Method for predicting soil ammonium nitrogen pollution space in rare earth mining area

Abstract

The invention discloses a method for predicting soil ammonium nitrogen pollution space in a rare earth mining area. Based on a spatial layering heterogeneity theory and a Bayesian theory, a spatial interpolation technology is combined, and an innovative layering Bayesian three-dimensional curved surface mean value model is provided. According to the model, layered modeling is introduced for the situation that pollutants in the rare earth mining area have high heterogeneity in the vertical direction, that is, the pollutants are subjected to layered treatment according to different depths, non-homogeneous distribution of the pollutants in different depth layers is captured, and the distribution difference of the pollutants in different stratums can be reflected more accurately.

Description

Technical Field

[0001] The invention belongs to the field of spatial prediction of ammonium nitrogen pollution, and specifically relates to a hierarchical Bayesian model, a mixed covariance matrix, and mining area environmental protection. Background Art

[0002] The in-situ leaching method of ion adsorption rare earth ores is prone to cause serious water and soil pollution problems in mining areas, among which ammonium nitrogen pollution is particularly prominent. Ammonium nitrogen pollution in rare earth mining areas shows significant autocorrelation and heterogeneity in spatial distribution. Spatial autocorrelation is mainly affected by environmental factors such as rainfall, terrain slope and mining activities, forming a three-dimensional spatial autocorrelation pattern of pollution. Spatial heterogeneity is closely related to the existence form of ammonium nitrogen and its leaching process in the soil.

[0003] With the closure of the mine, the source of ammonium nitrogen pollution was cut off, but the ammonium nitrogen remaining in the soil during the leaching process showed different degrees of aggregation in the soil at different depths due to leaching, which eventually led to spatial heterogeneity in the vertical direction. This complex spatial distribution characteristic of pollutants, coupled with the complex terrain of the mining area, makes the traditional prediction method perform poorly in dealing with the spatial distribution of pollution in the mining area. There are still some key problems: First, the spatial stratification heterogeneity is not fully considered. Many existing methods fail to consider the spatial stratification heterogeneity. The heterogeneity of pollutant distribution between different geological layers or depths has not been reasonably modeled; second, the influence of potential samples at different layers is ignored. Some methods do not fully consider the potential sample influence between different layers when modeling, especially in the presence of strong heterogeneity and weak autocorrelation, it is difficult to accurately reflect the correlation between pollutants at different levels; third, the spatial structure is not accurately captured due to the sparse borehole data. Even if the spatial stratification heterogeneity and the influence of samples at different levels are included in the modeling scheme, it is often difficult to accurately capture the spatial structure of pollutants when the borehole data is sparse. Since the spatial structure is usually expressed by semivariogram or covariance function, the parameters of these functions require sufficient sample support to ensure stable estimation. In stratified heterogeneity modeling, the reduction in the number of samples in the local layer will lead to inaccurate capture of the spatial structure of the local layer, thus affecting the predictive performance of the overall model.

[0004] These problems have a direct impact on the accuracy and robustness of model predictions. In particular, in the task of predicting the spatial distribution of pollutants in mining areas, there are factors such as sparse samples, strong heterogeneity, and complex terrain. The defects of traditional methods are particularly prominent. Therefore, for mining areas with obvious stratification characteristics, it is urgent to develop a robust modeling method to improve the accuracy of pollutant spatial distribution prediction to meet the needs of environmental protection and sustainable development of mining areas. Summary of the invention

[0005] To this end, the present invention provides a method for spatial prediction of soil ammonium nitrogen pollution in rare earth mining areas. Based on the theory of spatial stratified heterogeneity and Bayesian theory, combined with spatial interpolation technology, an innovative stratified Bayesian three-dimensional surface mean model is proposed to solve the problem of insufficient precision in the identification and processing of spatial heterogeneity of pollutants.

[0006] The specific implementation steps of the model are:

[0007] Step 1: Based on the characteristics of rare earth mining technology and ammonia nitrogen pollution, combined with the mountain topography and leaching path, divide the sampling area and determine the drilling location to complete sample collection and laboratory analysis.

[0008] Step 2: Identify the spatial pattern of ammonium nitrogen pollutants. The spatial autocorrelation and spatial stratified heterogeneity of ammonium nitrogen pollutants are identified by the Moran index and geographic detector, respectively, and the inter-layer samples and intra-layer samples are divided. The inter-layer samples are global samples with the mean removed.

[0009] Step 3: Perform spatial modeling based on the spatial pattern of the ammonium nitrogen pollutant. The specific implementation steps are: the first step is to design a global spatial structure information extraction mechanism; the second step is to design a mixed covariance matrix; the third step is to use the Markov chain Monte Carlo sampling method to calculate the posterior probability distribution of the covariance function parameters of the intra-layer spatial process and the inter-layer spatial process.

[0010] Step 4: Perform model prediction based on Bayesian theory according to the posterior probability distribution of the covariance function parameters of the intra-layer spatial process and the posterior probability distribution of the covariance function parameters of the inter-layer spatial process to obtain uncertainty estimation of the spatial prediction of ammonium nitrogen pollution.

[0011] Preferably, the Moran index is denoted as I, and its mathematical expression is:

[0012]

[0013] Where n is the number of samples, x i and x j represent the soil ammonium nitrogen concentration at the i-th and j-th locations, respectively. represents the mean value of the variable in the study area, W ij is x i and x j The spatial weight matrix between them, the value range of I is -1 to 1, I = -1 indicates a high negative correlation, I = 1 indicates a high positive correlation, and I = 0 indicates no correlation.

[0014] Preferably, the geographic detector is denoted as q, and its mathematical expression is:

[0015]

[0016] Among them, σ 2 represents the total variance of the observed samples in the entire study area, N is the number of observed samples in the entire study area, and N h represents the number of observation samples in each stratum, L represents the number of spatial layers divided, It represents the variance of observed samples in different strata h. The value range of q is 0 to 1. The closer q is to 1, the stronger the heterogeneity of the regional unit is. When q = 0, it means that there is no heterogeneity in the regional unit.

[0017] Preferably, the specific design steps of the global spatial structure information extraction mechanism design in step 3 are: multiple parameter fitting is performed using the global sample subset obtained by the random sampling method with replacement to obtain the prior information of the global spatial relationship in the hierarchical framework, wherein the prior information is the prior probability distribution of the estimated variogram parameters of the intra-layer spatial process and the inter-layer spatial process; thereby ensuring more robust parameter estimation;

[0018] Set the prior probability distribution of the variogram parameter to f prior (Θ):

[0019] f prior (Θ)={sill,range,nugget}

[0020] Among them, Θ represents the parameter group {sill, range, nugget}, still represents the base value of the variation function, range represents the range of the variation function, and nugget represents the nugget value of the variation function.

[0021] Preferably, the specific implementation method of the mixed covariance matrix design is: superimpose the covariances corresponding to the estimated points and the sampling points in different spatial processes to simultaneously consider the influence of different spatial processes at the estimated position. The spatial autocorrelation and the spatial stratification heterogeneity can be effectively combined in a unified framework to obtain intra-layer spatial processes and inter-layer spatial processes. The intra-layer spatial process refers to the spatial autocorrelation of pollutants within the same geological layer or depth layer. By calculating the covariance between sample points in the same layer, the similarity between these points is reflected. The larger the covariance, the stronger the autocorrelation of pollutant distribution between sample points; the inter-layer spatial process refers to the spatial stratification heterogeneity of the difference in pollutant distribution between different geological layers and depth layers. By calculating the covariance between sample points at different levels, the covariance between layers is small or even negative, which means that there are significant differences or reverse trends between pollutants in different strata.

[0022] Preferably, the expression for calculating the mixed covariance matrix is ​​as follows:

[0023]

[0024] in, Represents the point to be estimated s i and sampling point s j The covariance between Represents the point to be estimated s i and sampling point s j The spatial distance between in and θ between Represents the prior probability distribution of the covariance function parameters of the intra-layer spatial process and the inter-layer spatial process, f in (·) and f between (·) represent the covariance function of the intra-layer spatial process and the inter-layer spatial process, L i and L j Represent the points to be estimated s i and sampling point s j The layer where it is located.

[0025] Preferably, the Markov chain Monte Carlo sampling method (MCMC) is expressed as:

[0026] f posterior (Θ∣Y(s))∝f(Y(s)∣Θ)&f prior (Θ)

[0027] Among them, f posterior (Θ|Y(s)) represents the conditional probability distribution of parameter Θ under given observation samples, f(Y(s)|Θ) represents the conditional distribution probability of pollutant concentration under given parameter Θ, f prior (Θ) is the prior probability distribution of the variance function parameters.

[0028] Compared with the prior art, the present invention has the following beneficial effects:

[0029] 1. The present invention introduces spatial stratified heterogeneity modeling to stratify the spatial distribution of pollutants according to different depths and strata, which can accurately identify the pollution heterogeneity between different depth layers, breaking through the limitation of traditional spatial interpolation methods that only rely on single-level spatial structure modeling, and can cope with pollutant distribution with significant stratified heterogeneity characteristics. It solves the problem that traditional interpolation methods cannot handle strong heterogeneity in the vertical direction, improves the ability to capture complex pollution distribution in rare earth mining areas, and is suitable for pollution prediction in complex environments and multi-level structures.

[0030] 2. The present invention designs a strategy for obtaining prior information based on a repeated sampling mechanism. By borrowing global spatial information from other regions, additional support is provided for local parameter estimation, thereby improving the robustness of parameter estimation. The repeated sampling method can effectively increase the number of samples for parameter estimation, thereby ensuring that robust prediction results of pollutant spatial distribution can be obtained when samples are sparse. It not only improves the reliability of parameter estimation in sparse data scenarios, but also enhances the adaptability and prediction ability of the model, effectively making up for the defect of traditional methods that rely on large sample data.

[0031] 3. The present invention constructs a mixed covariance matrix to capture the spatial relationships within and between layers at the same time to solve the impact of spatial heterogeneity on the prediction performance of the model. It can effectively deal with complex spatial structure problems and provide a robust tool for modeling the spatial distribution of pollutants. BRIEF DESCRIPTION OF THE DRAWINGS

[0032] Figure 1 A flowchart for implementing the hierarchical Bayesian three-dimensional surface mean model provided by the present invention;

[0033] Figure 2 Implementation diagram of the global spatial structure information extraction mechanism;

[0034] Figure 3 Specific implementation diagram for the mixed covariance matrix;

[0035] Figure 4 It is an intuitive schematic diagram of the spatial boundary division of ammonium nitrogen pollution by the model of the present invention and other models;

[0036] Figure 5 This is a visualization effect diagram of the uncertainty prediction of the model of the present invention. DETAILED DESCRIPTION

[0037] In order to make the purpose, technical scheme and advantages of the invention more clear, the present invention will be further described below in conjunction with embodiments. Obviously, the described embodiments are part of the embodiments of the present invention, rather than all the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0038] The present invention provides a method for spatial prediction of soil ammonium nitrogen pollution in rare earth mining areas, which mainly uses the spatial hierarchical heterogeneity theory and Bayesian theory, combined with spatial interpolation technology, to propose an innovative hierarchical Bayesian three-dimensional surface mean model (HBM-MSN). The implementation steps of the model are as follows: Figure 1 As shown, the specific implementation steps are:

[0039] Step 1: Based on the characteristics of rare earth mining technology and ammonia nitrogen pollution, combined with the mountain topography and leaching path, divide the sampling area and determine the drilling location to complete sample collection and laboratory analysis.

[0040] Step 2: Identify the spatial pattern of ammonium nitrogen pollutants. The spatial autocorrelation and spatial stratified heterogeneity of ammonium nitrogen pollutants are identified by the Moran index and geographic detector, respectively, and the inter-layer samples and intra-layer samples are divided. The inter-layer samples are global samples with the mean removed.

[0041] Step 3: Perform spatial modeling based on the spatial pattern of the ammonium nitrogen pollutant. The specific implementation steps are: the first step is to design a global spatial structure information extraction mechanism; the second step is to design a mixed covariance matrix; the third step is to use the Markov chain Monte Carlo sampling method (MCMC) to calculate the posterior probability distribution of the covariance function parameters of the intra-layer spatial process and the inter-layer spatial process, which are respectively Figure 1 p(Θ I ) and p(Θ B ).

[0042] Step 4: Based on the posterior distribution of the intra-layer covariance parameter probability distribution and the inter-layer covariance parameter probability distribution, a Bayesian model prediction is performed to obtain an uncertainty estimate for the spatial prediction of ammonium nitrogen pollution. The specific effect is as follows: Figure 5 As shown, it can be seen that the top layer of soil in the rare earth mining area used for prediction is less polluted by ammonium nitrogen and has a low risk level. The high uncertainty area is mainly concentrated in the bottom layer in the southwest.

[0043] Preferably, the Moran index is denoted as I, and its mathematical expression is:

[0044]

[0045] Where n is the number of samples, x i and x j represent the soil ammonium nitrogen concentration at the i-th and j-th locations, respectively. represents the mean value of the variable in the study area, W ij is x i and x j The spatial weight matrix between them, the value range of I is -1 to 1, I = -1 indicates a high negative correlation, I = 1 indicates a high positive correlation, and I = 0 indicates no correlation.

[0046] Preferably, the geographic detector is denoted as q, and its mathematical expression is:

[0047]

[0048] Among them, σ 2represents the total variance of the observed samples in the entire study area, N is the number of observed samples in the entire study area, and N h represents the number of observation samples in each stratum, L represents the number of spatial layers divided, It represents the variance of observed samples in different strata h. The value range of q is 0 to 1. The closer q is to 1, the stronger the heterogeneity of the regional unit is. When q = 0, it means that there is no heterogeneity in the regional unit.

[0049] Preferably, the global spatial structure information extraction mechanism is designed, and its specific design steps are: multiple parameter fitting is performed using a global sample subset obtained by a random sampling method with replacement to obtain prior information on global spatial relations in a hierarchical framework, wherein the global samples are the intra-layer samples and inter-layer samples, and the prior information is the prior probability distribution of the estimated variance function parameters of the intra-layer spatial process and the inter-layer spatial process, which are respectively Figure 1 Θ in B and θ I ; Ensure more robust parameter estimation; The implementation diagram of the global spatial structure information extraction mechanism is as follows Figure 2 As shown in the figure, the variation function p(Θ G ), after repeated sampling and fitting processes, a large number of potential parameter values ​​are obtained;

[0050] Set the prior probability distribution of the variogram parameter to f prior (Θ):

[0051] f prior (Θ)={sill,range,nugget}

[0052] Among them, Θ represents the parameter group {sill, range, nugget}, still represents the base value of the variation function, range represents the range of the variation function, and nugget represents the nugget value of the variation function.

[0053] Preferably, the mixed covariance matrix design is specifically implemented by superimposing the covariances of the estimated point and the sampling point in different spatial processes to simultaneously consider the influence of different spatial processes at the estimated position. Figure 3As shown. The mixed covariance matrix design can effectively combine the spatial autocorrelation and the spatial stratified heterogeneity in a unified framework to obtain intra-layer spatial processes and inter-layer spatial processes. The intra-layer spatial process refers to the spatial autocorrelation of pollutants within the same geological layer or depth layer. By calculating the covariance between sample points in the same layer, it reflects the degree of similarity between these points. The larger the covariance, the stronger the autocorrelation of pollutant distribution between sample points; the inter-layer spatial process refers to the spatial stratified heterogeneity of pollutant distribution differences between different geological layers and depth layers. By calculating the covariance between sample points at different levels, the covariance between layers is small or even negative, which means that there are significant differences or reverse trends in pollutants between different strata.

[0054] Preferably, the expression for calculating the mixed covariance matrix is ​​as follows:

[0055]

[0056] in, Represents the point to be estimated s i and sampling point s j The covariance between Represents the point to be estimated s i and sampling point s j The spatial distance between in and θ between Represents the prior probability distribution of the covariance function parameters of the intra-layer spatial process and the inter-layer spatial process, f in (·) and f between (·) represent the covariance function of the intra-layer spatial process and the inter-layer spatial process, L i and L j Represent the points to be estimated s i and sampling point s j The layer where it is located.

[0057] Preferably, the Markov chain Monte Carlo sampling method (MCMC) is expressed as:

[0058] f posterior (Θ∣Y(s))∝f(Y(s)∣Θ)&f prior (Θ)

[0059] Among them, f posterior (Θ|Y(s)) represents the conditional probability distribution of parameter Θ under given observation sample conditions, f(Y(s)|Θ) represents the conditional distribution probability of ammonium nitrogen pollutant concentration under given parameter Θ, f prior (Θ) is the prior probability distribution of the variance function parameters.

[0060] The performance of the HBM-MSN of the present invention is compared with the three-dimensional ordinary Kriging model (3D-OK) and the three-dimensional layered mean surface model (3D-MSN) according to the two indicators of mean absolute error and root mean square error. The intuitive schematic diagram is shown in FIG. Figure 4 As shown, the relationship between the concentration of ammonium nitrogen and the grayscale under the action of different models can be seen. The visualized pollution threshold is that the concentration of ammonium nitrogen is greater than 7 mg / kg. According to the X and Y axes in the figure, the specific horizontal spatial position of the ammonium nitrogen pollutant can be seen. In the figure, (c) is the HBM-MSN described in the present invention. The figure shows that it captures the three-dimensional spatial distribution boundary of the pollutant very well, especially the details of the high-concentration area change more obviously, accurately shows the cumulative characteristics of the pollutant, and clearly delineates the boundaries of different pollution areas. In the figure, (a) and (b) are 3D-OK and 3D-MSN respectively. The figure shows that although the spatial boundary division effect of ammonium nitrogen of these two models also shows the spatial distribution of pollutants, they appear rough in detail processing, especially in the depiction of the pollutant distribution boundary, there is a certain ambiguity, and it is difficult to accurately capture the local concentration change. In the process of showing the gradual change of pollutant concentration, the HBM-MSN carefully shows the gradual change process of different depths and regions. In contrast, the 3D-OK and the 3D-MSN are not delicate enough in the performance of local concentration changes, especially the 3D-OK, which is easy to produce overly smooth prediction results and cannot accurately show local heterogeneity. It can be seen intuitively from the figure that the HBM-MSN can identify the changing patterns of pollutants at different levels, especially the heterogeneity of ammonia nitrogen pollutants in the vertical direction. This is because the HBM-MSN combines the spatial relationship within and between layers through the mixed covariance matrix, so that it can more accurately reflect the distribution differences of pollutants in different strata.

[0061] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. For those skilled in the art, the present invention may have various modifications and variations. Any modification, equivalent replacement, improvement, etc. made within the spirit and scope of the present invention shall be included in the protection scope of the present invention.

Claims

1. A method for spatial prediction of soil ammonium nitrogen pollution in rare earth mining areas, characterized by: The method is a hierarchical Bayesian three-dimensional surface mean model, and its specific implementation steps are: Step 1: Based on the characteristics of rare earth mining process and ammonia nitrogen pollution, combined with mountain topography and leaching path, divide the sampling area and determine the drilling location, complete sample collection and laboratory analysis; Step 2: Identify the spatial pattern of ammonium nitrogen pollutants, identify the spatial autocorrelation and spatial stratified heterogeneity of ammonium nitrogen pollutants through the Moran index and geographic detector, and divide the inter-layer samples and intra-layer samples, where the inter-layer samples are global samples with the mean removed; Step 3: Perform spatial modeling according to the spatial pattern of the ammonium nitrogen pollutant, and the specific implementation steps are: the first step is to design a global spatial structure information extraction mechanism; the second step is to design a mixed covariance matrix; the third step is to use the Markov chain Monte Carlo sampling method to calculate the posterior probability distribution of the covariance function parameters of the intra-layer spatial process and the inter-layer spatial process; Step 4: Perform model prediction based on Bayesian theory according to the posterior probability distribution of the covariance function parameters of the intra-layer spatial process and the posterior probability distribution of the covariance function parameters of the inter-layer spatial process to obtain uncertainty estimation of the spatial prediction of ammonium nitrogen pollution.

2. A method for spatial prediction of ammonium nitrogen pollution in soil in rare earth mining areas according to claim 1, characterized in that: The Moran index is denoted as I, and its mathematical expression is: Where n is the number of samples, x i and x j represents the soil ammonium nitrogen concentration at the i-th and j-th locations, respectively, x represents the mean value of the variable in the study area, and W ij is x i and x j The spatial weight matrix between them, the value range of I is -1 to 1, I = -1 indicates a high negative correlation, I = 1 indicates a high positive correlation, and I = 0 indicates no correlation; The geographic detector is denoted as q, and its mathematical expression is: Among them, σ 2 represents the total variance of the observed samples in the entire study area, N is the number of observed samples in the entire study area, and N h represents the number of observation samples in each stratum, L represents the number of spatial layers divided, It represents the variance of observed samples in different strata h. The value range of q is 0 to 1. The closer q is to 1, the stronger the heterogeneity of the regional unit is. When q = 0, it means that there is no heterogeneity in the regional unit.

3. A method for spatial prediction of ammonium nitrogen pollution in soil in rare earth mining areas according to claim 1, characterized in that: The specific implementation steps of the design of the global spatial structure information extraction mechanism in step 3 are: multiple parameter fitting is performed using the global sample subset obtained by the random sampling method with replacement to obtain the prior information of the global spatial relationship in the hierarchical framework, and the prior information is the prior probability distribution of the estimated variogram parameters of the intra-layer spatial process and the inter-layer spatial process; Set the prior probability distribution of the variogram parameter to f prior (Θ): f prior (Θ)={sill,range,nugget} Among them, Θ represents the parameter group {sill, range, nugget}, still represents the base value of the variation function, range represents the range of the variation function, and nugget represents the nugget value of the variation function.

4. A method for spatial prediction of ammonium nitrogen pollution in soil in rare earth mining areas according to claim 1, characterized in that: The specific implementation method of the mixed covariance matrix design is: superimposing the covariances corresponding to the estimated points and the sampling points in different spatial processes; The expression for calculating the mixed covariance matrix is ​​as follows: in, Represents the point to be estimated s i and sampling point s j The covariance between Represents the point to be estimated s i and sampling point s j The spatial distance between in and θ between Represents the prior probability distribution of the covariance function parameters of the intra-layer spatial process and the inter-layer spatial process, f in (·) and f between (·) represent the covariance function of the intra-layer spatial process and the inter-layer spatial process, L i and L j Represent the points to be estimated s i and sampling point s j The layer where it is located.

5. The method for spatial prediction of ammonium nitrogen pollution in soil in rare earth mining areas according to claim 1, characterized in that: The Markov chain Monte Carlo sampling method is expressed as: posterior (Θ∣Y(s))∝f(Y(s)∣Θ)&f prior (Θ) Among them, f posterior (Θ|Y(s)) represents the conditional probability distribution of parameter Θ under given observation samples, f(Y(s)|Θ) represents the conditional distribution probability of pollutant concentration under given parameter Θ, f prior (Θ) is the prior probability distribution of the variance function parameters.

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