Artificial intelligence weather forecast error analysis method based on mathematical decomposition
By decomposing AI-based weather forecasting errors using mathematical decomposition methods, the problem of uninterpretable error analysis in existing methods is solved. This enables low-cost, high-reliability error source analysis and improves the interpretability and debuggability of the model.
Patent Information
- Application Number
- CN202510830021.4
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-06-20
- Publication Date
- 2025-10-17
AI Technical Summary
Existing AI weather forecast error analysis methods lack explainability and make it difficult to trace errors back to specific physical processes, which limits the diagnosability and debuggability of the model.
An artificial intelligence-based weather forecast error analysis method based on mathematical decomposition is adopted. By extracting forecast data, reanalysis data and observation data, the reanalysis error, fitting error and forecast error are calculated respectively, and the error decomposition is performed to analyze the source of forecast error.
While maintaining low computational costs, the interpretability of error analysis is improved, the sources of forecast errors are accurately identified, and the diagnostic and debuggable nature of the model is enhanced.
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Abstract
Description
TECHNICAL FIELD
[0001] The present application relates to the technical field of weather forecast error analysis, and more particularly to an artificial intelligence weather forecast error analysis method based on mathematical decomposition. BACKGROUND
[0002] Weather forecast generally plays an important role in economic and social development and emergency management. Conventional weather forecast is based on a numerical weather prediction model, and observation data is used as a target to calibrate the model, and the prediction error depends on the fitting error of the model to the observation data. Therefore, the core of the traditional weather forecast error analysis method is to analyze the physical process in depth, to compare the differences under different physical schemes, and to calculate the energy and water balance at the regional or global scale, so as to lock the source of the system error of the weather forecast, so that the reliability of the error analysis method is higher and the interpretability is stronger, but the calculation cost is higher and it is difficult to perfectly represent the physical mechanism behind the error.
[0003] The emerging artificial intelligence weather forecast method inputs atmospheric reanalysis data into an artificial intelligence-based weather forecast model for weather prediction. The artificial intelligence-based weather forecast model is trained and tested based on atmospheric reanalysis data, and the reanalysis data is generated by fusing scattered historical observation data through a fixed version of a numerical model and a data assimilation system, generating three-dimensional atmospheric state data covering the global and time-continuous, which itself has errors. Therefore, the prediction error depends not only on the fitting error of the model to the reanalysis data, but also on the error of the reanalysis data relative to the observation data. Although the existing artificial intelligence weather forecast error analysis method reduces the calculation cost, it lacks interpretability, and it is difficult to trace the error to specific physical equations or physical processes such as radiation transmission, cloud microphysics, and boundary layer turbulence, limiting the model's diagnostic and debuggability, which is not conducive to effective improvement of weather forecast. SUMMARY
[0004] To solve the problem that the existing artificial intelligence weather forecast error analysis method has poor interpretability and is difficult to analyze the source of the prediction error, the present application proposes an artificial intelligence weather forecast error analysis method based on mathematical decomposition, which accurately analyzes the source of the prediction error under the premise of ensuring reliability, and improves the interpretability of the error analysis method.
[0005] In order to achieve the above technical effects, the technical solutions of the present application are as follows: In a first aspect, the present application proposes an artificial intelligence weather forecast error analysis method based on mathematical decomposition, comprising the following steps: S1. Extracting and preprocessing data required for artificial intelligence weather forecast error analysis, including forecast data, reanalysis data and observation data; S2. Calculating reanalysis error, fitting error and forecast error based on forecast data, reanalysis data and observation data, respectively; S3. Error decomposition of reanalysis error, fitting error and forecast error, based on the error decomposition result, the source of the forecast error is analyzed, and the analysis of the artificial intelligence weather forecast error is completed.
[0006] In the technical solution, first, the forecast data, reanalysis data and observation data required for artificial intelligence weather forecast error analysis are extracted and preprocessed; then, based on the forecast data, reanalysis data and observation data, the reanalysis error, fitting error and forecast error are calculated respectively; the error decomposition of the reanalysis error, fitting error and forecast error is carried out, based on the error decomposition result, the source of the forecast error is analyzed, and the analysis of the artificial intelligence weather forecast error is completed, the calculation process is simple, and the calculation cost is low. In addition, the method proposed by the present application is based on strict mathematical decomposition, which can accurately analyze the source of the forecast error under the premise of ensuring the reliability and low calculation cost of the weather forecast error analysis, and improve the explainability of the error analysis method.
[0007] Preferably, the preprocessing process is: unifying the time resolution of the forecast data , the reanalysis data and the observation data ; selecting grid point coordinates , extracting the specific forecast value corresponding to the time from the forecast data , the expression is:
[0008] wherein, is the grid point latitude, is the grid point longitude, is the time, is the forecast start time, is the forecast period; extracting the specific reanalysis data corresponding to the time from the reanalysis data , matching the spatial resolution of the specific reanalysis data to the same spatial resolution as the specific forecast value , the expression is:
[0009] based on the forecast data grid point coordinates of the observation station, and observation data from the observation station in time specific observation data , and the expression is: .
[0010] Preferably, the reanalysis error S2 is the error between the reanalysis data and the observation data , and the calculation expression is:
[0011] The fitting error S3 is the error between the prediction data and the reanalysis data , and the calculation expression is:
[0012] The prediction error S4 is the error between the prediction data and the observation data , and at the same time, the prediction error S4 is the sum of the reanalysis error S2 and the fitting error S3 , and the calculation expression is: .
[0013] Preferably, the error decomposition of the reanalysis error, the fitting error and the prediction error comprises: The reanalysis error, the fitting error and the prediction error are respectively decomposed into systematic errors and random errors, and the expression is:
[0014] wherein, is the systematic error of the reanalysis error S2 , is the random error of the reanalysis error S2 , is the systematic error of the fitting error S3 , is the random error of the fitting error S3 , is the systematic error of the prediction error S4 , is the random error of the prediction error S4 .
[0015] Preferably, the error decomposition further comprises: The prediction error S4 is decomposed into the reanalysis error S2 systematic error of the system fitting error systematic error of the system reanalysis error random error of the system fitting error random error of the fitting error the sum of the above, expressed as: .
[0016] Preferably, the error decomposition further comprises: decomposing the expectation of the square of the prediction error, expressed as:
[0017] wherein, is the systematic error part of the reanalysis error, is the interaction part of the reanalysis error and the systematic error part of the fitting error, is the systematic error part of the fitting error, is the random error part of the reanalysis error, is the interaction part of the reanalysis error and the random error part of the fitting error, is the random error part of the fitting error.
[0018] Preferably, S3 analyzes the source of the prediction error based on the error decomposition result, the process being: solving the systematic error part of the reanalysis error in the expectation of the square of the prediction error , expressed as:
[0019] solving the interaction 2 of the reanalysis error and the systematic error part of the fitting error in the expectation of the square of the prediction error , expressed as:
[0020] solving the systematic error part of the fitting error in the expectation of the square of the prediction error , expressed as:
[0021] solving the random error part of the reanalysis error in the expectation of the square of the prediction error , expressed as:
[0022] Solving the interaction of the random error part of the reanalysis error and the fitting error The proportion in the expectation of the square of the forecast error The expression is:
[0023] Solving the random error part of the fitting error The proportion in the expectation of the square of the forecast error The expression is:
[0024] Comparing the proportions of each part in the expectation of the square of the forecast error The part with the largest proportion is selected as the source of the forecast error, and the analysis of the artificial intelligence weather forecast error is completed.
[0025] In a second aspect, the application further provides an artificial intelligence weather forecast error analysis system based on mathematical decomposition, which comprises: A data extraction and preprocessing module is configured to extract data required for artificial intelligence weather forecast error analysis and perform preprocessing, and the required data includes forecast data, reanalysis data and observation data; An error calculation module is configured to calculate the reanalysis error, the fitting error and the forecast error based on the forecast data, the reanalysis data and the observation data, respectively, wherein the forecast error is the sum of the reanalysis error and the fitting error; An error decomposition analysis module is configured to perform error decomposition on the reanalysis error, the fitting error and the forecast error, and based on the error decomposition result, the source of the forecast error is analyzed, and the analysis of the artificial intelligence weather forecast error is completed.
[0026] In a third aspect, the application further provides a computer device, which comprises a memory, a processor and a computer program stored on the memory and executable by the processor, wherein the processor executes the computer program to implement the artificial intelligence weather forecast error analysis method based on mathematical decomposition.
[0027] In a fourth aspect, the application further provides a computer storage medium, which stores a computer program, and the computer program comprises program instructions, which, when executed by a computer, cause the computer to execute the artificial intelligence weather forecast error analysis method based on mathematical decomposition.
[0028] Compared with the prior art, the application has the following beneficial effects: The application provides an artificial intelligence weather forecast error analysis method based on mathematical decomposition, which comprises the following steps: firstly, extracting and preprocessing the forecast data, reanalysis data and observation data required for artificial intelligence weather forecast error analysis; secondly, calculating the reanalysis error, fitting error and forecast error based on the forecast data, reanalysis data and observation data; thirdly, performing error decomposition on the reanalysis error, fitting error and forecast error, and analyzing the source of the forecast error based on the error decomposition result, thereby completing the analysis of the artificial intelligence weather forecast error; and fourthly, calculating the process simply and at low cost. In addition, the method provided by the application is based on strict mathematical decomposition, can accurately analyze the source of the forecast error under the premise of ensuring the reliability of the weather forecast error analysis and low calculation cost, and improves the explainability of the error analysis method. BRIEF DESCRIPTION OF DRAWINGS
[0029] Figure 1 Fig. 1 shows a flowchart of an artificial intelligence weather forecast error analysis method based on mathematical decomposition according to an embodiment of the application; Figure 2 Fig. 2 shows the spatial distribution of the proportion of the system error part of the reanalysis error in the expectation of the square of the forecast error in the global grid artificial intelligence weather forecast error decomposition according to an embodiment of the application; Figure 3 Fig. 3 shows the spatial distribution of the proportion of the interaction of the system error parts of the reanalysis error and the fitting error in the expectation of the square of the forecast error according to an embodiment of the application; Figure 4 Fig. 4 shows the spatial distribution of the proportion of the system error part of the fitting error in the expectation of the square of the forecast error according to an embodiment of the application; Figure 5 Fig. 5 shows the spatial distribution of the proportion of the random error part of the reanalysis error in the expectation of the square of the forecast error according to an embodiment of the application; Figure 6 Fig. 6 shows the spatial distribution of the proportion of the interaction of the random error parts of the reanalysis error and the fitting error in the expectation of the square of the forecast error according to an embodiment of the application; Figure 7 Fig. 7 shows the spatial distribution of the proportion of the random error part of the fitting error in the expectation of the square of the forecast error according to an embodiment of the application; Figure 8A schematic diagram showing the reanalysis error, fitting error and correlation coefficient of the nine typical grids proposed in Embodiment 2 of the present application; Figure 9 A schematic diagram showing the expected decomposition result of the square of the prediction error of the nine typical grids proposed in Embodiment 2 of the present application; Figure 10 A schematic diagram showing the structure of an artificial intelligence weather prediction error analysis system based on mathematical decomposition proposed in Embodiment 3 of the present application; Figure 11 A schematic diagram showing the composition of a computer device proposed in Embodiment 4 of the present application. DETAILED DESCRIPTION
[0030] The accompanying drawings are only for illustrative purposes and should not be construed as limiting the present patent; In order to better illustrate the present embodiment, some parts of the drawings may be omitted, enlarged or reduced, and do not represent the actual size; It is understandable that some well-known content descriptions in the drawings may be omitted for those skilled in the art.
[0031] The technical solutions of the present application will be further described below in combination with the drawings and embodiments.
[0032] The positional relationship described in the drawings is only for illustrative purposes and should not be construed as limiting the present patent; Embodiment 1 The present embodiment proposes an artificial intelligence weather prediction error analysis method based on mathematical decomposition, and the flowchart of the method is shown in Figure 1 , which comprises the following steps: S1. Extracting the data required for artificial intelligence weather prediction error analysis and performing preprocessing, the required data including prediction data, reanalysis data and observation data; S2. Based on the prediction data, reanalysis data and observation data, calculating the reanalysis error, fitting error and prediction error, respectively; S3. Error decomposition of the reanalysis error, fitting error and prediction error, based on the error decomposition result, analyzing the source of the prediction error, and completing the analysis of the artificial intelligence weather prediction error.
[0033] In the embodiment, first, the prediction data, reanalysis data and observation data required for artificial intelligence weather prediction error analysis are extracted and preprocessed; then, based on the prediction data, reanalysis data and observation data, the reanalysis error, fitting error and prediction error are calculated respectively; the reanalysis error, fitting error and prediction error are error-decomposed, based on the error-decomposition result, the source of the prediction error is analyzed, the analysis of the artificial intelligence weather prediction error is completed, the calculation process is simple, and the calculation cost is low. In addition, the method proposed by the application is based on strict mathematical decomposition, which accurately analyzes the source of the prediction error under the premise of ensuring the reliability and low calculation cost of the weather prediction error analysis, and improves the explainability of the error analysis method.
[0034] Embodiment 2 In the embodiment, the preprocessing process in step S1 is: The time resolution of the unified prediction data , reanalysis data and observation data is unified; The grid point coordinates are selected from the prediction data to extract the specific prediction value at time , and the expression is:
[0035] wherein, is the grid point latitude, is the grid point longitude, is the time, is the prediction start time, is the prediction period; The specific reanalysis data at time is extracted from the reanalysis data , and the spatial resolution thereof is matched to the same spatial resolution as the specific prediction value , and the expression is:
[0036] Based on the grid point coordinates of the prediction data , the observation station is selected from the observation data of the observation station to extract the specific observation data at time , and the expression is: .
[0037] Specifically, the GraphCast forecast data, ERA5 reanalysis data and GHCNd observation data are read and preprocessed. The present embodiment reads the precipitation data in July from 2018 to 2024 through the Python third-party libraries Xarray and pandas, converts the observation data into grid data consistent with the forecast data, and calculates the 5-day cumulative precipitation of all data. The GraphCast is an artificial intelligence weather model developed by DeepMind, a subsidiary of Google, which mainly outputs weather forecast data. The training of the GraphCast model completely relies on ERA5 reanalysis data. It learns the physical patterns of weather evolution by analyzing ERA5 reanalysis data of global atmospheric and surface conditions over the past few decades. The ERA5 reanalysis data is the latest global atmospheric and surface state reanalysis dataset produced by the European Centre for Medium-Range Weather Forecasts. ERA5 is not a direct observation, but uses advanced numerical weather prediction models and data assimilation techniques to integrate all available historical global meteorological observation data (satellites, sounding, ground stations, buoys, aircraft, radars, etc.) to provide the closest possible global climate state in space and time. GHCNd is a global authoritative database of land surface meteorological daily value observations, and reanalysis data such as ERA5 also uses a large amount of GHCNd data as an input source.
[0038] The main implementation process is as follows: (1) The GraphCast forecast data and ERA5 reanalysis data are stored in NetCDF and GRIB respectively, and the GHCNd observation data is stored in TXT. The open_dataset function of Xarray is used to read the forecast data and reanalysis data, and the read_table function of pandas is used to read the observation data. The code for this process is encapsulated as a function load_data. The NetCDF is a Network Common Data Form, which is a self-describing, machine-independent binary file format for storing scientific data. GRIB is a highly compressed, indexed binary file format designed specifically for meteorological grid data. (2) The GHCNd observation data is converted into 0.25°x0.25° grid data according to the latitude and longitude of the observation station. The grid points containing only one observation station take the data of the observation station, the grid points containing multiple observation stations take the mean value of the observation stations, and the grid points without observation stations are not considered. (3) The 5-day cumulative precipitation in July is extracted from the forecast data, reanalysis data and observation data. The start and end times are July 1 to July 5, July 6 to July 10, July 11 to July 15, July 16 to July 20, July 21 to July 25 and July 26 to July 30. (4) The code of (2) and (3) is a function preprocess_data.
[0039] In this embodiment, the reanalysis error S2 is the error between the reanalysis data and the observation data , and the calculation expression is:
[0040] The fitting error S3 is the error between the forecast data and the reanalysis data , and the calculation expression is:
[0041] The forecast error S4 is the error between the forecast data and the observation data , and at the same time, the forecast error S4 is the sum of the reanalysis error S2 and the fitting error S3, and the calculation expression is: .
[0042] Specifically, this step extracts the GraphCast forecast data, ERA5 reanalysis data and GHCNd observation data at the corresponding grid points and the corresponding time, calculates the forecast error, the reanalysis error and the fitting error, this embodiment uses the Python third-party libraries Xarray and NumPy, and encapsulates the code into a function to calculate the forecast error, the reanalysis error and the fitting error by calling the corresponding function; The main implementation process is: (1) For all available grid points, extract the forecast data, reanalysis data and observation data; (2) Define the function calculate_error based on the forecast error, the reanalysis error and the fitting error through Python programming; (3) Call the calculate_error function for each grid to obtain the forecast error, the reanalysis error and the fitting error, which are respectively stored in variables named forecast_error, reanalysis_error and approximating_error; In this embodiment, the error decomposition of the reanalysis error, the fitting error and the forecast error includes: The reanalysis error, the fitting error and the forecast error are respectively decomposed into systematic error and random error, and the expression is:
[0043] wherein, is a systematic error of the reanalysis error is a random error of the reanalysis error is a systematic error of the fitting error is a random error of the fitting error is a systematic error of the prediction error is a random error of the prediction error In the embodiment, the error decomposition further comprises: decomposing the prediction error into a sum of a systematic error of the reanalysis error , a systematic error of the fitting error , a random error of the reanalysis error , and a random error of the fitting error
[0044] In the embodiment, the error decomposition further comprises: decomposing the expectation of the square of the prediction error, expressed as: .
[0045] In the embodiment, the error decomposition further comprises: decomposing the expectation of the square of the prediction error, expressed as:
[0046] wherein, is a systematic error of the reanalysis error, is an interaction of the reanalysis error and the systematic error of the fitting error, is a systematic error of the fitting error, is a random error of the reanalysis error, is an interaction of the reanalysis error and the random error of the fitting error, is a random error of the fitting error.
[0047] Specifically, this step decomposes the calculated reanalysis error, fitting error and prediction error based on the error decomposition mathematical model of the application, and the mathematical modeling process is realized by Python programming, mainly using Python third-party libraries NumPy and Scipy, and the code is packaged into functions, the corresponding functions are called, and the calculation process of error decomposition is modularly run; Specifically, the derivation process of decomposing the expectation of the square of the prediction error is:
[0048] wherein, , , , ; So another expression of is derived as:
[0049] And since wherein, , ,
[0050] So another expression of is derived as:
[0051] Specifically, the function is encapsulated as the function decompose_error; In this embodiment, the S3 analyzes the source of the forecast error based on the error decomposition result, and the process is as follows: Solving the system error part of the reanalysis error In the proportion of the square of the expectation of the forecast error , the expression is:
[0052] Figure 2 represents the system error part of the reanalysis error in the global grid artificial intelligence weather forecast error decomposition In the proportion of the square of the expectation of the forecast error , the deeper the depth of the red color, the greater the proportion of the system error part of the reanalysis error in the grid , the greater the area of the red color, the more the area of the reanalysis error in the grid , the higher the proportion of the system error part of the reanalysis error
[0053] Solving the interaction 2 of the system error parts of the reanalysis error and the fitting error In the proportion of the square of the expectation of the forecast error , the expression is:
[0054] Figure 3 represents the interaction 2 of the system error parts of the reanalysis error and the fitting error in the global grid artificial intelligence weather forecast error decomposition In the proportion of the square of the expectation of the forecast error The spatial distribution of the proportion of the strength of the interaction 2 between the systematic error part of the reanalysis error and the fitting error part in the global grid artificial intelligence weather forecast error decomposition, the deeper the depth of the red color, indicates that the grid where the reanalysis error and the fitting error part of the system error interact The greater the positive proportion of the strength of the interaction 2 between the systematic error part of the reanalysis error and the fitting error part in the global grid artificial intelligence weather forecast error decomposition, the greater the area of the red color, indicates that the grid where the reanalysis error and the fitting error part of the system error interact The more the area of the high positive proportion of the strength of the interaction 2 between the systematic error part of the reanalysis error and the fitting error part; the deeper the depth of the blue color, indicates that the grid where the reanalysis error and the fitting error part of the system error interact The greater the negative proportion of the strength of the interaction 2 between the systematic error part of the reanalysis error and the fitting error part; the greater the area of the blue color, indicates that the grid where the reanalysis error and the fitting error part of the system error interact The more the area of the high negative proportion of the strength of the interaction 2 between the systematic error part of the reanalysis error and the fitting error part.
[0055] Solving the random error part of the fitting error The proportion of the square of the expectation of the forecast error The expression is:
[0056] Figure 4 Indicates the random error part of the fitting error in the global grid artificial intelligence weather forecast error decomposition The proportion of the square of the expectation of the forecast error The spatial distribution of the proportion of the strength of the interaction 2 between the systematic error part of the fitting error in the global grid artificial intelligence weather forecast error decomposition, the deeper the depth of the red color, indicates that the grid where the fitting error of the system error The greater the proportion of the strength of the interaction 2 between the systematic error part of the fitting error; the greater the area of the red color, indicates that the grid where the fitting error of the system error The greater the area of the high proportion of the strength of the interaction 2 between the systematic error part of the fitting error.
[0057] Solving the random error part of the reanalysis error The proportion of the square of the expectation of the forecast error The expression is:
[0058] Figure 5 Indicates the random error part of the reanalysis error in the global grid artificial intelligence weather forecast error decomposition The proportion of the square of the expectation of the forecast error The spatial distribution of the proportion of the strength of the interaction 2 between the random error part of the reanalysis error in the global grid artificial intelligence weather forecast error decomposition, the deeper the depth of the red color, indicates that the grid where the random error part of the reanalysis error The greater the proportion of the strength of the interaction 2 between the random error part of the reanalysis error; the greater the area of the red color, indicates that the grid where the random error part of the reanalysis error The more the area of the high proportion of the strength of the interaction 2 between the random error part of the reanalysis error.
[0059] Solving the interaction between the random error part of the reanalysis error and the fitting error The expected square of the forecast error The proportion in is expressed as:
[0060] Figure 6 Represents the interaction between the random error part of the reanalysis error and the fitting error in the global grid AI weather forecast error decomposition The expected square of the forecast error The spatial distribution of the proportion intensity in the grid. The deeper the red color, the more the interaction between the random error part of the reanalysis error and the fitting error in the grid. The greater the positive ratio, the larger the red area, indicating the interaction between the random error part of the reanalysis error and the fitting error in the grid. The deeper the blue is, the more interaction between the random error of the reanalysis error and the fitting error in the grid. The greater the negative proportion of the blue area, the larger the blue area is, indicating the interaction between the random error part of the reanalysis error and the fitting error in the grid. The more areas with a higher negative proportion.
[0061] Solving for the random error portion of the fitting error The expected square of the forecast error The proportion in is expressed as:
[0062] Figure 7 Indicates the random error part of the fitting error in the global grid artificial intelligence weather forecast error decomposition The expected square of the forecast error The spatial distribution of the proportion intensity in the grid, the deeper the red, the more random error the fitting error in the grid. The greater the proportion of intensity, the larger the red area, indicating the random error part of the fitting error in the grid The more areas with a higher proportion.
[0063] Comparison of the systematic error portion of reanalysis errors , the interaction between the systematic error part of the reanalysis error and the fitting error 2 , the systematic error part of the fitting error , the random error part of the reanalysis error , the interaction between the random error part of the reanalysis error and the fitting error and the random error part of the fitting error The expected square of the forecast error The proportion in the forecast error is selected as the main source of the forecast error, and the analysis of the artificial intelligence weather forecast error is completed.
[0064] Specifically, the percentage of the total system error in the forecast error is:
[0065] The percentage of the total random error in the forecast error is:
[0066] Specifically, the implementation process of the step is: Based on Python programming, the total system error, the total random error, the system error part of the reanalysis error , the interaction of the system error part of the reanalysis error and the fitting error , the system error part of the fitting error , the random error part of the reanalysis error , the random error part of the reanalysis error and the fitting error , and the random error part of the fitting error The expectation of the square of the forecast error The proportion in the forecast error is analyzed, and the analysis process is packaged into a function analyse_error, all functions defined by S1-S4 are packaged and integrated into a forecast error decomposition class ErrorDecomposition, and saved as a.py format file; The ErrorDecomposition class function is called to build a class object, and the class methods load_data, preprocess_data, calculate_error, decompose_error and analyse_error are called in turn to obtain the contribution analysis of the reanalysis error and the fitting error to the forecast error; It can be seen that the error decomposition analysis method developed by the application has strong applicability, and is effective for the forecast error decomposition of the global grid. In most grids, the random error part of the reanalysis error contributes most to the forecast error, which indicates that the forecast error is mainly affected by the reanalysis error, and the improvement of the weather forecast model should mainly be aimed at the training data; Specifically, in the global grid artificial intelligence weather forecast error decomposition, 9 typical grids are selected to use the functions in the matplotlib library of Python to draw the schematic diagram of the relationship between the reanalysis error, the fitting error and the correlation coefficient; 9 typical grids are selected, and the functions in the matplotlib library of Python are used to draw the reanalysis error, the fitting error and the correlation coefficient, as shown in Figure 8 Figure 8 Fig. 9 shows nine subgraphs, and the horizontal axis of each subgraph represents the size of the reanalysis error, and the vertical axis represents the size of the fitting error, in units of d. The pink dots in each subgraph represent an observed error value, and the green dashed line represents the linear fitting relationship between the two errors, and r is the correlation coefficient, representing the linear correlation strength between the two errors. The forecast error decomposition result is shown in Figure 9 Fig. 10. Figure 9 Fig. 10 includes nine subgraphs, each of which includes the systematic error part of the reanalysis error , the interaction between the systematic error part of the reanalysis error and the fitting error , the systematic error part of the fitting error , the random error part of the reanalysis error , the interaction between the random error part of the reanalysis error and the fitting error , and the random error part of the fitting error occupies in the expectation of the square of the forecast error .
[0067] It can be seen that the error decomposition analysis method developed by the present application has strong reliability and interpretability, and can decompose the forecast error into six parts, among which the interaction between the random error of the reanalysis error and the random error of the fitting error is negative, indicating that the fitting error “offsets” part of the reanalysis error, reducing the forecast error, and indicating that the model corrects part of the error in the training data.
[0068] Embodiment 3 The present embodiment proposes an artificial intelligence weather forecast error analysis system based on mathematical decomposition, in which the system is used to implement the artificial intelligence weather forecast error analysis method based on mathematical decomposition proposed in embodiments 1 and 2, and the system structure diagram is shown in Figure 10 , which includes: A data extraction and preprocessing module is used to extract and preprocess the data required for artificial intelligence weather forecast error analysis, including forecast data, reanalysis data and observation data. An error calculation module is used to calculate the reanalysis error, fitting error and forecast error based on the forecast data, reanalysis data and observation data, respectively, wherein the forecast error is the sum of the reanalysis error and the fitting error. An error decomposition analysis module is used to perform error decomposition on the reanalysis error, fitting error and forecast error, and based on the error decomposition result, the source of the forecast error is analyzed to complete the analysis of the artificial intelligence weather forecast error.
[0069] Embodiment 4 In the embodiment, a computer device is provided, the computer device 100 includes a memory 101, a processor 102 and a computer program stored on the memory 101 and executable by the processor, the processor 102 executes the computer program to implement the artificial intelligence weather forecast error analysis method based on mathematical decomposition provided in Embodiment 1 and Embodiment 2, and a structure diagram of the computer device is shown in Figure 11
[0070] In the embodiment, a computer storage medium is provided, and the computer storage medium stores a computer program, the computer program includes program instructions, and the program instructions are executed by a computer to make the computer execute the artificial intelligence weather forecast error analysis method based on mathematical decomposition provided in Embodiment 1 and Embodiment 2.
[0071] Obviously, the above embodiments of the present application are only examples for clearly illustrating the present application, and are not intended to limit the implementation manners of the present application. Based on the above description, other different forms of changes or variations can be made by those skilled in the art. Here, it is not necessary and also impossible to enumerate all the implementation manners. Any modification, equivalent replacement and improvement made within the spirit and principle of the present application shall be included in the protection scope of the claims of the present application.
Claims
1. An artificial intelligence weather forecast error analysis method based on mathematical decomposition, characterized in that: The following steps are involved: S1. Extract and preprocess the data required for AI weather forecast error analysis, including forecast data, reanalysis data, and observation data; S2. Calculate the reanalysis error, fitting error, and forecast error based on the forecast data, reanalysis data, and observation data. S3. Perform error decomposition on the reanalysis error, fitting error, and forecast error. Based on the error decomposition results, analyze the source of the forecast error and complete the analysis of the AI weather forecast error.
2. The artificial intelligence weather forecast error analysis method based on mathematical decomposition according to claim 1, characterized in that: The pretreatment process is as follows: Unified forecast data , reanalysis data and observational data Time resolution; Selected grid point coordinates , from the forecast data Extract the corresponding Specific forecast value , the expression is: in, is the grid point latitude, is the grid point longitude, For time, is the forecast start time, For the foreseeable period; From the reanalysis data Extracted in time Specific reanalysis data , matching its spatial resolution to the specific forecast value The spatial resolution is the same as that of Based on forecast data The grid point coordinates of the selected observation station are obtained from the observation data of the observation station. Extracted in time Specific observation data , the expression is: 。 3. The artificial intelligence weather forecast error analysis method based on mathematical decomposition according to claim 2, characterized in that: S2 Reanalysis Error For reanalysis data With observational data The error between them can be calculated as: Fitting error For forecast data and reanalysis data The error between them can be calculated as: Forecast error For forecast data With observational data The error between Reanalysis error and fitting error The calculation expression is: 。 4. The artificial intelligence weather forecast error analysis method based on mathematical decomposition according to claim 3 is characterized in that: The error decomposition of the reanalysis error, the fitting error and the forecast error includes: The reanalysis error, fitting error and forecast error are decomposed into systematic error and random error respectively, and the expressions are: in, Reanalysis error The systematic error, Reanalysis error The random error, is the fitting error The systematic error, is the fitting error The random error, Forecast error The systematic error of Forecast error random error.
5. The artificial intelligence weather forecast error analysis method based on mathematical decomposition according to claim 4 is characterized in that: The error decomposition further includes: Decomposed into reanalysis errors Systematic error , fitting error Systematic error , reanalysis error Random error and fitting error Random error The sum of , the expression is: 。 6. The artificial intelligence weather forecast error analysis method based on mathematical decomposition according to claim 5, characterized in that: The error decomposition further includes: decomposing the expectation of the square of the forecast error, which is expressed as: in, is the systematic error part of the reanalysis error, is the interaction between the reanalysis error and the systematic error of the fitting error, is the systematic error part of the fitting error, is the random error part of the reanalysis error, is the interaction between the reanalysis error and the random error part of the fitting error, is the random error part of the fitting error.
7. The artificial intelligence weather forecast error analysis method based on mathematical decomposition according to claim 6, characterized in that: S3 describes the process of analyzing the source of the forecast error based on the error decomposition results. The process is as follows: Solving for the systematic error portion of the reanalysis error The expected square of the forecast error The proportion in is expressed as: Solving the interaction between the systematic error part of the reanalysis error and the fitting error2 The expected square of the forecast error The proportion in is expressed as: Solving for the systematic error portion of the fitting error The expected square of the forecast error The proportion in is expressed as: Solving for the random error portion of the reanalysis error The expected square of the forecast error The proportion in is expressed as: Solving for the interaction between the random error portion of the reanalysis error and the fitting error The expected square of the forecast error The proportion in is expressed as: Solving for the random error portion of the fitting error The expected square of the forecast error The proportion in is expressed as: Compare the expected square of the forecast error of each part The proportion of the largest proportion is selected as the main source of forecast error to complete the analysis of AI weather forecast errors.
8. An artificial intelligence weather forecast error analysis system based on mathematical decomposition, characterized in that: The system is used to implement the method of any one of claims 1 to 7, comprising: The data extraction and preprocessing module is used to extract and preprocess the data required for AI weather forecast error analysis. The required data includes forecast data, reanalysis data, and observation data. An error calculation module is used to calculate the reanalysis error, the fitting error and the forecast error based on the forecast data, the reanalysis data and the observation data, wherein the forecast error is the sum of the reanalysis error and the fitting error; The error decomposition and analysis module is used to decompose the reanalysis error, fitting error and forecast error. Based on the error decomposition results, the source of the forecast error is analyzed to complete the analysis of the artificial intelligence weather forecast error.
9. A computer device, characterized in that: The computer device includes a memory, a processor, and a computer program stored in the memory and executable by the processor. The processor executes the computer program to implement the method according to any one of claims 1 to 7.
10. A computer storage medium, characterized in that A computer program is stored thereon, the The computer program includes program instructions, and when the program instructions are executed by a computer, the computer is caused to execute the method according to any one of claims 1 to 7.