A parameter estimation design method for quality-conservative ocean models
By constructing a parameter estimation framework using an analytical four-dimensional ensemble variational method, the problems of adaptability and high computational cost in parameter estimation in the MaCOM model are solved, achieving efficient and portable parameter optimization and improving the simulation and forecast accuracy of the ocean model.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- TIANJIN UNIV
- Filing Date
- 2026-02-05
- Publication Date
- 2026-06-12
AI Technical Summary
Existing mass-conserving ocean model (MaCOM) parameter estimation methods suffer from problems such as reliance on empirical assignment, high computational cost, poor adaptability, and insufficient adaptability to sparse observations, making it difficult to meet the requirements of high portability, version compatibility, and long window adaptability.
A parameter estimation framework is constructed using a hybrid data assimilation method (analytical four-dimensional ensemble variation). By using ensemble perturbation and analytical derivation, tangent linearity and adjoint models are avoided. A pluggable optimization algorithm module is designed to adapt to complex marine dynamic models and optimize parameters such as bottom friction coefficient.
It significantly improves the long-term simulation stability and forecast accuracy of the model, reduces computational costs, enhances the portability and adaptability of parameter estimation, adapts to sparse observations, and meets the needs of long-term optimization.
Smart Images
Figure CN122197291A_ABST
Abstract
Description
Technical Field
[0001] This invention belongs to the field of marine numerical prediction and data assimilation technology, and relates to a parameter estimation design method for a mass-conserving marine model that is applicable to parameter estimation and accurate simulation of marine numerical models for complex dynamic systems. Background Technology
[0002] The Mass Conservation Ocean Model (MaCOM), as an independently developed operational ocean circulation model in my country, plays an irreplaceable role in marine environmental forecasting and dynamic process simulation. Its forecast accuracy directly impacts the reliability of related operations such as marine disaster early warning and resource development. However, parameter estimation in MaCOM and similar numerical models currently faces several technical bottlenecks, specifically as follows: 1. Limitations of traditional parameter assignment: Existing models rely heavily on empirical assignment for key parameters, lacking a systematic parameter estimation mechanism. This makes it difficult for the models to adapt to complex ocean dynamic processes, limiting their long-term simulation stability and forecast accuracy.
[0003] 2. Existing data assimilation methods lack adaptability: Sequential assimilation methods (such as ensemble Kalman filtering) are prone to sampling errors due to the limited size of the set, and there is a risk of underestimation of covariance and filter divergence; while non-sequential assimilation methods, such as three-dimensional variational methods, use static background error covariance matrices, lack time constraints, and have limited applicability; although four-dimensional variational methods can utilize spatiotemporal information, they rely on the construction and maintenance of tangent linear and adjoint models, which have high computational costs, complex implementation, poor compatibility with rapidly iterative and updated autonomous models, and poor portability.
[0004] 3. The challenge of adapting observational data to assimilation windows: Actual ocean observational data is sparse, and traditional methods are unable to effectively extract parameter signals within short assimilation windows; while the regulatory effect of parameters on the model needs to be reflected through long-term integration, short-window assimilation is difficult to balance the influence weights of the initial field and parameters, and cannot meet the long-term optimization needs of the model.
[0005] In summary, existing technologies fall short of MaCOM's core requirements for parameter estimation: high portability, version compatibility, adaptability to sparse observations, and adaptability to long windows. There is an urgent need to construct a parameter estimation framework that does not require complex adjoint models, is computationally efficient, and adapts to sparse observations, in order to overcome the limitations of empirical parameter assignment and improve the accuracy of model simulations and forecasts. Summary of the Invention
[0006] To address the problems existing in the prior art, this invention provides a parameter estimation scheme that is highly portable, computationally efficient, and adaptable to the complex ocean dynamics model MaCOM. It solves the problems of underestimation of covariance, filter divergence, high computational cost, and poor model compatibility of traditional methods by using a hybrid data assimilation method (analytical four-dimensional ensemble variational method). It breaks through the limitations of empirical parameter assignment and uses the bottom friction coefficient as an example for experimental verification, thereby improving the long-term simulation stability and forecast accuracy of the model.
[0007] The technical solution adopted by the present invention to achieve the above objectives is as follows: A parameter estimation design method for mass-conserving ocean models includes the following steps: S1 and MaCOM mode parameter configuration; S2. Preparation of observation data; S3. Construction of the parameter estimation framework; S4. Twin test execution; S5. Actual test execution: S6. Effect Verification and Analysis.
[0008] In S1, the experimental area was set in the Northwest Pacific Ocean from 98.5°E to 165°E and from 12°S to 52.5°N. The model's horizontal resolution was 1 / 24°, and it was divided into 75 vertical layers with a maximum water depth of 5902m. The model-driven data used the Japan Meteorological Agency's JRA55do atmospheric forcing dataset, which provides key parameters such as sea surface wind, air temperature, radiation, precipitation, air pressure, and runoff. The lateral boundary conditions used the Copernicus Ocean Environment Monitoring Service's GLORYS12 global ocean reanalysis product with a horizontal resolution of 1 / 12° to ensure high-resolution adaptability of the boundary field.
[0009] In step S2, two scenarios are set up: ideal experimental observation and real experimental observation. The observation data is prepared as follows: Ideal experimental observation: A realistic model with a bottom friction coefficient of 0.002 is constructed. Using the average data of a certain day as the initial field, after free integration for 5 days, ideal observations are generated based on the simulation results of that day. The sampling strategy is as follows: 1 sampling point is selected for every 100 grid points in the horizontal direction, and sampling is performed every 10 layers in the vertical direction. The sampling interval in the time dimension is 1 hour, covering sea surface height (SSH), sea surface temperature (SST), sea surface salinity (SSS), and vertical temperature and salinity profile elements. Real-world experimental observations: Collect real-world observation data, including sea surface temperature (SST) data provided by OSTIA, sea level anomaly (SLA) data from the Copernicus Marine Environment Monitoring Service, and temperature and salinity profile data from the World Ocean Database 2023. After standardization and outlier removal, a standardized observation dataset is formed.
[0010] S3 specifically includes: S3.1 Core Algorithm Design: Based on the core principle of the analytical four-dimensional ensemble variational method, the construction of tangent linearity and adjoint model is avoided through ensemble perturbation and analytical derivation. The specific implementation is as follows: Assume a certain dynamical system At the initial time, the parameters Evolution, moment The state variable can be represented as Introducing small perturbations Initial guess of parameters Then, by performing a first-order Taylor expansion, we obtain:
[0011] in, and These represent the deterministic and perturbation components of the state variable, respectively. Represents the dynamic evolution operator, Is The tangent linear model at the point, For higher-order remainders, we obtain ; Introducing the concept of sets, defining and ; in, The size of the set; and Let represent the set of state perturbations and the set of parameter perturbations, respectively. Then, we can further derive the evolution formula for the set perturbations: ; Since the perturbation is added to the parameters only at the initial time, the perturbation covariance matrix at the initial time is expressed as: Multiply both sides of the square by Then, by calculating the expected value, we can obtain: By using ensemble perturbation, the computation of tangent linear models and adjoint models is avoided, which greatly improves the portability of the parameter estimation framework and reduces the computational load.
[0012] The traditional incremental cost function takes the following form: Among them, the observation data, For the observation operator, For the observation error covariance matrix, variable substitution is used. This reduces the computational dimensionality to the sample space, decreasing the computational cost, and the cost function becomes: To avoid inverting the background error covariance matrix, a pseudo-inverse matrix is also calculated. Substitute for Then there is , in The cost function ultimately has the following expression: The gradient is: Final order The optimal parameters can then be solved. S3.2 Optimize strategy configuration: The design incorporates a pluggable optimization algorithm module that supports flexible integration and switching between Newton's method, L-BFGS algorithm, and conjugate gradient method. Users can choose the appropriate optimization method based on the complexity of the target mode, computational resource conditions, and parameter estimation accuracy requirements. In the MaCOM mode, Newton's method is more suitable. The design of the inflation factor adaptive adjustment module allows users to flexibly set the value range and verification rules of the inflation factor according to the accuracy requirements of parameter estimation, the coverage of the set, and the characteristics of the target pattern. The core implementation logic of this module is as follows: after generating the basic set by adding 10% Gaussian white noise to the initial parameter set, an inflation factor is introduced. The set dispersion is extended, and the extended formula is as follows: Among them, The expanded parameter set members, The mean of the initial parameter set, This is a member of the initial parameter set after adding Gaussian white noise.
[0013] In S4, the control group settings are as follows: the Ctrl group is set as a control, no parameter estimation is performed, and the bottom friction coefficient is set to 0.01. Assimilation experiment run: The assimilation window is set to 1 day, corresponding to 720 time steps of the model. Ideal observation data are input into the analytical four-dimensional ensemble variational framework. The cost function is iteratively optimized using Newton's method, and the optimized bottom friction coefficient value is output. Free integration verification: Substitute the optimized bottom friction coefficient into the MaCOM model and perform free integration for 15 days to compare the simulation errors of SSH, SST, SSS and vertical thermo-salt structure before and after optimization.
[0014] In S5, the assimilation window is expanded: considering the sparsity of real observation data, the assimilation window is set to 1 day, 3 days and 7 days, and parameter estimation operations are performed based on the parameter estimation framework respectively; parameter estimation and simulation: the bottom friction coefficient is optimized based on real observation data, the optimization results under each window are output, and the cost function reduction is evaluated.
[0015] In step S6, the mean error (ME) and root mean square error (RMSE) are used to evaluate the simulation performance. in, Let be the model variable value at time t; The true value of the variable at time t; The model simulation value is given at time t, the kth depth layer, and the i-th spatial sample. Let t be the true value of the variable at time t, the kth depth layer, and the i-th spatial sample; T is the total number of time sampling points; and N is the number of observation data.
[0016] This invention constructs a MaCOM parameter estimation framework based on analytical four-dimensional ensemble variation. It eliminates the need for complex tangent linear and adjoint models, achieving parameter estimation through ensemble perturbations and analytical derivation. It is compatible with mass conservation models and exhibits strong compatibility and high portability. The optimized parameters closely approximate the true values, significantly reducing simulation errors for multiple ocean elements and improving simulation performance in complex dynamic regions. Extending the assimilation window to 7 days can alleviate the problem of observation sparsity, meet the needs of long-term simulation and forecasting, and provide an efficient and feasible parameter estimation scheme for operational ocean forecasting, with broad application value. Attached Figure Description
[0017] Figure 1 This is the overall flowchart of the present invention.
[0018] Figure 2 This is a comparison of the RMSE of the temperature-salinity profile 15 days after optimization using the parameter estimation framework constructed in this invention in a thought experiment, with the actual parameters.
[0019] Figure 3 This is a graph showing the change in cost function before and after optimization for different assimilation windows in a real experiment. Detailed Implementation
[0020] The technical solution of the present invention will be described in detail below with reference to the accompanying drawings and embodiments: Example
[0021] like Figure 1 The parameter estimation design method for a mass-conserving ocean model, as shown, includes the following steps: S1, MaCOM mode parameter configuration: The experimental region was set in the Northwest Pacific Ocean (98.5°E~165°E, 12°S~52.5°N), with a horizontal resolution of 1 / 24° and a vertical division of 75 layers, reaching a maximum water depth of 5902m. The model-driven data used the Japan Meteorological Agency's JRA55do atmospheric forcing dataset, providing key parameters for sea surface wind, air temperature, radiation, precipitation, air pressure, and runoff. Lateral boundary conditions were achieved using the Copernicus Marine Environment Monitoring Service's GLORYS12 global ocean reanalysis product (horizontal resolution 1 / 12°) to ensure high-resolution adaptability of the boundary field.
[0022] S2. Preparation of observation data: This invention sets up two scenarios: ideal experimental observation and real experimental observation. The observation data is prepared as follows: Ideal experimental observation: A realistic model with a bottom friction coefficient of 0.002 was constructed. Using the daily average data from January 1, 2020 as the initial field, ideal observations were generated based on the simulation results from January 6, 2020 after 5 days of free integration. The sampling strategy was as follows: one sampling point was selected for every 100 grid points in the horizontal direction, and sampling was conducted every 10 layers in the vertical direction. The sampling interval in the time dimension was 1 hour, covering sea surface height (SSH), sea surface temperature (SST), sea surface salinity (SSS), and vertical temperature and salinity profile elements.
[0023] Real-world experimental observations: Collect real-world observation data, including sea surface temperature (SST) data provided by OSTIA, sea level anomaly (SLA) data from the Copernicus Marine Environment Monitoring Service, and temperature and salinity profile data from the World Ocean Database 2023. After standardization and outlier removal, a standardized observation dataset is formed.
[0024] S3. Construction of the parameter estimation framework: S3.1 Core Algorithm Design: Based on the core principle of the analytical four-dimensional set variational method, the construction of tangent linearity and adjoint model is avoided through set perturbation and analytical derivation. The specific implementation is as follows: Suppose a certain dynamic system At the initial time, the parameters Evolution, moment The state variable can be represented as Introducing small perturbations Initial guess of parameters Then, by performing a first-order Taylor expansion, we obtain: in, and These represent the deterministic component and the disturbance component of the state variable, respectively. Represents the dynamic evolution operator, Is Tangent linear model at the point, This is a higher-order remainder term and can be ignored. Therefore, we obtain... .
[0025] Introducing the concept of sets, defining and ; in, The size of the set; and Let represent the set of state perturbations and the set of parameter perturbations, respectively. Then, we can further derive the evolution formula for the set perturbations: .
[0026] Since this invention is applied to parameter estimation, perturbations are added to the parameters only at the initial time. The perturbation covariance matrix at the initial time can be expressed as: Multiply both sides of the square by Then, by calculating the expected value, we can obtain: Therefore, by using set perturbation, the computation of tangent linear model and adjoint model is avoided, which greatly improves the portability of the parameter estimation framework and reduces the amount of computation.
[0027] The traditional incremental cost function takes the following form: Among them, the observation data, For the observation operator, To represent the observation error covariance matrix, variable substitution was employed in this invention. This reduces the computational dimensionality to the sample space, decreasing the computational cost. Therefore, the cost function becomes: To avoid inverting the background error covariance matrix, a pseudo-inverse matrix is also calculated. To replace asking Then there is , in Therefore, the cost function ultimately has the following expression: The gradient is: Final order The optimal parameters can then be solved.
[0028] S3.2 Optimize strategy configuration: This invention designs a pluggable optimization algorithm module that supports the flexible integration and switching of various mainstream numerical optimization algorithms, including Newton's method, L-BFGS algorithm and conjugate gradient method. Users can choose the appropriate optimization method according to the complexity of the target mode, computational resource conditions and parameter estimation accuracy requirements. In MaCOM mode, Newton's method is more suitable.
[0029] This invention designs an adaptive adjustment module for the inflation factor, which allows users to flexibly set the value range and verification rules of the inflation factor according to the accuracy requirements of parameter estimation, the coverage of the set, and the characteristics of the target pattern.
[0030] The core implementation logic of this module is as follows: after generating the basic set by adding 10% Gaussian white noise to the initial parameter set, an inflation factor is introduced. The spread of the set is extended as follows:
[0031] Among them, The expanded parameter set members, The mean of the initial parameter set, This is a member of the initial parameter set after adding Gaussian white noise.
[0032] S4. Twin test execution: Control group settings: Set the Ctrl group (without parameter estimation, and the bottom friction coefficient set to 0.01) as a control.
[0033] Assimilation experiment run: The assimilation window is set to 1 day (corresponding to 720 time steps of the model). Ideal observation data are input into the analytical four-dimensional ensemble variational framework. The cost function is iteratively optimized using Newton's method, and the optimized bottom friction coefficient value is output.
[0034] Free integration verification: Substitute the optimized bottom friction coefficient into the MaCOM model and perform free integration for 15 days to compare the simulation errors of SSH, SST, SSS and vertical thermo-salt structure before and after optimization.
[0035] S5. Actual test execution: Assimilation window expansion: Considering the sparsity of real observation data, the assimilation window is set to 1 day, 3 days and 7 days, and parameter estimation operations are performed based on the parameter estimation framework respectively.
[0036] Parameter estimation and simulation: Optimize the bottom friction coefficient based on real observation data, output the optimization results under each window, and evaluate the cost function reduction.
[0037] S6. Effect Verification and Analysis: The simulation performance was evaluated using mean error (ME) and root mean square error (RMSE).
[0038] in, Let be the model variable value at time t; The true value of the variable at time t; The model simulation value is given at time t, the kth depth layer, and the i-th spatial sample. Let T be the true value of the variable at time t, the kth depth layer, and the i-th spatial sample; T is the total number of time sampling points; and N is the number of observation data.
[0039] Figure 2 The image shows a comparison of the RMSE of the temperature-salinity profile 15 days after the optimization parameters and the actual parameters. It can be seen that in terms of vertical structure, the RMSE of the optimized temperature profile decreased by a maximum of 0.06°C at depths shallower than 1000m, and the RMSE at depths deeper than 1000m was close to 0. The RMSE of the salinity profile decreased overall, and the simulation accuracy of the entire vertical layer was significantly improved. Figure 3The graph shows the cost function changes before and after the optimization of the actual experimental parameters for different assimilation windows. The actual experimental results show that when the assimilation window is set to 7 days, the cost function decreases by 6.999%, which is significantly better than the assimilation window settings of 1 day (0.025%) and 3 days (2.998%), fully demonstrating the adaptability advantage of long windows for sparse observation scenarios.
Claims
1. A parameter estimation design method for mass-conserving ocean models, characterized in that, Specifically, the following steps are included: S1 and MaCOM mode parameter configuration; S2, Preparation of observation data; S3. Construction of the parameter estimation framework; S4. Twin test execution; S5. Actual test execution: S6. Effect Verification and Analysis.
2. The parameter estimation and design method for a mass-conserving ocean model according to claim 1, characterized in that, In S1, the experimental area was set in the Northwest Pacific Ocean from 98.5°E to 165°E and from 12°S to 52.5°N. The model's horizontal resolution was 1 / 24°, and it was divided into 75 vertical layers with a maximum water depth of 5902m. The model-driven data used the Japan Meteorological Agency's JRA55do atmospheric forcing dataset, which provides key parameters such as sea surface wind, air temperature, radiation, precipitation, air pressure, and runoff. The lateral boundary conditions used the Copernicus Ocean Environment Monitoring Service's GLORYS12 global ocean reanalysis product with a horizontal resolution of 1 / 12°.
3. The parameter estimation and design method for a mass-conserving ocean model according to claim 1, characterized in that, In step S2, two scenarios are set up: ideal experimental observation and real experimental observation. The observation data is prepared as follows: Ideal experimental observation: A realistic model with a bottom friction coefficient of 0.002 is constructed. Using the average data of a certain day as the initial field, after free integration for 5 days, ideal observations are generated based on the simulation results of that day. The sampling strategy is as follows: 1 sampling point is selected for every 100 grid points in the horizontal direction, and sampling is performed every 10 layers in the vertical direction. The sampling interval in the time dimension is 1 hour, covering sea surface height (SSH), sea surface temperature (SST), sea surface salinity (SSS), and vertical temperature and salinity profile elements. Real-world experimental observations: Collect real-world observation data, including sea surface temperature (SST) data provided by OSTIA, sea level anomaly (SLA) data from the Copernicus Marine Environment Monitoring Service, and temperature and salinity profile data from the World Ocean Database 2023. After standardization and outlier removal, a standardized observation dataset is formed.
4. The parameter estimation and design method for a mass-conserving ocean model according to claim 1, characterized in that, S3 specifically includes: S3.1 Core Algorithm Design: Based on the core principle of the analytical four-dimensional set variational method, the construction of tangent linearity and adjoint model is avoided through set perturbation and analytical derivation. The specific implementation is as follows: Suppose a certain dynamic system At the initial time, the parameters Evolution, moment The state variable can be represented as Introducing small perturbations Initial guess of parameters Then, by performing a first-order Taylor expansion, we obtain: in, and These represent the deterministic and perturbation components of the state variable, respectively. Represents the dynamic evolution operator, Is The tangent linear model at the point, For higher-order remainders, we obtain ; Introducing the concept of sets, defining and ;in, The size of the set; and Let represent the set of state perturbations and the set of parameter perturbations, respectively. Then, we can further derive the evolution formula for the set perturbations: Since the parameters are perturbed only at the initial time, the perturbation covariance matrix at the initial time is expressed as: Multiply both sides of the square by Then, by calculating the expected value, we can obtain: ; The traditional incremental cost function takes the following form: Among them, the observation data, For the observation operator, For the observation error covariance matrix, variable substitution is used. The cost function becomes: To avoid inverting the background error covariance matrix, a pseudo-inverse matrix is also calculated. Substitute for Then there is , in The cost function ultimately has the following expression: The gradient is: Final order The optimal parameters can then be solved. S3.2 Optimize strategy configuration: The design incorporates a pluggable optimization algorithm module that supports flexible integration and switching between Newton's method, L-BFGS algorithm, and conjugate gradient method. Users can choose the appropriate optimization method based on the complexity of the target mode, computational resource conditions, and parameter estimation accuracy requirements. In the MaCOM mode, Newton's method is more suitable. The design of the inflation factor adaptive adjustment module allows users to flexibly set the value range and verification rules of the inflation factor according to the accuracy requirements of parameter estimation, the coverage of the set, and the characteristics of the target pattern. The core implementation logic of this module is as follows: after generating the basic set by adding 10% Gaussian white noise to the initial parameter set, an inflation factor is introduced. The set dispersion is extended, and the extended formula is as follows: Among them, The expanded parameter set members, The mean of the initial parameter set, This is a member of the initial parameter set after adding Gaussian white noise.
5. The parameter estimation and design method for a mass-conserving ocean model according to claim 1, characterized in that, In S4, the control group settings are as follows: the Ctrl group is set as a control, no parameter estimation is performed, and the bottom friction coefficient is set to 0.
01. Assimilation experiment run: The assimilation window is set to 1 day, corresponding to 720 time steps of the model. Ideal observation data are input into the analytical four-dimensional ensemble variational framework. The cost function is iteratively optimized using Newton's method, and the optimized bottom friction coefficient value is output. Free integration verification: Substitute the optimized bottom friction coefficient into the MaCOM model and perform free integration for 15 days to compare the simulation errors of SSH, SST, SSS and vertical thermo-salt structure before and after optimization.
6. The parameter estimation and design method for a mass-conserving ocean model according to claim 1, characterized in that, In S5, the assimilation window is expanded: considering the sparsity of real observation data, the assimilation window is set to 1 day, 3 days and 7 days, and parameter estimation operations are performed based on the parameter estimation framework respectively; parameter estimation and simulation: the bottom friction coefficient is optimized based on real observation data, the optimization results under each window are output, and the cost function reduction is evaluated.
7. The parameter estimation and design method for a mass-conserving ocean model according to claim 1, characterized in that, In step S6, the mean error (ME) and root mean square error (RMSE) are used to evaluate the simulation performance. in, Let be the model variable value at time t; The true value of the variable at time t; The model simulation value is given at time t, the kth depth layer, and the i-th spatial sample. Let T be the true value of the variable at time t, the kth depth layer, and the i-th spatial sample; T is the total number of time sampling points; and N is the number of observation data.