Regional numerical forecasting method and system based on multi-scale background field error covariance

Abstract

The invention discloses a regional numerical forecasting method and system based on multi-scale background field error covariance. The method comprises the following steps: firstly, constructing a multi-scale background field error covariance model containing different spatial scale error structures, then obtaining an initial atmospheric state and a boundary condition of a forecast area, and generating a background field set sample by using an ensemble forecast algorithm; thirdly, performing multi-scale decomposition on a background field set sample based on the model to obtain error components of different spatial scales, and determining a corresponding error covariance matrix; and combining the matrixes to form a complete multi-scale background field error covariance. Then, meteorological observation data are obtained, a variational assimilation algorithm is applied, optimal combination of the observation data and a background field set sample is achieved through multi-scale background field error covariance, and an optimal initial field is obtained; and finally, performing regional numerical forecasting based on the optimal initial field to obtain a future weather condition forecasting result of the forecast region. According to the method, the forecasting accuracy and reliability are improved.

Description

Technical Field

[0001] The present invention relates to the fields of meteorology and numerical weather prediction, particularly to data assimilation and prediction techniques for regional numerical weather prediction. Specifically, it relates to a regional numerical prediction method and system based on multi-scale background field error covariance. Background Art

[0002] In the field of modern meteorological prediction, regional numerical prediction methods play a crucial role. Traditional regional numerical prediction methods rely on a single-scale background field error covariance model, which has certain limitations in dealing with complex atmospheric dynamic systems. Specifically, atmospheric motion involves processes at multiple spatial scales, from large-scale weather systems to small and medium-scale local circulations, and there are complex interactions between these processes at different scales. However, a single-scale background field error covariance model is difficult to accurately describe such multi-scale characteristics, resulting in the inability to fully utilize observational information during the data assimilation process, thereby affecting the accuracy and reliability of the prediction.

[0003] In addition, traditional methods often adopt simplified assumptions when dealing with the spatial correlation of background field errors, such as the homogeneous isotropy assumption, which does not always hold in actual atmospheric motion. This simplification may lead to inaccurate expression of error statistical characteristics, thereby affecting the effect of data assimilation and the quality of prediction results.

[0004] Another challenge is how to effectively combine different sources and types of observational data. When traditional methods integrate multi-source observational data, it is often difficult to fully consider the contributions of different observations at different spatial scales, which results in the neglect or over-smoothing of some important small-scale features. Summary of the Invention

[0005] In view of this, embodiments of the present invention provide a regional numerical prediction method and system based on multi-scale background field error covariance to solve the above technical problems.

[0006] To achieve the above object, in a first aspect, a regional numerical prediction method based on multi-scale background field error covariance is provided, which includes the following steps:

[0007] S10: Construct a multi-scale background field error covariance model, which includes error structures at different spatial scales;

[0008] S20: Obtain the initial atmospheric state and boundary conditions of the prediction area, and generate a background field ensemble sample based on the initial atmospheric state and boundary conditions of the prediction area by using an ensemble prediction algorithm; the initial atmospheric state refers to the atmospheric state at the start time of the prediction, and the boundary conditions refer to the atmospheric state on the boundary of the prediction area;

[0009] S30: Based on the multi-scale background field error covariance model, perform multi-scale decomposition on the background field ensemble samples to obtain error components at different spatial scales; wherein, the error structures at different spatial scales are used to determine the scale range and decomposition rules of the multi-scale decomposition;

[0010] S40: Based on the error components at different spatial scales and applying the multi-scale background field error covariance model, respectively determine the error covariance matrices at the corresponding spatial scales; wherein, the multi-scale background field error covariance model is used to provide the structural information of the error covariance matrix and the parameter estimation method for determining the values of each parameter in the error covariance matrix;

[0011] S50: Combine the error covariance matrices at different spatial scales to form a complete multi-scale background field error covariance;

[0012] S60: Obtain meteorological observation data within the forecast area, and apply the variational assimilation algorithm. Use the multi-scale background field error covariance in the variational assimilation algorithm to achieve the optimal combination of the meteorological observation data and the background field ensemble samples, and obtain the optimal initial field;

[0013] S70: Based on the optimal initial field, perform regional numerical weather prediction to obtain the prediction results of the weather conditions within the forecast area for a period of time in the future.

[0014] In a second aspect, a regional numerical weather prediction system based on multi-scale background field error covariance is provided, which includes:

[0015] Meteorological observation equipment, used to obtain meteorological observation data within the forecast area;

[0016] Boundary condition acquisition equipment, used to obtain the atmospheric state data on the boundary of the forecast area. The boundary condition acquisition equipment includes: a receiving device for the output data of the large-scale numerical weather prediction model, used to receive the output data of the global numerical weather prediction model; a boundary meteorological observation station, set near the boundary of the forecast area, used to directly measure the boundary atmospheric state;

[0017] Data storage equipment, used to store the meteorological observation data within the forecast area, the boundary conditions, the atmospheric state on the boundary of the forecast area, and the background field ensemble samples;

[0018] Computing and processing equipment, communicatively connected to the meteorological observation equipment, the boundary condition acquisition equipment, and the data storage equipment. The computing and processing equipment includes a central processing unit and a memory, wherein a computer program is stored in the memory, and when the central processing unit executes the computer program, it implements any one of the methods described in the first aspect;

[0019] An output device, communicatively connected to the computing and processing device, for outputting a forecast result.

[0020] In some possible embodiments, the meteorological observation device includes a plurality of a surface meteorological station, an upper-air meteorological station, a weather radar, a meteorological satellite, and an automatic weather station.

[0021] The above technical solution has the following beneficial technical effects:

[0022] By constructing a multi-scale background field error covariance model, the present invention can more comprehensively and accurately describe the error structures at different spatial scales, thereby improving the statistical feature expression ability of the background field. Using the multi-scale decomposition technology and the corresponding error covariance matrix, different-scale observation information can be more effectively integrated, improving the efficiency and accuracy of data assimilation. Through a more accurate initial field analysis, the simulation ability of the regional numerical prediction model for atmospheric motions at various scales is improved, thereby enhancing the overall accuracy of the forecast result. This method can better adapt to different geographical conditions and weather systems, especially showing stronger forecasting ability under complex terrain and changing weather conditions. By separately processing and combining different-scale error components, the computational efficiency can be optimized while ensuring accuracy, making this method more suitable for operational applications. By capturing the multi-scale atmospheric motion characteristics, more abundant and detailed forecast products can be provided to meet the diverse needs of different users. Description of the Drawings

[0023] The drawings are used to better understand the present invention and do not constitute an improper limitation to the present invention. Among them:

[0024] Figure 1 is a flowchart of a regional numerical prediction method based on multi-scale background field error covariance according to an embodiment of the present invention;

[0025] Figure 2 is a specific flowchart of step S10 of an embodiment of the present invention;

[0026] Figure 3 is a specific flowchart of step S20 of an embodiment of the present invention;

[0027] Figure 4 is a specific flowchart of step S30 of an embodiment of the present invention;

[0028] Figure 5 is a specific flowchart of step S40 of an embodiment of the present invention;

[0029] Figure 6 is a specific flowchart of step S50 of an embodiment of the present invention;

[0030] Figure 7 is a specific flowchart of step S60 of an embodiment of the present invention;

[0031] Figure 8 is the specific flowchart of step S70 in the embodiment of the present invention;

[0032] Figure 9 is the functional block diagram of a regional numerical prediction system based on multi-scale background field error covariance in the embodiment of the present invention;

[0033] Figure 10 is the structural schematic diagram of the computer system in the embodiment of the present invention. Specific Embodiments

[0034] The following describes exemplary embodiments of the present invention with reference to the accompanying drawings. Various details of the embodiments of the present invention are included to facilitate understanding, and they should be considered merely exemplary. Therefore, those of ordinary skill in the art should recognize that various changes and modifications can be made to the embodiments described herein without departing from the scope and spirit of the present invention. Similarly, descriptions of well-known functions and structures are omitted below for clarity and conciseness.

[0035] The embodiment of the present invention provides a regional numerical prediction method based on multi-scale background field error covariance, aiming to improve the description ability of the background field error covariance model for atmospheric multi-scale dynamic processes, so as to more accurately depict the error structures at different spatial scales. By optimizing the utilization efficiency of observation information in the data assimilation process, especially in dealing with multi-source and multi-scale observation data, the capture ability of the prediction system for the characteristics of atmospheric motion at different scales is significantly enhanced. This method shows higher adaptability under complex terrain and variable weather conditions, provides a more accurate and reliable solution for regional numerical prediction, and further improves the overall accuracy and flexibility of the prediction.

[0036] Embodiment 1

[0037] Figure 1 is the flowchart of a regional numerical prediction method based on multi-scale background field error covariance in the embodiment of the present invention. As Figure 1 shown, it includes the following steps:

[0038] S10: Construct a multi-scale background field error covariance model, which includes error structures at different spatial scales;

[0039] S20: Obtain the initial atmospheric state and boundary conditions of the prediction area, and generate background field ensemble samples based on the initial atmospheric state and boundary conditions of the prediction area; the initial atmospheric state refers to the atmospheric state at the start time of the prediction, and the boundary conditions refer to the atmospheric state on the boundary of the prediction area;

[0040] S30: Based on the multi-scale background field error covariance model, perform multi-scale decomposition on the background field ensemble samples to obtain error components at different spatial scales; wherein, the error structures at different spatial scales are used to determine the scale range and decomposition rules of the multi-scale decomposition;

[0041] S40: Based on the error components at different spatial scales and applying the multi-scale background field error covariance model, respectively determine the error covariance matrices at the corresponding spatial scales; wherein, the multi-scale background field error covariance model is used to provide the structural information of the error covariance matrix and the parameter estimation method for determining the values of each parameter in the error covariance matrix;

[0042] S50: Combine the error covariance matrices at different spatial scales to form a complete multi-scale background field error covariance;

[0043] S60: Obtain the meteorological observation data in the forecast area and apply the variational assimilation algorithm. Use the multi-scale background field error covariance in the variational assimilation algorithm to achieve the optimal combination of the meteorological observation data and the background field ensemble samples, and obtain the optimal initial field;

[0044] S70: Based on the optimal initial field, perform regional numerical forecasting to obtain the prediction results of the weather conditions in the forecast area for a period of time in the future.

[0045] The regional numerical forecasting method based on multi-scale background field error covariance has the following advantages:

[0046] First of all, by constructing a multi-scale background field error covariance model, this method can more comprehensively and accurately describe the error structures at different spatial scales. This multi-scale characterization significantly improves the expression ability of the statistical characteristics of the background field error. Compared with the traditional single-scale method, the present invention can better capture the complexity and multi-scale characteristics of atmospheric motion, thereby improving the overall accuracy of forecasting.

[0047] Secondly, using the ensemble forecasting algorithm to generate background field ensemble samples and perform multi-scale decomposition enables this method to effectively characterize the error characteristics at different spatial scales. This method not only improves the representativeness of the background field but also provides rich information for subsequent error covariance estimation. By considering the error structures at different scales, the present invention can more accurately describe the uncertainty of the atmospheric state, thereby improving the reliability of forecasting.

[0048] Again, by separately determining the error covariance matrices at different spatial scales and combining them, the present method achieves a refined description of the background field error. This method for constructing multi-scale error covariance not only improves the accuracy of error statistical characteristics but also enhances the sensitivity of the prediction system to the characteristics of atmospheric motions at different scales. Therefore, the present invention can better adapt to complex weather systems and geographical conditions and provide more reliable prediction results.

[0049] Finally, using the multi-scale background field error covariance in the variational assimilation algorithm significantly improves the fusion efficiency of the observational data and the background field. This method can more effectively utilize the observational information at different scales and achieve the optimal combination of the observational data and the background field. By obtaining a more accurate optimal initial field, the present invention greatly improves the quality of the initial conditions for regional numerical prediction, thus significantly improving the accuracy and timeliness of the prediction.

[0050] As Figure 2 shown, in some embodiments, step S10 specifically includes the following sub-steps:

[0051] S11: Obtain historical meteorological data and historical numerical weather prediction data, and establish a data set for analyzing the characteristics of the background field error; wherein the historical numerical weather prediction data refers to the atmospheric state data obtained by simulating a historical time period using a historical version of the numerical weather prediction model.

[0052] Specifically, in this step, a comprehensive data set is established for analyzing the characteristics of the background field error. The historical meteorological data includes multi-source observational data from surface observation stations, upper-air soundings, satellites, radars, etc. over the past few years or decades. The historical numerical weather prediction data is the forecast field obtained by re-calculating the same historical time period using a numerical prediction model that is similar to the current operational model but not the latest version. For example, 10-year data from 2014 to 2024 can be selected, including observational data and forecast data obtained by re-calculating these 10 years using the 2020 version of the numerical prediction model. Such a data set can reflect the systematic differences between the model forecast and the actual observations and helps to identify the characteristics of the background field error.

[0053] S12: Conduct statistical analysis on the data set to identify the error patterns and spatial correlation structures at different spatial scales, where the spatial correlation structure refers to the mutual relationship and dependence degree of errors between different spatial positions.

[0054] Specifically, in this step, in-depth statistical analysis is performed on the dataset established in step S11. First, the difference between the forecast field and the observation field can be calculated to obtain the error field. Then, multi-scale analysis techniques (wavelet analysis or spectral analysis) are used to decompose the error field into different spatial scales. For each spatial scale, the statistical characteristics of the error are analyzed, such as mean, variance, skewness, and kurtosis. At the same time, the spatial correlation of the error also needs to be studied, for example, by calculating the autocorrelation function at different distances to describe the spatial dependence of the error. For example, it is found that at a scale of 500 kilometers, the temperature forecast error shows an obvious positive correlation, while at a scale of 50 kilometers, the correlation weakens rapidly.

[0055] S13: Design error covariance functions at multiple spatial scales based on the error patterns and spatial correlation structures.

[0056] Specifically, in this step, the error patterns and spatial correlation structures identified in S12 are used to design corresponding error covariance functions for each important spatial scale. These functions can accurately describe the statistical characteristics and spatial correlation of the error at that scale. For example, for the temperature field error at a large scale (e.g., 1000 kilometers), a Gaussian function can be used to describe its spatial correlation; while for the wind field error at a medium scale (e.g., 100 kilometers), a more complex function, such as a Bessel function, can be used to capture the anisotropic characteristics of the wind field error. The covariance function for each scale should be parameterized for subsequent adjustment and optimization.

[0057] S14: Combine the error covariance functions at multiple spatial scales to construct an initial multi-scale background field error covariance model.

[0058] Specifically, in this step, the error covariance functions at each scale designed in S13 are combined to form a complete multi-scale background field error covariance model. The combination method can adopt linear superposition, that is, adding the covariance functions at different scales with certain weights. Initially, the weights can be determined according to the variance magnitudes of the errors at each scale. For example, if there are covariance functions at three scales: large scale (1000 km), medium scale (100 km), and small scale (10 km), their weights can be initially set to 0.5, 0.3, and 0.2. This initial model will serve as the basis for subsequent verification and optimization.

[0059] S15: Use the current meteorological observation data and the current numerical weather forecast data to verify and optimize the initial multi-scale background field error covariance model to obtain the verification and optimization results; the current meteorological observation data refers to the actual meteorological observation data collected in the recent period; the current numerical weather forecast data refers to the atmospheric state data obtained by forecasting the future period using the latest version of the numerical weather forecast model.

[0060] Specifically, in this step, the latest observational data and forecast data are used to verify and optimize the initial model constructed in S14. Data from the most recent 3 - 6 months can be selected for verification. First, a data assimilation experiment is carried out using the initial model to compare the fitting degree between the assimilation result and the observation, as well as the impact on the forecasting effect. Then, by adjusting the parameters and weights of the covariance functions at each scale, the model performance is continuously optimized. For example, if it is found that the initial model does not accurately describe the mesoscale weather system, it is necessary to increase the weight of the mesoscale covariance function from 0.3 to 0.4 and fine - tune its parameters. Through multiple iterative experiments, a more realistic multi - scale background field error covariance model can be obtained.

[0061] S16: According to the verification and tuning results, determine the final multi - scale background field error covariance model, which includes the error structures and their weights at different spatial scales.

[0062] Specifically, based on the verification and tuning results of S15, the structure and parameters of the multi - scale background field error covariance model are finally determined. This final model should include several key components: (1) the error covariance functions and their specific parameters at each spatial scale; (2) the combined weights of the covariance functions at different scales; (3) possible descriptions of cross - scale correlations. For example, the final model can include three components: large scale (weight 0.45), mesoscale (weight 0.35), and small scale (weight 0.2), and each component has its specific mathematical expression and parameters. This final model will be used in the actual numerical forecasting system to improve the accuracy of the background field and the effect of data assimilation.

[0063] As Figure 3 shown, in some embodiments, step S20 specifically includes the following sub - steps:

[0064] S21: Obtain the output data of the global numerical weather prediction model, and extract the corresponding initial atmospheric state and boundary condition data according to the geographical scope of the forecast area.

[0065] Specifically, the purpose of this step is to provide the necessary initial conditions and boundary conditions for regional numerical forecasting. The global numerical weather prediction model (such as the ECMWF model of the European Centre for Medium - Range Weather Forecasts or the GFS model of the National Centers for Environmental Prediction in the United States) provides global - scale forecast data at a relatively coarse resolution (e.g., 0.5°×0.5°). According to the specific geographical scope of the forecast area (for example, Inner Mongolia region, longitude range 95°E - 127°E, latitude range 35°N - 55°N), data for this region and a larger area around it (e.g., extended outward by 5°) are extracted from the global model output. These data include the atmospheric state (such as temperature, humidity, wind field, etc.) at the initial time and the boundary condition data during the forecast period.

[0066] S22: Interpolate and adjust the initial atmospheric state and boundary condition data to make them adapt to the grid resolution and terrain features of the forecast area, and obtain the adjusted initial atmospheric state and boundary condition data.

[0067] Specifically, in this step, the coarse-resolution data obtained in S21 is adjusted to high-resolution data suitable for use in the regional model. For example, if the resolution of the regional model is 0.1°×0.1°, spatial interpolation needs to be performed on the 0.5°×0.5° global model data. The interpolation method can choose bilinear interpolation or a more complex spline interpolation method. In addition, the meteorological elements near the ground also need to be adjusted according to the high-resolution terrain data used in the regional model. For example, for the temperature field, the change in the vertical temperature gradient caused by the high-resolution terrain needs to be considered; for the wind field, the blocking and guiding effects of the terrain on the air flow need to be considered. These adjustments ensure that the initial field and boundary conditions match the terrain features of the regional model, which helps to reduce the imbalance in the initial stage of the model.

[0068] S23: Set the number of samples N of the ensemble forecasting algorithm, and this number of samples N determines the number of background field ensemble samples generated subsequently; and determine the initial field perturbation amplitude and boundary condition perturbation amplitude according to the historical forecast error statistics.

[0069] Specifically, the number of samples N of the ensemble forecasting algorithm is a key parameter, which needs to be balanced between computing resources and forecasting effects. The value range of N is between 20 and 100, and preferably 50 or 60. For example, N = 50 can be set. The perturbation amplitudes of the initial field and boundary conditions are determined based on historical forecast error statistics. The forecast errors in the past year can be analyzed, and the standard deviations of each meteorological element (such as temperature, wind speed, etc.) at different heights can be calculated. The perturbation amplitude is set to a certain proportion (50%-80%) of these standard deviations. For example, if the standard deviation of the historical forecast error of the 500hPa temperature field is 1.5°C, the standard deviation of the initial field temperature perturbation can be set to 1.2°C (80%). The boundary condition perturbation amplitude can be set similarly, but it needs to increase with time to reflect the growth of forecast uncertainty.

[0070] S24: Use the random perturbation method to generate N groups of initial field perturbations and N groups of boundary condition perturbations, and the perturbation amplitudes are controlled by the initial field perturbation amplitude and boundary condition perturbation amplitude; superimpose the N groups of initial field perturbations onto the adjusted initial atmospheric state respectively to form N groups of perturbed initial fields; superimpose the N groups of boundary condition perturbations onto the adjusted boundary condition data respectively to form N groups of perturbed boundary conditions.

[0071] Specifically, in this step, a random perturbation method is used to generate disturbances of the initial field and boundary conditions. The method includes Monte Carlo random sampling or a disturbance generation method based on singular vectors. Taking the Monte Carlo method as an example, a random number that obeys a normal distribution can be generated for each meteorological element of each grid point, and its standard deviation is controlled by the disturbance amplitude determined in step S23. In order to maintain physical consistency, these random disturbances also need to be processed for spatial correlation, such as smoothing using a Gaussian filter. After generating N groups of disturbances, they are superimposed on the initial field and boundary conditions obtained in step S22. For example, for the i-th sample (i=1,2,...,N), the initial value of its 500hPa temperature field can be: T_i=T_0+δT_i, where T_0 is the original temperature value and δT_i is the generated random disturbance.

[0072] S25: Using the regional numerical prediction model, perform integral calculations of preset durations on N groups of initial fields after disturbance and corresponding N groups of boundary conditions after disturbance, and generate one background field sample for each group of calculations, generating a total of N background field samples, thereby constituting a background field set sample.

[0073] Specifically, this step uses a regional numerical prediction model (such as the WRF model) to perform integral calculations on each set of initial fields and boundary conditions after disturbance. The preset duration can be 6 hours or 12 hours, which is enough for the model to produce meaningful forecasts without causing excessive forecast errors. For example, if your goal is to generate a background field set after 12 hours, then you need to perform a 12-hour model integration on each set of initial conditions and boundary conditions. Assuming N = 50, 50 different 12-hour forecast results will be obtained, each of which can be used as a background field sample. These 50 samples together constitute the background field set, reflecting the forecast uncertainty caused by the uncertainty of the initial and boundary conditions.

[0074] S26: Perform quality control on the background field set samples, remove unreasonable samples, and obtain optimized background field set samples.

[0075] Specifically, this step performs quality control on the generated background field ensemble samples. This step identifies and eliminates those samples that are physically unreasonable or statistically abnormal to improve the overall quality of the ensemble. The methods of quality control may include: (1) checking whether the key meteorological elements (temperature, humidity, air pressure, etc.) are within a reasonable range, for example, eliminating samples with an absolute temperature less than zero or a relative humidity greater than 100%; (2) performing checks on water vapor conservation and energy conservation, and eliminating samples that seriously violate these conservation laws; (3) using statistical methods to identify outliers, for example, calculating the mean and standard deviation of all samples at each grid point and eliminating samples that deviate from the mean by more than 3 standard deviations. After these quality control steps, 1-5 abnormal samples will be eliminated, and finally a more reliable background field ensemble will be obtained, for example, containing 45-49 high-quality samples. This optimized background field ensemble will be used in the subsequent data assimilation process.

[0076] As Figure 4 shown, in some embodiments, step S30 specifically includes the following sub-steps:

[0077] S31: Based on the different spatial scale error structures in the multi-scale background field error covariance model, determine the scale range and decomposition rules of the multi-scale decomposition.

[0078] Specifically, this step sets appropriate parameters for the subsequent multi-scale decomposition process. The multi-scale background field error covariance model contains error structures at different spatial scales, such as large scale (>1000 km), medium scale (100-1000 km), and small scale (<100 km). Based on these error structures, the scale range of the multi-scale decomposition can be determined. For example, the scale range can be set to 4 levels: large scale (>1000 km), medium scale (300-1000 km), small scale (100-300 km), and micro scale (<100 km). The decomposition rules define how to divide these scales in the frequency domain. One method is to use concentric circles to divide the two-dimensional frequency plane, and the radius of the circle corresponds to different wave numbers (or wavelengths). For example, it can be set that wave number k < 6 is the large scale, 6 ≤ k < 20 is the medium scale, 20 ≤ k < 60 is the small scale, and k ≥ 60 is the micro scale. The specific settings of these parameters should be adjusted according to the model resolution and the characteristics of the research area.

[0079] S32: Perform Fourier transform on each sample in the background field ensemble samples to transform each sample in the background field ensemble samples into the frequency domain.

[0080] Specifically, in this step, a two-dimensional fast Fourier transform (2D FFT) is performed on each background field sample. Suppose there is a set of 50 background fields, and each member is a 500×500 grid field (such as a 500 hPa height field). For each 500×500 grid field, 2D FFT is applied to convert it into a frequency-domain representation. After the conversion, what is obtained is still a 500×500 complex matrix, where each element of the matrix represents the amplitude and phase information of a specific frequency (or wave number) component in the original field. For example, the elements near the center of the matrix correspond to low-frequency (large-scale) components, while the elements far from the center correspond to high-frequency (small-scale) components. This frequency-domain representation enables easy multi-scale decomposition in the next step.

[0081] S33: According to the scale range and decomposition rules, perform multi-scale decomposition on each sample in the frequency domain, and decompose it into frequency components of different spatial scales.

[0082] Specifically, based on the scale range and decomposition rules determined in step S31, perform multi-scale decomposition on each sample in the frequency domain. Continuing with the previous example, for the 500×500 frequency-domain matrix, concentric circle filters can be used to extract frequency components of different scales. Specifically, four binary mask matrices can be created, corresponding to large scale, medium scale, small scale, and micro scale respectively. For example, in the large-scale mask matrix, the region where the wave number k < 6 has a value of 1, and other regions have a value of 0. Then, multiply the original frequency-domain matrix by each mask matrix to obtain four new frequency-domain matrices, each of which contains only the frequency information within the corresponding scale range. In this way, each background field sample is decomposed into four frequency components of different spatial scales.

[0083] S34: Perform an inverse Fourier transform on the frequency components of each spatial scale, convert the frequency components of each spatial scale back to the spatial domain, and obtain the error components of the corresponding spatial scale.

[0084] Specifically, in this step, perform a two-dimensional inverse fast Fourier transform (2D IFFT) on the frequency components of each spatial scale obtained in S33 to convert them back to the spatial domain. Continuing with the previous example, for each background field sample, there are now four 500×500 frequency-domain matrices, corresponding to large scale, medium scale, small scale, and micro scale respectively. Perform 2D IFFT on these four matrices respectively to obtain four 500×500 real matrices, which represent the components of the original background field at different spatial scales. For example, the large-scale component shows large-scale high-pressure or low-pressure systems, while the small-scale component reflects local topographic effects or the influence of convective systems. The sum of these components should be equal to the original background field sample.

[0085] S35: Apply the Fourier transform process in step S32, the multi-scale decomposition process in step S33, and the inverse Fourier transform process in step S34 to all background field set samples to obtain error components at different spatial scales.

[0086] Specifically, this step applies the processing procedures from step S32 to step S34 to all background field set samples. Suppose there are 50 background field set samples. After this series of processes, 50×4 = 200 spatial domain matrices will be obtained, that is, each original sample is decomposed into 4 error components at different spatial scales. These components can be used for subsequent analysis and data assimilation processes. For example, the ensemble mean and ensemble dispersion at each scale can be calculated to understand the forecast uncertainty at different spatial scales. This multi-scale decomposition allows for differential treatment of errors at different scales during the data assimilation process. For example, a larger correlation length can be used for large-scale errors, while a smaller correlation length can be used for small-scale errors, thereby improving the accuracy and efficiency of assimilation.

[0087] As Figure 5 shown, in some embodiments, step S40 specifically includes the following sub-steps:

[0088] S41: Based on the multi-scale background field error covariance model, determine the structural information of the error covariance matrix at each spatial scale.

[0089] Specifically, the multi-scale background field error covariance model assumes that errors at different spatial scales have different structural characteristics. In this step, an appropriate covariance matrix structure needs to be determined for each spatial scale. For example, for large-scale errors, it is assumed to have a longer correlation length and a larger variance; while for small-scale errors, it is assumed to have a shorter correlation length and a smaller variance. Specifically, a suitable covariance function can be selected for each scale. For example, for large scales (>1000km), the Gaussian function can be selected as the covariance function, and its correlation length is set to 1500km; for medium scales (300 - 1000km), the second-kind Bessel function can be selected, and the correlation length is set to 500km; for small scales (100 - 300km) and micro-scales (<100km), the exponential function can be selected, and the correlation lengths are set to 200km and 50km respectively. These selections will determine the basic structure of the error covariance matrix at each scale.

[0090] S42: Conduct statistical analysis on the error components at each spatial scale, and calculate the statistical characteristic quantities, which include the sample mean and sample variance.

[0091] Specifically, in this step, statistical analysis is performed using the error components at different spatial scales obtained in S35. Suppose there are 50 ensemble members, and each member has a 500×500 grid field at four spatial scales. For each spatial scale, the following statistical characteristic quantities need to be calculated: the sample mean, which is the average of the 50 members at each grid point, resulting in a 500×500 mean field; the sample variance, which is the variance calculated for the 50 members at each grid point, also resulting in a 500×500 variance field.

[0092] For example, for the large-scale error component, it is found that its mean field presents a large-scale positive and negative alternating pattern, reflecting systematic biases; while the variance field may show relatively large values in some regions (active weather system regions). For the small-scale error component, the mean field may be close to zero, while the variance field may show relatively large values in regions with complex terrain. These statistical characteristic quantities provide important bases for subsequent parameter estimation.

[0093] S43: Using the parameter estimation method provided by the multi-scale background field error covariance model and combining the statistical characteristic quantities, determine the parameter values in the error covariance matrix for each spatial scale.

[0094] Specifically, based on the covariance function structure determined in step S41 and the statistical characteristic quantities calculated in step S42, the specific parameters of the error covariance matrix for each spatial scale can be estimated. Parameter estimation methods include maximum likelihood estimation, method of moments, etc. Taking the large-scale error as an example, assume the use of a Gaussian covariance function:

[0095] where r is the distance between two points, σ2 is the variance, and L is the correlation length. The parameters can be estimated through the following steps: using the variance field calculated in S42, taking its spatial average as the initial estimate of σ2; calculating the sample covariance function, that is, calculating the covariance of the error field at different distances; using the non-linear least squares method to fit the sample covariance function to obtain the estimated value of L.

[0096] For other scales, similar methods can be adopted, but the specific estimation process needs to be adjusted according to different covariance function structures.

[0097] S44: Based on the structural information of the error covariance matrix for each spatial scale and the parameter values in the error covariance matrix for each spatial scale, construct the error covariance matrix for each spatial scale.

[0098] Specifically, in this step, the complete error covariance matrix is constructed using the structural information determined in step S41 and the parameter values estimated in step S43. For a 500×500 grid field, the complete covariance matrix would be a 250000×250000 matrix, and it is not practical to directly construct and store such a large matrix. Therefore, some approximation methods are adopted, such as: assuming that the covariance is homogeneous and isotropic, so that only a one-dimensional covariance function needs to be stored; using a sparse matrix representation and only storing the non-zero elements within the correlation length range; adopting the spectral representation or wavelet representation of the covariance matrix, which can greatly reduce the storage and computational requirements.

[0099] For example, for large-scale errors, the previously estimated σ2 and L can be used to calculate the covariance between any two points through the above Gaussian covariance function. In practical applications, only the values within the range of the correlation length 3L are calculated and stored, and other values are approximated as zero. For other scales, a similar method is adopted, but the corresponding covariance function and parameters are used.

[0100] S45: Normalize the error covariance matrices of each spatial scale to obtain the normalized error covariance matrices of each spatial scale.

[0101] Specifically, the normalization process is to ensure that the error covariance matrices of different spatial scales have appropriate weights when combined. The normalization method is to divide each covariance matrix by its trace (i.e., the sum of the diagonal elements). The specific steps are as follows: Calculate the trace of each scale covariance matrix. For example, for the large-scale error covariance matrix B_large, calculate tr(B_large). Divide each covariance matrix by its trace: B_large_norm = B_large / tr(B_large). Repeat this process for the covariance matrices of all scales.

[0102] After such processing, the trace of each normalized covariance matrix is equal to 1, ensuring the comparability of the contributions of each scale in subsequent combinations. For example, if the original large-scale error variances are generally larger than the small-scale error variances, this difference will be eliminated after normalization, making it possible to more flexibly adjust the relative importance of each scale.

[0103] S46: Perform a positive definiteness test and / or a condition number test on the normalized error covariance matrices of each spatial scale. When the test results do not meet the preset criteria, adjust the normalized error covariance matrices of each spatial scale to obtain the final error covariance matrices of each spatial scale that meet the requirements of numerical stability.

[0104] Specifically, in this step, by strictly controlling the numerical stability of the error covariance matrix, the smooth implementation of the subsequent data assimilation process is ensured.

[0105] First, perform a positive definiteness test on the matrix. The covariance matrix should be positive definite, which can be verified by calculating its eigenvalues. If non-positive eigenvalues are found, correct the positive definiteness of the matrix by replacing these eigenvalues with a small positive number to prevent instability in calculations.

[0106] Next, evaluate the numerical stability of the matrix through the condition number test. The condition number of a matrix is the ratio of its largest eigenvalue to its smallest eigenvalue, which can reflect the ill-conditioning degree of the matrix. Set a threshold for the condition number, for example, 10 6 , if the condition number of the matrix exceeds this threshold, it is considered that the matrix is numerically unstable and further processing is required to ensure calculation accuracy.

[0107] If the matrix fails to meet the above stability criteria, various adjustment methods can be adopted. First is eigenvalue truncation, where eigenvalues below a certain threshold are uniformly set to this threshold to avoid the influence of too small eigenvalues on the numerical characteristics of the matrix. Second, the covariance inflation method can be used to multiply the covariance matrix by a factor slightly greater than 1 (such as 1.01) to enhance its positive definiteness. In addition, a small positive number can be added to the diagonal of the matrix to simulate pseudo-observation errors, thereby increasing uncertainty and making the matrix more robust.

[0108] For example, if it is found that the condition number of a small-scale error covariance matrix reaches 10 8 , far exceeding the preset threshold of 10 6 , then through eigenvalue truncation, eigenvalues less than 10 times the largest eigenvalue -6 are set to this threshold, and the matrix is reconstructed accordingly. This adjustment not only controls the condition number within a reasonable range (not exceeding 10 6 ), but also ensures the positive definiteness of the matrix, which helps to improve the reliability and accuracy of the data assimilation process.

[0109] As Figure 6 shown, in some embodiments, step S50 specifically includes the following sub-steps:

[0110] S51: Determine the weight coefficients of each spatial scale error covariance matrix. The weight coefficients are used to adjust the contribution ratio of different spatial scale errors in the multi-scale background field error covariance.

[0111] In this step, a weight coefficient is assigned to the error covariance matrix for each spatial scale to reflect its relative importance in the overall background field error. The determination of these weight coefficients can be based on prior knowledge, experience, or obtained through objective methods. For example, assuming there are four spatial scales: large scale, medium scale, small scale, and micro scale, the initial weights can be set according to the understanding of atmospheric dynamics and the characteristics of numerical weather prediction models. One way of assignment is: the large-scale weight is 0.4, the medium-scale weight is 0.3, the small-scale weight is 0.2, and the micro-scale weight is 0.1. This assignment reflects that large-scale processes have a more significant impact on weather forecasting, while the contribution of small-scale processes is relatively small. Another method is to determine the weights by analyzing the spectral distribution of historical forecast errors. For example, a Fourier analysis can be performed on the forecast errors in the past month, calculate the proportion of error energy in different wave number ranges to the total error energy, and use these proportions as the weights for the corresponding scales. It should be noted that these weights can be dynamically adjusted according to seasons, geographical locations, or weather system types.

[0112] S52: Perform scale transformation on the error covariance matrices of each spatial scale to make them have the same spatial resolution and matrix size, and obtain the error covariance matrices of each spatial scale after scale transformation.

[0113] Specifically, since the error covariance matrices of different spatial scales may originally have different spatial resolutions, they need to be unified to a common resolution. Select the highest resolution as the target resolution. For example, assume the original resolutions of the four scales are: 100 km for the large scale, 50 km for the medium scale, 25 km for the small scale, and 10 km for the micro scale. All scales will be upscaled to 10 km. For scales with lower resolutions, interpolation operations are required. In the practical application of the multi-scale background field error covariance model, the covariance matrices of different scales may have different spatial resolutions. To unify these covariance matrices with different resolutions to the resolution required by the forecast model (e.g., 10 km), various interpolation and adjustment methods can be adopted. For the covariance matrices of the large scale and the medium scale, the computationally efficient bilinear interpolation method can be used to increase their resolution to 10 km. This method is simple and direct and is suitable for the relatively smooth large-scale field. In cases where a smoother transition is needed, especially for the medium-scale field, higher-order interpolation methods such as cubic spline interpolation can be selected to maintain the continuity and smoothness of the field. For the small-scale field or when it is necessary to maintain the spectral characteristics of the field, a spectral method can be adopted, that is, convert the covariance matrix to the spectral space, adjust the resolution in the spectral space, and then convert it back to the physical space. This method can better maintain the spatial structure characteristics of the field and is especially suitable for dealing with small-scale error fields with complex spatial variations.

[0114] For example, for a large-scale error covariance matrix, a 100km×100km grid can be refined into 10 sub-grids of 10km×10km. In this process, it is necessary to ensure that the interpolated matrix still maintains positive definiteness and physical consistency. In addition, for small-scale and micro-scale error covariances, some smoothing processes can be carried out to avoid non-physical small-scale noise at high resolutions.

[0115] S53: According to the weight coefficients, weight the error covariance matrices of each spatial scale after scale transformation to obtain the weighted error covariance matrices of each spatial scale.

[0116] In this step, apply the weight coefficients determined in step S51 to the error covariance matrices after scale transformation in step S52. The specific operation is to multiply the error covariance matrix of each scale by its corresponding weight coefficient.

[0117] In the multi-scale background field error covariance model, weight the error covariance matrices of different scales to reflect the relative importance of each scale in the overall error structure. Continuing with the previous example, the specific operation is as follows: For the large-scale error covariance matrix, assign a weight of 0.4 and calculate B_large_weighted = 0.4×B_large; the medium-scale error covariance matrix is assigned a weight of 0.3 to obtain B_medium_weighted = 0.3×B_medium; the small-scale error covariance matrix has a weight of 0.2 and calculate B_small_weighted = 0.2×B_small; finally, the micro-scale error covariance matrix is assigned a weight of 0.1 to obtain B_micro_weighted = 0.1×B_micro. Through this weighting method, according to the influence degree of each scale error in the actual atmospheric process, the contribution ratio of each scale in the final background field error covariance model can be reasonably allocated.

[0118] Among them, B_large, B_medium, B_small, and B_micro are the error covariance matrices of each spatial scale after scale transformation. This weighting operation ensures that when finally combined, the contribution of each scale is consistent with its preset importance. For example, the large-scale error will contribute 40% of the overall background field error covariance, while the micro-scale error only contributes 10%. This weighting method allows for flexible adjustment of the influence of different scale processes in data assimilation, thus enabling better adaptation to different weather systems and forecasting requirements.

[0119] S54: Superimpose the weighted error covariance matrices of each spatial scale to obtain the complete multi-scale background field error covariance.

[0120] In this final step, a simple algebraic sum operation is performed on the weighted spatial scale error covariance matrices obtained in S53 to obtain the final multi-scale background field error covariance matrix. The specific operation is as follows: B_total = B_large_weighted + B_medium_weighted + B_small_weighted + B_micro_weighted.

[0121] Among them, B_total is the final multi-scale background field error covariance matrix, and the right side is the sum of the four weighted scale error covariance matrices. This superposition process is actually the accumulation of error covariances at different scales at each grid point. For example, for any point (i,j) in the model domain, its total background field error variance will be:

[0122] B_total(i,j) = 0.4×B_large(i,j) + 0.3×B_medium(i,j) + 0.2×B_small(i,j) + 0.1×B_micro(i,j). Here, (i,j) represents the coordinates of the grid point. This expression describes the background field error variance at the grid point (i,j).

[0123] For the covariance between any two points (i,j) and (k,l), it can be expressed as:

[0124] B_total(i,j,k,l) = 0.4×B_large(i,j,k,l) + 0.3×B_medium(i,j,k,l) + 0.2×B_small(i,j,k,l) + 0.1×B_micro(i,j,k,l). Here, B(i,j,k,l) represents the covariance between the grid points (i,j) and (k,l).

[0125] Similarly, for the covariance between any two points (i,j) and (k,l), it is also the weighted sum of the covariances at each scale. This superposition method not only considers the contributions of each scale but also retains the interactions between them. For example, large-scale processes may modulate small-scale variations, and this effect is reflected in the final multi-scale covariance matrix.

[0126] It should be noted that although this superposition should produce a positive definite covariance matrix, due to the accumulation of numerical errors, additional positive definiteness checks and necessary adjustments can be performed. In addition, to reduce computational and storage requirements, some approximation methods can be adopted, such as using covariance localization techniques or adopting a compact representation form of the matrix.

[0127] Through this multi-scale combination method, the obtained background field error covariance matrix can more comprehensively describe the error characteristics at different spatial scales and their mutual relationships, thereby providing more accurate and comprehensive prior error information for the data assimilation system, which helps to improve the quality of the assimilation results and the accuracy of the forecasts.

[0128] As Figure 7 shown, in some embodiments, step S60 specifically includes the following sub-steps:

[0129] S61: Obtain multi-source meteorological observation data within the forecast area, including at least two of the following types of data: surface observation station data, radiosonde data, satellite observation data, and radar observation data.

[0130] In this step, it is necessary to collect various meteorological observation data within the forecast area. These data sources are diverse, and each data type provides information on different aspects of the atmospheric state. For example, surface observation station data includes near-surface meteorological elements such as temperature, humidity, air pressure, wind speed, and wind direction. These data are widely distributed but limited to the surface. Radiosonde data provides information on the vertical profile of the atmosphere, including temperature, humidity, air pressure, and wind field data at different heights, which is very important for understanding the three-dimensional structure of the atmosphere. Satellite observation data can provide large-scale atmospheric temperature and humidity profiles, as well as cloud cover, sea surface temperature, etc. information, especially suitable for areas with sparse traditional observations such as the ocean. Radar observation data can provide high spatio-temporal resolution precipitation and wind field information, which is particularly important for monitoring and forecasting severe convective weather. In actual operation, the Global Telecommunication System (GTS) of the World Meteorological Organization (WMO) can be used to obtain these data, or directly obtained from the data centers of each observation network.

[0131] S62: Screen the multi-source meteorological observation data, remove the data that do not meet the preset statistical thresholds and physical constraint conditions, and obtain the screened observation data.

[0132] Data quality control is a crucial step in the data assimilation process. In this step, it is necessary to strictly screen the observed data obtained in S61 to ensure that only high-quality data is used for the subsequent assimilation process. This screening process includes the following aspects: statistical threshold check, internal consistency check, temporal continuity check, spatial consistency check, and background field check. For example, for the temperature data of ground observation stations, the following check criteria can be applied: range check (-80°C < T < 60°C), temporal continuity check (|T(t)-T(t-1)| < 10°C, assuming an observation interval of 1 hour), spatial consistency check (|T - T_nearby| < 15°C, where T_nearby is the average temperature of other stations within 50 km), and background field check (|T - T_background| < 3σ, where σ is the standard deviation of the background field error). Data that does not meet these criteria will be marked as suspicious or directly excluded. Through such a screening process, the quality of the observed data used for assimilation can be significantly improved, thereby enhancing the accuracy of the final analysis field.

[0133] S63: Set the maximum number of iterations and the convergence threshold of the variational assimilation algorithm.

[0134] The variational assimilation algorithm is an iterative optimization process. To ensure that the algorithm can converge to a satisfactory solution within a reasonable time, appropriate termination conditions need to be set. This includes two parameters: the maximum number of iterations and the convergence threshold. The maximum number of iterations is the maximum number of loops allowed for the algorithm. The setting of this parameter requires a trade-off between computational efficiency and the quality of the solution. For three-dimensional variational assimilation (3D-Var), the maximum number of iterations can be set to 50 - 100 times; while for the more computationally complex four-dimensional variational assimilation (4D-Var), a larger value needs to be set, such as 200 - 300 times. The convergence threshold is used to determine whether the algorithm has reached a sufficiently good solution. The relative change in the cost function value between two adjacent iterations can be calculated. When this change is less than the preset threshold, the algorithm is considered to have converged. For example, the convergence threshold can be set to 1e -5 , that is, stop the iteration when the relative change in the cost function is less than 0.001%.

[0135] S64: Set the cost function of the variational assimilation algorithm, which is used to quantify the difference between the model variables and the screened observed data, as well as the difference between the model variables and the background field; among them, the model variables are the atmospheric state variables that need to be optimized through the variational assimilation process.

[0136] Specifically, the cost function defines the objective to be minimized. In the variational assimilation algorithm, the cost function consists of two parts: the observation term and the background term. The cost function can be expressed as:

[0137] J(x)=(x - xb ) T B -1 (x - x b )+(H(x)-y) T R -1 (H(x)-y), where x is the model variable, x b is the background field, B is the background error covariance matrix, H is the observation operator, y is the observation value, and R is the observation error covariance matrix. The first term (background term) quantifies the difference between the model variable and the background field, and the second term (observation term) quantifies the difference between the model variable and the observational data or observation value. For example, for the assimilation of the temperature field, x contains the temperature values on the entire three-dimensional grid, and x b is the temperature field of the short-term forecast, and y

[0138] contains the temperature observations from surface stations, radiosondes, and satellites. H may include vertical interpolation (interpolating the temperature at the model level to the observation height) and a radiative transfer model (converting the atmospheric temperature profile to the brightness temperature observed by satellites). In practical applications, some modifications can be made to the cost function, such as adding a balance constraint term, introducing the flow-dependent characteristics of the background error covariance, or for 4D-Var, introducing the time dimension into the cost function. By minimizing this cost function, an optimal estimate that is both close to the observations and not too far from the background field can be obtained.

[0139] S65: Perform the variational assimilation process, which is an iterative optimization process aimed at finding the model variable that minimizes the cost function. This process includes the following sub-steps:

[0140] S651: Calculate the mean of the background field ensemble samples and set the mean as the initial model variable used in the first iteration.

[0141] In this step, it is first necessary to generate or obtain a set of background field samples. These samples can be from an ensemble forecasting system or generated by adding perturbations to a single background field. Suppose there are 50 ensemble members, each containing the complete three-dimensional atmospheric state (temperature, wind field, humidity, etc.). Calculate the average value of these 50 members at each grid point to obtain an average background field. This average background field will be used as the initial guess for variational assimilation. For example, for the temperature field, it can be calculated as: T_initial(i,j,k) = (1 / 50) * ΣT_ensemble_m(i,j,k), where m = 1 to 50, and (i,j,k) represents the coordinates of the three-dimensional grid, and T_ensemble_m is the temperature field of the m-th ensemble member. Using the ensemble mean as the initial guess has several advantages: it represents the best estimate of the background field, it helps filter out extreme values or imbalances that may exist in individual members, and it provides a relatively smooth and physically consistent starting point for the subsequent iterative process.

[0142] S652: Calculate the first difference between the current model variables and the filtered observational data, and the second difference between the current model variables and the background field, respectively.

[0143] In this step, two differences need to be calculated: the observation increment (O - B) and the background increment (B - A). For the observation increment, it is necessary to use the observation operator H to map the model variables to the observation space and then compare them with the observed values. For example, for surface temperature observations: O - B = T_obs - H(T_model), where T_obs is the observed temperature and H(T_model) is the result of interpolating the model temperature to the location of the observation station. For the background increment, directly calculate the difference between the current model variables and the background field: B - A = T_background - T_model. These differences will be used to calculate the value and gradient of the cost function to guide the subsequent optimization process.

[0144] S653: Use the multi-scale background field error covariance as the weight to calculate the value of the cost function based on the first difference and the second difference.

[0145] In this step, the differences calculated in step S652 are used to evaluate the quality of the current solution. The formula for the cost function is as follows:

[0146] J = (B - A)B -1 (B - A) T +(O - B)R -1 (O - B) T .

[0147] Where B is the multi-scale background field error covariance matrix and R is the observation error covariance matrix. The specific calculation process is as follows: For the background term, multiply the background increment B - A by B-1 Multiply them, and then calculate the inner product of the multiplication result and (B - A). T For the observation term, multiply the observation increment O - B by R -1 and then calculate the inner product of the multiplication result and (O - B). T Add the two terms to obtain the final cost function value. B -1 represents the inverse matrix of the background field error covariance matrix B.

[0148] Using the multi-scale background field error covariance as the weight indicates that the error characteristics at different spatial scales are considered. This helps to more accurately describe the uncertainty of the background field, thus more reasonably weighing the background information and the observation information during the assimilation process.

[0149] S654: Use a numerical optimization method to adjust the current model variables to reduce the value of the cost function.

[0150] In this step, a numerical optimization algorithm is needed to update the model variables to reduce the cost function value. Optimization methods include the conjugate gradient method, quasi-Newton method, etc. Taking the conjugate gradient method as an example, its basic steps are as follows:

[0151] 1. Calculate the gradient of the cost function with respect to the current model variables:

[0152] where H T is the adjoint operator of the observation operator.

[0153] 2. Determine the search direction. In the first iteration, the search direction is the opposite direction of the gradient. In subsequent iterations, the search direction is a linear combination of the gradients.

[0154] 3. Conduct a one-dimensional search to determine the optimal step size in the search direction.

[0155] 4. Update the model variables: x_new = x_old + α * d, where α is the step size and d is the search direction. For example, assume that the temperature field is being assimilated, the temperature value at a certain grid point in the current iteration is 20°C, the calculated gradient is -0.5°C, the search direction is the opposite direction of the gradient 0.5°C, and the optimal step size is 0.8. Then the updated temperature value will be: 20°C + 0.8 * 0.5°C = 20.4°C. This process is performed simultaneously for all model variables, including temperature, wind field, humidity, etc. It should be noted that in actual operation, preconditioning techniques can be used to accelerate convergence. For example, using the square root of the B matrix as a preconditioner can significantly improve the condition number of the cost function and accelerate the convergence rate of the optimization process.

[0156] S655: Repeat steps S652 to S654 until the maximum number of iterations is reached or the convergence threshold is satisfied.

[0157] This step describes the iterative process of variational assimilation. The process of calculating the difference, evaluating the cost function, and updating the model variables will be continuously repeated until the termination condition is met. There are two termination conditions: reaching the maximum number of iterations, which is to ensure that the algorithm ends within a finite time. For example, if the maximum number of iterations is set to 100, the algorithm will stop after 100 iterations regardless of whether the ideal convergence state is reached. Meeting the convergence threshold, which is the criterion for judging whether the algorithm has found a good enough solution. The relative change in the cost function value between two adjacent iterations will be calculated. If the relative change is less than the preset convergence threshold, the algorithm is considered to have converged.

[0158] S66: Output the optimal model variables obtained from the variational assimilation process as the optimal initial field.

[0159] In this step, the final model variables obtained through iterative optimization are output as the optimal initial field. This optimal initial field represents the best estimate of the current atmospheric state, which comprehensively considers the background field information and all available observation information. Specifically, the optimal initial field includes the following elements: three-dimensional temperature field, three-dimensional wind field (including horizontal winds u, v, and vertical velocity w), three-dimensional humidity field (expressed as specific humidity or relative humidity), surface pressure field, and other possible variables (cloud water content, rain water content, etc.). These fields are stored in a grid form covering the entire forecast area. The output optimal initial field will be saved in a specific file format. These files not only contain the numerical values of various physical quantities but also contain relevant metadata, such as time stamps, geographical coordinate information, variable names, and units. This optimal initial field will be used as the input for the numerical weather prediction model to generate weather forecasts for a future period (such as the next 7 days). Since this initial field integrates all available observation information and prior knowledge, it can provide more accurate forecast results than simply using the background field. It should be noted that the quality of the optimal initial field directly affects the accuracy of the forecast. Therefore, in actual operations, initial field verification will be carried out, such as calculating the root mean square error between the initial field and independent observations, or conducting forecast experiments to evaluate the quality of the initial field. This helps to continuously improve the assimilation system and enhance the forecast accuracy.

[0160] As Figure 8 shown, in some embodiments, step S70 includes the following sub-steps:

[0161] S71: Set the parameters of the regional numerical weather prediction model based on the optimal initial field.

[0162] In this step, various parameters of the regional numerical weather prediction model need to be set according to the characteristics of the optimal initial field and the prediction requirements. These parameters include the spatial resolution, time step, and integration duration of the model. For example, for a mesoscale numerical weather prediction model, the following parameters may be set: the horizontal resolution is 3 km, the number of vertical levels is 50, the time step is 15 seconds, and the integration duration is 72 hours. The setting of these parameters needs to consider various factors such as computing resources, prediction accuracy requirements, and prediction lead time, and the optimal configuration needs to be determined through a large number of experiments. In addition, some parameters may need to be dynamically adjusted according to the characteristics of the initial field. For example, in the case of severe convective weather, the time step needs to be reduced to ensure numerical stability.

[0163] S72: Input the optimal initial field and the boundary conditions of the prediction area into the regional numerical weather prediction model. The boundary conditions include static boundary conditions and time-varying atmospheric boundary conditions.

[0164] In this step, the optimal initial field obtained in step S66 and the boundary conditions of the prediction area need to be input into the regional numerical weather prediction model. The optimal initial field contains the atmospheric state at the start time of the prediction, including the three-dimensional temperature field, wind field, humidity field, and surface pressure field, etc. The boundary conditions are divided into two categories: static boundary conditions and time-varying atmospheric boundary conditions. The static boundary conditions include terrain height, land use type, vegetation cover, soil type, etc., and these data are from a high-resolution geographic information database. The time-varying atmospheric boundary conditions describe the change of the atmospheric state over time at the boundary of the prediction area and are obtained from the prediction results of a larger-scale global model. For example, for a regional model covering Inner Mongolia, the prediction results of the Global Forecast System (GFS) can be used as the lateral boundary conditions and updated every 6 hours. These boundary conditions have an important impact on the prediction results of the regional model, especially for longer lead-time predictions. In actual operation, it is necessary to ensure the consistency of the initial field and the boundary conditions in space and time to avoid generating unphysical perturbations during the model integration process.

[0165] S73: Use the parameters of the regional numerical weather prediction model to perform the integration calculation of the regional numerical weather prediction model, simulate the temporal evolution process of the atmospheric state, and save the atmospheric state variables obtained from the integration calculation at the preset output time points. The saved atmospheric state variables are the prediction results of the weather conditions in the prediction area for a period of time in the future.

[0166] Specifically, in this process, the regional numerical weather prediction model is based on the initial field and boundary conditions, uses the set parameters, and simulates the temporal evolution of the atmospheric state by solving the atmospheric dynamics and thermodynamics equations. Specifically, the model calculates the changes in variables such as temperature, pressure, wind speed, and humidity at each grid point at each time step. This process involves the parameterization of multiple physical processes, such as radiation transfer, cloud microphysics, boundary layer turbulence, etc. For example, when simulating the development of convection, the model calculates processes such as atmospheric instability, water vapor transport, and latent heat release due to condensation. The model integration continues until the predetermined forecast period, such as 72 hours or 168 hours. During the integration process, the model saves the calculated atmospheric state variables at the preset output time points (every hour or every 3 hours). These saved variables constitute the prediction results of the weather conditions in the forecast area for a period of time in the future. For example, for a 72-hour forecast, the results can be output every 3 hours, obtaining 24 forecast fields. Each forecast field contains three-dimensional temperature, wind field, humidity field, and two-dimensional variables such as surface pressure and precipitation. These original model output results provide the basic data for the subsequent production of forecast products.

[0167] S74: Post-process the saved atmospheric state variables to obtain processed weather condition prediction data.

[0168] In this step, post - processing of the original model output results saved in S73 is required to obtain more practical and understandable weather condition prediction data. The post - processing process includes the following aspects: Data interpolation, which interpolates the data at model grid points to specific stations or higher - resolution grids. For example, interpolating the model output at a 3 - kilometer resolution to a 1 - kilometer resolution grid to provide more detailed local forecasts. Physical quantity conversion, which converts the physical quantities directly output by the model into more commonly used meteorological elements. For example, converting specific humidity to relative humidity, converting the wind speed at pressure levels to the wind speed at 10 - meter height, etc. Statistical post - processing: applying statistical methods to correct the systematic biases of the model. Statistical methods include Model Output Statistics (MOS), Kalman filtering, etc. For example, using the model forecasts and observed data for the past month to establish a MOS equation for temperature forecasting to correct the temperature forecasting biases of the model at specific locations. Diagnostic calculations, which calculate some complex meteorological indices or diagnostic quantities based on the model output. For example, calculating Convective Available Potential Energy (CAPE), vertical wind shear, etc., for severe convective weather forecasting. Probabilistic forecast product generation, if an ensemble forecasting system is used, various probabilistic forecast products also need to be calculated, such as precipitation probability, extreme temperature probability, etc. Through these post - processing steps, more refined, accurate, and practical weather condition prediction data can be obtained.

[0169] S75: Based on the processed weather condition prediction data, generate and output the weather condition prediction results for a future period within the final forecast area.

[0170] In this last step, based on the processed weather condition prediction data obtained in step S74, the final forecast product is generated and output. This process includes the following aspects: Forecast product design, which designs various forecast products according to the needs of different users. For example, for the general public users, the daily weather overview for the next 7 days can be generated, including the maximum temperature, minimum temperature, weather phenomena, precipitation probability, etc.; for professional users, more detailed forecast elements may be required, such as the temperature, humidity, wind direction and speed, air pressure, etc. per hour. Visualization processing: converting the numerical forecast results into intuitive graphs or charts. For example, generating contour maps or filled maps of temperature, precipitation, wind fields, etc.; making weather trend charts for the next few days; making radar echo extrapolation maps for severe convective weather, etc. Text forecast generation, which generates descriptive weather forecast texts based on the numerical forecast results and combined with the experience of forecasters. This can adopt natural language processing technology to achieve the automatic generation of forecast texts. Early warning information production, which means that if the forecast results show that there may be disastrous weather, corresponding early warning information needs to be produced. For example, when the predicted precipitation exceeds the heavy rain standard, a heavy rain early warning information is generated. Product release, which releases the generated forecast products through various channels, such as the official website of the meteorological department, mobile apps, social media platforms, etc.

[0171] Embodiment 2

[0172] As Figure 9 shown, this embodiment provides a regional numerical weather prediction system 200 based on multi-scale background field error covariance, which includes:

[0173] A meteorological observation device 210 for obtaining meteorological observation data within the forecast area;

[0174] A boundary condition acquisition device 220 for obtaining the atmospheric state data on the boundary of the forecast area. The boundary condition acquisition device includes: a receiving device for the output data of the large-scale numerical weather prediction model, which is used to receive the output data of the global numerical weather prediction model; a boundary meteorological observation station, which is set near the boundary of the forecast area and is used to directly measure the boundary atmospheric state;

[0175] A data storage device 230 for storing the meteorological observation data within the forecast area, the boundary conditions, the atmospheric state on the boundary of the forecast area, and the background field ensemble samples;

[0176] A computing and processing device 240, which is communicatively connected to the meteorological observation device 210, the boundary condition acquisition device 220, and the data storage device 230. The computing and processing device 240 includes a central processing unit and a memory, wherein a computer program is stored in the memory, and when the central processing unit executes the computer program, it implements any one of the methods described in the first aspect;

[0177] An output device 250, communicatively connected to the computing and processing device 240, for outputting a prediction result.

[0178] In some embodiments, the meteorological observation device includes a plurality of a surface meteorological station, an upper-air meteorological station, a meteorological radar, a meteorological satellite, and an automatic weather station.

[0179] Those skilled in the art can clearly understand that, for the convenience and conciseness of description, only the above division of each functional unit and module is used as an example. In practical applications, the above functions can be allocated to different functional units and modules according to needs, that is, the internal structure of the device is divided into different functional units or modules to complete all or part of the functions described above. Each functional unit and module in the embodiments can be integrated into one processing unit, or each unit can exist physically alone, or two or more units can be integrated into one unit. The above integrated unit can be implemented in the form of hardware or in the form of a software functional unit. In addition, the specific names of each functional unit and module are only for the convenience of mutual distinction and do not limit the protection scope of the present application. The specific working processes of the units and modules in the above system can refer to the corresponding processes in the foregoing method embodiments and will not be elaborated herein.

[0180] The embodiment of the present invention further provides a computer-readable storage medium, on which a computer program is stored, and when the program is executed by a processor, it implements any one of the above methods.

[0181] When the integrated module / unit is implemented in the form of a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on this understanding, to implement all or part of the processes in the above-described embodiment methods of the present invention, it can also be completed by a computer program instructing relevant hardware. The computer program can be stored in a computer-readable storage medium. When the computer program is executed by a processor, the steps of the above-described various method embodiments can be implemented. Among them, the computer program includes computer program code, and the computer program code can be in the form of source code, object code, executable file, or some intermediate form, etc. The computer-readable medium can include: any entity or device capable of carrying the computer program code, recording medium, USB flash drive, mobile hard disk, magnetic disk, optical disk, computer memory, read-only memory (ROM), random access memory (RAM), electrical carrier signal, telecommunication signal, and software distribution medium, etc. Of course, there are other ways of readable storage media, such as quantum memory, graphene memory, etc. It should be noted that the content included in the computer-readable medium can be appropriately increased or decreased according to the requirements of legislation and patent practice within the jurisdiction. For example, in some jurisdictions, according to legislation and patent practice, the computer-readable medium does not include electrical carrier signals and telecommunication signals.

[0182] The present invention also provides an electronic device. The electronic device according to an embodiment of the present invention includes: one or more processors; a storage device for storing one or more programs, and when the one or more programs are executed by the one or more processors, the one or more processors implement the method provided by the present invention.

[0183] Reference is made below to Figure 10 , which shows a schematic structural diagram of a computer system 800 suitable for implementing the electronic device of the embodiment of the present invention. Figure 10 The electronic device shown is only an example and should not impose any limitation on the functions and usage scope of the embodiments of the present invention.

[0184] As Figure 10 shown, the computer system 800 includes a central processing unit (CPU) 801, which can perform various appropriate actions and processes according to the program stored in the read-only memory (ROM) 802 or the program loaded from the storage section 808 into the random access memory (RAM) 803. In the RAM 803, various programs and data required for the operation of the computer system 800 are also stored. The CPU 801, ROM 802, and RAM 803 are connected to each other through a bus 804. The input / output (I / O) interface 805 is also connected to the bus 804.

[0185] The following components are connected to the I / O interface 805: an input section 806 including a keyboard, a mouse, etc.; an output section 807 including a cathode ray tube (CRT), a liquid crystal display (LCD), etc. and a speaker, etc.; a storage section 808 including a hard disk, etc.; and a communication section 809 including a network interface card such as a LAN card, a modem, etc. The communication section 809 performs communication processing via a network such as the Internet. A drive 810 is also connected to the I / O interface 805 as needed. A removable medium 811 such as a magnetic disk, an optical disk, a magneto-optical disk, a semiconductor memory, etc. is installed on the drive 810 as needed so that a computer program read therefrom is installed into the storage section 808 as needed.

[0186] Specifically, according to the embodiments disclosed in the present invention, the process described in the above main step diagram can be implemented as a computer software program. For example, an embodiment of the present invention includes a computer program product, which includes a computer program carried on a computer-readable medium, and the computer program includes program codes for executing the method shown in the main step diagram. In the above embodiment, the computer program can be downloaded and installed from the network through the communication section 809, and / or installed from the removable medium 811. When the computer program is executed by the central processing unit 801, the above functions defined in the system of the present invention are executed.

[0187] It should be noted that the computer-readable medium shown in the present invention can be a computer-readable signal medium or a computer-readable storage medium or any combination of the two. The computer-readable storage medium can be, for example, but not limited to, an electrical, magnetic, optical, electromagnetic, infrared, or semiconductor system, apparatus, or device, or any combination of the above. More specific examples of the computer-readable storage medium can include, but are not limited to: an electrical connection having one or more wires, a portable computer disk, a hard disk, a random access memory (RAM), a read-only memory (ROM), an erasable programmable read-only memory (EPROM or flash memory), an optical fiber, a portable compact disk read-only memory (CD-ROM), an optical storage device, a magnetic storage device, or any suitable combination of the above.

[0188] The flowcharts and block diagrams in the accompanying drawings illustrate the possible architectures, functions, and operations of systems, methods, and computer program products according to various embodiments of the present invention. In this regard, each block in the flowchart or block diagram may represent a module, a segment of a program, or a part of code, and the above-mentioned module, segment of a program, or part of code contains one or more executable instructions for implementing the specified logical function. It should also be noted that in some alternative implementations, the functions marked in the blocks may occur in a different order than that marked in the accompanying drawings. For example, two consecutive blocks shown may actually be executed substantially in parallel, and they may sometimes be executed in the reverse order, depending on the functions involved. It should also be noted that each block in the block diagram or flowchart, as well as combinations of blocks in the block diagram or flowchart, can be implemented by a dedicated hardware-based system that performs the specified functions or operations, or can be implemented by a combination of dedicated hardware and computer instructions.

[0189] The above specific embodiments do not constitute a limitation on the protection scope of the present invention. Those skilled in the art should understand that various modifications, combinations, sub-combinations, and substitutions may occur depending on design requirements and other factors. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention shall be included within the protection scope of the present invention.

Claims

1. A regional numerical prediction method based on multi-scale background field error covariance, characterized in that: The following steps are involved: S10: Construct a multi-scale background field error covariance model, which includes error structures at different spatial scales; S20: acquiring the initial atmospheric state and boundary conditions of the forecast area, and generating a background field ensemble sample using an ensemble forecast algorithm based on the initial atmospheric state and boundary conditions of the forecast area; the initial atmospheric state refers to the atmospheric state at the start time of the forecast, and the boundary conditions refer to the atmospheric state at the boundary of the forecast area; S30: Based on the multi-scale background field error covariance model, perform multi-scale decomposition on the background field set samples to obtain error components of different spatial scales; wherein the error structures of different spatial scales are used to determine the scale range and decomposition rules of multi-scale decomposition; S40: Based on the error components of different spatial scales, and applying the multi-scale background field error covariance model, respectively determine the error covariance matrices of corresponding spatial scales; wherein the multi-scale background field error covariance model is used to provide structural information of the error covariance matrix and a parameter estimation method for determining the parameter values ​​of each item in the error covariance matrix; S50: combining the error covariance matrices of different spatial scales to form a complete multi-scale background field error covariance; S60: Acquire meteorological observation data in the forecast area, and apply a variational assimilation algorithm, using the multi-scale background field error covariance in the variational assimilation algorithm to achieve an optimal combination of the meteorological observation data and the background field set samples, and obtain an optimal initial field; S70: Perform regional numerical forecast based on the optimal initial field to obtain the forecast result of weather conditions in the forecast area for a period of time in the future.

2. The method according to claim 1, characterized in that Step S10 specifically includes the following sub-steps: S11: Acquire historical meteorological data and historical numerical weather forecast data, and establish a data set for analyzing background field error characteristics; wherein the historical numerical weather forecast data refers to atmospheric state data obtained by simulating a historical time period using a historical version of a numerical weather forecast model; S12: performing statistical analysis on the data set to identify error patterns and spatial correlation structures at different spatial scales, wherein the spatial correlation structure refers to the mutual relationship and dependence degree of errors at different spatial locations; S13: designing error covariance functions of multiple spatial scales based on the error pattern and the spatial correlation structure; S14: combining the error covariance functions of the multiple spatial scales to construct an initial multi-scale background field error covariance model; S15: using current meteorological observation data and current numerical weather forecast data, verifying and tuning the initial multi-scale background field error covariance model to obtain verification and tuning results; the current meteorological observation data refers to actual meteorological observation data collected in a recent period of time; the current numerical weather forecast data refers to atmospheric state data obtained by using the latest version of the numerical weather forecast model to forecast a period of time in the future; S16: According to the verification and tuning results, a final multi-scale background field error covariance model is determined, which includes error structures of different spatial scales and their weights.

3. The method according to claim 1, characterized in that Step S20 specifically includes the following sub-steps: S21: Obtain output data of a global numerical weather forecast model, and extract corresponding initial atmospheric state and boundary condition data according to the geographical scope of the forecast area; S22: interpolating and adjusting the initial atmospheric state and the boundary condition data to adapt the data to the grid resolution and terrain characteristics of the forecast area, thereby obtaining adjusted initial atmospheric state and boundary condition data; S23: setting the sample number N of the ensemble prediction algorithm, which determines the number of background field ensemble samples generated subsequently; and determining the initial field disturbance amplitude and the boundary condition disturbance amplitude according to historical forecast error statistics; S24: using a random perturbation method to generate N groups of initial field perturbations and N groups of boundary condition perturbations, wherein the perturbation amplitude is controlled by the initial field perturbation amplitude and the boundary condition perturbation amplitude; superimposing the N groups of initial field perturbations on the adjusted initial atmospheric state to form N groups of perturbed initial fields; superimposing the N groups of boundary condition perturbations on the adjusted boundary condition data to form N groups of perturbed boundary conditions; S25: using a regional numerical prediction model, performing integral calculations of preset durations on N groups of initial fields after disturbance and corresponding N groups of boundary conditions after disturbance, generating one background field sample for each group of calculations, and generating a total of N background field samples, thereby forming a background field set sample; S26: Performing quality control on the background field set samples, eliminating unreasonable samples, and obtaining optimized background field set samples.

4. The method according to claim 1, characterized in that: Step S30 specifically includes the following sub-steps: S31: determining a scale range and a decomposition rule of multi-scale decomposition based on different spatial scale error structures in the multi-scale background field error covariance model; S32: Perform Fourier transform on each sample in the background field set sample, and convert each sample in the background field set sample into the frequency domain; S33: performing multi-scale decomposition on each sample in the frequency domain according to the scale range and the decomposition rule, and decomposing it into frequency components of different spatial scales; S34: performing inverse Fourier transform on the frequency components of each spatial scale, converting the frequency components of each spatial scale back to the spatial domain, and obtaining the error components of the corresponding spatial scale; S35: Perform the Fourier transform processing in step S32, the multi-scale decomposition processing in step S33 and the inverse Fourier transform processing in step S34 on all background field set samples to obtain error components of different spatial scales.

5. The method according to claim 1, characterized in that Step S40 specifically includes the following sub-steps: S41: Determine structural information of the error covariance matrix of each spatial scale based on the multi-scale background field error covariance model; S42: performing statistical analysis on the error components of each spatial scale, and calculating statistical characteristic quantities, which include sample mean and sample variance; S43: using the parameter estimation method provided by the multi-scale background field error covariance model and combining the statistical feature quantity to determine the parameter values ​​in the error covariance matrix of each spatial scale; S44: constructing an error covariance matrix of each spatial scale based on the structural information of the error covariance matrix of each spatial scale and the parameter values ​​in the error covariance matrix of each spatial scale; S45: normalizing the error covariance matrix of each spatial scale to obtain a normalized error covariance matrix of each spatial scale; S46: Perform a positive definiteness test and / or a condition number test on the normalized error covariance matrix of each spatial scale. When the test result does not meet the preset standard, adjust the normalized error covariance matrix of each spatial scale to obtain the final error covariance matrix of each spatial scale that meets the numerical stability requirements.

6. The method according to claim 1, characterized in that Step S50 specifically includes the following sub-steps: S51: determining a weight coefficient of each spatial scale error covariance matrix, wherein the weight coefficient is used to adjust the contribution ratio of the error covariance of different spatial scales to the multi-scale background field error covariance; S52: performing a scale transformation on the error covariance matrix of each spatial scale so that the error covariance matrix has the same spatial resolution and matrix size, thereby obtaining the scale-transformed error covariance matrix of each spatial scale; S53: weighting the spatial scale error covariance matrices after the scale transformation according to the weight coefficient to obtain weighted spatial scale error covariance matrices; S54: superimposing the weighted error covariance matrices of each spatial scale to obtain a complete multi-scale background field error covariance.

7. The method according to claim 1, characterized in that Step S60 specifically includes the following sub-steps: S61: Obtain multi-source meteorological observation data in the forecast area, including at least two of the following types of data: ground observation station data, sounding balloon data, satellite observation data and radar observation data; S62: Screening the multi-source meteorological observation data to remove data that does not meet preset statistical thresholds and physical constraints, and obtaining screened observation data; S63: Set the maximum number of iterations and convergence threshold of the variational assimilation algorithm; S64: setting a cost function of the variational assimilation algorithm, which is used to quantify the difference between the model variable and the filtered observation data, and the difference between the model variable and the background field; wherein the model variable is an atmospheric state variable that needs to be optimized through the variational assimilation process; S65: Execute the variational assimilation process, including the following steps: S651: Calculate the average value of the background field set samples, and set the average value as the initial pattern variable used in the first iteration; S652: respectively calculating a first difference between the current pattern variable and the filtered observation data, and a second difference between the current pattern variable and the background field; S653: using the multi-scale background field error covariance as a weight, and calculating a value of a cost function according to the first difference and the second difference; S654: Use a numerical optimization method to adjust the current mode variable to reduce the value of the cost function; S655: Repeat steps S652 to S654 until the maximum number of iterations is reached or the convergence threshold is met; S66: Output the optimal model variables obtained by the variational assimilation process as the optimal initial field.

8. The method according to claim 1, characterized in that Step S70 includes the following sub-steps: S71: Based on the optimal initial field, setting parameters of the regional numerical forecast model; S72: inputting the optimal initial field and the boundary conditions of the forecast area into a regional numerical forecast model, wherein the boundary conditions include static boundary conditions and time-varying atmospheric boundary conditions; S73: using the parameters of the regional numerical forecast model, executing the integral calculation of the regional numerical forecast model, simulating the time evolution process of the atmospheric state, and saving the atmospheric state variables obtained by the integral calculation at a preset output time point, wherein the saved atmospheric state variables are the forecast results of the weather conditions in the forecast area for a period of time in the future; S74: post-processing the saved atmospheric state variables to obtain processed weather condition forecast data; S75: Based on the processed weather condition forecast data, generate and output the final weather condition forecast result for a period of time in the future within the forecast area.

9. A regional numerical prediction system based on multi-scale background field error covariance, characterized in that: include: Meteorological observation equipment, used to obtain meteorological observation data within the forecast area; A boundary condition acquisition device is used to acquire atmospheric state data on the boundary of the forecast area, and the boundary condition acquisition device includes: a receiving device for large-scale numerical forecast model output data, which is used to receive output data of the global numerical forecast model; a boundary meteorological observation station is set near the boundary of the forecast area, which is used to directly measure the boundary atmospheric state; A data storage device for storing meteorological observation data within the forecast area, the boundary conditions, the atmospheric state on the boundary of the forecast area, and a set of background field samples; A computing and processing device, which is in communication with the meteorological observation device, the boundary condition acquisition device and the data storage device, wherein the computing and processing device comprises a central processing unit and a memory, wherein a computer program is stored in the memory, and when the central processing unit executes the computer program, the method according to any one of claims 1 to 8 is implemented; An output device is connected to the computing and processing device for outputting forecast results.

10. A regional numerical prediction system based on multi-scale background field error covariance according to claim 9, characterized in that: The meteorological observation equipment includes multiple ones of ground meteorological stations, high-altitude meteorological stations, meteorological radars, meteorological satellites and automatic weather stations.

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