Troposphere water vapor chromatography method and device based on compressed sensing

Abstract

The invention discloses a troposphere water vapor chromatography method and device based on compressed sensing, and belongs to the technical field of atmospheric water vapor monitoring. The method comprises the steps that historical observation data are acquired, three-dimensional voxel grid division is carried out, the resolution is adjusted in the horizontal direction according to the density of an observation station, and non-uniform layering is adopted in the vertical direction; based on GNSS and meteorological data, inclined path water vapor content is extracted as a chromatography observation value; constructing a horizontal constraint, a vertical constraint and an ERA5 prior constraint based on the voxel grid, and forming a traditional tomography equation; sub-regions are divided based on historical ERA5 data, and a self-adaptive sample set is constructed in combination with PWV correlation coefficient screening, water vapor density threshold screening and sounding data screening; and performing centralization processing on the sample, obtaining a dictionary matrix through principal component analysis, reconstructing the tomographic equation in combination with the dictionary matrix, solving a sparse coefficient, and reconstructing the three-dimensional water vapor density. According to the invention, the precision, the stability and the temporal-spatial resolution of water vapor chromatography are improved.

Description

Technical Field

[0001] This invention belongs to the field of atmospheric water vapor monitoring technology, specifically relating to a tropospheric water vapor chromatography method and apparatus based on compressed sensing. Background Technology

[0002] The troposphere is a crucial component of Earth's atmosphere, containing approximately 90% of the world's water vapor. Spatiotemporal variations in water vapor directly influence weather processes, particularly the occurrence and development of extreme weather events. Therefore, achieving high spatiotemporal resolution three-dimensional water vapor monitoring is of great significance for meteorological forecasting, climate research, and disaster prevention and mitigation.

[0003] Traditional three-dimensional water vapor detection methods, such as radiosondes and microwave radiometers, while highly accurate, suffer from limitations such as sparse spatial coverage, high cost, and difficulty in continuous observation. Global Navigation Satellite Systems (GNSS), with their wide coverage, all-weather capability, and low cost, have become a crucial data source for acquiring atmospheric water vapor information. Tropospheric tomography based on GNSS signals can invert the three-dimensional water vapor density distribution of a region by utilizing multipath signals passing through the atmosphere, compensating for the spatial continuity deficiencies of traditional methods. However, this technology faces a fundamental challenge: the geometrical distribution of GNSS signal paths (forming an "inverted cone") results in a severe lack of observational information in the lower and edge regions, causing the tomographic inversion equations to become ill-posed (ill-posed), leading to unstable and limited-accuracy solutions.

[0004] To address this issue, existing technologies primarily improve upon the model by introducing prior constraints, fusing multi-source data, and optimizing inversion algorithms. For example, they enhance model stability by adding Gaussian-weighted horizontal smoothing constraints, vertical constraints based on exponential decay models, or by incorporating numerical weather prediction and radiosonde data as additional information. However, these improved schemes, exemplified by Chinese patent (publication number: CN120953543A), still rely on traditional linear algebra methods such as singular value decomposition (SVD) to directly solve the least squares problem after constraints in their core inversion algorithm. Such methods have two inherent limitations: First, their use of prior information is relatively static and direct, usually only selecting the mean of recent ERA5 data as a fixed background field input, failing to fully explore the dynamic change patterns in historical data that are highly correlated with the current state of water vapor; Second, methods such as SVD are essentially "passive" regularizations for ill-conditioned problems caused by observation sparsity. Although a mathematical solution can be obtained by adding constraints, they do not actively utilize the inherent structural features of the water vapor field itself (such as spatial smoothness and sparsity in a specific transform domain) to guide the reconstruction process. Therefore, under extreme weather conditions with extremely poor signal geometry or drastic changes in water vapor, the stability and spatiotemporal resolution of the inversion still need to be improved.

[0005] In recent years, the ERA5 reanalysis data released by the European Centre for Medium-Range Weather Forecasts (ECMWF) has provided high-quality, consistent temperature and humidity background fields for tomographic inversion due to its high spatiotemporal resolution and multi-barosphere structure. Meanwhile, compressed sensing theory offers a new approach to solving the signal reconstruction problem under sparse observations. Its core lies in utilizing the sparsity of the signal in a certain transform domain to achieve accurate reconstruction with data at a much lower sampling rate than traditional methods. This theory has been successfully applied in fields such as medical imaging and ionospheric tomography.

[0006] Although existing studies have attempted to incorporate compressed sensing into GNSS water vapor tomography and utilize L1 norm regularization to improve inversion, current methods still have significant limitations: they typically employ fixed dictionaries, lacking dynamic adaptability to the time-varying characteristics of regional water vapor; their sample selection mechanisms are insufficient, failing to fully utilize prior information such as ERA5 to construct representative training sets; and the model's temporal resolution is limited by the update cycle of auxiliary data (such as InSAR), making it difficult to capture rapid changes in water vapor. Therefore, how to organically combine the high-quality prior information of ERA5 data with the adaptive sparse reconstruction capability of compressed sensing to significantly improve the accuracy, robustness, and spatiotemporal resolution of GNSS water vapor tomography under sparse observation conditions has become a pressing technical problem to be solved in this field. Summary of the Invention

[0007] To address the aforementioned technical problems, this invention provides a tropospheric water vapor tomography method and apparatus based on compressed sensing. By introducing a sample selection mechanism, an adaptive sparse dictionary is constructed based on ERA5 data and combined with GNSS multipath observation data to achieve high-precision inversion of tropospheric three-dimensional water vapor density and related accuracy analysis. By constructing a reasonable compressed sensing dictionary for tomography, sparse reconstruction of water vapor density is achieved. This results in high-precision tropospheric three-dimensional water vapor tomography, effectively improving the accuracy, robustness, and spatiotemporal resolution of three-dimensional water vapor density under different weather conditions.

[0008] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0009] A tropospheric water vapor chromatography method based on compressed sensing, the method comprising:

[0010] Step S1: Acquire historical observation data and perform three-dimensional voxel mesh generation;

[0011] Step S2: Extract the zenith wet delay from GNSS and meteorological observation data, and calculate the oblique path water vapor content based on the zenith wet delay as the observation value of GNSS water vapor tomography;

[0012] Step S3: Construct horizontal constraints based on the divided three-dimensional voxel mesh, construct vertical constraints based on the water vapor elevation calculated from the prior water vapor density, construct prior constraints based on the water vapor density calculated from the historical temperature and relative humidity of ERA5, and combine the observed values ​​to obtain the equation of the traditional tomographic constraint model.

[0013] Step S4: Divide the area into sub-regions based on the location of the station, and in each sub-region, sequentially screen the correlation coefficient of atmospheric precipitable water volume (PWV) and the total PWV threshold, screen the water vapor density layer by layer based on the ERA5 prior constraint, and screen the water vapor density based on the radiosonde data. Then merge the screened samples from each sub-region to obtain the final sample set for compressed sensing.

[0014] Step S5: Center the final sample set, obtain the dictionary matrix through principal component analysis, recombine the traditional tomography model equations according to the dictionary matrix, solve for the sparsity coefficients, and reconstruct the three-dimensional water vapor density.

[0015] On the other hand, the present invention provides a tropospheric water vapor chromatography apparatus based on compression sensing, comprising:

[0016] The partitioning module is used to acquire historical observation data and perform three-dimensional voxel mesh partitioning.

[0017] The observation module is used to extract the zenith wet delay from GNSS and meteorological observation data, and calculate the oblique path water vapor content based on the zenith wet delay as the observation value of GNSS water vapor tomography.

[0018] The constraint module is used to construct horizontal constraints based on the divided three-dimensional voxel mesh, construct vertical constraints based on the water vapor elevation calculated based on the prior water vapor density, construct prior constraints based on the water vapor density calculated based on the historical temperature and relative humidity of ERA5, and combine the observed values ​​to obtain the equation of the traditional tomographic constraint model.

[0019] The sample construction module is used to divide the area into sub-regions based on the location of the station, and then sequentially screen the correlation coefficient of atmospheric precipitable water volume (PWV) and the total PWV threshold within each sub-region, as well as screen the water vapor density layer by layer based on the ERA5 prior constraint and screen the water vapor density based on the radiosonde data. The samples screened in each sub-region are then merged to obtain the final sample set for compressed sensing.

[0020] The reconstruction module is used to center the final sample set, obtain the dictionary matrix through principal component analysis, recombine the traditional tomography model equations according to the dictionary matrix, solve the sparsity coefficients, and reconstruct the three-dimensional water vapor density.

[0021] Thirdly, the present invention provides an electronic device, comprising: one or more processors; a memory for storing one or more programs; wherein, when the one or more programs are executed by the one or more processors, the one or more processors implement the aforementioned tropospheric water vapor chromatography method based on compressed sensing.

[0022] Fourthly, the present invention provides a computer-readable storage medium having executable instructions stored thereon, which, when executed by a processor, enable the processor to implement the aforementioned tropospheric water vapor chromatography method based on compressed sensing.

[0023] The beneficial effects of this invention are as follows:

[0024] First, by innovatively introducing and integrating multi-source information such as ERA5 reanalysis data, GNSS observations, meteorological data, and radiosonde data, a more complete and spatiotemporally representative prior constraint system for the tomographic model was constructed, which significantly improved the physical consistency and stability of the model's initial values ​​and improved the inversion accuracy from the source.

[0025] Secondly, an adaptive sample selection and construction mechanism for compressed sensing was creatively designed. This method dynamically divides sub-regions based on the station location and comprehensively utilizes PWV time series correlation coefficient screening, total water vapor deviation threshold screening, and water vapor density layer-by-layer screening based on ERA5 and radiosonde data. This enables intelligent and refined selection of historical samples, ensuring that the constructed sparse transform dictionary can accurately capture the spatiotemporal distribution characteristics of the current regional water vapor field, effectively overcoming the limitations of traditional fixed dictionaries.

[0026] Finally, principal component analysis (PCA) and the Lasso sparse regularization algorithm were organically combined to form a complete compressed sensing solution framework. This framework uses PCA to extract the main variation patterns of the water vapor field as a dictionary matrix, and achieves robust sparse coefficient solving under limited observation conditions through L1 regularization, ultimately reconstructing a high-precision three-dimensional water vapor density field. This technical approach effectively alleviates the ill-posedness of the model caused by the sparse geometric distribution of GNSS signals, significantly improves the anti-interference capability, spatiotemporal resolution, and adaptability to different weather conditions of tomographic inversion, and provides reliable technical support for refined meteorological monitoring and services. Attached Figure Description

[0027] Figure 1 This is a flowchart of a tropospheric water vapor chromatography method based on compressed sensing according to the present invention;

[0028] Figure 2 This shows the distribution of sub-regions based on the method of this invention;

[0029] Figure 3 For sample screening process;

[0030] Figure 4 This provides a three-dimensional water vapor distribution display of chromatography results obtained using traditional methods.

[0031] Figure 5 This is a three-dimensional water vapor distribution display of the chromatography results of the method of the present invention. Detailed Implementation

[0032] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0033] This invention provides a method and apparatus for tropospheric water vapor tomography based on compressed sensing. This method utilizes ERA5 atmospheric reanalysis data, GNSS station observations, and meteorological sensor observations, combined with a sample selection mechanism, compressed sensing, and tomographic equation construction, to extract high-precision three-dimensional water vapor density (WVD) information, thus achieving tropospheric water vapor tomography based on compressed sensing. This method offers advantages such as high extraction accuracy, strong robustness, and high spatiotemporal resolution, making it suitable for applications such as space weather monitoring and meteorological services.

[0034] like Figure 1 As shown, the tropospheric water vapor chromatography method based on compression sensing of the present invention specifically includes the following steps:

[0035] Step S1, Voxel division of the tomographic region: acquire historical observation data and perform three-dimensional voxel grid division. Adjust the resolution in the horizontal direction according to the station distribution density, and adopt a non-uniform layering method with denser bottom and sparser top in the vertical direction.

[0036] A certain number of densely and evenly distributed GNSS receiver stations were selected, ensuring that each station had meteorological file output capabilities and included at least one radiosonde station within the region for subsequent accuracy verification of the inversion results. The horizontal division of voxels, i.e., the horizontal resolution of the tomography, could be adjusted according to the station distribution density within the tomographic region. The vertical resolution, however, employed a non-uniform stratification method, set based on the pressure layer distribution characteristics of the ERA5 reanalysis data, referencing 37 altitude layers. This was combined with the vertical distribution pattern of water vapor—higher water vapor content and higher resolution in the lower atmosphere, and lower water vapor content and lower resolution in the upper atmosphere—to complete the vertical stratification design of the voxels.

[0037] Step S2, Construction of the tomographic observation equation: The double-difference network solution algorithm based on GAMIT extracts the zenith wet delay (ZWD) from GNSS and meteorological observation data, and converts it into slant wet delay (SWD) by combining the projection function and horizontal gradient information. Then, the slant water vapor content (SWV) is obtained through the conversion coefficient as the observation value of GNSS water vapor tomography.

[0038] Extracting SWD based on elevation angle, azimuth angle, and horizontal gradient information:

[0039] (1)

[0040] In the formula, Represents the wet mapping function, and These represent the satellite's cutoff elevation angle and azimuth angle, respectively. and These are the wet delay horizontal gradient terms in the north-south and east-west directions, respectively. This represents the post-hoc residual correction of the observed values. Represents the water vapor gas constant. The density of liquid water ( ), This represents the weighted average temperature of the atmosphere. The value 16.48 represents the atmospheric refractive constant. The value is 377600. The water vapor value along the oblique path can be expressed as the integral of the water vapor density along the signal path:

[0041] (2)

[0042] In the formula, This represents the water vapor density within a voxel through which the m-th signal passes. Let m represent the path of the m-th signal from the satellite to the receiver. In GNSS water vapor tomography, GNSS signals can be discretized using voxel blocks. It is represented as the sum of the products of the intercept of the m-th signal as it crosses the grid and the water vapor density. A vector consisting of all available signals:

[0043] (3)

[0044] In the formula, This represents the intercept of the signal within the three-dimensional voxel (i,j,k) grid. This represents the estimated water vapor density value within the corresponding grid, which can be further expressed as a matrix in the following form:

[0045] (4)

[0046] In the formula, The coefficient matrix of the observation equation contains the intercepts corresponding to the grid numbers. It is a column matrix composed of unknown parameters such as water vapor density.

[0047] Step S3: Construction of tomographic constraint equations: Horizontal constraints are constructed based on the divided three-dimensional voxel mesh, vertical constraints are constructed based on the water vapor elevation calculated from the prior water vapor density, and prior constraints are constructed based on the water vapor density calculated from the historical temperature and relative humidity of ERA5, thus obtaining the traditional tomographic constraint model equations.

[0048] In GNSS water vapor tomography, the horizontal constraint assumption is that the water vapor distribution between adjacent voxels is continuous. A functional relationship between the water vapor density of the target voxel block and the surrounding voxel blocks is constructed, and the weights are calculated using a Gaussian weighted method.

[0049] (5)

[0050] In the formula, This represents the distance from other voxel meshes to the target mesh. Distance The corresponding weights, This is the preset smoothing factor.

[0051] The vertical constraint assumes that the water vapor density decreases exponentially with altitude, and the vertical constraint equation is:

[0052] (6)

[0053] In the formula, , and , They represent the first Layer and first The water vapor density and height of the layer, This represents the water vapor elevation calculated from historical water vapor density data. The coefficient representing the vertical constraint.

[0054] The prior constraints are calculated using historical ERA5 temperature and relative humidity at corresponding altitudes. The saturated vapor pressure is calculated from the temperature, and further calculated from the vapor pressure, leading to the vapor density. The vapor density at the center of each voxel is then bilinearly interpolated. The coefficient matrix of the prior constraints... It is a unit array.

[0055] (7)

[0056] (8)

[0057] In the formula, The water vapor density is represented by the ERA5 grid. For the corresponding height grid point temperature, The saturated water vapor pressure at the grid points, The relative humidity of the grid points.

[0058] Finally, considering the observation equations and the three constraints, the matrix of the traditional tomographic model equations can be expressed as:

[0059] (9)

[0060] In the formula, and These are the coefficient matrices for the horizontal and vertical constraints, respectively. and All values ​​are 0. For a priori 3D grid The constrained value matrix formed, Equation (4) is a matrix composed of the unknown parameter water vapor density.

[0061] Step S4, ERA5 Sample Screening: Based on historical ERA5 sample data, sub-regions are divided according to the location of the station. Within each sub-region, PWV correlation coefficient screening and PWV total threshold screening are performed sequentially. Water vapor density is screened layer by layer according to ERA5 prior constraints and water vapor density is screened a second time based on radiosonde data. The samples screened in each sub-region are merged to obtain the final sample set used for compressed sensing.

[0062] like Figure 2 The diagram shows the sub-region distribution based on this method. Since the station distribution is relatively sparse compared to the tomographic voxel grid, and given the latitude and longitude center coordinates of the stations and each grid, the Euclidean distance from the center of each bottom voxel to each station can be calculated, and each voxel can be assigned to the nearest station.

[0063] (10)

[0064] In the formula, This represents the distance from the center point of the voxel to the station. and They represent latitude and longitude respectively, with subscripts. and These correspond to voxels and station numbers, respectively. This creates several sub-regions, matching the number of stations. The ERA5 historical water vapor density data for each sub-region is used to represent the water vapor distribution characteristics of that region. Subsequent sample selection is performed independently within each sub-region.

[0065] Figure 3The overall sample selection process is presented. When a station in a sub-region has PWV observations, the grid PWV is calculated based on ERA5 single-layer historical data, and samples from the past 3 hours are extracted using a sliding time window. The Pearson correlation coefficient between this sample and the station's PWV sequence is calculated, and samples with a correlation coefficient of not less than 0.6 are selected as strongly correlated samples and retained, then sorted according to their correlation coefficient. Through correlation coefficient screening, water vapor samples with similar water vapor changes in the recent time period can be obtained. It is still necessary to determine whether their total water vapor volume is similar, and simultaneously apply a 2mm PWV deviation threshold to remove samples that do not meet the requirements, resulting in a candidate set that is similar to the current total water vapor volume state.

[0066] The above results show that the total vertical water vapor volume at a certain latitude and longitude is similar, but further judgment is needed on the water vapor density at different altitudes. A prior constraint matrix based on ERA5 is introduced to screen water vapor density thresholds for samples at each altitude in each sub-region: using 2 g / m³ as the water vapor density threshold, historical ERA5 samples are first compared epoch-by-epoch with the recent ERA5 prior constraint matrix, and samples exceeding the threshold are removed; if no samples are retained, the threshold is appropriately relaxed to ensure the sample quantity; subsequently, historical radiosonde data is introduced. Since radiosonde data only includes single-point observations, a secondary screening and removal process is performed at the location of the radiosonde station, using the same threshold, for sub-regions with different sample epochs.

[0067] The number of samples retained after screening varies from sub-region to sub-region. Using the sub-region with the fewest samples as a benchmark, samples closest to its water vapor profile are searched for and matched in each of the remaining sub-regions. This process generates a new candidate set from all complete sample vectors. Considering the possibility of the threshold being too high or too low, an option can be chosen to perform additional hierarchical distance calculation based on the similarity of water vapor distribution. The sub-region with the largest number of samples is selected as the final sample set. S4 is re-executed and the final sample set is updated at each tomographic epoch.

[0068] Step S5, Compressed Sensing Sparse Reconstruction: The final sample set is centered, and a dictionary matrix is ​​obtained through principal component analysis (PCA). The centered matrix is ​​further constructed into a covariance matrix and eigenvalue decomposition is performed. The eigenvectors are sorted to construct the dictionary matrix. The traditional tomography model equations are recombined based on the dictionary matrix. The sparse coefficients are solved using the Lasso regularization method. The three-dimensional water vapor density is reconstructed based on the sparse coefficients, the dictionary matrix, and the sample mean.

[0069] Since the dictionary matrix is ​​constructed from the final sample set obtained in step S4, it is adaptively updated with each tomographic epoch sample update, thus distinguishing it from compressed sensing reconstruction with a fixed dictionary. Firstly, the final sample set matrix obtained in step S4... Centralize the sample and remove the mean. This forms a centered matrix for principal component analysis (PCA). This processing method can eliminate the average differences between different samples, highlight the variation characteristics of the water vapor density field, and reduce the interference of low-rank or strongly correlated components on sparse reconstruction.

[0070] (11)

[0071] Subsequently, the centralized Construct the covariance matrix for each sample. And perform eigenvalue decomposition:

[0072] (12)

[0073] To represent the transpose, select its eigenvectors, sort them, and construct a dictionary matrix. .

[0074] The traditional tomographic model equations obtained in step S3 are combined with the dictionary matrix obtained in this step to form the following:

[0075] (13)

[0076] For intermediate parameters, For designing a matrix Combined with dictionary matrix The resulting perception matrix, This is the centered observation vector matrix after removing the field average.

[0077] To solve for the sparse coefficient vector By introducing L1 regularization under L2 norm constraints, overfitting is suppressed and the solution is guaranteed to converge in the sparse domain:

[0078] (14)

[0079] In the formula, For the sparse regularization coefficients, an adaptive selection method is used. First, the lower bound of regularization is calculated when all sparse coefficients shrink to 0. Due to the sparsity of Lasso and More relevant, smoother path, within the interval Generate 20 log-interval candidate factors:

[0080] (15)

[0081] To ensure algorithm convergence, we tried to continuously change... The value of is chosen to balance the sparsity of the solution and the accuracy of the observation fitting, while ensuring that the optimization problem is solvable.

[0082] Dictionary matrix obtained using PCA The sparse coefficients are obtained by combining Lasso regularization. The centered water vapor density can be obtained by adding back the mean of the samples before centering, and finally the three-dimensional water vapor density can be reconstructed. :

[0083] (16)

[0084] Compared with the singular value decomposition (SVD) method, the compressed sensing sparse reconstruction method uses the dictionary matrix constructed by PCA to obtain a sparse representation of centered three-dimensional water vapor. It can obtain a more robust solution under finite observation conditions through Lasso regularization, thus alleviating the ill-posed problem caused by GNSS ray sparsity. Figure 4 This figure presents the three-dimensional water vapor distribution from conventional tomographic results, serving as a comparative illustration of the reconstruction characteristics of conventional constrained solutions within a selected region. It shows the horizontal slices and vertical profiles of the three-dimensional water vapor density at different altitudes. Figure 4 It can be seen that although the variation in upper-level water vapor density is relatively gradual, the inversion field in the lower-level region exhibits obvious blocky undulations and abrupt changes between grids, lacking continuous transitions between adjacent grids, and containing unreasonable high / low value patches in some local locations. These phenomena indicate that traditional methods are insufficient in characterizing the lower-level water vapor structure under sparse observation conditions, resulting in poor smoothness and stability of the tomographic results, making it difficult to obtain high-resolution three-dimensional water vapor distributions.

[0085] Figure 5 This figure illustrates the three-dimensional water vapor distribution obtained from the tomography results of the method of this invention. It shows the reconstructed three-dimensional water vapor density distribution in the vertical profile and horizontal slices of a selected area, visually reflecting the continuous spatial variation characteristics of water vapor. As can be seen from the figure, the water vapor density decreases exponentially with increasing altitude. The distribution of water vapor in the lower atmosphere exhibits significant horizontal heterogeneity due to the influence of topography and meteorological conditions, while the distribution in the upper atmosphere tends to be more uniform. This result verifies that the method of this invention can stably and with high resolution reconstruct the three-dimensional water vapor structure that conforms to atmospheric physics under sparse GNSS observation conditions, demonstrating the effectiveness of the method in improving tomographic accuracy and spatiotemporal resolution.

[0086] On the other hand, the present invention provides a tropospheric water vapor chromatography device based on compression sensing, which includes various modules capable of implementing the various steps of the aforementioned method, specifically including:

[0087] The partitioning module is used to acquire historical observation data and perform three-dimensional voxel mesh partitioning.

[0088] The observation module is used to extract the zenith wet delay from GNSS and meteorological observation data, and calculate the oblique path water vapor content based on the zenith wet delay as the observation value of GNSS water vapor tomography.

[0089] The constraint module is used to construct horizontal constraints based on the divided three-dimensional voxel mesh, construct vertical constraints based on the water vapor elevation calculated based on the prior water vapor density, construct prior constraints based on the water vapor density calculated based on the historical temperature and relative humidity of ERA5, and combine the observed values ​​to obtain the equation of the traditional tomographic constraint model.

[0090] The sample construction module is used to divide the sub-regions according to the location of the station, and then perform PWV correlation coefficient screening and PWV total threshold screening in each sub-region, water vapor density screening based on ERA5 prior constraints, and water vapor density screening based on radiosonde data. The samples after screening in each sub-region are merged to obtain the final sample set for compressed sensing.

[0091] The reconstruction module is used to center the final sample set, obtain the dictionary matrix through principal component analysis, recombine the traditional tomography model equations according to the dictionary matrix, solve the sparsity coefficients, and reconstruct the three-dimensional water vapor density.

[0092] Thirdly, the present invention provides an electronic device, comprising: one or more processors; a memory for storing one or more programs; wherein, when the one or more programs are executed by the one or more processors, the one or more processors implement the aforementioned tropospheric water vapor chromatography method based on compressed sensing.

[0093] Fourthly, the present invention provides a computer-readable storage medium having executable instructions stored thereon, which, when executed by a processor, enable the processor to implement the aforementioned tropospheric water vapor chromatography method based on compressed sensing.

[0094] The specific embodiments described above further illustrate the purpose, technical solution, and beneficial effects of the present invention. It should be understood that the above descriptions are merely specific embodiments of the present invention and are not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A tropospheric water vapor chromatography method based on compressed sensing, characterized in that, The method includes: Step S1: Acquire historical observation data and perform three-dimensional voxel mesh generation; Step S2: Extract the zenith wet delay from GNSS and meteorological observation data, and calculate the oblique path water vapor content based on the zenith wet delay as the observation value of GNSS water vapor tomography; Step S3: Construct horizontal constraints based on the divided three-dimensional voxel mesh, construct vertical constraints based on the water vapor elevation calculated from the prior water vapor density, construct prior constraints based on the water vapor density calculated from the historical temperature and relative humidity of ERA5, and combine the observed values ​​to obtain the equation of the traditional tomographic constraint model. Step S4: Divide the area into sub-regions based on the location of the station, and in each sub-region, sequentially screen the correlation coefficient of atmospheric precipitable water volume (PWV) and the total PWV threshold, screen the water vapor density layer by layer based on the ERA5 prior constraint, and screen the water vapor density based on the radiosonde data. Then merge the screened samples from each sub-region to obtain the final sample set for compressed sensing. Step S5: Center the final sample set, obtain the dictionary matrix through principal component analysis, recombine the traditional tomography model equations according to the dictionary matrix, solve for the sparsity coefficients, and reconstruct the three-dimensional water vapor density.

2. The tropospheric water vapor chromatography method based on compressed sensing according to claim 1, characterized in that, In step S1, when dividing the three-dimensional voxel grid, the resolution in the horizontal direction is adjusted according to the station distribution density, and a non-uniform layering method with denser bottom and sparser top is adopted in the vertical direction. The layering is set according to the pressure layer distribution characteristics of the ERA5 reanalysis data.

3. The tropospheric water vapor chromatography method based on compressed sensing according to claim 1, characterized in that, In step S2, when extracting the zenith wet delay, a double-difference network solution algorithm is used for processing; when converting the zenith wet delay into the slant path wet delay, it is necessary to combine the wet mapping function, the cutoff elevation angle, the azimuth angle, and the wet delay horizontal gradient terms in the north-south and east-west directions for calculation.

4. The tropospheric water vapor chromatography method based on compressed sensing according to claim 1, characterized in that, In step S3, the horizontal constraint uses a Gaussian weighted method to establish a continuous relationship between the water vapor density of the target voxel and the surrounding voxels; the vertical constraint uses a model in which the water vapor density decreases exponentially with height, and establishes the constraint relationship between adjacent height layers based on the water vapor elevation calculated from historical water vapor density data.

5. The tropospheric water vapor chromatography method based on compressed sensing according to claim 1, characterized in that, In step S4, the division of sub-regions is achieved by calculating the Euclidean distance from the center of each voxel to each station and assigning the voxel to the nearest station; the PWV correlation coefficient screening is specifically as follows: calculate the Pearson correlation coefficient between the grid PWV of the historical ERA5 samples and the station PWV sequence, and retain samples with a correlation coefficient not lower than a preset threshold.

6. The tropospheric water vapor chromatography method based on compressed sensing according to claim 5, characterized in that, In step S4, the total PWV threshold screening uses 2 mm as the deviation threshold; the water vapor density layer-by-layer screening uses 2 g per cubic meter as the initial threshold; the historical ERA5 samples are compared with the ERA5 prior constraint matrix epoch by epoch and samples exceeding the threshold are removed.

7. The tropospheric water vapor chromatography method based on compressed sensing according to claim 1, characterized in that, In step S5, the final sample set is centered, a covariance matrix is ​​constructed, and eigenvalue decomposition is performed. The dictionary matrix is ​​constructed by sorting its eigenvectors; the sparse coefficients are solved using the Lasso regularization method, and the regularization coefficients are selected in an adaptive manner: first, the lower bound of the regularization coefficients that shrinks all sparse coefficients to 0 is calculated, and then multiple candidate coefficients with logarithmic intervals are generated between the lower bound and zero for iterative solution to balance the sparsity of the solution and the accuracy of observation fitting.

8. A tropospheric water vapor chromatography device based on compression sensing, characterized in that, include: The partitioning module is used to acquire historical observation data and perform three-dimensional voxel mesh partitioning. The observation module is used to extract the zenith wet delay from GNSS and meteorological observation data, and calculate the oblique path water vapor content based on the zenith wet delay as the observation value of GNSS water vapor tomography. The constraint module is used to construct horizontal constraints based on the divided three-dimensional voxel mesh, construct vertical constraints based on the water vapor elevation calculated based on the prior water vapor density, construct prior constraints based on the water vapor density calculated based on the historical temperature and relative humidity of ERA5, and combine the observed values ​​to obtain the equation of the traditional tomographic constraint model. The sample construction module is used to divide the sub-regions according to the location of the station, and then perform PWV correlation coefficient screening and PWV total threshold screening in each sub-region, water vapor density screening based on ERA5 prior constraints, and water vapor density screening based on radiosonde data. The samples after screening in each sub-region are merged to obtain the final sample set for compressed sensing. The reconstruction module is used to center the final sample set, obtain the dictionary matrix through principal component analysis, recombine the traditional tomography model equations according to the dictionary matrix, solve the sparsity coefficients, and reconstruct the three-dimensional water vapor density.

9. An electronic device, characterized in that, include: One or more processors; Memory, used to store one or more programs; When one or more programs are executed by the one or more processors, the one or more processors implement the tropospheric water vapor chromatography method based on compressed sensing as described in any one of claims 1-7.

10. A computer-readable storage medium, characterized in that, It stores executable instructions that, when executed by a processor, enable the processor to implement the tropospheric water vapor chromatography method based on compressed sensing as described in any one of claims 1-7.

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