and Unchanged; when At that time, increase the number of set members to 1.2 to 1.5 times the current size and expand. ;when When this happens, the set is expanded to the maximum number of set members and global manifold relearning is initiated, while the assimilation time step is shortened.

[0091] The specific implementation of step S05 is as follows: Based on the fused historical time-series characteristics of the adjusted and corrected set analysis members, input the sediment erosion and deposition state spatial prediction model. The input layer is designed with 4 to 8 causal dilated convolution parallel branches, and the dilation rate of each branch is... ( , Using increments of 4 to 8, local time-series patterns at tidal cycle, flood process, and seasonal trend scales are extracted respectively. The outputs of each branch are fused through a learnable time-varying gating matrix and then fed into the backbone of the Mamba structured state-space model. The discretization matrix of the state-space equations of the Mamba structured state-space model backbone is shown below. The range of characteristic values ​​is determined by sediment settling time. The constraints are expressed in the following formula:

[0092] ;

[0093] In the formula, Sediment settling time, in units of Water depth, unit: Sediment settling velocity, unit: Kármán's constant, typically taken as 0.41, is dimensionless. Units are ,and The dimensions are uniform, and the ratios on both sides are dimensionless. The corresponding frequency range is mapped to the discretized matrix. The spectral radius constraint interval makes It has a physically interpretable temporal memory structure. The network internally designs a self-referential iterative refinement module, which injects the initial prediction output back into the input layer and concatenates it with the fused historical time-series features. Through 2 to 3 internal iterations, it gradually reduces the residual between the prediction value and the physical conservation constraints. Each iteration assimilates the latest observation increment to correct the hidden state vector.

[0094] Set member state vector matrix The singular value decomposition formula is expressed as follows:

[0095] ;

[0096] In the formula, Left singular vector matrix A singular value diagonal matrix It is a right singular vector matrix; retain the first... The state vectors of the members of the main singular value mode reconstruction set ,in , , These are the corresponding submatrices after truncation. The range of values ​​is 50–100, determined through experiments balancing reconstruction error and computational cost at different truncation orders. The output layer outputs hourly predicted fields of sediment thickness and suspended sediment concentration, along with estimates of prediction uncertainty. The total number of network layers is 12–24, with hidden state vector dimensions ranging from 128–512, determined through grid search experiments on historical datasets. The training dataset consists of at least 5 years of hourly hydrological and sediment observation records. After spatiotemporal registration and quality control, the dataset is divided into training, validation, and test sets in an 8:1:1 ratio. A logarithmic transformation is performed on the suspended sediment concentration sequence, and sample pairs are truncated using a sliding window with a length of 720–2160 time steps. Training employs an adaptive moment estimation weight decay optimizer, with an initial learning rate ranging from [value missing]. to The training loss function is a weighted combination of the mean squared error term and the physical conservation constraint penalty term. The weight of the physical conservation constraint penalty term increases linearly from 0 to the target value in the first 50 training rounds. The target value is determined by ablation experiments on the validation set. The training process adopts a cosine annealing learning rate scheduling strategy, with 100 to 300 training rounds. After each round, the root mean square error is evaluated on the validation set and an early stopping mechanism is used to prevent overfitting.

[0097] To better understand and implement this invention, a specific application scenario of the invention is provided below as Example 2: To verify the effectiveness of the invention, technicians selected a tidal estuary area as the test scenario. This area is affected by both runoff and tides, resulting in drastic changes in scouring and deposition, making it a typical complex scenario for verifying sediment prediction methods. Technicians collected hourly hydrological and sediment observation records for this area over seven consecutive years, hourly output data from the concurrent three-dimensional sediment numerical model, and concurrent multi-temporal satellite remote sensing inversion water depth data. The total data covered various typical hydrological conditions, including dry season, flood season, and storm surge season. After spatiotemporal registration and quality control, the data was divided into training set, validation set, and test set in an 8:1:1 ratio. A logarithmic transformation was performed on the suspended sediment concentration sequence to compress the dynamic range of the heavy-tailed distribution. A sliding window was used to extract sample pairs, with the sliding window length set to 1440 time steps.

[0098] During the data preprocessing stage, technicians first completed coordinate registration and format standardization of the three types of data sources according to the steps in S01. Each data source was then resampled to a unified grid with a horizontal resolution of 250m and a temporal resolution of 1h. Outliers were quality controlled and removed using a three-standard-deviation criterion, and missing grid points were completed using spatiotemporal kriging interpolation. The test area was divided into 4320 valid grid points, covering approximately half of the grid points in both the deep trench and shallow shoal areas.

[0099] During the multi-source data fusion phase, technicians calculated the optical detectability index for each grid point according to the steps in S02. Through on-site synchronous measurements and satellite overpass comparison experiments, the effective optical detection threshold was determined using regression analysis of 32 sets of experimental data. Statistical results show that when the suspended sediment concentration during the flood peak exceeds a certain critical concentration threshold, approximately 38% of the grid points trigger a switch to the multibeam bathymetry data source, effectively avoiding interference from high-sediment-laden water bodies on the accuracy of satellite water depth inversion. The initial weights of the Wasserstein barycentric distribution were obtained by normalizing the reciprocal of the historical root mean square error of each data source over 60 assimilation time steps. The main parameters are shown in Table 1.

[0100] Table 1. Main Parameter Configuration Table for Multi-Source Data Fusion

[0101]

[0102] In the set assimilation phase, technicians performed the set analysis step within the framework of the physically constrained manifold embedding adaptive local set transformation filtering algorithm, following the steps in S03. The diffusion mapping algorithm performed manifold learning on the set member state vectors from the historical 100 assimilation time steps, extracting low-dimensional intrinsic manifold coordinates. The low-dimensional embedding dimension was determined to be 8 dimensions using the eigenvalue decay curve. The covariance localization radius for the deep trench region was set to 2.2 times that of the shallow shoal region, and long-distance spurious covariance was truncated using the Gaspari-Cohn function. The set member state vectors were compressed using singular value decomposition, retaining the first 75 principal singular value modes for low-rank compression. The vectors were stored in FP16 format and computed in FP32 format, reducing memory usage by approximately 60% compared to the uncompressed scheme.

[0103] During the adaptive adjustment phase of assimilation quality, technicians calculated the siltation fusion quality assessment value according to the steps in S04. The weighting coefficients were determined based on statistical analysis of the error distribution of 20 historical assimilation experiments and calibration using the Neyman-Pearson criterion. , , Set to 0.4, 0.4, and 0.2 respectively, as reference values. , , Determined based on historical statistical averages under normal hydrological conditions. In the test set, the peak flood period... The average value was 0.72, triggering an increase in the number of set members from the initial 50 to 70, and the covariance localization radius increased accordingly; during storm surge... The value reached a maximum of 0.91, triggering global manifold relearning. The assimilation time step was shortened from 1 hour to 0.5 hours, and the number of set members was expanded to the preset maximum of 100, allowing the assimilation quality to be restored in a timely manner. Figure 3As shown, the dynamic changes in the scour-deposition fusion quality assessment value with hydrological conditions can clearly reflect the assimilation status at different hydrological stages, verifying the effectiveness of the adaptive adjustment mechanism.

[0104] In the prediction phase, technicians constructed a state-space prediction model for sediment erosion and deposition based on the steps in S05. The model uses the Mamba structured state-space model as its backbone, with the input layer designed as having six parallel branches of causal dilated convolutions, and the dilation rate according to... ( The network has 18 layers, with a hidden state vector dimension of 256. The self-referenced iterative refinement module performs 3 internal iterations. The state-space equation discretization matrix... The spectral radius constraint interval is based on sediment settling time. The typical water depth of the test area has been determined. Take 5m as an example, sediment settling velocity Pick m / s, Kármán constant Taking 0.41, the calculation yields... Approximately 40667s, or about 11.3h, the frequency range corresponding to this characteristic time scale is mapped to a discretized matrix. The spectral constraint interval couples the latent state evolution rhythm with the physical process of sediment deposition. The model was trained for 200 epochs on the training set using the AdamW optimizer, with an initial learning rate of... A cosine annealing learning rate scheduling strategy was adopted, with the root mean square error of the validation set as the early stopping criterion. The optimal model showed a reduction in the root mean square error of suspended sediment concentration prediction and the root mean square error of scour and sedimentation thickness prediction on the validation set compared to the baseline model of the short-term memory network. The suspended sediment concentration prediction results under different hydrological stages are shown in Table 2.

[0105] Table 2 Comparison of Root Mean Square Errors in Suspended Sediment Concentration Prediction at Different Hydrological Stages

[0106]

[0107] like Figure 2 As shown, the evolution of the fusion analysis field point estimation and assimilation uncertainty over time clearly demonstrates the Wasserstein centroid distribution fusion method's effective ability to handle the distribution differences of multi-source data at different hydrological stages. The log-normal distribution characteristics of the flood peak period are preserved, and no pseudo-multimodal phenomenon appears in the fusion analysis field.

[0108] Compared to the combination of traditional weighted mean fusion and classical ensemble Kalman filtering, this invention represents a fundamental advancement in technical principles. Traditional weighted mean fusion, based on the linear superposition assumption, performs simple weighting on multi-source data with different distribution patterns. When sediment concentration exhibits a heavy-tailed distribution during peak flood periods, linear superposition inevitably disrupts the geometric structure of the distribution, producing a pseudo-multimodal phenomenon inconsistent with physical reality. This invention, however, replaces linear fusion with a Wasserstein centroid distribution, achieving geometric interpolation between distributions within an optimal transmission framework, fundamentally eliminating the disruption to the geometric structure caused by the linear superposition assumption. At the ensemble integration level, classical ensemble Kalman filtering performs ensemble updates in Euclidean space, neglecting the nonlinear manifold structure of the sediment dynamic system's state space. When the number of ensemble members is finite, covariance estimation errors can easily lead to filter divergence. This invention extracts low-dimensional intrinsic manifold coordinates through a diffusion mapping algorithm, strictly constraining the weight updates of the ensemble analysis step within the manifold tangent space. This ensures that the ensemble update step always follows the inherent nonlinear geometric structure of the sediment dynamic system, effectively avoiding the risk of filter divergence. At the predictive model level, traditional long short-term memory networks struggle to capture long-range dependencies in hourly sediment time series spanning several years due to the vanishing gradient problem. In contrast, the Mamba structured state-space model handles long series with linear time complexity and endows the discretized matrix with a physically interpretable time memory structure through Rouse theory spectrum constraints. This allows the latent state evolution rhythm of the predictive model to be deeply coupled with the physical process of sediment deposition. This physical constraint enables the model to maintain reasonable predictive behavior even under extreme hydrological conditions outside the test set, rather than relying solely on extrapolation based on statistical data patterns.

[0109] It should be noted that the variables involved in this invention are explained in detail in Tables 3 and 4.

[0110] Table 3. Variable Explanation Table (Part 1)

[0111]

[0112] Table 4. Variable Explanation Table (Part Two)

[0113]

[0114] 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 dynamically fusing and predicting spatio-temporal data of sediment scouring and silting, characterized in that, Includes the following steps: Collect multi-temporal satellite remote sensing inversion water depth data, field measured hydrological and sediment sequence data and time-by-time output data of three-dimensional sediment numerical model, complete coordinate registration and format standardization processing according to unified spatiotemporal resolution, and construct a spatiotemporal data assimilation framework. Based on the data from each data source in the spatiotemporal data assimilation framework, the optical detectability index of each data source is calculated. For areas where the optical detectability index is lower than the effective optical detection threshold, the data source is switched to a multibeam bathymetry data source. Based on the historical verification error statistics of each data source, a concentration-dependent adaptive observation error weight is set for each data source. The Wasserstein centroid distribution of the multi-source data is calculated, and the fusion analysis field point estimate and assimilation uncertainty are output. Based on the fusion analysis field point estimation and assimilation uncertainty, within the framework of the physical constraint manifold embedding adaptive local ensemble transformation filtering algorithm, low-dimensional intrinsic manifold coordinates are extracted, the covariance localization radius is dynamically calculated, non-uniform localization schemes are applied to the deep trench region and the shallow shoal region respectively, the analysis weight vector is projected onto the low-dimensional intrinsic manifold tangent space, the ensemble analysis step is completed and the manifold projection correction is performed, and the corrected ensemble analysis members are output. Based on the corrected set analysis members, the set dispersion, observational information statistics and manifold projection residuals are calculated and substituted into the scour-deposition dynamic fusion quality assessment function to obtain the scour-deposition fusion quality assessment value. The number of set members and the localization radius of covariance are adjusted according to the interval to which the scour-deposition fusion quality assessment value belongs, triggering set expansion or set reduction processing. Based on the fusion historical time series characteristics of the adjusted and corrected set analysis members, the input is the spatial prediction model of sediment erosion and deposition state, and the output is the hourly prediction field of erosion and deposition thickness and the prediction field of suspended sediment concentration.

2. The method according to claim 1, wherein, The spatiotemporal data assimilation framework refers to a data fusion architecture that integrates multi-temporal satellite remote sensing inversion water depth data, field measured hydrological and sediment sequence data, and time-by-time output data from three-dimensional sediment numerical models, after coordinate registration and format standardization using a unified spatiotemporal grid.

3. The method according to claim 2, wherein, The optical detectability index refers to a dimensionless index calculated by combining the backscattering intensity of water in the satellite multispectral bands with the estimated suspended sediment concentration. It is used to determine whether the current optical depth of the water body meets the effective detection conditions for satellite depth inversion.

4. The method according to claim 3, characterized in that, The effective optical detection threshold was determined by conducting on-site synchronous measurements and satellite overpass comparison experiments under different sediment concentration gradients, statistically analyzing the segmented inflection points of the inversion error as sediment concentration changes, and then performing regression analysis.

5. The method for dynamic fusion and prediction of spatiotemporal data of sediment erosion and deposition according to claim 4, characterized in that, The concentration-dependent adaptive observation error weight refers to the diagonal elements of the observation error covariance matrix that dynamically changes with the suspended sediment concentration in the water body. The higher the suspended sediment concentration, the greater the error weight of the water depth data retrieved by satellite remote sensing. The mapping relationship between the weight and the suspended sediment concentration is determined through multiple on-site synchronous observation experiments and error statistical regression.

6. The method according to claim 5, wherein, The calculation of the Wasserstein centroid distribution adopts the Sinkhorn iterative algorithm, which models the estimates of the same sediment state variable from multiple sources as probability distributions carrying uncertainty. The Wasserstein-2 distance is used to measure the distribution difference, the conditional mean of the Wasserstein centroid distribution is used as the fusion analysis field point estimate, and the conditional variance of the Wasserstein centroid distribution is used as the assimilation uncertainty output.

7. The method according to claim 6, wherein, The extraction of low-dimensional intrinsic manifold coordinates is specifically achieved by using the diffusion mapping algorithm to perform manifold learning on the state vectors of set members. The diffusion mapping algorithm is implemented by constructing a heat kernel similarity matrix between data points and performing spectral decomposition on the normalized Laplacian matrix.

8. The method according to claim 7, wherein, The covariance localization radius is dynamically calculated based on the product of the estimated sediment transport velocity and the assimilation time step. The ratio of the covariance localization radius of the deep trough region to that of the shallow shoal region is determined through geomorphic unit clustering experiments and assimilation error sensitivity analysis.

9. The method according to claim 8, wherein, The interval to which the sludge-flushing fusion quality assessment value belongs corresponds to three processing strategies: when the sludge-flushing fusion quality assessment value is lower than the first quality threshold, the current number of set members and the localization radius of covariance remain unchanged; when the sludge-flushing fusion quality assessment value is between the first quality threshold and the second quality threshold, the number of set members is increased and the localization radius of covariance is expanded; when the sludge-flushing fusion quality assessment value is not lower than the second quality threshold, the set is expanded to the maximum number of set members and global manifold relearning processing is initiated.

10. The method according to claim 9, wherein, The sediment erosion and deposition state-space prediction model uses the Mamba structured state-space model as its backbone. The input layer incorporates multiple causal dilated convolution parallel branches, with the dilation rate of each branch calculated according to... The outputs of each causal dilatational convolution parallel branch are arranged in an ascending order and then fused through a learnable time-varying gating matrix before being fed into the backbone of the Mamba structured state-space model.

Images