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

Abstract

The invention belongs to the technical field of distributed hydrology, and particularly relates to a distributed hydrology model parameter calibration method based on a deep neural network substitution model, which comprises the following steps: acquiring meteorological data and geographic information, and generating meteorological data and geographic data required by a distributed hydrology model; a multi-scale parameter regionalization method is introduced, and geophysical feature data and distributed hydrological model parameters are associated through a transfer function; the distributed hydrological model is operated for simulation, and corresponding simulation values are generated to serve as sample data; constructing an input and output relationship of a deep neural network substitution model approximate distributed hydrological model, and training by using simulated sample data; and performing parameter optimization on the neural network substitution model by using an SCE-UA optimization algorithm, wherein a to-be-optimized parameter is a coefficient of the transfer function. According to the method, the efficiency and the precision of parameter calibration of the distributed hydrological model are remarkably improved, and an important technical reference is provided for parameter estimation of a region without data or a region lacking data.

Description

Technical Field

[0001] The present invention belongs to the technical field of distributed hydrology, and particularly relates to a method for calibrating parameters of a distributed hydrological model based on a deep neural network surrogate model. Background Art

[0002] Distributed hydrological models can effectively utilize data such as remote sensing and geographic information, and reasonably characterize the spatial heterogeneity of input and output. They have unique advantages in studying the impact of human activities and natural environmental changes on the watershed hydrological cycle. However, the structure of distributed hydrological models is complex and the parameter dimension is relatively high, resulting in a huge challenge for parameter calibration.

[0003] Traditionally, parameter calibration mainly relies on local or global optimization algorithms, among which SCE-UA (Shuffled Complex Evolution) is one of the most commonly used global optimization methods. SCE-UA simulates the biological evolution process, uses multiple complexes to perform global search in the high-dimensional parameter space, and gradually converges to the optimal solution by combining the crossover and selection mechanisms. However, although SCE-UA performs excellently in terms of global search ability, its application in distributed hydrological models still has limitations. The search mechanism of SCE-UA is relatively complex and usually requires running the original physical model thousands of times, resulting in a huge computational load. Secondly, the convergence speed of SCE-UA is relatively slow. Although it has global search ability, in the high-dimensional parameter space, the search efficiency decreases with the increase of dimension, resulting in a slow parameter optimization process, which further exacerbates the computational bottleneck of calibrating complex distributed hydrological models. At the same time, the performance of the SCE-UA algorithm depends to a certain extent on the selection of initial parameters, such as the size and number of the initial population and the adjustment strategy during the evolution process. The rationality of these parameter settings directly affects the convergence speed and optimization effect of the algorithm.

[0004] To reduce the computational burden, optimization algorithms based on statistical surrogate models are widely adopted. Such methods mainly rely on shallow surrogate models, such as polynomial regression, random forest, 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 an adaptive update mechanism can achieve better optimization results at a lower computational cost. 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 is a global optimization method based on an adaptive surrogate model developed by Wang et al. 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 with SCE-UA, ASMO has a lower computational cost because the computational cost of the statistical surrogate model is much smaller than that of the physical model, thus reducing the number of calls to the original model to improve the optimization efficiency.

[0005] Although existing optimization methods based on surrogate models have reduced the computational cost and improved the optimization efficiency to a certain extent, they still have the following significant drawbacks: Traditional statistical surrogate models have poor accuracy when used to construct high-dimensional mapping relationships, and the computational efficiency is significantly reduced; in addition, the method of constructing the statistical relationship between model parameters and the objective function lacks flexibility. When the objective function or simulation 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 applied in the hydrological field. By increasing the network depth and applying non-linear activation functions, deep learning models have significantly improved the approximation ability of high-dimensional non-linear mapping relationships. Due to their differentiable characteristics, deep learning models can be used as surrogate models to imitate the operating mechanism of the original physical model, thus completely replacing its input-output relationship. However, the current research on parameter calibration of deep neural network surrogate models is still relatively limited, and their application potential in distributed hydrological models has not been fully explored. Summary of the Invention

[0007] Objective of the Invention: The present invention proposes a distributed hydrological model parameter calibration method based on a deep neural network surrogate model, which combines the SCE-UA parameter calibration method to optimize the parameters of the distributed hydrological model VIC. At the same time, the multi-scale parameter regionalization (MPR) method is introduced to further reduce the parameter dimension 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 an important technical reference for distributed model parameter calibration in data-scarce or data-deficient areas.

[0008] Technical Solution: The distributed hydrological model parameter calibration method based on a deep neural network surrogate model of the present invention includes the following steps: S1: Collect meteorological data of the study area; S2: Collect geographical data, soil and vegetation data of the study area; S3: Build a distributed hydrological model and determine the target variables and calibration parameters; S4: Collect geophysical characteristic data of the study area, associate the geophysical characteristic data with the calibration parameters of the distributed hydrological model through a transfer function, introduce the multi-scale parameter regionalization method to optimize the coefficients in the transfer function and generate a set of calibration parameter samples; S5: Run the distributed hydrological model, use the collected data of the study area to simulate the target variables, and generate corresponding simulated values; S6: Build a deep neural network surrogate model to simulate the input-output relationship of the distributed hydrological model, use the meteorological data and the set of calibration parameter samples as inputs, and use the simulated values of the distributed hydrological model as outputs to train the deep neural network surrogate model; S7: Use the SCE-UA algorithm to optimize the parameters of the deep neural network surrogate model, where the objective function of the SCE-UA algorithm is the root mean square error between the simulated values output by the deep neural network surrogate model and the measured values, and the parameters to be optimized are the coefficients of the transfer function; S8: Return the optimized coefficients of the transfer function and calculate the optimized calibration parameters.

[0009] To further improve the above technical solution, the distributed hydrological model is a variable infiltration capacity model, the meteorological data includes precipitation, temperature, atmospheric pressure, incident shortwave radiation, incident longwave radiation, vapor pressure and wind speed, and a meteorological forcing variable file is made for the time resolution and spatial resolution of the meteorological data.

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

[0011] Furthermore, the transfer function of the variable infiltration curve parameter B is: ; The transfer function of the maximum base flow velocity Ds is: ; The transfer function of the maximum base flow velocity fraction Dm at the start of the nonlinear base flow is: ; The transfer function of the maximum soil moisture fraction Ws at the occurrence of the nonlinear base flow is: ; The transfer function of 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 of the drainage parameter E2 of the second soil layer is: ; Among them, is a global parameter; is a transfer function coefficient; is the standard elevation deviation; is the sub-grid field water content; is the saturated soil water content; is the proportion of the grid area where the soil water content reaches saturation when the average soil water content is Wf; is the Brooks–Corey equation parameter; is the saturated hydraulic conductivity of the soil; is the soil pore size distribution parameter; is the soil layer thickness parameter.

[0012] Furthermore, the geophysical characteristic data are from the Chinese Soil Hydraulic Parameter Dataset and the Chinese 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 characteristic data; generating multiple groups of transfer function coefficients using the Latin hypercube sampling method; restricting the generated multiple groups of transfer function coefficients to ensure their physical rationality; converting the restricted parameter values to the units required by the model; and returning the optimized transfer function coefficients, and calculating the calibrated parameters through the transfer function.

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

[0015] Further, the input-output sample set is divided into a training data set, a validation data set, and a test data set according to 4:2:1; the input-output data at each grid point is used as a group of training samples, the input of each group of training samples includes 30-day 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, and each grid cell contains data with a time length of two years.

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

[0017] Further, the parameter optimization steps of the SCE-UA algorithm include: defining the objective function as the root mean square error between the simulated value and the measured value output by the LSTM neural network model; determining the parameter to be optimized as the transfer function coefficient; setting the number of subpopulations, the number of individuals in each subpopulation, the total number of individuals, the maximum number of function calls, and the convergence check parameter; generating an initial population by 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; returning the optimal transfer function coefficient and its corresponding minimum root mean square error.

[0018] Beneficial effects: Compared with the prior art, the advantages of the present invention are as follows: The method for calibrating parameters of a distributed hydrological model based on a deep neural network surrogate model proposed by the present invention, in combination with the SCE-UA parameter calibration method, realizes efficient, accurate, and universal parameter optimization of the distributed hydrological model VIC, providing new ideas and technical support for basin hydrological simulation. The LSTM neural network model can effectively replace the complex VIC physical model, significantly reducing the computational burden, and is more flexible and accurate than traditional statistical surrogate models. The LSTM neural network model has significant advantages in dealing with high-dimensional non-linear mapping relationships. Multi-scale parameter regionalization (MPR) significantly reduces the parameter dimension and ensures the spatial continuity and heterogeneity of the parameter field by establishing physical constraint relationships between geographical attributes and model parameters and guaranteeing spatial continuity, and combines remote sensing hydrological element data as the calibration target, not only reducing the limitation of calibrating only relying on runoff data but also improving the applicability of the model in data-deficient areas.

[0019] The present invention significantly improves the simulation accuracy and computational 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 values in scientific research, engineering practice, and economic benefits. By combining the LSTM neural network model, the SCE-UA optimization method, and the MPR parameter regionalization technology, the present invention significantly improves the efficiency, accuracy, and applicability of parameter calibration of the distributed hydrological model, having important technical advantages and social and economic values: (1) Efficiency improvement: The LSTM neural network model combined with the SCE-UA optimization method significantly reduces the computational load of parameter calibration, avoiding the high-cost problem of the traditional method that requires running the physical model thousands of times, and greatly reducing the computational time and resource consumption. The LSTM surrogate model has unique advantages in capturing the complex non-linear characteristics of the hydrological model. The increaseability of its network depth and non-linear activation function can approximate complex mapping relationships and adapt to multi-dimensional non-linear characteristics; the memory gating mechanism can capture the long-term dependence and short-term fluctuations of time-series data, being suitable for dynamic changes and delay effects; at the same time, it has strong robustness to noise data and can better adapt to complex basin environments and multi-source heterogeneous data inputs.

[0020] (2) Accuracy improvement: The LSTM neural network model has significant advantages in dealing with high-dimensional non-linear mapping relationships, can more accurately imitate the simulation process of the VIC model, and significantly improves the simulation accuracy and spatial consistency.

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

[0022] (4)Application value: By associating geophysical characteristics with model parameters, the MPR method significantly reduces the parameter dimension and ensures the spatial continuity and heterogeneity of the parameter field. Based on the calibration of the coefficients of the transfer function using remote sensing data, distributed parameters can be obtained, which not only improves the accuracy of hydrological simulation, but also enables calibration without relying on observed runoff in data - scarce or data - deficient areas, thus significantly enhancing the accuracy and reliability of hydrological simulation and providing a scientific basis for water resource management, disaster warning, and ecological protection. Brief Description of the Drawings

[0023] Figure 1 is the flow chart of the method of the present invention; Figure 2 is the schematic diagram of the internal structure of the LSTM memory unit in the present invention; Figure 3 is the schematic diagram of the spatial distribution of Bias and CC of the LSTM model and the VIC model in simulating ET from 2011 to 2013; Figure 4 is the schematic diagram of the time - series comparison of the LSTM model and the VIC model in simulating ET; Figure 5 is the schematic diagram of the distribution of RMSE, KGE, and CC of ASMO and LSTM - SCE during the validation period; Figure 6 is the scatter plot of the ASMO and LSTM - SCE models and the GLEAM product in simulating evapotranspiration during the validation period. Detailed Embodiments

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

[0025] Embodiment 1: The distributed hydrological model parameter calibration method based on the deep - neural - network surrogate model provided by the present invention combines the SCE - UA parameter calibration method to optimize the parameters of the distributed hydrological model VIC (Variable Infiltration Capacity); meanwhile, the multi - scale parameter regionalization (MPR) method is introduced to further reduce the parameter dimension and ensure the spatial continuity of the parameters. This method not only significantly improves the efficiency and accuracy of the distributed hydrological model parameter calibration, but also provides an important technical reference for the distributed model parameter calibration in data - scarce or data - deficient areas. The specific steps are as follows: Step 1: Data collection and processing Collect meteorological data as the driving data for the distributed hydrological model VIC, including precipitation, air temperature, atmospheric pressure, incident shortwave radiation, incident longwave radiation, vapor pressure, and wind speed; process the time resolution and spatial resolution of the meteorological data to produce a meteorological forcing variable file. Here, the upper region of the Bengbu Hydrological Station in the Huaihe River Basin is selected as the study area, covering the upper reaches of the Huaihe River Basin, which is a rectangular area (30.75°-35°N, 111.75°-117.75°E). The spatial resolution of the distributed hydrological model VIC is 0.25°×0.25°, so the corresponding grid size of the study area is 24×17.

[0026] Step 2: Collection of surface information Collect the surface information of the basin, including the size and shape of the map grid, as well as the geographical location, terrain shielding information, regional area, and vegetation coverage ratio of each grid cell, determine the characteristics and attributes of the grid cells, and produce a surface parameter file.

[0027] Step 3: Preparation of basic data Collect data such as the geographical information, soil characteristics, and vegetation attributes of the basin, and use the ArcGIS platform to preprocess the basic geographical spatial data (such as coordinate system registration, classification, and parameter extraction, etc.) to prepare a default parameter file. Among them: the geographical information includes latitude, longitude, and surface elevation; the soil characteristics cover aspects such as surface type, soil type, soil layer thickness, soil bulk density, and soil density; the vegetation attributes include aspects such as vegetation type, leaf area index, vegetation height, root depth, and root ratio; the soil hydrological parameters include the maximum saturated hydraulic conductivity, average temperature under vegetation cover, soil water content curve parameters, etc.; the model control parameters determine whether the running grid points of the model and the soil freezing algorithm are activated, etc., and the leaf area index and surface albedo come from the vegetation sample library.

[0028] Step 4: Construction of the distributed hydrological model VIC Construct the distributed hydrological model VIC to simulate the runoff or evapotranspiration of the target area. Here, the parameters are calibrated by simulating the evapotranspiration rate. The target calibration parameters of the VIC model include the variable infiltration curve parameter (B), the maximum base flow velocity (Ds), the fraction of the maximum base flow velocity at the start of the nonlinear base flow (Dm), the fraction of the maximum soil moisture at the occurrence of the nonlinear base flow (Ws), the thickness of the second soil layer (D2), the thickness of the third soil layer (D3), and the drainage parameter of the second soil layer (E2).

[0029] Step 5: Acquisition of reference data Use remote sensing hydrological elements or evapotranspiration data as the "measured values" to evaluate the simulation performance of the VIC model, and the evapotranspiration data is 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 associates fine-scale geophysical features with model parameters through transfer functions and promotes them to the selected modeling spatial scale to provide a continuous and seamless parameter field. In the parameter estimation process, the coefficients in the transfer function are optimized ( ), rather than directly adjusting the original parameters of the model, thereby achieving dimensionality reduction in the distributed model parameter calibration process.

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

[0032] Table 1 Comparison table of regional transfer functions of parameters to be calibrated for the VIC model Detailed information on all variables in Table 1 is provided in Table 2 .

[0033] Table 2 Parameter variable comparison table of transfer function Random generation through design of experiments (DoE) methods The value of is used to generate the 7 model parameters of each grid through the 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. Detailed information on all variables in Table 1 can be found in Table 2.

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

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

[0036] (4) Conditional restrictions: restrict 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: Return the optimized transfer function coefficient ( ) and the calculated model parameters (B, Ds, Dm, Ws, E2, D2, D3) are used for evapotranspiration simulation calculation of the VIC model.

[0039] Step 7: Construction of the LSTM-based surrogate model for the VIC model An LSTM network model is used to mimic the non-linear process of evapotranspiration simulation in the VIC model to establish a surrogate model.

[0040] The LSTM (Long Short-Term Memory) network is a special type of recurrent neural network (RNN) that can effectively process long-sequence time-series data and solve the problems of vanishing gradients and exploding gradients that are prone to occur in the modeling process of traditional RNNs. By introducing input gates, forget gates, output gates, and internal memory cells, LSTM can better capture long-term dependencies in time-series data and significantly improve the modeling ability for non-linear time-series data. Therefore, LSTM is very suitable as a surrogate model for mimicking the non-linear process of evapotranspiration simulation in the VIC model. The internal structure of the LSTM memory unit is shown in the appendix Figure 2 .

[0041] The steps for constructing the LSTM surrogate model are as follows: (1) Input and output of the model: The construction and parameter optimization of the LSTM surrogate model 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 evapotranspiration simulation value of the VIC model as the target output, the LSTM network can learn the non-linear mapping relationship of the VIC model.

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

[0043] (3) Dataset division: The 700 sets of samples are divided into a training dataset (400 sets), a validation dataset (200 sets), and a test dataset (100 sets); the input-output data at each grid point is used as a set of training samples. The input of each set of samples includes 30 days of meteorological input and model parameters, and the target value is the evapotranspiration value simulated by the VIC on the 30th day; the training dataset contains a total of 400 sets of samples × 408 grid cells = 163,200 grid cells, and each grid cell contains data with a time length of two years.

[0044] (4)Hyperparameter settings of the model: The hyperparameters of the LSTM model are optimized and selected through the grid search method. The specific settings are as follows: Number of memory cells: 128; Training batch size: 400; Maximum number of training epochs: 200; Learning rate: 0.0001; Number of hidden layers: 128; Sequence length (lookback window size): 7; Loss function: Root Mean Square Error (RMSE).

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

[0046] Step 8: Optimize the parameters of the LSTM surrogate model using SCE-UA Use the SCE-UA method to calibrate the parameters of the LSTM model. Based on the already constructed LSTM model, simulate the evapotranspiration value according to the input data of the model, compare the output data with the "true" observed evapotranspiration data, calculate the RMSE of each grid time series, and then calculate the average RMSE of the entire grid surface. Continuously find new parameter sets through the SCE-UA method to calibrate the parameters and reduce the simulation error, so that the model can more accurately describe the evapotranspiration process.

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

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

[0049] (2) Optimize parameters: Determine that the parameters to be optimized are the transfer function coefficients ( ), 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, and 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 enough computing resources to find the optimal solution. Convergence check parameters: kstop: Set the number of loops for convergence check to 10; pcento: Set the percentage threshold for the change of the objective function to 0.1%; peps: Set the relative size threshold of the parameter space to 0.001.

[0054] (7) Generate the initial population: Generate the initial population through random sampling, and the population size is npt.

[0055] (8) Calculate the objective function values 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 small to large according to the objective function value (RMSE).

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

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

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

[0060] (13) Shuffle the subpopulations: Combine all subpopulations, reorder them, and form a new population.

[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 met, 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 by the present 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, the present invention significantly improves the simulation accuracy and calculation efficiency. At the same time, this method provides reliable technical support for parameter calibration in data-scarce or data-deficient areas, and has important application values in scientific research, engineering practice and economic benefits.

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

[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 can be 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 performance: During the low evaporation stage, the simulation results of the LSTM model and the VIC model are highly consistent, showing strong stability. However, under high evaporation conditions and during the seasonal transition period, there are certain underestimation and fluctuation problems with the LSTM model, indicating that its simulation ability under extreme conditions still needs to be further optimized. The results are shown in Figure 5 .

[0068] 2. Optimization effect of LSTM-SCE parameter calibration By combining the LSTM surrogate model with the SCE-UA optimization method, the present invention has achieved significant improvements in parameter calibration efficiency and simulation accuracy: (1) Simulation accuracy: The average RMSE of the LSTM-SCE method during the validation period is 0.849, a 6.1% reduction compared to the traditional method (ASMO). The grid ratio with RMSE within 0.9 reaches 76.7%, a 52.4% increase compared to the traditional method. The results are shown in Figure 5 .

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

[0070] (3) Stability and correlation: The LSTM-SCE method is superior to the traditional method 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. Application effect of the MPR method The parameter calibration method combining remote sensing data and the MPR method can effectively reduce the parameter dimension and ensure the spatial continuity of parameters. The specific performance is as follows: (1) Parameter dimension reduction: By optimizing the transfer function coefficient ( ) instead of directly adjusting the original model parameters, 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 distributed model parameter calibration in data-scarce or data-deficient areas, providing an important technical reference for related research.

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

Claims

1. A distributed hydrological model parameter calibration method based on a deep neural network surrogate model, characterized in that It includes the following steps: S1: Collect meteorological data of the research area; S2: Collect geographical data, soil and vegetation data of the research area; S3: Build a distributed hydrological model to determine the target variables and calibration parameters; S4: Collect geophysical characteristic data of the research area, associate the geophysical characteristic data with the calibration parameters of the distributed hydrological model through a 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 of the research area to simulate the target variables, and generate corresponding simulation values; S6: Build a deep neural network surrogate model to simulate the input-output relationship of the distributed hydrological model, use the meteorological data and the calibration parameter sample set as inputs, and use the simulation values of the distributed hydrological model as outputs to train the deep neural network surrogate model; S7: Use the SCE-UA algorithm to optimize the parameters of the deep neural network surrogate model, where the objective function of the SCE-UA algorithm is the root mean square error between the simulation values output by the deep neural network surrogate model and the measured values, and the parameters to be optimized are the coefficients of the transfer function; S8: Return the optimized coefficients of the transfer function and calculate the optimized calibration parameters.

2. The distributed hydrological model parameter calibration method based on the deep neural network surrogate model according to claim 1, wherein The distributed hydrological model is a variable infiltration capacity model. The meteorological data includes precipitation, temperature, atmospheric pressure, incident short-wave radiation, incident long-wave radiation, vapor pressure and wind speed. For the time resolution and spatial resolution of the meteorological data, a meteorological forcing variable file is made.

3. The distributed hydrological model parameter calibration method based on the deep neural network surrogate model according to claim 1, wherein The parameters to be calibrated include the variable infiltration curve parameter B, the maximum base flow velocity Ds, the maximum base flow velocity fraction Dm at the beginning of the nonlinear base flow, the maximum soil moisture fraction Ws at the occurrence of the nonlinear base flow, the thickness D2 of the second soil layer, the thickness D3 of the third soil layer, and the drainage parameter E2 of the second soil layer.

4. The method for calibrating the parameters of the distributed hydrological model based on the deep neural network surrogate model according to claim 3, wherein The transfer function of the variable infiltration curve parameter B is as follows: ; The transfer function of the maximum base flow velocity Ds is as follows: ; The transfer function of the maximum base flow velocity fraction Dm at the start of the non-linear base flow is: ; The transfer function of the maximum soil moisture fraction Ws where the nonlinear base flow occurs is: ; The transfer function of the thickness D2 of the second soil layer is as follows: ; The transfer function of the thickness D3 of the third soil layer is as follows: ; The transfer function of the drainage parameter E2 of the second soil layer is as follows: ; Among them, is a global parameter; is a transfer function coefficient; is the standard elevation deviation; is the sub-grid field water content; is the saturated soil water content; is the proportion of the grid area where the soil water content reaches saturation when the average soil water content is Wf; is the Brooks–Corey equation parameter; is the saturated hydraulic conductivity of the soil; is the soil pore size distribution parameter; is the soil layer thickness parameter.

5. The distributed hydrological model parameter calibration method based on the deep neural network surrogate model according to claim 1, characterized in that The geophysical characteristic data comes from the Chinese soil hydraulic parameter dataset and the Chinese surface simulation soil database.

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

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

8. The distributed hydrological model parameter calibration method based on the deep neural network surrogate model according to claim 7, wherein The input-output sample set is divided into a training data set, a validation data set and a test data set according to 4:2:1; the input-output data at each grid point is used as a group of training samples, the input of each group of training samples includes 30-day meteorological data and the model calibration parameters, the target value is the simulated value of the target variable output by the distributed hydrological model on the 30th day, and each grid cell contains data with a time length of two years.

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

10. The distributed hydrological model parameter calibration method based on the deep neural network surrogate model according to claim 7, wherein The parameter optimization steps of the SCE-UA algorithm include: defining the objective function as the root mean square error between the simulated value and the measured value output by the LSTM neural network model; determining the parameter to be optimized as the transfer function coefficient; setting the number of subpopulations, the number of individuals in each subpopulation, the total number of individuals, the maximum number of function calls and the convergence check parameter; generating an initial population by 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; returning the optimal transfer function coefficient and its corresponding minimum root mean square error.

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