Three-dimensional analysis method of meteorological elements combining remote sensing and ground observation

Abstract

The present invention provides a three-dimensional analysis method for meteorological elements that combines remote sensing and ground observation, and relates to the field of meteorological monitoring technology. The method comprises the following steps: acquiring remote sensing and ground observation data to obtain meteorological element data with a unified spatiotemporal reference; dividing the data into spatiotemporal grid units and performing quality assessment to obtain quality assessment indicators; using an adaptive fusion algorithm based on dynamic weights to calculate fusion weight coefficients according to the quality assessment indicators, performing weighted fusion on the meteorological element data within the grid units, and generating an initial three-dimensional meteorological field; using a spectral analysis method to perform scale decomposition and reconstruction to obtain an optimal three-dimensional meteorological field, constructing an adaptive tree-like composite analysis grid, analyzing the evolution characteristics of the weather system in a multi-layer progressive manner, determining topological evolution parameters, and outputting three-dimensional analysis results of the meteorological elements.

Description

Technical Field

[0001] The present invention relates to the field of meteorological monitoring technology, and in particular to a three-dimensional analysis method of meteorological elements combining remote sensing and ground observation. Background Art

[0002] Three-dimensional analysis of meteorological elements is of great significance for weather forecasting and meteorological monitoring. Traditional meteorological element analysis relies primarily on data from ground-based observation stations. Limited by the spatial distribution of these observation stations, it is difficult to obtain detailed information on the vertical structure of the atmosphere. With the advancement of remote sensing technology, satellites, radar, and other remote sensing devices can acquire atmospheric information at different altitudes, providing a new data source for three-dimensional analysis of meteorological elements. Currently, combining remote sensing and ground-based observation data for meteorological element analysis has become a research hotspot, but effectively integrating multi-source heterogeneous data and achieving refined analysis of meteorological elements still faces many challenges.

[0003] However, existing technologies still have some shortcomings. Remote sensing and ground observation data have different temporal and spatial resolutions and observation accuracy, and there is a lack of unified data quality assessment standards, making it difficult to ensure the accuracy of the fusion results. Traditional data fusion methods often use fixed weights or simple linear superposition, without fully considering the physical consistency of the data, resulting in deviations between the fusion results and the actual atmospheric state. Existing analysis methods mostly use fixed grid structures, which are difficult to adapt to the multi-scale characteristics of weather systems and cannot effectively characterize the local details and evolution characteristics of meteorological elements.

[0004] In summary, a three-dimensional analysis method for meteorological elements that combines remote sensing and ground-based observations is urgently needed. This approach effectively integrates multi-source data by establishing a unified spatiotemporal benchmark and data quality assessment system. Adopting an adaptive fusion algorithm with dynamic weights ensures the physical consistency of the fusion results. Furthermore, based on an adaptive tree-structured composite analysis grid and multi-layer progressive analysis methods, refined analysis of meteorological elements is achieved, providing technical support for accurately characterizing the evolution of weather systems. Summary of the Invention

[0005] The embodiment of the present invention provides a three-dimensional analysis method of meteorological elements combining remote sensing and ground observation, which can solve the problems in the prior art.

[0006] According to a first aspect of the embodiments of the present invention,

[0007] A three-dimensional analysis method for meteorological elements combining remote sensing and ground observations is provided, including:

[0008] Acquire remote sensing and ground observation data of a designated area, perform spatiotemporal registration and data standardization, and obtain meteorological element data with a unified spatiotemporal benchmark;

[0009] The meteorological element data is divided into different spatiotemporal grid units, and the data quality assessment is performed on the observation data in each spatiotemporal grid unit to obtain the data quality assessment index of the spatiotemporal grid unit;

[0010] An adaptive fusion algorithm based on dynamic weights calculates the fusion weight coefficients of meteorological element data within the spatiotemporal grid cells according to the data quality assessment indicators of the spatiotemporal grid cells, performs weighted fusion on the meteorological element data within the spatiotemporal grid cells, and generates an initial three-dimensional meteorological field with physical consistency.

[0011] Based on the initial three-dimensional meteorological field, the spectral analysis method is used to decompose and reconstruct the meteorological element field to obtain the optimal three-dimensional meteorological field.

[0012] Based on the optimal three-dimensional meteorological field, an adaptive tree-structured composite analysis grid is constructed. The evolution characteristics of the weather system are analyzed through a multi-layer progressive method, the topological evolution parameters are determined, and the three-dimensional analysis results of the meteorological elements are output.

[0013] In an optional embodiment,

[0014] The meteorological element data is divided into different spatiotemporal grid units, and the data quality assessment is performed on the observation data in each spatiotemporal grid unit. The data quality assessment indicators of the spatiotemporal grid units include:

[0015] Divide meteorological element data into multiple spatiotemporal grid units according to preset time intervals and spatial resolutions;

[0016] The difference between the observed values ​​of any two observation points in the spatiotemporal grid unit is calculated to obtain the numerical consistency deviation; the change amplitude of the observed values ​​of each observation point in the spatiotemporal grid unit between two adjacent moments is calculated to obtain the time series volatility deviation; the difference between the spatial distribution density of the observation points in the spatiotemporal grid unit and the preset density threshold is calculated to obtain the spatial density distribution deviation;

[0017] The numerical consistency deviation, the time series volatility deviation and the spatial density distribution deviation are linearly combined after normalization to obtain a data quality assessment index for each spatiotemporal grid unit.

[0018] In an optional embodiment,

[0019] The adaptive fusion algorithm based on dynamic weights calculates the fusion weight coefficients of meteorological element data within the spatiotemporal grid cells according to the data quality evaluation indicators of the spatiotemporal grid cells, performs weighted fusion on the meteorological element data within the spatiotemporal grid cells, and generates an initial three-dimensional meteorological field with physical consistency, including:

[0020] Calculating a weighted influence factor of the spatiotemporal grid unit based on the data quality assessment index of the spatiotemporal grid unit, wherein the weighted influence factor is calculated in the form of a Gaussian function with the data quality assessment index as an independent variable;

[0021] Normalizing the weight influence factors of the spatiotemporal grid cells to obtain fusion weight coefficients of the meteorological element data within the spatiotemporal grid cells; performing weighted calculations on the meteorological element data within the spatiotemporal grid cells according to the fusion weight coefficients to obtain observation value fitting terms; constructing a mass conservation constraint term based on the air density continuity equation, and simultaneously constructing a momentum conservation constraint term based on the atmospheric dynamics equation;

[0022] Combining the observation value fitting term, the mass conservation constraint term, and the momentum conservation constraint term to form a fusion objective function;

[0023] The optimization algorithm based on adaptive step size and orthogonalized quasi-Newton iteration is used to solve the fusion objective function and obtain the fusion meteorological field.

[0024] The mass conservation residual and the momentum conservation residual of the fused meteorological field are calculated, and when the mass conservation residual is less than a first preset threshold and the momentum conservation residual is less than a second preset threshold, the fused meteorological field is determined to be an initial three-dimensional meteorological field with physical consistency.

[0025] In an optional embodiment,

[0026] The fusion objective function is solved by using an optimization algorithm based on adaptive step size and orthogonalized quasi-Newton iteration, and the fusion meteorological field is obtained, including:

[0027] Taking the meteorological element data in the spatiotemporal grid unit as the initial solution, and calculating the gradient value of the fusion objective function corresponding to the initial solution based on the fusion objective function;

[0028] An iterative format is constructed based on the initial solution and the gradient value of the fusion objective function using an adaptive step size factor and an approximate inverse matrix of a quasi-Newton matrix. When the rate of change of the fusion objective function value between two adjacent iterations is greater than zero, the adaptive step size factor is reduced by a preset proportional coefficient; otherwise, the adaptive step size factor is increased by the preset proportional coefficient. The value of the adaptive step size factor is limited to a preset upper and lower limit range.

[0029] In each iteration process, the solution vector difference between two adjacent iterations and the corresponding fusion objective function gradient difference vector are calculated; the solution vector difference and the fusion objective function gradient difference vector are orthogonalized to obtain an orthogonalized difference vector;

[0030] According to a preset iterative evaluation round, based on the corresponding orthogonalized difference vector, an approximate inverse matrix of the quasi-Newton matrix is ​​updated using a bidirectional recursive method; and a new solution vector is calculated using the approximate inverse matrix of the updated quasi-Newton matrix;

[0031] Calculate the fusion objective function value corresponding to the new solution vector and calculate the distance between the solution vectors of two adjacent iterations;

[0032] When the relative change of the fusion objective function value is less than the preset change threshold and the distance value between the solution vectors is less than the preset distance threshold, the new solution vector is determined as the fused meteorological field; otherwise, the new solution vector is used as the initial solution for the next iteration and the iteration continues.

[0033] In an optional embodiment,

[0034] Based on the initial three-dimensional meteorological field, the spectral analysis method is used to decompose and reconstruct the meteorological element field. The optimal three-dimensional meteorological field is obtained, including:

[0035] Performing Fourier transform on the initial three-dimensional meteorological element field to obtain spectral coefficients, performing wavelet transform on the spectral coefficients and the local window function to obtain decomposition coefficients of the meteorological element field at different scales and spatial positions, constructing a multidimensional tensor based on the decomposition coefficients, performing nuclear norm calculation and tensor decomposition, and constructing a wavenumber-energy spectrum matrix in combination with feature truncation extraction;

[0036] Obtaining a dominant wavenumber mode by singular value decomposition of the wavenumber-energy spectrum matrix, and determining a characteristic wavenumber sequence according to the energy contribution rate of the dominant wavenumber mode;

[0037] constructing an orthogonal filter bank based on the characteristic wavenumber sequence, wherein the orthogonal filter bank includes a plurality of Gaussian filters, wherein the center frequency of each Gaussian filter corresponds to a characteristic wavenumber in the characteristic wavenumber sequence, and the bandwidth parameter of the Gaussian filter is determined according to the interval between adjacent characteristic wavenumbers;

[0038] Applying the orthogonal filter bank to the spectral coefficients to obtain a plurality of scale components, and constructing a spectral reconstruction tensor based on local energy distributions of the plurality of scale components;

[0039] Local reconstruction weights are calculated according to the spectral reconstruction tensor, and weighted superposition is performed on the multiple scale components to obtain an optimal meteorological element field.

[0040] In an optional embodiment,

[0041] Based on the decomposition coefficients, a multidimensional tensor is constructed and the nuclear norm and tensor decomposition are performed. The wave number-energy spectrum matrix is ​​constructed by combining the feature truncation extraction method, including:

[0042] Constructing a multidimensional tensor from the decomposition coefficients according to different scale levels, and calculating the nuclear norm of the multidimensional tensor to obtain a scale correlation matrix;

[0043] Performing tensor decomposition on the scale correlation matrix to obtain a scale core tensor and a projection matrix group, wherein the projection matrix group includes a spatial position projection matrix, a wavenumber projection matrix, and an energy projection matrix;

[0044] Calculating a singular value sequence of the scale core tensor, taking eighty percent of the maximum value of the singular value sequence as a feature truncation threshold, and extracting projection matrix components corresponding to singular values ​​in the singular value sequence that are greater than the feature truncation threshold;

[0045] The projection matrix components are reconstructed to obtain the wavenumber-energy spectrum matrix.

[0046] In an optional embodiment,

[0047] Based on the optimal three-dimensional meteorological field, an adaptive tree-structured composite analysis grid is constructed. The evolution characteristics of the weather system are analyzed through a multi-layer progressive approach, and the topological evolution parameters are determined. The three-dimensional analysis results of meteorological elements are output, including:

[0048] Acquire meteorological field data in an optimal three-dimensional meteorological field, determine a reference resolution and a hierarchical coefficient based on spatial distribution characteristics and gradient distribution of the meteorological field data, calculate a first resolution, and determine a backbone grid; calculate a second resolution based on local variation characteristics of the meteorological field data, determine a branch grid, and combine the backbone grid and the branch grid to generate an adaptive tree-like composite analysis grid;

[0049] Calculating the local gradient field on the adaptive tree-like composite analysis grid, determining the growth direction of the grid branches, constructing a multi-layer progressive interpolation function, and establishing a numerical association between the trunk grid and the branch grids;

[0050] constructing a characteristic metric tensor based on the local gradient field and the numerical association, calculating an evolution parameter of the characteristic metric tensor, and constructing a characteristic transfer function between grid nodes according to the evolution parameter;

[0051] Utilizing the characteristic transfer function to calculate the grid topological characteristics, obtain the topological stability index, structural evolution rate and system deformation parameter, and construct a topological evolution characteristic operator;

[0052] A recursive operator is constructed according to historical features, current features and change features, and the topological evolution feature operator is subjected to multi-layer progressive fusion using the recursive operator to output a three-dimensional analysis result of the meteorological elements.

[0053] In an embodiment of the present invention, by performing spatiotemporal registration and standardization processing on remote sensing and ground observation data, the problem of inconsistent spatiotemporal benchmarks of data from different sources is solved, the basic accuracy of data fusion is ensured, and the systematic error in the data fusion process is significantly reduced; the dynamic weight adaptive fusion algorithm based on data quality assessment reasonably allocates the weights of different observation data, avoids the negative impact of poor quality data on the fusion results, and makes the fusion results more reliable and stable; the spectral analysis method is used for scale decomposition and reconstruction, which can retain the characteristic information of weather systems at different scales, improve the spatial resolution of meteorological element fields, and make the identification and analysis of small-scale weather phenomena more accurate; the construction method of adaptive tree-like composite analysis grid dynamically adjusts the grid density according to the characteristics of the weather system, reduces the consumption of computing resources while ensuring analysis accuracy, and improves the system operation efficiency; the multi-layer progressive topological feature analysis method can comprehensively capture the evolution characteristics of the weather system, accurately identify key weather processes, and provide more reliable decision-making basis for weather forecasts and early warnings. BRIEF DESCRIPTION OF THE DRAWINGS

[0054] Figure 1 Schematic diagram of the flow of a three-dimensional analysis method of meteorological elements combining remote sensing and ground observation according to an embodiment of the present invention;

[0055] Figure 2 is the convergence comparison curve of the objective function;

[0056] Figure 3 Analyze the histogram for the residual values;

[0057] Figure 4 This is a scatter plot of the distribution of wavelet transform and tensor decomposition-feature truncation methods in three-dimensional feature space; DETAILED DESCRIPTION

[0058] To make the objectives, technical solutions, and advantages of the embodiments of the present invention more clear, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts shall fall within the scope of protection of the present invention.

[0059] The following specific embodiments are used to describe the technical solution of the present invention in detail. The following specific embodiments can be combined with each other, and the same or similar concepts or processes may not be described in detail in some embodiments.

[0060] Figure 1 FIG. 1 is a flow chart of a three-dimensional meteorological element analysis method combining remote sensing and ground observation according to an embodiment of the present invention. Figure 1As shown, the method includes:

[0061] Acquire remote sensing and ground observation data of a designated area, perform spatiotemporal registration and data standardization, and obtain meteorological element data with a unified spatiotemporal benchmark;

[0062] The meteorological element data is divided into different spatiotemporal grid units, and the data quality assessment is performed on the observation data in each spatiotemporal grid unit to obtain the data quality assessment index of the spatiotemporal grid unit;

[0063] An adaptive fusion algorithm based on dynamic weights calculates the fusion weight coefficients of meteorological element data within the spatiotemporal grid cells according to the data quality assessment indicators of the spatiotemporal grid cells, performs weighted fusion on the meteorological element data within the spatiotemporal grid cells, and generates an initial three-dimensional meteorological field with physical consistency.

[0064] Based on the initial three-dimensional meteorological field, the spectral analysis method is used to decompose and reconstruct the meteorological element field to obtain the optimal three-dimensional meteorological field.

[0065] Based on the optimal three-dimensional meteorological field, an adaptive tree-structured composite analysis grid is constructed. The evolution characteristics of the weather system are analyzed through a multi-layer progressive method, the topological evolution parameters are determined, and the three-dimensional analysis results of the meteorological elements are output.

[0066] In a specific embodiment, during the data acquisition and spatiotemporal registration stage, various remote sensing observation data within the study area are obtained, including meteorological elements such as temperature, humidity, and wind field observed by satellites, and conventional observation data from ground meteorological stations are obtained at the same time. In the spatiotemporal registration process, a time series interpolation method is used to unify the data into the same time series in view of the differences in time resolution of different data sources. For spatial registration, a bilinear interpolation algorithm based on a geographic coordinate system is used to map data of different spatial resolutions into a unified grid system. Data standardization processing includes unit unification and numerical normalization, and an improved min-max normalization method is used for numerical conversion, while a moving window method is combined for outlier identification and processing.

[0067] In the spatiotemporal gridding and quality assessment phase, a three-dimensional grid system was established based on the spatial extent of the study area and data characteristics. Gridding took into account longitude, latitude, and altitude, ensuring that the grid size was appropriate for the spatial scale of the weather system. Data quality was assessed using a multi-metric comprehensive approach, including the calculation of a data integrity index to assess the spatial representativeness of the data based on the spatiotemporal coverage of the observations; a data consistency index to assess the degree of consistency between data from different sources using an improved correlation analysis method; and a data reliability index to estimate the credibility of the data based on the error characteristics of the observation equipment and the observing environment. Finally, these indicators were combined into a unified quality assessment metric using an adaptive weighting method.

[0068] During the adaptive data fusion phase, a dynamic weighting function is constructed based on the aforementioned quality assessment metrics. Weight calculation utilizes an adaptive weight adjustment algorithm based on data quality, which automatically adjusts fusion weights based on dynamic changes in data quality. A weighted average method is applied to the observational data within each spatiotemporal grid cell, while physical constraints are introduced to ensure that the fusion results adhere to the fundamental laws of atmospheric dynamics. For areas where observational data are missing, an interpolation algorithm is used to perform spatial interpolation to generate a complete initial three-dimensional meteorological field.

[0069] During the spectral analysis and reconstruction phase, the initial three-dimensional meteorological field undergoes spectral decomposition. Using the Fast Fourier Transform algorithm, the meteorological field is decomposed into different frequency domains to analyze the characteristics of weather systems at different scales. An optimized bandpass filter is designed in the frequency domain to effectively remove noise signals while preserving the key characteristics of the weather system. The time domain signal is reconstructed through an inverse transform. During the reconstruction process, iterative optimization methods are used to adjust the reconstruction parameters to ensure that the reconstructed three-dimensional meteorological field retains the physical characteristics of the weather system to the greatest extent possible.

[0070] In the final adaptive meshing and topology analysis phase, based on the reconstructed optimal three-dimensional meteorological field, a tree-like meshing algorithm is employed to adaptively adjust the mesh density according to the gradient characteristics of the meteorological element field, refining the mesh in areas of active weather systems. Topological feature analysis employs a multi-layered, progressive analysis approach, extracting characteristic parameters of the weather system, such as location, intensity, and movement, layer by layer, from large to small scales. The system's development trend is determined by calculating the temporal evolution of these characteristic parameters, ultimately generating a complete three-dimensional analysis result that provides a quantitative description of the evolving characteristics of the weather system.

[0071] In this embodiment, a method combining dynamic weight adaptive fusion and physical constraints is used to solve the weight distribution problem of remote sensing and ground observation data in the fusion process, ensure the physical consistency of the fusion results, and effectively improve the analysis accuracy of the three-dimensional meteorological field; achieve effective separation and retention of weather system characteristics at different scales, overcome the limitations of traditional methods in dealing with multi-scale weather systems, and improve the spatial resolution of meteorological element fields; enable the grid density to be automatically adjusted according to the activity level of the weather system, while ensuring computational efficiency, improving the analysis accuracy of key areas and achieving the optimal configuration of computing resources; can accurately capture the evolution characteristics of the weather system, provide a quantitative description basis for the development trend of the weather system, and improve the level of understanding of the evolution laws of the weather system.

[0072] In an optional embodiment, the meteorological element data is divided into different spatiotemporal grid units, and data quality assessment is performed on the observation data in each spatiotemporal grid unit. The data quality assessment indicators of the spatiotemporal grid units include:

[0073] Divide meteorological element data into multiple spatiotemporal grid units according to preset time intervals and spatial resolutions;

[0074] The difference between the observed values ​​of any two observation points in the spatiotemporal grid unit is calculated to obtain the numerical consistency deviation; the change amplitude of the observed values ​​of each observation point in the spatiotemporal grid unit between two adjacent moments is calculated to obtain the time series volatility deviation; the difference between the spatial distribution density of the observation points in the spatiotemporal grid unit and the preset density threshold is calculated to obtain the spatial density distribution deviation;

[0075] The numerical consistency deviation, the time series volatility deviation and the spatial density distribution deviation are linearly combined after normalization to obtain a data quality assessment index for each spatiotemporal grid unit.

[0076] In one specific implementation, data is partitioned according to both temporal and spatial dimensions. An appropriate time interval, such as one hour, is selected and the observation data is grouped according to this time interval. A spatial grid size, such as 10 km x 10 km, is also set, dividing the study area into regular grid cells. This creates a grid cell system that spans both temporal and spatial dimensions, with each grid cell containing all observation data within a specific time period and spatial range.

[0077] For each spatiotemporal grid unit, three types of deviation indicators are calculated. The first type is numerical consistency deviation: within the same grid unit, take any two observation points, calculate the degree of difference between their observation values, repeat this process for all possible pairs of observation points in the grid, and finally take the average of all difference values ​​to obtain the numerical consistency deviation of the grid unit. The second type is time series volatility deviation: for each observation point in the grid unit, calculate the change in its observation value at two adjacent moments, evaluate whether this change exceeds a reasonable range, and perform statistics on the time change characteristics of all observation points in the grid to obtain a volatility deviation that reflects the temporal continuity of the data. The third type is spatial density distribution deviation: set an ideal observation point density threshold, calculate the distribution density of observation points in the actual grid unit, compare the two, and evaluate the spatial representativeness of the observation data.

[0078] Finally, a comprehensive evaluation index is calculated. First, the three types of deviations are normalized to a uniform range of 0-1. Then, weight coefficients are set based on the impact of each type of deviation on data quality. The three normalized deviations are weighted and combined to produce the final data quality evaluation index. A smaller value indicates better data quality within that grid cell.

[0079] For example, consider a 10 km x 10 km area in a city's meteorological observation network, with the time period being 10:00 AM to 11:00 AM on March 10, 2024. Within this spatiotemporal grid cell are five automatic weather stations and two sounding stations, observing temperature data.

[0080] Calculate the numerical consistency deviation: For example, at 10:30 a.m., the temperatures measured by five automatic stations were 25.3°C, 25.5°C, 25.2°C, 25.4°C, and 25.6°C, respectively, while the temperatures measured by two sounding stations were 25.4°C and 25.3°C. Calculate the temperature difference between any two stations and average all the differences, assuming an average deviation of 0.2°C.

[0081] Calculating time series volatility deviation: For example, at one of the automatic stations, the temperature sequence every 10 minutes between 10:00 AM and 11:00 AM was: 25.1°C, 25.2°C, 25.3°C, 25.5°C, 25.4°C, and 25.3°C. The temperature change between adjacent moments was calculated to assess whether it conformed to normal temperature variations, yielding an indicator reflecting the temporal continuity of the data.

[0082] Calculation of spatial density distribution deviation: The ideal number of observation stations in the 10 km × 10 km area should be 10 (preset density threshold), but there are only 7 observation stations in reality. The difference between the actual observation point density and the ideal density is calculated to obtain the deviation value of spatial representativeness.

[0083] After normalizing these three deviation values, assuming they are 0.2, 0.15, and 0.3 respectively, and setting the weights to 0.4, 0.3, and 0.3 respectively, the final calculated data quality assessment index for this spatiotemporal grid unit is 0.217, indicating that the data quality in this grid unit is good.

[0084] In this embodiment, a refined assessment of the quality of the observation data is achieved through the division of spatiotemporal grid units and the design of multi-dimensional evaluation indicators. By combining the numerical comparison between adjacent observation points and the analysis of time series volatility, outliers and mutation points in the observation data can be effectively identified. This method not only takes into account the consistency of data in space, but also pays attention to the continuity of data in the time dimension, thereby improving the accuracy of identifying abnormal data; the introduction of spatial density distribution deviation assessment solves the problem of the impact of uneven spatial distribution of observation data on data quality assessment. By comparing with the preset density threshold, the spatial representativeness of the observation data can be accurately assessed, providing a reliable quality reference for subsequent data processing; the comprehensive evaluation method based on normalization processing and linear combination realizes the effective fusion of evaluation indicators of different dimensions. This method not only maintains the independence of the indicators of each dimension, but also reflects the degree of influence of different indicators on data quality through weight configuration, making the final evaluation results more scientific and practical.

[0085] In an optional embodiment, an adaptive fusion algorithm based on dynamic weights calculates fusion weight coefficients of meteorological element data within a spatiotemporal grid unit according to data quality assessment indicators of the spatiotemporal grid unit, performs weighted fusion on the meteorological element data within the spatiotemporal grid unit, and generates an initial three-dimensional meteorological field with physical consistency, including:

[0086] Calculating a weighted influence factor of the spatiotemporal grid unit based on the data quality assessment index of the spatiotemporal grid unit, wherein the weighted influence factor is calculated in the form of a Gaussian function with the data quality assessment index as an independent variable;

[0087] Normalizing the weight influence factors of the spatiotemporal grid cells to obtain fusion weight coefficients of the meteorological element data within the spatiotemporal grid cells; performing weighted calculations on the meteorological element data within the spatiotemporal grid cells according to the fusion weight coefficients to obtain observation value fitting terms; constructing a mass conservation constraint term based on the air density continuity equation, and simultaneously constructing a momentum conservation constraint term based on the atmospheric dynamics equation;

[0088] Combining the observation value fitting term, the mass conservation constraint term, and the momentum conservation constraint term to form a fusion objective function;

[0089] The optimization algorithm based on adaptive step size and orthogonalized quasi-Newton iteration is used to solve the fusion objective function and obtain the fusion meteorological field.

[0090] The mass conservation residual and the momentum conservation residual of the fused meteorological field are calculated, and when the mass conservation residual is less than a first preset threshold and the momentum conservation residual is less than a second preset threshold, the fused meteorological field is determined to be an initial three-dimensional meteorological field with physical consistency.

[0091] In one specific embodiment, a weighted influence factor is calculated based on the data quality assessment index of the spatiotemporal grid cell. The specific process is as follows: for each grid cell, its data quality assessment index is substituted into a Gaussian function to calculate the weighted influence factor. Grid cells with better data quality receive a larger weighted influence factor. The weighted influence factors of all grid cells are then normalized so that their sum equals 1, resulting in the fusion weight coefficient for the meteorological element data within each grid cell.

[0092] The fusion objective function is constructed, which includes three parts: the first part is the observation value fitting term, which is obtained by weighted calculation of the meteorological element data within the grid unit; the second part is the mass conservation constraint term, which is constructed based on the air density continuity equation to ensure that the fusion result satisfies the law of conservation of mass; the third part is the momentum conservation constraint term, which is constructed based on the atmospheric dynamics equation to ensure that the fusion result conforms to the law of conservation of momentum.

[0093] An optimization algorithm is used to solve the fusion objective function. Adaptive step size and orthogonalized quasi-Newton iteration method are used to gradually optimize the solution through multiple iterations until a fused meteorological field that meets the convergence conditions is obtained.

[0094] Perform a physical consistency check. Calculate the mass conservation residual and momentum conservation residual of the fused meteorological field and compare them to preset thresholds. Only when both residuals are less than their respective thresholds can the fused meteorological field be considered physically consistent and suitable for use as the initial 3D meteorological field.

[0095] For example, it is assumed that meteorological data fusion is performed in a certain area at 10:00 on March 10, 2024, with a spatial range of 100 km × 100 km and a vertical direction from the ground to an altitude of 10 km.

[0096] The data quality assessment index for a particular grid cell is 0.2 (smaller values ​​indicate better quality). Substituting this into the Gaussian function yields a weighted influence factor of 0.85. Normalizing the weighted influence factors for all grid cells yields a final fusion weight coefficient of 0.15 for this grid cell.

[0097] The observation value fitting item includes the temperature, air pressure, wind speed and other element data within the grid unit, multiplied by the corresponding weight coefficient 0.15; the mass conservation constraint item considers that the change of air density over time must satisfy the continuity equation; the momentum conservation constraint item considers that the air flow movement must comply with the law of conservation of momentum.

[0098] For the optimization solution, the initial step size is set to 0.1. Through iterative calculations, the step size and search direction are updated with each iteration. For example, if the objective function value decreases by 20% after the first iteration, the step size is increased to 0.12. If the objective function value increases after a certain iteration, the step size is reduced to 0.08. Finally, after 50 iterations, the fused meteorological field is obtained.

[0099] The calculated mass conservation residual is 0.001 (less than the preset first threshold of 0.005), and the momentum conservation residual is 0.002 (less than the preset second threshold of 0.008). Therefore, it is confirmed that the fused meteorological field has good physical consistency and can be used as the initial three-dimensional meteorological field.

[0100] In this embodiment, by introducing a Gaussian weight distribution mechanism based on data quality, differentiated fusion of observation data is achieved, which not only fully utilizes the advantages of high-quality data, but also effectively reduces the negative impact of low-quality data on the fusion results, thereby improving the reliability of the fusion results; a fusion objective function design method combining multiple physical constraints is adopted, and while ensuring the accuracy of data fitting, mass conservation and momentum conservation constraints are introduced, which not only ensures the consistency of the fusion results with the observation data, but also ensures the physical rationality of the fusion field, avoiding the non-physical solution that may be caused by simple mathematical interpolation; through the physical consistency verification mechanism of residual threshold control, the quality control of the fusion results is achieved, ensuring that the final three-dimensional meteorological field meets the observation constraints and conforms to the basic laws of atmospheric physics, providing a high-quality initial field for subsequent numerical meteorological forecasts.

[0101] In an optional embodiment, an optimization algorithm based on adaptive step size and orthogonalized quasi-Newton iteration is used to solve the fusion objective function, and the fused meteorological field is obtained, including:

[0102] Taking the meteorological element data in the spatiotemporal grid unit as the initial solution, and calculating the gradient value of the fusion objective function corresponding to the initial solution based on the fusion objective function;

[0103] An iterative format is constructed based on the initial solution and the gradient value of the fusion objective function using an adaptive step size factor and an approximate inverse matrix of a quasi-Newton matrix. When the rate of change of the fusion objective function value between two adjacent iterations is greater than zero, the adaptive step size factor is reduced by a preset proportional coefficient; otherwise, the adaptive step size factor is increased by the preset proportional coefficient. The value of the adaptive step size factor is limited to a preset upper and lower limit range.

[0104] In each iteration process, the solution vector difference between two adjacent iterations and the corresponding fusion objective function gradient difference vector are calculated; the solution vector difference and the fusion objective function gradient difference vector are orthogonalized to obtain an orthogonalized difference vector;

[0105] According to a preset iterative evaluation round, based on the corresponding orthogonalized difference vector, an approximate inverse matrix of the quasi-Newton matrix is ​​updated using a bidirectional recursive method; and a new solution vector is calculated using the approximate inverse matrix of the updated quasi-Newton matrix;

[0106] Calculate the fusion objective function value corresponding to the new solution vector and calculate the distance between the solution vectors of two adjacent iterations;

[0107] When the relative change of the fusion objective function value is less than the preset change threshold and the distance value between the solution vectors is less than the preset distance threshold, the new solution vector is determined as the fused meteorological field; otherwise, the new solution vector is used as the initial solution for the next iteration and the iteration continues.

[0108] In one specific implementation, the existing meteorological data within the spatiotemporal grid cells is used as the starting point for the solution, i.e., the initial solution. This initial solution is then substituted into the constructed fusion objective function to calculate the gradient value at the initial solution location. This gradient value indicates the direction of optimization improvement.

[0109] In order to efficiently search for the optimal solution, it is necessary to determine an appropriate search step size, and an adaptive step size factor is used to dynamically adjust the search step size. At the same time, to speed up convergence, the approximate inverse matrix of the quasi-Newton matrix is ​​introduced to approximate the second-order derivative information of the objective function. Specifically, an initial step size factor is set, and at each iteration, the step size factor is adjusted by comparing the fused objective function values ​​obtained from the previous and next iterations. If the objective function value obtained in the latter iteration is larger than that in the previous one, it means that the step size may be too large. In this case, the step size factor is reduced according to a pre-set proportional coefficient. Conversely, if the objective function value in the latter iteration is smaller, it means that the current search direction is valid, and the step size factor is appropriately increased to speed up convergence. To avoid excessive step size adjustment, upper and lower limits are set to constrain the value range of the step size factor.

[0110] During each iterative calculation, the approximate inverse of the quasi-Newton matrix needs to be updated to more accurately approximate the second-order derivative of the objective function. This update process specifically involves calculating the difference between the solution vectors obtained from two consecutive iterations, which reflects the direction of change in the solution. Simultaneously, the difference vector of the corresponding fused objective function gradient is calculated, which reflects the gradient change. To improve the numerical stability of the calculation, these two difference vectors need to be orthogonalized to make them mutually orthogonal, resulting in the orthogonalized difference vector.

[0111] The orthogonalized difference vector is used to update the approximate inverse of the quasi-Newton matrix based on a pre-defined number of iterative evaluation rounds. This update is performed using a bidirectional recursive approach, which considers both forward and backward information to construct a more accurate approximate inverse matrix. After the update is complete, the new approximate inverse matrix and the current gradient information are used to calculate the next solution vector.

[0112] Each time a new solution vector is obtained, it is necessary to calculate the fusion objective function value corresponding to the solution vector and the distance value between this new solution vector and the solution vector of the previous iteration. These two calculation results are used to determine whether the iteration can be terminated: when the relative change in the fusion objective function value (that is, the ratio of the difference between the objective function values ​​of two adjacent iterations to the current value) is less than the preset change threshold, and the distance value between the solution vectors obtained from two adjacent iterations is also less than the preset distance threshold, it means that the iteration has converged to a satisfactory result. At this time, the final solution vector can be determined as the final fusion meteorological field. If the convergence condition is not met, the newly obtained solution vector is used as the initial solution for the next round of iteration, and the iterative calculation process continues.

[0113] For example, meteorological data fusion is performed within a certain atmospheric observation area. The initial data includes the temperature field, pressure field, and wind field data at 10:00 on March 10, 2024. This data is selected as the initial solution, and the calculated initial fusion objective function value is 100, corresponding to a gradient value of 0.5.

[0114] The initial step size factor is set to 0.1, the upper limit is 0.5, the lower limit is 0.01, and the adjustment scale factor is 1.2. In the first iteration, the new solution vector reduces the objective function value to 80, indicating that the search direction is valid, so the step size factor is increased to 0.12. After the second iteration, the objective function value increases to 85, indicating that the step size is too large, so the step size factor is reduced to 0.1.

[0115] During the iteration process, the changes in the solution vector and the gradient vector are continuously calculated. For example, during the third iteration, the change in the temperature field solution vector is 0.5°C, and the corresponding gradient change is 0.2. These changes are orthogonalized to obtain the orthogonalized difference vector, which is used to update the approximate inverse matrix of the quasi-Newton matrix.

[0116] The number of iterative evaluation rounds was set to 10. In the fourth iteration, the orthogonalized difference vector was used to update the approximate inverse matrix through bidirectional recursion. Using the updated approximate inverse matrix, the new solution vector for the temperature field was recalculated to be 15.2°C.

[0117] The relative change threshold for the fusion objective function value was set to 0.001, and the solution vector distance threshold was set to 0.01. After 50 iterations, the ratio of the difference between the objective function values ​​of two consecutive iterations to the current value was 0.0008, which was less than the change threshold of 0.001. Simultaneously, the distance between two consecutive solution vectors was 0.008, which was less than the distance threshold of 0.01. This indicated that the iterations had converged, so the solution vector obtained from the 50th iteration was determined as the final fused meteorological field.

[0118] In existing technologies, meteorological data fusion typically uses variational assimilation or optimal interpolation methods. Variational assimilation primarily achieves data fusion by constructing a cost function and finding its minimum. However, its optimization process typically employs fixed-step gradient descent or conjugate gradient methods. These methods are prone to slow convergence and falling into local optimal solutions when processing highly nonlinear meteorological data. Optimal interpolation methods primarily rely on statistically relevant information for interpolation calculations. While computationally efficient, they struggle to ensure that the fusion results meet atmospheric dynamics constraints, resulting in poor physical consistency.

[0119] Aiming at the problems existing in the existing technology, improvements have been made in the following aspects:

[0120] In terms of optimization algorithm design, an adaptive step-size mechanism is introduced. This mechanism dynamically adjusts the search step size by monitoring changes in the objective function value in real time. When the optimization results improve, the step size is increased to accelerate convergence; when the results deteriorate, the step size is reduced to ensure stability. Upper and lower bounds on the step size are also set to avoid numerical instability caused by excessive step-size adjustments. This adaptive mechanism achieves a better balance between optimization efficiency and stability than fixed step-size methods.

[0121] Matrix approximation: A bidirectional recursive approach is used to update the approximate inverse of the quasi-Newton matrix, and orthogonalization is introduced to improve numerical stability. Compared to the traditional BFGS (Broyden-Fletcher-Goldfarb-Shanno) algorithm, this approach improves the accuracy of matrix approximation while maintaining computational efficiency, allowing the optimization process to better capture the second-order information of the objective function.

[0122] In terms of convergence judgment: a dual convergence judgment mechanism based on the relative change of the fusion objective function value and the solution vector distance value is designed. This is more reliable than the single objective function value judgment and can more accurately judge whether the iterative process is truly converged.

[0123] exist Figure 2The figure shows a comparison of the convergence performance of this solution with traditional methods. By the 10th iteration, the objective function value of this solution had dropped to 45.2, while the traditional variational assimilation method and optimal interpolation method required 25 and 35 iterations, respectively, to reach similar levels. By the 50th iteration, the objective function value of this solution had dropped to 8.3, 47.1% lower than the traditional variational assimilation method (15.7) and 62.9% lower than the optimal interpolation method (22.4), respectively. In particular, this solution exhibited faster convergence in the first 20 iterations, fully demonstrating the effectiveness of the adaptive step size and bidirectional recursive update strategy.

[0124] exist Figure 3 The performance of the three methods in maintaining physical consistency is demonstrated in the paper. For mass conservation, the proposed method achieved a residual value of 0.015 kg / m³, which is 34.8% lower than the traditional variational assimilation method (0.023 kg / m³) and 46.4% lower than the optimal interpolation method (0.028 kg / m³). For momentum conservation, the proposed method achieved a residual value of 0.008 N·s / m³, also significantly lower than the other two methods.

[0125] In this embodiment, the starting point of the improvement is to solve the three main problems existing in the existing meteorological data fusion method: low convergence efficiency of the optimization process; insufficient stability of numerical calculations; and poor physical consistency of the fusion results. The above improvements have achieved significant results. Compared with the fixed step size method, the convergence speed has increased by about 40%, and the number of iterations has been reduced by about 30%; when processing strong nonlinear meteorological element data, the probability of numerical divergence has been reduced by about 50%; the root mean square error of the fusion result has been reduced by about 25% compared with the traditional method, and the residual values ​​of mass conservation and momentum conservation have been reduced by about 35% and 30% respectively. The improvement effect enables the method of this application to realize meteorological data fusion more efficiently and stably, while ensuring that the fusion results have better physical consistency, providing a more reliable initial field for meteorological numerical forecasting.

[0126] In an optional embodiment, based on the initial three-dimensional meteorological field, a spectral analysis method is used to perform scale decomposition and reconstruction on the meteorological element field to obtain the optimal three-dimensional meteorological field, including:

[0127] Performing Fourier transform on the initial three-dimensional meteorological element field to obtain spectral coefficients, performing wavelet transform on the spectral coefficients and the local window function to obtain decomposition coefficients of the meteorological element field at different scales and spatial positions, constructing a multidimensional tensor based on the decomposition coefficients, performing nuclear norm calculation and tensor decomposition, and constructing a wavenumber-energy spectrum matrix in combination with feature truncation extraction;

[0128] Obtaining a dominant wavenumber mode by singular value decomposition of the wavenumber-energy spectrum matrix, and determining a characteristic wavenumber sequence according to the energy contribution rate of the dominant wavenumber mode;

[0129] constructing an orthogonal filter bank based on the characteristic wavenumber sequence, wherein the orthogonal filter bank includes a plurality of Gaussian filters, wherein the center frequency of each Gaussian filter corresponds to a characteristic wavenumber in the characteristic wavenumber sequence, and the bandwidth parameter of the Gaussian filter is determined according to the interval between adjacent characteristic wavenumbers;

[0130] Applying the orthogonal filter bank to the spectral coefficients to obtain a plurality of scale components, and constructing a spectral reconstruction tensor based on local energy distributions of the plurality of scale components;

[0131] Local reconstruction weights are calculated according to the spectral reconstruction tensor, and weighted superposition is performed on the multiple scale components to obtain an optimal meteorological element field.

[0132] In one specific embodiment, the initial three-dimensional meteorological element field is subjected to frequency domain transformation. The meteorological element field data is converted to the frequency domain via Fourier transform to obtain corresponding spectral coefficients. Then, a suitable local window function is selected and these spectral coefficients are subjected to wavelet transform processing to obtain decomposition coefficients of the meteorological element field at different spatial scales and locations. These decomposition coefficients reflect the energy distribution characteristics of the meteorological field at different scales.

[0133] Next, these decomposition coefficients are organized into a multidimensional tensor at different scale levels. The nuclear norm of this multidimensional tensor is calculated to obtain a matrix describing the correlations between different scales. This correlation matrix is ​​then subjected to tensor decomposition to extract its core features. Within the resulting singular value sequence, 80% of the maximum singular value is selected as the feature truncation threshold. The eigenvectors corresponding to singular values ​​greater than this threshold are extracted, and these eigenvectors are used to reconstruct the wavenumber-energy spectrum matrix.

[0134] The obtained wavenumber-energy spectrum matrix is ​​subjected to singular value decomposition, and the dominant wavenumber modes are extracted from the decomposition results. The energy contribution rates of these dominant wavenumber modes are calculated, and the wavenumbers whose cumulative contribution rates reach a preset threshold are selected as characteristic wavenumber sequences, in descending order of energy contribution. These characteristic wavenumber sequences reflect the most important spatial scale characteristics of the meteorological field.

[0135] Based on the selected characteristic wavenumber sequence, a set of orthogonal Gaussian filters is constructed. Each Gaussian filter uses a wavenumber in the characteristic wavenumber sequence as its center frequency, and the filter bandwidth is determined by the interval between adjacent characteristic wavenumbers. This filter bank can effectively separate meteorological features of different scales.

[0136] The constructed orthogonal filter bank is applied to the previously obtained spectral coefficients to generate multiple components at different scales. The local energy distribution characteristics of these scale components are calculated, and a spectral reconstruction tensor is constructed based on this. Finally, the weight coefficients for each scale component in the reconstruction process are calculated based on the spectral reconstruction tensor. By weighted superposition of these scale components, the final optimal meteorological element field is obtained.

[0137] For example, assume that the temperature field data within a certain area of ​​1000 km×1000 km×10 km at 10:00 on March 10, 2024 is processed.

[0138] First, the temperature field data was Fourier transformed to obtain the spectral coefficients. A Gaussian window function was selected as the local window function, with a window size of 100 km. The spectral coefficients were then subjected to a wavelet transform to obtain decomposition coefficients at different scales (e.g., 2 km, 10 km, 50 km, etc.) and locations.

[0139] These decomposition coefficients are organized into a three-dimensional tensor (scale dimension × longitude dimension × latitude dimension), and the nuclear norm is calculated to obtain the scale correlation matrix. The correlation matrix is ​​subjected to tensor decomposition. Assuming the maximum singular value is 10, a threshold of 8 (80% of the maximum singular value) is used for feature truncation. The corresponding eigenvectors are extracted and reconstructed to obtain the wavenumber-energy spectrum matrix.

[0140] Perform singular value decomposition on the wavenumber-energy spectrum matrix. Suppose it is found that the modal energy contribution rates of wavenumbers 2, 5, and 10 (unit: per 100 km) are 50%, 30%, and 15%, respectively. Their cumulative contribution rates reach 95%, exceeding the preset 90% threshold. Therefore, these three wavenumbers are selected as the characteristic wavenumber sequence.

[0141] Based on these three characteristic wavenumbers, three Gaussian filters are constructed with center frequencies of 2, 5, and 10, respectively. The bandwidth parameters are determined according to the interval between adjacent wavenumbers. For example, the bandwidth of the first filter is 3 (the difference with the adjacent wavenumber 5), the second is 5, and the third is 5.

[0142] Applying this set of filters to the original spectral coefficients yields three scale components. The local energy distribution of each scale component is calculated to construct a spectral reconstruction tensor. Based on the reconstruction tensor, the weights of the three scale components are calculated as 0.5, 0.3, and 0.2, respectively. Finally, the three scale components are weighted and superimposed according to these weights to obtain the final temperature field.

[0143] The processing method in this embodiment can not only separate meteorological features of different spatial scales, but also retain the spatial location information of these features. Compared with the traditional single-scale analysis method, it improves the ability to identify local features, can better retain the characteristics of small-scale weather systems, and reduces information loss in the feature extraction process; compared with the direct spectral analysis method, it can more accurately capture the dominant wavenumber mode in the meteorological field and improve the accuracy of feature extraction; considering the correlation between different scales, it effectively reduces the recognition rate of false features; the adaptive filter design method improves the accuracy of scale separation and reduces the crosstalk between scale components compared to the fixed parameter filtering scheme; the weighted reconstruction scheme guided by the spectral reconstruction tensor ensures the physical rationality of the final reconstruction result. Compared with the traditional equal-weight superposition method, it reduces the root mean square error of the reconstruction result and improves the spatial correlation coefficient.

[0144] In an optional embodiment, constructing a multidimensional tensor based on the decomposition coefficients and performing nuclear norm calculation and tensor decomposition, and constructing a wavenumber-energy spectrum matrix in combination with feature truncation extraction includes:

[0145] Constructing a multidimensional tensor from the decomposition coefficients according to different scale levels, and calculating the nuclear norm of the multidimensional tensor to obtain a scale correlation matrix;

[0146] Performing tensor decomposition on the scale correlation matrix to obtain a scale core tensor and a projection matrix group, wherein the projection matrix group includes a spatial position projection matrix, a wavenumber projection matrix, and an energy projection matrix;

[0147] Calculating a singular value sequence of the scale core tensor, taking eighty percent of the maximum value of the singular value sequence as a feature truncation threshold, and extracting projection matrix components corresponding to singular values ​​in the singular value sequence that are greater than the feature truncation threshold;

[0148] The projection matrix components are reconstructed to obtain the wavenumber-energy spectrum matrix.

[0149] In a specific embodiment, the first important step is to systematically organize the decomposition coefficients obtained in the previous step. It is necessary to establish a complete three-dimensional index system, including the latitude and longitude index of the spatial position, the wave number index, and the energy level index. At each determined grid point position, all the decomposition coefficients under different wave numbers corresponding to the point are first collected. Then, for the coefficient value under each wave number, the corresponding energy value is calculated, and it is divided into different energy levels according to the energy size. Finally, these organized data are filled into the pre-established tensor structure in the order of position, wave number, and energy to form a complete multidimensional tensor.

[0150] To calculate the nuclear norm of a constructed multidimensional tensor, the three-dimensional tensor must first be expanded into a series of matrix slices. A singular value decomposition (SVD) operation is performed on each matrix slice to obtain the corresponding singular values. The singular values ​​of all slices are summed to obtain the overall nuclear norm. The resulting nuclear norm values ​​for different dimensional combinations are then reorganized to form a correlation matrix that describes scale-correlation characteristics.

[0151] A high-order singular value decomposition method is used for tensor decomposition. First, the tensor is expanded along the spatial position dimension, and the covariance matrix in this dimension is calculated. The covariance matrix is ​​then subjected to eigenvalue decomposition to obtain the projection matrix corresponding to the spatial position. Using the same processing method, tensor expansion and decomposition operations are performed on the wavenumber dimension and energy dimension, respectively, to obtain the projection matrices corresponding to these two dimensions. In calculating the spatial position projection matrix, it is necessary to construct a spatial correlation matrix and extract its eigenvectors. The wavenumber projection matrix is ​​obtained by calculating the correlation coefficients between different wavenumbers based on wavenumber spectrum analysis. The energy projection matrix is ​​obtained by analyzing the energy distribution characteristics, constructing an energy conversion relationship matrix, and then solving it.

[0152] When calculating the singular values ​​of a core tensor, it is necessary to first expand the core tensor into a two-dimensional matrix. The eigenvalues ​​and eigenvectors of this expanded matrix are calculated, and the resulting eigenvalues ​​are sorted in descending order to obtain a singular value sequence. The eigenvector corresponding to each singular value is also recorded. To perform feature truncation, the maximum value in the singular value sequence is first found and multiplied by 0.8 to obtain a truncation threshold. The entire singular value sequence is then traversed, marking all singular value locations greater than the threshold. The eigenvectors corresponding to these locations are extracted as the primary feature components.

[0153] To reconstruct the spectral matrix, the corresponding column vectors are first extracted from each projection matrix based on the positions of the retained singular values. These extracted column vectors are then orthogonalized to ensure orthogonality, while also checking and adjusting the directional consistency of each vector. These processed eigenvectors are then reorganized according to their original dimensions, and the inner products between the eigenvectors are calculated to obtain correlation coefficients. Finally, a wavenumber-energy spectrum matrix is ​​constructed based on these correlation coefficients, and the reconstructed matrix is ​​normalized.

[0154] For example, consider processing temperature field data for a 100×100 grid in a specific region. First, the original decomposition coefficients are organized into a four-dimensional tensor based on 100 longitude points, 100 latitude points, 10 wavenumbers, and 5 energy levels. Each grid point contains decomposition coefficients for 10 different wavenumbers, which are then classified into five different energy levels after energy calculation. This four-dimensional tensor is then expanded into 50 100×100 matrices. The singular values ​​of each matrix are calculated, for example, to obtain the sequence [15, 12, 8, 5, 3]. The nuclear norm is summed to construct a 10×5 scale correlation matrix. This tensor decomposition yields a 100×8 spatial position projection matrix, a 10×4 wavenumber projection matrix, a 5×3 energy projection matrix, and an 8×4×3 core tensor. The singular value sequence of the core tensor is [10, 8, 6, 4, 2, 1]. The truncation threshold is 8, and the eigenvector corresponding to the singular value 10 is retained. Finally, a 10×5 wavenumber-energy spectrum matrix is ​​reconstructed.

[0155] Throughout the entire process, special attention must be paid to the stability of numerical calculations to ensure the continuity and conservation of physical quantities. Unifying units when calculating energy values, controlling the condition number during matrix decomposition, and ensuring the orthogonality of eigenvectors during reconstruction are all key factors in ensuring the accuracy of the calculation results.

[0156] This embodiment is based on multiscale analysis methods in meteorology. Traditional meteorological multiscale analysis primarily uses methods such as Fourier transforms and wavelet transforms, which have been widely used to process the multiscale characteristics of atmospheric motion. Furthermore, this technology draws on tensor decomposition and feature extraction techniques from data science, which have demonstrated excellent results in analyzing multidimensional data.

[0157] The existing means of implementation include: the traditional Fourier spectrum analysis method, which obtains the wavenumber spectrum by performing Fourier transform on the meteorological field, but this method cannot obtain spatial local information at the same time; the wavelet transform method, which can obtain time-frequency localization information, but has high computational complexity when processing multidimensional data, and it is difficult to maintain the correlation between the features of each dimension; the empirical mode decomposition method, which can adaptively decompose the signal, but is prone to modal aliasing, affecting the physical meaning of the decomposition results; the traditional filtering method, which uses a fixed-parameter filter for scale separation, is difficult to adapt to the characteristic differences of different weather systems.

[0158] In response to the problems existing in the prior art, this embodiment makes the following improvements: tensor decomposition technology is introduced into meteorological multi-scale analysis, and the multi-scale characteristics of the meteorological field are represented by constructing a multi-dimensional tensor, thereby maintaining the correlation between features of different dimensions; the dominant features are extracted by using nuclear norm calculation and feature truncation, which reduces the computational complexity and improves the accuracy of feature extraction; an adaptive filter group based on characteristic wavenumber is designed, so that the filtering parameters can be automatically adjusted according to the actual data characteristics; a weighted reconstruction scheme based on the spectral reconstruction tensor is proposed, which optimizes the combination of components of different scales.

[0159] The improved technology is mainly based on the following considerations: the meteorological element field has obvious multi-scale characteristics, and more effective methods are needed to separate and identify these characteristics; there are complex interactions between meteorological characteristics at different scales, and the correlation between these characteristics needs to be maintained; different types of weather systems have different characteristic scales, and the method needs to have good adaptability; the amount of meteorological data is large, and it is necessary to improve computing efficiency and reduce storage requirements.

[0160] Figure 4 The distribution characteristics of the tensor decomposition-feature truncation method and the traditional wavelet transform method in the feature space are demonstrated. The horizontal axis represents the wave number (1-10), the vertical axis represents the energy level (1-5), and the depth axis represents the feature intensity (0-100). The feature points (square marks) of this technical solution show a clear hierarchical distribution. The feature points in the high energy area (>80) are highly clustered and evenly distributed in space, indicating that the extracted features have good physical continuity. The feature points (circular marks) of the traditional method based on wavelet transform show greater discreteness, especially in the energy level conversion area where obvious blank bands appear, indicating the discontinuity of feature extraction. Through quantitative analysis, the spatial correlation coefficient of the feature points of this technical solution reaches 0.92, which is significantly higher than 0.76 of the wavelet transform method.

[0161] In this embodiment, compared with traditional methods, the correlation between multi-scale features can be better maintained, and the accuracy and completeness of feature extraction are improved; through feature truncation and tensor operations, the processing efficiency is significantly improved and the storage requirements are reduced; the adaptive filter group can better adapt to the characteristics of different weather systems, and the universality of the method is improved; the weighted reconstruction scheme improves the physical rationality of the final result and improves the reconstruction quality.

[0162] In an optional embodiment, an adaptive tree-like composite analysis grid is constructed based on the optimal three-dimensional meteorological field, and the evolution characteristics of the weather system are analyzed in a multi-layer progressive manner to determine the topological evolution parameters. The three-dimensional analysis results of the meteorological elements are outputted, including:

[0163] Acquire meteorological field data in an optimal three-dimensional meteorological field, determine a reference resolution and a hierarchical coefficient based on spatial distribution characteristics and gradient distribution of the meteorological field data, calculate a first resolution, and determine a backbone grid; calculate a second resolution based on local variation characteristics of the meteorological field data, determine a branch grid, and combine the backbone grid and the branch grid to generate an adaptive tree-like composite analysis grid;

[0164] Calculating the local gradient field on the adaptive tree-like composite analysis grid, determining the growth direction of the grid branches, constructing a multi-layer progressive interpolation function, and establishing a numerical association between the trunk grid and the branch grids;

[0165] constructing a characteristic metric tensor based on the local gradient field and the numerical association, calculating an evolution parameter of the characteristic metric tensor, and constructing a characteristic transfer function between grid nodes according to the evolution parameter;

[0166] Utilizing the characteristic transfer function to calculate the grid topological characteristics, obtain the topological stability index, structural evolution rate and system deformation parameter, and construct a topological evolution characteristic operator;

[0167] A recursive operator is constructed according to historical features, current features and change features, and the topological evolution feature operator is subjected to multi-layer progressive fusion using the recursive operator to output a three-dimensional analysis result of the meteorological elements.

[0168] In a specific embodiment, after obtaining the data of the optimal three-dimensional meteorological field, it is necessary to analyze the spatial distribution characteristics of the data. Check the changes in meteorological elements in three-dimensional space, focusing on the sudden change areas and gentle areas of the values. At the same time, calculate the gradient distribution of the entire field, and identify areas with drastic gradient changes and areas with relatively gentle gradients. Based on these characteristics, determine the baseline resolution, and this resolution serves as the reference standard for the entire grid system. Then set the hierarchical coefficient to control the density of grids at different levels. Calculate the first resolution based on the baseline resolution and the hierarchical coefficient, and use this resolution to establish a backbone grid. The backbone grid covers the entire analysis area and constitutes the basic framework of the grid system.

[0169] Analyze the local variation characteristics of meteorological data, focusing on the magnitude and frequency of local value changes. In areas of significant variation, calculate the required second resolution, which is typically finer than the first resolution. Based on the second resolution, establish a branch grid, primarily located in areas of drastic meteorological fluctuations. Combine the main and branch grids in a tree-like structure to form an adaptive tree-like composite analysis grid.

[0170] On the established composite analysis grid, the local gradient field is calculated for each grid cell. The direction and magnitude of the gradient field determine the growth direction of the grid branches, which in turn determines the extension pattern of the branch grids. A multi-layered, progressive interpolation function system is constructed to establish numerical connections between the main grid and the branch grids, ensuring a smooth transition between data at different resolutions.

[0171] Based on the calculated local gradient field and the numerical correlation between the meshes, a feature metric tensor is constructed. This tensor contains information about the relationships between mesh nodes and local features. Evolution parameters of this feature metric tensor are calculated, reflecting the temporal changes in the mesh structure. Based on these evolution parameters, a feature transfer function is constructed between mesh nodes, describing how features are transferred between them.

[0172] Using the characteristic transfer function to analyze the topological characteristics of the mesh, three key metrics were calculated: the topological stability index, the structural evolution rate, and the system deformation parameter. The topological stability index reflects the stability of the mesh structure, the structural evolution rate describes the rate of change in the mesh morphology, and the system deformation parameter characterizes the overall structural deformation. Based on these three metrics, a topological evolution characteristic operator was constructed.

[0173] Historical feature data is collected and combined with current and changing features to construct a recursive operator. This recursive operator captures the evolution of features. This recursive operator is used to perform a multi-layer progressive fusion of topological evolution feature operators, ultimately generating a complete 3D analysis result.

[0174] For example, let's analyze the temperature field of a certain area at 10:00 on March 10, 2024. The area is 1000 km × 1000 km × 10 km, and the initial data resolution is 10 km.

[0175] Analysis of the spatial distribution of the temperature field revealed a significant temperature gradient between 0 and 2 km near the ground, while the temperature gradient was more gradual between 2 and 10 km. A baseline resolution of 5 km was established, with a layer coefficient of 2. A primary resolution of 10 km was calculated, and a backbone grid covering the entire area was established.

[0176] Analysis revealed areas of extreme temperature variation near the ground, requiring a secondary resolution of 2.5 km. Branch grids were established in these areas, primarily distributed between the 0-2 km altitude layer. The two grids were combined into a tree structure to form a composite analysis grid.

[0177] By calculating the gradient field on the composite grid, it was found that the temperature gradient is primarily distributed in the vertical direction. Based on this, it was determined that the growth direction of the branch grids should primarily extend in the vertical direction. A cubic spline interpolation function was established to transfer data between the main grid and the branch grids.

[0178] A characteristic metric tensor was constructed, containing information about temperature differences and spatial distances between grid nodes. The tensor's evolution parameters were calculated, revealing that the temporal variations in the temperature field are primarily concentrated near the surface layer. Based on this information, a characteristic transfer function was constructed to describe the transfer of temperature characteristics between grid cells.

[0179] The calculated topological stability index shows that the near-ground grid structure needs more frequent updates. The structural evolution rate indicates that changes in the temperature field mainly occur during the warming process after sunrise. The system deformation parameters reflect the vertical structural characteristics of the temperature field.

[0180] Finally, a recursive operator is constructed by combining the temperature field evolution characteristics of the previous hour, the current temperature distribution characteristics, and the temperature change trend. The recursive operator is used to fuse the topological features and ultimately obtain a complete three-dimensional temperature field analysis result.

[0181] In this embodiment, through the design of an adaptive tree-like composite analysis grid, a finer resolution is adopted in areas where meteorological elements change drastically, while a relatively sparse grid distribution is maintained in areas where changes are gentle. This ensures the analysis accuracy of key areas while avoiding the waste of computing resources. A numerical association is established between the trunk grid and the branch grids, achieving a smooth transition between grids of different resolutions. The introduction of a feature metric tensor ensures the physical rationality of feature transfer between grid nodes, effectively avoiding the numerical false oscillations that occur in traditional methods. The grid system is organized in a tree structure, and the number of computing nodes is significantly reduced by dynamically adjusting the grid distribution. At the same time, the design of the feature transfer function optimizes the numerical calculation process and reduces the computational complexity of the algorithm. The method of determining the growth direction of the grid branches based on the local gradient field enables the grid structure to adaptively follow the changing characteristics of meteorological elements. The introduction of the topological evolution feature operator enhances the adaptability of the method to different weather systems. By constructing a recursive operator, historical features, current features, and change features are organically combined, ensuring the continuity of the analysis results in time and space, and improving the spatiotemporal consistency of the analysis results.

[0182] The present invention may be a method, an apparatus, a system and / or a computer program product. The computer program product may include a computer-readable storage medium carrying computer-readable program instructions for executing various aspects of the present invention.

[0183] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the above embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the above embodiments, or replace some or all of the technical features therein with equivalents. However, these modifications or replacements do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A three-dimensional analysis method of meteorological elements combining remote sensing and ground observations, characterized by: include: Acquire remote sensing and ground observation data of a designated area, perform spatiotemporal registration and data standardization, and obtain meteorological element data with a unified spatiotemporal benchmark; The meteorological element data is divided into different spatiotemporal grid units, and the data quality assessment is performed on the observation data in each spatiotemporal grid unit to obtain the data quality assessment index of the spatiotemporal grid unit; An adaptive fusion algorithm based on dynamic weights calculates the fusion weight coefficients of meteorological element data within the spatiotemporal grid cells according to the data quality assessment indicators of the spatiotemporal grid cells, performs weighted fusion on the meteorological element data within the spatiotemporal grid cells, and generates an initial three-dimensional meteorological field with physical consistency. Based on the initial three-dimensional meteorological field, the spectral analysis method is used to decompose and reconstruct the meteorological element field to obtain the optimal three-dimensional meteorological field. Based on the optimal three-dimensional meteorological field, an adaptive tree-structured composite analysis grid is constructed. The evolution characteristics of the weather system are analyzed through a multi-layer progressive approach, the topological evolution parameters are determined, and the three-dimensional analysis results of meteorological elements are output, including: Acquire meteorological field data in an optimal three-dimensional meteorological field, determine a reference resolution and a hierarchical coefficient based on spatial distribution characteristics and gradient distribution of the meteorological field data, calculate a first resolution, and determine a backbone grid; calculate a second resolution based on local variation characteristics of the meteorological field data, determine a branch grid, and combine the backbone grid and the branch grid to generate an adaptive tree-like composite analysis grid; Calculating the local gradient field on the adaptive tree-like composite analysis grid, determining the growth direction of the grid branches, constructing a multi-layer progressive interpolation function, and establishing a numerical association between the trunk grid and the branch grids; constructing a characteristic metric tensor based on the local gradient field and the numerical association, calculating an evolution parameter of the characteristic metric tensor, and constructing a characteristic transfer function between grid nodes according to the evolution parameter; Utilizing the characteristic transfer function to calculate the grid topological characteristics, obtain the topological stability index, structural evolution rate and system deformation parameter, and construct a topological evolution characteristic operator; A recursive operator is constructed according to historical features, current features and change features, and the topological evolution feature operator is subjected to multi-layer progressive fusion using the recursive operator to output a three-dimensional analysis result of the meteorological elements.

2. The method according to claim 1, characterized in that The meteorological element data is divided into different spatiotemporal grid units, and the data quality assessment is performed on the observation data in each spatiotemporal grid unit. The data quality assessment indicators of the spatiotemporal grid units include: Divide meteorological element data into multiple spatiotemporal grid units according to preset time intervals and spatial resolutions; The difference between the observed values ​​of any two observation points in the spatiotemporal grid unit is calculated to obtain the numerical consistency deviation; the change amplitude of the observed values ​​of each observation point in the spatiotemporal grid unit between two adjacent moments is calculated to obtain the time series volatility deviation; the difference between the spatial distribution density of the observation points in the spatiotemporal grid unit and the preset density threshold is calculated to obtain the spatial density distribution deviation; The numerical consistency deviation, the time series volatility deviation and the spatial density distribution deviation are linearly combined after normalization to obtain a data quality assessment index for each spatiotemporal grid unit.

3. The method according to claim 1, characterized in that The adaptive fusion algorithm based on dynamic weights calculates the fusion weight coefficients of meteorological element data within the spatiotemporal grid cells according to the data quality evaluation indicators of the spatiotemporal grid cells, performs weighted fusion on the meteorological element data within the spatiotemporal grid cells, and generates an initial three-dimensional meteorological field with physical consistency, including: Calculating a weighted influence factor of the spatiotemporal grid unit based on the data quality assessment index of the spatiotemporal grid unit, wherein the weighted influence factor is calculated in the form of a Gaussian function with the data quality assessment index as an independent variable; Normalizing the weight influence factors of the spatiotemporal grid cells to obtain fusion weight coefficients of the meteorological element data within the spatiotemporal grid cells; performing weighted calculations on the meteorological element data within the spatiotemporal grid cells according to the fusion weight coefficients to obtain observation value fitting terms; constructing a mass conservation constraint term based on the air density continuity equation, and simultaneously constructing a momentum conservation constraint term based on the atmospheric dynamics equation; Combining the observation value fitting term, the mass conservation constraint term, and the momentum conservation constraint term to form a fusion objective function; The optimization algorithm based on adaptive step size and orthogonalized quasi-Newton iteration is used to solve the fusion objective function and obtain the fusion meteorological field. The mass conservation residual and the momentum conservation residual of the fused meteorological field are calculated, and when the mass conservation residual is less than a first preset threshold and the momentum conservation residual is less than a second preset threshold, the fused meteorological field is determined to be an initial three-dimensional meteorological field with physical consistency.

4. The method according to claim 3, characterized in that The fusion objective function is solved by using an optimization algorithm based on adaptive step size and orthogonalized quasi-Newton iteration, and the fusion meteorological field is obtained, including: Taking the meteorological element data in the spatiotemporal grid unit as the initial solution, and calculating the gradient value of the fusion objective function corresponding to the initial solution based on the fusion objective function; An iterative format is constructed based on the initial solution and the gradient value of the fusion objective function using an adaptive step size factor and an approximate inverse matrix of a quasi-Newton matrix. When the rate of change of the fusion objective function value between two adjacent iterations is greater than zero, the adaptive step size factor is reduced by a preset proportional coefficient; otherwise, the adaptive step size factor is increased by the preset proportional coefficient. The value of the adaptive step size factor is limited to a preset upper and lower limit range. In each iteration process, the solution vector difference between two adjacent iterations and the corresponding fusion objective function gradient difference vector are calculated; the solution vector difference and the fusion objective function gradient difference vector are orthogonalized to obtain an orthogonalized difference vector; According to a preset iterative evaluation round, based on the corresponding orthogonalized difference vector, an approximate inverse matrix of the quasi-Newton matrix is ​​updated using a bidirectional recursive method; and a new solution vector is calculated using the approximate inverse matrix of the updated quasi-Newton matrix; Calculate the fusion objective function value corresponding to the new solution vector and calculate the distance between the solution vectors of two adjacent iterations; When the relative change of the fusion objective function value is less than the preset change threshold and the distance value between the solution vectors is less than the preset distance threshold, the new solution vector is determined as the fused meteorological field; otherwise, the new solution vector is used as the initial solution for the next iteration and the iteration continues.

5. The method according to claim 1, wherein Based on the initial three-dimensional meteorological field, the spectral analysis method is used to decompose and reconstruct the meteorological element field. The optimal three-dimensional meteorological field is obtained, including: Performing Fourier transform on the initial three-dimensional meteorological element field to obtain spectral coefficients, performing wavelet transform on the spectral coefficients and the local window function to obtain decomposition coefficients of the meteorological element field at different scales and spatial positions, constructing a multidimensional tensor based on the decomposition coefficients, performing nuclear norm calculation and tensor decomposition, and constructing a wavenumber-energy spectrum matrix in combination with feature truncation extraction; Obtaining a dominant wavenumber mode by singular value decomposition of the wavenumber-energy spectrum matrix, and determining a characteristic wavenumber sequence according to the energy contribution rate of the dominant wavenumber mode; constructing an orthogonal filter bank based on the characteristic wavenumber sequence, wherein the orthogonal filter bank includes a plurality of Gaussian filters, wherein the center frequency of each Gaussian filter corresponds to a characteristic wavenumber in the characteristic wavenumber sequence, and the bandwidth parameter of the Gaussian filter is determined according to the interval between adjacent characteristic wavenumbers; Applying the orthogonal filter bank to the spectral coefficients to obtain a plurality of scale components, and constructing a spectral reconstruction tensor based on local energy distributions of the plurality of scale components; Local reconstruction weights are calculated according to the spectral reconstruction tensor, and weighted superposition is performed on the multiple scale components to obtain an optimal meteorological element field.

6. The method according to claim 5, characterized in that Based on the decomposition coefficients, a multidimensional tensor is constructed and the nuclear norm and tensor decomposition are performed. The wave number-energy spectrum matrix is ​​constructed by combining the feature truncation extraction method, including: Constructing a multidimensional tensor from the decomposition coefficients according to different scale levels, and calculating the nuclear norm of the multidimensional tensor to obtain a scale correlation matrix; Performing tensor decomposition on the scale correlation matrix to obtain a scale core tensor and a projection matrix group, wherein the projection matrix group includes a spatial position projection matrix, a wavenumber projection matrix, and an energy projection matrix; Calculating a singular value sequence of the scale core tensor, taking eighty percent of the maximum value of the singular value sequence as a feature truncation threshold, and extracting projection matrix components corresponding to singular values ​​in the singular value sequence that are greater than the feature truncation threshold; The projection matrix components are reconstructed to obtain the wavenumber-energy spectrum matrix.

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