Regional underground water burial depth distribution estimation method based on Bayesian deep learning

Abstract

The invention discloses a method for estimating the burial depth distribution of regional underground water based on Bayesian deep learning, and the method comprises the steps: employing discrete observation well position data, and combining the multi-source data, such as rainfall, evapotranspiration, temperature, gradient, distance to a nearest surface water body, soil type, land utilization type, and underground water reserve, as input factors; and establishing a nonlinear mapping relation between the underground water burial depth and the input factors through a Bayesian deep learning model. According to the method, the model is trained and verified by using the measured data at the observation points, and then the regional groundwater burial depth distribution is estimated based on the input factor data of the research area, so that the problem of insufficient coverage of a traditional groundwater monitoring network can be effectively solved, and the regional groundwater burial depth distribution characteristics can be described with relatively high spatial resolution; and scientific support is provided for sustainable utilization and ecological protection of regional underground water resources. The method has universality and is suitable for underground water burial depth prediction in different areas and under various data conditions.

Description

Technical Field

[0001] The present invention relates to the field of hydrology and deep learning technology, and specifically to a method for estimating regional groundwater depth distribution based on Bayesian deep learning. Background Art

[0002] Groundwater resources play an important role in agriculture, industry and drinking water supply. In addition, groundwater is also an important guarantee for maintaining ecological and environmental security. Groundwater depth is a direct indicator of the availability of groundwater resources, and changes in groundwater depth are also closely related to the stability of the ecosystem. Conducting groundwater depth forecasting research and estimating the regional distribution of groundwater depth can timely optimize the formulation of groundwater exploitation plans and ecological and environmental protection strategies, thereby achieving sustainable development of water resources and ecological and environmental protection.

[0003] There are many groundwater depth prediction technologies. Traditional groundwater monitoring mainly relies on field observation well networks to obtain depth data. However, due to the high construction and maintenance costs, the observation well network coverage is often insufficient, making it difficult to fully grasp the regional groundwater depth distribution. Existing studies mostly use geostatistical methods for spatial interpolation, but such methods are difficult to fully utilize environmental factor information and have limited prediction accuracy.

[0004] With the development of remote sensing, geographic information and other technologies, data on various environmental factors are becoming increasingly abundant, providing a data basis for the development of new groundwater depth estimation methods. Deep learning technology has also made important breakthroughs in recent years and has shown great potential in the field of environmental prediction, especially Bayesian deep neural networks (BNNs), which have attracted much attention due to their uncertainty estimation capabilities. However, there are relatively few studies on the application of Bayesian deep learning to regional groundwater depth estimation, and there is an urgent need to develop relevant technical methods. Summary of the invention

[0005] The purpose of the present invention is to provide a method for estimating the spatial distribution of groundwater depth based on Bayesian deep learning. Combining the advantages of the Bayesian deep learning network model, by integrating easily accessible environmental factors from multiple sources, an innovative low-cost, high-precision regional groundwater depth probability estimation method is proposed, which provides an efficient supplement to traditional methods to solve the problems raised in the above-mentioned background technology.

[0006] In order to solve the above technical problems, the present invention provides the following technical solutions: The regional groundwater depth distribution estimation method based on Bayesian deep learning includes the following steps: Collect groundwater depth observation data in the study area and extract environmental factor data corresponding to the locations of all monitoring wells according to longitude and latitude; Standardize and quality control the groundwater depth observation data and environmental factor data of the study area; The environmental factor data and the groundwater depth observation data are used as model input samples and output samples respectively, and training wells and verification wells are divided; Based on the training wells, the Bayesian deep neural network is trained using the Stein variational gradient descent algorithm to obtain a regional groundwater depth distribution estimation model; Optimize and adjust the regional groundwater depth distribution estimation model based on the validation well; Based on the regional groundwater depth distribution estimation model, the SHAP interpretation algorithm is used to calculate the contribution of each environmental factor data to the predicted groundwater depth; The regional groundwater depth distribution estimation model is used to predict the groundwater depth distribution, and the standard deviation of the predicted groundwater depth distribution results is calculated to evaluate the uncertainty of the regional groundwater depth distribution estimation model.

[0007] At the same time, the groundwater depth distribution map and its uncertainty distribution map of the study area can be generated based on the prediction results of the regional groundwater depth distribution estimation model and its uncertainty results, providing decision support for water resources management.

[0008] According to the above technical solution, the environmental factor data include course, slope, aspect, terrain position index, terrain roughness index, terrain humidity index, water flow accumulation, vegetation coverage, vegetation index, land use, soil type, land bulk density, precipitation, temperature, evapotranspiration, latitude and longitude coordinate projection, distance from the river, and groundwater reserves.

[0009] The accumulated water flow is the accumulated water flow simulated based on the terrain data.

[0010] Among them, the environmental factor data obtained are rasterized. In addition, the calculation formulas of the rasterized terrain position index TPI, terrain roughness index TRI, terrain wetness index TWI and vegetation coverage FVC are as follows: ; ; ; in, is the middle elevation of the sliding window, is the elevation of the grid points except the middle of the window, As is the upstream cumulative area, and β is the slope. The sliding window side length is 11 grids, and n represents the number of grid points.

[0011] ; in, and They represent the 99th and 1st percentiles of NDVI of all grids in the study area, respectively. Represents the vegetation index.

[0012] According to the above technical solution, the steps of training the regional groundwater depth distribution estimation model include: Determine the structure of the Bayesian deep neural network basic model and its parameters, wherein the Bayesian deep neural network basic model parameters include the number of neurons, the number of hidden layers, and the number n of Bayesian deep neural network basic models, and initialize the prior distribution of the Bayesian deep neural network basic model parameters; wherein the number of Bayesian deep neural network basic models is also referred to as the number of parameter particles set by the Stein variational gradient descent algorithm; The training data in the training well is input into the Bayesian deep neural network basic model for training. During the training process, the Stein variational gradient descent algorithm is used to update the parameters of the Bayesian deep neural network basic model, and the posterior distribution of the parameters of the Bayesian deep neural network basic model is continuously approached until the Bayesian deep neural network basic model converges and the training is completed.

[0013] The Stein variational gradient descent algorithm updates the Bayesian deep neural network parameter steps including: Calculate the log joint probability and kernel function of each Bayesian neural network base model parameter to measure the similarity between the empirical distribution and the approximate posterior distribution, where the empirical distribution is a conceptual reference used to describe the true posterior distribution approximated or estimated by the observed data; Based on the logarithmic joint probability and kernel function of each Bayesian neural network basic model parameter, each Bayesian deep neural network parameter is updated: the Bayesian neural network basic model parameter update calculation formula is: ; ; In the formula, Kernel function representing the parameters of the basic model of the Bayesian neural network; Represents the logarithmic joint probability of the parameters of the Bayesian neural network basic model; represents the gradient function; It is a particle in the parameter particle set, used to provide gradient information for the current parameter; Indicates the optimal update direction of the Bayesian neural network basic model parameters, Represents the parameters in each Bayesian neural network base model; represents the learning rate of the Bayesian neural network basic model parameter update, m represents the number Np of Bayesian neural network basic models, represents the updated Bayesian neural network basic model parameters, represents the unupdated Bayesian neural network basic model parameters, Represents the optimal update direction of the Bayesian neural network basic model parameters when not updated.

[0014] represents the gradient of the logarithmic joint probability of the parameters of the Bayesian neural network basic model, Represents the gradient of the kernel function.

[0015] The logarithmic joint probability of the parameters of the Bayesian neural network basic model is obtained by adding the logarithm of the likelihood function and the logarithm of the prior distribution of the parameters of the Bayesian neural network basic model. The likelihood function adopts Gaussian distribution and the parameter prior uses gamma distribution.

[0016] Among them, the regional groundwater depth distribution estimation model is a Bayesian neural network system trained using the Stein variational gradient descent algorithm (SVGD). The SVGD algorithm efficiently approximates the posterior distribution of network parameters, thereby quantifying the uncertainty of the neural network. The SVGD algorithm requires a deterministic neural network as a basic model. The prior distribution of network parameters is specifically set to the prior of the gamma distribution, and the likelihood function uses the Gaussian distribution.

[0017] According to the above technical solution, the basic model structure of the Bayesian deep neural network includes an input layer, a hidden layer and an output layer. The hidden layer is composed of multiple fully connected layers, each of which is followed by a batch normalization layer, a ReLU activation function and a dropout layer.

[0018] According to the above technical solution, the Nash coefficient and the root mean square error are used as judgment criteria to determine whether the groundwater depth distribution estimation model in the region meets the forecast accuracy. If it does not meet the forecast accuracy, the groundwater depth distribution estimation model in the region is continuously optimized and adjusted until the forecast accuracy is met.

[0019] According to the above technical solution, the contribution of a certain environmental factor data to the prediction of groundwater depth is: ; In the formula, represents the SHAP interpretation algorithm, represents the sample prediction value corresponding to a certain environmental factor, represents the average predicted value constant of all training samples of a certain environmental factor, Indicates the sample prediction value corresponding to a certain environmental factor The number of corresponding input features, Indicates the sample prediction value corresponding to a certain environmental factor The corresponding input features The attribution value of is the input feature of an environmental factor data.

[0020] According to the above technical solution, the average value of the output results of the regional groundwater depth distribution estimation model is calculated. and standard deviation , the upper and lower limits of the prediction confidence interval are The standard deviation is used as the uncertainty quantification indicator, and the average value of the output results of the regional groundwater depth distribution estimation model is used as the uncertainty quantification indicator. As the prediction result of groundwater depth distribution; among them, z is 1.64~2.58, which represents the 90%~99% confidence interval of the forecast result, that is, the forecast result has a 90%~99% probability of falling within this interval.

[0021] An embodiment includes a storage medium having a computer program stored thereon, and when the computer program is executed by a processor, the steps of a method for estimating regional groundwater depth distribution based on Bayesian deep learning as described in the above technical solution are implemented.

[0022] It also includes an embodiment, a computer device, including a storage medium, a processor, and a computer program stored in the storage medium and executable by the processor. When the computer program is executed by the processor, the steps of a method for estimating regional groundwater depth distribution based on Bayesian deep learning as described in the above technical solution are implemented.

[0023] Compared with the prior art, the beneficial effects achieved by the present invention are as follows: by constructing a Bayesian deep learning network and establishing a nonlinear mapping relationship between groundwater depth and input factors (environmental factors) through a Bayesian deep learning model, the present invention can achieve high-resolution spatial distribution estimation of groundwater depth and quantify the uncertainty of the model, thereby providing a basis for the rational allocation of water resources and environmental protection in the future.

[0024] It also includes an embodiment, a computer device, including a storage medium, a processor, and a computer program stored in the storage medium and executable by the processor. When the computer program is executed by the processor, the steps of a method for estimating regional groundwater depth distribution based on Bayesian deep learning as described in the above technical solution are implemented.

[0025] Compared with the prior art, the beneficial effects achieved by the present invention are as follows: by constructing a Bayesian deep learning network and establishing a nonlinear mapping relationship between groundwater depth and input factors (environmental factors) through a Bayesian deep learning model, the present invention can achieve high-resolution spatial distribution estimation of groundwater depth and quantify the uncertainty of the model, thereby providing a basis for the rational allocation of water resources and environmental protection in the future. BRIEF DESCRIPTION OF THE DRAWINGS

[0026] The accompanying drawings are used to provide a further understanding of the present invention and constitute a part of the specification. Together with the embodiments of the present invention, they are used to explain the present invention and do not constitute a limitation of the present invention. In the accompanying drawings: Figure 1It is a flowchart of the steps of the method for estimating regional groundwater depth distribution based on Bayesian deep learning of the present invention; Figure 2 It is a schematic diagram of the parameter updating process of the regional groundwater depth distribution estimation model; Figure 3 It is a forecast accuracy evaluation chart based on the regional groundwater depth distribution estimation model in the training set and the validation set; Figure 4 It is a regional groundwater depth distribution estimation map based on the regional groundwater depth distribution estimation model; Figure 5 It is a quantitative map of regional groundwater depth uncertainty based on the regional groundwater depth distribution estimation model; Figure 6 3 is a comparison diagram of the contribution of various input features to the groundwater depth in this embodiment. DETAILED DESCRIPTION

[0027] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of 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.

[0028] The present invention takes a semi-arid region in northwest China as an example, predicts the spatial distribution of groundwater depth in the region and surrounding areas, and quantifies the uncertainty of the prediction results. The specific steps are as follows: Figure 1 As shown in Figure 1, the groundwater depth prediction steps are divided into seven stages, as follows: Phase 1: Obtain groundwater depth monitoring data from 233 groundwater monitoring wells in the region from the first to the fourth quarter of 2019, as well as the geographical locations of the groundwater monitoring wells.

[0029] Phase 2: According to the geographical location of the groundwater monitoring wells, the environmental factor data of the corresponding location are extracted, specifically the monthly average precipitation, evapotranspiration and temperature grid data covering the entire study area in 2019 are extracted and converted into quarterly average data. The annual average elevation, vegetation cover, land use, soil type, and groundwater storage grid data covering the entire study area in 2019 are extracted. Based on the elevation data, the slope, aspect, terrain position index, terrain roughness index, terrain wetness index, cumulative flow and vegetation cover are calculated for subsequent estimation.

[0030] Based on the groundwater depth monitoring data and environmental factor data, a point-based input-output sample set is constructed. The input sample is the environmental factor data, and the output sample is the groundwater depth. 80% of the wells are randomly divided as training wells and 20% as verification wells. Each well has sample data for 4 quarters.

[0031] Phase 3: Determine the basic model structure of the Bayesian deep neural network and the prior distribution of its network parameters. The basic model structure of the Bayesian deep neural network includes an input layer, a hidden layer, and an output layer. The hidden layer consists of multiple fully connected layers, each of which is followed by a batch normalization layer, a ReLU activation function, and a dropout layer.

[0032] Among them, the basic model structure of the Bayesian deep neural network uses 2 hidden layers, 64 neurons, a dropout rate of 0.1, a learning rate of 0.03, a sample batch size of 32 for the training set, and 16 for the validation set.

[0033] The input samples (environmental factors) in the training wells are put into the Bayesian deep neural network basic model structure to train the regional groundwater depth distribution estimation model, and the Stein variational gradient descent algorithm is used to iteratively train the approximate parameter posterior distribution to obtain the optimal parameter distribution of the regional groundwater depth distribution estimation model until the Bayesian deep neural network basic model converges and the training is completed to obtain the regional groundwater depth distribution estimation model. The steps of training the regional groundwater depth distribution estimation model are as follows: Figure 2 shown.

[0034] Stage 4: Optimize and adjust the regional groundwater depth distribution estimation model based on the verification wells. Specifically, input samples from the verification wells into the regional groundwater depth distribution estimation model obtained using the training well data to predict the groundwater depth. The Nash coefficient and root mean square error index are used to evaluate the prediction accuracy of the regional groundwater depth distribution estimation model based on the predicted groundwater depth. If the prediction accuracy does not meet the requirements, return to stage 3 to optimize and adjust the parameters of the regional groundwater depth distribution estimation model until the prediction accuracy is met.

[0035] Among them, since the network parameters of the regional groundwater depth distribution estimation model that meets the forecast accuracy obey the posterior distribution, the output groundwater depth estimation result is also a distribution. The average value of the output result of the regional groundwater depth distribution estimation model is calculated. and standard deviation , taking the mean value as the prediction result and the standard deviation to quantify the uncertainty. And the mean value of the model output result is estimated based on the regional groundwater depth distribution and standard deviation , the upper and lower limits of the prediction confidence interval are ， Here z can be taken as 1.96, which represents the 95% confidence interval of the forecast result, that is, there is a 95% probability that the forecast result will fall within this interval.

[0036] Phase 5: Based on the regional groundwater depth distribution estimation model that meets the forecast accuracy obtained in Phase 4, the SHAP algorithm is used to calculate the contribution of each input feature of all samples to the output (SHAP value), and the absolute value of the SHAP value of all samples is averaged and normalized to obtain Figure 6 The SHAP result diagram shows that the vertical axis is the input feature of the regional groundwater depth distribution estimation model, and the horizontal axis is the normalized result after the average absolute value of each feature SHAP value. Figure 6 As can be seen from the figure, the location (latitude and longitude) of the well, soil type and vegetation cover are the more important input features.

[0037] Among them, the contribution of a certain environmental factor to the prediction of groundwater depth is: ; In the formula, represents the SHAP interpretation algorithm, represents the sample prediction value corresponding to a certain environmental factor, represents the average predicted value constant of all training samples of a certain environmental factor, Indicates the sample prediction value corresponding to a certain environmental factor The number of corresponding input features, Indicates the sample prediction value corresponding to a certain environmental factor The corresponding input features The attribution value of is the input feature of an environmental factor data.

[0038] Phase 6: Use the regional groundwater depth estimation model that meets the forecast accuracy to predict the groundwater depth, and use the Nash coefficient and root mean square error index to evaluate the regional groundwater depth estimation model. The evaluation results of the regional groundwater depth estimation model accuracy index are as follows: Figure 3 As shown, Figure 3 The left picture in the middle is the scatter plot of the accuracy estimation of the training set, and the right picture is the scatter plot of the accuracy estimation of the validation set. The closer the scatter points in the scatter plot are to y=x, the better the prediction accuracy is. Figure 3 The Nash coefficient of the prediction accuracy of the training set is 0.90, and the Nash coefficient of the prediction accuracy of the validation set is 0.84. It can be seen that the regional groundwater depth distribution estimation model has good prediction accuracy.

[0039] Phase 7: Based on the regional groundwater depth distribution estimation model that meets the forecast accuracy obtained in Phase 4 and the input feature (environmental factor) raster data covering the entire study area obtained in Phase 1, the raster data is unified to a resolution of 0.1°, and all input features (environmental factors) are integrated as input to the regional groundwater depth distribution estimation model based on Bayesian deep learning, and the output is a 0.1° groundwater depth distribution map of the entire region ( Figure 4) and uncertainty distribution map ( Figure 5 ),in Figure 4 (a), (b), (c), and (d) represent the spatial distribution maps of groundwater depth in the first, second, third, and fourth quarters of 2019, respectively; Figure 5 (a), (b), (c), and (d) represent the uncertainty distribution maps for the first, second, third, and fourth quarters of 2019, respectively. The groundwater depth distribution map and uncertainty distribution map can provide decision support for water resources management.

[0040] It should be noted that, in this article, relational terms such as first and second, etc. are only used to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Moreover, the terms "include", "comprise" or any other variants thereof are intended to cover non-exclusive inclusion, so that a process, method, article or device including a series of elements includes not only those elements, but also other elements not explicitly listed, or also includes elements inherent to such process, method, article or device.

[0041] Finally, it should be noted that the above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art can still modify the technical solutions described in the aforementioned embodiments or replace some of the technical features therein by equivalents. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

Claims

1. A method for estimating regional groundwater depth distribution based on Bayesian deep learning, characterized in that: The steps include: Collect groundwater depth observation data in the study area and extract environmental factor data corresponding to the locations of all monitoring wells according to longitude and latitude; Standardize and quality control the groundwater depth observation data and environmental factor data of the study area; The environmental factors corresponding to the monitoring well locations and the groundwater depth observation data are used as model input samples and output samples, respectively, and training wells and verification wells are divided; Based on the training wells, the Bayesian deep neural network is trained using the Stein variational gradient descent algorithm to obtain a regional groundwater depth distribution estimation model; Optimize and adjust the regional groundwater depth distribution estimation model based on the validation well; Based on the regional groundwater depth distribution estimation model, the SHAP interpretation algorithm is used to calculate the contribution of each environmental factor data to the predicted groundwater depth; Based on the environmental factor data and using the regional groundwater depth distribution estimation model, the regional groundwater depth distribution is predicted, and the standard deviation of the predicted groundwater depth result distribution is calculated to evaluate the uncertainty of the regional groundwater depth distribution estimation model prediction.

2. The method for estimating regional groundwater depth distribution based on Bayesian deep learning according to claim 1 is characterized in that: The environmental factor data include elevation, slope, aspect, terrain position index, terrain roughness index, terrain humidity index, water flow accumulation, vegetation coverage, vegetation index, land use type, soil type, land bulk density, precipitation, temperature, evapotranspiration, latitude and longitude coordinate projection, distance from the river, and groundwater reserves.

3. The method for estimating regional groundwater depth distribution based on Bayesian deep learning according to claim 1 is characterized in that: The steps of training the regional groundwater depth distribution estimation model include: Determine the structure of the Bayesian deep neural network basic model and its parameters, wherein the Bayesian deep neural network basic model parameters include the number of neurons, the number of hidden layers, and the number n of Bayesian deep neural network basic models, and initialize the prior distribution of the Bayesian deep neural network basic model parameters; wherein the number of Bayesian deep neural network basic models is also referred to as the number of parameter particles set by the Stein variational gradient descent algorithm; The training data in the training well is input into the Bayesian deep neural network basic model for training. During the training process, the Stein variational gradient descent algorithm is used to update the parameters of the Bayesian deep neural network basic model, and the posterior distribution of the parameters of the Bayesian deep neural network basic model is continuously approached until the Bayesian deep neural network basic model converges and the training is completed.

4. The method for estimating regional groundwater depth distribution based on Bayesian deep learning according to claim 3 is characterized in that: The Bayesian deep neural network basic model includes an input layer, a hidden layer and an output layer, wherein the hidden layer is composed of multiple fully connected layers, each of which is followed by a batch normalization layer, a ReLU activation function and a dropout layer.

5. The method for estimating regional groundwater depth distribution based on Bayesian deep learning according to claim 1 is characterized in that: The Nash coefficient and the root mean square error are used as judgment criteria to determine whether the regional groundwater depth distribution estimation model meets the forecast accuracy. If it does not meet the forecast accuracy, the regional groundwater depth distribution estimation model is continuously optimized and adjusted until the forecast accuracy is met.

6. The method for estimating regional groundwater depth distribution based on Bayesian deep learning according to claim 1 is characterized in that: Contribution of a certain environmental factor data to the prediction of groundwater depth: ； In the formula, represents the SHAP interpretation algorithm, represents the sample prediction value corresponding to a certain environmental factor, represents the average predicted value constant of all training samples of a certain environmental factor, Indicates the sample prediction value corresponding to a certain environmental factor The number of corresponding input features, Indicates the sample prediction value corresponding to a certain environmental factor The corresponding input features The attribution value of is the input feature of an environmental factor data.

7. The method for estimating regional groundwater depth distribution based on Bayesian deep learning according to claim 1 is characterized in that: Calculate the average value of the regional groundwater depth distribution estimation model output results and standard deviation , the upper and lower limits of the forecast confidence interval are The standard deviation is used as the uncertainty quantification indicator, and the average value of the output results of the regional groundwater depth distribution estimation model is used as the uncertainty quantification indicator. As the prediction result of groundwater depth distribution, Take 1.64~2.

58.

8. A storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the steps of the method for estimating regional groundwater depth distribution based on Bayesian deep learning as described in any one of claims 1 to 7 are implemented.

9. A computer device, characterized in that: It includes a storage medium, a processor, and a computer program stored in the storage medium and executable by the processor. When the computer program is executed by the processor, the steps of the method for estimating regional groundwater depth distribution based on Bayesian deep learning as described in any one of claims 1 to 7 are implemented.

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