Multi-step Spatiotemporal Prediction Method for Basin-scale Runoff Based on the Combination of Static and Dynamic Graphs

Abstract

A multi-step spatio-temporal prediction method for basin-scale runoff based on the combination of static and dynamic graphs, which includes extracting temporal and spatial characteristics of the runoff of each runoff monitoring station in a prediction basin over a period of historical time, generating a static river channel distance map, a static elevation difference map and a dynamic graph for all runoff monitoring stations, and fusing the three graphs to establish a runoff prediction model to predict the runoff of all runoff monitoring stations. The runoff prediction model includes an input layer, M levels of processing structures and a linear layer. The input layer inputs the runoff sequences of each runoff monitoring station in a prediction basin over a period of historical time; each level of processing structure extracts temporal and spatial characteristics respectively to obtain the output of the current level, and then serves as the input of the next level of processing structure; the outputs of M levels are also used as the input of the linear layer, and the linear layer finally outputs the predicted runoff of all runoff monitoring stations, which can effectively improve the accuracy of multi-step prediction of basin-scale runoff.

Description

Technical Field

[0001] The present invention belongs to the technical field of river runoff prediction, and particularly relates to a multi-step spatio-temporal prediction method for basin-scale runoff based on the combination of static and dynamic graphs. Background Technique

[0002] Runoff simulation is to predict future hydrological conditions based on historical runoff time series. Accurate and reliable daily runoff prediction results are of great significance for water resource management, disaster prevention and mitigation, and power generation and energy supply. Runoff is susceptible to natural and human factors and has obvious characteristics of complexity, nonlinearity, and time-variation. Usually, runoff simulation uses process-based model prediction, that is, runoff prediction is carried out by describing the physical processes of the hydrological cycle. However, at the same time, the requirements for complex meteorological and underlying surface data and the high dependence on expert experience limit its further application. In addition to process-based models, thanks to the continuous increase in data information and the rapid development of computer capabilities, data-driven models have gradually been more widely used. Different from process-based models, data-driven models learn the mapping function between historical feature inputs and expected outputs without exploring the physical mechanism of the basin water cycle. They have the advantages of low data requirements and little dependence on professional knowledge. In order to better fit nonlinear sequences, machine learning methods have been introduced into the field of geoscience. In particular, deep learning models have achieved great success in time series prediction. In terms of runoff prediction, two variants of recurrent neural networks (RNNs), namely long short-term memory artificial neural networks (LSTMs) and gated recurrent units (GRUs), have recently become popular in identifying the potential features of input sequences.

[0003] Although a lot of work has been done on runoff prediction using deep learning models, there are still some deficiencies that need to be further explored. First of all, previous models rarely paid attention to the spatial dependence between downstream and upstream runoff monitoring stations. Most of the previously established runoff prediction models only captured the temporal characteristics of the input sequence itself, that is, they were limited to temporal prediction models and did not consider spatial information. Since downstream stations are affected by static factors (such as river channel distance and elevation difference) and directly receive runoff from upstream, there is rich spatial correlation between upstream and downstream runoff monitoring stations. In addition to being affected by static factors, downstream runoff is also affected by the spatial heterogeneity of different upstream sub-basins, mainly including dynamic climate conditions upstream (such as precipitation and evapotranspiration) and underlying surface conditions (such as soil moisture). Static and dynamic spatial characteristics jointly determine the contribution degree of runoff from different upstream stations to downstream confluence. Therefore, making good use of the rich spatial characteristics between runoff monitoring stations in the river network will effectively improve the prediction accuracy. Secondly, few models are specifically designed for runoff prediction at the basin scale, especially for upstream tributary stations with relatively small flow rates. Since they are more vulnerable to natural and human factors, the simulation of these runoff monitoring stations is more complex. The basin scale not only refers to the number of runoff monitoring stations to be predicted and their distribution in space, but more importantly, regarding them as a whole through their spatial connections and making predictions simultaneously. Summary of the Invention

[0004] In view of the deficiencies of the prior art, the object of the present invention is to provide a multi-step spatio-temporal prediction method for basin-scale runoff based on the combination of static and dynamic graphs, which can effectively improve the accuracy of multi-step prediction of basin-scale runoff and provide basic flood situation forecast data for the efficient development and utilization of water resources and flood disaster mitigation.

[0005] In order to solve the above technical problems, the technical solution adopted by the present invention is as follows:

[0006] A multi-step spatio-temporal prediction method for basin-scale runoff based on the combination of static and dynamic graphs, comprising:

[0007] Extract the temporal characteristics of the runoff of each runoff monitoring station in the prediction basin over a period of historical time;

[0008] Perform spatial feature extraction, generate a static river channel distance map, a static elevation difference map and a dynamic graph for all runoff monitoring stations in the prediction basin. Among them, the static river channel distance is used to represent the river channel distance between the upstream runoff monitoring station and the downstream runoff monitoring station, the static river channel distance map is used to represent the river channel distance relationship between each runoff monitoring station, the static elevation difference is used to represent the elevation difference between the upstream runoff monitoring station and the downstream runoff monitoring station, the static elevation difference map is used to represent the elevation difference relationship between each runoff monitoring station, and the dynamic graph is used to simulate the dynamic hydrological process. Integrate the static river channel distance map, the static elevation difference map and the dynamic graph to obtain the spatial characteristics of the runoff of each runoff monitoring station;

[0009] A runoff prediction model is established to predict the runoff of all runoff monitoring stations. The runoff prediction model includes an input layer, M levels of processing structures, and a linear layer. The M levels of processing structures are connected in sequence from low to high. The input layer inputs the runoff sequences of each runoff monitoring station in a prediction basin over a period of historical time. Each level of the processing structure performs time feature extraction and spatial feature extraction to obtain the output of the current level, and this level of output is used as the input of the next level of the processing structure. At the same time, the outputs of the M levels are input into the linear layer through skip connections, and finally the predicted runoff of all runoff monitoring stations in the prediction basin is output.

[0010] Further, the input layer inputs the runoff sequences of each runoff monitoring station in a prediction basin over a period of historical time. The runoff sequence of each runoff monitoring station over a period of historical time is:

[0011]

[0012] where t is the total number of days, 1 ≤ n ≤ N, and N is the number of runoff monitoring stations in the prediction basin;

[0013] The runoff of each runoff monitoring station over a period of historical time is linearly combined into a time-series combined feature X‘ = [X1, X2,... X N T .

[0014] Further, a gated temporal convolutional network GTCN is constructed. The time-series combined feature X‘ extracted is input into the network and trained to achieve time feature extraction.

[0015] Further, a graph structure of a static river channel distance map, a static elevation difference map, and a dynamic map is established. The static river channel distance map is represented as Graph1 = (V, E, A1), the static elevation difference map is represented as Graph2 = (V, E, A2), and the dynamic map is Graph3 = (V, E, A3);

[0016] where V is a set of vertices corresponding to the runoff monitoring stations in the river network, E is a set of directed edges showing the one-way flow path from the upstream runoff monitoring station to the downstream runoff monitoring station, and A1, A2, and A3 are all weighted adjacency matrices.

[0017] Further, in the process of generating the static river channel distance map, a threshold Gaussian kernel is used to represent and generate the weighted adjacency matrix A1 = (W ij ) N×N :

[0018]

[0019] In the formula, W ij ​Denote the directed edge weight from the upstream runoff monitoring station i to the downstream runoff monitoring station j, d ij is the distance along the river channel from the upstream runoff monitoring station to the downstream runoff monitoring station, Denote the dimension as N×N, k thre Denote the threshold, taking 0.1, σ1 represents the standard deviation of d ij The number of runoff monitoring stations in the predicted basin, and the value is taken according to actual needs.

[0020] Furthermore, in the process of generating the static elevation difference map, a threshold Gaussian kernel is used to represent and generate the weighted adjacency matrix A2=(W ed ) N×N :

[0021]

[0022] In the formula, W ed Denote the directed edge weight from the upstream runoff monitoring station e to the downstream runoff monitoring station d, d ed is the difference in altitude between the upstream runoff monitoring station and the downstream runoff monitoring station, Denote the dimension as N×N, k thre Denote the threshold, taking 0.1, σ2 represents the standard deviation of ded, and N is the number of runoff monitoring stations in the predicted basin, and the value is taken according to actual needs.

[0023] Furthermore, a graph attention network GAT is introduced to model the dynamic runoff process and adaptively learn hidden features. The graph attention network consists of a shared operator Composed of:

[0024]

[0025] In the formula, Denote the dimension as 2×B′, e pq is the attention coefficient, characterizing the importance of the features in runoff monitoring station p to runoff monitoring station q, Denote the dimension as B×B′, B is the number of input features, and B′ is the number of output features, Denote the input features,. T Denote the transpose operation, || denotes the merging operation. The formula only selects the first-order neighbors of runoff monitoring station q and itself to calculate. To standardize the attention coefficients of all selected runoff monitoring stations p, the softmax function is used:

[0026]

[0027] Obtain an adaptive weighted adjacency matrix A3 = (α pq ) N×N .

[0028] Furthermore, use the graph convolutional layer GCL to fuse the static river channel distance map, the static elevation difference map, and the dynamic map into a whole. The graph convolutional layer GCL is described as a diffusion process with K steps:

[0029]

[0030] where L k is the normalized adjacency matrix in the k-th diffusion, L ij = A1 / rowsum(A1), L ed = A2 / rowsum(A2), L pq = A3 / rowsum(A3).

[0031] Furthermore, multiple-level skip connections are integrated into the linear layer output to predict the predicted runoff of all runoff monitoring stations in the basin. The calculation formula is:

[0032]

[0033] where input is the output of each level processing structure, || is the array concatenation operation (concatenation), as the input of the final linear layer, RELU is the activation function, Linear represents the linear layer, the specific calculation of Linear depends on the number of neurons in the linear layer, Output is the final multi-step flow prediction result, M is the number of all levels, and 1 ≤ m ≤ M.

[0034] Compared with the prior art, the present invention has the following advantages and beneficial effects:

[0035] The present invention proposes a multi-step spatio-temporal prediction method for runoff at the basin scale based on the combination of static and dynamic graphs to enhance the static and dynamic spatial dependencies between upstream and downstream runoff monitoring stations. First, time feature extraction is performed to capture the time correlation between runoff monitoring stations. Secondly, a static river channel distance map, a static elevation difference map, and a dynamic map are generated to learn and predict the static and dynamic spatial features of all runoff monitoring stations in the basin, so as to further improve the prediction accuracy. Moreover, a runoff prediction model is established to perform spatio-temporal prediction jointly through time features and spatial features. The established runoff prediction model can effectively improve the accuracy of multi-step prediction of runoff at the basin scale, providing basic water regime forecast data for the efficient development and utilization of water resources and the mitigation of floods. Brief Description of the Drawings

[0036] Figure 1 It is a framework diagram of the runoff prediction model of the present invention.

[0037] Figure 2 This is the implementation flowchart of the runoff prediction of the present invention.

[0038] Figure 3 This is the flowchart of the multi-step spatio-temporal prediction method for basin-scale runoff based on the combination of static and dynamic graphs of the present invention.

[0039] Figure 4 This is the flowchart of the runoff prediction of the present invention.

[0040] Figure 5 This is the flowchart of the runoff prediction of the present invention. Detailed implementation manners

[0041] Next, the technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with the accompanying drawings in the embodiments of the present invention.

[0042] The present invention provides a multi-step spatio-temporal prediction method for basin-scale runoff based on the combination of static and dynamic graphs, as Figures 1 - 3 shown, including:

[0043] Extract the time characteristics of the runoff of each runoff monitoring station in the prediction basin over a period of historical time;

[0044] Perform spatial feature extraction, generate a static river channel distance map, a static elevation difference map and a dynamic graph for all runoff monitoring stations in the prediction basin. Among them, the static river channel distance is used to represent the river channel distance between the upstream runoff monitoring station and the downstream runoff monitoring station, the static river channel distance map is used to represent the river channel distance relationship between each runoff monitoring station, the static elevation difference is used to represent the difference in altitude between the upstream runoff monitoring station and the downstream runoff monitoring station, the static elevation difference map is used to represent the difference in altitude relationship between each runoff monitoring station, and the dynamic graph is used to simulate the dynamic hydrological process. Integrate the static river channel distance map, the static elevation difference map and the dynamic graph to obtain the spatial characteristics of the runoff of each runoff monitoring station;

[0045] Establish a runoff prediction model to predict the runoff of all runoff monitoring stations. The runoff prediction model includes an input layer, M levels of processing structures and a linear layer, and the M levels of processing structures are connected in sequence from low to high. The input layer inputs the runoff sequence of each runoff monitoring station in the prediction basin over a period of historical time; each level of processing structure performs time feature extraction and spatial feature extraction to obtain the output of the current level, and this level of output is used as the input of the next level of processing structure; at the same time, the outputs of the M levels are input to the linear layer through skip connections, and finally the predicted runoff of all runoff monitoring stations in the prediction basin is output.

[0046] The present invention proposes a multi-step spatio-temporal prediction method for runoff at the basin scale based on the combination of static and dynamic graphs (hereinafter referred to as HSDSTM) to enhance the static and dynamic spatial dependence between upstream and downstream runoff monitoring stations. First, time feature extraction is carried out to capture the time correlation between runoff monitoring stations. Secondly, static river distance maps, static elevation difference maps and dynamic graphs are generated to learn and predict the static and dynamic spatial features of all runoff monitoring stations in the basin, so as to further improve the prediction accuracy. Moreover, a runoff prediction model is established to conduct spatio-temporal prediction jointly through time features and spatial features. The established runoff prediction model can effectively improve the accuracy of multi-step prediction of runoff at the basin scale and provide basic flood situation forecast data for the efficient development and utilization of water resources and the mitigation of floods.

[0047] The present invention proposes a multi-step spatio-temporal prediction method for runoff at the basin scale based on the combination of static and dynamic graphs, which can predict the runoff at multiple future time steps according to the runoff information of the prediction basin over a period of history and through the runoff prediction model proposed by the present invention. For example, taking days as the scale, it can predict the runoff of runoff monitoring stations for multiple days in the future.

[0048] In the present invention, the input layer inputs the runoff of each runoff monitoring station in the prediction basin over a period of history. The runoff of each runoff monitoring station over a period of history is:

[0049]

[0050] where t is the total number of days, 1 ≤ n ≤ N, and N is the number of runoff monitoring stations in the prediction basin;

[0051] The runoff of each runoff monitoring station over a period of history is linearly combined into a time-series combined feature X‘ = [X1, X2,... X N T ,

[0052] A gated time series convolutional network GTCN is constructed, and the time feature extraction is realized by inputting the extracted time-series combined feature X‘ into the network and training.

[0053] Specifically, a gated time series convolutional network GTCN is constructed. The processing structure of level 1 inputs the time-series combined feature X‘ into the gated time series convolutional network GTCN and trains it to realize the time feature extraction of the processing structure of level 1. The processing structures of levels 2 to M input the output of the previous level into the gated time series convolutional network GTCN and train it to realize the time feature extraction of the processing structures of levels 2 to M.

[0054] ​Previous models tended to extract temporal features through RNN-based models (such as LSTM and GRU). However, this type of model has the disadvantages of gradient explosion or vanishing and instability, which is not conducive to the prediction of the model. The present invention proposes a multi-step spatio-temporal prediction method for basin-scale runoff based on the combination of static and dynamic graphs, constructs a gated temporal convolutional network GTCN to extract temporal features, and GTCN is a CNN-based model, which can effectively avoid this disadvantage and has shared filters and more stable gradients. This is also the advantage of choosing GTCN.

[0055] For runoff monitoring stations with upstream and downstream relationships, the closer their distances along the river channel, the more similar their runoff characteristics are likely to be in space. Therefore, a static river channel distance map is used to obtain the distances of each runoff monitoring station along the river channel. In addition, gravity causes runoff to flow from higher altitude river sections to lower altitude river sections, and the greater the elevation difference, the more likely the runoff is to flow downstream. Therefore, a static elevation difference map is used to obtain the elevations of each runoff monitoring station.

[0056] Establish the graph structures of the static river channel distance map, the static elevation difference map, and the dynamic graph.

[0057] The static river channel distance map is represented as Graph1=(V, E, A1);

[0058] The static elevation difference map is represented as Graph2=(V, E, A2);

[0059] The dynamic graph is Graph3=(V, E, A3);

[0060] Among them, V is a set of vertices corresponding to the runoff monitoring stations in the river network, E is a set of directed edges showing the one-way flow path from the upstream runoff monitoring station to the downstream runoff monitoring station. A1, A2, and A3 are all weighted adjacency matrices. For the three constructed graphs, their V and E are the same, but they have different weighted adjacency matrices.

[0061] In the present invention, during the process of generating the static river channel distance map, the static river channel distance refers to the distance along the river channel from the upstream runoff monitoring station to the downstream runoff monitoring station. In a directed graph, the river channel distance from downstream to upstream is ∞. For two runoff monitoring stations without upstream and downstream relationships, the distance is also equal to ∞.

[0062] Due to the strong autocorrelation of the runoff monitoring stations themselves, a weighted adjacency matrix with self-loops is considered. Correspondingly, the distance from a runoff monitoring station to itself is 0. The longer the distance, the weaker the spatial correlation between the two runoff monitoring stations. A threshold Gaussian kernel is used to represent and generate the weighted adjacency matrix A1=(W ij ) N×N :

[0063]

[0064] In the formula, W ij represents the directed edge weight from the upstream runoff monitoring station i to the downstream runoff monitoring station j, and d ij is the distance along the river channel from the upstream runoff monitoring station to the downstream runoff monitoring station, represents that d ij has a dimension of N×N, represents a dimension of N×N, and k thre represents the threshold, taking 0.1, σ1 represents the standard deviation of d ij and N is the number of runoff monitoring stations in the predicted basin, which is taken according to actual needs.

[0065] In the present invention, during the process of generating the static elevation difference map, the static elevation difference is the difference in altitude between the upstream runoff monitoring station and the downstream runoff monitoring station. The static elevation difference is a natural factor driving the river flow. Similarly, the difference between two runoff monitoring stations without an upstream and downstream relationship is ∞, and the difference between a runoff monitoring station and itself is 0. The steeper the terrain, the more obvious the trend of runoff flowing downstream. In the static elevation difference map, a threshold Gaussian kernel is used to represent and generate the weighted adjacency matrix A2=(W ed ) N×N :

[0066]

[0067] In the formula, W ed represents the directed edge weight from the upstream runoff monitoring station e to the downstream runoff monitoring station d, and d ed is the difference in altitude between the upstream runoff monitoring station and the downstream runoff monitoring station, represents that d ed has a dimension of N×N, represents a dimension of N×N, and k thre represents the threshold, taking 0.1, σ2 represents the standard deviation of d ed and N is the number of runoff monitoring stations in the predicted basin, which is taken according to actual needs.

[0068] In the present invention, the above-mentioned static river channel distance map and static elevation difference map provide a static information basis for spatial information capture. However, it cannot simulate dynamic hydrological processes. Therefore, the present invention simulates dynamic hydrological processes by generating a dynamic map. Specifically, a graph attention network GAT is introduced to model the dynamic runoff process and adaptively learn hidden features. The graph attention network consists of a shared operator as follows:

[0069]

[0070] In the formula, represents has a dimension of 2×B′, represents a dimension of 2×B′, and e pq is the attention coefficient, which characterizes the importance of the features in runoff monitoring station p to runoff monitoring station q. represents that the dimension of W is B×B′, represents a dimension of B×B′, where B is the number of input features and B′ is the number of output features. represents the input feature,.... T represents the transpose operation, and || represents the merging operation. The formula only selects the first-order neighbors of runoff monitoring station q and itself to calculate. To standardize the attention coefficients of all selected runoff monitoring stations p, the softmax function is used:

[0071]

[0072] to obtain the adaptive weighted adjacency matrix A3 = (α pq ) N×N .

[0073] In step 3, a graph convolutional layer GCL is established.

[0074] After generating the static channel distance map, static elevation difference map, and dynamic map, the graph convolutional layer GCL is used to fuse the static channel distance map, static elevation difference map, and dynamic map into a whole. The graph convolutional layer GCL is described as a diffusion process with K steps:

[0075]

[0076] In the formula, L k is the normalized adjacency matrix in the k-th diffusion, and L ij = A1 / rowsum(A1), L ed = A2 / rowsum(A2), L pq = A3 / rowsum(A3).

[0077] In step 4, a runoff prediction model is established. The runoff prediction model combines temporal features and spatial features to extract spatio-temporal features for spatio-temporal prediction together. Figure 1 shows the framework of the model. To better learn spatio-temporal features from the runoff of each runoff monitoring station in the prediction basin over a period of historical time, the runoff prediction model is designed to contain multiple levels of processing structures. Spatio-temporal prediction is carried out through temporal features and spatial features together.

[0078] The runoff prediction model includes an input layer, M levels of processing structures, and a linear layer. The M levels of processing structures are connected in sequence from low to high. The input layer inputs the runoff sequences of each runoff monitoring station in the prediction basin over a period of historical time. Each level of the processing structure performs time feature extraction and spatial feature extraction to obtain the output of the current level, and this level of output serves as the input to the next level of the processing structure. At the same time, all levels are integrated into the linear layer through skip connections, and finally the predicted runoff of all runoff monitoring stations in the prediction basin is output. The calculation formula is as follows:

[0079]

[0080] In the formula, input is the intermediate level output of each level of the processing structure, || is the array concatenation operation (concatenation), serving as the input to the final linear layer, RELU is the activation function, Linear represents the linear layer, the specific calculation of Linear depends on the number of neurons in the linear layer, Output is the final multi-step flow prediction result, M is the number of all levels, and 1 ≤ m ≤ M.

[0081] In the invention embodiment, that is, for Figure 1 each hidden layer shown, the spatial features are respectively extracted once using the graph convolutional layer GCL. The processing structure of level 1 captures the runoff spatio-temporal information of each runoff monitoring station in the prediction basin over a period of historical time. The processing structure of level 2 captures the output of level 1 as the input to the processing structure of level 2, and the last level processes the output of the second-to-last level of the processing structure. As the level increases, the intermediate layer correspondingly learns more and more distant time information, and at the same time all levels are integrated into the linear layer through skip connections to output the predicted runoff of all runoff monitoring stations in the prediction basin.

[0082] Specifically, the steps for establishing a runoff prediction model to predict the runoff of all runoff monitoring stations specifically include:

[0083] Step 1.1: Initialize the model runoff prediction model. This operation includes preparing the historical flow data of all predicted runoff monitoring stations as input and setting the level value of Level to 1;

[0084] Step 1.2: Extract the spatio-temporal features of the current level of the processing structure. For each level of the processing structure, time feature extraction and spatial feature extraction are respectively performed to obtain the output of the current level. This level of output serves as the input to the next level of the processing structure, and at the same time this level of output participates in the skip connection and is integrated into the linear layer;

[0085] Step 1.3: Perform a loop for the remaining levels to extract the spatio-temporal features of all levels. The operation is the same as step 1.2;

[0086] Step 1.4: Output the prediction results through the linear layer. After concatenating the output results of all levels and passing them through the activation function ReLU, input them into the linear layer. The output result of the linear layer is the predicted runoff of all runoff monitoring stations in the predicted basin, that is, the multi-step runoff spatio-temporal prediction result.

[0087] In Step 1.2, the current hidden layer spatial information of GTCN is extracted through GCL.

[0088] The following details the specific implementation of the basin-scale runoff multi-step spatio-temporal prediction model based on the combination of static and dynamic graphs involved in the present invention.

[0089] In an embodiment of the present invention, taking the Mississippi River Basin as an example, 25 representative runoff monitoring stations in the basin are selected as the prediction objects to construct static and dynamic graph structures. The runoff sequences of the 25 runoff monitoring stations from April 1, 2004 to November 30, 2021 are used as the prediction period, and the entire prediction period is divided into a training period, a validation period, and a test period according to a ratio of 7:2:1. Based on graph theory, the river network of the Mississippi River Basin is generalized as a graph, and the selected runoff monitoring stations are regarded as a whole through spatial correlation for spatio-temporal prediction. Figure 4 Shows the overview of the example area. Figure 5 Represents the upstream and downstream relationships of some runoff monitoring stations.

[0090] The application effect of the spatio-temporal prediction model of the present invention is compared with traditional time prediction models LSTM, GRU, one-dimensional convolutional neural network (hereinafter referred to as 1dCNN), and GTCN. At the same time, the historical runoff information of the past 30 days is used to predict the runoff of the next 5 days. In order to cover all past information, a runoff prediction model consisting of two-level processing structures is adopted, and both two-level processing structures have a dilation factor sequence: 1, 2, 4, 8. The diffusion step size is set to 2, and the learning rate is initialized to 0.001 in the Adam optimizer. Four evaluation indicators are used for model prediction accuracy comparison, including mean absolute error (hereinafter referred to as MAE), mean absolute percentage error (hereinafter referred to as MAPE), root mean square error (hereinafter referred to as RMSE), and Nash efficiency coefficient (hereinafter referred to as NSE).

[0091] The present invention extends traditional time prediction to spatio-temporal prediction by using graph convolutional layers (GCLs) to combine static and dynamic spatial information. Table 1 shows the comparison results between traditional time prediction models and the proposed hydrological-scale runoff multi-step spatio-temporal prediction method HSDSTM based on the combination of static and dynamic graphs during the test period. The results show that after adopting the graph convolutional layer GCL, HSDSTM outperforms all the compared time prediction models in terms of four evaluation metrics. Compared with the best GTCN among the four compared time prediction models, the MAE of HSDSTM is increased by 14.20% on average, the MAPE is increased by 19.07% on average, and the RMSE is increased by 12.02% on average, which benefits from its learning of static and dynamic spatial information. Among the four evaluation metrics, the relative metric MAPE has the largest improvement. This indicates that regardless of the location of the runoff monitoring station (upstream or downstream) and the flow rate, the predicted runoff values of the simulated runoff monitoring stations are closer to the original values.

[0092] Table 1 Comparison of results between traditional time prediction models and the hydrological-scale runoff multi-step spatio-temporal prediction method HSDSTM based on the combination of static and dynamic graphs during the test period

[0093]

[0094]

[0095] Obviously, those skilled in the art can make various changes and modifications to the present invention without departing from the spirit and scope of the present invention. Thus, if these modifications and variations of the present invention fall within the scope of the claims of the present invention and their equivalent technologies, the present invention is also intended to include these changes and modifications.

Claims

1. A multi-step spatio-temporal prediction method for runoff at the basin scale based on the combination of static and dynamic graphs, characterized in that Including: Performing time feature extraction on the runoff of each runoff monitoring station in the predicted basin over a period of historical time; Performing spatial feature extraction, generating a static river channel distance map, a static elevation difference map, and a dynamic map for all runoff monitoring stations in the predicted basin. Among them, the static river channel distance is used to represent the river channel distance between the upstream runoff monitoring station and the downstream runoff monitoring station, the static river channel distance map is used to represent the river channel distance relationship between each runoff monitoring station, the static elevation difference is used to represent the difference in altitude between the upstream runoff monitoring station and the downstream runoff monitoring station, the static elevation difference map is used to represent the elevation difference relationship between each runoff monitoring station, and the dynamic map is used to simulate the dynamic hydrological process. Integrating the static river channel distance map, the static elevation difference map, and the dynamic map to obtain the spatial features of the runoff of each runoff monitoring station; Establishing a runoff prediction model to predict the runoff of all runoff monitoring stations. The runoff prediction model includes an input layer, M levels of processing structures, and a linear layer. The M levels of processing structures are connected in sequence from low to high. The input layer inputs the runoff sequences of each runoff monitoring station in the predicted basin over a period of historical time; Each level of processing structure performs time feature extraction and spatial feature extraction to obtain the output of the current level, and this level of output is used as the input of the next level of processing structure; At the same time, the outputs of the M levels are input into the linear layer through skip connections, and finally the predicted runoff of all runoff monitoring stations in the predicted basin is output; Establish the graph structures of the static river channel distance map, the static elevation difference map, and the dynamic map. The static river channel distance map is represented as , the static elevation difference map is represented as , and the dynamic map is ; Among them, is a set of vertices corresponding to the runoff monitoring stations in the river network, is a set of directed edges showing the one-way flow path from the upstream runoff monitoring station to the downstream runoff monitoring station, , , are all weighted adjacency matrices; During the process of generating the static elevation difference map, a threshold Gaussian kernel is used to represent and generate a weighted adjacency matrix : In the formula, represents the directed edge weight from the upstream runoff monitoring station e to the downstream runoff monitoring station d. is the difference in elevation between the upstream and downstream runoff monitoring stations. , represents a dimension of , represents the threshold value, taking 0.

1. represents the standard deviation of, where N is the number of runoff monitoring stations in the predicted basin and is determined according to actual needs.

2. The multi-step spatio-temporal runoff prediction method at the basin scale based on the combination of static and dynamic graphs according to claim 1, wherein: The input layer inputs the runoff sequences of each runoff monitoring station in the predicted basin over a period of historical time. The runoff sequence of each runoff monitoring station over a period of historical time is: where t is the total number of days, , and is the number of runoff monitoring stations in the predicted basin; Linearly combine the runoff of each runoff monitoring station over a period of historical time into a time-series combined feature .

3. The method for multi-step spatio-temporal prediction of basin-scale runoff based on the combination of static and dynamic graphs according to claim 2, wherein: Construct a gated temporal convolutional network (GTCN) to achieve temporal feature extraction by extracting temporal combined features and inputting them into the network for training. Input into the network and train it to achieve temporal feature extraction.

4. The multi-step spatio-temporal runoff prediction method at the basin scale based on the combination of static and dynamic graphs according to claim 1, characterized in that: During the process of generating the static river channel distance map, a threshold Gaussian kernel is used to represent and generate a weighted adjacency matrix : In the formula, represents the directed edge weight from the upstream runoff monitoring station i to the downstream runoff monitoring station j, is the distance along the river course from the upstream runoff monitoring station to the downstream runoff monitoring station, , represents a dimension of , represents the threshold value, taking 0.1, represents the standard deviation of, where N is the number of runoff monitoring stations in the predicted basin and is determined according to actual needs.

5. The multi-step spatio-temporal runoff prediction method at the basin scale based on the combination of static and dynamic graphs according to claim 1, characterized in that: The graph attention network (GAT) is introduced to model the dynamic runoff process and adaptively learn hidden features. The graph attention network consists of a shared operator as follows: In the formula, , indicates that the dimension is , is the attention coefficient, representing the importance of the features in runoff monitoring station p to runoff monitoring station q. , indicates that the dimension is , B is the number of input features, is the number of output features, represents the input features, represents the transpose operation, represents the merging operation. The formula only selects the first-order neighbors of runoff monitoring station q and itself for calculation. To standardize the attention coefficients of all selected runoff monitoring stations p, the softmax function is used: Obtain an adaptive weighted adjacency matrix .

6. The method for multi-step spatio-temporal prediction of basin-scale runoff based on the combination of static and dynamic graphs according to claim 1, characterized in that: Using the graph convolutional layer GCL to integrate the static river channel distance map, the static elevation difference map, and the dynamic map into a whole. The graph convolutional layer GCL is described as a diffusion process with K steps: In the formula, is the normalized adjacency matrix in the k-th diffusion, , , .

7. The method for multi-step spatio-temporal prediction of basin-scale runoff based on the combination of static and dynamic graphs according to claim 1, characterized in that: Multiple levels of skip connections are integrated into the linear layer to output the predicted runoff of all runoff monitoring stations in the predicted basin. The calculation formula is: Wherein, is the output of the processing structure at each level, is the array concatenation operation, As the input of the final linear layer, RELU is the activation function, and Linear represents the linear layer. The specific calculation of Linear depends on the number of neurons in the linear layer, is the final multi-step traffic prediction result, and M is the number of all levels, .

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