Method for Inverting Water Depth of High-Sediment-Concentration Water Bodies Based on Multispectral Remote Sensing

Abstract

The present invention provides a method for retrieving water depth of high sediment-laden water based on multi-spectral remote sensing, belonging to the technical field of remote sensing water depth retrieval. The method includes: collecting a number of multi-spectral remote sensing images and measured data of the target area; using the preprocessed multi-spectral remote sensing images to determine the spectral reflectance characteristics, and combining with the suspended sediment concentration to generate a spectral feature parameter matrix through normalization; constructing an initial water depth retrieval model based on the spectral reflectance characteristics and the measured water depth values; introducing geographical coordinates and a spatial weighting mechanism to optimize the initial water depth retrieval model; inputting the spectral feature parameter matrix into the optimized water depth retrieval model to generate an initial water depth retrieval result; locating the sub-areas in the target area where the error exceeds the error threshold, and correcting the outliers in these sub-areas based on the spatial interpolation method, and optimizing the spectral feature parameter matrix to generate an optimized water depth retrieval result. This method improves the accuracy and stability of water depth retrieval.

Description

Technical Field

[0001] The present invention belongs to the technical field of remote sensing water depth inversion, and particularly relates to a method for inverting the water depth of high-sediment-laden water bodies based on multispectral remote sensing. Background Art

[0002] For rivers with high sediment content such as the Yellow River, due to the combined action of multiple factors such as waves, tides, ocean currents, and storms in its delta area, the terrain changes dynamically and drastically, and tidal channels swing frequently or even disappear. Accurately measuring the dynamic changes in water depth of such terrains is of great significance for understanding the evolution mechanism of this region and implementing effective resource management. However, existing water depth measurement technologies face various challenges in high-sediment environments.

[0003] Traditional acoustic sounding devices (such as Doppler velocity profilers and multibeam sonar systems) in high-sediment-laden water bodies are significantly affected by suspended sediment concentration and complex bottom sediments, resulting in a significant decrease in measurement accuracy. In addition, these devices are costly, complex to maintain, and have limited coverage, and are not suitable for large-scale and rapid water depth sounding. Passive remote sensing has become an important means for water depth measurement due to its ability to obtain data over a large range and quickly. By analyzing the relationship between the reflectance of the water column and the water depth, water depth inversion is achieved. However, in high-sediment environments, traditional optical models face the following problems: 1) The scattering and absorption effects of suspended sediment distort the spectral signal, leading to a decrease in inversion accuracy. 2) The diversity of river bottom sediments significantly interferes with the reflectance, increasing the uncertainty of the model. 3) Spectral mixing effects and multiple scattering effects complicate the parameterization of the model.

[0004] In view of the above problems, existing methods are difficult to meet the accuracy and efficiency requirements of water depth measurement in the complex environment of high-sediment-laden water bodies, and thus this invention is specifically proposed. Summary of the Invention

[0005] To overcome the problems existing in the related technologies, the disclosed embodiments of the present invention provide a method for inverting the water depth of high-sediment-laden water bodies based on multispectral remote sensing. By optimizing the spectral characteristics of remote sensing images, fully considering the influence of suspended sediment concentration and bottom sediment type, a water depth inversion model suitable for high-sediment environments is established. By introducing spatial non-stationarity analysis and combining with geographically weighted regression technology, the adaptability of the model in complex geographical environments and the spatial continuity of the results are improved. At the same time, by using advanced non-linear modeling means and data correction technologies, the accuracy and stability of water depth inversion are significantly improved.

[0006] On the one hand, the present invention provides a method for inverting the water depth of high-sediment-laden water bodies based on multispectral remote sensing, and the method includes:

[0007] Collect a number of multispectral remote sensing images and measured data of the target area and perform preprocessing, where the measured data includes measured water depth values, suspended sediment concentrations, and geographical coordinates at different position points;

[0008] Using the preprocessed multi-spectral remote sensing image, determine the spectral reflectance characteristics, and combine with the suspended sediment concentration to generate a spectral feature parameter matrix through normalization;

[0009] Based on the spectral reflectance characteristics and the measured water depth values, capture the non-linear relationship between the water depth and the spectral reflectance characteristics through variable screening and non-linear regression, and construct an initial water depth inversion model;

[0010] Introduce the geographical coordinates and the spatial weighting mechanism, and construct a non-stationary weight matrix through a neural network to optimize the initial water depth inversion model;

[0011] Input the spectral feature parameter matrix into the optimized water depth inversion model to generate an initial water depth inversion result;

[0012] Analyze the error distribution characteristics, locate the sub-regions in the target area where the error exceeds the error threshold, and correct the outliers in this sub-region based on the spatial interpolation method, optimize the spectral feature parameter matrix, and generate an optimized water depth inversion result.

[0013] In an embodiment of the present invention, using the preprocessed multi-spectral remote sensing image, determine the spectral reflectance characteristics, and combine with the suspended sediment concentration to generate a spectral feature parameter matrix, including:

[0014] Using the preprocessed multi-spectral remote sensing image, calculate the reflectance of different single bands;

[0015] Calculate the logarithm ratio of the reflectance of different single bands to obtain the band reflectance logarithm ratio;

[0016] Calculate the ratio of the reflectance of different single bands to obtain the band reflectance ratio, where the spectral reflectance characteristics include the reflectance of different single bands, the band reflectance logarithm ratio, and the band reflectance ratio;

[0017] Calculate the correlation coefficient between the band reflectance ratio and the suspended sediment concentration, and screen out the band reflectance ratio corresponding to the correlation coefficient exceeding the correlation threshold as the sensitive band reflectance ratio sensitive to the change of the suspended sediment concentration;

[0018] Establish an association model between the suspended sediment concentration and the sensitive band reflectance ratio, and calculate the suspended sediment concentration index according to this association model;

[0019] Integrate the reflectance of different single bands, the band reflectance logarithm ratio, and the suspended sediment concentration index, and generate a spectral feature parameter matrix through normalization.

[0020] In one embodiment of the present invention, based on the spectral reflectance characteristics and the measured water depth values, a non-linear relationship between the water depth and the spectral reflectance characteristics is captured through variable screening and non-linear regression, and a water depth inversion model is initially established, including:

[0021] Combined with the reflectance of different single bands and the corresponding measured water depth values, using the correlation coefficient index, the correlation between the band and the water depth is initially evaluated, and the significantly correlated bands and the corresponding band reflectance ratios are initially identified;

[0022] Taking the significantly correlated bands and the corresponding band reflectance ratios as independent variables and the water depth as the dependent variable, a water depth inversion model is initially constructed;

[0023] The significantly correlated band and the corresponding band reflectance ratio are successively screened and corrected through multivariate regression;

[0024] The correlation between the band and the water depth is corrected through residual analysis and non-linear regression methods;

[0025] Introducing the logarithm ratio of the band reflectance and the sediment concentration index to optimize the initially constructed water depth inversion model to obtain the initial water depth inversion model.

[0026] In one embodiment of the present invention, introducing the geographical coordinates and the spatial weighting mechanism, a non-stationary weight matrix is constructed through a neural network to optimize the initial water depth inversion model, including:

[0027] Based on the geographical coordinates, a spatial weighted neural network is designed using a neural network model to construct a non-stationary weight matrix, and the non-stationary weight matrix includes the spatial weights of each position point;

[0028] Integrating the measured water depth values and the corresponding spectral reflectance characteristics to construct a data set and dividing the data set into a training set, a validation set and a test set;

[0029] During the modeling process, the distances from the estimated position points of the training set, the validation set and the test set to all training position points are calculated as the inputs of the spatial weighted neural network, and the spatial weights of the estimated position points are obtained from the output layer;

[0030] Adding the non-stationary weight matrix to the initial water depth inversion model to optimize the initial water depth inversion model.

[0031] In one embodiment of the present invention, adding the non-stationary weight matrix to the initial water depth inversion model to optimize the initial water depth inversion model, including:

[0032] Calculating the least squares coefficient from the training set;

[0033] Multiply the spatial weight by the least - square coefficient to obtain a non - stationary coefficient;

[0034] Update the initial water - depth inversion model according to the product of the non - stationary coefficient and the corresponding independent variable to obtain a water - depth prediction value;

[0035] Combine the water - depth prediction value and the measured water - depth value, and evaluate the model performance through a cross - validation method during the model training stage to optimize the water - depth inversion model.

[0036] In an embodiment of the present invention, evaluating the model performance through a cross - validation method during the model training stage to optimize the water - depth inversion model includes:

[0037] Adopt K - fold cross - validation, divide the data set into several subsets of equal size. In each iteration, select one subset as the validation set and the remaining subsets as the training set;

[0038] Use the training set to train the water - depth inversion model, optimize the weights and biases of the spatial weighted neural network. During each training process, calculate the least - square coefficient based on the training set and calculate the non - stationary weight using the spatial distance;

[0039] After the training is completed, calculate the water - depth prediction value from the validation set, compare it with the corresponding measured water - depth value, and determine the error index of the model after each training;

[0040] In each iteration, use different subsets as the validation set and the remaining subsets as the training set. After all K iterations are completed, calculate the average value of the error indexes of all validation sets as the total evaluation index during the model training stage to evaluate the model performance.

[0041] In an embodiment of the present invention, combine the error index, analyze the error distribution characteristics, locate the sub - regions in the target area where the error exceeds the error threshold, and determine whether there are outliers in the measured data corresponding to the sub - regions;

[0042] If there are outliers, correct the outliers in the sub - region using a spatial interpolation method; if there are no outliers, reduce the error fluctuation in the sub - region through a smoothing technique.

[0043] In an embodiment of the present invention, correcting the outliers in the sub - region using a spatial interpolation method includes:

[0044] Select representative sampling position points to cover the target area;

[0045] Calculate the spatial distance between each pair of sampling position points, calculate the semivariance according to the distance and the difference value between the sampling position points, and form a semivariogram;

[0046] Fit the semivariogram and determine the model parameters;

[0047] Apply the ordinary Kriging method, and based on the semivariogram and the sampling location point data, predict each location point to determine the interpolation result;

[0048] Use the interpolation result to optimize the spectral feature parameter matrix input to the water depth inversion model to generate an optimized water depth inversion result.

[0049] In an embodiment of the present invention, the preprocessing of several multispectral remote sensing images includes:

[0050] Screen the image data quality of the several multispectral remote sensing images, and screen out the remote sensing images with a cloud content in the image data less than a cloud content threshold;

[0051] Perform radiometric correction, atmospheric correction, and geometric correction operations on the screened remote sensing images, including:

[0052] Through radiometric correction, correct the gain and bias parameters of the sensor, remove the sensor noise, and restore the actual radiance of the image;

[0053] Through atmospheric correction, remove the influence of aerosols and molecular scattering in the atmosphere on the image;

[0054] Based on the known geographic coordinates, perform orthorectification on the image to eliminate the geometric distortion caused by the sensor position and terrain changes;

[0055] Crop the corrected remote sensing image to the target range;

[0056] Preprocess the measured data, including:

[0057] Perform standardization processing on the measured data, including removing outliers, filling in missing values, unifying units and coordinate systems;

[0058] Crop the measured data after standardization processing to the target range.

[0059] In an embodiment of the present invention, the multispectral remote sensing images include remote sensing images of different single bands, and the single band includes a blue band, a green band, a red band, and a near-infrared band.

[0060] As can be seen from the above solutions, the advantages of the present invention are:

[0061] The method for retrieving water depth of high sediment-laden water based on multi-spectral remote sensing disclosed by the present invention preprocesses by collecting several multi-spectral remote sensing images and measured data of the target area, determines spectral reflectance characteristics by using the preprocessed multi-spectral remote sensing images, and combines with the suspended sediment concentration to generate a spectral feature parameter matrix through normalization; based on the spectral reflectance characteristics and the measured water depth values, captures the non-linear relationship between the water depth and the spectral reflectance characteristics through variable screening and non-linear regression, and constructs an initial water depth inversion model; introduces geographical coordinates and a spatial weighting mechanism, constructs a non-stationary weight matrix through a neural network, and optimizes the initial water depth inversion model; inputs the spectral feature parameter matrix into the optimized water depth inversion model to generate an initial water depth inversion result; analyzes the error distribution characteristics, locates the sub-regions in the target area where the error exceeds the error threshold, and corrects the outliers in the sub-regions based on the spatial interpolation method, optimizes the spectral feature parameter matrix, and generates an optimized water depth inversion result. This method optimizes the spectral characteristics of remote sensing images, fully considers the influence of suspended sediment concentration and bottom substrate type, and establishes a water depth inversion model applicable to high sediment environments. By introducing spatial non-stationarity analysis and combining with geographically weighted regression technology, the adaptability of the model in complex geographical environments and the spatial continuity of the results are improved. At the same time, by using advanced non-linear modeling means and data correction technology, the accuracy and stability of water depth inversion are significantly improved. Brief Description of the Drawings

[0062] Figure 1 is the overall flowchart of the method for retrieving water depth of high sediment-laden water based on multi-spectral remote sensing provided by the embodiment of the present invention;

[0063] Figure 2 is a schematic diagram of the measured water depth at a specific example grid point;

[0064] Figure 3 is a schematic diagram of local spatial points of the measured water depth values of this example;

[0065] Figure 4 is a schematic diagram of the water depth inversion result obtained by implementing the method of the present invention for this example. Detailed Embodiments

[0066] In order to make the above objects, features, and advantages of the present invention more obvious and understandable, the following detailed description of the specific embodiments of the present invention will be given with reference to the accompanying drawings. Many specific details are set forth in the following description in order to fully understand the present invention. However, the present invention can be implemented in many other ways different from those described herein, and those skilled in the art can make similar improvements without departing from the connotation of the present invention. Therefore, the present invention is not limited by the specific embodiments disclosed below.

[0067] Please refer to Figure 1 as shown in Figure 1The figure shows a schematic diagram of the overall process of the water depth inversion method for high sediment-laden water bodies based on multispectral remote sensing provided by an embodiment of the present invention.

[0068] The water depth inversion method for high sediment-laden water bodies based on multispectral remote sensing specifically includes the following steps:

[0069] Step S1: Collect a number of multispectral remote sensing images and measured data of the target area and perform preprocessing, where the measured data includes water depth measured values, suspended sediment concentrations, and geographical coordinates at different position points.

[0070] In one embodiment, first collect a number of multispectral remote sensing images of the target area, including remote sensing images of different single bands. The single bands include the blue band, green band, red band, and near-infrared band. Combine hyperspectral images (if available) to ensure that the images cover the target spatial and temporal ranges. Collect the measured data of the target area, including information such as water depth measured values, suspended sediment concentrations, and geographical coordinates (including longitude and latitude) at different position points, and record the sampling time, sampling position, and data quality information.

[0071] In one embodiment, it is further necessary to perform preprocessing on the multispectral remote sensing images and the measured data. In this embodiment, the preprocessing methods for the multispectral remote sensing images and the measured data are different. For the multispectral remote sensing images, first screen the image data quality of the number of multispectral remote sensing images, and select the remote sensing images with a cloud cover less than a cloud cover threshold. In one embodiment, the cloud cover threshold is set to 20%, and generate a user folder for storing calculation data. Otherwise, first collect the multispectral remote sensing images. Then perform operations of radiometric correction, atmospheric correction, and geometric correction on the selected remote sensing images to ensure the quality and reliability of the image data. Specifically, through radiometric correction, correct the gain and bias parameters of the sensor, remove the sensor noise, and restore the actual radiance of the image to ensure that the radiance value of the image is accurate and reliable. Through atmospheric correction, for example, use the 6S model or other atmospheric correction methods to remove the influence of aerosols, molecular scattering, etc. in the atmosphere on the image. The corrected image reflects the true reflectance of the ground surface to ensure the accuracy of the analysis results. For geometric correction, based on the known geographical coordinates, perform orthorectification on the image to eliminate geometric distortions caused by sensor position and terrain changes, and ensure that the image is accurately aligned with the actual geographical location.

[0072] For the measured data, perform standardization processing on the measured data, including removing outliers (such as by the 3σ method or box plot method), filling in missing values, and unifying the units and coordinate systems.

[0073] Finally, define the target range, including spatial boundaries and time windows, to ensure the consistency between remote sensing images and measured data; crop the corrected remote sensing images and standardized processed data to the target range, and generate unified raster files and vector files.

[0074] Step S2: Use the preprocessed multi-spectral remote sensing images to determine spectral reflectance characteristics, and combine with the suspended sediment concentration to generate a spectral feature parameter matrix through normalization.

[0075] In one embodiment, use the preprocessed multi-spectral remote sensing images (i.e., the remote sensing image raster files obtained in the above step S1) to determine spectral reflectance characteristics, including characteristics such as reflectance of different single bands, logarithm ratio of band reflectance, and ratio of band reflectance.

[0076] First, use the preprocessed multi-spectral remote sensing images to calculate the reflectance of different single bands such as the blue band, green band, red band, and near-infrared band, and extract the trend of reflectance change.

[0077] Then, adopt the method of band logarithm ratio. Since the ratio change caused by depth is much greater than the ratio change caused by bottom albedo change, this indicates that different bottom albedos at a constant depth will still have the same ratio. By calculating the logarithm ratio of different single-band reflectances, the band reflectance logarithm ratio k1 is obtained to eliminate the non-linear influence of bottom reflectance. For example, in one embodiment, calculate the logarithm ratio of the reflectance of the blue band and the green band, i.e., ln(nblue) / ln(ngreen), where nblue is the reflectance of the blue band, ngreen is the reflectance of the green band, and n is a constant, a fixed value. When any reflectance value is input, the band reflectance logarithm ratio k1 is selected to be positive.

[0078] Calculate the ratio of different single-band reflectances, such as the ratio of the reflectance of the blue band and the green band, the ratio of the reflectance of the green band and the red band, the ratio of the reflectance of the blue band and the red band, etc., to obtain the band reflectance ratio and analyze the non-linear change of band reflectance.

[0079] Furthermore, calculate the correlation coefficient between the band reflectance ratio and the suspended sediment concentration, and screen out the band reflectance ratios corresponding to the correlation coefficients exceeding the correlation threshold (i.e., high correlation) as the sensitive band reflectance ratios sensitive to the change of the suspended sediment concentration. In one embodiment, the Pearson correlation coefficient is adopted, and the correlation between the band reflectance ratio and the suspended sediment concentration is specifically:

[0080] (1),

[0081] where X and Y represent the band reflectance ratio and the suspended sediment concentration respectively, and represents the mean of X and Y, and r is the correlation coefficient.

[0082] An association model between the suspended sediment concentration and the ratio of reflectances in the sensitive bands is established, the scattering and absorption effects of the suspended sediment concentration on the bands are analyzed, and the suspended sediment concentration index is calculated according to this association model. Specifically, the ratio of reflectances in the selected sensitive bands is used as the independent variable, and the suspended sediment concentration SSC is used as the dependent variable. A suitable regression model (such as linear regression, non-linear regression, or machine learning model) is selected to construct the association model between the suspended sediment concentration SSC and the ratio of reflectances in the sensitive bands m. Taking power regression as an example, the association model is as described in Equation (2);

[0083] (2),

[0084] where a is the coefficient, b is the power, m is the ratio of reflectances in the sensitive bands, is the suspended sediment concentration.

[0085] The prediction ability and robustness of the association model are verified using evaluation metrics (such as R², MSE). If the verification is passed, the suspended sediment concentration index k2 for each pixel is calculated. The suspended sediment concentration index k2 is obtained through the association model, as shown in Equation (3);

[0086] (3),

[0087] The reflectances of different single bands, the logarithm ratio of band reflectances k1, and the suspended sediment concentration index k2 are integrated and normalized to generate a spectral feature parameter matrix for use as the input to the subsequent water depth inversion model.

[0088] Step S3: Based on the spectral reflectance characteristics and the measured water depth values, capture the non-linear relationship between the water depth and the spectral reflectance characteristics through variable screening and non-linear regression, and construct an initial water depth inversion model.

[0089] In one embodiment, for each band, each sample point (i.e., each measurement point) has a reflectance value and a measured water depth value, so that each band will have a set of reflectances and corresponding water depth data. Then, the correlation coefficient is calculated for each set of data to obtain the correlation between each band and the water depth. By combining the reflectances of different single bands with the corresponding water depths and using a correlation coefficient metric, such as the Spearman coefficient, as shown in Equation (4), the correlation between the band and the water depth is initially evaluated, and the significantly correlated bands and the corresponding ratios of band reflectances are initially identified. Generally, the larger the absolute value of the correlation coefficient, the stronger the correlation.

[0090] (4),

[0091] Among them, is the correlation coefficient, represents the rank of the normalized single-band reflectance sample x i , represents the rank of the measured water depth sample y i , and are the average ranks of R(x) and R(y), respectively.

[0092] Then, the significantly correlated bands and the corresponding band reflectance ratios are used as independent variables (j = 1, 2, …, k), and the water depth is used as the dependent variable to preliminarily construct a water depth inversion model, that is:

[0093] (5),

[0094] where k is the number of explanatory variables, and β j (j = 1, 2, …, k) are coefficients that can be obtained by least squares calculation, is the error term.

[0095] Furthermore, the preliminarily constructed water depth inversion model is corrected. First, the significantly correlated bands and the corresponding band reflectance ratios are successively screened and corrected through multiple variable regression. Specifically, in one embodiment, methods such as stepwise regression or ridge regression are used to further screen and correct the significantly correlated bands and the corresponding band reflectance ratios to reduce the influence of multicollinearity. Taking the stepwise regression method as an example, the independent variable x k is introduced. Assuming the model is y = β 0 +β 1 x 1 +...+β (k-1) x (k-1) +e, considering whether the variable x k can be introduced into the model, the hypothesis condition H: β k = 0 is proposed, and a significance test is performed on it, and the statistic F is listed, as shown in Equation (6);

[0096] (6),

[0097] is the residual sum of squares of the model when the hypothesis condition H holds (k - 1 variables), is the independent variable x kThe sum of squared residuals of the model after successful introduction (k variables), where q and p - k - 1 represent degrees of freedom. In stepwise regression, usually q = 1. When the assumption condition H holds, it follows an F - distribution with degrees of freedom 1 and p - k - 1. When it is too large (generally greater than the 0.05 upper quantile), the assumption condition H is rejected, indicating that the variable is significantly enough, and then this variable is introduced. Traverse all variables outside the model and introduce the independent variable corresponding to the maximum statistic F.

[0098] Consider removing variables. Similarly, assume the model is y = β 0 +β 1 x 1 +...+β k x k +e. Consider whether the independent variable x k can be removed from the model. Propose the hypothesis H: β k = 0. The statistic F is the same as above. When it is too small (less than the 0.05 upper quantile), the hypothesis condition H is accepted, indicating that the independent variable is not significant, and then this independent variable is removed. Traverse all variables within the model and remove the independent variable corresponding to the minimum statistic F.

[0099] In addition, it should be noted that in one removal or introduction process, only one variable is changed. Any variable can enter and exit the model any number of times. When a variable is successfully removed, continue to remove until the removal fails, then start to introduce new variables. When a variable is successfully introduced, stop introducing and immediately start to remove the original variable. When the introduction fails, the stepwise regression ends, break out of the loop, and output the result.

[0100] Then, through residual analysis and non - linear regression methods (such as polynomial regression, generalized additive model), the correlation between the band and water depth is corrected. Residual analysis is an important means to evaluate the fitting effect of the regression model. Through the residual plot, it can be intuitively judged whether the model meets the basic assumptions (such as linear assumption, normality assumption, etc.). In water depth inversion, residual analysis can help identify problems such as outliers, non - linear relationships, or heteroscedasticity in the relationship between the band and water depth. Polynomial regression can effectively correct the non - linear relationship between the band and water depth and improve the inversion accuracy. For example, existing technologies have shown that by increasing the degree of the polynomial to improve the water depth inversion model, the feature dimension of the model can be expanded, enabling the inversion model to fit correctly and thus improving the inversion accuracy. Since residual analysis and non - linear regression methods are existing technologies, this application will not introduce them in detail.

[0101] In one embodiment, the logarithm ratio of the band reflectance and the sediment concentration index are further introduced, non - linear terms and interaction terms are introduced to optimize the model structure, so as to further optimize the preliminarily constructed water depth inversion model and obtain the initial water depth inversion model.

[0102] Step S4: Introduce the geographical coordinates and spatial weighting mechanism, construct a non-stationary weight matrix through a neural network, and optimize the initial water depth inversion model.

[0103] In one embodiment, the geographical coordinates and spatial weighting mechanism are further introduced, a non-stationary weight matrix is constructed through a neural network, and the initial water depth inversion model is optimized to address the impact of spatial heterogeneity on the model.

[0104] Specifically, based on the geographical coordinates, the variation of the corresponding characteristic parameters can be regarded as different fluctuations of the "average relationship" caused by spatial non-stationarity. Utilizing the excellent fitting ability of the neural network model, a spatial weighted neural network is designed to construct a non-stationary weight matrix, which contains the spatial weights of each location point, to construct a geographical neural network weighted regression model (GNNWR) to update the initial water depth inversion model constructed in the above steps. The spatial weighted neural network uses the spatial distance d i and spatial weights as its input layer and output layer, and inserts hidden layers as needed, as shown in Equation (7).

[0105] (7),

[0106] where, is the distance from the estimated location point i to all training location points, and respectively represent the longitude and latitude of location point i, represents the spatial weight of location point i, and SWNN represents the spatial weighted neural network.

[0107] Then, integrate the measured water depth values and the corresponding spectral reflectance characteristics to construct a dataset and randomly divide this dataset into a training set, a validation set, and a test set. The training set is used to optimize the network weights and biases of the spatial weighted neural network, and the validation dataset is used to determine whether the model is overfitting after each training. After training is completed, use the test dataset to evaluate the generalization ability and prediction ability of the model through a similar validation process. During the modeling process, in combination with Equation (7), calculate the distance from the estimated location point k i to all training location points d i as the input of the spatial weighted neural network, and obtain the spatial weight i of the estimated location point k from the output layer , each weight corresponds to a predefined independent variable, as shown in Equation (8), k is the number of independent variables, that is, the non-stationary weight matrix obtained is:

[0108] (8),

[0109] where, is the estimated location point ki The spatial weight, is a non-stationary weight matrix.

[0110] Furthermore, the non-stationary weight matrix is added to the initial water depth inversion model to optimize the initial water depth inversion model. Specifically, the least-squares coefficient representing the average relationship is calculated from the training set , and the spatial weight is multiplied by the least-squares coefficient to obtain the non-stationary coefficient , that is:

[0111] (9),

[0112] where j = 1, 2, …, k, .

[0113] Combining Equation (5) and Equation (9), according to the product of the non-stationary coefficient and the corresponding independent variable , the initial water depth inversion model is updated to:

[0114] (10),

[0115] where, represents the water depth, the non-stationary coefficient and the corresponding independent variable , that is, the significantly correlated bands and the corresponding band reflectance ratios.

[0116] The water depth prediction value is obtained. See Equation (11). Equation (11) can be expressed in matrix form as Equation (12), where:

[0117] (11),

[0118] (12),

[0119] where, .

[0120] The goodness of fit of the geospatial neural network weighted regression model and the least-squares model is tested. For the least-squares model, its estimated value is . Let , then . Then the geospatial neural network weighted regression model and the least-squares model can be described as Equation (13). If The value is close to 1. Then there is no significant difference between the geospatial neural network weighted regression model and the least squares model. For Equation (14), given a significance level α, if the distribution function , it can be inferred that the fitting effect of the geospatial neural network weighted regression model on the dataset is significantly better than that of the least squares model. Where:

[0121] (13),

[0122] (14),

[0123] Wherein, can represent or , , represents the identity matrix; , , is the residual generation matrix, and tr is the trace of the matrix.

[0124] Combining the predicted water depth value and the measured water depth value, the performance of the model is evaluated through a cross-validation method during the model training stage to optimize the water depth inversion model. In one embodiment, K-fold cross-validation is adopted, and the dataset is divided into K subsets of equal size. In each iteration, one subset is selected as the validation set, and the remaining K-1 subsets are used as the training set. During each iteration, the training set is used to train the water depth inversion model to optimize the weights and biases of the spatial weighted neural network. During each training process, the least squares coefficients are calculated based on the training set, and the non-stationary weights are calculated using the spatial distance; after the training is completed, the predicted water depth value is calculated by the validation set and compared with the measured water depth value to determine the error index of the model after each training. For example, the mean absolute percentage error (MAPE), root mean square error (RMSE), mean absolute error (MAE), R² score, and corrected Akaike information criterion ( ) etc.

[0125] Among them, the mean absolute percentage error is expressed as: ;

[0126] The root mean square error is expressed as: ;

[0127] The mean absolute error is expressed as: ;

[0128] The R² score is expressed as: ;

[0129] The corrected Akaike information criterion is expressed as: ;

[0130] Among them, is the measured water depth value, is the predicted water depth value, .

[0131] In each iteration process, different subsets are used as the validation set, and the remaining subsets are used as the training set. After all K iterations are completed, the average value of the error metrics of all validation sets is calculated as the total evaluation metric in the model training stage to evaluate the model performance. By analyzing the changes in the error metrics of each validation, the stability of the water depth inversion model is evaluated. A model with high stability should show similar performance on different validation sets. By evaluating the prediction ability of the model on different data subsets, it is ensured that the optimized water depth inversion model still has high prediction accuracy under different conditions.

[0132] Step S5: Input the spectral feature parameter matrix into the optimized water depth inversion model to generate an initial water depth inversion result.

[0133] After obtaining the spectral feature parameter matrix through the above step S4 and the optimized water depth inversion model through step S5, inputting the spectral feature parameter matrix into the optimized water depth inversion model can generate an initial water depth inversion result.

[0134] Step S6: Analyze the error distribution characteristics, locate the sub-regions in the target region where the error exceeds the error threshold, and correct the outliers in this sub-region based on the spatial interpolation method to optimize the spectral feature parameter matrix and generate the optimized water depth inversion result.

[0135] In one embodiment, in combination with the error metrics calculated in step S4 above, such as accuracy evaluation metrics like coefficient of determination (R²), root mean square error (RMSE), and corrected Akaike information criterion (AICC), analyze the error distribution characteristics, locate the sub-regions in the target area where the error exceeds the error threshold, and determine whether there are outliers in the measured data corresponding to the sub-regions. If there are no outliers, reduce the error fluctuations in the sub-regions through smoothing techniques (such as existing techniques like local regression and moving average). If there are outliers, use spatial interpolation methods to correct the outliers in the sub-regions to ensure the spatial continuity of the results. In one embodiment, the Kriging interpolation method is selected. Specifically, representative sampling location points are selected to cover the target area, and the sampling location points that deviate significantly from the normal range are removed or corrected to avoid affecting the interpolation results. Then, calculate the spatial distance between each pair of sampling location points, calculate the semi-variogram based on the distance and difference value between the sampling location points to form a semi-variogram function; select a suitable data model (such as spherical model, exponential model, or Gaussian model) to fit the semi-variogram function and determine the model parameters (such as sill, range, nugget); apply the ordinary Kriging method, and based on the semi-variogram function and the sampling location point data, predict each unknown location point, as shown in Equation (15), and at the same time estimate the prediction error (Kriging variance) , as shown in Equation (16), evaluate the reliability of the interpolation results, and determine the interpolation results.

[0136] (15),

[0137] (16),

[0138] where, is the predicted value of the unknown location point , is the weight, is the known value of the sampling location point . The weight is obtained by solving the Kriging equation to minimize the prediction error. is the

[0139] Kriging variance, is the location point and the semi-variogram between, μ is the Lagrange multiplier.

[0140] Finally, use the interpolation results to optimize the spectral feature parameter matrix input to the water depth inversion model, and generate optimized water depth inversion results, including an inversion layer file and multi-resolution distribution data. Refer to Figures 2 - 4 as described Figure 2 is a schematic diagram of the measured water depth at a certain example grid point, Figure 3Schematic diagram of local spatial points of measured water depth values; Figure 4 Schematic diagram of the water depth inversion result obtained by implementing the method of the present invention.

[0141] In one embodiment, the optimized water depth inversion result is further output and visualized. By extracting the water depth inversion result within the target time range, high-precision raster and vector data files are generated; statistical analysis is carried out, and a precision evaluation report is output, including the index range and spatial distribution characteristics; a visualized image of the water depth distribution is generated, including an isobath map and a time series change map; the suspended sediment concentration and the inverted water depth are superimposed to generate a comprehensive distribution map; the analysis report of the water depth change trend in the study area is generated by combining the inversion result with the remote sensing image, providing support for subsequent geomorphic monitoring and river channel management.

[0142] In summary, the water depth inversion method for high-sediment-laden water bodies based on multi-spectral remote sensing disclosed in the present invention is based on multi-spectral remote sensing technology. By optimizing the spectral characteristics of remote sensing images, fully considering the influence of suspended sediment concentration and substrate type, a water depth inversion model applicable to high-sediment environments is established. By introducing spatial non-stationarity analysis and combining with geographically weighted regression technology, the adaptability of the model in complex geographical environments and the spatial continuity of the results are improved. At the same time, by using advanced non-linear modeling means and data correction technology, the accuracy and stability of water depth inversion are significantly improved.

[0143] The above specific embodiments do not constitute a limitation to the protection scope of the present invention. Those skilled in the art should understand that various modifications, combinations, sub-combinations and substitutions can be made according to design requirements and other factors. Any modifications, equivalent substitutions and improvements made within the spirit and principle of the present invention shall be included within the protection scope of the present invention.

Claims

1. A method for inverting water depth of high-sand-content water bodies based on multispectral remote sensing, characterized in that: The method includes: Collect and pre-process a number of multispectral remote sensing images and measured data of the target area, wherein the measured data includes measured values ​​of water depth, suspended sediment concentration, and geographic coordinates at different locations; Using the pre-processed multi-spectral remote sensing image, determining the spectral reflectance characteristics, and combining the suspended sediment concentration, normalizing and generating a spectral characteristic parameter matrix; Based on the spectral reflectance characteristics and the measured water depth values, the nonlinear relationship between the water depth and the spectral reflectance characteristics is captured through variable screening and nonlinear regression to construct an initial water depth inversion model; The geographic coordinates and spatial weighting mechanism are introduced, a non-stationary weight matrix is ​​constructed through a neural network, and an initial water depth inversion model is optimized; Inputting the spectral characteristic parameter matrix into the optimized water depth inversion model to generate an initial water depth inversion result; The error distribution characteristics are analyzed, the sub-region in the target area where the error exceeds the error threshold is located, and the outliers in the sub-region are corrected based on the spatial interpolation method, the spectral characteristic parameter matrix is ​​optimized, and the optimized water depth inversion result is generated.

2. The method according to claim 1, characterized in that The pre-processed multi-spectral remote sensing image is used to determine the spectral reflectance characteristics, and combined with the suspended sediment concentration, a spectral characteristic parameter matrix is ​​generated, including: Utilizing the pre-processed multispectral remote sensing image, calculating the reflectivity of different single bands; Calculate the logarithmic ratio of different single-band reflectances to obtain the logarithmic ratio of band reflectances; Calculating the ratio of reflectances of different single bands to obtain the band reflectance ratio, wherein the spectral reflectance characteristics include the reflectances of different single bands, the logarithmic ratio of the band reflectances, and the band reflectance ratio; Calculating the correlation coefficient between the reflectivity ratio of the band and the suspended sediment concentration, and screening out the reflectivity ratio of the band corresponding to the correlation coefficient exceeding the correlation threshold as the reflectivity ratio of the sensitive band sensitive to the change of the suspended sediment concentration; Establishing a correlation model between the suspended sediment concentration and the reflectivity ratio of the sensitive band, and calculating a suspended sediment concentration index according to the correlation model; The reflectances of different single bands, the logarithmic ratio of the band reflectances, and the suspended sediment concentration index are integrated and normalized to generate a spectral characteristic parameter matrix.

3. The method according to claim 2, characterized in that Based on the spectral reflectance characteristics and the measured water depth values, the nonlinear relationship between water depth and spectral reflectance characteristics is captured through variable screening and nonlinear regression, and a water depth inversion model is preliminarily established, including: Combining the reflectivity of different single bands with the corresponding measured water depth, using the correlation coefficient index, preliminarily evaluate the correlation between the bands and the water depth, and preliminarily identify the significantly correlated bands and the corresponding band reflectivity ratios; The significantly correlated bands and the corresponding band reflectivity ratios were used as independent variables, and the water depth was used as the dependent variable to preliminarily construct a water depth inversion model. The significantly correlated bands and the corresponding band reflectance ratios were screened and corrected one by one through multivariate regression; The correlation between the band and the water depth was corrected by residual analysis and nonlinear regression methods; The band reflectivity logarithmic ratio and the sediment concentration index are introduced to optimize the initially constructed water depth inversion model to obtain the initial water depth inversion model.

4. The method according to claim 3, characterized in that The geographic coordinates and spatial weighting mechanism are introduced, a non-stationary weight matrix is ​​constructed through a neural network, and the initial water depth inversion model is optimized, including: Based on the geographic coordinates, a spatially weighted neural network is designed using a neural network model to construct a non-stationary weight matrix, wherein the non-stationary weight matrix includes a spatial weight of each location point; Integrate the measured water depth values ​​and the corresponding spectral reflectance features to construct a data set and divide the data set into a training set, a validation set and a test set; In the modeling process, the distances from the estimated position points of the training set, the validation set and the test set to all the training position points are calculated as the input of the spatial weighted neural network, and the spatial weights of the estimated position points are obtained by the output layer; The non-stationary weight matrix is ​​added to the initial water depth inversion model to optimize the initial water depth inversion model.

5. The method according to claim 4, characterized in that Adding the non-stationary weight matrix to the initial water depth inversion model to optimize the initial water depth inversion model comprises: Calculating least squares coefficients from the training set; Multiplying the spatial weight by the least squares coefficient to obtain a non-stationary coefficient; According to the product of the non-stationary coefficient and the corresponding independent variable, the initial water depth inversion model is updated to obtain a water depth prediction value; The water depth prediction value is combined with the water depth measured value, and the model performance is evaluated in the model training stage through a cross-validation method to optimize the water depth inversion model.

6. The method according to claim 5, characterized in that The model performance is evaluated during the model training phase by a cross-validation method to optimize the water depth inversion model, including: K-fold cross validation is used to divide the data set into several subsets of equal size. In each iteration, one subset is selected as the validation set and the remaining subsets are used as the training set. The water depth inversion model is trained using the training set to optimize the weights and biases of the spatially weighted neural network, and in each training process, the least squares coefficients are calculated based on the training set, and the non-stationary weights are calculated using the spatial distance; After the training is completed, the water depth prediction value is calculated from the validation set and compared with the corresponding water depth measured value to determine the error index of the model after each training; In each iteration, a different subset is used as the validation set, and the remaining subsets are used as the training set. After all K iterations are completed, the average error index of all validation sets is calculated as the total evaluation index of the model training stage to evaluate the model performance.

7. The method according to claim 6, characterized in that In combination with the error index, the error distribution characteristics are analyzed, the sub-region in the target region where the error exceeds the error threshold is located, and whether there are abnormal values ​​in the measured data corresponding to the sub-region; If there are outliers, the spatial interpolation method is used to correct the outliers in the sub-region; if there are no outliers, the smoothing technology is used to reduce the error fluctuation in the sub-region.

8. The method according to claim 7, characterized in that Spatial interpolation methods are used to correct outliers in this sub-region, including: Selecting representative sampling locations to cover the target area; Calculate the spatial distance between each pair of sampling points, calculate the semivariance based on the distance and difference between the sampling points, and form a semivariogram; Fitting the semivariogram to determine model parameters; Apply the ordinary kriging method, predict each location point according to the semivariogram and sampling location point data, and determine the interpolation result; The interpolation result is used to optimize the spectral feature parameter matrix input into the water depth inversion model to generate an optimized water depth inversion result.

9. The method according to claim 1, characterized in that: Preprocessing of several multispectral remote sensing images includes: Screening the image data quality of the plurality of multispectral remote sensing images, and screening out remote sensing images whose image data cloud content is less than a cloud content threshold; Perform radiation correction, atmospheric correction, and geometric correction operations on the selected remote sensing images, including: Through radiation correction, the gain and bias parameters of the sensor are corrected, the sensor noise is removed, and the actual radiation brightness of the image is restored; Through atmospheric correction, the influence of aerosol and molecular scattering in the atmosphere on the image is removed; Based on known geographic coordinates, the image is orthorectified to eliminate geometric distortion caused by changes in sensor position and terrain; Crop the corrected remote sensing image to the target range; Preprocessing the measured data includes: Standardizing the measured data, including removing outliers, filling missing values, and unifying units and coordinate systems; The measured data after the normalization process is clipped to a target range.

10. The method according to claim 1, characterized in that The multispectral remote sensing image includes remote sensing images of different single bands, and the single band includes a blue band, a green band, a red band and a near-infrared band.

Images