Infrared hyperspectral data assimilation and evaluation method and system
By using radiation transmission model and four-dimensional variational assimilation system in the OSSEs framework, the problem of evaluating the impact of different spectral resolutions on numerical weather forecasts is solved, and the accuracy and reliability of forecasts are improved.
Patent Information
- Application Number
- CN202510381117.7
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-03-28
- Publication Date
- 2025-05-02
AI Technical Summary
When using infrared hyperspectral data for numerical weather forecasting, it is difficult to effectively assimilate and evaluate the impact of different spectral resolutions on the forecasting effect, resulting in insufficient forecast accuracy and reliability.
By using the radiation transmission model to generate infrared hyperspectral simulation data in the OSSEs framework, and combining the four-dimensional variational assimilation system for data assimilation and forecast field generation, the impact of different spectral resolutions on forecast effect is evaluated.
It improves the accuracy of infrared hyperspectral data assimilation and the reliability of forecast field, guides the design of meteorological satellite instruments and the improvement of data assimilation systems, and improves the accuracy and reliability of numerical forecasts.
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Abstract
Description
Technical Field
[0001] The present invention relates to the technical field of data processing, and in particular to an infrared hyperspectral data assimilation and evaluation method and system. Background Art
[0002] In recent years, the integration of satellite data into numerical weather prediction (NWP) models has significantly improved the accuracy of weather forecasts. Among various types of satellite observation data, infrared (IR) radiation data is particularly important due to its rich information content and global coverage. These data provide valuable information on the vertical temperature and humidity profiles of the atmosphere, which is crucial for the accurate initialization of NWP models. Observation System Simulation Experiments (OSSEs) are a method of using simulated observations to evaluate the potential impact of new observation systems. They are often used before satellite payloads are launched or for the evaluation of new observation deployments or assimilation strategies. On this basis, this application proposes an infrared hyperspectral data assimilation and evaluation method. Based on the OSSEs framework of the domestic numerical forecast model CMA-GFS, the impact of different spectral resolutions on the assimilation effect of infrared hyperspectral data is analyzed. Summary of the invention
[0003] To achieve the purpose of the present invention, the present application provides an infrared hyperspectral data assimilation and evaluation method, comprising: Step S1: Generate infrared hyperspectral simulation data using the radiation transfer model according to satellite orbit parameters, instrument observation geometry parameters and ERA5 data set; Step S2: preprocessing the infrared hyperspectral simulation data, and using a four-dimensional variational assimilation forecasting system to assimilate the infrared hyperspectral simulation data to obtain an analysis field and a forecast field; Step S3: determining the error covariance matrix and the observation error covariance matrix of the background field according to the analysis field and the background field, and obtaining the optimized analysis field result based on the four-dimensional variational assimilation system; and predicting the result of the forecast field in the next few days according to the optimized analysis field result, and evaluating the performance of the forecast field.
[0004] In some specific embodiments, step S1 includes: Calculate the position and observation time of the ground observation point according to the satellite sub-satellite point position, the satellite scanning step angle, and the detector layout settings; The satellite zenith angle, satellite azimuth angle, solar zenith angle and solar azimuth angle are calculated according to the satellite subsatellite point position, ground observation point position and solar position; According to the location and time of the ground observation points, the ERA5 dataset is temporally and spatially matched, and the temporally and spatially matched ERA5 dataset is used as the background field of the radiation transfer model.
[0005] In some specific embodiments, step S1 further includes: Infrared hyperspectral simulation data are generated using a radiation transfer model based on the atmospheric profile, the transmittance coefficient of the infrared hyperspectrometer, and the satellite zenith angle, satellite azimuth angle, solar zenith angle, and solar azimuth angle.
[0006] In some specific embodiments, step S2 further includes: The infrared hyperspectral simulation data is preprocessed by channel selection, quality control, observation error and deviation correction.
[0007] In some specific embodiments, step S3 includes: The four-dimensional variational assimilation system determines the variables that are closest to the actual atmospheric conditions based on the theory of minimizing the cost function.
[0008] To achieve the same invention purpose, the present application also provides an infrared hyperspectral data assimilation and evaluation system, including: Data generation module: used to generate infrared hyperspectral simulation data based on satellite orbit parameters, instrument observation geometry parameters and ERA5 data set using radiation transfer model; Forecast field generation module: used for preprocessing the infrared hyperspectral simulation data, and assimilating the infrared hyperspectral simulation data using a four-dimensional variational assimilation forecasting system to obtain an analysis field and a forecast field; Performance evaluation module: used to determine the error covariance matrix and observation error covariance matrix of the background field based on the analysis field and the background field, and obtain the optimized analysis field results based on the four-dimensional variational assimilation system; and predict the results of the forecast field in the next few days based on the optimized analysis field results, and evaluate the performance of the forecast field.
[0009] In some specific embodiments, the data generation module is used to: Calculate the position and observation time of the ground observation point according to the satellite sub-satellite point position, the satellite scanning step angle, and the detector layout settings; The satellite zenith angle, satellite azimuth angle, solar zenith angle and solar azimuth angle are calculated according to the satellite subsatellite point position, ground observation point position and solar position; According to the location and time of the ground observation points, the ERA5 dataset is temporally and spatially matched, and the temporally and spatially matched ERA5 dataset is used as the background field of the radiation transfer model.
[0010] In some specific embodiments, the data generation module is further used to: Infrared hyperspectral simulation data are generated using a radiation transfer model based on the atmospheric profile, the transmittance coefficient of the infrared hyperspectrometer, and the satellite zenith angle, satellite azimuth angle, solar zenith angle, and solar azimuth angle.
[0011] In some specific embodiments, the forecast field generation module is used to: The infrared hyperspectral simulation data is preprocessed by channel selection, quality control, observation error and deviation correction.
[0012] In some specific embodiments, the performance evaluation module includes: The four-dimensional variational assimilation system determines the variables that are closest to the actual atmospheric conditions based on the theory of minimizing the cost function.
[0013] Beneficial effects of the above technical solution: The infrared hyperspectral data assimilation and evaluation method and system of the present application provide strong support for the research and application in the field of meteorological forecasting by using simulation data to evaluate and optimize the forecasting system. It can also guide the design of meteorological satellite instruments and the improvement of data assimilation systems by evaluating the impact of spectral resolution on numerical forecasting, thereby improving the accuracy and reliability of numerical forecasting. BRIEF DESCRIPTION OF THE DRAWINGS
[0014] In order to more clearly illustrate the technical solutions in the embodiments of the present application, the drawings required for use in the description of the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present application. For those skilled in the art, other drawings can be obtained based on these drawings without creative work.
[0015] Figure 1 A schematic flow chart of an infrared hyperspectral data assimilation and evaluation method provided by an embodiment of the present invention; Figure 2a A schematic diagram of the improvement percentage of the root mean square error of the temperature field of an infrared hyperspectral data assimilation and evaluation method provided by an embodiment of the present invention; Figure 2b A schematic diagram of the improvement percentage of the root mean square error of the humidity field of an infrared hyperspectral data assimilation and evaluation method provided by an embodiment of the present invention; Figure 3 A schematic diagram of the variation of abnormal correlation coefficients of the height fields in the northern and southern hemispheres of an infrared hyperspectral data assimilation and evaluation method provided by an embodiment of the present invention; Figure 4 A schematic diagram of the structure of an infrared hyperspectral data assimilation and evaluation system provided for one embodiment of the present invention. DETAILED DESCRIPTION
[0016] The technical solutions in the embodiments of the present invention will be described clearly and completely below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, rather than all the embodiments.
[0017] Examples of the embodiments are shown in the accompanying drawings, wherein the same or similar symbols throughout represent the same or similar elements or elements with the same or similar functions. The embodiments described below with reference to the accompanying drawings are exemplary and are intended to be used to explain the present invention, and should not be construed as limiting the present invention.
[0018] Embodiment 1 An embodiment of the present invention provides an infrared hyperspectral data assimilation and evaluation method, referring to Figure 1 As shown, including: Step S1: Generate infrared hyperspectral simulation data using the radiation transfer model based on satellite orbit parameters, instrument observation geometry parameters and ERA5 data sets. The atmospheric motion can be predicted using the atmospheric observation data and the atmospheric motion trajectory, and a cloud motion model can be established through the atmospheric motion trajectory, and then the cloud motion model is added to the radiation transfer model.
[0019] In a specific embodiment of the present invention, step S1 includes: Calculate the position and observation time of the ground observation point according to the satellite sub-satellite point position, the satellite scanning step angle, and the detector layout settings; The satellite zenith angle, satellite azimuth angle, solar zenith angle and solar azimuth angle are calculated according to the satellite subsatellite point position, ground observation point position and solar position; According to the location and time of the ground observation points, the ERA5 dataset is temporally and spatially matched, and the temporally and spatially matched ERA5 dataset is used as the background field of the radiation transfer model.
[0020] In a specific embodiment of the present invention, step S1 further includes: Infrared hyperspectral simulation data are generated using a radiation transfer model based on the atmospheric profile, the transmittance coefficient of the infrared hyperspectrometer, and the satellite zenith angle, satellite azimuth angle, solar zenith angle, and solar azimuth angle.
[0021] Step S2: preprocessing the infrared hyperspectral simulation data, and using a four-dimensional variational assimilation forecasting system to assimilate the infrared hyperspectral simulation data to obtain an analysis field and a forecast field.
[0022] In a specific embodiment of the present invention, step S2 further includes: The infrared hyperspectral simulation data is preprocessed by channel selection, quality control, observation error and deviation correction.
[0023] Specifically, the OSSEs in this application use the four-dimensional variational assimilation system of CMA-GFS4.2. Compared with three-dimensional variational assimilation, the four-dimensional variational assimilation system can more effectively assimilate 50% more observational data, significantly reducing the error amplitude of analysis and forecasting. The assimilation window length of the four-dimensional variational assimilation system of CMA-GFS is six hours. Four-dimensional variational assimilation is a time dimension extension of three-dimensional variational assimilation, and has the ability to implicitly transfer the initial background error covariance within the assimilation window. The four-dimensional variational assimilation method is based on the theory of minimizing the cost function to obtain the variables that are closest to the actual atmospheric conditions (within the time window to T): ; In the formula, and Denote the analysis field and the background field respectively, B denotes the error covariance matrix of the background field, R denotes the observation error covariance matrix, Indicates time Time The mode integral of , H represents the observation operator, i Indicates time.
[0024] Step S3: determining the error covariance matrix and the observation error covariance matrix of the background field according to the analysis field and the background field, and obtaining the optimized analysis field result based on the four-dimensional variational assimilation system; and predicting the result of the forecast field in the next few days according to the optimized analysis field result, and evaluating the performance of the forecast field.
[0025] In a specific embodiment of the present invention, step S3 includes: The four-dimensional variational assimilation system determines the variables that are closest to the actual atmospheric conditions based on the theory of minimizing the cost function.
[0026] In this application, the temperature information and water vapor information of infrared hyperspectral data are assimilated, and the focus is on the improvement effect of the assimilation of temperature information and water vapor information on the temperature field and humidity field. Taking the fifth generation atmospheric reanalysis data (ERA5) of the European Center for Medium-Range Weather Forecasts (ECMWF) as a reference, temperature and specific humidity are used as check factors, and the root mean square error (RMSE) of the check factors is calculated to illustrate the impact of infrared data assimilation of different spectral resolutions on the analysis. The results are shown in the figure. Figure 2a , Figure 2b shown.
[0027] Figure 2aThe percentage of improvement of RMSE of temperature field is given. In general, the southern hemisphere is better than the tropics, and the tropics are better than the northern hemisphere. This is mainly because the conventional observation data in the southern hemisphere are scarce. The assimilation of infrared satellite data can effectively fill the observation data in this area, so the temperature field at different altitudes in the southern hemisphere has improved. The assimilation of 0.625cm-1 infrared simulation data has a better effect on the improvement of temperature field than 0.5cm-1. The northern hemisphere and East Asia are better than conventional observation data. The difference in the assimilation effect of infrared data of different resolutions is not very significant. For the southern hemisphere with scarce observation data, the assimilation of infrared data plays a major role in improving the analysis field.
[0028] Figure 2b The percentage improvement of RMSE of humidity field is given. Overall, the improvement of humidity field is smaller than that of temperature field. The improvement of 0.625cm-1 data assimilation on analysis field is better than that of the other two spectral resolution data assimilation.
[0029] In order to evaluate the impact of infrared data with different spectral resolutions on the forecast, a 240-hour forecast was made with 1200 UTC as the starting point. The forecast results were compared with the FNL forecast field. ACC (anomaly correlation coefficient) is often used to evaluate the forecasting skills of the model. A higher ACC that evaluates the correlation between the forecast field and the reference analysis field indicates that the correlation between the forecast field and the reference analysis field is higher, indicating that the model results perform better. According to WMO standards, when the ACC of the 500hpa height field exceeds 0.6, the meteorological forecast results are usable. However, the purpose of this article is not to illustrate the impact of the assimilation of infrared simulation data on the increase in the number of effective forecast days, but to illustrate the impact of infrared data with different spectral resolutions on the forecast through ACC. From Figure 3 It can be seen that for the control experiment and the three groups of observation experiments, for the northern hemisphere, ACC starts to change from 72h. Due to the assimilation of 0.625cm-1 simulation data, from T+0 to T+216h, ACC of 0.625 experiment>0.5 experiment>control experiment, from T+216h. For the southern hemisphere, due to the scarcity of observation data in the southern hemisphere, satellite data fills the gap in observation data, and ACC starts to change from 24h. ACC of 0.625 experiment>0.5 experiment>control experiment.
[0030] In this application, OSSEs are constructed to evaluate the impact of different spectral resolutions on the assimilation and prediction of infrared hyperspectral data. Under the OSSE framework, it includes an infrared data simulation system based on orbit, satellite observation and instrument parameters, a four-dimensional variational assimilation system, a numerical prediction system and its assimilation prediction evaluation. In order to evaluate the impact of different spectral resolutions on the assimilation and prediction of infrared data, four groups of experiments (control experiments + 3 groups of observation experiments) were carried out. From the perspective of preprocessing of infrared simulation data, the impact of assimilation on the analysis field and the impact of the forecast field, the results show that the assimilation of 0.625cm-1 spectral resolution infrared data improves the analysis field and forecast field better than the assimilation and prediction effect of 0.5cm-1 spectral resolution infrared data. Especially in the case of scarce observation data in the southern hemisphere and only assimilation of infrared simulation data, the effect advantage of 0.625cm-1 spectral resolution infrared data is more significant. Future work can provide a reference for the parameter setting of infrared hyperspectral instruments and their orbit settings for the new generation of polar-orbiting satellites.
[0031] Embodiment 2 An embodiment of the present invention provides an infrared hyperspectral data assimilation and evaluation system, comprising: Data generation module 10: used to generate infrared hyperspectral simulation data using a radiation transfer model according to satellite orbit parameters, instrument observation geometric parameters and ERA5 data sets; The forecast field generation module 20 is used to pre-process the infrared hyperspectral simulation data and assimilate the infrared hyperspectral simulation data using a four-dimensional variational assimilation forecasting system to obtain an analysis field and a forecast field; Performance evaluation module 30: used to determine the error covariance matrix and observation error covariance matrix of the background field based on the analysis field and the background field, and obtain the optimized analysis field results based on the four-dimensional variational assimilation system; and predict the results of the forecast field in the next few days based on the optimized analysis field results, and evaluate the performance of the forecast field.
[0032] In a specific embodiment of the present invention, the data generation module 10 is used to: Calculate the position and observation time of the ground observation point according to the satellite sub-satellite point position, the satellite scanning step angle, and the detector layout settings; The satellite zenith angle, satellite azimuth angle, solar zenith angle and solar azimuth angle are calculated according to the satellite subsatellite point position, ground observation point position and solar position; According to the location and time of the ground observation points, the ERA5 dataset is temporally and spatially matched, and the temporally and spatially matched ERA5 dataset is used as the background field of the radiation transfer model.
[0033] In a specific embodiment of the present invention, the data generation module 10 is further used for: Infrared hyperspectral simulation data are generated using a radiation transfer model based on the atmospheric profile, the transmittance coefficient of the infrared hyperspectrometer, and the satellite zenith angle, satellite azimuth angle, solar zenith angle, and solar azimuth angle.
[0034] In a specific embodiment of the present invention, the forecast field generation module 20 is used to: The infrared hyperspectral simulation data is preprocessed by channel selection, quality control, observation error and deviation correction.
[0035] In a specific embodiment of the present invention, the performance evaluation module 30 includes: The four-dimensional variational assimilation system determines the variables that are closest to the actual atmospheric conditions based on the theory of minimizing the cost function.
[0036] The above is only a specific embodiment of the present invention, but the protection scope of the present invention is not limited thereto. Any person skilled in the art can easily think of changes or substitutions within the technical scope disclosed by the present invention, which should be included in the protection scope of the present invention. Therefore, the protection scope of the present invention should be based on the protection scope of the claims.
[0037] Each embodiment in this specification is described in a progressive manner, and each embodiment focuses on the differences from other embodiments. The same or similar parts between the embodiments can be referenced to each other. The embodiments of the present invention are described with reference to the flowcharts and / or block diagrams of the methods, terminal devices (systems), and computer program products according to the embodiments of the present invention. It should be understood that each process and / or box in the flowchart and / or block diagram, as well as the combination of the processes and / or boxes in the flowchart and / or block diagram, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing terminal device to produce a machine, so that the instructions executed by the processor of the computer or other programmable data processing terminal device generate instructions for implementing the functions in the process. Figure 1 A process or multiple processes and / or boxes Figure 1 These computer program instructions can also be stored in a computer-readable memory that can guide a computer or other programmable data processing terminal device to work in a specific way, so that the instructions stored in the computer-readable memory produce a product including an instruction device, which implements the functions specified in the process. Figure 1 A process or multiple processes and / or boxes Figure 1These computer program instructions can also be loaded onto a computer or other programmable data processing terminal device, so that a series of operation steps are executed on the computer or other programmable terminal device to produce a computer-implemented process, so that the instructions executed on the computer or other programmable terminal device provide for implementing the process in the process. Figure 1 A process or multiple processes and / or boxes Figure 1 The steps of the functions specified in one or more boxes. Although the preferred embodiments of the embodiments of the present invention have been described, those skilled in the art may make additional changes and modifications to these embodiments once they know the basic creative concept. Therefore, the attached claims are intended to be interpreted as including the preferred embodiments and all changes and modifications that fall within the scope of the embodiments of the present invention. Finally, it should be noted that, in this article, relational terms such as first and second, etc. are only used to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply that there is any such actual relationship or order between these entities or operations. Moreover, the terms "include", "comprise" or any other variant thereof are intended to cover non-exclusive inclusion, so that the process, method, article or terminal device including a series of elements includes not only those elements, but also other elements that are not explicitly listed, or also includes elements inherent to such process, method, article or terminal device. In the absence of more restrictions, the elements defined by the sentence "including one..." do not exclude the existence of other identical elements in the process, method, article or terminal device including the elements.
[0038] The method and device provided by the present invention are introduced in detail above. Specific examples are used in this article to illustrate the principle and implementation mode of the present invention. The description of the above embodiments is only used to help understand the method of the present invention and its core idea. At the same time, for those skilled in the art, according to the idea of the present invention, there will be changes in the specific implementation mode and application scope. In summary, the content of this specification should not be understood as limiting the present invention.
[0039] In the description of this specification, the description with reference to the terms "one embodiment", "some embodiments", "example", "specific example", "one specific embodiment" or "some examples" etc. means that the specific features, structures, materials or characteristics described in conjunction with the embodiment or example are included in at least one embodiment or example of the present invention. In this specification, the schematic representation of terms does not necessarily refer to the same embodiment or example. Moreover, the specific features, structures, materials or characteristics described may be combined in any one or more embodiments or examples in a suitable manner.
[0040] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present application, rather than to limit it. Although the present application has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or make equivalent replacements for some of the technical features therein. However, these modifications or replacements do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present application.
Claims
1. A method for assimilation and evaluation of infrared hyperspectral data, characterized in that: include: Step S1: Generate a background field based on satellite orbit parameters, instrument observation geometry parameters and ERA5 data set, and generate infrared hyperspectral simulation data using a radiation transfer model; Step S2: preprocessing the infrared hyperspectral simulation data, and assimilating the infrared hyperspectral simulation data using a four-dimensional variational assimilation forecasting system to obtain an analysis field and a forecast field; Step S3: determining the error covariance matrix and the observation error covariance matrix of the background field according to the analysis field and the background field, and obtaining an optimized analysis field result based on a four-dimensional variational assimilation system; And predict the results of the forecast field in the next few days based on the optimized analysis field results, and evaluate the performance of the forecast field.
2. The infrared hyperspectral data assimilation and evaluation method according to claim 1, characterized in that: Step S1 includes: Calculate the position and observation time of the ground observation point according to the satellite sub-satellite point position, the satellite scanning step angle, and the detector layout settings; The satellite zenith angle, satellite azimuth angle, solar zenith angle and solar azimuth angle are calculated according to the satellite subsatellite point position, ground observation point position and solar position; According to the location and time of the ground observation points, the ERA5 dataset is temporally and spatially matched, and the temporally and spatially matched ERA5 dataset is used as the background field of the radiation transfer model.
3. The infrared hyperspectral data assimilation and evaluation method according to claim 2, characterized in that: Step S1 also includes: Infrared hyperspectral simulation data are generated using a radiation transfer model based on the atmospheric profile, the transmittance coefficient of the infrared hyperspectrometer, and the satellite zenith angle, satellite azimuth angle, solar zenith angle, and solar azimuth angle.
4. The infrared hyperspectral data assimilation and evaluation method according to claim 1, characterized in that: Step S2 also includes: The infrared hyperspectral simulation data is preprocessed by channel selection, quality control, observation error and deviation correction.
5. The infrared hyperspectral data assimilation and evaluation method according to claim 1, characterized in that: Step S3 includes: The four-dimensional variational assimilation system determines the variables that are closest to the actual atmospheric conditions based on the theory of minimizing the cost function.
6. An infrared hyperspectral data assimilation and evaluation system, characterized in that: include: Data generation module: used to generate infrared hyperspectral simulation data based on satellite orbit parameters, instrument observation geometry parameters and ERA5 data set using radiation transfer model; Forecast field generation module: used for preprocessing the infrared hyperspectral simulation data, and assimilating the infrared hyperspectral simulation data using a four-dimensional variational assimilation forecasting system to obtain an analysis field and a forecast field; Performance evaluation module: used to determine the error covariance matrix and observation error covariance matrix of the background field according to the analysis field and the background field, and obtain the optimized analysis field result based on the four-dimensional variational assimilation system; And predict the results of the forecast field in the next few days based on the optimized analysis field results, and evaluate the performance of the forecast field.
7. The infrared hyperspectral data assimilation and evaluation system according to claim 6, characterized in that: The data generation module is used for: Calculate the position and observation time of the ground observation point according to the satellite sub-satellite point position, the satellite scanning step angle, and the detector layout settings; The satellite zenith angle, satellite azimuth angle, solar zenith angle and solar azimuth angle are calculated according to the satellite subsatellite point position, ground observation point position and solar position; According to the location and time of the ground observation points, the ERA5 dataset is temporally and spatially matched, and the temporally and spatially matched ERA5 dataset is used as the background field of the radiation transfer model.
8. The infrared hyperspectral data assimilation and evaluation system according to claim 7, characterized in that: The data generation module is also used for: Infrared hyperspectral simulation data are generated using a radiation transfer model based on the atmospheric profile, the transmittance coefficient of the infrared hyperspectrometer, and the satellite zenith angle, satellite azimuth angle, solar zenith angle, and solar azimuth angle.
9. The infrared hyperspectral data assimilation and evaluation system according to claim 6, characterized in that: The forecast field generation module is used for: The infrared hyperspectral simulation data is preprocessed by channel selection, quality control, observation error and deviation correction.
10. The infrared hyperspectral data assimilation and evaluation system according to claim 6, characterized in that: The performance evaluation module includes: The four-dimensional variational assimilation system determines the variables that are closest to the actual atmospheric conditions based on the theory of minimizing the cost function.
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