Multi-lake model automatic calibration method based on random search algorithm

Abstract

The invention discloses a multi-lake model automatic calibration method based on a random search algorithm. The method comprises the following steps: S1, data preparation and operation environment initialization; s2, parameter space construction and search control setting; s3, candidate parameter combination generation; s4, parameter writing and multi-model operation; s5, output analysis and time sequence alignment are carried out; s6, performance evaluation and effectiveness judgment; s7, performing global random search and optimal candidate screening; s8, local refined searching and optimal parameter updating are carried out; s9, summarizing results and determining final parameters; according to the method, unified initialization, parameter writing, synchronous operation and analysis and evaluation record output are performed on four lake models including FLake, GLM, GOTM and Simstrap under the same framework, manual configuration and repeated trial and error are remarkably reduced, and calibration efficiency and reproducibility are improved.

Description

Technical Field

[0001] This invention relates to the field of numerical simulation and model parameter optimization technology for lake hydrothermal processes, specifically to an automatic calibration method for multi-lake models based on a random search algorithm. Background Technology

[0002] Simulation and prediction of lake ice conditions (such as ice thickness evolution) are of great significance in hydrological process research, ecological and safety management in cold regions. Due to differences in structural assumptions, parameterization schemes, and the physical meaning of parameters among different lake models, the same lake often requires separate calibration under different models. Furthermore, the calibration process typically relies on expert experience and extensive trial and error, resulting in problems such as long processing times, repetitive work, and poor reproducibility. To improve the consistency of multi-model simulations, enhance the fit to observations, and reduce manual workload, a calibration method is urgently needed that can drive the synchronous operation of multiple models under a unified process, automatically evaluate, record, and iteratively optimize them.

[0003] Existing model calibration processes often focus on a single model, requiring manual configuration and repeated runs, making it difficult to achieve synchronous parameter tuning of multiple models within a unified framework. Furthermore, they lack systematic control over parameter boundaries, experimental validity, and abnormal conditions (such as timeouts, missing outputs, and misaligned time series), which can easily lead to misjudgments or unreproducible results due to single-test failures. In addition, traditional calibration strategies do not adequately explore the parameter space, are prone to getting trapped in local optima, and lack automated result aggregation, log tracking, and traceable configuration backup mechanisms, making it difficult to support engineering applications of multi-model coupled lake ice condition simulation and prediction scenarios. Summary of the Invention

[0004] The purpose of this invention is to provide an automatic calibration method for multi-lake models based on a random search algorithm, so as to solve the problems mentioned in the background art.

[0005] To achieve the above objectives, the present invention provides the following technical solution: an automatic calibration method for a multi-lake model based on a random search algorithm, comprising the following steps:

[0006] S1: Data preparation and runtime environment initialization: Taking the target lake as the simulation object, prepare model-driven data and observation data in a unified manner, and perform raster clipping and time consistency processing on the model-driven data and observation data; initialize the multi-model joint runtime environment, clarify the configuration file paths, runtime framework and R runtime environment parameters of the four lake models FLake, GLM, GOTM and Simstrat, and back up and standardize the original configuration files of each model.

[0007] S2: Parameter Space Construction and Search Control Settings: Based on the physical processes of lakes and the physical meaning of parameters, determine the parameters to be calibrated for each lake model and their reasonable value range, and construct the parameter search space; set the number of global random searches, the number of local refinement search disturbances, and the maximum allowable timeout for a single model run;

[0008] S3: Candidate parameter combination generation: Within the parameter search space, sampling is performed according to a preset random search strategy. Discrete parameters are sampled using integers, and continuous parameters are sampled using uniform floating-point sampling. Multiple sets of candidate parameter combinations containing the parameter values ​​of the four lake models and satisfying physical rationality constraints are generated.

[0009] S4: Parameter writing and multi-model operation: Write each set of candidate parameters into the configuration files of the four lake models respectively, keeping the file structure and comments unchanged; drive the multiple models to run automatically under the same meteorological forcing conditions through a unified model scheduling framework, monitor the running status, record logs and execute timeout control;

[0010] S5: Output Analysis and Time Series Alignment: Analyze the output results of each model, extract the ice thickness time series, and align it with the measured ice thickness data according to a unified time reference; mark parameter combinations with missing output, failed analysis, or mismatched time as invalid experiments;

[0011] S6: Performance Evaluation and Effectiveness Determination: Calculation of the Coefficient of Determination R 2 The root mean square error (RMSE), mean absolute error (MAE), and bias are considered valid if and only if all evaluation indices of the four models are finite and computable.

[0012] S7: Global Random Search and Optimal Candidate Selection: Perform a global random search a set number of times, sort the valid experimental results according to the target evaluation index, and select the optimal parameter combination as the initial candidate for local refinement search;

[0013] S8: Local Refinement Search and Optimal Parameter Update: Starting with the optimal candidate parameter combination, generate a local perturbation parameter combination in its parameter neighborhood, repeat the process from S4 to S6, and update the optimal parameter record in real time until the preset number of perturbations is reached or the performance improvement is no longer significant.

[0014] S9: Results Summary and Final Parameter Determination: Based on all valid experimental results, determine the optimal parameter combination as the final calibration parameters, and output a unified parameter search record table, optimal parameters and evaluation indicators, configuration file backup, simulation result file and operation log.

[0015] Furthermore, in S1, the model-driven data includes wind speed at a height of 10m, air temperature, relative humidity, downwave radiation, downwave radiation, sea level air pressure, surface air pressure, precipitation, and snowfall data; the observation data is the measured ice thickness data of the target lake; and the time consistency processing includes unified time resolution, standardized timestamp format, and data interpolation for missing time nodes.

[0016] Furthermore, in S2, the reasonable range of values ​​for the parameters to be calibrated is determined based on the lake's physical characteristics, the model parameterization scheme, and relevant scientific research literature; the number of global random searches, the number of local refinement search perturbations, and the maximum allowable timeout for a single model run can be flexibly configured according to simulation requirements.

[0017] Furthermore, in S3, the accuracy of uniform floating-point sampling can be adjusted according to the sensitivity of the model parameters. When the parameter sensitivity is high, a higher sampling accuracy is used, and when the parameter sensitivity is low, the sampling accuracy can be reduced.

[0018] Furthermore, in S4, the unified model scheduling framework uses R language to develop a batch writing program for multi-lake model parameters, and combines Python programming language to build a random parameter search and operation control module to realize the automated synchronous operation of multiple models.

[0019] Furthermore, in S5, the time dimension alignment process must ensure that the simulated ice thickness time series and the measured ice thickness data are matched one-to-one at all time points, without any time misalignment or missing data.

[0020] Furthermore, in S6, the performance evaluation indicators are calculated based on the corresponding nodes of the time-aligned simulated ice thickness data and the measured ice thickness data, using a point-by-point comparison method. All evaluation indicators are quantified values.

[0021] Furthermore, in step S8, the neighborhood range of the parameter to be calibrated is ±5% to ±15% of the parameter value corresponding to the initial candidate parameter combination, and the specific disturbance range can be flexibly configured according to the parameter characteristics.

[0022] Furthermore, in S9, the output simulation result file is stored in NetCDF format, the running log is stored in text format, and all output files contain unique identification information for easy traceability and management.

[0023] Compared with the prior art, the beneficial effects of the present invention are:

[0024] Unified process for multiple models and high degree of automation: Under the same framework, four lake models, namely FLake, GLM, GOTM and Simstrat, are initialized in a unified manner, parameters are written, synchronously run, output parsing and evaluation records are generated, which significantly reduces manual configuration and repeated trial and error, and improves calibration efficiency and reproducibility.

[0025] Global random search combined with local refinement results in more thorough optimization: First, a large-scale random search is used to explore the parameter space with broad coverage, and then local refinement is performed in the neighborhood of the optimal solution. This balances globality and refinement, reduces the risk of getting stuck in local optima, and improves fitting accuracy.

[0026] Rigorous validity determination improves the reliability of results: The R-squared value is determined if and only if all four models are computable and have finite values. 2 The rule of "only when the test is deemed valid" avoids incorrect updates of optimal parameters due to single-model anomalies and improves the robustness of the calibration process.

[0027] End-to-end traceability facilitates reproduction and auditing: The parameter combinations, evaluation indicators of each model, running status and timestamps of each experiment are continuously written into the results file, and the optimal summary table is output to form a complete parameter-performance mapping, which facilitates subsequent reproduction, comparative analysis and experience accumulation.

[0028] It possesses engineering-grade operational assurance and interactive intervention capabilities: It reduces the risk of failure in large-scale batch experiments through operational protection mechanisms such as timeout control, while providing an interactive mechanism so that users can view parameter status and make manual adjustments and reruns at any stage, achieving a combination of automatic search and expert experience.

[0029] Highly scalable and widely applicable: The method can be configured with evaluation metrics, number of searches, thresholds and local perturbation ranges, and can be extended to joint calibration tasks of more lake models or more observation variables, making it suitable for scientific research and operational deployment scenarios. Attached Figure Description

[0030] Figure 1 This is a flowchart of the method of the present invention;

[0031] Figure 2 This is a simulation diagram of ice thickness after calibration of lake model parameters according to an embodiment of the present invention. Detailed Implementation

[0032] The technical solutions of the present invention will be clearly and completely described below with reference to the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the scope of protection of the present invention.

[0033] Please see Figure 1-2 This invention provides an automatic calibration method for a multi-lake model based on a random search algorithm, comprising the following steps:

[0034] S1: Data Preparation and Runtime Environment Initialization: Taking the target lake as the simulation object, model-driven data and observation data are prepared uniformly. Raster clipping and time consistency processing are performed on the model-driven data and observation data. The multi-model joint runtime environment is initialized, clarifying the configuration file paths, runtime frameworks, and R runtime environment parameters for the four lake models: FLake, GLM, GOTM, and Simstrat. The original configuration files for each model are backed up and standardized. Model-driven data includes 10m height wind speed, air temperature, relative humidity, downwave radiation, downwave radiation, sea level pressure, surface pressure, precipitation, and snowfall data. Observation data consists of measured ice thickness data for the target lake. Time consistency processing includes uniform time resolution, standardized timestamp format, and data interpolation for missing time nodes.

[0035] S2: Parameter Space Construction and Search Control Settings: Based on the physical processes of lakes and the physical meaning of parameters, determine the parameters to be calibrated for each lake model and their reasonable value ranges, and construct the parameter search space; set the number of global random searches, the number of local refinement search perturbations, and the maximum allowable timeout for a single model run; the reasonable value range of the parameters to be calibrated is determined based on the physical characteristics of lakes, the model parameterization scheme, and relevant scientific research literature; the number of global random searches, the number of local refinement search perturbations, and the maximum allowable timeout for a single model run can be flexibly configured according to simulation requirements;

[0036] S3: Candidate parameter combination generation: Within the parameter search space, sampling is performed according to a preset random search strategy. Discrete parameters are sampled using integers, and continuous parameters are sampled using uniform floating-point sampling. Multiple sets of candidate parameter combinations containing the parameter values ​​of the four lake models and satisfying physical rationality constraints are generated. The precision of uniform floating-point sampling can be adjusted according to the sensitivity of the model parameters. Higher sampling precision is used when the parameter sensitivity is high, and the sampling precision can be reduced when the parameter sensitivity is low.

[0037] S4: Parameter writing and multi-model operation: Each set of candidate parameters is written to the configuration files of the four lake models, keeping the file structure and comments unchanged; the unified model scheduling framework drives the multiple models to run automatically under the same meteorological forcing conditions, monitors the running status, records logs and executes timeout control; the unified model scheduling framework uses R language to develop a batch writing program for multi-lake model parameters, and combines Python programming language to build a random parameter search and running control module to realize the automated synchronous operation of multiple models;

[0038] S5: Output Analysis and Time Series Alignment: Analyze the output results of each model, extract the ice thickness time series, and align it with the measured ice thickness data according to a unified time benchmark; mark parameter combinations with missing output, failed analysis, or mismatched time as invalid experiments; the time dimension alignment process must ensure that the simulated ice thickness time series and the measured ice thickness data are paired one-to-one at all time points, with no time misalignment or missing data;

[0039] S6: Performance Evaluation and Effectiveness Determination: Calculation of the Coefficient of Determination R 2 The root mean square error (RMSE), mean absolute error (MAE), and bias are used to determine the validity of the experiment if and only if all evaluation indicators of the four models are finite and computable values. The performance evaluation indicators are calculated based on the corresponding nodes of the time-aligned simulated ice thickness data and the measured ice thickness data, and are obtained by point-by-point comparison. All evaluation indicators are quantitative values.

[0040] S7: Global Random Search and Optimal Candidate Selection: Perform a global random search a set number of times, sort the valid experimental results according to the target evaluation index, and select the optimal parameter combination as the initial candidate for local refinement search;

[0041] S8: Local Refinement Search and Optimal Parameter Update: Starting with the optimal candidate parameter combination, generate a local perturbation parameter combination in its parameter neighborhood, repeat the process from S4 to S6, and update the optimal parameter record in real time until the preset number of perturbations is reached or the performance improvement is no longer significant; the value neighborhood range of the parameter to be calibrated is ±5% to ±15% of the parameter value corresponding to the initial candidate parameter combination, and the specific perturbation range can be flexibly configured according to the parameter characteristics;

[0042] S9: Results Summary and Final Parameter Determination: Based on all valid experimental results, determine the optimal parameter combination as the final calibration parameters, and output a unified parameter search record table, optimal parameters and evaluation indicators, configuration file backup, simulation result file and operation log; the output simulation result file is stored in NetCDF format, the operation log is stored in text format, and all output files contain unique identification information for easy traceability and management.

[0043] Example:

[0044] Using Xiaoxingkai Lake as a simulated case, this paper elaborates on the specific implementation process, including the entire process of data preparation, environment configuration, parameter setting, model operation, result evaluation, and parameter determination. The specific steps are as follows:

[0045] S1: Data Preparation and Runtime Environment Initialization

[0046] Target lake selection: Xiaoxingkai Lake was selected as the simulation object. This lake is located in a cold region and has typical ice evolution characteristics, making it suitable for multi-model calibration studies.

[0047] Data preparation: Field ice thickness observation data of Lake Xiaoxingkai from January 16, 2025 to February 18, 2025 were collected with a time resolution of 1 hour. The data sources were a combination of field manual measurement and instrument observation to ensure data accuracy.

[0048] Model-driven data preparation: The input data for the model simulation uses ERA5 reanalysis data downloaded from ECMWF, covering the period from September 1, 2024 to August 31, 2025, with a time resolution of 1 hour. The included indicators are: wind speed at 10m height (m / s), air temperature (°C), relative humidity (%), and downwave radiation (W / m²). 2 Downward longwave radiation (unit: W / m) 2 The data includes sea level pressure (Pa), surface pressure (Pa), precipitation (mm), and snowfall (mm). The ERA5 raster data was cropped using the vector boundary of Lake Lesser Khanka, retaining only the raster data within the Lake Lesser Khanka region. The cropped data was then mean-calculated to obtain the average driving data for the Lake Lesser Khanka region, which was used as input for model simulation.

[0049] Data preprocessing: Time consistency processing is performed on the observation data and model-driven data, and the timestamp format of all data is unified to "year-month-day hour:minute:second". For individual missing time nodes in the observation data, linear interpolation is used to complete them, ensuring the integrity and temporal continuity of the data.

[0050] Runtime Environment Initialization: A multi-model joint runtime environment was built based on the LakeEnsemblR multi-lake model integration platform. A batch parameter writing and automatic execution program for the multi-lake models was developed using R language, and a random parameter search and execution control module was built using Python programming language. The configuration file storage path for the four lake models (FLake, GLM, GOTM, and Simstrat) was specified as "D: / Lake_Model / Config / ". The runtime framework adopted the standard runtime interface of LakeEnsemblR, and the R runtime environment version was 4.2.3. Before parameter adjustment, the original configuration files of the four models were backed up at "D: / Lake_Model / Config_Backup / ", and the configuration files were standardized according to the LakeEnsemblR specification, unifying the parameter naming format and units.

[0051] S2: Parameter Space Construction and Search Control Settings

[0052] Determination of calibration parameters: Based on the physical characteristics of Lake Xiaoxingkai (such as lake area, water depth, and substrate type), the parameterization schemes of each lake model, and relevant research literature, the calibration parameters and reasonable value ranges for each model are determined as follows:

[0053] For the FLake model, parameters related to the thermocline structure, optical processes, and bottom heat exchange were selected as the objects to be calibrated, including the thermocline morphological relaxation coefficient c_relax_C (0.01–0.3), the optical extinction scaling factor frac_optic (0.9–1.2), the initial water temperature of the mixed layer T_wML_in (3–5 °C), the thickness of the thermally active sedimentary layer depth_bs_lk (1–3 m), and the outer boundary temperature of the sedimentary layer T_bs_lk (3–7 °C).

[0054] For the GLM model, the parameters to be calibrated are mainly set for the wind-induced mixing and sediment heat transfer processes, including the wind speed scaling factor (0.9–1.2), the shear mixing efficiency coefficient (coef_mix_shear) (0.1–0.3), and the sediment thermal conductivity (sed_heat_Ksoil) (0.1–0.5 W·m⁻¹·K⁻¹).

[0055] For the GOTM model, considering the impact of atmospheric forcing uncertainty on lake thermal processes, scaling factors are introduced for calibration of multiple meteorological elements, including cloud.scale_factor, humidity.scale_factor, airp.scale_factor, 10 m wind speed U and V component scaling factors u10.scale_factor and v10.scale_factor, shortwave radiation scaling factor swr.scale_factor, and 2 m air temperature scaling factor airt.scale_factor, all with values ​​set to the range of 0.9–1.2.

[0056] For the Simstrat model, parameters related to turbulent mixing, wind energy input, radiation, and phase change processes are selected as parameters to be calibrated, including the minimum turbulent kinetic energy k_min (1×10⁻⁻⁶). 5 –1×10⁻ 4m²·s⁻²), the proportion of wind energy converted to long-wave oscillations in the lake a_seiche (0.1–0.5), wind-related long-wave parameters a_seiche_w (0.1–0.5), wind forcing correction factor f_wind (0.9–1.2), aerodynamic drag parameters at 10 m height c10 (0.5–1.0), volumetric drag coefficient cd (0.01–0.04), the absorption ratios of short-wave radiation by water and ice surfaces p_sw_water (0.1–1.0) and p_sw_ice (0.0–1.0), water surface albedo wat_albedo (0.0–0.9), phase change freezing temperature freez_temp (0.0–0.05 °C), and geothermal flux hego (4–10 W·m⁻²).

[0057] Parameter search space construction: Integrate the parameters to be calibrated and their value ranges of the above models to construct a unified parameter search space. This space covers the reasonable value range of all parameters to be calibrated, ensuring the comprehensiveness of parameter sampling.

[0058] Search control parameter settings: Set the number of global random searches N_ITER=4000, which means performing 4000 global random sampling and model runs; the number of local refinement search perturbations LOCAL_REFINE_ITERS=200, which means generating 200 sets of local perturbation parameter combinations in the neighborhood of the global optimal parameters; the maximum allowable timeout for a single model run R_TIMEOUT=180 seconds (3 minutes). If the model run time corresponding to a certain set of parameters exceeds 180 seconds, the run will be automatically terminated and marked as timeout failure.

[0059] S3: Generation of candidate parameter combinations

[0060] Based on the parameter search space constructed using S2, a random sampling procedure is implemented using the Python programming language to generate candidate parameter combinations according to a preset random search strategy:

[0061] For discrete parameters to be calibrated, there are no discrete parameters to be calibrated in this embodiment, and all parameters are continuous. If they exist, integer sampling is used.

[0062] For all continuous parameters to be calibrated, a uniform floating-point sampling method is used, with sampling precision retaining 4 decimal places to ensure the accuracy of parameter values.

[0063] With a global random search count of N_ITER=4000, 4000 candidate parameter combinations are generated. Each combination contains all parameter values ​​to be calibrated for the four models: FLake, GLM, GOTM, and Simstrat. All parameter values ​​are within the reasonable range set by S2, satisfying the physical rationality constraint. The generated candidate parameter combinations are stored in the format "parameter combination number_model name.csv" at "D: / Lake_Model / Parameter_Sets / " for easy subsequent retrieval and management.

[0064] S4: Parameter Writing and Multi-Model Execution

[0065] Write an R language program to batch write parameters, read each candidate parameter combination generated by S3, and write it into the configuration files corresponding to the four models: FLake, GLM, GOTM, and Simstrat. During the writing process, strictly maintain the original configuration file structure and annotation information, and only replace the values ​​of the parameters to be calibrated.

[0066] The LakeEnsemblR unified scheduling interface drives four models to automatically perform ice thickness simulation calculations under the same meteorological forcing conditions (i.e., ERA5 reanalysis data processed by S1). The models run sequentially according to their parameter combination numbers, with each parameter combination corresponding to one complete synchronous run of the four models. During model execution, a Python script monitors the running status of each model in real time and records running logs. Log entries include parameter combination number, model name, run start time, run end time, and running status (success / failure / timeout). If a model's run time reaches the set maximum allowable timeout of 180 seconds without completion, the run of that model and other models with the corresponding parameter combination is automatically terminated, the experiment is marked as a timeout failure, and the process begins with the next parameter combination. All running logs are stored in the path "D: / Lake_Model / Run_Logs / ", and the log files are in text format and named according to the run date.

[0067] S5: Output parsing and time series alignment

[0068] After the model runs, the output results of each model are parsed using an R language script. The output file formats of FLake, GLM, GOTM and Simstrat models are their standard output formats. During the parsing process, ice thickness time series data of each model are extracted, with a time resolution of 1 hour, consistent with the measured data.

[0069] Using the timeline of the measured ice thickness data as a benchmark, the ice thickness time series of the four models obtained from the analysis are aligned in terms of time dimension to ensure that the simulated ice thickness data of each model is paired with the measured ice thickness data at each time node (e.g., 00:00, 01:00, etc. on January 16, 2025). If any of the following situations occur during the output analysis process, the set of parameters is marked as an invalid experiment:

[0070] The output file of a certain model is missing or cannot be opened;

[0071] The complete ice thickness time series was not extracted after parsing (more than 5 time nodes were missing).

[0072] The simulated ice thickness time series does not match the time range of the measured ice thickness data, or cannot be aligned by timestamps (time misalignment exceeds 30 minutes).

[0073] The labeling information for invalid trials is stored in the file “D: / Lake_Model / Invalid_Trials.csv”, which includes the parameter combination number, the reason for invalidity, and the labeling time.

[0074] S6: Performance Evaluation and Effectiveness Determination

[0075] Based on the measured ice thickness data after time alignment using S5 and the simulated ice thickness sequences of the four models, the performance evaluation indicators of each model, including the coefficient of determination R, were calculated using the hydroGOF package in R. 2 The calculation of Root Mean Square Error (RMSE), Mean Absolute Error (MAE), and Bias is strictly performed according to the standard calculation formulas for each indicator.

[0076] Coefficient of determination R 2 : The degree of linear correlation between simulated and measured values ​​is quantified, with a value range of [-∞, 1], and the closer to 1, the stronger the correlation;

[0077] Root mean square error (RMSE): reflects the average deviation between simulated and measured values; the smaller the value, the higher the fitting accuracy.

[0078] Mean Absolute Error (MAE): Reflects the average absolute deviation between simulated and measured values; the smaller the value, the better the fit.

[0079] Bias: Reflects the systematic deviation of the simulated values. A positive value indicates that the simulated values ​​are generally too high, and a negative value indicates that the simulated values ​​are generally too low.

[0080] According to the preset validity judgment rules, the experimental results of each parameter combination are judged: if and only if the R-values ​​of the four models FLake, GLM, GOTM, and Simstrat are within the range of 1, 2, 3, 4, 5, 6, 7, 8, 9, 1 ...1, 1, 2, 1, 2When RMSE, MAE, and Bias are all finite and computable values ​​(i.e., there are no outliers such as infinity or NaN), the parameter experiment is considered valid. If any model has any evaluation index that is not computable or is an outlier, the experiment is considered invalid. The performance evaluation metrics of all valid experiments are stored in the file "D: / Lake_Model / Valid_Trials_Metrics.csv", which includes the parameter combination number, the four evaluation metrics of each model, and the experiment validity indicator.

[0081] S7: Global Random Search and Optimal Candidate Selection

[0082] After 4000 global random searches, all valid experimental results were collected, i.e., the data in the file "D: / Lake_Model / Valid_Trials_Metrics.csv". The valid experimental results were sorted using the minimization of the root mean square error (RMSE) as the objective evaluation metric; the smaller the RMSE, the higher the ranking. The parameter combination with the smallest overall RMSE among the four models was selected as the initial candidate parameter combination for the local refinement search. This parameter combination corresponds to the minimum overall RMSE of the four models in the valid experiments, indicating the best fit. This initial candidate parameter combination was stored in the file "D: / Lake_Model / Global_Optimal_Params.csv", containing the values ​​of the parameters to be calibrated for each model and the corresponding performance evaluation metrics.

[0083] S8: Local Refinement Search and Optimal Parameter Update

[0084] Starting with the globally optimal candidate parameter combination obtained through S7 filtering, local perturbation parameter combinations are generated within the neighborhood of each parameter to be calibrated. In this embodiment, the local perturbation range is set to ±10% of the initial candidate parameter value. For example, if the initial value of a parameter is 0.7, the perturbation range is 0.63 to 0.77. Following the setting of LOCAL_REFINE_ITERS=200 for the number of local refinement search perturbations, 200 sets of local perturbation parameter combinations are generated within the aforementioned neighborhood. The generation method also employs uniform floating-point sampling to ensure a uniform distribution of the perturbation parameters.

[0085] For each set of local perturbation parameter combinations, repeat the complete process of S4, S5, and S6 to calculate the performance evaluation index of the four models corresponding to each combination. During the local refinement search, compare the performance of the newly generated local perturbation parameter combinations with the current optimal parameter combinations in real time: if the joint RMSE of the new combination (the average of the RMSEs of the four models) is less than the joint RMSE of the current optimal combination, or if the RMSE of one model decreases significantly while the performance of other models does not decrease significantly, then update the optimal parameter record and use the new combination as the current optimal parameter combination.

[0086] The local refinement search continues until 200 sets of local perturbation parameter combinations have been run and evaluated, or the performance improvement of 30 consecutive parameter combinations is less than 1% (i.e. the performance improvement is no longer significant). At this point, the local refinement search stops, and the final optimal parameter combination is recorded.

[0087] S9: Results Summary and Final Parameter Determination

[0088] All valid experimental results from global random search and local refinement search were collected, including parameter combinations, performance evaluation metrics for each model, runtime logs, configuration file backups, etc., and then comprehensively organized and analyzed. The optimal parameter combination was determined under the joint RMSE condition, combined with R... 2 The final combination of calibration parameters was determined by using indicators such as MAE and Bias. This combination performed best in all valid experiments and enabled the simulated ice thickness results of the four lake models to achieve the best fit with the measured data.

[0089] The following result files should be output uniformly to ensure the traceability and reproducibility of the entire calibration process:

[0090] The parameter search record table (search_all_trials.csv) contains the parameter combination numbers of all valid trials, the values ​​of the parameters to be calibrated for each model, the performance evaluation indicators of each model, and the trial validity identifier. The storage path is "D: / Lake_Model / Result_Summary / ".

[0091] The optimal parameter and evaluation metric file (search_best_summary.csv) contains the final calibration parameter combinations and the corresponding R-values ​​for each model. 2 RMSE, MAE, and Bias are stored in the same way as above.

[0092] Configuration file backup: All configuration files and original backup files used in the experiments are centrally stored in "D: / Lake_Model / Config_Backup_Final / ";

[0093] Simulation results file: The ice thickness simulation results of the four models corresponding to the final optimal parameter combination are stored in NetCDF format and the path is "D: / Lake_Model / Simulation_Results / ";

[0094] Run log summary: The run logs of all experiments are summarized in chronological order and a log summary file (run_logs_summary.txt) is generated and stored in the path "D: / Lake_Model / Run_Logs / Final / ".

[0095] Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art can still modify the technical solutions described in the foregoing embodiments or make equivalent substitutions for some of the technical features. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. An automatic calibration method for a multi-lake model based on a random search algorithm, characterized in that: Includes the following steps: S1: Data preparation and runtime environment initialization: Taking the target lake as the simulation object, prepare model-driven data and observation data in a unified manner, and perform raster clipping and time consistency processing on the model-driven data and observation data; initialize the multi-model joint runtime environment, clarify the configuration file paths, runtime framework and R runtime environment parameters of the four lake models FLake, GLM, GOTM and Simstrat, and back up and standardize the original configuration files of each model. S2: Parameter Space Construction and Search Control Settings: Based on the physical processes of lakes and the physical meaning of parameters, determine the parameters to be calibrated for each lake model and their reasonable value range, and construct the parameter search space; set the number of global random searches, the number of local refinement search disturbances, and the maximum allowable timeout for a single model run; S3: Candidate parameter combination generation: Within the parameter search space, sampling is performed according to a preset random search strategy. Discrete parameters are sampled using integers, and continuous parameters are sampled using floating-point sampling. Multiple sets of candidate parameter combinations containing the parameter values ​​of the four lake models and satisfying physical rationality constraints are generated. S4: Parameter writing and multi-model running: Write each set of candidate parameters into the configuration files of the four lake models respectively, keeping the file structure and comments unchanged; A unified model scheduling framework drives multiple models to run automatically under the same meteorological forcing conditions, monitors the running status, records logs and executes timeout control. S5: Output Analysis and Time Series Alignment: Analyze the output results of each model, extract the ice thickness time series, and align it with the measured ice thickness data according to a unified time reference; mark parameter combinations with missing output, failed analysis, or mismatched time as invalid experiments; S6: Performance Evaluation and Effectiveness Determination: Calculating the Coefficient of Determination R 2 The experiment is considered valid if and only if all four evaluation indices of the model are valid and computable. S7: Global Random Search and Optimal Candidate Selection: Perform a global random search a set number of times, sort the valid experimental results according to the target evaluation index, and select the optimal parameter combination as the initial candidate for local refinement search; S8: Local Refinement Search and Optimal Parameter Update: Starting with the optimal candidate parameter combination, generate a local perturbation parameter combination in its parameter neighborhood, repeat the process from S4 to S6, and update the optimal parameter record in real time until the preset number of perturbations is reached or the performance improvement is no longer significant. S9: Results Summary and Final Parameter Determination: Based on all valid experimental results, determine the optimal parameter combination as the final calibration parameters, and output a unified parameter search record table, optimal parameters and evaluation indicators, configuration file backup, simulation result file and operation log.

2. The automatic calibration method for a multi-lake model based on a random search algorithm according to claim 1, characterized in that: In S1, the model-driven data includes wind speed at 10m height, air temperature, relative humidity, downwave radiation, downwave radiation, sea level pressure, surface pressure, precipitation, and snowfall data; the observation data is the measured ice thickness data of the target lake; the time consistency processing includes unified time resolution, standardized timestamp format, and data interpolation for missing time nodes.

3. The automatic calibration method for a multi-lake model based on a random search algorithm according to claim 1, characterized in that: In S2, the reasonable range of values ​​for the parameters to be calibrated is determined based on the physical characteristics of the lake, the model parameterization scheme, and relevant scientific research literature. The number of global random searches, the number of local refinement search perturbations, and the maximum allowable timeout for a single model run can be flexibly configured according to simulation requirements.

4. The automatic calibration method for a multi-lake model based on a random search algorithm according to claim 1, characterized in that: In S3, the accuracy of uniform floating-point sampling can be adjusted according to the sensitivity of the model parameters. When the parameter sensitivity is high, a higher sampling accuracy is used, and when the parameter sensitivity is low, the sampling accuracy can be reduced.

5. The automatic calibration method for a multi-lake model based on a random search algorithm according to claim 1, characterized in that: In S4, the unified model scheduling framework uses R language to develop a batch writing program for multi-lake model parameters, and combines Python programming language to build a random parameter search and operation control module to realize the automated synchronous operation of multiple models.

6. The automatic calibration method for a multi-lake model based on a random search algorithm according to claim 1, characterized in that: In S5, the time dimension alignment process must ensure that the simulated ice thickness time series and the measured ice thickness data are matched one-to-one at all time points, without any time misalignment or missing data.

7. The automatic calibration method for a multi-lake model based on a random search algorithm according to claim 1, characterized in that: In S6, the performance evaluation index is calculated based on the corresponding nodes of the time-aligned simulated ice thickness data and the measured ice thickness data, and is obtained by point-by-point comparison. All evaluation indexes are quantitative values.

8. The automatic calibration method for a multi-lake model based on a random search algorithm according to claim 1, characterized in that: In step S8, the neighborhood range of the parameter to be calibrated is ±5% to ±15% of the parameter value corresponding to the initial candidate parameter combination. The specific disturbance range can be flexibly configured according to the parameter characteristics.

9. The automatic calibration method for a multi-lake model based on a random search algorithm according to claim 1, characterized in that: In S9, the output simulation result files are stored in NetCDF format, the running logs are stored in text format, and all output files contain unique identification information for easy traceability and management.

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