Distributed hydrological model parameter calibration method based on deep neural network surrogate model

Abstract

This invention belongs to the field of distributed hydrological technology, specifically relating to a method for calibrating parameters of a distributed hydrological model based on a deep neural network substitution model. The method includes: collecting meteorological and geographic information to generate the meteorological and geographic data required for the distributed hydrological model; introducing a multi-scale parameter regionalization method to correlate geophysical feature data with the parameters of the distributed hydrological model through a transfer function; running the distributed hydrological model for simulation to generate corresponding simulated values ​​as sample data; constructing a deep neural network substitution model to approximate the input-output relationship of the distributed hydrological model and training it using the simulated sample data; and using the SCE-UA optimization algorithm to optimize the parameters on the neural network substitution model, where the parameters to be optimized are the coefficients of the transfer function. This invention significantly improves the efficiency and accuracy of distributed hydrological model parameter calibration, providing important technical reference for parameter estimation in areas with no or insufficient data.

Description

Technical Field

[0001] This invention belongs to the field of distributed hydrological technology, specifically relating to a method for calibrating parameters of a distributed hydrological model based on a deep neural network substitution model. Background Technology

[0002] Distributed hydrological models can effectively utilize data such as remote sensing and geographic information to reasonably characterize the spatial heterogeneity of inputs and outputs, giving them unique advantages in studying the impact of human activities and natural environmental changes on the watershed hydrological cycle. However, the complex structure and high parameter dimensionality of distributed hydrological models make parameter calibration a significant challenge.

[0003] Traditionally, parameter calibration relies primarily on local or global optimization algorithms, with Shuffled Complex Evolution (SCE-UA) being one of the most commonly used global optimization methods. SCE-UA simulates biological evolution, utilizing multiple complexes to perform a global search in a high-dimensional parameter space, and gradually converges to the optimal solution through crossover and selection mechanisms. However, despite its excellent global search capabilities, SCE-UA's application in distributed hydrological models remains limited. The search mechanism of SCE-UA is complex, typically requiring thousands of runs of the original physical model, resulting in a massive computational load. Secondly, SCE-UA's convergence speed is slow. Although it possesses global search capabilities, in a high-dimensional parameter space, search efficiency decreases with increasing dimensionality, leading to a slow parameter optimization process and further exacerbating the computational bottleneck in calibrating complex distributed hydrological models. Simultaneously, the performance of the SCE-UA algorithm depends to some extent on the selection of initial parameters, such as the size and number of the initial population and the adjustment strategies during the evolutionary process. The appropriateness of these parameter settings directly affects the algorithm's convergence speed and optimization effect.

[0004] To reduce computational burden, optimization algorithms based on statistical surrogate models are widely adopted. These methods primarily rely on shallow surrogate models, such as multinomial regression, random forests, and Gaussian process regression, to approximate the response surface between the objective function and model parameters. Combining classical optimization algorithms with statistical surrogate models and introducing adaptive update mechanisms can achieve better optimization results with lower computational costs. Examples include ASMO (Adaptive Surrogate Modeling-based Optimization) for single-objective optimization, MO-ASMO (Multi-objective ASMO) for multi-objective optimization, and ASMO-PODE (ASMO-parameter optimization and distribution estimation) for posterior distribution estimation. Among them, ASMO, developed by Wang et al., is a global optimization method based on an adaptive surrogate model. It updates the surrogate model by adaptively sampling new points, thereby gradually approaching the optimal solution of the physical model during the optimization process. Compared to SCE-UA, ASMO has lower computational costs because the computational cost of the statistical surrogate model is much lower than that of the physical model, thus reducing the number of calls to the original model and improving optimization efficiency.

[0005] Although existing optimization methods based on alternative models have reduced computational costs and improved optimization efficiency to some extent, they still have the following significant drawbacks: traditional statistical alternative models have poor accuracy when used to construct high-dimensional mapping relationships, and their computational efficiency is significantly reduced; in addition, the way of constructing statistical relationships between model parameters and objective functions lacks flexibility, and when the objective function or the simulated year changes, the entire optimization process needs to be re-executed, resulting in a large computational burden.

[0006] In recent years, deep learning models have been widely used in the field of hydrology. By increasing network depth and applying nonlinear activation functions, deep learning models have significantly improved their ability to approximate high-dimensional nonlinear mappings. Due to their differentiability, deep learning models can serve as alternative models, mimicking the operating mechanism of the original physical models and thus completely replacing their input-output relationships. However, current research on parameter calibration of alternative models based on deep neural networks is still relatively limited, and their application potential in distributed hydrological models has not yet been fully explored. Summary of the Invention

[0007] Objective: This invention proposes a parameter calibration method for distributed hydrological models based on deep neural network substitution models. It combines the SCE-UA parameter calibration method to optimize the parameters of the distributed hydrological model VIC. Simultaneously, it introduces a multi-scale parameter regionalization (MPR) method to further reduce parameter dimensionality and ensure spatial continuity. This method not only significantly improves the efficiency and accuracy of distributed hydrological model parameter calibration but also provides important technical reference for parameter calibration in data-free or data-scarce areas.

[0008] Technical solution: The distributed hydrological model parameter calibration method based on a deep neural network substitution model described in this invention includes the following steps: S1: Collect meteorological data for the study area; S2: Collect geographical, soil, and vegetation data for the study area; S3: Construct a distributed hydrological model and determine the target variables and calibration parameters; S4: Collect geophysical feature data of the study area, associate the geophysical feature data with the calibration parameters of the distributed hydrological model through the transfer function, introduce a multi-scale parameter regionalization method to optimize the coefficients in the transfer function and generate a calibration parameter sample set; S5: Run the distributed hydrological model, use the collected data from the study area to simulate the target variable, and generate the corresponding simulated values; S6: Construct a deep neural network alternative model to simulate the input-output relationship of the distributed hydrological model. The meteorological data and calibration parameter sample set are used as inputs, and the simulated values ​​of the distributed hydrological model are used as outputs to train the deep neural network alternative model. S7: Use the SCE-UA algorithm to optimize the parameters of the deep neural network replacement model, wherein the objective function of the SCE-UA algorithm is the root mean square error between the simulated value and the measured value of the deep neural network replacement model output, and the parameters to be optimized are the coefficients of the transfer function; S8: Returns the optimized transfer function coefficients and calculates the optimized calibration parameters.

[0009] To further improve the above technical solution, the distributed hydrological model is a variable permeability model, and the meteorological data includes precipitation, air temperature, atmospheric pressure, incident shortwave radiation, incident longwave radiation, vapor pressure, and wind speed. A meteorological forced variable file is created to improve the temporal and spatial resolution of the meteorological data.

[0010] Furthermore, the parameters to be calibrated include the variable infiltration curve parameter B, the maximum baseflow velocity Ds, the maximum baseflow velocity fraction Dm at the start of the nonlinear baseflow, the maximum soil moisture fraction Ws at the occurrence of the nonlinear baseflow, the thickness of the second soil layer D2, the thickness of the third soil layer D3, and the drainage parameter E2 of the second soil layer.

[0011] Furthermore, the transfer function of parameter B in the variable infiltration curve is: ; The transfer function of the maximum base current velocity Ds is: ; The transfer function of the maximum base current velocity fraction Dm at the beginning of the nonlinear base current is: ; The transfer function of the maximum soil moisture fraction Ws at the location where the nonlinear baseflow occurs is: ; The transfer function for the thickness D2 of the second soil layer is: ; The transfer function of the thickness D3 of the third soil layer is: ; The transfer function for the drainage parameter E2 of the second soil layer is: ; in, These are global parameters; These are the transfer function coefficients; This refers to the standard elevation deviation; The field water content of the sub-grid; This represents the saturated soil moisture content. This represents the proportion of grid areas where the soil moisture content reaches saturation when the average soil moisture content is Wf. For Brooks–Corey equation parameters; The saturated hydraulic conductivity of the soil; Soil pore size distribution parameters; This refers to the soil layer thickness parameter.

[0012] Furthermore, the geophysical characteristic data are derived from the China Soil Hydraulic Parameter Dataset and the China Surface Simulation Soil Database.

[0013] Furthermore, the multi-scale parameter regionalization method includes the following steps: determining the form of the transfer function; reading the geophysical feature data; generating multiple sets of transfer function coefficients using the Latin hypercube sampling method; restricting the generated multiple sets of transfer function coefficients to ensure their physical rationality; converting the restricted parameter values ​​into units required by the model; and returning the optimized transfer function coefficients, and obtaining calibration parameters through transfer function calculation.

[0014] Furthermore, the deep neural network replacement model is an LSTM neural network model, and the model construction includes the following steps: generating a calibration parameter sample set using the multi-scale parameter regionalization method; running the distributed hydrological model based on each set of calibration parameter samples to obtain the simulation results of the target variable; using the collected meteorological data and calibration parameter samples as input to the LSTM neural network model, and taking the simulated value of the target variable output by the distributed hydrological model as the output; dividing the input and output sample sets into training datasets, validation datasets, and test datasets; setting the hyperparameters of the LSTM neural network model, and performing model training, validation, and testing.

[0015] Furthermore, the input and output sample sets are divided into training dataset, validation dataset, and test dataset in a 4:2:1 ratio. The input-output data at each grid point is used as a set of training samples. The input of each set of training samples includes 30 days of meteorological data and model calibration parameters. The target value is the simulated value of the target variable output by the distributed hydrological model on the 30th day. Each grid cell contains data for a two-year period.

[0016] Furthermore, the hyperparameters of the LSTM neural network model include: number of memory units: 128; training batch size: 400; maximum training epochs: 200; learning rate: 0.0001; hidden layers: 128; sequence length: 7; loss function: root mean square error.

[0017] Furthermore, the parameter optimization steps of the SCE-UA algorithm include: defining the objective function as the root mean square error between the simulated and measured values ​​output by the LSTM neural network model; determining the parameters to be optimized as the transfer function coefficients; setting the number of subpopulations, the number of individuals in each subpopulation, the total number of individuals, the maximum number of function calls, and convergence check parameters; generating an initial population through random sampling and calculating the objective function value of the initial population; sorting the population according to the objective function value and recording the optimal solution; dividing the population into multiple subpopulations and evolving each subpopulation; shuffling the subpopulations to form a new population; performing a convergence check, and stopping the optimization if the convergence condition is met; and returning the optimal transfer function coefficients and their corresponding minimum root mean square error.

[0018] Beneficial Effects: Compared with existing technologies, the advantages of this invention are as follows: The distributed hydrological model parameter calibration method based on a deep neural network substitution model proposed in this invention, combined with the SCE-UA parameter calibration method, achieves efficient, accurate, and universal parameter optimization of the distributed hydrological model VIC, providing new ideas and technical support for watershed hydrological simulation. The LSTM neural network model can effectively replace the complex VIC physical model, significantly reducing the computational burden. Compared with traditional statistical substitution models, it is more flexible and accurate, demonstrating significant advantages in handling high-dimensional nonlinear mapping relationships. Multi-scale parameter regionalization (MPR) establishes physical constraints between geographic attributes and model parameters, ensuring spatial continuity, significantly reducing parameter dimensionality, and ensuring the spatial continuity and heterogeneity of the parameter field. Combined with remote sensing hydrological element data as the calibration target, it not only reduces the limitations of calibration relying solely on runoff data but also improves the model's applicability in data-scarce regions.

[0019] This invention significantly improves simulation accuracy and computational efficiency. Simultaneously, the method provides reliable technical support for parameter calibration in areas with no or insufficient data, possessing significant application value in scientific research, engineering practice, and economic benefits. By combining an LSTM neural network model, the SCE-UA optimization method, and MPR parameter regionalization technology, this invention significantly improves the efficiency, accuracy, and applicability of parameter calibration for distributed hydrological models, exhibiting significant technical advantages and socio-economic value. (1) Efficiency improvement: The LSTM neural network model combined with the SCE-UA optimization method significantly reduces the computational load of parameter calibration, avoids the high cost problem of running the physical model thousands of times in traditional methods, and greatly reduces the computation time and resource consumption. The LSTM alternative model has unique advantages in capturing the complex nonlinear characteristics of hydrological models. Its network depth can be increased and its nonlinear activation function can approximate complex mapping relationships, adapting to multidimensional nonlinear characteristics; the memory gating mechanism can capture the long-term dependence and short-term fluctuations of time series data, making it suitable for dynamic changes and delay effects; at the same time, it has strong robustness to noisy data and is more adaptable to complex watershed environments and multi-source heterogeneous data input.

[0020] (2) Improved accuracy: The LSTM neural network model has a significant advantage in handling high-dimensional nonlinear mapping relationships. It can more accurately mimic the simulation process of the VIC model, significantly improving simulation accuracy and spatial consistency.

[0021] (3) Scientific value: This invention provides a new technical path for the calibration of hydrological model parameters, promotes the application of deep learning in the field of hydrology, and provides important theoretical and methodological support for related research.

[0022] (4) Application Value: The MPR method significantly reduces the dimensionality of parameters by associating geophysical features with model parameters, while ensuring the spatial continuity and heterogeneity of the parameter field. Based on the coefficients of the calibration transformation function using remote sensing data, distributed parameters can be obtained, which not only improves the accuracy of hydrological simulation, but also allows for calibration without relying on observed runoff in areas with no or insufficient data. This significantly improves the accuracy and reliability of hydrological simulation, providing a scientific basis for water resource management, disaster early warning, and ecological protection. Attached Figure Description

[0023] Figure 1 This is a flowchart of the method of the present invention; Figure 2 This is a schematic diagram of the internal structure of the LSTM memory cell in this invention; Figure 3 This is a schematic diagram of the spatial distribution of Bias and CC in ET simulations using the LSTM and VIC models from 2011 to 2013. Figure 4 This is a diagram comparing the time series simulations of ET using the LSTM model and the VIC model. Figure 5 This is a schematic diagram of the RMSE, KGE, and CC distributions of ASMO and LSTM-SCE during the validation period. Figure 6 This is a scatter plot of the simulated evapotranspiration of the ASMO and LSTM-SCE models and the GLEAM product during the validation period. Detailed Implementation

[0024] The technical solution of the present invention will be described in detail below with reference to the accompanying drawings, but the scope of protection of the present invention is not limited to the embodiments described.

[0025] Example 1: The distributed hydrological model parameter calibration method based on a deep neural network substitution model provided by this invention optimizes the parameters of the distributed hydrological model VIC (Variable Infiltration Capacity) by combining the SCE-UA parameter calibration method. Simultaneously, a multi-scale parameter regionalization (MPR) method is introduced to further reduce the parameter dimensionality and ensure the spatial continuity of the parameters. This method not only significantly improves the efficiency and accuracy of distributed hydrological model parameter calibration but also provides important technical reference for distributed model parameter calibration in areas with no or insufficient data. The specific steps are as follows: Step 1: Data Acquisition and Processing Meteorological data, including precipitation, air temperature, atmospheric pressure, incident shortwave radiation, incident longwave radiation, vapor pressure, and wind speed, were collected as driving data for the distributed hydrological model VIC. The temporal and spatial resolutions of the meteorological data were processed to create a meteorological forced variable file. The study area, located in the upper reaches of the Huai River basin near the Bengbu hydrological station, is a rectangular region (30.75°–35°N, 111.75°–117.75°E). The spatial resolution of the distributed hydrological model VIC is 0.25° × 0.25°, therefore the grid size corresponding to the study area is 24 × 17.

[0026] Step 2: Surface Information Collection Collect surface information about the watershed, including the size and shape of the map grid, the geographical location of each grid cell, topographic shading information, area and vegetation cover ratio, determine the characteristics and attributes of the grid cells, and create surface parameter files.

[0027] Step 3: Basic Data Preparation Data on the watershed's geographic information, soil properties, and vegetation attributes were collected, and basic geospatial data were preprocessed using the ArcGIS platform (e.g., coordinate system registration, classification, and parameter extraction) to prepare default parameter files. Specifically: geographic information included latitude, longitude, and surface elevation; soil properties covered surface type, soil species, soil thickness, soil bulk density, and soil volume; vegetation attributes included vegetation species, leaf area index, vegetation height, root depth, and root proportion; soil hydrological parameters included maximum saturated hydraulic conductivity, mean water temperature under vegetation cover, and soil moisture content curve parameters; model control parameters determined the model's operating grid points and whether the soil freezing algorithm was activated, with leaf area index and surface albedo derived from a vegetation sample database.

[0028] Step 4: Construction of the Distributed Hydrological Model (VIC) A distributed hydrological model, VIC, is constructed to simulate runoff or evapotranspiration in the target area. Here, the evapotranspiration calibration parameters are determined by simulation. The target calibration parameters of the VIC model include the variable infiltration curve parameters (B), the maximum baseflow velocity (Ds), the maximum baseflow velocity fraction at the start of nonlinear baseflow (Dm), the maximum soil moisture fraction at the occurrence of nonlinear baseflow (Ws), the thickness of the second soil layer (D2), the thickness of the third soil layer (D3), and the drainage parameters of the second soil layer (E2).

[0029] Step 5: Obtaining Reference Data The simulation performance of the VIC model was evaluated using remote sensing hydrological elements or evapotranspiration data as “measured values”, with evapotranspiration data obtained by downloading GLEAM v3.7a.

[0030] Step 6: Application of the MPR method The multi-scale parameter regionalization (MPR) method is applied for parameter transfer and optimization. The MPR method correlates fine-scale geophysical features with model parameters through a transfer function and upscales them to the selected modeling spatial scale to provide a continuous, seamless parameter field. During parameter estimation, the coefficients in the transfer function are optimized (…). Instead of directly adjusting the original parameters of the model, this achieves dimensionality reduction in the distributed model parameter calibration process.

[0031] The geophysical data used in this method are from the China Soil Hydraulic Parameters Dataset and the China Surface Simulation Soil Database. Adjustable parameters and their transfer functions are shown in Table 1.

[0032] Table 1. Comparison of Regionalized Transfer Functions for Parameters to be Calibrated in the VIC Model For detailed information on all variables in Table 1, please refer to Table 2.

[0033] Table 2. Parameter Variable Comparison Table for Transfer Functions Randomization was generated using the Design of Experiments (DoE) method. The values ​​are used to generate 7 model parameters for each grid through a transfer function. The specific steps are as follows: (1) Determine the form of the transfer function. The adjustable parameters and their transfer functions are shown in Table 1. For detailed information on all variables in Table 1, please refer to Table 2.

[0034] (2) Data preparation. Read high-resolution data: Read fine-scale geophysical feature data from the input file, such as saturated hydraulic conductivity (Ks), field water content (Wf) of subgrids and saturated soil water content (Wm).

[0035] (3) Parameter generation: n sets of transfer function coefficients are generated using a uniform random sampling method. The initial values ​​are uniformly distributed between [0, 1) and scaled to the actual range [bl, bu) by a linear transformation.

[0036] (4) Condition constraints: Limit the optimized parameter values ​​to ensure their physical rationality.

[0037] (5) Unit conversion: Convert the optimized parameter values ​​into the units required by the model.

[0038] (6) Return result: Returns the optimized transfer function coefficients ( The calculated model parameters (B, Ds, Dm, Ws, E2, D2, D3) are used for evapotranspiration simulation calculations of the VIC model.

[0039] Step 7: Building an LSTM-based alternative to the VIC model An alternative model is established by using an LSTM network model to simulate the nonlinear process of evapotranspiration, mimicking the VIC model.

[0040] LSTM (Long Short-Term Memory) networks are a special type of recurrent neural network (RNN) capable of effectively handling long-sequence time-series data and addressing the vanishing and exploding gradient problems that traditional RNNs often encounter during modeling. By introducing input gates, forget gates, output gates, and internal memory cells, LSTM can better capture long-term dependencies in time-series data, significantly improving its ability to model nonlinear time-series data. Therefore, LSTM is well-suited as an alternative model for mimicking the VIC model to simulate the nonlinear process of evapotranspiration. The internal structure of the LSTM memory cell is shown in the appendix. Figure 2 .

[0041] The steps to construct an LSTM alternative model are as follows: (1) Model input and output: The construction of the LSTM alternative model and parameter optimization are independent of each other. By using the meteorological input and parameter input of the VIC model as the input of the LSTM and the simulated evapotranspiration value of the VIC model as the target output, the LSTM network can learn the nonlinear mapping relationship of the VIC model.

[0042] (2) Parameter sampling and sample generation: Different parameters are generated through random sampling. The above MPR method is used to generate 700 sets of corresponding parameter sample fields, and each set of parameters is brought back to the VIC model to generate 700 sets of corresponding evapotranspiration simulation values.

[0043] (3) Data set partitioning: The 700 sets of samples were divided into training dataset (400 sets), validation dataset (200 sets) and test dataset (100 sets); the input-output data at each grid point was used as a set of training samples. The input of each set of samples included 30 days of meteorological input and model parameters, and the target value was the evapotranspiration value simulated by VIC on the 30th day; the training dataset contained a total of 400 sets of samples × 408 grid units = 163,200 grid units, and each grid unit contained data for a two-year period.

[0044] (4) Hyperparameter settings of the model: The hyperparameters of the LSTM model were optimized and selected by grid search method. The specific settings are as follows: Number of memory units: 128; Batch size: 400; Maximum number of training epochs: 200; Learning rate: 0.0001; Hidden size: 128; Length of the training instance: 7; Loss function: Root mean square error (RMSE).

[0045] (5) Model training and validation: The LSTM model is trained using the training dataset (400 samples) and the model parameters are optimized using the backpropagation algorithm; the Adam optimizer is used to update the model weights to minimize the RMSE loss function; the generalization ability of the model is evaluated using the validation dataset (200 samples) to avoid overfitting; the model hyperparameters, such as learning rate and batch size, are adjusted according to the performance of the validation set; the final performance of the model is evaluated using the test dataset (100 samples); and the simulation accuracy of the model is quantified by the RMSE statistical index.

[0046] Step 8: Optimize the parameters of the LSTM alternative model using SCE-UA The SCE-UA method is used to calibrate the parameters of the LSTM model. Based on the already constructed LSTM model, the evapotranspiration value is simulated according to the model's input data. The output data is compared with the "real" observed evapotranspiration data. The RMSE of each grid time series is calculated, and then the average RMSE of the entire grid surface is calculated. By continuously searching for new parameter sets to calibrate the parameters through the SCE-UA method, the simulation error is reduced, thereby making the model more accurately describe the evapotranspiration process.

[0047] SCE-UA (Shuffled Complex Evolution-University of Arizona) is a highly efficient global optimization algorithm proposed by Duan et al. in 1992. This method combines the principles of biological evolution, simplex algorithms, and genetic algorithms. By simulating the evolutionary process in nature, it can efficiently find the global optimum in a complex parameter space. The SCE-UA algorithm is particularly suitable for high-dimensional, nonlinear, and nonconvex optimization problems, and therefore has been widely used in the parameter optimization of distributed hydrological models.

[0048] The specific steps for SCE-UA parameter optimization are as follows: (1) Objective function: The objective function is defined as the RMSE between the evapotranspiration values ​​simulated by the LSTM model and the evapotranspiration data from GLEAM. The objective is to minimize the RMSE.

[0049] (2) Parameter optimization: The parameters that need to be optimized are the transfer function coefficients ( There are a total of 8 parameters.

[0050] (3) Number of subpopulations: Set the number of subpopulations ngs to 8 (the default value is the number of optimization parameters nopt).

[0051] (4) Set the number of individuals npg in each subpopulation. Each individual is a parameter combination containing 8 parameter values.

[0052] (5) Total number of individuals: Calculate the total number of individuals npt, the formula is: npt = npg * ngs.

[0053] (6) Maximum number of function calls: Set the maximum number of function calls maxn to 3000 to ensure that the algorithm has sufficient computing resources to find the optimal solution. Convergence check parameters: kstop: Set the number of loops for convergence check to 10; pcento: Set the threshold for the percentage change of the objective function to 0.1%; peps: Set the threshold for the relative size of the parameter space to 0.001.

[0054] (7) Generate the initial population: Generate the initial population by random sampling. The population size is npt.

[0055] (8) Calculate the objective function value of the initial population: For each individual, call the LSTM model to calculate its corresponding evapotranspiration simulation value, compare it with the GLEAM evapotranspiration data, and calculate and record the RMSE.

[0056] (9) Sort the population: Sort the population from smallest to largest according to the objective function value (RMSE).

[0057] (10) Record the optimal solution: Record the optimal solution in the current population (i.e. the individual with the smallest RMSE) and its corresponding parameter values.

[0058] (11) Subpopulation division and evolution: The population is divided into ngs subpopulations (each subpopulation contains npg individuals).

[0059] (12) Evolve each subpopulation: Select a simplex from the subpopulation containing nps = nopt + 1 points. Generate new points using operations such as reflection, contraction, and random generation, and calculate their objective function values. Replace the worst point in the simplex with the new points and update the subpopulation.

[0060] (13) Mixed subpopulation: All subpopulations are merged, reordered, and a new population is formed.

[0061] (14) Convergence check: Calculate the geometric range gnrng of the parameter space in the current population. Check whether the change in the objective function value in the last kstop cycles is less than pcento. If the convergence condition (gnrng < peps or the change in the objective function is less than pcento) is satisfied, stop the optimization.

[0062] (15) Return the optimal solution: Return the optimal parameter values ( ) and their corresponding minimum RMSE.

[0063] (16) Substitute the optimal parameter values into the preset conversion function in step (6) to obtain the distributed parameters of the model, and input them into the model for evapotranspiration calculation.

[0064] The deep surrogate model based on the deep neural network LSTM proposed in this invention, combined with the SCE-UA parameter calibration method, realizes the efficient, accurate and universal parameter optimization of the distributed hydrological model VIC. Through the significant advantages of the LSTM surrogate model in dealing with high-dimensional non-linear mapping relationships, and the guarantee of spatial continuity by the multi-scale parameter regionalization (MPR) method, this invention significantly improves the simulation accuracy and calculation efficiency. At the same time, this method provides reliable technical support for parameter calibration in data-free or data-deficient areas, and has important application value in scientific research, engineering practice and economic benefits.

[0065] From the aspects of the performance of the LSTM surrogate model, the parameter optimization effect and applicability, etc., combined with specific experimental data, elaborate the technical effects of this invention in detail.

[0066] 1. Performance evaluation of the LSTM surrogate model As a surrogate model, LSTM can effectively imitate the simulation process of the VIC model, showing high accuracy and stability. By comparing the evapotranspiration simulation results of the LSTM model and the VIC model in the Huaihe River Basin from 2011 to 2013, as Figure 3 shown, the following conclusions are drawn: (1) Accuracy index: The Nash-Sutcliffe efficiency coefficient (NSE) of the LSTM model is 0.919, the average value of the bias (Bias) is 0.074, and the average value of the correlation coefficient (CC) is 0.923, indicating that the LSTM model can highly restore the evapotranspiration simulation results of the VIC model in most cases. The results are shown in Figure 4 .

[0067] (2) Stability: During the low evaporation phase, the simulation results of the LSTM model and the VIC model are highly consistent, demonstrating strong stability. However, under high evaporation conditions and during seasonal transitions, the LSTM model exhibits some underestimation and fluctuation issues, indicating that its simulation capability under extreme conditions still needs further optimization. See the results below. Figure 5 .

[0068] 2. Optimization effect of LSTM-SCE parameter calibration By combining the LSTM substitution model with the SCE-UA optimization method, this invention achieves significant improvements in parameter calibration efficiency and simulation accuracy. (1) Simulation accuracy: The average RMSE of the LSTM-SCE method during the validation period was 0.849, which was 6.1% lower than that of the traditional method (ASMO). The proportion of grids with RMSE within 0.9 reached 76.7%, which was 52.4% higher than that of the traditional method. The results are shown in […]. Figure 5 .

[0069] (2) Spatial consistency: In the Kling-Gupta efficiency coefficient (KGE) index, the grid ratio of LSTM-SCE is 40.2% above 0.6, significantly higher than the 4.7% of the traditional method; and 75.9% above 0.5, which is 50.9% higher than the traditional method. In the correlation coefficient (CC) index, the grid ratio of LSTM-SCE is 49.8% above 0.8, which is 9.1% higher than the traditional method.

[0070] (3) Stability and Correlation: The LSTM-SCE method outperforms traditional methods in terms of error control, correlation, and simulation stability, further verifying its spatial consistency and accuracy in hydrological simulation. The results are shown in […]. Figure 6 .

[0071] 3. The application effect of the MPR method Combining remote sensing data with the MPR method for parameter calibration can effectively reduce parameter dimensionality and ensure spatial continuity of parameters. Specifically: (1) Parameter dimensionality reduction: by optimizing the transfer function coefficients ( Instead of directly adjusting the original parameters of the model, the MPR method significantly reduces the complexity of parameter optimization; (2) Spatial continuity: The parameter field generated by the MPR method has continuity and physical rationality, and is suitable for the calibration of distributed model parameters in areas with no data or lack of data, providing important technical reference for related research.

[0072] As described above, although the invention has been shown and described with reference to specific preferred embodiments, it should not be construed as limiting the invention itself. Various changes in form and detail may be made without departing from the spirit and scope of the invention as defined in the appended claims.

Claims

1. A method for calibrating parameters of a distributed hydrological model based on a deep neural network substitution model, characterized in that, Includes the following steps: S1: Collect meteorological data for the study area; S2: Collect geographical, soil, and vegetation data for the study area; S3: Construct a distributed hydrological model and determine the target variables and calibration parameters; S4: Collect geophysical feature data of the study area, associate the geophysical feature data with the calibration parameters of the distributed hydrological model through the transfer function, introduce a multi-scale parameter regionalization method to optimize the coefficients in the transfer function and generate a calibration parameter sample set; S5: Run the distributed hydrological model, use the collected data from the study area to simulate the target variable, and generate the corresponding simulated values; S6: Construct a deep neural network replacement model, which is an LSTM neural network model, to simulate the input-output relationship of the distributed hydrological model. The meteorological data and calibration parameter sample set are used as inputs, and the simulated values ​​of the distributed hydrological model are used as outputs to train the deep neural network replacement model. S7: The SCE-UA algorithm is used to optimize the parameters of the deep neural network replacement model. The parameter optimization steps of the SCE-UA algorithm include: defining the objective function as the root mean square error between the simulated and measured values ​​of the LSTM neural network model output; determining the parameters to be optimized as the transfer function coefficients; setting the number of subpopulations, the number of individuals in each subpopulation, the total number of individuals, the maximum number of function calls, and convergence check parameters; generating an initial population through random sampling and calculating the objective function value of the initial population; sorting the population according to the objective function value and recording the optimal solution; dividing the population into multiple subpopulations and evolving each subpopulation; shuffling the subpopulations to form a new population; performing a convergence check, and stopping the optimization if the convergence condition is met; and returning the optimal transfer function coefficients and their corresponding minimum root mean square error. S8: Returns the optimized transfer function coefficients and calculates the optimized calibration parameters.

2. The method for calibrating parameters of a distributed hydrological model based on a deep neural network substitution model according to claim 1, characterized in that, The distributed hydrological model is a variable permeability model. The meteorological data includes precipitation, air temperature, atmospheric pressure, incident shortwave radiation, incident longwave radiation, vapor pressure, and wind speed. A meteorological forced variable file is created based on the temporal and spatial resolution of the meteorological data.

3. The method for calibrating parameters of a distributed hydrological model based on a deep neural network substitution model according to claim 1, characterized in that, The calibration parameters include variable infiltration curve parameter B, maximum baseflow velocity Ds, maximum baseflow velocity fraction Dm at the start of nonlinear baseflow, maximum soil moisture fraction Ws at the occurrence of nonlinear baseflow, second soil layer thickness D2, third soil layer thickness D3, and second soil layer drainage parameter E2.

4. The method for calibrating parameters of a distributed hydrological model based on a deep neural network substitution model according to claim 3, characterized in that, The transfer function of parameter B in the variable infiltration curve is: ; The transfer function of the maximum base current velocity Ds is: ; The transfer function of the maximum base current velocity fraction Dm at the beginning of the nonlinear base current is: ; The transfer function of the maximum soil moisture fraction Ws at the location where the nonlinear baseflow occurs is: ; The transfer function for the thickness D2 of the second soil layer is: ; The transfer function of the thickness D3 of the third soil layer is: ; The transfer function for the drainage parameter E2 of the second soil layer is: ; in, These are global parameters; These are the transfer function coefficients; This refers to the standard elevation deviation; This represents the field moisture content of the sub-grid. This represents the saturated soil moisture content. The average soil moisture content of the grid reaches the field moisture content of the subgrid. At that time, the proportion of grid areas where the soil moisture content reached saturation; For Brooks–Corey equation parameters; The saturated hydraulic conductivity of the soil; Soil pore size distribution parameters; This refers to the soil layer thickness parameter.

5. The method for calibrating parameters of a distributed hydrological model based on a deep neural network substitution model according to claim 1, characterized in that, The geophysical feature data are from the China Soil Hydraulic Parameters Dataset and the China Surface Simulation Soil Database.

6. The method for calibrating parameters of a distributed hydrological model based on a deep neural network substitution model according to claim 4, characterized in that, The multi-scale parameter regionalization method includes the following steps: determining the form of the transfer function; reading the geophysical feature data; generating multiple sets of transfer function coefficients using the Latin hypercube sampling method; restricting the generated multiple sets of transfer function coefficients to ensure their physical rationality; converting the restricted parameter values ​​into units required by the distributed hydrological model; and returning the optimized transfer function coefficients, and calculating the calibration parameters through the transfer function.

7. The method for calibrating parameters of a distributed hydrological model based on a deep neural network substitution model according to claim 4, characterized in that, The LSTM neural network model construction includes the following steps: generating a calibration parameter sample set using the multi-scale parameter regionalization method; running the distributed hydrological model based on each set of calibration parameter samples to obtain the simulation results of the target variable; using the collected meteorological data and calibration parameter samples as inputs to the LSTM neural network model, and taking the simulated value of the target variable output by the distributed hydrological model as the output; dividing the input and output sample sets into training datasets, validation datasets, and test datasets; setting the hyperparameters of the LSTM neural network model, and performing model training, validation, and testing.

8. The method for calibrating parameters of a distributed hydrological model based on a deep neural network substitution model according to claim 7, characterized in that, The input and output sample sets are divided into training dataset, validation dataset and test dataset according to a ratio of 4:2:

1. The input-output data at each grid point is used as a set of training samples. The input of each set of training samples includes 30 days of meteorological data and model calibration parameters. The target value is the simulated value of the target variable output by the distributed hydrological model on the 30th day. Each grid cell contains data for a two-year period.

9. The method for calibrating parameters of a distributed hydrological model based on a deep neural network substitution model according to claim 7, characterized in that, The hyperparameters of the LSTM neural network model include: number of memory units: 128; training batch size: 400; maximum training epochs: 200; learning rate: 0.0001; hidden layers: 128; sequence length: 7; loss function: root mean square error.

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