An interpretable lake spatial water level simulation method and system considering spatio-temporal correlation

Abstract

An interpretable lake spatial water level simulation method and system considering spatio-temporal correlation, belonging to the technical field of lake water level simulation. First, establish a basin graph structure and an adjacency matrix, construct a lake spatial water level simulation model based on a graph spatio-temporal neural network, and segment the data set based on the equal-frequency binning method; secondly, train the lake spatial water level simulation model and optimize the hyperparameter combination; finally, quantify the impact of each inflow runoff on the lake spatial water level. The system includes a memory, a processor, and a computer program stored on the memory and executable on the processor. By capturing the temporal correlation and spatial correlation of each hydrological representative station in the basin, the present invention can accurately simulate the dynamic response process of the lake spatial water level to many inflow runoffs; based on the interpretability method, analyze the spatio-temporal differential contributions of each inflow runoff to the lake spatial water level fluctuations, break through the limitations of the "black box" of traditional machine learning models, and contribute to the precise management and green development of the basin.

Description

Technical Field

[0001] The present invention belongs to the technical field of lake water level simulation, and relates to an interpretable lake spatial water level simulation method and system considering spatio-temporal correlation. Background Art

[0002] Lakes are an important component of the global fresh water resources and play an irreplaceable role in aspects such as runoff regulation, flood control and disaster reduction, and ecological protection. Water level is a key indicator in lake water resources management, which not only reflects the internal hydrological situation of the lake, but its fluctuations also profoundly affect many aspects such as river water and sediment transport, lake water quality conditions, and habitat habitats. However, in recent years, the large-scale construction of upstream reservoirs has significantly changed the hydrological situation of the lakes. During the impounding period, the water level has dropped significantly, leading to the early start and extension of the dry season, and even causing a series of ecological problems such as the deterioration of lake water quality and the degradation of wetland ecological functions. In order to clarify the impact degree of upstream reservoirs on the lake hydro-ecology and scientifically guide reservoir operation, it is particularly important to accurately simulate the spatial water level response of the lake and clarify the response mechanism of the lake to the incoming water from different directions. However, affected by many rivers with different directions and different runoff magnitudes, the spatio-temporal distribution of the lake water level shows a high degree of complexity and dynamics, bringing huge challenges to accurately simulating the spatial water level fluctuations of the lake.

[0003] Process models that finely model the basin based on physical equations provide the possibility to accurately and comprehensively reflect the response of the lake spatial water level to river runoff. By constructing a detailed grid, the process model can simulate the spatio-temporal dynamic response of characteristics such as the inundation morphology, spatial water level, and water flow direction of the lake. For example, Chinese invention patent 202210071934.9 discloses a method for deeply coupling a one-dimensional and a two-dimensional hydrodynamic model of rivers and lakes, which divides the research area into several one-dimensional partitions and two-dimensional partitions and performs dimensionality reduction connection on them, and gradually calculates the one-dimensional cross-section flow data and the planar velocity field data at each time step. However, although the process model can provide a deep understanding of the response of the lake spatial water level to various runoff, the model construction depends on complex terrain parameters with high spatio-temporal resolution, and its iterative solution requires high computational costs. This technical threshold not only restricts the regional applicability promotion of the model, but also makes it difficult to effectively couple with multi-objective optimization models and is not applicable to the optimization research of future reservoir operation rules.

[0004] With the development and innovation of computer technology, data-driven models have gradually become a new trend in watershed hydrological modeling due to their extremely high computational efficiency and powerful learning ability for non-linear associations of high-dimensional data. In particular, deep learning models represented by LSTM and GRU have achieved remarkable results in time series data prediction and have been widely applied. For example, Chinese Patent 202410494656.7 discloses a method for conformal prediction of lake water levels by integrating Copula functions and deep learning, which corrects the prediction results of the LSTM model in two stages using the cumulative distribution function and Copula functions, considering the correlation between multiple random variables and the dependence between prediction time steps, and predicts the lake water levels based on the calibrated LSTM model. Chinese Patent 202410730759.9 discloses a method for predicting the upstream intrusion of saltwater in estuary areas using machine learning algorithms, preferably inputting salinity sequences and external driving factors and inputting them into the gated recurrent unit GRU model to predict the salinity values of the upstream intrusion of saltwater in estuary areas during the dry season at different lead times. However, these models focus on the extraction and prediction of time series features and have obvious deficiencies in dealing with spatially correlated data. For lakes, their water level fluctuations are not only affected by the hydraulic exchange between rivers and lakes, but there are also intricate hydraulic connections inside, and there are close spatial correlations and mutual influences between different regions. Therefore, effectively capturing the spatial correlations within the lake area and between it and external runoff is crucial for improving the simulation accuracy of lake spatial water levels.

[0005] In addition to the challenges in model construction, deep learning models also face the problem of limited interpretability in analyzing the runoff response of lakes. Although they show extraordinary potential in simulation accuracy, they are usually still regarded as "black boxes" and it is difficult to explain the contribution degree of each inflow to the hydrological fluctuations of the lake's spatio-temporal heterogeneity, including reservoir discharges, and cannot provide in-depth guidance for the response time and response degree of the lake to reservoir operation. Their opaque internal decision-making logic limits a deeper understanding of the runoff response mechanism and the optimization and guidance of future watershed regulation. Summary of the Invention

[0006] Aiming at the problems existing in the prior art, the present invention provides an interpretable lake spatial water level simulation method and system considering spatio-temporal correlation. On the basis of the traditional consideration of the temporal correlation of hydrological characteristics, the present invention takes into account the hydraulic impacts of multiple inflows into the lake and the mutual correlation of the internal spatial water levels of the lake, and fully integrates the temporal correlation and spatial correlation of the basin hydrological characteristics based on the graph spatio-temporal neural network, so as to accurately simulate the differential water level response processes at multiple stations in different lake areas within the lake. In addition, the present invention also analyzes the response mechanism of the lake spatial water level to multiple inflows into the lake based on the interpretability method, quantifies the contributions of different inflows into the lake to the water level fluctuations at each station of the lake, and solves the problem of limited interpretability widely existing in the existing deep learning models. The present invention combines advanced machine learning technologies with an interpretability analysis framework, which can not only efficiently and accurately simulate the lake spatial water level, provide strong technical support for lake hydrological modeling, but also analyze the spatio-temporal differential contributions of each inflow into the lake, including reservoir releases, to the lake spatial water level fluctuations, providing a profound mechanism understanding and scientific guidance for basin water resources scheduling management and sustainable development.

[0007] To achieve the above object, the present invention provides the following technical solutions:

[0008] An interpretable lake spatial water level simulation method considering spatio-temporal correlation, comprising the following steps:

[0009] Step 1, establish a basin graph structure and an adjacency matrix;

[0010] Step 2, construct a lake spatial water level simulation model based on the graph spatio-temporal neural network;

[0011] Step 3, segment the dataset based on the equal-frequency binning method;

[0012] Step 4, train the lake spatial water level simulation model and optimize the hyperparameter combination;

[0013] Step 5, quantify the impacts of each inflow into the lake on the lake spatial water level.

[0014] Further, step 1 is as follows:

[0015] Step 1.1, based on the river network system near the lake, determine the inflow and outflow channels of the lake, as well as the internal partitioning and flow directions of the lake. At least one hydrological representative station is selected for each inflow channel into the lake and each lake partition, and the selected hydrological representative stations need to have long-term, continuous, and consistent historical observation data. According to the geographical location and hydrological characteristic differences, the hydrological representative stations include two types: inflow into the lake runoff stations and lake water level stations.

[0016] Step 1.2, generalize the basin graph structure.

[0017] The basin map structure consists of a node set and an edge set. Nodes are used to represent the hydrological representative stations selected in Step 1.1, including river runoff nodes representing the incoming river runoff stations and lake water level nodes representing the lake water level stations . Edges represent the hydraulic connections between hydrological representative stations, including the edges outside the lake, pointing from the river runoff nodes to the lake water level nodes , representing the impact of incoming river runoff on the lake water level; and the edges inside the lake, pointing from the lake water level nodes to the lake water level nodes , representing the associated impact between the water levels inside the lake. Both types of edges are directed edges, and the direction is consistent with the water flow direction.

[0018] Step 1.3, set the adjacency matrix.

[0019] The information update and transmission of the basin map structure are represented by an adjacency matrix A of dimension as shown in formula (1). N is the number of nodes in the basin map structure, including P river runoff nodes and Q lake water level nodes. When and only when there is an edge pointing from node p to node q, the element . .

[0020] (1)

[0021] Furthermore, Step 2 is as follows:

[0022] The input of the lake spatial water level simulation model is the runoff characteristics, including the runoff sequences of all incoming river runoff in the past and current H time periods, and the output is the water level characteristics of all lake water level stations at the current time period. As shown in the following formula,

[0023] (2)

[0024] Among them, is the runoff characteristic at time t, , P represents the number of river runoff nodes. is the water level characteristic at time t, , Q represents the number of lake water level nodes. H is the number of time periods of the input runoff characteristics, is the mapping function.

[0025] There is a significant spatio-temporal correlation between the input runoff characteristics and the output water level characteristics. Specifically, there is a long-term time series dependence in the runoff sequence, and this dependence continuously acts on the water level fluctuations at time t; at the same time, the runoff characteristics of the incoming river and the water level characteristics of the internal partitions of the lake Together, they constitute the complete graph structure at time t, and the spatial correlation between them is also an important factor affecting the spatial water level fluctuation of the lake. Therefore, the present invention integrates three spatio-temporal correlation learning modules to construct a lake spatial water level simulation model based on a graph spatio-temporal neural network. Specifically: First, a long short-term memory network module, abbreviated as the LSTM module, is introduced to mine the temporal correlation of the runoff sequence and aggregate and reduce the dimension of the runoff sequence from the time dimension. Second, a graph convolutional neural network module, abbreviated as the GCN module, is constructed to preliminarily simulate the lake spatial water level based on the spatial correlation between the incoming lake runoff and the neighboring lake water levels, and assign the initial feature values at time t to the lake water level nodes. Finally, a residual graph convolutional neural network module, abbreviated as the ResGCN module, is used to further consider the spatial correlation between the lake water level nodes on the basis of considering the influence of the incoming lake runoff, and accurately simulate the lake spatial water level.

[0026] Step 2.1, capturing the temporal correlation and reducing the dimension of the runoff sequence based on the LSTM module. The LSTM module takes the runoff sequences of the past and current H time periods of all P incoming lake runoff stations in the basin as the input. First, the LSTM unit of the LSTM module captures the temporal correlation in the runoff sequences of each incoming lake channel in the basin, extracts and updates the runoff characteristics of each incoming lake runoff station at each time step, and outputs the hidden states of each time period . Subsequently, based on the fully connected layer of the LSTM module, the hidden states of H time periods of each incoming lake runoff station are linearly combined through a weight matrix to reduce the dimension of the incoming lake runoff sequence from the time dimension, and a non-linear transformation is performed through an activation function, and finally the aggregated runoff characteristics of each incoming lake runoff station after aggregation are output .

[0027] Step 2.2, preliminarily calculating the lake spatial water level based on the GCN module. The GCN module takes the aggregated runoff characteristics of each incoming lake runoff station output by the LSTM module as the input, learns the hydraulic influence of each incoming lake runoff station on its neighboring lake water level stations, and outputs the preliminary estimated water level characteristics of Q lake water level stations in the basin , providing the input for the accurate estimation of the lake spatial water level of the subsequent ResGCN module. In the GCN module, the considered spatial correlation only includes the edges existing outside the lake as described in step 1.2, which point from the river runoff nodes to the lake water level nodes . The information transfer within the GCN module can be characterized as:

[0028] (3)

[0029] (4)

[0030] Among them, the GCN module includes one or several GCN layers, represents the input features of the l-th GCN layer; represents the output features of the l-th GCN layer, and at the same time is the input features of the (l + 1)-th GCN layer; A is the adjacency matrix described in step 1.3, and I is the corresponding identity matrix. and are respectively the adjacency matrix with self-loops superimposed and its degree matrix, which is used for the normalization of the adjacency matrix. is a learnable weight matrix. represents the sigmoid activation function.

[0031] Step 2.3, accurately simulate the spatial water level of the lake based on the ResGCN module. The ResGCN module first concatenates the runoff characteristics of the incoming river channels at time t in formula (1) and the initial estimated water level characteristics of each lake water level station output by the GCN module to obtain the all-node features at time t , and uses it as the input of the ResGCN module. Subsequently, based on the ResGCN module, considering both the influence of the incoming lake runoff on the adjacent lake water levels and the mutual influence between the lake spatial water levels, accurately simulate the lake spatial water level and output it. In the ResGCN module, the considered spatial associations include both the edges existing outside the lake as described in step 1.2, pointing from the river runoff nodes to the lake water level nodes , and also cover the edges existing inside the lake, pointing from the lake water level nodes to the lake water level nodes . The information transfer of the ResGCN module is shown in the following formula. First, perform graph convolution operation, and then sum the graph convolution result with the input of the ResGCN module as the output of the ResGCN module.

[0032] (5)

[0033] Furthermore, step 3 is as follows:

[0034] Step 3.1, equal-frequency binning of data. First, organize the historical observation data of each hydrological representative station described in step 1.1, interpolate the data outliers and missing values, and then perform min-max normalization on the processed historical observation data to obtain a data set. Subsequently, using the water level mean of all lake water level stations in each time period as an index and the hydrological characteristics of all hydrological representative stations in each time period as a unit, sort the data set, and evenly divide the data set into M bins according to the sorting, and the number of time periods of the data contained in each bin is the same.

[0035] Step 3.2, Dataset Division. Divide the dataset into a training set, a validation set, and a test set. Randomly select 20% of the data samples from each bin interval to form an independent test set. And adopt the K-fold cross-validation method to randomly divide the remaining 80% of the non-test set samples in each bin into K subsets with the same number of time periods. Finally, combine the k-th subset of each bin into the k-th fold of the validation set, and combine the remaining subsets into the k-th fold of the training set. Where k = 1, 2, …, K.

[0036] Further, Step 4 is as follows:

[0037] Step 4.1, Hyperparameter Setting. The lake spatial water level simulation model contains multiple hyperparameters, including the number of layers of LSTM units, the number of hidden nodes of LSTM units, the batch size, the learning rate, and the weight decay rate. Assign multiple candidate values to each hyperparameter, and combine all candidate values of each hyperparameter to construct a hyperparameter combination set.

[0038] Step 4.2, Optimize the Hyperparameter Combinations of the Lake Spatial Water Level Simulation Model. Select an optimization method and a loss function, and use the K-fold training set to train the lake spatial water level simulation model under each hyperparameter combination case to obtain the optimal model for each hyperparameter combination. Input the K validation sets into the optimal model of each hyperparameter combination, select the accuracy evaluation index, and calculate the average accuracy of the validation set of the optimal model. Subsequently, retrain the lake spatial water level simulation model under each hyperparameter combination case with all non-test set samples, input the test set into the optimal model of each hyperparameter combination obtained by retraining, and calculate the test set accuracy using the accuracy evaluation index. Finally, the hyperparameter combination selected when both the average accuracy of the validation set and the test set accuracy reach the optimal is the optimized hyperparameter combination.

[0039] Further, Step 5 is as follows:

[0040] Step 5.1, Calculate the Marginal Contribution of In-lake Runoff to the Fluctuation of Lake Spatial Water Level.

[0041] Select the explanatory samples from the dataset described in Step 3.1, and call the SHAP algorithm to calculate the marginal contribution of each in-lake runoff, including reservoir discharge, to the lake spatial water level, which is characterized as a SHAP value matrix with the dimension of the number of in-lake runoff stations × the number of lake water level stations.

[0042] Step 5.2, Analyze the Lag Time of the Influence of In-lake Runoff on Lake Spatial Water Level.

[0043] Taking the in-lake runoff station p and the lake water level station q as an example, extract the marginal contribution of the in-lake runoff station p to the lake water level station q at different lag times from the SHAP value matrix, and the lag times of the in-lake runoff corresponding to the 2 or 3 SHAP values with the largest values are the lag times of the influence of the in-lake runoff p on the lake water level station q.

[0044] Step 5.3, quantify the impact degree of the inflow into the lake on the spatial water level of the lake.

[0045] Normalize and percentageize the marginal contribution of each inflow into the lake at each lag time to the specified lake water level station q to obtain the time period runoff contribution rate; sum the time period runoff contribution rates of the same inflow into the lake at different lag times to obtain the total contribution rate of each inflow into the lake to the lake water level station q; sort the total contribution rates of each inflow into the lake from large to small, and the larger the total contribution rate, the stronger the impact of the corresponding inflow into the lake on the lake water level station q.

[0046] A computer system includes a memory, a processor, and a computer program stored on the memory and executable on the processor. When the processor executes the computer program, the steps of the above method are implemented.

[0047] The present invention has the following beneficial effects:

[0048] Based on the LSTM module with superior performance in temporal correlation extraction and the GCN and ResGCN modules that can effectively capture the spatial correlation of the basin, the present invention constructs a lake spatial water level simulation model based on a graph spatio-temporal neural network. By capturing the temporal correlation and spatial correlation of each hydrological representative station in the basin, the model effectively learns the complex hydraulic influence of each inflow into the lake on the lake spatial water level, and accurately simulates the dynamic response process of the lake spatial water level to many inflows into the lake including the upstream reservoir discharge. At the same time, based on the interpretability method, the present invention analyzes the response time of the lake spatial water level to each inflow into the lake, quantifies the impact degree of different inflows into the lake on the lake water level fluctuation, breaks through the limitation of the "black box" of the traditional machine learning model, provides model support and scientific basis for the lake water resources scheduling management, and helps to achieve the precise management and green development of the basin. Description of the Drawings

[0049] Figure 1 It is a flow chart of an interpretable lake spatial water level simulation method considering spatio-temporal correlation provided by the present invention;

[0050] Figure 2 It is a schematic diagram of the graph structure in the embodiment. Detailed Embodiment

[0051] The following further describes the present invention with specific embodiments.

[0052] The present invention selects the Dongting Lake Basin to carry out an interpretable lake spatial water level simulation method considering spatio-temporal correlation. Combining the technical solution and the drawings, the detailed embodiment is described in detail, which specifically includes the following steps:

[0053] Step 1, establish the basin graph structure and the adjacency matrix.

[0054] Step 1.1: Based on the river network near the lake, determine the inflow and outflow channels of the lake, as well as the internal partitions and flow directions within the lake. At least one hydrological representative station is selected for each inflow channel and lake partition, and the selected hydrological representative stations need to have long-term, continuous, and consistent historical observation data. According to the differences in geographical location and hydrological characteristics, the hydrological representative stations include two types: inflow runoff stations and lake water level stations.

[0055] In this embodiment, Dongting Lake includes five inflow runoffs, namely the diversions of the main stream of the Yangtze River in the three-outlet area and the inflows of the Lishui River, Yuanjiang River, Zishui River, and Xiangjiang River in the four-river area. The Three Gorges Reservoir, Shimen, Taoyuan, Taojiang, and Xiangtan stations are successively selected as the hydrological representative stations of the main stream of the Yangtze River, the Lishui River, the Yuanjiang River, the Zishui River, and the Xiangjiang River, and they are also the inflow runoff stations for the derivation of the lake spatial water level.

[0056] The interior of Dongting Lake is divided into three lake areas, which are the West Dongting Lake, South Dongting Lake, and East Dongting Lake in the order of the water flow direction. Their hydrological representative stations are Nanju and Xiaoheju stations, Yangliutan and Yingtian stations, and Lujiao and Chenglingji stations respectively, which are the lake water level stations for the derivation of the lake spatial water level.

[0057] Step 1.2: Generalize the structure of the basin map.

[0058] The basin map structure consists of a node set and an edge set. Nodes are used to represent the hydrological representative stations selected in Step 1.1, including the river runoff nodes representing the inflow runoff stations and the lake water level nodes representing the lake water level stations. . Edges represent the hydraulic connections between hydrological representative stations, including the edges outside the lake, which point from the river runoff nodes to the lake water level nodes , representing the influence of the inflow runoff on the lake water level; and the edges inside the lake, which point from the lake water level nodes to the lake water level nodes , representing the associated influence between the water levels inside the lake. Both types of edges are directed edges, and the direction is consistent with the water flow direction. The map structure of this embodiment is as shown in Figure 2 .

[0059] Step 1.3: Set the adjacency matrix. The information update and transmission of the basin map structure are represented by an adjacency matrix A of dimension as shown in formula (1), where N is the number of nodes in the basin map structure, including P river runoff nodes and Q lake water level nodes. When and only when there is an edge pointing from node p to node q, the element . In this embodiment, there are P = 5 river runoff nodes and Q = 6 lake water level nodes, and the dimension of the adjacency matrix A of the map structure is 11×11.

[0060] (1)

[0061] Step 2, construct a lake spatial water level simulation model based on a graph spatio-temporal neural network;

[0062] Construct a lake spatial water level simulation model. The input of the lake spatial water level simulation model is runoff characteristics, including runoff sequences of all inflows into the lake in the past and current H time periods, and the output is the water level characteristics of all lake water level stations at the current time period. As shown in the following formula,

[0063] (2)

[0064] where, is the runoff characteristic at time t, , P represents the number of river runoff nodes, and the value in the embodiment is 5. is the water level characteristic at time t, , Q represents the number of lake water level nodes, and the value in the embodiment is 6. H is the number of time periods of the input runoff characteristics, and the value in the embodiment is 50. is the mapping function.

[0065] There is a significant spatio-temporal correlation between the input runoff characteristics and the output water level characteristics. Specifically, there is a long-term temporal dependence in the runoff sequence, and this dependence continuously acts on the water level fluctuations at time t; meanwhile, the runoff characteristics of the inflow river channels and the water level characteristics of the internal partitions of the lake

[0066] Step 2.1, capture the temporal correlation of the runoff sequence and reduce the dimension based on the LSTM module. The LSTM module takes the runoff sequences of all P inflow river stations in the basin in the past and current H time periods As the input. First, the LSTM cells of the LSTM module capture the temporal correlations in the runoff sequences of the river channels flowing into the lake in the basin. At each time step, the runoff characteristics of each runoff station flowing into the lake are extracted and updated, and the hidden states of each period are output. . Subsequently, based on the fully connected layer of the LSTM module, the hidden states of H periods of each runoff station flowing into the lake are linearly combined through the weight matrix , reducing the dimension of the runoff sequence flowing into the lake in the time dimension, and performing a non-linear transformation through the activation function, and finally outputting the aggregated runoff characteristics of each runoff station flowing into the lake. .

[0067] Step 2.2, preliminarily calculate the spatial water level of the lake based on the GCN module. The GCN module takes the aggregated runoff characteristics of each runoff station flowing into the lake output by the LSTM module as the input, learns the hydraulic influence of each runoff station flowing into the lake on its neighboring lake water level stations, and outputs the preliminary estimated water level characteristics of Q lake water level stations in the basin , providing the input for the precise estimation of the spatial water level of the lake by the subsequent ResGCN module. In the GCN module, the considered spatial correlations only include the edges existing outside the lake as described in Step 1.2, pointing from the river runoff nodes to the lake water level nodes. . The information transfer within the GCN module can be characterized as:

[0068] (3)

[0069] (4)

[0070] where the GCN module contains one or several GCN layers, represents the input features of the l-th GCN layer; represents the output features of the l-th GCN layer, and is also the input features of the l+1-th GCN layer; A is the adjacency matrix described in Step 1.3, and I is the corresponding identity matrix. and are respectively the adjacency matrix with self-loops superimposed and its degree matrix, used for the normalization of the adjacency matrix. is the learnable weight matrix. represents the sigmoid activation function. In this embodiment, the constructed GCN module contains 1 GCN layer.

[0071] Step 2.3, precisely simulate the spatial water level of the lake based on the ResGCN module. The ResGCN module first concatenates the runoff characteristics of the river channels flowing into the lake at time t in formula (1) and the preliminary estimated water level characteristics of each lake water level station output by the GCN module , all node features at time t are obtained , and used as the input of the ResGCN module. Subsequently, based on the ResGCN module, considering both the impact of the inflow runoff on the adjacent lake water levels and the mutual influence between the lake spatial water levels, the lake spatial water levels are accurately simulated and its output. In the ResGCN module, the considered spatial associations include both the edges existing outside the lake, from the river runoff nodes to the lake water level nodes as described in step 1.2 , and also cover the edges existing inside the lake, from the lake water level nodes to the lake water level nodes . The information transfer of the ResGCN module is shown in the following formula. First, a graph convolution operation is performed, and then the graph convolution result is summed with the input of the ResGCN module as the output of the ResGCN module.

[0072] (5)

[0073] Step 3, segment the dataset based on the equal-frequency binning method;

[0074] Step 3.1, data equal-frequency binning. First, organize the historical observation data of each hydrological representative station described in step 1.1, interpolate the data outliers and missing values, and then perform min-max normalization on the processed historical observation data to obtain the dataset. Among them, the historical observation data selected in this embodiment are the daily-scale flow or water level data of all hydrological representative stations in the basin from 2009 to 2023, and the runoff characteristic of the Three Gorges Reservoir is the discharge. Subsequently, using the water level mean of all lake water level stations in each period as the index and the hydrological characteristics of all hydrological representative stations in each period as the unit, the dataset is sorted and evenly divided into M bins, and the number of time periods of the data contained in each bin is the same. In this embodiment, the number of bins is set to 30.

[0075] Step 3.2, dataset division. Divide the dataset into a training set, a validation set, and a test set. Randomly select 20% of the data samples from each bin interval to form an independent test set. The embodiment adopts a 5-fold cross-validation method, and randomly divides the remaining 80% of the non-test set samples in each bin into 5 subsets with the same number of time periods. Finally, the k-th subset of each bin is combined into the k-th fold of the validation set, and the remaining subsets are combined into the k-th fold of the training set. Among them, k = 1, 2, 3, 4, 5.

[0076] Step 4, train the lake spatial water level simulation model and optimize the hyperparameter combination;

[0077] Step 4.1, Hyperparameter setting. The lake spatial water level simulation model contains multiple hyperparameters, including the number of layers of LSTM units, the number of hidden nodes of LSTM units, batch size, learning rate, and weight decay rate. Assign multiple candidate values to each hyperparameter, and combine all candidate values of each hyperparameter to construct a hyperparameter combination set. In this embodiment, the range of candidate values for the number of layers of LSTM units is [1, 2, 3], the range of candidate values for the number of hidden nodes of LSTM units is [8, 16, 32], the range of candidate values for batch size is [32, 64, 128], the range of candidate values for learning rate is [0.01, 0.05, 0.001, 0.005], and the range of candidate values for weight decay rate is [0.01, 0.001, 0.0001]. Therefore, there are 3×3×3×4×3 = 324 hyperparameter combinations in the hyperparameter combination set.

[0078] Step 4.2, Optimize the hyperparameter combination of the lake spatial water level simulation model. In the embodiment, the Adam optimization method and the loss function of mean square error minimization are selected. The lake spatial water level simulation model in each hyperparameter combination case is trained using a 5-fold training set to obtain the optimal model for each hyperparameter combination. Input the 5 validation sets into the optimal model of each hyperparameter combination, select the accuracy evaluation index, and calculate the average accuracy of the validation set of the optimal model. Subsequently, retrain the lake spatial water level simulation model in each hyperparameter combination case using all non-test set samples, input the test set into the optimal model of each hyperparameter combination obtained from the retraining, and calculate the test set accuracy using the accuracy evaluation index. Finally, the hyperparameter combination selected when both the average accuracy of the validation set and the test set accuracy reach the optimum is the optimized hyperparameter combination.

[0079] In this embodiment, when the number of layers of LSTM units takes the value of 1, the number of hidden nodes of LSTM units takes the value of 8, the batch size takes the value of 64, the learning rate takes the value of 0.001, and the weight decay rate takes the value of 0.0001, both the average accuracy of the validation set and the test set accuracy of the lake spatial water level simulation model reach the optimum. At this time, the Pearson correlation coefficient and root mean square error of the validation set are 0.984 and 0.44 m respectively, and the Pearson correlation coefficient and root mean square error of the test set are 0.985 and 0.42 m respectively, both of which are globally optimal.

[0080] Step 5, Quantify the impact of each incoming lake runoff on the lake spatial water level.

[0081] Step 5.1, Calculate the marginal contribution of the incoming lake runoff to the lake spatial water level fluctuation.

[0082] Select the interpretation samples from the dataset described in step 3.1, and call the SHAP algorithm to calculate the marginal contributions of each inflow runoff into the lake, including reservoir discharge, to the spatial water level of the lake, which is characterized as a SHAP value matrix with the dimension of the number of inflow runoff stations × the number of lake water level stations. In this embodiment, the independent test set described in step 3.2 is selected as the interpretation sample, and the marginal contributions of the runoff sequences of the Three Gorges Reservoir, Shimen, Taoyuan, Taojiang, and Xiangtan stations to the water level fluctuations of the Nanju, Xiaohezui, Yangliutan, Yingtian, Lujiao, and Chenglingji stations are calculated respectively, that is, a SHAP value matrix with the dimension of 5×6.

[0083] Step 5.2, analyze the lag time of the impact of inflow runoff on the spatial water level of the lake.

[0084] Taking the inflow runoff station p and the lake water level station q as an example, extract the marginal contributions of the inflow runoff station p to the lake water level station q at different lag times from the SHAP value matrix, and the lag times of the inflow runoff corresponding to the 2 or 3 largest SHAP values are the impact lag times of the inflow runoff p on the lake water level station q.

[0085] In this embodiment, the lag times of the impact of the discharge of the Three Gorges Reservoir on the water levels of the Nanju, Yangliutan, and Chenglingji stations are analyzed. For the Nanju station, the 3 largest marginal contributions of the discharge of the Three Gorges Reservoir are 0.0103, 0.0097, and 0.0093 respectively, and the corresponding impact lag times are 0 days, 2 days, and 1 day respectively; for the Yangliutan station, the 3 largest marginal contributions of the discharge of the Three Gorges Reservoir are 0.0069, 0.0068, and 0.0060 respectively, and the corresponding impact lag times are 3 days, 2 days, and 1 day respectively; for the Chenglingji station, the 3 largest marginal contributions of the discharge of the Three Gorges Reservoir are 0.0119, 0.0114, and 0.0107 respectively, and the corresponding impact lag times are 3 days, 2 days, and 4 days respectively. Therefore, the impact lag times of the discharge of the Three Gorges Reservoir on the water levels of the Nanju, Yangliutan, and Chenglingji stations are 0 - 2 days, 1 - 3 days, and 2 - 4 days respectively.

[0086] Step 5.3, quantify the impact degree of inflow runoff on the spatial water level of the lake.

[0087] Normalize and percentageize the marginal contributions of each inflow runoff at each lag time to the specified lake water level station q to obtain the period runoff contribution rate; sum the period runoff contribution rates of the same inflow runoff at different lag times to obtain the total contribution rate of each inflow runoff to the lake water level station q; sort the total contribution rates of each inflow runoff from large to small, and the larger the total contribution rate, the stronger the impact of the corresponding inflow runoff on the lake water level station q.

[0088] In this embodiment, the influence degrees of the runoff sequences of the Three Gorges Reservoir, Shimen, Taoyuan, Taojiang, and Xiangtan stations on the water levels of the Nanju and Yingtian stations are quantified respectively. Among them, the total contribution rates of the Three Gorges Reservoir, Shimen, Taoyuan, Taojiang, and Xiangtan stations to the Nanju station are 40%, 17%, 25%, 10%, and 8% in sequence. Therefore, the influence degrees of each inflowing lake runoff on the water level fluctuation of the Nanju station from strong to weak are as follows: the mainstream of the Yangtze River, the Yuanjiang River, the Lishui River, the Zishui River, and the Xiangjiang River; the total contribution rates of the Three Gorges Reservoir, Shimen, Taoyuan, Taojiang, and Xiangtan stations to the Yingtian station are 40%, 15%, 18%, 10%, and 17% in sequence. Therefore, the influence degrees of each inflowing lake runoff on the water level fluctuation of the Yingtian station from strong to weak are as follows: the mainstream of the Yangtze River, the Yuanjiang River, the Xiangjiang River, the Lishui River, and the Zishui River.

[0089] The above-described embodiments only represent the implementation modes of the present invention, but should not be construed as limiting the scope of the present invention patent. It should be noted that for those skilled in the art, without departing from the concept of the present invention, several modifications and improvements can still be made, and these all belong to the protection scope of the present invention.

Claims

1. An interpretable lake spatial water level simulation method considering spatio-temporal correlation, characterized in that It includes the following steps: Step 1, establish the basin map structure and the adjacency matrix; Step 2, construct a lake spatial water level simulation model based on the graph spatio-temporal neural network; Integrate the long short-term memory network module, the graph convolutional neural network module, and the residual graph convolutional neural network module to construct a lake spatial water level simulation model based on the graph spatio-temporal neural network. First, introduce the long short-term memory network module, abbreviated as the LSTM module, to mine the temporal correlation of the runoff sequence and aggregate and reduce the dimension of the runoff sequence from the time dimension. Second, construct the graph convolutional neural network module, abbreviated as the GCN module, and based on the spatial correlation between the incoming lake runoff and the water levels of neighboring lakes, preliminarily simulate the lake spatial water level and assign the initial feature values at time t to the lake water level nodes. Finally, adopt the residual graph convolutional neural network module, abbreviated as the ResGCN module, and on the basis of considering the influence of the incoming lake runoff, further consider the spatial correlation between the lake water level nodes to accurately simulate the lake spatial water level; The input of the lake spatial water level simulation model is the runoff characteristics, including the runoff sequences of all incoming lake runoffs in the past and current total H periods, and the output is the water level characteristics of all lake water level stations in the current period; as shown in the following formula, (2) Among them, is the runoff characteristic at time t, , where P represents the number of river runoff nodes; is the water level characteristic at time t, , where Q represents the number of lake water level nodes; H is the number of time periods of the input runoff characteristic, is the mapping function; Step 3, segment the dataset based on the equal-frequency binning method; Step 4, train the lake spatial water level simulation model and optimize the hyperparameter combination; Step 5, quantify the influence of each incoming lake runoff on the lake spatial water level, specifically: Step 5.1, calculate the marginal contribution of the incoming lake runoff to the lake spatial water level fluctuation; Step 5.2, analyze the lag time of the influence of the incoming lake runoff on the lake spatial water level; Step 5.3, quantify the influence degree of the incoming lake runoff on the lake spatial water level.

2. The interpretable lake spatial water level simulation method considering spatio-temporal correlation according to claim 1, characterized in that The specific content of the above-mentioned Step 1 is as follows: Step 1.1, based on the river network system near the lake, determine the inflow and outflow channels of the lake, as well as the internal partitions and flow directions of the lake; select at least one hydrological representative station in each incoming lake channel and lake partition, and the selected hydrological representative stations need to have long-term, continuous, and consistent historical observation data; according to the geographical location and hydrological characteristics differences, the hydrological representative stations include two types: incoming lake runoff stations and lake water level stations; Step 1.2, generalize the basin map structure; The basin map structure consists of a node set and an edge set; the nodes are used to represent the hydrological representative stations selected in Step 1.1, including river runoff nodes representing the river inflow stations into the lake and lake water level nodes representing the lake water level stations ; Edges represent the hydraulic connections between hydrological representative stations, including the edges outside the lake, pointing from the river runoff nodes to the lake water level nodes, which characterize the impact of the inflow runoff on the lake water level; and the edges inside the lake, pointing from the lake water level nodes to the lake water level nodes, which characterize the associated impact between the water levels inside the lake; both types of edges are directed edges, and the direction is consistent with the water flow direction; Step 1.3, set the adjacency matrix; The information update and transmission of the river basin map structure are represented by an adjacency matrix A with a dimension of as shown in formula (1), where N is the number of nodes in the river basin map structure, including P river runoff nodes and Q lake water level nodes; when and only when there is an edge pointing from node p to node q, the element ; (1) 。 3. An interpretable lake spatial water level simulation method considering spatio-temporal correlation according to claim 2, characterized in that, The specific content of the above-mentioned Step 2 is as follows: Step 2.1, capture and reduce the dimension of the temporal correlation of the runoff sequence based on the LSTM module; The LSTM module takes the runoff sequences of the past and current H time periods of all P inflow stations in the basin as input. First, the LSTM unit of the LSTM module captures the temporal correlation in the runoff sequences of each inflow river channel in the basin, extracts and updates the runoff characteristics of each inflow station at each time step, and outputs the hidden states of each time period. ; Subsequently, based on the fully connected layer of the LSTM module, the hidden states of H time periods of each inflow runoff station are linearly combined through the weight matrix, reducing the dimension of the inflow runoff sequence in the time dimension, and performing a non-linear transformation through the activation function, and finally outputting the aggregated runoff characteristics of each inflow runoff station after aggregation. ; Step 2.2, preliminarily calculate the lake spatial water level based on the GCN module; The GCN module takes the aggregated runoff characteristics of each incoming lake runoff station output by the LSTM module as input, learns the hydraulic influence of each incoming lake runoff station on its neighboring lake water level stations, and outputs the preliminary estimated water level characteristics of Q lake water level stations in the basin , providing input for the precise estimation of the lake spatial water level of the subsequent ResGCN module; Step 2.3, accurately simulate the lake spatial water level based on the ResGCN module; The ResGCN module first concatenates the runoff characteristics of the river channels flowing into the lake at time t in formula (1) and the initial estimated water level characteristics of each lake water level station output by the GCN module to obtain the characteristics of all nodes at time t and uses it as the input of the ResGCN module; subsequently, based on the ResGCN module, considering both the impact of the inflow runoff on the adjacent lake water levels and the mutual influence between the lake spatial water levels, it accurately simulates the lake spatial water levels and outputs it.

4. An interpretable lake spatial water level simulation method considering spatio-temporal correlation according to claim 3, characterized in that, In the above-mentioned Step 2.2, the information transfer in the GCN module is characterized as: (3) (4) Among them, the GCN module includes one or several GCN layers, represents the input features of the l-th GCN layer; represents the output features of the l-th GCN layer and is also the input features of the (l + 1)-th GCN layer; A is the adjacency matrix described in step 1.3, and I is the corresponding identity matrix; and are respectively the adjacency matrix with self-loops superimposed and its degree matrix, which is used for the normalization of the adjacency matrix; is a learnable weight matrix; represents the sigmoid activation function.

5. An interpretable lake spatial water level simulation method considering spatio-temporal correlation according to claim 3, characterized in that In the step 2.3, the information transfer of the ResGCN module is shown in formula (5). First, graph convolution operation is performed, and then the result of graph convolution is summed with the input of the ResGCN module as the output of the ResGCN module; (5) 。 6. The interpretable lake spatial water level simulation method considering spatio-temporal correlation according to claim 3, characterized in that, The specific content of the above-mentioned Step 3 is as follows: Step 3.1, data equal-frequency binning; Sort out the historical observation data of each hydrological representative station in Step 1.1, interpolate the data outliers and missing values, and perform maximum-minimum normalization on the processed historical observation data to obtain the dataset; Subsequently, using the water level mean of all lake water level stations in each period as an index and the hydrological characteristics of all hydrological representative stations in each period as a unit, sort the dataset and evenly divide the dataset into M bins according to the sorting, and the number of periods of data contained in each bin is the same; Step 3.2: Divide the dataset into a training set, a validation set, and a test set.

7. An interpretable lake spatial water level simulation method considering spatio-temporal correlation according to claim 6, characterized in that, Specifically, Step 3.2 is as follows: Randomly select 20% of the data samples from each bin interval to form an independent test set; and adopt the K-fold cross-validation method to randomly divide the remaining 80% of the non-test set samples in each bin into K subsets with the same number of time periods; finally, combine the k-th subset of each bin into the k-th fold of the validation set, and the remaining subsets are combined into the k-th fold of the training set, where k = 1, 2, …, K.

8. An interpretable lake spatial water level simulation method considering spatio-temporal correlation according to claim 6, characterized in that, The specific content of Step 4 is as follows: Step 4.1: Hyperparameter setting; The lake spatial water level simulation model contains multiple hyperparameters, including the number of layers of LSTM units, the number of hidden nodes of LSTM units, batch size, learning rate, and weight decay rate; assign multiple candidate values to each hyperparameter, and combine all candidate values of each hyperparameter to construct a hyperparameter combination set; Step 4.2: Optimize the hyperparameter combination of the lake spatial water level simulation model; Select an optimization method and a loss function, and use the K-fold training set to train the lake spatial water level simulation model under each hyperparameter combination case to obtain the optimal model for each hyperparameter combination; input the K validation sets into the optimal model of each hyperparameter combination, select an accuracy evaluation index, and calculate the average accuracy of the validation set of the optimal model; Subsequently, retrain the lake spatial water level simulation model under each hyperparameter combination case using all non-test set samples, input the test set into the optimal model of each hyperparameter combination obtained from the retraining, and calculate the test set accuracy using the accuracy evaluation index; finally, the hyperparameter combination selected when both the average accuracy of the validation set and the test set accuracy reach the optimal is the optimal hyperparameter combination.

9. An interpretable lake spatial water level simulation method considering spatio-temporal correlation according to claim 8, characterized in that The specific content of Step 5 is as follows: Step 5.1: Calculate the marginal contribution of the incoming lake runoff to the fluctuation of the lake spatial water level; Select explanatory samples from the dataset, and call the SHAP algorithm to calculate the marginal contribution of each incoming lake runoff, including reservoir discharge, to the lake spatial water level, which is characterized as a SHAP value matrix with the dimension of the number of incoming lake runoff stations × the number of lake water level stations; Step 5.2: Analyze the lag time of the influence of the incoming lake runoff on the lake spatial water level; Taking the incoming lake runoff station p and the lake water level station q as an example, extract the marginal contribution of the incoming lake runoff station p to the lake water level station q at different lag times from the SHAP value matrix, and the lag times of the incoming lake runoff corresponding to the 2 or 3 SHAP values with the largest values are the influence lag times of the incoming lake runoff p on the lake water level station q; Step 5.3: Quantify the influence degree of the incoming lake runoff on the lake spatial water level; Normalize and percentageize the marginal contribution of each incoming lake runoff at each lag time to the specified lake water level station q to obtain the time period runoff contribution rate; sum the time period runoff contribution rates of the same incoming lake runoff at different lag times to obtain the total contribution rate of each incoming lake runoff to the lake water level station q; sort the total contribution rates of each incoming lake runoff from large to small, and the larger the total contribution rate, the stronger the influence of the corresponding incoming lake runoff on the lake water level station q.

10. A computer system for implementing the interpretable lake spatial water level simulation method considering spatio-temporal correlation according to any one of claims 1-9, characterized in that, The computer system includes a memory, a processor, and a computer program stored in the memory and executable on the processor.

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