High-sand-content water body water depth inversion method based on multispectral remote sensing

Abstract

The invention provides a high-sand-content water body water depth inversion method based on multispectral remote sensing, and belongs to the technical field of remote sensing water depth inversion. The method comprises the following steps: collecting a plurality of multispectral remote sensing images and actually measured data of a target area; determining spectral reflectivity characteristics by using the preprocessed multispectral remote sensing image, and generating a spectral characteristic parameter matrix in a normalization manner in combination with the suspended sediment concentration; constructing an initial water depth inversion model based on the spectral reflectivity characteristics and the water depth measured value; geographic coordinates and a space weighting mechanism are introduced, 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; and positioning a sub-region with an error exceeding an error threshold in the target region, correcting an abnormal value of the sub-region based on a spatial interpolation method, optimizing the spectral characteristic parameter matrix, and generating an optimized water depth inversion result. The method improves the precision and stability of water depth inversion.

Description

Technical Field

[0001] The invention belongs to the technical field of remote sensing water depth inversion, and in particular relates to a water depth inversion method for a high-sand content water body based on multi-spectral remote sensing. Background Art

[0002] For rivers with high sand content, such as the Yellow River, the topography of its delta region changes dramatically due to the combined effects of multiple factors such as waves, tides, currents and storms, and tidal gullies frequently swing or even disappear. Accurately measuring the dynamic changes in water depth of such terrain is of great significance for understanding the evolution mechanism of the region and implementing effective resource management. However, existing water depth measurement technology faces multiple challenges in high sand content environments.

[0003] The measurement accuracy of traditional acoustic depth sounding equipment (such as Doppler current profilers and multi-beam sonar systems) in highly sandy water bodies is significantly reduced due to the influence of suspended sediment concentration and complex bottom sediments. In addition, these devices are costly, complex to maintain, and have limited coverage, making them unsuitable for large-scale rapid depth measurement. Passive remote sensing has become an important means of water depth measurement due to its ability to obtain data over a large range and quickly. Water depth inversion is achieved by analyzing the relationship between water column reflectivity and water depth. However, in a highly sandy environment, traditional optical models face the following problems: 1) The scattering and absorption effects of suspended sediment distort the spectral signal, resulting in reduced inversion accuracy. 2) The diversity of riverbed sediments significantly interferes with reflectivity, increasing the uncertainty of the model. 3) Spectral mixing effects and multiple scattering effects complicate the model parameterization process.

[0004] In view of the above problems, the existing methods are difficult to meet the accuracy and efficiency requirements of water depth measurement in complex environments with high sand content, and this invention is specially proposed. Summary of the invention

[0005] In order to overcome the problems existing in the related art, the disclosed embodiment of the present invention provides a method for water depth inversion of high-sand content water bodies based on multispectral remote sensing. By optimizing the spectral characteristics of remote sensing images and fully considering the influence of suspended sediment concentration and bottom type, a water depth inversion model suitable for high-sand content environments is established. By introducing spatial non-stationarity analysis and combining 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 utilizing advanced nonlinear modeling methods and data correction technology, the accuracy and stability of water depth inversion are significantly improved.

[0006] On the one hand, the present invention provides a method for inverting water depth of a high-sand-content water body based on multispectral remote sensing, the method comprising: 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.

[0007] In one embodiment of the present invention, the spectral reflectance characteristics are determined by using the pre-processed multi-spectral remote sensing image, 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.

[0008] In one embodiment of the present invention, based on the spectral reflectance characteristics and the measured water depth value, the nonlinear relationship between the water depth and the spectral reflectance characteristics is captured by 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 are screened and corrected one by one through multivariate regression; The correlation between the band and the water depth is 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.

[0009] In one embodiment of the present invention, 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, 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.

[0010] In one embodiment of the present invention, the non-stationary weight matrix is ​​added to the initial water depth inversion model to optimize the initial water depth inversion model, including: 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.

[0011] In one embodiment of the present invention, the model performance is evaluated in the model training stage 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.

[0012] In one embodiment of the present invention, the error distribution characteristics are analyzed in combination with the error index, a sub-region in the target region where the error exceeds the error threshold is located, and it is determined whether there is an abnormal value 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.

[0013] In one embodiment of the present invention, a spatial interpolation method is used in the sub-region to correct outliers, 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.

[0014] In one embodiment of the present invention, preprocessing a plurality of 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.

[0015] In one embodiment of the present invention, 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.

[0016] It can be seen from the above scheme that the advantages of the present invention are: The invention discloses a method for inverting water depth of a high-sand-content water body based on multispectral remote sensing. The method collects a number of multispectral remote sensing images and measured data of a target area and performs preprocessing. The preprocessed multispectral remote sensing images are used to determine the spectral reflectance characteristics, and the spectral characteristic parameter matrix is ​​normalized and generated in combination with the suspended sediment concentration; based on the spectral reflectance characteristics and the measured value of the water depth, the nonlinear relationship between the water depth and the spectral reflectance characteristics is captured through variable screening and nonlinear regression, and an initial water depth inversion model is constructed; geographic coordinates and a 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; the spectral characteristic parameter matrix is ​​input into the optimized water depth inversion model to generate an initial water depth inversion result; the error distribution characteristics are analyzed, the sub-area in the target area where the error exceeds the error threshold is located, and the outliers of the sub-area are corrected based on the spatial interpolation method, the spectral characteristic parameter matrix is ​​optimized, and the optimized water depth inversion result is generated. The method optimizes the spectral characteristics of remote sensing images, fully considers the influence of suspended sediment concentration and bottom type, and establishes a water depth inversion model suitable for a high-sand-content environment. By introducing spatial non-stationarity analysis and combining it 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 nonlinear modeling methods and data correction technology, the accuracy and stability of water depth inversion are significantly improved. BRIEF DESCRIPTION OF THE DRAWINGS

[0017] Figure 1 It is an overall flow chart of a method for inverting water depth of a high-sand-content water body based on multispectral remote sensing provided by an embodiment of the present invention; Figure 2 It is a schematic diagram of the measured water depth at a specific example grid point; Figure 3 It is a schematic diagram of the local spatial points of the measured water depth values ​​of this example; Figure 4 It is a schematic diagram of the water depth inversion result obtained by executing the method of the present invention on this example. DETAILED DESCRIPTION

[0018] In order to make the above-mentioned objects, features and advantages of the present invention more obvious and easy to understand, the specific embodiments of the present invention are described in detail below in conjunction with the accompanying drawings. In the following description, many specific details are set forth to facilitate a full understanding of 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 violating the connotation of the present invention, so the present invention is not limited by the specific implementation disclosed below.

[0019] See also Figure 1 As shown, Figure 1 The figure shows a schematic diagram of the overall process of a method for inverting water depth of a high-sand content water body based on multispectral remote sensing provided by an embodiment of the present invention.

[0020] The water depth inversion method of high-sand-content water body based on multispectral remote sensing specifically includes the following steps: Step S1, collecting a number of multispectral remote sensing images and measured data of the target area and preprocessing them, wherein the measured data includes measured values ​​of water depth, suspended sediment concentration, and geographic coordinates of different locations.

[0021] In one embodiment, firstly, a plurality of multispectral remote sensing images of the target area are collected, including remote sensing images of different single bands, which include blue band, green band, red band and near infrared band, combined with hyperspectral images (if available), to ensure that the images cover the target spatial range and time range. The measured data of the target area are collected, including the measured water depth values, suspended sediment concentration, geographic coordinates (including longitude and latitude) and other information at different locations, and the sampling time, sampling location and data quality information are recorded.

[0022] In one embodiment, it is further necessary to pre-process the multispectral remote sensing images and the measured data. In this embodiment, the pre-processing methods of the multispectral remote sensing images and the measured data are different. For multispectral remote sensing images, the image data quality of the multispectral remote sensing images is first screened, and remote sensing images whose image data cloud content is less than a cloud content threshold are screened. In one embodiment, the cloud content threshold is set to 20%, and a user folder is generated for storing the calculated data. Otherwise, the multispectral remote sensing images are first collected. Then, the operations of radiation correction, atmospheric correction, and geometric correction are performed on the screened remote sensing images to ensure the quality and reliability of the image data. Specifically, through radiation correction, the gain and bias parameters of the sensor are corrected, the sensor noise is removed, the actual radiation brightness of the image is restored, and the radiation value of the image is ensured to be accurate and reliable. Through atmospheric correction, for example, the 6S model or other atmospheric correction methods are used to remove the effects of aerosols, molecular scattering, etc. in the atmosphere on the image. The corrected image reflects the true reflectivity of the surface, ensuring the accuracy of the analysis results. For geometric correction, the image is orthorectified based on known geographic coordinates to eliminate geometric distortion caused by changes in sensor position and terrain, ensuring that the image is accurately aligned with the actual geographic location.

[0023] The measured data are standardized by removing outliers (such as by the 3σ method or the box plot method), filling in missing values, and unifying units and coordinate systems.

[0024] Finally, define the target range, including spatial boundaries and time windows, to ensure the consistency between the remote sensing image and the measured data; crop the above-mentioned corrected remote sensing image and standardized processing to the target range, and generate unified raster files and vector files.

[0025] Step S2: using the pre-processed multi-spectral remote sensing image to determine the spectral reflectance characteristics, and combining the suspended sediment concentration to normalize and generate a spectral characteristic parameter matrix.

[0026] In one embodiment, the preprocessed multispectral remote sensing image (i.e., the remote sensing image raster file obtained in step S1 above) is used to determine spectral reflectance characteristics, including reflectance of different single bands, logarithmic ratio of band reflectance, and ratio of band reflectance.

[0027] Firstly, the preprocessed multispectral remote sensing image is used to calculate the reflectance of different single bands such as blue band, green band, red band and near-infrared band, and the reflectance change trend is extracted.

[0028] Then, using the band logarithmic ratio method, the ratio change caused by depth is much greater than the ratio change caused by the change in bottom albedo, which indicates that different bottom albedo will still have the same ratio at a constant depth. By calculating the logarithmic ratio of different single-band reflectivities, the band reflectivity logarithmic ratio k1 is obtained to eliminate the nonlinear effect of the bottom reflectivity. For example, in one embodiment, the logarithmic ratio of the reflectivity of the blue band and the green band is calculated, that is, ln(nblue) / ln(ngreen), where nblue is the reflectivity of the blue band, ngreen is the reflectivity of the green band, and n is a constant, which is a fixed value. Given any reflectivity value input, the band reflectivity logarithmic ratio k1 is selected to be positive.

[0029] The ratios of different single-band reflectances are calculated, such as the ratio of the blue band to the green band reflectance, the ratio of the green band to the red band reflectance, the ratio of the blue band to the red band reflectance, etc., to obtain the band reflectance ratio in order to analyze the nonlinear change of the band reflectance.

[0030] Furthermore, the correlation coefficient between the band reflectivity ratio and the suspended sediment concentration is calculated, and the band reflectivity ratio corresponding to the correlation coefficient exceeding the correlation threshold (i.e., high correlation) is selected as the sensitive band reflectivity ratio that is sensitive to the change in the suspended sediment concentration. In one embodiment, the Pearson correlation coefficient is used, and the correlation between the band reflectivity ratio and the suspended sediment concentration is specifically: (1) Among them, X and Y represent the band reflectivity ratio and suspended sediment concentration, respectively. and represents the mean of X and Y, and r is the correlation coefficient.

[0031] Establish a correlation model between the suspended sediment concentration and the reflectivity ratio of the sensitive band, analyze the scattering and absorption effects of the suspended sediment concentration on the band, and calculate the suspended sediment concentration index based on the correlation model. Specifically, use the selected sensitive band reflectivity ratio as the independent variable, the suspended sediment concentration SSC as the dependent variable, and select a suitable regression model (such as linear regression, nonlinear regression or machine learning model) to construct a correlation model between the suspended sediment concentration SSC and the sensitive band reflectivity ratio m. Taking power regression as an example, the correlation model is as described in formula (2); (2) Among them, a is the coefficient, b is the power, and m is the reflectivity ratio of the sensitive band. is the suspended sediment concentration.

[0032] Use evaluation indicators (such as R², MSE) to verify the prediction ability and robustness of the correlation model. If the verification is passed, calculate the suspended sediment concentration index k2 of each pixel point, and obtain the suspended sediment concentration index k2 through the correlation model, as shown in formula (3); (3) The reflectance of different single bands, the band reflectance logarithm ratio k1, and the suspended sediment concentration index k2 are integrated and normalized to generate a spectral characteristic parameter matrix to be used as an input for the subsequent water depth inversion model.

[0033] Step S3: Based on the spectral reflectance characteristics and the measured water depth value, 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.

[0034] In one embodiment, for each band, each sample point (i.e., each measurement point) has a reflectivity value and a measured water depth value, so that each band has a set of reflectivity 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 reflectivity of different single bands with the corresponding water depth, a correlation coefficient index, such as the Spearman coefficient, is used, such as formula (4), to preliminarily evaluate the correlation between the band and the water depth, and preliminarily identify the significantly correlated bands and the corresponding band reflectivity ratios. Generally, the larger the absolute value of the correlation coefficient, the stronger the correlation.

[0035] (4) in, is the correlation coefficient, Represents the normalized single-band reflectance sample x i rank, Represents the sample of measured water depth value y i rank, and are the average ranks of R(x) and R(y) respectively.

[0036] Then, the significantly correlated bands and the corresponding band reflectance ratios were used as independent variables. (j=1,2,…,k), water depth As the dependent variable, a preliminary water depth inversion model is constructed, namely: (5) Among them, k is the number of explanatory variables, β j (j=1,2,…,k) are coefficients, which can be calculated by least squares. is the error term.

[0037] Furthermore, the preliminary constructed water depth inversion model is corrected by first screening and correcting the significantly correlated bands and the corresponding band reflectivity ratios through multivariate regression. Specifically, in one embodiment, a method such as stepwise regression or ridge regression is used to further screen and correct the significantly correlated bands and the corresponding band reflectivity ratios to reduce the impact of multicollinearity. Taking the stepwise regression method as an example, the independent variable x is introduced. k , assuming that the model is y=β0+β1x1+...+β (k-1) x (k-1) +e, consider the variable x k Whether the model can be introduced, then the hypothesis condition H:β is proposed k =0, perform a significance test on it and list the statistic F, see formula (6); (6) is the residual sum of squares of the model when the assumption condition H is met (k-1 variables), is the independent variable x k The residual sum of squares (k variables) of the model after successful introduction. q and pk-1 represent the degrees of freedom. In stepwise regression, q=1. When the assumption condition H is met, it follows the F distribution with degrees of freedom of 1 and pk-1. When it is too large (generally greater than the upper 0.05 quantile), the assumption condition H is rejected. If the variable is significant enough, the variable is introduced. Traverse all variables outside the model and introduce the independent variable that maximizes the statistic F.

[0038] Consider removing the variable. Similarly, assume that the model is y=β0+β1x1+...+β k x k +e, consider the independent variable x k Can it be eliminated from the model? Propose hypothesis H:β k =0, the statistic F is the same as above. When it is too small (less than the upper 0.05 quantile), the hypothesis condition H is accepted. The independent variable is not significant, so the independent variable is eliminated, and all variables in the model are traversed to eliminate the independent variable that minimizes the statistic F.

[0039] In addition, it should be noted that in a process of elimination or introduction, only one variable is changed, and any variable can enter and exit the model any number of times. When a variable is successfully eliminated, it is necessary to continue to eliminate it until the elimination fails, and then new variables can be introduced. When a variable is successfully introduced, the introduction is stopped and the original variable is immediately eliminated. When the introduction fails, the stepwise regression ends, the loop is exited, and the results are output.

[0040] Then, the correlation between the band and the water depth is corrected through residual analysis and nonlinear regression methods (such as polynomial regression and generalized additive model). Residual analysis is an important means to evaluate the fitting effect of the regression model. The residual graph can intuitively judge whether the model meets the basic assumptions (such as linear assumptions, normality assumptions, etc.). In water depth inversion, residual analysis can help identify outliers, nonlinear relationships, or heteroscedasticity in the relationship between the band and the water depth. Polynomial regression can effectively correct the nonlinear relationship between the band and the water depth and improve the inversion accuracy. For example, studies in the prior art have shown that improving the water depth inversion model by increasing the degree of the polynomial can expand the model feature dimension, make the inversion model fit correctly, and thus improve the inversion accuracy. Residual analysis and nonlinear regression methods are prior art and are not introduced in detail in this application.

[0041] In one embodiment, the band reflectivity logarithmic ratio and the sediment concentration index are further introduced, nonlinear terms and interaction terms are introduced, and the model structure is optimized to further optimize the water depth inversion model initially constructed above and obtain the initial water depth inversion model.

[0042] Step S4, introducing the geographic coordinates and spatial weighting mechanism, constructing a non-stationary weight matrix through a neural network, and optimizing the initial water depth inversion model.

[0043] In one embodiment, the geographic 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.

[0044] Specifically, based on the geographic coordinates, the changes in the corresponding characteristic parameters can be regarded as different fluctuations of the "average relationship" caused by spatial non-stationarity. By utilizing the superior 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 weight of each location point, to construct a geographic 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 insert hidden layers as needed, see formula (7).

[0045] (7) in, To estimate the distance from 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 spatial weighted neural network.

[0046] Then, the measured water depth values ​​and the corresponding spectral reflectance characteristics are integrated to construct a data set and the data set is randomly divided into a training set, a validation set, and a test set, wherein the training set is used to optimize the network weights and bias of the spatial weighted neural network, and the validation data set is used to determine whether the model is overfitting after each training. After the training is completed, the generalization ability and prediction ability of the model are evaluated through a similar validation process using the test data set. In the modeling process, the estimated position point k of the training set, validation set, and test set is calculated in combination with formula (7): i To all training positions d i The distance is used as the input of the spatial weighted neural network, and the estimated position point k is obtained by the output layer. i The spatial weight , each weight corresponds to a predefined independent variable, see formula (8), k is the number of independent variables, that is, the non-stationary weight matrix is: (8) in, is the estimated position point k i The spatial weight of is a non-stationary weight matrix.

[0047] 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. , the spatial weight With the least squares coefficient Multiply to get the non-stationary coefficient ,Right now: (9) Where j=1,2,…,k, .

[0048] Combining equation (5) and equation (9), according to the non-stationary coefficient The corresponding independent variable The product of , updates the initial water depth inversion model as: (10) in, Indicates water depth, non-stationary coefficient The corresponding independent variable , that is, the significantly correlated bands and the corresponding band reflectivity ratios.

[0049] Get the predicted water depth , see formula (11), use the matrix form of formula (11) It can be expressed as formula (12), where: (11) , (12) , in, .

[0050] The goodness of fit of the geographic neural network weighted regression model and the least squares model was tested. For the least squares model, the estimated value is ,make ,but Then the geographic neural network weighted regression model and the least squares model can be described as formula (13), if The value of is close to 1. Then there is no significant difference between the geographic neural network weighted regression model and the least squares model. For formula (14), given a significance level α, if the distribution function , we can infer that the geographic neural network weighted regression model has a significantly better fitting effect on the data set than the least squares model. Among them: (13) (14) in, Can be expressed or , , represents the identity matrix; , , is the residual generator matrix and tr is the trace of the matrix.

[0051] Combined with the predicted water depth value and the measured water depth value, the model performance is evaluated in the model training stage through the cross-validation method to optimize the water depth inversion model. In one embodiment, K-fold cross-validation is used to divide the data set into K subsets of equal size. In each iteration, a subset is selected as a validation set, and the remaining K-1 subsets are used as training sets. During each iteration, the water depth inversion model is trained using the training set to optimize the weights and biases of the spatially weighted neural network. During each training process, the least squares coefficients are calculated based on the training set, and the spatial distance is used to calculate the non-stationary weights. After the training is completed, the water depth prediction value is calculated from the validation set and compared with the measured water depth value to determine the error index of the model after each training. For example, mean absolute percentage error (MAPE), root mean square error (RMSE), mean absolute error (MAE), R² score and modified Akaike information criterion ( )wait.

[0052] The mean absolute percentage error is expressed as: ; The root mean square error is expressed as: ; The mean absolute error is expressed as: ; The R² score is expressed as: ; The modified Akaike information criterion is expressed as: ; in, is the measured water depth, is the predicted water depth, .

[0053] In each iteration, different subsets are used as validation sets, and the remaining subsets are used as training sets. 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. The stability of the water depth inversion model is evaluated by analyzing the changes in the error index of each validation. 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.

[0054] Step S5: input the spectral characteristic parameter matrix into the optimized water depth inversion model to generate an initial water depth inversion result.

[0055] After obtaining the spectral characteristic parameter matrix through the above step S4 and obtaining the optimized water depth inversion model through step S5, the spectral characteristic parameter matrix is ​​input into the optimized water depth inversion model to generate an initial water depth inversion result.

[0056] Step S6, analyzing the error distribution characteristics, locating the sub-region in the target area where the error exceeds the error threshold, and correcting the outliers in the sub-region based on the spatial interpolation method, optimizing the spectral feature parameter matrix, and generating the optimized water depth inversion result.

[0057] In one embodiment, in combination with the error index calculated in the above step S4, such as calculating R square (R²), root mean square error (RMSE), modified Akaike information criterion (AICC) and other accuracy evaluation indicators, the error distribution characteristics are analyzed, the sub-region in the target area where the error exceeds the error threshold is located, and it is determined whether there are outliers in the measured data corresponding to the sub-region. If there are no outliers, the error fluctuation is reduced by smoothing technology (such as local regression, moving average and other existing technologies) in the sub-region. If there are outliers, the spatial interpolation method is used in the sub-region to correct the outliers to ensure the spatial continuity of the results. In one embodiment, the Kriging interpolation method is selected, specifically, representative sampling position points are selected to cover the target area, and sampling position points that are obviously deviated from the normal range are eliminated or corrected to avoid affecting the interpolation results. Then, the spatial distance between each pair of sampling locations is calculated, and the semivariance is calculated based on the distance and difference between the sampling locations to form a semivariogram. A suitable data model (such as a spherical model, exponential model or Gaussian model) is selected to fit the semivariogram and determine the model parameters (such as sill, range, nugget value). The ordinary kriging method is used to predict each unknown location based on the semivariogram and the sampling location data, as shown in formula (15), and the prediction error (kriging variance) is estimated at the same time. , see formula (16), evaluate the reliability of the interpolation result and determine the interpolation result.

[0058] (15) (16) in, Is an unknown location The predicted value of is the weight, is the sampling location The known value of . It is obtained by solving the Kriging equation to minimize the prediction error. Yes Liggin variance, It is a location point and The semivariance between them, μ is the Lagrange multiplier.

[0059] Finally, the interpolation result is used to optimize the spectral characteristic parameter matrix input into the water depth inversion model, and an optimized water depth inversion result is generated, including an inversion layer file and multi-resolution distribution data. Figure 2-Figure 4 As stated, Figure 2 is a schematic diagram of the measured water depth at a certain example grid point. Figure 3 It is a schematic diagram of local spatial points of measured water depth values; Figure 4 A schematic diagram of the water depth inversion result obtained by executing the method of the present invention.

[0060] In one embodiment, the optimized water depth inversion results are further output and visualized. By extracting the water depth inversion results within the target time range, high-precision raster and vector data files are generated; statistical analysis is performed to output an accuracy evaluation report, including the indicator range and spatial distribution characteristics; a water depth distribution visualization image is generated, including a depth contour map and a time series change map; suspended sediment concentration and inverted water depth are superimposed to generate a comprehensive distribution map; the inversion results are combined with remote sensing images to generate an analysis report on the water depth change trend in the study area, providing support for subsequent landform monitoring and river management.

[0061] In summary, the method for water depth inversion of high-sand content water bodies based on multispectral remote sensing disclosed in the present invention is based on multispectral remote sensing technology. By optimizing the spectral characteristics of remote sensing images and fully considering the influence of suspended sediment concentration and bottom type, a water depth inversion model suitable for high-sand content environments is established. By introducing spatial non-stationarity analysis and combining 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 utilizing advanced nonlinear modeling methods and data correction technology, the accuracy and stability of water depth inversion are significantly improved.

[0062] The above specific implementations do not constitute a limitation on the protection scope of the present invention. It should be understood by those skilled in the art that various modifications, combinations, sub-combinations and substitutions can be made according to design requirements and other factors. Any modification, equivalent substitution and improvement made within the spirit and principle of the present invention should be included in 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.

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