Multi-model space-time combination flood peak prediction method fusing physical constraints

Abstract

The invention relates to a multi-model space-time combination flood peak prediction method fusing physical constraints, which comprises the following steps of: acquiring static space data, dynamic time sequence data and boundary data of a research drainage basin, converting the static space data of the digital elevation model into a grid matrix, and calculating the dynamic time sequence data of the research drainage basin according to the grid matrix and the dynamic time sequence data of the research drainage basin; representing an elevation value of each geographic position, extracting gradient features by using gradient calculation according to the elevation values, and performing normalization processing on the gradient features to obtain normalized gradient features; a CNN-Bi-LSTM-Transform prediction model is constructed, the prediction model comprises a spatio-temporal data alignment module, a CNN convolutional network, a spatio-temporal feature splicing module, a bidirectional long and short term memory network and a Transform module, the prediction model is trained, and a loss function during training adopts a physical constraint loss function composed of mean square error loss and water conservation constraint terms and is used for flood peak prediction.

Description

Technical Field

[0001] The present invention belongs to the technical field of flood forecasting, and particularly relates to a multi-model spatio-temporal combined flood peak prediction method integrating physical constraints. Background Art

[0002] In recent years, with the intensification of global climate change, flood disasters have occurred frequently, especially in urban and watershed flood management, which faces huge challenges. Traditional flood prediction methods such as empirical formulas and hydrodynamic models often have difficulty in accurately predicting complex flood scenarios, especially under the intertwined action of multiple influencing factors. With the continuous intensification of climate change, the dynamic changes of factors such as precipitation, watershed topography, and riverbed changes have brought greater uncertainty and challenges to flood prediction.

[0003] In order to improve the accuracy of flood peak prediction, in recent years, many studies have begun to apply machine learning and deep learning methods to the field of flood prediction. However, current research mainly focuses on flood peak prediction through time series data, while ignoring the processing of spatial data. The dynamic process of floods is not only closely related to time factors but also to spatial information such as the geographical characteristics of the watershed and the riverbed topography. For example, the change trends between different regions of the riverbed and different water levels are different. Therefore, simply relying on time series data may not be able to comprehensively capture the spatial dynamic characteristics of floods, resulting in errors in prediction results.

[0004] There are still some problems in the application of existing deep learning methods in flood forecasting, especially in the extraction of spatio-temporal features, the integration of physical constraints, and the real-time performance and interpretability of the models, where there is still room for further improvement. For example, Moon et al. (2023) considered the time characteristics of rainfall data at each rain gauge in the watershed by using a long short-term memory (LSTM) network and a fully connected layer, realized the fusion of data features, and improved the forecasting accuracy. Liu et al. (2022) showed excellent performance in predicting the monthly flow of the Yangtze River by using a Transformer neural network with past water levels and oscillations as inputs. The focus of these studies indicates that deep learning models need to select model structures that conform to physical principles, so different neural network structures should be used to match different data structures. In addition, these existing studies still do not consider the characteristics of spatial data and physical constraints sufficiently, and there are certain limitations in dealing with complex spatio-temporal dependence relationships. Although convolutional operations can effectively extract spatial features, due to their local perception nature, they tend to lose some key information. Although LSTM performs well in time series modeling, there are still certain limitations in capturing long-term global spatio-temporal dependence relationships, especially in the face of complex flood scenarios. In addition, most existing models focus on improving the shallow structure of deep learning itself and its coupling with other methods, while ignoring the characteristics of the runoff process.

[0005] Therefore, the present invention proposes a spatio-temporal flood peak prediction method that integrates CNN, Bi-LSTM, and Transformer, which can simultaneously process spatial and temporal features, capture complex spatio-temporal dependencies through deep learning modeling, and combine physical constraints to improve the accuracy of flood peak prediction, thereby providing more scientific decision-making support for flood prevention and control. Summary of the Invention

[0006] Aiming at the problems of insufficient spatio-temporal data fusion ability, limited long-term prediction accuracy, and lack of physical consistency in existing flood peak prediction methods, the technical problem to be solved by the present invention is to provide a multi-model spatio-temporal combined flood peak prediction method that integrates physical constraints.

[0007] The technical solution adopted by the present invention to solve the above technical problems is as follows:

[0008] A multi-model spatio-temporal combined flood peak prediction method that integrates physical constraints, the prediction method includes the following:

[0009] Obtain the static spatial data, dynamic time series data, and boundary data of the research basin of the river. The static spatial data includes at least the digital elevation model (DEM). Convert the static spatial data of the digital elevation model (DEM) into a raster matrix, representing the elevation value of each geographical location. Use gradient calculation to extract the slope feature Slope according to the elevation value, and perform normalization processing on the slope feature Slope to obtain the normalized slope feature S norm ; The dynamic time series data includes at least flow rate and water level;

[0010] Construct a CNN-Bi-LSTM-Transformer prediction model:

[0011] The CNN-Bi-LSTM-Transformer prediction model includes a spatio-temporal data alignment module, a CNN convolutional network, a spatio-temporal feature splicing module, a bidirectional long short-term memory network Bi-LSTM, and a Transformer module.

[0012] The spatio-temporal data alignment module aligns the spatial data with the dynamic time series data of the basin in the following way: convert the basin boundary data to the same coordinate system as the DEM data to ensure spatial alignment of the basin boundary data and the DEM data; then rasterize the basin boundary according to the pixel grid size of the DEM data to make the basin location match the spatial resolution of the DEM; then use nearest neighbor interpolation to perform spatial alignment on the basin boundary and the DEM raster data to ensure that the spatial features of each raster cell of the DEM match the data of the corresponding basin location.

[0013] After the spatio-temporal data alignment, the normalized slope feature S norm and the DEM data are used as the input to the CNN convolutional network. The CNN convolutional network extracts spatial features. The dimension of the spatial features output by the last layer of the CNN convolutional network is the same as the dimension of the hidden state of the Bi-LSTM. The spatial features extracted by the CNN convolutional network are used to initialize the initial hidden state and the initial cell state of the bidirectional long short-term memory network Bi-LSTM as the spatial constraint of the Bi-LSTM;

[0014] The spatio-temporal feature splicing module is used to perform spatio-temporal splicing on the aligned dynamic time-series features and the spatial features extracted by the CNN to obtain a joint feature matrix;

[0015] The joint feature matrix is input into the Bi-LSTM after spatial constraint, and then combined with the position encoding and processed by the Transformer module to generate flood peak prediction results, including flood peak discharge, peak water level and the corresponding occurrence time;

[0016] So far, the constructed CNN-Bi-LSTM-Transformer prediction model is obtained;

[0017] The CNN-Bi-LSTM-Transformer prediction model is trained, and the loss function during training adopts a physical constraint loss function Its expression is:

[0018]

[0019] Among them, is the mean square error loss, is the water conservation constraint term, and λ1 and λ2 are weight coefficients;

[0020] The trained CNN-Bi-LSTM-Transformer prediction model is used for flood peak prediction.

[0021] Furthermore, the static spatial data also includes remote sensing image data. The remote sensing image data is also spatially aligned with the DEM data in terms of coordinates, resolution and values. The dynamic time-series data also includes rainfall; the calculation formula of the water conservation constraint term is:

[0022]

[0023] Among them, Q is the flow rate, v is the flow velocity, and RR is the rainfall; the value ranges of λ1 and λ2 are 0.5 to 1.0.

[0024] Furthermore, the slope feature is calculated by the following formula:

[0025]

[0026] Among them, and represent the gradients in the horizontal and vertical directions respectively; Z is the elevation value at each position in the DEM data.

[0027] Furthermore, the processing process of the spatio-temporal feature splicing module is as follows: Set the training batch as B, divide the aligned dynamic time-series data into multiple sequence segments according to a preset time window, and each sequence segment contains at least 24 - 72 hours of water level and flow data; then perform sliding window normalization on each sequence segment, and the normalized sequence segment is represented as (B, T, D);

[0028] Perform spatio-temporal splicing on the normalized sequence segment (B, T, D) and the spatial feature vector (B, F spatial ) extracted by CNN to obtain a joint feature matrix (B, T, D + F spatial );

[0029] Among them, T is the time step, and D is the dimension of dynamic time-series features.

[0030] Furthermore, after the CNN - Bi - LSTM - Transformer prediction model outputs the flood peak prediction result, a graded early warning signal is generated in combination with the dynamic flood threshold determination method.

[0031] The process of the dynamic flood threshold determination method is as follows:

[0032] Calculate the theoretical critical flow threshold Q c :

[0033]

[0034] Among them, Q c is the theoretical critical flow threshold, Q manning is the theoretical flow obtained from the Manning formula, Q continuity is the theoretical flow obtained from the discretized water volume conservation equation; γ is a weight parameter, with a range between 0 and 1. A larger value is taken for γ in steady flow, and a smaller value is taken for γ in sudden floods; n is the roughness coefficient, A is the cross-sectional area of the water flow, R h is the hydraulic radius, S is the water surface slope, R rain is the rainfall, and P is the wetted perimeter;

[0035] Perform data-driven threshold correction on the theoretical critical flow threshold Q c according to the following formula:

[0036] Q threshold = α·Q c ,

[0037] Among them, Q threshold is the new corrected threshold, α is the probabilistic threshold adjustment coefficient, and the historical disaster data (Q t , H t , R t , S t ) is obtained by using random forest learning, that is, α = f ML (Q t , H t , R t , S t ); f ML represents random forest, Q t is the real-time flow rate, H t is the water level, R t is the rainfall intensity, and S t is the soil saturation.

[0038] Furthermore, the generation rule of the graded warning signal is:

[0039] Yellow warning: When the predicted peak flow Q pred ≥ 0.8Q threshold ;

[0040] Orange warning: When Q pred ≥ Q threshold ;

[0041] Red warning: When Q pred ≥ 1.2Q threshold .

[0042] Furthermore, fuse the observed data and the model prediction value Q pred , and use the Kalman filter to dynamically update and adjust the model weight parameters; the state prediction equation of the Kalman filter is:

[0043]

[0044] Among them, Δt is the time step, L is the river reach length, g is the acceleration due to gravity, and B is the river width; is the predicted state at time step t; is the optimal estimated state of the previous time step that integrates historical observed data, that is, using the state prediction equation according to physical laws and using the state estimate of the previous moment to predict the state of the current moment; F t is the state transition matrix, which describes the dynamic evolution law of the system from t - 1 to t according to the discretized water conservation equation and the Saint-Venant equation. The first row reveals that the flow rate change is driven by the flow velocity v and the gravity effect, and the second row indicates that the water level change is determined by the flow rate change and the channel cross-section parameter B / A;

[0045] The covariance prediction equation is:

[0046]

[0047] Among them, P t|t-1 is the predicted state covariance matrix, representing the uncertainty of the predicted state; P t-1|t-1 is the state covariance matrix of the previous time step; Q t is the process noise covariance matrix.

[0048] Furthermore, a feedback optimization mechanism is set. If there are false alarms or missed alarms in the early warning for 3 consecutive times, the model will be triggered to retrain:

[0049]

[0050] Among them, the first equation is the model weight update formula, W new is the updated model weight parameter; W old is the model parameter before update; η is the learning rate, used to control the step size of parameter update; is the gradient of the feedback loss function with respect to the weight; is the feedback loss function, Q pred is the peak flood data predicted by the model; Q obs is the actual observed peak flood data.

[0051] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0052] (1) The method of the present invention maps the terrain features extracted by CNN to the initial state of Bi-LSTM, so that the initial states of the forward LSTM and the backward LSTM are respectively generated by spatial features, guiding the model to pay attention to the differential effects of terrain on flood evolution and recession, integrating spatial prior knowledge and adopting a physical constraint loss function, jointly optimizing the data-driven loss (MSE) and the physical conservation loss, and realizing high-precision, interpretable and adaptive flood prediction through a multi-model collaborative architecture and deep physical-data fusion.

[0053] (2) The method of the present invention fully combines spatial data and temporal data. It uses CNN to process spatial data and Bi-LSTM to process temporal data (one-dimensional time series). Through spatio-temporal splicing, the output of CNN is aligned and can be used as the initial hidden state and cell state of Bi-LSTM, enabling Bi-LSTM to perceive spatial terrain features in the first step, which helps to model the runoff propagation path. LSTM processes temporal data to generate a sequence of hidden states. Then, the output of Bi-LSTM is used as the input of Transformer, and positional encoding (PE) is added. Finally, Transformer further captures global temporal dependencies through multi-head attention, ensuring the combination of local + global temporal features and improving the model's ability to model long-term trends. The present invention effectively utilizes three network structures, namely convolutional neural network (CNN), bidirectional long short-term memory network (Bi-LSTM), and Transformer module, to form an integrated model. Bi-LSTM first learns local features, and then Transformer learns global features. The integrated model can comprehensively process complex spatio-temporal features, significantly improving the accuracy of flood prediction, especially in complex river basins and variable flood scenarios, and can better predict flood peaks and occurrence times.

[0054] (3) The present invention uses a physical-data fusion method, taking the water conservation equation as a constraint for model training. It combines with a deep learning model to ensure that the model follows hydrological physical laws, making the model output conform to actual physical laws, avoiding unreasonable prediction results that may occur in traditional data-driven methods, and still being able to ensure reasonable flood peak predictions under data insufficiency or extreme weather conditions. The introduction of the physical constraint loss function is optimized during the training process to ensure that the model not only improves prediction accuracy but also has stronger interpretability and adaptability. The water conservation equation ensures that the prediction results conform to actual hydrological laws. By jointly optimizing the data-driven loss and physical consistency loss, the generalization ability of the model and its robustness under extreme events are significantly improved. Compared with traditional methods, the present invention can not only improve the accuracy of flood peak prediction but also better simulate and explain the flood dynamic process, providing more reliable scientific support for flood control scheduling and disaster management.

[0055] (4) The present invention uses data such as historical water levels and precipitation to predict future flood changes. It can use a large amount of historical data to train the model, thereby revealing the spatio-temporal correlation in the flood process and providing more accurate forecast results. It processes spatial and temporal features simultaneously, captures complex spatio-temporal dependencies through deep learning modeling, improves the accuracy of flood peak prediction, and further provides more scientific decision-making support for flood prevention and control.

[0056] (5) In the present invention, the self-attention mechanism of Transformer is utilized to enhance the ability to model global spatio-temporal dependence relationships. The self-attention mechanism can effectively capture the complex correlations between different time steps and between different spatial regions, thereby significantly improving the accuracy of flood peak prediction. By combining a convolutional neural network (CNN), a bidirectional long short-term memory network (Bi-LSTM), and a Transformer module, it is applicable to flood forecasting in various river basins and complex flood scenarios, and can provide scientific decision-making support for flood control scheduling and disaster management.

[0057] (6) In the present invention, temporal data and spatial data are spliced spatio-temporally, enhancing the multi-source association between terrain and temporal data such as water level and flow rate, and revealing the coupled effects of terrain on runoff paths and rainfall on runoff volume. The water conservation equation is introduced into the physical constraint loss function to optimize model training, avoiding the output of pure data-driven models that violates physical laws.

[0058] (7) Based on the Manning formula, the present invention calculates the theoretical threshold, dynamically corrects the threshold coefficient through a machine learning model (such as a random forest), and on this basis, a three-level early warning trigger mechanism is established, with graded responses according to the degree of threshold exceedance. After combining Kalman filtering for post-processing to eliminate prediction noise and update model parameters. Compared with traditional models, the present invention realizes high-precision joint prediction of flood peak flow, peak water level, and occurrence time, effectively supports flood control scheduling and disaster emergency decision-making in complex scenarios across river basins, and significantly improves the stability and interpretability of prediction results. Description of the Drawings

[0059] Figure 1 It is a framework diagram of a multi-model spatio-temporal combined flood peak prediction method with physical constraints fused in the present invention.

[0060] Figure 2 It is a data flow diagram of a multi-model spatio-temporal combined flood peak prediction method with physical constraints fused in the present invention. Detailed Embodiments

[0061] The technical solutions of the present invention will be further described in detail below in conjunction with the drawings and specific embodiments, but are not used to limit the protection scope of this application.

[0062] The multi-model spatio-temporal combined flood peak prediction method with physical constraints fused in the present invention includes the following contents:

[0063] The dataset required by the present invention includes two parts: spatial data and temporal data. The spatial data is the digital elevation data (DEM) of a certain river basin, and the temporal data is the water level, flow rate, and precipitation data of a certain river basin.

[0064] Obtain the static spatial data, dynamic time-series data, and watershed boundary data of the study watershed. The static spatial data includes at least the digital elevation model (DEM). Convert the static spatial data of the DEM into a raster matrix to represent the elevation value of each geographical location. Use gradient calculation to extract the slope feature Slope based on the elevation value, and perform normalization processing on the slope feature Slope to obtain the normalized slope feature S. norm The dynamic time-series data includes at least flow rate and water level.

[0065] Construct a CNN-Bi-LSTM-Transformer prediction model:

[0066] The CNN-Bi-LSTM-Transformer prediction model includes a spatio-temporal data alignment module, a CNN convolutional network, a spatio-temporal feature splicing module, a bidirectional long short-term memory network (Bi-LSTM), and a Transformer module.

[0067] The spatio-temporal data alignment module aligns the spatial data with the dynamic time-series data of the watershed in the following way: Convert the watershed boundary data to the same coordinate system as the DEM data to ensure spatial alignment between the watershed boundary data and the DEM data; then rasterize the watershed boundary according to the pixel grid size of the DEM data to make the watershed location match the spatial resolution of the DEM; finally, use nearest neighbor interpolation to perform spatial alignment between the watershed boundary and the DEM raster data to ensure that the spatial features of each raster cell of the DEM match the data of the corresponding watershed location.

[0068] After spatio-temporal data alignment, use the normalized slope feature S norm and the DEM data as the input to the CNN convolutional network. Use the CNN convolutional network to extract spatial features. The dimension of the spatial features output by the last layer of the CNN convolutional network is consistent with the hidden state dimension of the Bi-LSTM. Initialize the initial hidden state and initial cell state of the bidirectional long short-term memory network (Bi-LSTM) with the spatial features extracted by the CNN convolutional network as the spatial constraint of the Bi-LSTM.

[0069] The spatio-temporal feature splicing module is used to perform spatio-temporal splicing on the aligned dynamic time-series features and the spatial features extracted by the CNN to obtain a joint feature matrix.

[0070] Input the joint feature matrix into the spatially constrained Bi-LSTM, and then, after being processed by the Transformer module in combination with positional encoding, map it to the prediction space through a fully connected layer to generate flood peak prediction results, including flood peak flow rate, peak water level, and the corresponding occurrence time.

[0071] So far, the constructed CNN-Bi-LSTM-Transformer prediction model is obtained;

[0072] Train the CNN-Bi-LSTM-Transformer prediction model, and use the physical constraint loss function as the loss function during training Its expression is:

[0073]

[0074] Among them, is the mean square error loss, is the water conservation constraint term, and λ1 and λ2 are weight coefficients;

[0075] Use the trained CNN-Bi-LSTM-Transformer prediction model for flood peak prediction.

[0076] Furthermore, the CNN includes at least 4 convolutional layers, pooling layers and fully connected layers. The size of the convolutional kernel in each layer is 3×3, the stride is 1, and the padding mode is "same"; after each convolution, a batch normalization layer and a LeakyReLU activation function are connected; the spatial feature dimension output by the last layer is the same as the hidden state dimension of the Bi-LSTM, that is, the relationship is satisfied:

[0077] d CNN =d LSTM

[0078] Among them, d CNN is the CNN output feature dimension, and d LSTM is the single-layer hidden state dimension of the Bi-LSTM.

[0079] The fully connected layer includes a three-layer structure: the first layer has 512 hidden units, and the activation function is LeakyReLU; the second layer has 256 hidden units, and the activation function is Swish; the output layer is a linear activation function.

[0080] Furthermore, the processing process of the spatio-temporal feature splicing module is: set the training batch as B, divide the aligned dynamic time series data into multiple sequence segments according to a preset time window, and each sequence segment contains at least 24 hours of water level and flow data; then perform sliding window normalization on each sequence segment to eliminate seasonal trends, and the normalization formula is:

[0081]

[0082] Among them, μ window and σ window are the mean and standard deviation of the data within the window respectively;

[0083] The standardized sequence segment is represented as (B, T, D);

[0084] The standardized sequence segment (B, T, D) is spatio-temporally concatenated with the spatial feature vector (B, F spatial ) extracted by the CNN to obtain a joint feature matrix (B, T, D + F spatial );

[0085] Among them, B represents the batch size, T is the time step, and D is the dynamic feature dimension (including three features: water level, flow rate, and rainfall. In this embodiment, D takes the value of 3).

[0086] Furthermore, the input of the Bi-LSTM is the joint feature matrix (B, T, D + F spatial ), and the output is It includes a two-layer bidirectional structure, with the number of hidden units in each layer ranging from 256 to 512, and the dropout rate is set to 0.2 to 0.4; the hidden states of the forward and backward LSTMs are fused by concatenation, and the output dimension after fusion satisfies:

[0087] d Bi-LSTM = 2 × d LSTM

[0088] Among them, d LSTM is the number of hidden units in a single-layer LSTM.

[0089] Furthermore, the number of encoder layers of the Transformer module is 6 to 8 layers, and the number of heads in each layer of the multi-head attention mechanism is 12 to 16; the position encoding adopts a combination of sine and cosine functions, and the calculation formula is:

[0090]

[0091] Among them, pos is the time step position, d model is the feature dimension, i is the feature dimension index, that is, a certain dimension of the Transformer word vector. PE (pos,2i) represents the sine encoding value of the time step t in the 2i-th dimension, and PE (pos,2i+1) represents the cosine encoding value of the time step t in the (2i + 1)-th dimension.

[0092] Furthermore, the calculation formula of the multi-head attention mechanism is:

[0093] MultiHead(Q, K, V) = Concat(head1,..., head h )W O

[0094] Among them, the calculation of each attention head is:

[0095]

[0096] Among them, is a trainable parameter matrix, and d k is the dimension of the key vector. i is mainly used to represent the index of the i-th attention head.

[0097] Furthermore, the observed data and the model predicted value Q are fused pred , and the Kalman filter is used to dynamically update and adjust the model weight parameters; the state prediction equation of the Kalman filter is:

[0098]

[0099] Among them, Δt is the time step, L is the river reach length, g is the acceleration due to gravity, and B is the channel width; is the predicted state at time step t; is the optimal estimated state of the previous time step that incorporates historical observed data, that is, using the state prediction equation according to physical laws and the state estimate of the previous moment to predict the state of the current moment; F t is the state transition matrix, which describes the dynamic evolution law of the system from t - 1 to t according to the discretized water conservation equation and the Saint-Venant equation. The first row reveals that the flow rate change is driven by the flow velocity v and the action of gravity, and the second row indicates that the water level change is determined by the flow rate change and the channel cross-section parameter B / A.

[0100] Furthermore, in the model training process, a physical constraint loss function is adopted, and its expression is:

[0101]

[0102] Among them, is the mean square error loss, is the water conservation constraint term, and its calculation formula is:

[0103]

[0104] Q is the flow rate, v is the flow velocity, and RR is the rainfall; λ1 and λ2 are weight coefficients, and their value ranges are 0.5 - 1.0.

[0105] Example 1

[0106] The present invention provides a multi-model spatio-temporal combined flood peak prediction method integrating physical constraints, such as Figure 1As shown in the figure, first, static spatial data is used for preprocessing, and then a CNN convolutional network is used to extract spatial features for initializing the initial state of the Bi-LSTM. The dynamic time-series data is input into the Bi-LSTM after spatio-temporal splicing processing to capture local temporal dependencies. Subsequently, the output sequence of the Bi-LSTM is embedded into the Transformer module, and the global spatio-temporal dependencies are extracted through the encoder-decoder structure and the multi-head attention mechanism, and finally the flood peak prediction result is generated. The specific steps are as follows:

[0107] Step 1: Convert the static spatial data of the digital elevation model (DEM) into a raster matrix, representing the elevation value of each geographical location. Calculate the slope feature Slope according to the formula based on the gradient as:

[0108]

[0109] where and represent the gradients in the horizontal direction (x-axis) and vertical direction (y-axis) respectively. Z is the elevation of each position in the DEM data. The slope feature can help the model understand the flow velocity of water in different regions, thereby predicting the propagation speed of water flow in the basin, and further guiding the model to simulate the flood process with a data pattern that is more in line with physical laws.

[0110] For the slope feature Slope, perform normalization processing to ensure the consistency of the model under different feature scales:

[0111]

[0112] where S t is the extracted slope feature, μ S and σ S are the mean and standard deviation of the slope feature respectively, and S norm is the normalized slope feature.

[0113] Align the spatial data with the time-series data of the basin in the following way: Convert the basin boundary data to the same coordinate system as the DEM data to ensure their spatial alignment; rasterize the basin boundary to ensure its docking with the pixel grid of the DEM data, and match it through the basin location and the spatial resolution of the DEM; use nearest neighbor interpolation to spatially dock the basin boundary with the DEM raster data to ensure that the spatial features of each raster cell match the corresponding basin location data. By aligning the basin location with the DEM data, ensure that the spatial features extracted from the DEM can be correctly corresponding to the corresponding basin area, which enables the subsequent flood prediction model to combine time-series data and spatial features for more accurate flood prediction.

[0114] To better extract spatial features, the three components of the convolutional layer, pooling layer, and fully connected layer in the CNN architecture need to capture local topographic feature details, compress redundant information, and generate high-dimensional spatial feature vectors, respectively, providing an accurate initial state for the Bi-LSTM. Among them, the convolutional layer uses three convolutional operations. The size of each convolutional kernel is 3×3, the stride is 1, the padding mode is "same", the activation function is LeakyReLU, and the negative slope is 0.2. The spatial features are gradually extracted. The output formula of the k-th layer of convolution is:

[0115] C (k) =LeakyReLU(W (k) *C (k-1) +b (k) )

[0116] Among them, is the normalized data after input splicing, forming a multi-channel input to enhance feature diversity. C (k) is the feature map output by the k-th layer of convolution, with a dimension of H k ×W k ×D k , where H k and W k are the height and width of the feature map, and D k is the number of convolutional kernels in the k-th layer, that is, the number of output channels; C (k-1) is the output feature map of the k-1 layer, serving as the input of the k-th layer. W (k) represents the weight matrix of each layer of convolutional kernel, which performs a convolution operation with the input data to extract features. b (k) is the bias term of the k-th layer, with a dimension of D k . The activation function LeakyReLU enables the network to learn complex patterns and data relationships. Secondly, the role of the pooling layer is mainly to compress redundant information. The maximum pooling operation P (k) =MaxPool 2×2 (C (k) ) compresses the feature size. The maximum value of k is 3, retaining significant features and reducing the computational amount. After that, the fully connected layer flattens the pooled features and maps them to a high-dimensional space to obtain the spatial feature vector F spatial .

[0117] F spatial =W fc ·Flatten(P (3) )+b fc

[0118] P (3) is the feature map output by the last layer of pooling, with a dimension of H k ×W k ×D k。Flatten(P (3) ) flattens the pooled feature map into a one-dimensional vector with a length of H k ×W k ×D k 。W fc is the weight matrix of the fully connected layer, with a dimension of d LSTM ×H k ×W k ×D k 。b fc is the bias term of the fully connected layer, with a dimension of d LSTM 。F spatial is the finally generated spatial feature vector, which is used to initialize the initial state of the Bi-LSTM. Ensure the compatibility of subsequent state initialization.

[0119] The dataset used in this embodiment is from a certain watershed in Iowa, USA, from October 1, 2011 (wet year 2012) to September 30, 2018 (wet year 2018), including its spatial data and time series data such as precipitation, flow, and water level.

[0120] Step 2 The spatial feature vector F generated by the CNN spatial , which is used to initialize the initial hidden state h0 and the initial cell state C0 of the Bi-LSTM, indicating that at the beginning stage of the time series, the initial state of the LSTM already contains spatial information. The initialization formula is:

[0121] h0 = W h ·F spatial + b h

[0122] C0 = W C ·F spatial + b C

[0123] Among them, is the trainable weight matrix, b h , b C is the bias term.

[0124] The initialization of the reverse LSTM is similar to that of the forward LSTM, but since the reverse LSTM processes the sequence from back to front, the representation of its initial state will reflect the reverse sequence information. The initialization formula is:

[0125]

[0126] Among them, the weight matrices of the forward and backward LSTMs are trained independently to avoid information confusion between directions. The spatial feature vector is directly mapped to the initial state of the bidirectional LSTM through linear transformation to ensure that the model integrates topographic prior knowledge at the initial stage of temporal modeling. Since the forward LSTM and the backward LSTM process the forward time series (i.e., the flood evolution process) and the backward time series (i.e., the recession process) respectively, the spatial features need to affect the two differently. The forward LSTM focuses on capturing the driving force of the terrain on the flood evolution speed (such as steep slopes accelerating the water flow), and the backward LSTM focuses on capturing the influence of the terrain on flood retention and recession (such as depressions delaying the recession).

[0127] During the temporal processing of the Bi-LSTM, the hidden states of the forward and backward LSTMs are transmitted in different directions respectively, and finally fused through concatenation or weighting:

[0128]

[0129] By directly using the spatial features extracted by the CNN to initialize the state of the Bi-LSTM, it is ensured that the model can make full use of spatial data (such as riverbed topographic information) and provide effective background information for subsequent time series modeling. The initialization of spatial features provides powerful context information for the LSTM, enabling the Bi-LSTM to better capture the dynamic changes in the time series, especially in the prediction of temporal data such as water level and flow rate. The Bi-LSTM can capture both forward and backward time dependencies, so more accurate predictions can be obtained when modeling the spatio-temporal characteristics of floods.

[0130] To ensure the effectiveness of the backward LSTM initialization, it is necessary to maintain its gradient stability. Therefore, the initial state gradient of the backward LSTM needs to be decoupled from the forward LSTM to avoid parameter update conflicts during training. The dimension of the spatial feature vector F spatial needs to match the dimension of the single-layer LSTM hidden state, that is, d LSTM = dim(F spatial ), and the initial state parameters W h , etc. need to avoid gradient explosion through weight initialization. Xavier initialization is a commonly used initialization method. Its core idea is to make the output variance of each layer as equal as possible, which can avoid gradient disappearance and gradient explosion. The specific formula is as follows:

[0131]

[0132] Let d LSTM= 256, the weight range of Xavier uniform initialization is approximately [-0.034, 0.034][-0.034, 0.034] (3 / 256 ≈ 0.0343 / 256 ≈ 0.034). After training, the mean squared error (MSE) of the bidirectional long short-term memory network on the test set is reduced by 15% compared to random initialization, and the convergence speed is increased by 20%. For the gain adjustment of the LeakyReLU activation function, the gain of Xavier initialization is modified according to the selected activation function. Here, the gain of the LeakyReLU activation function is calculated as where α is the negative slope of LeakyReLU, usually chosen as 0.2.

[0133] Step 3: Spatiotemporal splicing

[0134] The aligned dynamic time series data is divided into multiple sequence segments according to a preset time window. Each segment contains water level, flow rate, and rainfall data for 24 to 72 hours. Perform sliding window normalization on each sequence segment to eliminate seasonal trends. The normalization formula is:

[0135]

[0136] where, μ window and σ window are the mean and standard deviation of the data within the window, respectively;

[0137] Perform spatiotemporal splicing on the normalized sequence segment (B, T, D) and the spatial feature vector (B, F spatial ) extracted by the CNN convolutional network, where B represents the batch size, T is the time step, and D is the dynamic feature dimension (such as 3 features of water level, flow rate, and rainfall).

[0138] First, expand the dimension of the spatial features. Expand the spatial feature vector from (B, F spatial ) to (B, T, F spatial ), that is, replicate it T times along the time step dimension T, so that each time step is appended with the same spatial features. Then, perform feature dimension splicing. Concatenate the expanded spatial features (B, T, F spatial ) and the dynamic time series data (B, T, D) along the feature axis to generate a joint feature matrix (B, T, D + F spatial ). Through splicing, it is possible to simultaneously perceive the time dynamic changes (such as rising water level) and spatial static attributes (such as terrain influence), enhancing the global understanding of the flood evolution process.

[0139] Before inputting the joint feature matrix into the Bi-LSTM, use Min-Max normalization to normalize the features to ensure that all features are within the same range. The Min-Max normalization formula is as follows:

[0140]

[0141] Among them, x is the original data value, x min and x max are the minimum and maximum values of this feature, x normalized is the data after normalization.

[0142] The Bi-LSTM network includes two layers of bidirectional structures, with 256 hidden units in each layer, and the dropout rate is set to 0.2; the hidden states of the forward and backward LSTMs are fused by concatenation, and the output dimension after fusion satisfies:

[0143] d Bi-LSTM = 2 × d LSTM

[0144] The joint feature matrix is input into the Bi-LSTM network to capture local temporal dependencies and generate a temporal feature output. The update equation of the forward LSTM of the Bi-LSTM is as follows.

[0145] f t = σ(W f · [h t-1 , x t + b f )

[0146] Among them, f t is the forget gate, i t is the input gate, C t is the cell state, o t is the output gate, h t is the hidden state, x t is the current input:

[0147] The forget gate determines which information to discard from the cell state at the previous time step. It uses the current input x t and the hidden state h t-1 at the previous time step. The output f t of the forget gate is a value between 0 and 1, where 0 means "forget all information" and 1 means "retain all information".

[0148] i t = σ(W i · [h t-1 , x t + b i )

[0149] The input gate determines which information will be updated into the cell state. It calculates the activation value i through the current input x t and the hidden state h t-1 at the previous time step.t , this value also lies between 0 and 1 and controls how much new information should be added.

[0150]

[0151] This formula calculates the candidate value of the cell state These values may be added to the existing cell state. It uses the current input and the previous hidden state to generate candidate values and ensures that the output values remain within a reasonable range through the tanh activation function.

[0152]

[0153] The cell state is updated by combining the cell state C of the previous time step t-1 and the newly generated candidate cell state The forget gate f t and the input gate i t weight the existing cell state and the new candidate state respectively, enabling the network to "remember" or "forget" the required information.

[0154] o t = σ(W o · [h t-1 , x t + b o )

[0155] The output gate determines which parts of the cell state will be output. It is calculated based on the current input x t and the hidden state h of the previous time step t-1 The output of the output gate is also a value between 0 and 1.

[0156] h t = o t * tanh(C t )

[0157] The final hidden state is calculated by applying the output gate to the updated cell state. Applying the tanh activation function to the cell state C t keeps the value range within a reasonable interval and modulates the final hidden state through the output gate o t .

[0158] The hidden state update of the reverse LSTM is as follows:

[0159]

[0160] The final output of the bidirectional LSTM is:

[0161]

[0162] In Step 4, first, the dimension of the sequential feature sequence output by the bidirectional LSTM is adjusted to be the same as the input dimension of the Transformer module to ensure data compatibility and efficient computation. The hidden state sequence H output by the bidirectional LSTM Bi-LSTM is as follows:

[0163]

[0164] After that, the output dimension of the Bi-LSTM is mapped to the standard input dimension d of the Transformer through a fully connected layer model :

[0165] X in = H Bi-LSTM · W proj + b proj

[0166] where H Bi-LSTM is the output feature sequence of the Bi-LSTM; W proj is the trainable parameter of the fully connected layer, which is used to map the output dimension of the Bi-LSTM to the standard input dimension of the Transformer; b proj is the bias parameter of the fully connected layer, which is used to adjust the feature offset after the linear transformation. Doing so can avoid calculation errors or information loss caused by dimension mismatch.

[0167] The number of encoder layers of the Transformer module is set to 6 - 8 layers, and the number of heads of the multi-head attention mechanism in each layer is 12 - 16. By stacking multiple layers of Transformer encoders, high-order spatio-temporal features are abstracted layer by layer, enhancing the model's ability to express complex flood evolution patterns. Through hierarchical feature learning, local sequential fluctuations can be captured shallowly, and global associations across time steps such as the rainfall-runoff-peak flood chain reaction can be modeled deeply; its complex pattern parsing supports the joint modeling of extreme events such as flash floods and non-stationary sequences such as recession delays.

[0168] The positional encoding uses a combination of sine and cosine functions to add the position information of the time step to the Transformer input, making up for its defect of being unable to perceive the sequence order and enhancing the model's ability to model time-dependent relationships. Therefore, the position of each time step is encoded using a combination of sine and cosine functions:

[0169]

[0170] where pos is the time step position and d model is the feature dimension. The positional encoding is added element-wise to the input features:

[0171] X encoded = Xin +PE

[0172] Doing so can not only explicitly label the chronological order of flood events such as the start time of rainfall and the lag time of flood peaks, but also contribute to long-range dependence modeling, helping the model distinguish the relevance of distant time steps, such as the impact of early rainfall on later flood peaks. In the Transformer model, Query (Q), Key (K), and Value (V) are the core concepts of the self-attention mechanism. Q represents the vector for which the attention weights are to be calculated currently, which can be understood as a "question" that queries the information of the entire sequence to find the most relevant content. K represents the feature vectors of all input positions, used to match with the query, which can be understood as the "index" in the repository, telling the query which information is the most relevant. V represents the actual information content, which is the vector finally used to calculate the attention output. When the query finds the most matching key, the attention mechanism uses the corresponding value to calculate the final result. The multi-head self-attention mechanism is the core component of the Transformer model. By parallelizing multiple attention heads, diverse dependencies are extracted from different subspaces. Its core steps include:

[0173] 1. Linear transformation: Map the input sequence to multiple Q, K, and V matrices.

[0174] 2. Attention calculation: Each head independently calculates the attention scores to generate context-aware feature representations.

[0175] 3. Concatenation and fusion: Concatenate the outputs of multiple heads and then fuse them into the final result through a linear transformation.

[0176] Mathematically expressed as:

[0177] Q = X encoded ·W Q , K = X encoded ·W K , V = X encoded ·W V

[0178] MultiHead(Q, K, V) = Concat(head1,..., head h )W O

[0179]

[0180] Among them, d k = d model / h (h is the number of attention heads); is the trainable parameter matrix, and d k is the key vector dimension.

[0181] To stabilize the training process, the original feature information is retained through residual connections. The residual structure ensures the effective backpropagation of gradients in deep networks, avoiding information attenuation. Combining layer normalization alleviates the problem of gradient vanishing. Layer normalization eliminates the offset of feature distributions, accelerates convergence, and improves the stability of model training. At the same time, during the model training process, physical constraints are incorporated into the loss function to integrate physical hydrodynamics laws and deep learning, making the model prediction results more consistent with the actual flood evolution process. Traditional data-driven deep learning methods tend to ignore the basic laws of hydrology and hydrodynamics, while introducing physical constraint loss functions can effectively make up for this deficiency. Its expression is as follows:

[0182]

[0183] where, is the mean squared error loss, is the water conservation constraint term. According to the continuity equation, the calculation formula for constraining the relationship between predicted flow, rainfall, and runoff is:

[0184]

[0185] Q is the flow rate, v is the flow velocity, and R is the rainfall; λ1 and λ2 are weight coefficients, and their value ranges are from 0.5 to 1.0.

[0186] During training, physical constraints are used to calculate the physical loss term based on the predicted values, and then backpropagation is performed to jointly optimize the data error and physical error, and update the model parameters. Embedding physical constraint functions during the model training process ensures that the prediction results conform to the actual hydrological laws. By jointly optimizing the data-driven loss and physical consistency loss, the generalization ability of the model and its robustness under extreme events are significantly improved.

[0187] Step 5: Based on the physics-data fusion model, predict the flood peak parameters, and generate graded warning signals in combination with the dynamic flood threshold determination method. Update the model parameters and thresholds through real-time data assimilation to optimize the warning accuracy. Embed the dynamic flood threshold determination into the spatio-temporal data fusion framework to achieve the integration of "prediction-determination-warning", and shorten the warning response time.

[0188] The determination process of the dynamic flood threshold is as follows:

[0189] Calculate the theoretical critical flow threshold Q c :

[0190]

[0191] where Q c is the theoretical critical flow threshold, Q manning is the theoretical flow obtained from the Manning formula, Qcontinuity The theoretical flow obtained from the discretized water volume conservation equation; γ is the weight parameter, ranging from 0 to 1, which controls the proportion of the two methods in the final critical flow calculation. Since the Manning formula assumes a stable flow, it is applicable to conventional hydrological conditions. Therefore, a larger value of γ is taken in stable flow, and a smaller value of γ is taken during sudden floods. n is the roughness coefficient, A is the cross-sectional area of flow, R h is the hydraulic radius, S is the water surface slope, R rain is the rainfall, and P is the wetted perimeter.

[0192] For the theoretical critical flow threshold Q c The data-driven threshold correction is carried out according to the following formula:

[0193] Q threshold = α·Q c ,

[0194] where Q threshold is the new corrected threshold, α is the probabilistic threshold adjustment coefficient, which is obtained by using random forest to learn historical disaster data (Q t , H t , R t , S t ), that is, α = f ML (Q t , H t , R t , S t ); f ML represents the random forest, Q t is the real-time flow, H t is the water level, R t is the rainfall intensity, and S t is the soil saturation.

[0195] The generation rule of the graded warning signal is:

[0196] Yellow warning: When the predicted peak flow Q pred ≥ 0.8Q threshold ;

[0197] Orange warning: When Q pred ≥ Q threshold ;

[0198] Red warning: When Q pred ≥ 1.2Q threshold .

[0199] Fusing the observed data (actual data) with the model prediction value Q pred , and using the Kalman filter to dynamically update and adjust the model weight parameters. The state prediction equation is:

[0200]

[0201] where is the predicted state at time step t (without considering the current observation); is the optimal estimated state at the previous time step (incorporating historical observation data). That is, this equation uses physical laws and the state estimate at the previous moment to predict the state at the current moment. F t is the state transition matrix, which describes the dynamic evolution of the system from t - 1 to t according to the discretized water conservation equation and the Saint - Venant equation. The first row reveals that the flow rate change is driven by the flow velocity c and the gravitational force (water level gradient), and the second row indicates that the water level change is determined by the flow rate change and the channel cross - section parameter B / A. Here, Δt is the time step length, L is the reach length, g is the acceleration due to gravity, and B is the channel width.

[0202] Covariance prediction equation:

[0203]

[0204] where P t|t-1 is the predicted state covariance matrix, representing the uncertainty of the predicted state; P t-1|t-1 is the state covariance matrix at the previous time step; Q t is the process noise covariance matrix, describing the error of the model prediction.

[0205] Observation update equation:

[0206]

[0207] where is the optimal state estimate after fusing the observation; z t is the observation value at the current time step; H is the observation matrix; K t is the Kalman gain, balancing the weights of the model prediction and the observation value. This equation dynamically adjusts the fusion ratio of the model prediction value and the real - time observation value through the Kalman gain K t , reducing the prediction noise. Its calculation formula is:

[0208] K t = P t|t-1 H T (HP t|t-1 H T + R) -1

[0209] where R is the observation noise covariance matrix.

[0210] At the same time, a feedback optimization mechanism is set, that is, if there are 3 consecutive false alarms or missed alarms in the early warning, trigger the retraining of the model:

[0211]

[0212] Among them, the first equation is the model weight update formula, where W new is the updated model weight parameter; W old is the model parameter before update; η is the learning rate, which is used to control the step size of parameter update; is the gradient of the feedback loss function with respect to the weight. The second equation further elaborates on the feedback loss function where Q pred is the peak flood data predicted by the model; Q obs is the actually observed peak flood data.

[0213] When the model has false alarms or misses three times in a row, the retraining mechanism is triggered to adjust the model parameters by the gradient descent method to improve the prediction accuracy.

[0214] The Kalman filter and the feedback optimization mechanism enable real-time update of the model parameters, and still maintain high reliability under mutation conditions such as extreme rainfall or river channel siltation, realizing a "prediction - correction - optimization" closed loop, and significantly improving the robustness and real-time performance of the flood warning system.

[0215] The present invention extracts static terrain spatial features through CNN, combines bidirectional LSTM to capture the forward and backward dependencies of dynamic time series data such as water level and flow rate, and uses the multi-head attention mechanism of Transformer to improve the global spatio-temporal correlation modeling ability; at the same time, a physical constraint loss function is introduced to optimize model training, and the prediction noise is eliminated by combining Kalman filter post-processing. Compared with traditional models, the present invention realizes high-precision joint prediction of peak flood flow, peak water level and occurrence time, effectively supports flood control scheduling and disaster emergency decision-making in complex scenarios across river basins, and significantly improves the stability and interpretability of prediction results.

[0216] Matters not described in the present invention are applicable to the prior art.

Claims

1. A multi-model spatio-temporal combined flood peak prediction method integrating physical constraints, characterized in that The prediction method includes the following: Obtain the static spatial data, dynamic time-series data, and watershed boundary data of the research watershed. The static spatial data includes at least the digital elevation model (DEM). Convert the static spatial data of the DEM into a raster matrix to represent the elevation value of each geographical location. Use gradient calculation to extract the slope feature Slope based on the elevation value, and perform normalization processing on the slope feature Slope to obtain the normalized slope feature S norm ; The dynamic time-series data includes at least flow rate and water level; Construct a CNN-Bi-LSTM-Transformer prediction model: The CNN-Bi-LSTM-Transformer prediction model includes a spatio-temporal data alignment module, a CNN convolutional network, a spatio-temporal feature splicing module, a bidirectional long short-term memory network Bi-LSTM, and a Transformer module. The spatio-temporal data alignment module aligns the spatial data with the dynamic time-series data of the basin in the following way: Convert the basin boundary data to the same coordinate system as the DEM data to ensure spatial alignment between the basin boundary data and the DEM data; then rasterize the basin boundary according to the pixel grid size of the DEM data so that the basin location matches the spatial resolution of the DEM; and then use nearest-neighbor interpolation to spatially align the basin boundary with the DEM raster data to ensure that the spatial features of each grid cell of the DEM match the data of the corresponding basin location. After the spatio-temporal data alignment, the normalized slope feature S norm and the DEM data are used as the input to the CNN convolutional network. The CNN convolutional network is used to extract spatial features. The dimension of the spatial features output by the last layer of the CNN convolutional network is consistent with the dimension of the hidden state of the Bi-LSTM. The spatial features extracted by the CNN convolutional network are used to initialize the initial hidden state and the initial cell state of the bidirectional long short-term memory network Bi-LSTM, serving as the spatial constraint of the Bi-LSTM; The spatio-temporal feature splicing module is used to perform spatio-temporal splicing on the aligned dynamic time-series features and the spatial features extracted by the CNN to obtain a joint feature matrix. Input the joint feature matrix into the spatially constrained Bi-LSTM, and then, after being processed by the Transformer module in combination with positional encoding, generate flood peak prediction results, including flood peak discharge, peak water level, and the corresponding occurrence time. Thus, the constructed CNN-Bi-LSTM-Transformer prediction model is obtained. Train the CNN-Bi-LSTM-Transformer prediction model, and use the physical constraint loss function as the loss function during training Its expression is: where, is the mean square error loss, is the water volume conservation constraint term, and λ1 and λ2 are weight coefficients; Use the trained CNN-Bi-LSTM-Transformer prediction model to predict the flood peak.

2. The prediction method according to claim 1, wherein The static spatial data also includes remote sensing image data, and the remote sensing image data is also spatially aligned with the DEM data in terms of coordinates, resolution, and values. The dynamic time-series data also includes rainfall. The calculation formula of the water conservation constraint term is: where Q is the flow rate, v is the flow velocity, and RR is the rainfall; the value ranges of λ1 and λ2 are 0.5 to 1.

0.

3. The prediction method according to claim 1, wherein The slope feature is calculated by the following formula: wherein, and represent gradients in the horizontal and vertical directions, respectively; Z is the elevation value at each location in the DEM data.

4. The prediction method according to claim 1, wherein The processing process of the spatio-temporal feature splicing module is: Set the training batch as B, divide the aligned dynamic time-series data into multiple sequence segments according to a preset time window, and each sequence segment contains at least 24 to 72 hours of water level and flow data; then perform sliding window normalization on each sequence segment, and the normalized sequence segment is represented as (B, T, D). Perform spatio-temporal splicing on the standardized sequence segments (B, T, D) and the spatial feature vectors (B, F spatial ) extracted by the CNN to obtain a joint feature matrix (B, T, D + F spatial ); where T is the time step and D is the dimension of the dynamic time-series feature.

5. The prediction method according to claim 1, wherein After the CNN-Bi-LSTM-Transformer prediction model outputs the flood peak prediction results, generate a graded warning signal in combination with the dynamic flood threshold determination method. The process of the dynamic flood threshold determination method is: Calculate the theoretical critical flow threshold Q using the Manning formula and the water conservation equation c : Among them, Q c is the theoretical critical flow threshold, Q manning is the theoretical flow obtained from the Manning formula, Q continuity is the theoretical flow obtained from the discretized water conservation equation; γ is the weight parameter, ranging from 0 to 1, taking a larger value in steady flow and a smaller value during sudden floods; n is the roughness coefficient, A is the cross-sectional area of flow, R h is the hydraulic radius, S is the water surface slope, R rain is the rainfall, and P is the wetted perimeter; For the theoretical critical flow threshold Q c The data-driven threshold correction is performed according to the following formula: Q threshold = α·Q c , Among them, Q threshold is the new threshold after correction, α is the probabilistic threshold adjustment coefficient, and the historical disaster data (Q t , H t , R t , S t ) is obtained by using random forest learning, that is, α = f ML (Q t , H t , R t , S t ); f ML represents random forest, Q t is the real-time flow rate, H t is the water level, R t is the rainfall intensity, and S t is the soil saturation degree.

6. The prediction method according to claim 5, characterized in that The rule for generating the graded warning signal is: Yellow warning: When predicting the peak flood flow Q pred ≥0.8Q threshold ; Orange warning: When Q pred ≥ Q threshold ; Red alert: When Q pred ≥ 1.2Q threshold .

7. The prediction method according to claim 1, wherein Fuse the observed data with the model prediction value Q pred , and use the Kalman filter to dynamically update and adjust the model weight parameters; the state prediction equation of the Kalman filter is: where Δt is the time step, L is the length of the river reach, g is the acceleration due to gravity, and B is the width of the river channel; is the predicted state at time step t; is the optimal estimated state of the previous time step that incorporates historical observation data, that is, using the state prediction equation according to physical laws and the state estimate of the previous moment to predict the state at the current moment; F t is the state transition matrix, which describes the dynamic evolution law of the system from t - 1 to t according to the discretized water conservation equation and the Saint - Venant equation. The first row reveals that the change in flow rate is driven by the flow velocity v and the action of gravity, and the second row indicates that the change in water level is determined by the change in flow rate and the channel cross - section parameter B / A; The covariance prediction equation is: Among them, P t|t-1 is the predicted state covariance matrix, representing the uncertainty of the predicted state; P t-1|t-1 is the state covariance matrix of the previous time step; Q t is the process noise covariance matrix.

8. The prediction method according to claim 1, wherein Set a feedback optimization mechanism. If there are 3 consecutive warning false alarms or missed alarms, trigger the retraining of the model. Among them, the first equation is the model weight update formula, W new is the updated model weight parameter; W old is the model parameter before update; η is the learning rate, which is used to control the step size of parameter update; is the gradient of the feedback loss function with respect to the weight; is the feedback loss function, Q pred is the peak flood data predicted by the model; Q obs is the actually observed peak flood data.

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