Prediction method of time-varying parameters of hydrological model based on ensemble Kalman filter and deep residual network

Abstract

The present invention discloses a method for predicting time-varying parameters of a hydrological model based on an ensemble Kalman filter and a deep residual network, comprising: obtaining multi-source data of a watershed; obtaining historical time series data of time-varying parameters of a hydrological model using an ensemble Kalman filter method; constructing a deep residual network prediction model based on a convolutional neural network; training the model, inputting the acquired hydrological and meteorological data from future climate models into the trained model, and outputting the time-varying parameters of the hydrological model under future scenarios. The present invention solves the problem of obtaining historical data of time-varying parameters of a hydrological model using a data assimilation method, and predicts future changes in the parameters of the hydrological model through a deep residual network and future climate model data, providing a new data-driven method for the dynamic prediction of hydrological model parameters, and providing more powerful technical support for future water resources management and responding to climate change challenges.

Description

Technical Field

[0001] The present invention belongs to the technical field of hydrological prediction, and in particular relates to a method for predicting time-varying parameters of a hydrological model based on ensemble Kalman filtering and a deep residual network. Background Art

[0002] Previous hydrological simulation studies have mostly treated key parameters (such as watershed storage capacity and infiltration rate) as fixed values. However, these parameters are often affected by multiple factors such as climate change, land use change, and human activities, and thus exhibit significant time-varying characteristics. This leads to a decrease in the prediction accuracy of hydrological models when faced with complex and non-stationary hydrological processes. Therefore, obtaining historical data on the time-varying parameters of hydrological models and predicting future trends not only helps improve the accuracy of hydrological simulations but also provides a more scientific and timely basis for decision-making in flood warnings, water resources management, and other areas.

[0003] In order to obtain historical data on the time-varying parameters of hydrological models, many studies have begun to use data assimilation methods, including Kalman filtering. However, traditional Kalman filtering usually assumes that the system is linear or weakly nonlinear, which makes it difficult to cope with complex hydrological processes.

[0004] With the development of artificial intelligence (AI) technology, numerous studies have utilized machine learning and deep learning to solve various problems in hydrology. In the field of future prediction of hydrological data, deep learning algorithms such as convolutional neural networks (CNNs) and long short-term memory networks (LSTMs) offer advantages over traditional statistical methods in solving nonlinear problems. However, deep learning algorithms, such as CNNs, still have certain limitations. For example, they are prone to vanishing gradients when constructing multi-level nonlinear mappings. This restricts the application of deep network structures and prevents the full realization of deep learning's advantages in complex pattern recognition. Summary of the Invention

[0005] The purpose of the present invention is to provide a method for predicting time-varying parameters of hydrological models based on ensemble Kalman filtering and deep residual networks, so as to solve the technical problems in the prior art that hydrological model parameters cannot be effectively obtained using observation data and future data trends cannot be reasonably predicted under the background of climate change.

[0006] In order to solve the above technical problems, the present invention adopts the following solutions:

[0007] The method for predicting time-varying parameters of a hydrological model based on an ensemble Kalman filter and a deep residual network includes the following steps:

[0008] Step S1: Obtain multi-source data: Integrate multi-dimensional and multi-source data as input information for subsequent model construction and parameter calibration.

[0009] Step S2: Utilize the Ensemble Kalman Filter (ENKF) method to obtain historical time series data for the time-varying parameters of the hydrological model. Ensemble Kalman Filtering effectively handles nonlinearities in the system by sampling state uncertainty, ensuring high estimation accuracy even in nonlinear scenarios. Furthermore, the dynamic data assimilation process of the ENKF method continuously adjusts the hydrological model parameters, capturing the system's time-varying characteristics and thus improving the accuracy of model predictions. Traditional methods often lack this real-time update mechanism.

[0010] Step S3: Build a prediction model based on a combination of a convolutional neural network and a deep residual network. This model extracts local features from the input data and captures global features through multi-level processing, thereby capturing the complex nonlinear relationships between multi-source data and the time-varying parameters of the hydrological model. The deep residual network (ResNet) can automatically extract local features from the input data and capture complex nonlinear relationships through multi-layer convolution and pooling operations. In particular, it can address degradation issues by making it easier for gradients to flow into the external network.

[0011] Step S4: The hydrological data and meteorological data obtained in step S1 and the time-varying parameters of the text model constructed in step S2 are combined into a historical time series data set in chronological order, and the data set is divided into a training set and a test set in a ratio of 7:3. The mean square error (MSE) is used as the loss function, and the deep residual network model constructed in step S3 is trained using the training set. The trained model is verified using the validation set, and the target optimization is performed using the mean square loss function to determine the coefficient R 2 To evaluate the metric, the trained prediction model is evaluated.

[0012] Step S5: Input the multi-source hydrological and meteorological data obtained from the future climate model into the trained prediction model, and output the time-varying parameters of the hydrological model under the future scenario.

[0013] Further optimization, the data obtained in step S1 includes historical meteorological data, soil data, land use data, terrain data, runoff observation and runoff characteristic data obtained through meteorological data products.

[0014] Further optimization, the step S2 specifically includes:

[0015] Step S2.1: Set the state variables as the time-varying parameters of the hydrological model and the observation variables as the input data obtained in step S1, and construct the state transfer equation containing process noise and the observation equation containing observation error:

[0016] State transition equation: (1);

[0017] Observation equation: (2);

[0018] In the above formula, is the state variable predicted based on the time-varying parameters of the hydrological model at the current moment; C t-1 is the time-varying parameter value of the hydrological model at the previous moment; f () is a nonlinear function that describes the evolution of state variables; is the process noise vector, which represents the random changes of state variables caused by various uncertain factors between time steps (t-1) and t; y t is the observed variable obtained at the current moment, H () is the observation operator that maps state variables to the observation space and describes the observation variables; v t is the observation error vector at the current moment, which represents the random change of the observation variable due to measurement error.

[0019] Step S2.2: Initialize the background field and predict the state value at the next moment, specifically including:

[0020] Step S2.2.1: Set an initial state value based on prior knowledge or historical data as the basis for subsequent updated predictions.

[0021] Step S2.2.2: Combine the predicted state and the new observation data and use the Kalman gain to update the hydrological model parameter state:

[0022] (3);

[0023] In the above formula, C t is the time-varying parameter value of the hydrological model at the current moment after update; K is a weight factor used to determine the influence of observation data on state correction during the update process; y t is the observation data obtained at the current moment.

[0024] Further optimization, the step S3 specifically includes:

[0025] Step S3.1: The hydrological data and meteorological data at time t obtained in step S1 and the time-varying parameter values ​​of the hydrological model at time t obtained in step S2 are concatenated according to the dimensionality requirements to form the input vector of the prediction model:

[0026] (4);

[0027] In the above formula, represents the input vector at time t;H(t) 、 M(t) 、 C(t) They represent hydrological data, meteorological data, and time-varying parameter values ​​of the hydrological model respectively.

[0028] Step S3.2: Input the input vector into the convolutional neural network and convert it into an initial input feature map suitable for the convolution operation. The convolution kernel is used to slide on the input feature map to perform the convolution operation. Multiple convolution kernels operate in parallel to extract multiple local features of the input data at the same time. After the convolution operation is completed, the bias term is added to the convolution result, which is then used as the input of the activation function. After the activation function is processed, a new feature map is obtained. The expression is:

[0029] (5);

[0030] In the above formula, After convolution, bias adjustment and nonlinear activation, l The feature map output by the layer will be used as the input of the next layer (if any) , continue to participate in the feature extraction process of the network; It is an activation function that enables the model to better fit complex nonlinear relationships; For the l Layer convolution kernel weight, the convolution kernel is passed through the input feature map Slide up and perform convolution operation to extract local feature patterns in the input data. Represents convolution operation; different W (l) The value determines the type of features captured by the convolution kernel, such as edges, textures, etc. Indicates the l− The output feature map of layer 1 contains the data features extracted by the previous layers; For the l The bias term of the layer offsets the result of the convolution operation, increases the fitting ability of the model, avoids all outputs being concentrated near the origin, and enables the model to better learn data features.

[0031] Then, the feature map output by the convolutional layer is input to the pooling layer. The pooling layer uses the pooling function Pool() to downsample the feature map and extract the maximum value in the local area, which is expressed as:

[0032] (6);

[0033] In the above formula, Pool(⋅) is a pooling function used to downsample the feature map output by the convolutional layer.

[0034] Step S3.3 uses residual connections to build a deep residual network: To build a deep network and avoid the vanishing gradient problem, residual connections are used in each residual module. Specifically, in the first residual module, the initial input feature map and the feature map obtained after processing in step S3.2 are directly added as the output of the residual module; multiple residual modules are stacked in sequence, and the output of the previous residual module serves as the input of the next residual module; through multi-layer residual calculation, the entire deep residual network is expressed as:

[0035] (7);

[0036] In the above formula, is the residual function of the entire deep residual network, reflecting the initial input feature map Extract feature information from all levels passed through to the final output; It is the set of all parameters to be learned in the model, including the convolution kernels and biases of each layer in all residual modules. These parameters are continuously adjusted during the training process of the network so that the residual function can better fit the data. L is the total number of residual modules, that is, the number of layers in the network, l ∈[1, L ]; is the output feature map after processing by L residual modules, and is the final feature representation of the initial input feature map after multi-layer convolution, activation, and pooling operations.

[0037] Step S3.4: The original historical time series data of the time-varying parameters of the hydrological model C(t) Combined with the residual information learned from the deep residual network, the time-varying parameters of the hydrological model at future moments are predicted, which can be expressed as:

[0038] (8);

[0039] In the above formula, is the predicted value of the time-varying parameters of the hydrological model at future moments.

[0040] Through this step, the historical time series data of the time-varying parameters of the hydrological model C(t) On the basis of the deep residual network, the residuals learned from the current hydrological and meteorological data are used to calibrate and predict the future parameters of the hydrological model. For example, if the historical time series data of the time-varying parameters of the hydrological model represent the current water storage capacity of the basin, the residuals By capturing the nonlinear impact of current meteorological data such as precipitation and temperature on water storage capacity, the two can be added together to obtain the predicted value of water storage capacity at future times.

[0041] Compared with the prior art, the present invention has the following beneficial effects:

[0042] 1. The present invention uses a data assimilation method that combines integrated Kalman filtering with a hydrological model to construct a historical time series data of hydrological model parameters based on observation data correction. This process effectively integrates multi-source data such as water level, meteorology, and underlying surface to obtain historical data that is closer to the actual value, thus compensating for the uncertainty of a single model.

[0043] 2. The prediction model designed by the present invention, which is based on a combination of convolutional neural networks and deep residual networks, captures the complex nonlinear relationship between various natural conditions such as hydrology and meteorology and the parameters of the hydrological model. The use of residual connections effectively alleviates the gradient vanishing problem, allowing the model layers to be deeper, thereby improving the expressive power.

[0044] 3. The deep residual network model described in this invention can use the current state as a basis to correct future trends in hydrological model parameters through learning residuals, provided by future climate models providing hydrological and meteorological data. This provides a new data-driven approach for the dynamic prediction of future hydrological model parameters, thereby providing stronger technical support for future water resources management and addressing climate change challenges. BRIEF DESCRIPTION OF THE DRAWINGS

[0045] Figure 1 This is a flow chart of the method for predicting time-varying parameters of a hydrological model based on ensemble Kalman filtering and deep residual network according to the present invention;

[0046] Figure 2 Schematic diagram of the deep residual neural network model of the present invention;

[0047] Figure 3 The time-varying trends of water storage capacity in different continents under future scenarios;

[0048] Figure 4 The temporal trends of water storage capacity in different climate zones under future scenarios. DETAILED DESCRIPTION

[0049] The technical solution of the present invention is described in detail below with reference to the embodiments, but the protection scope of the present invention is not limited to the embodiments.

[0050] In this embodiment, calculation and analysis are performed on a total of 2,683 river basins worldwide.

[0051] like Figure 1 As shown in FIG, the method for predicting time-varying parameters of a hydrological model based on an ensemble Kalman filter and a deep residual network specifically includes the following steps:

[0052] Step S1: Obtain multi-source data on global watersheds required for calculation. The data used in this embodiment includes global-scale historical meteorological data, soil data, land use data, topographic data, runoff observations and runoff characteristics data obtained through meteorological products, and future hydrological and meteorological data obtained through climate models.

[0053] All data use a spatial resolution of 0.5°. Given the different temporal and spatial spans of different data sources, the time span of all historical data selected is 1980-2015. Specific data and sources can be found in Table 1:

[0054] Table 1 Data types and sources obtained

[0055] ;

[0056] In addition, a total of 20 climate models are selected in this example to predict future climate information. All data are from the Sixth Coupled Model Intercomparison Project (CMIP6). The data cover the historical period (1970-2014), the near future period (2015-2059), and the far future period (2060-2100). The future climate models are shown in Table 2.

[0057] Table 2 Climate model

[0058] ;

[0059] Step S2: Using the ensemble Kalman filter method, construct the historical time series data of the time-varying parameters of the hydrological model.

[0060] In this embodiment, the basin water storage capacity (CWSC) is used as the target parameter of the hydrological model. At the beginning of the calculation, a water storage capacity value is randomly assigned to each basin. After that, the parameters are identified using the ensemble Kalman filter algorithm, and the hydrological model parameters and state variables are updated simultaneously. Specifically, it can be expressed as:

[0061] Step S2.1: Based on the hydrological model, the prediction process of the ensemble Kalman filter algorithm is expressed by the following equation:

[0062] (9);

[0063] In the above formula, is the CWSC value predicted based on the time-varying parameters of the hydrological model at the current moment; C t-1 is the CWSC value of the hydrological model at the previous moment; f () is a nonlinear function that describes the evolution of state variables; is the process noise, which represents the state change caused by internal or external uncertainty of the system.

[0064] Step S2.2: Initialize the background field and predict the state value at the next moment, specifically including:

[0065] Step S2.2.1: Set an initial state value based on prior knowledge or historical data as the basis for subsequent predictions.

[0066] Step S2.2.2: Combine the predicted state and the new observation data and use the Kalman gain to update the hydrological model parameter state:

[0067] (10);

[0068] In the above formula, C t is the CWSC value of the hydrological model at the current moment after update; K is a weight factor used to determine the influence of observation data on state correction during the update process; y t The actual observation data obtained at the current moment, in this case, the historical observation data of hydrology, meteorology, and underlying surface; H is a mapping operator used to map CWSC to the observation space.

[0069] In this embodiment, the above calculations are used to obtain the global watershed water storage capacity (CWSC) values ​​from 1980 to 2015. The watershed water storage capacity values ​​for the grid at 23.75°N and 31.25°E are shown in Table 3.

[0070] Table 3 CWSC values ​​of the basin at 23.75°N and 31.25°E from 1980 to 2015

[0071] ;

[0072] Step S3: Construct a prediction model based on the combination of convolutional neural network (CNN) and deep residual network (Deep Residual Network, ResNet). The entire network structure can not only extract local features in the input data, but also capture global features through multi-level processing, and then establish a fine mapping relationship. The schematic diagram of the deep residual network model structure is shown in the figure. Figure 2 The specific steps are as follows:

[0073] Step 3.1: Combine the hydrological and meteorological data obtained in step 1 and the time series data of the watershed storage capacity parameters in step 2 to form the input vector of the model, which is expressed as:

[0074] (11);

[0075] In the above formula, represents the input vector at time t; H(t) 、 M(t) 、 C(t) Represents the historical time series data of hydrology, meteorology and water storage capacity respectively.

[0076] Step 3.2: Input the input vector into the convolutional neural network and convert it into an initial input feature map suitable for convolution operation. The convolution kernel is used to slide on the input feature map to perform convolution operation. Multiple convolution kernels operate in parallel to extract multiple local features of the input data at the same time. After the convolution operation is completed, the bias term is added to the convolution result, which is then used as the input of the activation function. After the activation function is processed, a new feature map is obtained, which is:

[0077] (12);

[0078] In the above formula, After convolution, bias adjustment and nonlinear activation, l The feature map output by the layer will be used as the input of the next layer (if any) , continue to participate in the feature extraction process of the network; It is an activation function that enables the model to better fit complex nonlinear relationships; For the l Layer convolution kernel weight, the convolution kernel is passed through the input feature map Slide up to perform convolution operation to extract local feature patterns in the input data. The symbol * represents convolution operation. W (l) The value determines the type of features captured by the convolution kernel, such as edges, textures, etc. To indicate the l− The output feature map of layer 1 contains various data features extracted by previous layers; For the l The bias term of the layer offsets the result of the convolution operation, increases the fitting ability of the model, avoids all outputs being concentrated near the origin, and enables the model to better learn data features.

[0079] Then, the feature map output by the convolutional layer is input to the pooling layer, and the pooling layer uses the pooling function Pool() to downsample the feature map and extract the maximum value in the local area.

[0080] Step S3.3 uses residual connections to build a deep residual network: To build a deep network and avoid the vanishing gradient problem, residual connections are used in each residual module. Specifically, in a residual module, the initial input feature map and the feature map obtained after processing in step S3.2 are directly added as the output of the residual module; multiple residual modules are stacked in sequence, and the output of the previous residual module serves as the input of the next residual module; through multi-layer residual calculation, the entire deep residual network is expressed as:

[0081] (13);

[0082] In the above formula, The residual function learned by the entire deep residual network reflects the feature information extracted from all levels from input to final output; is the set of all parameters to be learned in the model, including the convolution kernels and biases of each layer in all residual modules; L is the total number of residual modules, that is, the number of layers in the network, l ∈[1, L ], is the output feature map after processing by L residual modules, and is the final feature representation of the initial input feature map after multi-layer convolution, activation, and pooling operations.

[0083] Step S3.4: The original historical time series data of the time-varying parameters of the hydrological model C(t) Combined with the residual information learned from the deep residual network, the time-varying parameters of the hydrological model at future moments are predicted, which can be expressed as:

[0084] (14);

[0085] In the above formula, is the predicted value of the time-varying parameters of the hydrological model at future moments.

[0086] Step S4: The hydrological data and meteorological data obtained in step S1, as well as the time-varying parameters of the hydrological model constructed in step S2, are combined into a historical time series data set in chronological order, and the data set is divided into a training set and a test set in a ratio of 7:3. The deep residual network model constructed in step S3 is trained using the training set with the mean square error (MSE) as the loss function, and the trained model is verified using the validation set. The mean square loss function is used for target optimization to determine the coefficient R 2 is the evaluation indicator.

[0087] In this embodiment, the determination coefficient R of the final training model between the training set and the test set is 2 They are 0.9291 and 0.8273 respectively. The model performance is good and meets the simulation and prediction requirements.

[0088] Step S5: Input the hydrological and meteorological data in the future climate model obtained in step S1 into the trained network model, and output the predicted value of the watershed water storage capacity of the time-varying parameters of the hydrological model under the future scenario.

[0089] In this example, the global river basin water storage capacity is calculated and predicted, and the distribution of global river basin water storage capacity under the SSP2-4.5 and SSP5-8.5 emission scenarios for many years in the future (2015-2100) is finally obtained; among which SSP2-4.5 represents a moderate greenhouse gas emission scenario and SSP5-8.5 represents a very high greenhouse gas emission scenario.

[0090] Overall, significant differences in river basin water storage capacity exist across continents and regions, reflecting the combined influence of climate, topography, vegetation, and other factors on water storage. River basin water storage capacity is relatively high in the Americas (particularly the Amazon Basin in South America), Central Africa, and Southeast and Southern Asia. In contrast, arid and semi-arid regions, such as the Sahara Desert in northern Africa and inland areas of Central Asia, have lower water storage capacity. This is because humid regions, with abundant rainfall and good vegetation cover, favor water storage, while arid regions, with scarce rainfall and high evaporation, struggle to retain water.

[0091] Furthermore, under the SSP2-4.5 scenario, changes in the global hydrological system are relatively mild, and changes in the distribution of water storage capacity in river basins are somewhat predictable and adaptable. However, under the SSP5-8.5 scenario, more dramatic climate change is expected. High radiative forcing will lead to instability in the climate system, altering precipitation patterns and making changes in the distribution of water storage capacity in river basins more complex. Sudden increases and decreases in water storage capacity in some regions, and frequent alternations between droughts and floods are possible, posing greater challenges to regional water resource management and ecosystem stability.

[0092] Figure 3 is the time-varying trend line of water storage capacity of different continents under future scenarios; Figure 3 Panels (a), (b), (c), (d), (e), and (f) show the time-varying trend lines of water storage capacity for Asia, Africa, Oceania, Europe, North America, and South America, respectively. In the figure, AWI-SSP245 represents the water storage capacity of river basins on different continents predicted under a moderate greenhouse gas emissions scenario using the AWI-CM-1-1-MR climate model developed by the Helmholtz Centre for Ocean Research Kiel in Germany; AWI-SSP585 represents the water storage capacity of river basins on different continents predicted under a very high greenhouse gas emissions scenario using the AWI-CM-1-1-MR climate model developed by the Helmholtz Centre for Ocean Research Kiel in Germany. MPI-SSP245 represents the predicted water storage capacity of river basins in different continents under a moderate greenhouse gas emissions scenario using the AWI-CM-1-1-MR climate model developed by the Max Planck Institute for Meteorology in Germany; MPI-SSP585 represents the predicted water storage capacity of river basins in different continents under a very high greenhouse gas emissions scenario using the AWI-CM-1-1-MR climate model developed by the Max Planck Institute for Meteorology in Germany.

[0093] Figure 4 The time-varying trend line of water storage capacity in different climate zones around the world under future scenarios. Figure 4 Panels (a), (b), (c), (d), (e), and (f) show the temporal trends in water storage capacity for the global, temperate, equatorial, arid, inland, and polar regions, respectively. This analysis reveals the impact of climate change on the global hydrological system through spatial distribution, regional differences, and temporal trends, providing multi-scale support for scientific research, policy development, and water resources management.

[0094] The above is merely an example of the implementation of the present invention in a specific river basin, but the scope of protection of the present invention is not limited thereto. If a person skilled in the art is inspired by the above and designs methods and embodiments similar to the technical solution without inventive means without departing from the inventive purpose of the present invention, they shall fall within the scope of protection of the present invention.

Claims

1. A method for predicting time-varying parameters of hydrological models based on ensemble Kalman filtering and deep residual networks, characterized by: The steps include: Step S1: Obtain multi-source data of the watershed and integrate multi-dimensional and multi-source data as input information for subsequent model construction and parameter calibration; multi-source data includes historical meteorological data, soil data, land use data, topographic data, runoff observation and runoff characteristic data obtained through meteorological data products; Step S2: using the ensemble Kalman filter method to obtain historical time series data of the time-varying parameters of the hydrological model; Step S3: Construct a prediction model based on a combination of convolutional neural networks and deep residual networks. This prediction model extracts local features from the input data and captures global features through multi-level processing, thereby obtaining the complex nonlinear relationship between multi-source data and historical time series data of time-varying parameters of the hydrological model. Step S4: The data obtained in step S1 and the historical time series data of the time-varying parameters of the hydrological model constructed in step S2 are combined into a historical time series data set in chronological order, and the data set is divided into a training set and a test set in a ratio of 7:3; the prediction model constructed in step S3 is trained using the training set, and the trained prediction model is verified using the verification set. The target optimization is performed using the mean square error (MSE) as the loss function to determine the coefficient R 2 Evaluate the trained prediction model for the evaluation metrics; Step S5: Input the multi-source hydrological and meteorological data obtained from the future climate model into the trained prediction model, and output the time-varying parameters of the hydrological model under the future scenario.

2. The method for predicting time-varying parameters of a hydrological model based on an ensemble Kalman filter and a deep residual network according to claim 1 is characterized in that: The step S2 specifically includes: Step S2.1: Set the state variables as the time-varying parameters of the hydrological model and the observation variables as the input data obtained in step S1, and construct the state transfer equation containing process noise and the observation equation containing observation error: State transition equation: (1); Observation equation: (2); In the above formula, is the state variable predicted based on the time-varying parameters of the hydrological model at the current moment; C t-1 is the time-varying parameter value of the hydrological model at the previous moment; f () is a nonlinear function that describes the evolution of state variables; is the process noise vector, which represents the random changes of state variables caused by various uncertain factors between time steps (t-1) and t; y t is the observed variable obtained at the current moment, H () is the observation operator that maps state variables to the observation space and describes the observation variables; v t is the observation error vector at the current moment, which represents the random change of the observation variable due to measurement error; Step S2.2: Initialize the background field and predict the state value at the next moment, specifically including: Step S2.2.1: Set an initial state value based on prior knowledge or historical data as the basis for subsequent predictions; Step S2.2.2: Combine the predicted state and the new observation data and use the Kalman gain to update the hydrological model parameter state, which is expressed as: （3）； In the above formula, C t is the time-varying parameter value of the hydrological model at the current moment after update; K is a weight factor used to determine the influence of observation data on state correction during the update process; y t is the observation data obtained at the current moment.

3. The method for predicting time-varying parameters of a hydrological model based on an ensemble Kalman filter and a deep residual network according to claim 2 is characterized in that: The step S3 specifically includes: Step S3.1: The hydrological data and meteorological data at time t obtained in step S1 and the time-varying parameter values ​​of the hydrological model at time t obtained in step S2 are concatenated according to the dimensionality requirements to form the input vector of the prediction model: （4）； In the above formula, represents the input vector at time t; H(t) 、 M(t) 、 C(t) They represent hydrological data, meteorological data, and time-varying parameter values ​​of hydrological models respectively; Step S3.2: Input the input vector into the convolutional neural network and convert it into an initial input feature map suitable for the convolution operation. The convolution kernel is used to slide on the input feature map to perform the convolution operation. Multiple convolution kernels operate in parallel to extract multiple local features of the input data at the same time. After the convolution operation is completed, the bias term is added to the convolution result, which is then used as the input of the activation function. After the activation function is processed, a new feature map is obtained. The expression is: （5）； In the above formula, After convolution, bias adjustment and nonlinear activation, l Feature map of layer output; is the activation function; For the l Layer convolution kernel weights; Indicates the l− Output feature map of layer 1; Represents the convolution operation; For the l The bias term of the layer; Then, the feature map output by the convolution layer is input to the pooling layer, and the pooling function Pool() is used to downsample the feature map and extract the maximum value in the local area, which is expressed as: （6）； In the above formula, Pool(⋅) is a pooling function used to downsample the feature map output by the convolutional layer; Step S3.3 uses residual connections to construct a deep residual network: in the residual module, the initial input feature map and the feature map obtained after processing in step S3.2 are directly added as the output of the first residual module; multiple residual modules are stacked in sequence, and the output of the previous residual module is used as the input of the next residual module. Through multi-layer residual calculation, the entire deep residual network is obtained, which is expressed as: （7）； In the above formula, is the residual function of the entire deep residual network, reflecting the initial input feature map Extract feature information from all levels passed through to the final output; is the set of all parameters to be learned in the model, including the convolution kernels and biases of each layer in all residual modules; L is the total number of residual modules, that is, the number of layers in the network, l ∈[1, L ]; is the output feature map after processing by L residual modules, which is the final feature representation of the initial input feature map after multi-layer convolution, activation and pooling operations; Step S3.4: The original historical time series data of the time-varying parameters of the hydrological model C(t) Combined with the residual information learned from the deep residual network, the time-varying parameters of the hydrological model at future moments are predicted, which can be expressed as: （8）； In the above formula, is the predicted value of the time-varying parameters of the hydrological model at future moments.

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