CN114357770A - A tropospheric chromatography method - Google Patents

Abstract

The present invention provides a tropospheric tomography method, which comprises adding, on the basis of the water vapor data measured by the existing GNSS, the layered atmospheric precipitable water observation value data obtained by the geostationary satellite Fengyun 4A, and the layered atmosphere obtained by the Fengyun 4A can be Precipitation observations include low-level water vapor observations, middle-level water vapor observations, and high-level water vapor observations, and reasonably determine the weight ratio of the water vapor data measured by GNSS and the layered atmospheric precipitable water vapor data obtained by Fengyun 4A. , obtain a more accurate tropospheric tomography model, and perform tropospheric tomography under the tropospheric tomography model. The present invention attaches the stratified water vapor data of the Fengyun satellite with high temporal and spatial resolution to the tomographic model, which can greatly reduce the ill-posedness of the traditional tomographic model and build a more accurate tropospheric tomographic model, thereby obtaining a better tropospheric water vapor density distribution.

Description

A tropospheric chromatography method

technical field

The invention belongs to the field of meteorological forecasting, and particularly relates to atmospheric water vapor detection and a tropospheric tomographic method.

Background technique

Although the content of water vapor in the atmosphere is relatively small, it is an important factor in the global energy balance. Due to the phase transition effect of water vapor, it has various states such as rain, fog, cloud, and snow, which is an important factor causing weather changes. , and is also the main driving force for the formation and evolution of severe weather. In weather forecasting, the understanding of the water vapor content in the atmosphere, the changes of water vapor, and the temporal and spatial distribution determines the success or failure of short-term nowcasting, and the analysis of the humidity field in the atmosphere will directly affect the accuracy of numerical forecasting. The troposphere is the lowest layer of the Earth's atmosphere that is in contact with the ground. It has the highest atmospheric density and concentrates more than 90% of atmospheric water vapor. In space geodesy, tropospheric delay has gradually become an important research direction of modern space geodetic technology. Due to the unstable characteristics of tropospheric water vapor in space and time, the signal delay caused by water vapor has become one of the main factors affecting the accuracy of space geodesy. . Therefore, detecting and obtaining high-precision water vapor content is of great significance for making more accurate meteorological forecasts and strengthening the early warning of extreme weather disasters, as well as the development of space geodetic research.

The traditional atmospheric water vapor detection methods include: water vapor radiometer, radiosonde and meteorological satellite earth observation, etc., and the use of global navigation and positioning (GNSS) technology to remotely sense atmospheric water vapor content is an emerging atmospheric detection technology developed in the 1990s. When a satellite signal passes through the troposphere, it interacts with the atmospheric medium it comes in contact with, resulting in a delay effect in time and propagation path, known as refraction. By establishing the functional relationship between the retardation and the atmospheric refractive index, an important meteorological parameter, precipitable water (PWV), is estimated. As a powerful supplement to traditional atmospheric detection methods, GNSS detection of water vapor has the advantages of global coverage, real-time continuity, all-weather and high precision, and is an important means of modern water vapor detection. Because the zenith precipitable water content only contains one-dimensional information of tropospheric water vapor content, it cannot directly reflect the vertical distribution information of atmospheric water vapor content, so its application in meteorological research is limited. In 1992, based on the tomography technology in the medical field, Bevis first proposed the tropospheric tomography technique, that is, the tropospheric water vapor density image is reconstructed using the oblique path precipitable water vapour (SWV) along different rays penetrating the model space from all directions. The GNSS-based tropospheric tomography technology can effectively obtain the four-dimensional distribution of water vapor with high precision and high spatiotemporal density. At the same time, it has many advantages such as low cost, simple operation, and all-weather monitoring, which provides the possibility for grasping the spatiotemporal changes of tropospheric water vapor. It can be said that the study of tropospheric tomography technology has important scientific significance and application value for strengthening the monitoring of multi-dimensional dynamic changes of global atmospheric water vapor and promoting the development of modern meteorological forecasting services.

The ill-posed problem of the tropospheric tomography model is the main reason that affects the accuracy of the tomographic results. At present, the commonly used solutions to this problem mainly include the following categories:

Optimized tomographic grid division model: The division of tomographic grids is no longer roughly ruled, but adaptively divided according to the distribution of ground GNSS stations and satellite constellations, or combined with terrain and other factors , so that the grid is traversed by the GNSS signal lines as much as possible to reduce the ill-posedness of the tomographic model. However, due to the "inverted cone" distribution characteristics of GNSS signal lines, this method has limited effect, and there are still a large number of grids that are not crossed by GNSS signal lines.

Add empirical constraints: According to the distribution characteristics of water vapor in the troposphere, add empirical constraints, mainly including horizontal constraints, vertical constraints and boundary constraints, and participate in the solution of tomographic equations to obtain more reliable tomographic solutions . However, due to the instability of the atmospheric system, the empirical constraints are often inconsistent with the actual water vapor distribution, which will lead to distortion of the tomographic solution, and it is difficult to obtain reliable tomographic results.

Fusion of multi-source water vapor information: The non-GNSS water vapor information is introduced into the tomographic model as a strong constraint, which can reduce the distortion effect of the solution results caused by inaccurate empirical constraints. The ones that have been introduced so far include: global reanalysis or forecast water vapor data, PWV differential data from synthetic aperture radar interferometry, PWV images acquired by satellite sensors such as the Moderate Resolution Imaging Spectrometer and the Atmospheric Infrared Sounder. These external water vapor signals are all complete PWV signals passing through the grid from the top of the tomographic model to the bottom of the model, which can improve the ill-posedness of the tomographic model, but the improvement is limited, and it is easy to increase the redundancy of the tomographic equations.

Therefore, the traditional tomographic model has a large number of grids that are not passed through by the signal, the tomographic equations are seriously ill-posed, and the tomographic inversion result has a large error. The non-GNSS water vapor information of the tomographic model fused with the external water vapor information is introduced into the tomographic model as a strong constraint, which can reduce the distortion effect of the solution results caused by the inaccurate empirical constraints. The current study mainly uses the complete PWV signal that passes through the grid from the top of the tomographic model to the bottom of the model. This signal contains the sum of the water vapor unknowns of all grids in the vertical direction it pierces, which can improve the ill-posedness of the tomographic model, but the improvement is limited, and it is easy to increase the redundancy of the tomographic equations.

Chinese invention patent CN201711033706.8 discloses a three-dimensional water vapor detection method based on function basis, including steps: 1. Receive and calculate observation data; 2. Calculation of atmospheric troposphere parameters; Calculation; 4. Establish a function-based observation equation; 5. Establish a priori constraint equation; 6. Establish a 3D water vapor tomography model based on a function basis; 7. Determine the weight ratios of various parameters in the function-based 3D water vapor tomography model; 8. Calculation of parameters to be estimated and display of results for a three-dimensional water vapor tomography model based on function basis. Based on the function-based observation equation, the invention establishes a new function-based analytical model, and by introducing the function-based observation equation, the spatial continuity of the water vapor density parameters to be estimated is guaranteed, the number of parameters to be estimated is reduced, and the structure of the tomographic model is enhanced. Stability ensures the accuracy and reliability of reconstructed water vapor results. The method of this patent reduces the number of chromatographic unknowns and effectively improves the ill-posedness of the chromatographic equations. However, this patent uses a function basis to describe the continuity of atmospheric water vapor in horizontal space. However, the actual water vapor distribution is complex and changeable, and cannot be completely described by a set of functions, so there is a large error.

Therefore, there is a need in the art for a new tropochromatographic method.

SUMMARY OF THE INVENTION

In order to solve the above problems and establish a more accurate tropospheric tomographic modeling method and theory, the present invention develops a geostationary satellite stratified water vapor integrated with high spatial and temporal resolution on the basis of absorbing the advantages of the existing additional externally constrained water vapor tomography Data tropospheric tomography method, which uses the Fengyun geostationary satellite stratified water vapor data with high spatial and temporal resolution for the first time as the tomographic constraint, which greatly reduces the ill-posedness of the tomographic model, and can obtain a water vapor distribution that is closer to the actual chromatography products.

The present invention provides a tropospheric tomography method, which comprises adding, on the basis of the water vapor data measured by the existing GNSS, the layered atmospheric precipitable water observation value data obtained by the geostationary satellite Fengyun 4A, and the layered atmosphere obtained by the Fengyun 4A can be Precipitation observations include low-level water vapor observations, middle-level water vapor observations, and high-level water vapor observations, and reasonably determine the weight ratio of the water vapor data measured by GNSS and the layered atmospheric precipitable water vapor data obtained by Fengyun 4A. , obtain a more accurate tropospheric tomography model, and perform tropospheric tomography under the tropospheric tomography model.

In a specific embodiment, the two types of water vapor data are evaluated respectively by using sounding data, the ratio of the obtained intermediate errors is used as a weight ratio, and a multiplicative algebraic reconstruction technique is used to iteratively solve the tropospheric tomographic model. chromatographic equations.

In a specific embodiment, the initial water vapor density field required for the iteration of the multiplicative algebraic reconstruction technique is provided by the US Weather and Environmental Prediction Center.

In a specific embodiment, establishing the more accurate tropospheric tomography model includes the following steps:

Along the path l of the GNSS receiver to the GNSS satellite signal line, the relationship between the oblique path precipitable water volume _SWV and the water vapor density Nw is expressed as an integral:

The integral for each SWV signal line is approximated by:

SWV(i)=∑ _j AS(i,j)x(j) (2)

Among them, ΔS(i, j) is the intercept of the i-th signal line passing through the j-th grid, and x(j) is the unknown water vapor density of the j-th grid;

The layered PWV data inverted by Fengyun 4A is added to the constraints of the tomographic model for joint tomographic inversion; the layered PWV data of Fengyun 4A is also established according to equation (2), but because Fengyun 4A is determined based on sigma pressure coordinates The boundary of the layered PWV data needs to be converted into the geometric height of the tomographic model; the fifth-generation global atmospheric reanalysis surface pressure provided by the European Centre for Medium-Range Weather Forecasts is used to determine the pressure value at the boundary of the layered PWV data

为第i个风云4A水汽图像像素中心点的第五代全球大气再分析地表气压，即ERA5地表气压；where σ _k is the sigma coefficient, specifically 1.0, 0.9, 0.7 and 0.3;

The fifth generation global atmospheric reanalysis surface pressure for the i-th Fengyun 4A water vapor image pixel center point, that is, the ERA5 surface pressure;

Then use the ERA5 layered potential data to interpolate to obtain the potential at the boundary of each layered PWV data, and use the following approximation to obtain the corresponding geometric height H:

H=Φ/g (4)

where Φ is the potential at the boundary of each layered PWV data, and g is the gravitational acceleration;

Finally, the horizontal constraints, vertical constraints and top-level constraints are introduced to obtain the tropospheric tomographic function model that integrates the stratified water vapor of Fengyun 4A:

Among them, B _GNSS , B _FY and V are coefficient matrices; X is the water vapor density unknown vector; SWV _GNSS is the GNSS SWV observation value; LPW _FY is the Fengyun 4A layered PWV observation value, including the low layer water vapor observation value and the middle layer water vapor observation value and high-level water vapor observations; and then reasonably determine the weight ratio of the Fengyun 4A layered PWV data and the water vapor data measured by GNSS.

Advantages of the present invention:

The method of the invention improves the accuracy of tropospheric tomography results by integrating the wind-cloud layered water vapor model. The present invention attaches the Fengyun satellite layered water vapor data with high temporal and spatial resolution to the tomographic model, which can greatly reduce the ill-posedness of the traditional tomographic model and build a more accurate tropospheric tomographic model, thereby obtaining a better tropospheric water vapor density distribution. Compared with the traditional model, the integrated wind-cloud layered water vapor tomography model proposed by the present invention can significantly improve the tomographic solution accuracy. Therefore, the present invention can effectively make up for the theoretical defects of the traditional model, and determine the water vapor density field structure more accurately.

In addition, compared with the patent CN201711033706.8, the present invention does not divide the tomographic grid in the horizontal space, while the present invention divides the horizontal space into a uniform grid; the patent improves the tomographic grid by reducing the number of tomographic unknowns The equation is ill-posed, and the present invention improves the ill-posedness by increasing the actual observation constraint, that is, increasing the number of equations.

Description of drawings

Fig. 1 is a schematic diagram of the tropospheric tomography model incorporating the stratified water vapor of Fengyun 4A.

Figure 2 shows the distribution of root mean square errors of water vapor tomography inversion using traditional models in Hunan Province.

Fig. 3 is a distribution diagram of root mean square error of water vapor tomography inversion using the new model of the present invention incorporating the wind-cloud layered water vapor data in Hunan Province.

FIG. 4 is a comparison diagram of the vertical profile of water vapor density between the data of the Huaihua Sounding Station in Hunan Province and the traditional tomographic method and the new tomographic method of the present invention.

FIG. 5 is a comparison diagram of the vertical profile of water vapor density between the data of the Chenzhou Sounding Station in Hunan Province and the traditional tomographic method and the new tomographic method of the present invention.

Detailed ways

Troposphere: The layer of the atmosphere closest to the Earth's surface, containing about 75% of the atmosphere's mass and more than 90% of the water vapor mass.

Tropospheric tomography: Inversion calculation is performed based on the tropospheric delay information obtained by ray scanning, and an image of the distribution law of water vapor density in the measured troposphere is reconstructed.

GNSS: Global Positioning and Navigation System, including China's Beidou, Europe's Galileo, Russia's GLONASS and the United States GPS four systems.

The invention solves the ill-posed problem of improving the tomographic model by integrating the meteorological satellite water vapor product in the tropospheric tomographic modeling. In the process of establishing a tropospheric tomography model, the prior art generally discretizes the tomographic region through regular grid blocks, and assumes that the water vapor density of each grid block is uniformly distributed and remains unchanged within a certain period of time. Then, according to the grid punctured by the GNSS signal, the functional relationship between the corresponding grid unknown and the signal line oblique path precipitable water (SWV) is established, and then a tomographic equation system is formed to invert the tropospheric water vapor density. However, due to the fixed location of ground GNSS stations and the omnidirectional distribution of satellite constellations, the GNSS signal lines have the characteristics of an inverted cone distribution, which leads to a large number of grids in the tomographic model that are not crossed by the signal lines, which makes the The system of tomographic equations creates ill-posed problems. In order to reduce the ill-posedness of the tomographic equations and obtain a tomographic solution closer to the actual water vapor distribution, a joint tomographic inversion can be performed by adding external multi-source water vapor signals. The current tomographic model that integrates multi-source water vapor information mainly uses the vertical PWV signal that passes through the grid from the top of the tomographic model to the bottom of the model. The sum of all gridded water vapor unknowns in the vertical direction of . The constraints established by the external TPW signal can improve the ill-posedness of the tomographic model, but the improvement is limited, and it is easy to conflict with the GNSS TPW located in the same plane grid, increasing the redundancy of the tomographic equations.

On the basis of absorbing the advantages of the existing additional externally constrained water vapor tomography, the present invention develops a tropospheric tomography method that integrates geostationary satellite layered water vapor data with high spatial and temporal resolution. The satellite stratified water vapor data, as a tomographic constraint, greatly reduces the ill-posedness of the tomographic model, and can obtain a tomographic product that is closer to the actual water vapor distribution.

This patent improves the shortcomings of the traditional tomographic model, and uses the Fengyun geostationary satellite layered water vapor data with high temporal and spatial resolution as the tomographic constraint, which greatly reduces the ill-posedness of the tomographic model, and can obtain closer to the Chromatography product with actual water vapor distribution. The principle and process are as follows:

Along the GNSS receiver to GNSS satellite signal line path l, the relationship between _SWV and water vapor density Nw can be expressed as an integral:

SWV=∮ _l N _w d _l (1)

Based on a series of SWVs in all directions of the tomographic space, the tropospheric tomography technique can invert the spatial distribution of tropospheric water vapor density. The traditional tomography method is to establish a grid model in the tomography area, and assuming that the water vapor density in each voxel is constant and uniformly distributed during the tomography period, each grid in the tomography model is a water vapor density. Unknown. So the integral for each SWV signal line can be approximated as:

SWV(i)=∑j ΔS(i, _j )x(j) (2)

Among them, ΔS(i, j) is the intercept of the i-th signal line passing through the j-th grid, and x(j) is the unknown water vapor density of the j-th grid.

Fengyun-4 satellite (Fengyun-4A) is a second-generation geostationary orbit (GEO) quantitative remote sensing meteorological satellite developed by the Eighth Research Institute of China Aerospace Science and Technology Corporation (Shanghai Institute of Aerospace Technology). It adopts a three-axis stabilization control scheme. Continuous and stable operation will greatly improve the detection level of my country's geostationary meteorological satellites. From 0:00 on May 8, 2018, users in China and the Asia-Pacific region can officially receive the data of "Fengyun-4" A star.

Based on the traditional tomographic model, the present invention proposes to add the layered PWV data inverted by the Fengyun 4A satellite to the tomographic model to form constraints for joint tomographic inversion. The layered PWV data of Fengyun 4A also establishes an equation according to formula (2), but since Fengyun 4A determines the boundary of layered PWV data based on sigma pressure coordinates, it needs to be converted into the geometric height of the tomographic model. The present invention adopts the fifth-generation global atmospheric reanalysis (ERA5) surface pressure provided by the European Centre for Medium-Range Weather Forecasts (ECMWF) to determine the pressure value at the boundary of the layered PWV data

为第i个风云4A水汽图像像素中心点的ERA5地表气压。where σ _k is the sigma coefficient, specifically 1.0, 0.9, 0.7 and 0.3;

is the ERA5 surface pressure at the center point of the i-th Fengyun 4A water vapor image pixel.

Then use the ERA5 layered potential data to interpolate to obtain the potential at the boundary of each layered PWV data, and use the following approximation to obtain the corresponding geometric height H:

H=Φ/g (4)

where Φ is the potential at the boundary of each layered PWV data, and g is the gravitational acceleration.

Finally, by introducing horizontal constraints, vertical constraints and top-level constraints, the tropospheric tomographic function model incorporating the stratified water vapor of Fengyun 4A can be obtained:

Among them, B _GNSS , B _FY and V are coefficient matrices; X is the water vapor density unknown vector; SWV _GNSS is the GNSS SWV observation value; LPW _FY is the Fengyun 4A layered PWV observation value, including low-level water vapor (LPW-LOW), Water vapor (LPW-MID) and high-level water vapor (LPW-HIGH). Fig. 1 is a schematic diagram of the tropospheric tomography model incorporating the stratified water vapor of Fengyun 4A.

Considering the inconsistency in accuracy between the Fengyun 4A layered PWV data and the water vapor data measured by GNSS, it is necessary to reasonably determine the weight ratio of the two types of data. The present invention uses sounding data to evaluate two types of water vapor data respectively, and uses the ratio of the obtained mid-error as the weight ratio. Multiplicative Algebraic Reconstruction Technology (MART) uses an iterative method to reconstruct images, avoids matrix inversion, and has the advantage of good convergence in a short period of time. The invention adopts MART to iteratively solve the tomographic equation system, and the initial water vapor density field required for the iteration is provided by the American Meteorological Environment Prediction Center.

Based on the observation data of Hunan Province Continuous Operation Tracking Station Network (HNCORS), a large-scale water vapor tomography inversion in Hunan Province is realized by using the method of merging wind-cloud layered water vapor tomography proposed in the present invention. The results show that this method can significantly improve the water vapor layer. The accuracy of the analysis results. Fig. 2 is the distribution diagram of root mean square error of using traditional model to perform water vapor tomographic inversion in Hunan Province, and Fig. 3 is that Hunan Province uses the new model of the present invention that is integrated with wind-cloud layered water vapor data to perform water vapor tomographic inversion The root mean square error distribution of . Figures 2 and 3 are the root mean square error (RMSE error) of the tomographic results of its model compared with the ERA5 reanalysis data.

As can be seen from the original images of Figures 2 and 3, Figure 2 is shown in orange as a whole, and Figure 3 is shown in blue as a whole. Looking at the data in various parts of Hunan in the figure, we can see that in the traditional model, the RMSE error compared with the ERA5 reanalysis data in most areas of Hunan Province is between 1.7 and 2.5 g/m ³ , and the large area is concentrated at 1.8 to 2.3 g/m. between g/m ³ . However, the RMSE error of the tomographic results obtained from the new model provided by the present invention compared with the ERA5 reanalysis data in most areas of Hunan Province is between 0.2 and 1.7 g/m ³ , and is especially concentrated in 0.5 to 1.3 g/m ³ . between. It can be seen that in most of the tomographic regions, the new model and the new method obtained a smaller RMSE than the traditional model, indicating that the new method can improve the quality of the tomographic results as a whole.

Figures 4 and 5 show the comparison results of the tomography and the vertical profiles of the water vapor density at the two sounding stations in Huaihua, Hunan and Chenzhou, Hunan, respectively. It is evident from Figures 4 and 5 that the results of the new model and the new method are more in line with the sounding water vapour profiles. The statistical results show that, compared with the Huaihua sounding station in Hunan, the RMSE of the traditional model and method and the new model and method are 0.99 and 0.52 g/m ³ respectively, and the RMSE reduction rate reaches 47.47%; compared with the Chenzhou sounding station in Hunan, the RMSE is reduced by The 1.47 g/m ³ of the conventional model was reduced to 0.95 g/m ³ , and the RMSE was reduced by 35.37%. It can be seen that the new model and new method can significantly improve the accuracy of the tomographic results and obtain a more realistic three-dimensional water vapor distribution.

The traditional tropospheric tomography model only adds empirical horizontal constraints, vertical constraints and top-level constraints, and the tomographic results are not ideal. Taking the complete satellite PWV signal with high spatial resolution as the constraint condition reduces the ill-posedness of the tomographic equations to a certain extent and improves the accuracy of the tomographic results. However, the improvement of the ill-posedness of the tomographic model by the complete PWV signal is limited, and it is easy to increase the redundancy of the tomographic equations, so that the modeling accuracy of the tomographic model is still not high. In addition, there is still a lack of research on applying geostationary satellite stratified water vapor data with high spatial and temporal resolution to tomographic models. The present invention attaches the Fengyun satellite layered water vapor data with high temporal and spatial resolution to the tomographic model, which can greatly reduce the ill-posedness of the traditional tomographic model and build a more accurate tropospheric tomographic model, thereby obtaining a better tropospheric water vapor density distribution. For example, applying the method proposed by the present invention in an actual case can better invert the change information of the spatial distribution of water vapor density, realize the accurate inversion of the water vapor density value at any point in space, and improve the overall accuracy of the tomographic results compared with the traditional method. . Based on a large number of comparative analyses, the integrated wind-cloud layered water vapor tomography model proposed by the present invention can significantly improve the tomographic solution accuracy compared with the traditional model. Therefore, the present invention can effectively make up for the theoretical defects of the traditional model, and determine the water vapor density field structure more accurately.

The optional embodiments of the embodiments of the present invention have been described in detail above with reference to the accompanying drawings, but the embodiments of the present invention are not limited to the specific details of the above-mentioned embodiments. The technical solution undergoes a variety of simple modifications, and these simple modifications all belong to the protection scope of the embodiments of the present invention.

Claims (4)

1. a tropospheric tomography method, is characterized in that, on the basis of the water vapor data of existing GNSS measurement, add the layered atmospheric precipitable precipitable value data obtained by static satellite Fengyun 4A, the layered data obtained by described Fengyun 4A. Atmospheric precipitable water vapor observations include low-layer water vapor observations, middle-layer water vapor observations, and upper-layer water vapor observations, and it is reasonable to determine the difference between the water vapor data measured by GNSS and the layered atmospheric precipitable water vapor data obtained by Fengyun 4A. A more accurate tropospheric tomography model was obtained, and tropospheric tomography was performed under the tropospheric tomography model. 2. method according to claim 1 is characterized in that, utilize sounding data to carry out evaluation to described two kinds of water vapor data respectively, take the ratio of middle error obtained as weight ratio, and adopt multiplication algebraic reconstruction technique to iteratively solve described. A system of tomographic equations in a tropospheric tomographic model. 3 . The method according to claim 1 , wherein the initial water vapor density field required for the iteration of the multiplicative algebraic reconstruction technique is provided by the American Meteorological and Environmental Prediction Center. 4 . 4. The method according to any one of claims 1 to 3, wherein establishing the more accurate tropospheric tomography model comprises the following steps: Along the path l of the GNSS receiver to the GNSS satellite signal line, the relationship between the oblique path precipitable water volume SWV and the water vapor density Nw is expressed as an integral: SWV=∮ _l N _w d _l (1) The integral for each SWV signal line is approximated by: SWV(i)=∑j ΔS(i, _j )x(j) (2) Among them, ΔS(i, j) is the intercept of the i-th signal line passing through the j-th grid, and x(j) is the unknown water vapor density of the j-th grid; The layered PWV data inverted by Fengyun 4A is added to the constraints of the tomographic model for joint tomographic inversion; the layered PWV data of Fengyun 4A is also established according to equation (2), but because Fengyun 4A is determined based on sigma pressure coordinates The boundary of the layered PWV data needs to be converted into the geometric height of the tomographic model; the fifth-generation global atmospheric reanalysis surface pressure provided by the European Centre for Medium-Range Weather Forecasts is used to determine the pressure value at the boundary of the layered PWV data

where σ _k is the sigma coefficient, specifically 1.0, 0.9, 0.7 and 0.3;

The fifth generation global atmospheric reanalysis surface pressure for the i-th Fengyun 4A water vapor image pixel center point, that is, the ERA5 surface pressure; Then use the ERA5 layered potential data to interpolate to obtain the potential at the boundary of each layered PWV data, and use the following approximation to obtain the corresponding geometric height H: H=Φ/g (4) where Φ is the potential at the boundary of each layered PWV data, and g is the gravitational acceleration; Finally, the horizontal constraints, vertical constraints and top-level constraints are introduced to obtain the tropospheric tomographic function model that integrates the stratified water vapor of Fengyun 4A:

Among them, B _GNSS , B _FY and V are coefficient matrices; X is the water vapor density unknown vector; SWV _GNSS is the GNSS SWV observation value; LPW _FY is the Fengyun 4A layered PWV observation value, including the low layer water vapor observation value and the middle layer water vapor observation value and high-level water vapor observations; and then reasonably determine the weight ratio of the Fengyun 4A layered PWV data and the water vapor data measured by GNSS.

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