Multi-target flood forecasting method based on coupling of Xinanjiang model and deep learning
By combining the Xin'anjiang model with multi-objective optimization and information fusion using deep learning, the problems of model uncertainty and physical consistency in traditional hydrological forecasting methods have been solved, achieving high-precision and interpretable flood forecasting results.
Patent Information
- Application Number
- CN202511979847.3
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-12-25
- Publication Date
- 2026-05-15
AI Technical Summary
Traditional hydrological forecasting methods suffer from large model uncertainties and poor physical consistency of forecast results when characterizing complex hydrological systems. They are difficult to meet the requirements of accuracy and physical rationality of flood peak and flood volume at the same time. Single-objective optimization leads to unstable parameter selection, and pure data-driven models lack physical mechanisms, resulting in prediction distortion under extreme conditions.
A multi-objective flood forecasting method based on the Xin'anjiang model coupled with deep learning is adopted. The NSE, VE, and PE indices are optimized collaboratively by the NSGA-II optimization algorithm. The nonlinear relationship is captured by combining the PatchTST deep learning model. Physical state variables are introduced for feature expansion and information fusion to form an end-to-end highly robust forecasting framework.
It achieves high accuracy, physical consistency and interpretability in flood forecasting under extreme conditions, improves the model's generalization ability and adaptability, and significantly improves the forecast accuracy of NSE, VE and PE.
Smart Images
Figure CN122046897A_ABST
Abstract
Description
Technical Field
[0001] This invention belongs to the field of flood forecasting technology, specifically relating to a multi-objective flood forecasting method based on the Xin'anjiang model coupled with deep learning. Background Technology
[0002] Hydrological systems are influenced by multiple factors, including the spatiotemporal heterogeneity of precipitation, dynamic changes in the underlying surface, and disturbances from human activities. Their response processes exhibit strong nonlinearity, time-varying characteristics, and high dimensionality. Traditional forecasting methods, when characterizing such complex systems, often suffer from simplistic physical mechanisms and insufficient data assimilation capabilities. This leads to a significant amplification of model uncertainties during extreme events (such as short-duration torrential rains and floods), limiting the operational applicability of forecast results.
[0003] Current hydrological forecasting technologies are mainly divided into two categories: physical mechanism-driven models and data-driven models. Physical mechanism-based hydrological models are the core tools for flood forecasting. These models simulate rainfall-runoff processes by constructing runoff generation and concentration physical equations, and their parameters have clear physical meanings. However, due to the complexity of hydrological processes and the simplification assumptions of the models, their ability to characterize dynamic nonlinear processes is limited, leading to significant errors in peak and volume predictions. Furthermore, traditional parameter calibration methods often employ single-objective optimization, making it difficult to balance the conflict between peak and volume errors and physical rationality.
[0004] In recent years, deep learning models, represented by LSTM and Transformer, have made progress in the field of hydrological forecasting. These models learn the rainfall-runoff mapping relationship directly from historical data through end-to-end training, demonstrating advantages in complex nonlinear modeling. However, purely data-driven models completely ignore hydrological physical mechanisms, which may lead to anti-physical results under extreme conditions. In addition, the black-box nature of deep learning models reduces the reliability of prediction results, making it difficult to meet the rigid requirements of physical consistency in water conservancy projects.
[0005] Traditional hydrophysical models (such as the Xin'anjiang model), limited by simplified physical equations, struggle to adequately describe highly nonlinear dynamic hydrological processes, particularly exhibiting a significant drop in forecast accuracy under extreme conditions. A key challenge lies in the inability of single-objective parameter calibration methods to simultaneously satisfy competing critical accuracy metrics in flood forecasting: maximizing the Nash-Sutcliffe Efficiency coefficient (NSE), reflecting the goodness of fit to the overall process; ensuring the Volume Error coefficient (VE), representing the accuracy of total flood volume, is as close to 1 as possible; and ensuring the Peak Error coefficient (PE), characterizing the peak flood, is also as close to 1 as possible. This often leads to unbalanced parameter selection, resulting in unstable model performance under different flood characteristics. Furthermore, while purely data-driven deep learning models possess powerful nonlinear fitting capabilities, their complete detachment from physical mechanisms makes predictions prone to physical inconsistencies (such as violations of hydrological continuity or water conservation) under extreme scenarios outside the training data range. Moreover, their decision-making process is like a "black box," lacking interpretability and impacting the practical reliability of forecast results. Summary of the Invention
[0006] To overcome the shortcomings of the existing technologies, the present invention aims to provide a multi-objective flood forecasting method based on the Xin'anjiang model coupled with deep learning. This method features multi-objective collaborative parameter optimization, balancing accuracy and physical consistency, accurate conversion of watershed geographic information, and end-to-end robust design. It can synergistically improve the three key forecast accuracy indicators of NSE, VE, and PE, and ensure that the forecast results have a solid physical basis and good interpretability.
[0007] To achieve the above objectives, the technical solution adopted by the present invention is as follows: A multi-objective flood forecasting method based on the Xin'anjiang model coupled with deep learning includes the following steps; Step 1: Geographic Information Processing The ArcGIS platform was used to extract the digital water system and sub-unit boundaries of the target watershed, and elevation data was processed. Based on the distribution of rainfall stations, the Thiessen polygon method was used to calculate the watershed surface rainfall. Step 2: Hydrological Data Processing Systematically collect hydrological data of the target watershed, calculate the watershed surface rainfall based on the weight coefficients of each rain gauge obtained in step 1, thereby obtaining the hourly average surface rainfall sequence and secondary flood dataset of the target watershed, and divide the dataset into training set and validation set; This allows for the deep integration of the static geographic framework constructed in step 1 with dynamic hydrological process data, laying a unified and reliable data foundation for subsequent model training and validation. Step 3: Co-optimization of physical model parameters: Using the Nash efficiency coefficient (NSE), flood volume coefficient (VE), and flood peak coefficient (PE) as multi-objective functions, the NSGA-II optimization algorithm was used to calibrate the parameters of the Xin'anjiang three-source water model, generate the Pareto optimal solution set, and select the robust parameter combination. Step 4: Hybrid driving model coupling: The physical state variables (simulated runoff) output by the optimized Xin'anjiang model are input together with the surface average rainfall sequence and the secondary flood dataset into the PatchTST deep learning model. The Transformer architecture is used to capture the nonlinear relationship between physical state and flow, generate corrected flow, and finally output high-precision forecast results.
[0008] In step 1, the elevation data processing flow begins with the terrain analysis stage. Based on the ArcGIS platform, hydrological analysis is performed using the original elevation data DEM of the watershed. Through depression filling and runoff accumulation calculation, the spatial distribution of the watershed river network is extracted and the boundaries of sub-watersheds are delineated, generating a vector layer with topological relationships. Then, based on the coordinates of the rainfall stations distributed within the region, the control area of each station is divided using the Thiessen polygon method, and the areal rainfall weight matrix is calculated, thereby transforming the discrete station rainfall data into a watershed-scale areal average rainfall sequence.
[0009] The Thiessen polygon method calculates average rainfall based on rainfall data from discretely distributed rain gauges. It involves connecting all adjacent rain gauges into a triangle, drawing the perpendicular bisectors of each side of the triangle, and then creating a polygon around each rain gauge. The rainfall within this polygon is represented by the rainfall from a single rain gauge contained within it; this polygon is called the Thiessen polygon. Thus, a network of multiple rain gauges within a region or watershed constitutes a Thiessen polygon network. The average rainfall for the region or watershed is obtained by multiplying the weight coefficient of each polygon in the network by the rainfall data from each rain gauge and summing the results. The formula is as follows: In the formula: The average rainfall over the watershed area; For the first in the basin Weighting coefficients for calculating the polygonal area of each rain gauge station; For the first Rainfall at each rain gauge station during the same period.
[0010] Specifically: The process begins with acquiring DEM elevation data of the study area from a geospatial data cloud platform; First, a topographic analysis is performed on the DEM. By calculating the direction of water flow and identifying closed depressions, it is determined whether there are sinks in the terrain. If sinks exist, depression filling operations are performed to eliminate depression interference and generate a DEM without depressions. If there are no sinks, the original DEM is used directly as the basis for subsequent analysis. Subsequently, the flow is calculated based on the corrected DEM, and potential river networks are extracted by setting flow thresholds: the larger the threshold, the sparser the selected channels, and vice versa; after vectorizing the raster river networks that meet the thresholds, the river network topology is enhanced through river linking and hierarchical operations to clarify the river level and connectivity. The length of the water flow is calculated using a DEM without depressions. Combined with manually or automatically captured pouring points, the watershed boundary is generated using a watershed tool, and the final watershed extent is determined using a mask extraction tool. Based on the delineation of the watershed spatial scope and combined with the distribution data of rainfall stations within the watershed, the Thiessen polygon method was used to divide the control area of each rainfall station. Finally, the rainfall observed at each station was weighted and averaged using the proportion of the area of each Thiessen polygon to the total area of the basin, resulting in the areal rainfall distribution that reflects the overall precipitation situation of the basin. The entire process, through multi-step coupling of topographic correction, hydrological simulation and spatial interpolation, realizes the transformation from discrete elevation data to continuous areal precipitation characteristics.
[0011] In step 2, data cleaning is first performed to remove outliers, and spatial kriging is used to imput missing rainfall and evaporation data. Based on the obtained continuous areal precipitation characteristics, the areal average rainfall sequence is calculated, and then the spatiotemporal distribution characteristics of rainfall, peak flow frequency, and flood duration curve are statistically analyzed. Representative rainfall-flood events are selected and divided into calibration, validation, and testing datasets. Finally, the datasets are compiled according to the standard time series format of the Xin'anjiang model to form a standardized input that can be directly used for model parameter calibration and accuracy verification.
[0012] The data is organized into a strictly equal-interval, complete sequence according to the standard time series format of the Xin'anjiang model. The purpose of this step is to organize the cleaned, imputed, analyzed, and filtered data into a structured text file that the Xin'anjiang model can directly recognize and read.
[0013] In step 4, the NSGA-II optimized Xin'anjiang physical model is deeply integrated with the PatchTST deep learning model to form a collaborative forecasting framework. NSGA-II serves as the parameter optimization engine, using the Nash efficiency coefficient (NSE), flood volume coefficient (VE), and peak flood coefficient (PE) to calibrate the parameters of the Xin'anjiang Three-Source Model and generate the Pareto optimal solution set.
[0014] The specific operating steps of the NSGA-II are as follows: Step 1: Initialize the population N sets of parameters for the Xin'anjiang model are randomly generated, with each set of parameters corresponding to an "individual"; an initial population of size N is formed. , ; Step 2: Based on the parent generation New populations are obtained by performing evolutionary operations such as crossover and mutation. Given a population size of N, explore uncovered regions in the parameter space to avoid getting trapped in local optima; and Population merged into In the process, high-quality parameter combinations from the past are preserved to prevent the loss of excellent solutions; non-dominated sets are constructed, and cluster distances are calculated, from which individuals are selected to be added. In the middle, priority is given to individuals with lower hierarchical levels and larger cluster distances, until... The number of individuals is N, and the optimal parameter sets of NSE, VE, and PE are optimized to avoid the parameters being overly concentrated on a certain characteristic. Step 3: Check if the termination condition is met. If yes, the iteration ends; otherwise, go to Step 2.
[0015] By incorporating the physical state variables output by the Xin'anjiang model as key inputs to PatchTST, and through four innovations—physical variable feature expansion, hydrological adaptation through a segmentation mechanism, business integration of loss functions, and customized pre-training tasks—the general PatchTST is transformed into a dedicated engine for flood forecasting, solving the problem of physical distortion in pure data-driven models during extreme events.
[0016] In Step 3, the PatchTST time series model is used to couple with the simulated runoff of the Xin'anjiang River; physical state variables are used as feature enhancements, and physical quantities such as simulated runoff and soil moisture content of each layer output by the Xin'anjiang model are used to provide physical constraints on the hydrological process for PatchTST. The Transformer model consists of an encoder and a decoder based on a self-attention stacked module. Unlike the attention in sequence-to-sequence learning, the input source and output target sequences are encoded with position before being embedded into the encoder and decoder. From a high-level perspective, the Transformer encoder is actually a stack of multiple identical layers. This application adopts multi-source heterogeneous data fusion to uniformly encode the physical variables of the Xin'anjiang hydrological model and the original data in the Transformer embedding layer, and distinguishes the data types through position encoding.
[0017] The results of parallel computation of multiple attention heads are used. Each attention head focuses on different subspace information. At the same time, due to the adoption of parallel computation, the calculation method of multi-head attention also changes accordingly, as shown in formula (1). … (1) In the formula: the input matrix includes the query matrix Q, the key matrix K, and the value matrix V; When this mechanism is running, the source of the query information is the final output of the decoder's self-attention sublayer, while the key and value data are taken from the encoder's output. For each attention head (i from 1 to h), a projection is created for each head using three sets of parameter matrices unique to that head. Used for projecting query vectors. Used for projecting key vectors. Used for projecting value vectors, these matrices linearly transform the original Q, K, V to different feature spaces, allowing each head to focus on different aspects of the input; The projected Q, K, and V values are fed into the attention function to calculate the output of the i-th head. This process is performed in parallel, with each head working independently to capture different types of relationships in the input sequence; The output results of all h attention heads … The features are concatenated along the feature dimension to form a large matrix.
[0018] The concatenated large matrix is then combined with an output projection matrix. Multiplication is performed, followed by final linear projection. This step aims to fuse information, integrating different feature information captured by multiple heads. Dimensionality reduction and transformation are then performed, mapping the concatenated high-dimensional features back to the desired dimension for input into subsequent feedforward network layers.
[0019] This application uses an attention mechanism to guide the physical aspects of a hydrological model. It introduces a physical correlation weight matrix into the multi-head attention calculation formula, thereby constructing different mask matrices based on physical variables, enabling the model to adjust the attention weights according to different flood tasks.
[0020] In addition, the Transformer architecture also involves two important formulas. Formula (2) is the calculation method of the Feed-Forward Neural Network (FFN), which is used to perform nonlinear transformation on the input features at each location.
[0021] In the formula: The feature vector representing the current position. For Transformer, It is the output calculated and processed through self-attention or cross-attention mechanisms. and These are the weight matrices for the first and second fully connected layers, respectively. and These are the bias vectors for the first and second fully connected layers, respectively. This is the definition of the ReLU (Rectified Linear Unit) activation function. It performs a non-linear transformation on the output of the first linear layer, setting values less than 0 to 0. This is a key step in introducing non-linearity, enabling the model to learn more complex functions.
[0022] During the calculation process, the input vector First, with the weight matrix Multiply and add bias. This achieves dimensionality upscaling; then, the ReLU activation function is applied to the intermediate results, and the activated results are compared with the weight matrix. Multiply and add bias. This achieves dimensionality reduction transformation. The role of the feedforward neural network is to process and transform information at each location. It complements the attention mechanism and is an indispensable part of the Transformer architecture.
[0023] Formula (3) represents residual connections and layer normalization, which are key technologies in the Transformer model used to alleviate the vanishing gradient problem and accelerate model training.
[0024] (3) In the formula: This represents a specific sub-layer operation. Each Transformer layer typically contains two such sub-layers: an attention sub-layer and a feedforward neural network sub-layer. This is the core operation of residual connections. It takes the input of the sublayer... Directly with the output of the sublayer Adding them together allows the gradient to propagate directly back to earlier layers, thus greatly alleviating the vanishing gradient problem in deep networks. It is a layer normalization operation. It normalizes all feature dimensions of a single sample. By normalizing the output of a layer, the input distribution of each layer can be made more stable, thus allowing for a larger learning rate and accelerating model convergence.
[0025] The beneficial effects of this invention are: The main benefits of this invention are reflected in three aspects: improved accuracy, enhanced physical properties, and improved robustness. First, comprehensive synergistic optimization is achieved on the core accuracy indicators (NSE, VE, PE). NSGA-II multi-objective optimization directly targets the three most important accuracy indicators for flood forecasting (NSE - overall process, VE - total amount, PE - peak value) to synergistically optimize the parameters of the Xin'anjiang model, fundamentally overcoming the inherent defects of single-objective optimization and significantly improving the performance of the physical foundation of the hybrid model.
[0026] The coupled model leverages the complementary advantages of physical mechanisms and data-driven approaches: optimizing the high-quality physical state information provided by the Xin'an River lays a solid foundation for the data model; PatchTST's powerful pattern learning capabilities accurately capture complex nonlinear details and dynamics that are difficult for physical models to represent, ultimately achieving breakthrough improvements in the three major indicators of NSE (overall fit), VE (flood total balance), and PE (flood peak accuracy), with overall accuracy surpassing that of a single model or simple integration.
[0027] Secondly, physical consistency and interpretability are significantly enhanced. The key physical state variables output by the Xin'anjiang model are explicitly incorporated into the learning process of PatchTST, "embedding" hydrophysical constraints into the deep learning model. This enables the model to produce physically meaningful results that follow basic principles during both the training and prediction phases. At the same time, by analyzing the characteristic importance of the physical state variables, the model provides interpretable evidence at the physical mechanism level for the prediction results.
[0028] Finally, the model's generalization ability and practicality are improved: the robust parameter solution set obtained by multi-objective optimization, combined with the inherent structural robustness of PatchTST (such as block processing to enhance noise resistance), makes the hybrid model more adaptable to different watersheds or changing environments; the final generated high-precision, highly physically consistent flood forecast provides a powerful and reliable technical tool for improving the timeliness of watershed flood warnings, the refinement of reservoir flood control scheduling, and the scientific nature of urban waterlogging prevention and control. Attached Figure Description
[0029] Figure 1 This is a schematic diagram of the structure of the Xin'anjiang-PatchTST coupled flood forecasting model in this application.
[0030] Figure 2 This is a structural diagram of the Xin'anjiang model with three water sources.
[0031] Figure 3 This is a flowchart of the DEM elevation data processing for this application.
[0032] Figure 4 This is the overall process of the NSGA-II algorithm.
[0033] Figure 5 It is the Transformer model structure.
[0034] Figure 6 It is the core structure of the Transformer encoder.
[0035] Figure 7 It is a multi-head attention mechanism.
[0036] Figure 8 This is the basic structure of the self-supervised PatchTST model.
[0037] Figure 9 This is a schematic diagram illustrating the performance on the training set of flood data from four events: 20160501, 20160527, 20160614, and 20160624.
[0038] Figure 10 The diagram shows the experimental results for May 1, 2016, May 27, 2016, June 14, 2016, and June 24, 2016.
[0039] Figure 11 This is a schematic diagram illustrating the performance of the flood event on April 23, 2018.
[0040] Figure 12 This is a schematic diagram of the experimental results for the flood event on April 23, 2018. Detailed Implementation
[0041] The present invention will now be described in further detail with reference to the accompanying drawings.
[0042] like Figure 1 As shown in the diagram, the Xin'anjiang-PatchTST coupled flood forecasting model provided by this invention includes the following steps: Step 1: Geographic Information Processing The ArcGIS platform was used to extract the digital water system and sub-unit boundaries of the target watershed, and the Thiessen polygon method was used to calculate the watershed surface rainfall based on the distribution of rainfall stations. Step 2: Hydrological Data Processing Systematically collect hydrological data of the target watershed, construct a dataset, perform data cleaning and preprocessing on the dataset to obtain hourly rainfall-evaporation sequences and secondary flood datasets of the target watershed, and divide the dataset into training set and validation set; Step 1 extracts the digital water system and sub-basin boundaries, and uses the Thiessen polygon method to construct the spatial physical framework of the basin and the areal rainfall calculation method, providing crucial spatial analysis units and core algorithms for Step 2. Step 2 then systematically processes hydrological data to generate hourly rainfall-evaporation sequences and secondary flood datasets that strictly correspond to the spatial units determined in Step 1. This deeply integrates the static geographic framework constructed in Step 1 with dynamic hydrological process data, laying a unified and reliable data foundation for subsequent model training and validation.
[0043] Step 3: Co-optimization of physical model parameters: Using Nash efficiency coefficient (NSE), flood volume coefficient (VE), and peak flood coefficient (PE) as multi-objective functions, the NSGA-II optimization algorithm was used to calibrate the parameters of the Xin'anjiang three-source water model, generate the Pareto optimal solution set, and select the robust parameter combination. Step 4: Hybrid driving model coupling: The optimized Xin'anjiang model outputs physical state variables (simulated runoff) along with the original hydrological and meteorological data, which are then input into the PatchTST deep learning model. The Transformer architecture captures the nonlinear relationship between physical state and flow, generating corrected flow and ultimately outputting high-precision forecast results. Step 1 involves DEM analysis using the ArcGIS platform, including depression filling, river network extraction, and Thiessen polygon method for calculating areal rainfall, providing a precise spatial basis for hydrological data processing in Step 2. Step 2 then processes the hydrological data, performing data cleaning, interpolation, and dataset partitioning to generate training and validation sets. Finally, Step 3 utilizes these datasets and employs the NSGA-II multi-objective optimization algorithm, with NSE, VE, and PE as objective functions, to calibrate the Xin'anjiang model parameters, ensuring the robustness of the parameter combination.
[0044] Figure 2 This is a structural diagram of the Xin'anjiang model with three water sources used in this invention. The Xin'anjiang model is a conceptual hydrological model, mainly applied in humid and semi-humid regions, and has been widely used in real-time flood forecasting.
[0045] The Xin'anjiang model with three water sources is currently widely used. Considering that the soil structure can be divided into loose soil layer, dense soil layer, and groundwater aquifer, the Xin'anjiang model divides the water source into surface runoff, interflow, and groundwater runoff, hence the name Xin'anjiang model with three water sources.
[0046] The Xin'anjiang Three-Source Model divides the watershed into sub-watersheds with the same number of rain gauges. The rainfall at each rain gauge is used as the average rainfall for the sub-watershed to calculate runoff. Evaporation is calculated in three stages based on different soil moisture contents. Slope runoff refers to the flow of water such as surface runoff, interflow, and groundwater before the runoff, and is calculated using the unit hydrograph method. Channel runoff refers to the process of water converging in the channel, simulating the channel's regulation and storage effect on water flow, and is calculated using a lag algorithm.
[0047] In the model, the evapotranspiration calculation adopts a three-layer evaporation calculation mode. The input is the conversion factor K of the measured water surface evaporation of the evaporator and the watershed evapotranspiration capacity. The parameters of the model are the water storage capacity of the upper, lower and deep layers WUM, WLM and WDM (WM=WUM+WLM+WDM) and the deep layer evapotranspiration coefficient C; the output is the watershed evapotranspiration of the upper, lower and deep layers EU, EL and ED (E=EU+EL+ED). The calculation includes three time-varying parameters: soil moisture content at each layer, WU, WL, and WD (W = WU + WL + WD). WM, E, and W represent the total watershed storage capacity, evapotranspiration, and soil moisture content, respectively.
[0048] The model comprises four levels: evapotranspiration calculation, runoff generation calculation, three-source water division, and confluence calculation. The physical meaning of the model parameters at each level and the recommended value range are shown in Table 1.
[0049] Table 1. Calculation modules and parameter value ranges for the Xin'anjiang model. Evapotranspiration parameters include K, UM, LM, and C. K is the evapotranspiration capacity conversion factor, which is the ratio of the watershed's evapotranspiration capacity to the measured water surface evaporation value. This parameter controls the total water balance and is therefore crucial for water volume calculations. UM is the upper water storage capacity, which includes the amount intercepted by vegetation. LM is the lower water storage capacity. C is the deep water evapotranspiration coefficient. It is determined by the proportion of deep-rooted vegetation in the watershed area and is also related to the value of UM+LM; the larger this value, the more difficult deep water evapotranspiration becomes.
[0050] The parameters for watershed runoff include WM, B, and IM. WM represents the watershed's water storage capacity, an indicator of its drought severity. WM is generally divided into upper UM, lower LM, and deep DM. B is the power of the water storage capacity curve. It reflects the uneven distribution of water storage capacity across the watershed. Generally, the larger the watershed and the more diverse the geological and topographical features, the larger the B value. However, it should be noted that the B value is related to UM, but they are not entirely independent. For the same watershed water storage capacity curve, if WM increases, B decreases accordingly, and vice versa. IM is the ratio of impermeable area to the total watershed area.
[0051] Water source delineation parameters include SM, EX, KI, and KG. SM is the average free water storage capacity of the watershed, which plays a decisive role in the amount of surface runoff and is therefore very important. EX is the free water storage capacity curve index, which indicates the uneven distribution of free water capacity. KI is the outflow coefficient of the free water reservoir to groundwater runoff, and KG is the outflow coefficient of the free water reservoir to groundwater runoff. These two outflow coefficients are connected in parallel, and their sum represents the rate of free water outflow.
[0052] The confluence parameters include CS, CI, CG; KE, and XE. CS is the river network water receding coefficient. CI is the receding coefficient of interflow reservoirs. CG is the receding coefficient of groundwater reservoirs. KE is the propagation time of flood waves in the river reach in the Muskingum method of river confluence. XE is the flow-to-gravity ratio coefficient in the Muskingum method of river confluence. It is a unified condition that reflects both the physical meaning of the Muskingum method and satisfies its numerical calculation stability.
[0053] Before parameter calibration, geographic information processing is performed first. The watershed extent and areal rainfall weight matrix are obtained from the original elevation data (DEM).
[0054] Figure 3 This is a flowchart of the DEM elevation data processing used in this invention. The elevation data processing flow begins with the terrain analysis stage. Based on the ArcGIS platform, hydrological analysis is performed using the original watershed elevation data (DEM). Through operations such as depression filling and runoff accumulation calculation, the spatial distribution of the watershed river network is extracted and sub-watershed boundaries are delineated, generating a vector layer with topological relationships to provide an accurate geospatial framework for subsequent hydrological simulations. Then, based on the coordinates of the rainfall stations distributed within the region, the control area of each station is divided using the Thiessen polygon method, and the areal rainfall weight matrix is calculated, thereby transforming the discrete station rainfall data into a watershed-scale areal average rainfall sequence.
[0055] The process begins with acquiring DEM elevation data of the study area from a geospatial data cloud platform. First, topographic analysis is performed on the DEM, calculating water flow direction and identifying closed depressions to determine if sinks exist. If sinks exist, depression filling is performed to eliminate depression interference, generating a DEM without depressions; if no sinks exist, the original DEM is used directly as the basis for subsequent analysis.
[0056] Subsequently, flow rates were calculated based on the corrected DEM, and potential river networks were extracted by setting flow thresholds: the higher the threshold, the sparser the selected channels, and vice versa. After vectorizing the raster river networks that met the thresholds, the river network topology was further enhanced through river linking and hierarchical operations to clarify river class and connectivity. Simultaneously, flow lengths were calculated using a DEM without depressions, and combined with manually or automatically captured spillways, watershed boundaries were generated using watershed tools, and the final watershed extent was determined using mask extraction tools.
[0057] Based on the delineation of the watershed's spatial scope and combined with rainfall station distribution data within the watershed, the Thiessen polygon method was used to divide the control area of each rainfall station (i.e., any location belongs to the nearest rainfall station). Finally, using the proportion of each Thiessen polygon area to the total watershed area as weight, a weighted average of the station-observed rainfall was calculated to obtain the areal rainfall distribution results reflecting the overall precipitation situation of the watershed. The entire process, through multi-step coupling of topographic correction, hydrological simulation, and spatial interpolation, achieved a scientific transformation from discrete elevation data to continuous areal precipitation characteristics.
[0058] In terms of hydrological data processing, this application, based on hourly historical rainfall, evaporation, and flow data from rain gauges and hydrological stations, first performs data cleaning to remove outliers and then uses spatial kriging to imput missing rainfall and evaporation data. Next, it statistically analyzes the spatiotemporal distribution characteristics of rainfall, peak flow frequency, and flood duration curves. Based on this, representative rainfall-flood events are selected and divided into calibration, validation, and testing datasets. Finally, the datasets are compiled according to the standard time series format of the Xin'anjiang model to form standardized inputs that can be directly used for model parameter calibration and accuracy verification.
[0059] In the process of co-optimizing the physical model parameters, this application adopts NSGA-II (fast nondominated sorting genetic algorithm). NSGA-II is one of the most popular evolutionary multi-objective optimization algorithms and has been applied to the field of flood forecasting. The innovation of this invention lies in the deep integration of the NSGA-II optimized Xin'anjiang physical model with the PatchTST deep learning model to form a collaborative forecasting framework.
[0060] In this invention, NSGA-II serves as the parameter optimization engine, calibrating the parameters of the Xin'anjiang Three-Source Model using flood-specific objective functions (NSE, VE, PE) to generate a Pareto-optimal solution set. The innovative design involves binding core flood operational indicators as the objective function while simultaneously considering physical boundary constraints on the parameters to ensure the solution set conforms to hydrological mechanisms. Compared to traditional applications, NSGA-II here is merely a tool for optimizing physical model parameters; its output (robust parameter combinations and flood time series) is not the endpoint but rather the starting point of deep coupling.
[0061] The following describes the core algorithm flow and overall steps of NSGA-II.
[0062] NSGA-II Algorithm Description: The core idea of fast non-dominated sorting is to construct a partially ordered set and pop the population into m subsets. , ,..., Subpopulations do not intersect with each other, and ... At the same time, for Each individual in the model is defined with a clustering distance, and when selecting offspring, individuals with lower hierarchies and larger clustering distances are given priority.
[0063] Let the population pop size be N, and the two vectors { }and{ },in, This represents the number of individuals that dominate individual i. Let i represent the set of individuals dominated by individual i. This represents the clustering distance of individual i. This represents the function value of individual i on sub-goal m.
[0064] Algorithm 1: Construction of Non-Dominated Sets Algorithm 2: Cluster distance between individuals The overall steps of the NSGA-II algorithm are as follows: Figure 4 As shown: Step 1: Initialize the population N sets of Xin'anjiang model parameter combinations are randomly generated (such as runoff generation parameters WM, B, and confluence parameters CS, KI, etc.), with each set of parameters corresponding to an "individual". An initial population of size N is formed. , ; Step 2: Based on the parent generation New populations are obtained by performing evolutionary operations such as crossover and mutation. Given a population size of N, explore uncovered regions in the parameter space to avoid getting trapped in local optima; and Population merged into In the process, high-quality parameter combinations from the past are preserved to prevent the loss of excellent solutions; non-dominated sets are constructed, and cluster distances are calculated, from which individuals are selected to be added. In the middle, priority is given to individuals with lower hierarchical levels and larger cluster distances, until... The number of individuals is N, and the optimal parameter sets of NSE, VE, and PE are optimized to avoid the parameters being overly concentrated on a certain characteristic. Step 3: Check if the termination condition is met. If yes, the iteration ends; otherwise, go to Step 2.
[0065] Traditional time series forecasting models (such as PatchTST) typically use raw meteorological and hydrological data (rainfall, evaporation, etc.) directly. This application innovatively incorporates physical state variables output from the Xin'anjiang model as key inputs to PatchTST. Through four innovations—physical variable feature expansion, block-based hydrological adaptation, loss function integration, and pre-training task customization—the general-purpose PatchTST is transformed into a dedicated flood forecasting engine, solving the problem of physical distortion in pure data-driven models during extreme events.
[0066] This application employs the PatchTST time series model to couple with simulated runoff from the Xin'anjiang River. PatchTST has achieved state-of-the-art results in long-term prediction. This application uses physical variables as feature enhancements, employing simulated runoff and soil moisture content at various layers, as output from the Xin'anjiang model, to provide physical constraints on hydrological processes for PatchTST.
[0067] The Transformer model, proposed alongside the attention mechanism, is a revolutionary product in deep learning, fundamentally changing natural language processing and time series prediction, and forming the basis for later large-scale artificial intelligence models. The most valuable aspect of the Transformer model is its complete abandonment of traditional recurrent neural networks and convolutional neural networks for parallel processing of sequential data. Instead, it learns and captures dependencies in sequential data through self-attention mechanisms and multi-layer feedforward neural networks. This approach offers three main advantages: first, it enables parallel computation of sequential data; second, the self-attention mechanism weakens the influence of distance, completely solving the gradient vanishing problem in RNNs when processing long-term sequences; and third, it provides greater flexibility, handling input sequences of variable length and adapting to various scenarios.
[0068] like Figure 5 As shown, the Transformer model consists of an encoder and a decoder based on self-attention stacked modules. Unlike sequence-to-sequence learning attention, the input source and output target sequences are positionally encoded before being embedded into the encoder and decoder. From a high-level perspective, the Transformer encoder is actually a stack of multiple identical layers, such as... Figure 6 This application employs multi-source heterogeneous data fusion, uniformly encoding the physical variables of the Xin'anjiang hydrological model and the original data in the Transformer embedding layer, and distinguishing data types through positional encoding.
[0069] Multi-head attention, based on the attention mechanism, utilizes the results of parallel computation by multiple attention heads. The specific principle is as follows: Figure 7 As shown, multiple attention heads are used for parallel computation, with each head focusing on different subspace information. At the same time, due to the adoption of parallel computation, the computation method of multi-head attention also changes accordingly, as shown in formula (1).
[0070] … (1) This application uses an attention mechanism to guide the physical aspects of a hydrological model. It introduces a physical correlation weight matrix into the multi-head attention calculation formula, thereby constructing different mask matrices based on physical variables, enabling the model to adjust the attention weights according to different flood tasks.
[0071] In addition, the Transformer architecture also involves two important formulas. Formula (2) is the calculation method of the Feed-Forward Neural Network (FFN), which is used to perform nonlinear transformation on the input features at each location.
[0072] Formula (3) represents residual connections and layer normalization, which are key technologies in the Transformer model used to alleviate the vanishing gradient problem and accelerate model training.
[0073] (3) In summary, the components of Transformer work together to achieve efficient modeling of sequential data. The multi-head attention mechanism captures the dependencies within the sequence, while the feedforward neural network performs non-linear transformations on the features. This design enables the Transformer model to perform well in a variety of deep learning tasks.
[0074] PatchTST utilizes the Patching and Transformer architecture, and also includes channel independence for handling multivariate time series. The architecture is as follows: Figure 8As shown. Through patching operations, the model can extract local semantics by looking at groups of time steps instead of individual time steps. Ordinary PatchTST uses fixed-length blocks, while this application adopts a flood season-oriented design of patching to dynamically divide blocks according to flood response characteristics: the block mode switching is triggered by the soil moisture content change rate output by the Xin'anjiang model. During the dry season, large blocks are used to extract long-term trends, and during the rainy season, small blocks are automatically switched to capture sudden changes in rainfall intensity.
[0075] Furthermore, PatchTST possesses self-supervised learning capabilities. By masking a portion of the data, PatchTST can use self-supervised representation learning to capture the abstract representation of the data. Based on this feature, this application employs self-supervised pre-training for flood pattern extraction. Before formal training, historical flood events are used for pre-training, randomly masking typical flood process lines and requiring the model to reconstruct the masked flood peak intervals. This can potentially improve prediction performance. In summary, since flood prediction typically involves multi-source data, including rainfall, water level, and flow rate, which have different temporal resolutions and characteristics, PatchTST can capture the complex temporal dependencies and has high interpretability, giving it a certain advantage in flood prediction.
[0076] Based on the forecast and measured values from the coupled flood forecasting model, the proposed Xin'anjiang-PatchTST flood forecasting method is comprehensively compared, analyzed and evaluated from multiple dimensions, including Nash efficiency coefficient, flood volume error, flood peak error, and flood arrival time.
[0077] like Figure 9 , Figure 10 As shown, the Xin'anjiang-PatchTST flood forecasting method is trained using flood data from four events: 20160501, 20160527, 20160614, and 20160624. The diagram illustrates the performance of the Xin'anjiang-PatchTST flood forecasting method on the training set.
[0078] According to the hydrological forecast accuracy level table, the Xin'anjiang-PatchTST flood forecasting method achieves Class A accuracy in total runoff error and peak flow error on the training set, with relatively small peak time error, and a comprehensive rating of Class B accuracy.
[0079] like Figure 11 , Figure 12 As shown, the performance of each flood forecasting method was verified using the flood event of April 23, 2018. The experimental results show that the Xin'anjiang-PatchTST flood forecasting method achieves better prediction results than the PatchTST model and the Xin'anjiang model in terms of total runoff error, peak flow error, peak occurrence time error, and coefficient of determination.
Claims
1. A multi-objective flood forecasting method based on the Xin'anjiang model coupled with deep learning, characterized in that, Includes the following steps; Step 1: Use the ArcGIS platform to extract the digital water system and sub-unit boundaries of the target watershed, process the elevation data, and use the Thiessen polygon method to divide the watershed based on the distribution of rainfall stations to obtain the weight coefficients of each rainfall station. Step 2: Systematically collect hydrological data of the target watershed, calculate the watershed surface rainfall based on the weight coefficients of each rain gauge obtained in Step 1, thereby obtaining the hourly average surface rainfall sequence and secondary flood dataset of the target watershed, and divide the dataset into training set and validation set; Step 3: Using the Nash efficiency coefficient (NSE), flood volume coefficient (VE), and flood peak coefficient (PE) as multi-objective functions, the NSGA-II optimization algorithm is used to calibrate the parameters of the Xin'anjiang model with three water sources, generate the Pareto optimal solution set, and select the robust parameter combination. Step 4: Input the physical state variables output by the optimized Xin'anjiang model, the surface average rainfall sequence, and the secondary flood dataset into the PatchTST deep learning model. The Transformer architecture is used to capture the nonlinear relationship between physical state and flow, generate corrected flow, and finally output high-precision forecast results.
2. The multi-objective flood forecasting method based on the Xin'anjiang model coupled with deep learning as described in claim 1, characterized in that, In step 1, the elevation data processing flow begins with the terrain analysis stage. Based on the ArcGIS platform, hydrological analysis is performed using the original elevation data DEM of the watershed. Through depression filling and runoff accumulation calculation, the spatial distribution of the watershed river network is extracted and the boundaries of sub-watersheds are delineated, generating a vector layer with topological relationships. Then, based on the coordinates of the rainfall stations distributed within the region, the control area of each station is divided using the Thiessen polygon method, and the areal rainfall weight matrix is calculated, thereby transforming the discrete station rainfall data into a watershed-scale areal average rainfall sequence.
3. The multi-objective flood forecasting method based on the Xin'anjiang model coupled with deep learning according to claim 2, characterized in that, The Thiessen polygon method calculates the average rainfall based on the rainfall data from discretely distributed rain gauges. It involves connecting all adjacent rain gauges into a triangle, drawing the perpendicular bisectors of each side of the triangle, and then using these perpendicular bisectors to form a polygon around each rain gauge. The rainfall within this polygon is represented by the rainfall from a single rain gauge within that polygon. Finally, the areal average rainfall for the region or watershed is obtained by multiplying the weight coefficients of each polygon in the polygon network by the rainfall data from each rain gauge and summing the results. The formula is as follows: In the formula: The average rainfall over the watershed area; For the first in the basin Weighting coefficients for calculating the polygonal area of each rain gauge station; For the first Rainfall at each rain gauge station during the same period.
4. The multi-objective flood forecasting method based on the Xin'anjiang model coupled with deep learning according to claim 3, characterized in that, The process begins with acquiring DEM elevation data of the study area from a geospatial data cloud platform; First, a terrain analysis is performed on the DEM. By calculating the direction of water flow and identifying closed depressions, it is determined whether there are sinks in the terrain. If sinks exist, a depression filling operation is performed to eliminate depression interference and generate a DEM without depressions. If there is no sink point, the original DEM will be used directly as the basis for subsequent analysis. Subsequently, the flow is calculated based on the corrected DEM, and potential river networks are extracted by setting flow thresholds: the larger the threshold, the sparser the selected channels, and vice versa; after vectorizing the raster river networks that meet the thresholds, the river network topology is enhanced through river linking and hierarchical operations to clarify the river level and connectivity. The length of the water flow is calculated using a DEM without depressions. Combined with manually or automatically captured pouring points, the watershed boundary is generated using a watershed tool, and the final watershed extent is determined using a mask extraction tool. Based on the delineation of the watershed spatial scope and combined with the distribution data of rainfall stations within the watershed, the Thiessen polygon method was used to divide the control area of each rainfall station. Finally, the rainfall observed at each station was weighted and averaged using the proportion of the area of each Thiessen polygon to the total area of the basin, resulting in the areal rainfall distribution that reflects the overall precipitation situation of the basin. The entire process, through multi-step coupling of topographic correction, hydrological simulation and spatial interpolation, realizes the transformation from discrete elevation data to continuous areal precipitation characteristics.
5. The multi-objective flood forecasting method based on the Xin'anjiang model coupled with deep learning according to claim 4, characterized in that, In step 2, data cleaning is first performed to remove outliers, and spatial kriging is used to imput missing rainfall and evaporation data. Based on the obtained continuous areal precipitation characteristics and areal average rainfall sequences, the spatiotemporal distribution characteristics of rainfall, peak flow frequency, and flood duration curves are statistically analyzed. Representative areal average rainfall sequences are then selected and divided into calibration, validation, and testing periods. Finally, the data are compiled according to the standard time series format of the Xin'anjiang model to form a standardized input that can be directly used for model parameter calibration and accuracy verification.
6. The multi-objective flood forecasting method based on the Xin'anjiang model coupled with deep learning according to claim 5, characterized in that, In step 4, the NSGA-II optimized Xin'anjiang physical model is deeply integrated with the PatchTST deep learning model to form a collaborative forecasting framework. NSGA-II serves as the parameter optimization engine, using flood-specific objective functions NSE, VE, and PE to calibrate the parameters of the Xin'anjiang Three-Source Model and generate a Pareto optimal solution set. The specific operating steps of the NSGA-II are as follows: Step 1: Initialize the population N sets of parameters for the Xin'anjiang model are randomly generated, with each set of parameters corresponding to an "individual"; an initial population of size N is formed. , ; Step 2: Based on the parent generation New populations are obtained by performing evolutionary operations such as crossover and mutation. Population size N, explore uncovered regions in the parameter space; and Population merged into In the process, high-quality parameter combinations from history are retained; non-dominated sets are constructed, and cluster distances are calculated. Individuals are then selected from these sets and added to the dataset. In the middle, priority is given to individuals with lower hierarchical levels and larger cluster distances, until... The number of individuals is N, and the optimal parameter sets of NSE, VE, and PE are optimized simultaneously. Step 3: Check if the termination condition is met. If yes, the iteration ends; otherwise, go to Step 2. By incorporating the physical state variables output by the Xin'anjiang model as key inputs to PatchTST, the general PatchTST is transformed into a dedicated engine for flood forecasting.
7. A multi-objective flood forecasting method based on the Xin'anjiang model coupled with deep learning as described in claim 6, characterized in that, In Step 3, the PatchTST time series model is used to couple with the simulated runoff of the Xin'anjiang River; physical state variables are used as feature enhancements, and physical quantities such as simulated runoff and soil moisture content of each layer output by the Xin'anjiang model are used to provide physical constraints on the hydrological process for PatchTST. The Transformer model consists of an encoder and a decoder based on a self-attention stacked module. The input source and output target sequences are encoded with positional codes before being embedded into the encoder and decoder. The Transformer encoder is a stack of multiple identical layers. It adopts multi-source heterogeneous data fusion to uniformly encode the physical variables of the Xin'anjiang hydrological model and the original data in the Transformer embedding layer, and distinguishes the data types through positional codes.
8. A multi-objective flood forecasting method based on the Xin'anjiang model coupled with deep learning as described in claim 7, characterized in that, Based on attention, the results of parallel computation of multiple attention heads are used. Through parallel computation of multiple attention heads, each head focuses on different subspace information. At the same time, parallel computation is adopted, as shown in formula (1). … (1) In the formula: the input matrix includes the query matrix Q, the key matrix K, and the value matrix V; For each attention head (i from 1 to h), a projection is created for each head using three sets of parameter matrices unique to that head. Used for projecting query vectors. Used for projecting key vectors. Used for projecting value vectors; The projected Q, K, and V values are fed into the attention function to calculate the output of the i-th head. Each head works independently, capturing different types of relationships in the input sequence; The output results of all h attention heads … The features are concatenated along the feature dimension to form a large matrix. The concatenated large matrix is then combined with an output projection matrix. Multiply and then perform the final linear projection; Formula (2) is the calculation method of the feedforward neural network, which is used to perform nonlinear transformation on the input features at each position; the input features are the output of the multi-head attention mechanism; In the formula: The feature vector representing the current position; It is the output calculated and processed through self-attention or cross-attention mechanisms; and These are the weight matrices for the first and second fully connected layers, respectively. and These are the bias vectors of the first and second fully connected layers, respectively. This is the definition of the ReLU activation function; it performs a non-linear transformation on the output of the first linear layer, setting values less than 0 to 0. During the calculation process, the input vector First, with the weight matrix Multiply and add bias. This achieves dimensionality upscaling; then, the ReLU activation function is applied to the intermediate results, and the activated results are compared with the weight matrix. Multiply and add bias. To achieve dimensionality reduction transformation; Formula (3) represents residual connections and layer normalization, which are used to alleviate the gradient vanishing problem and accelerate model training; (3) In the formula: This represents a specific sub-layer operation; each Transformer layer typically contains two such sub-layers: an attention sub-layer and a feedforward neural network sub-layer. This is the core operation of residual join; It is a layer normalization operation; The Transformer enables efficient modeling of rainfall sequences from various hydrological stations obtained in step 2 and simulated flow data from the Xin'anjiang model obtained in step 3. The multi-head attention mechanism captures the dependencies within the sequences, while the feedforward neural network performs nonlinear transformations on the features to generate corrected flow, ultimately outputting high-precision forecast results.