A variable-resolution Beidou three-dimensional water vapor inversion method and system

Abstract

The present invention discloses a variable-resolution Beidou three-dimensional water vapor inversion method, comprising: slicing a continuous vertical space using horizontally parallel spheres, characterizing the water vapor field on each slice using spherical cap harmonics; assuming that the wet refractive index at a set altitude layer does not vary horizontally, reconstructing the wet delay outside the tomographic space by extending the slices; based on the aforementioned assumption, representing the wet refractive index at any point in the tomographic space by linear interpolation of the wet refractive indices at the corresponding positions of the two nearest slices; and utilizing the functional relationship between the oblique path wet delay and the wet refractive index, solving the coefficients of the water vapor field characterization using spherical cap harmonics on the slice plane using the least squares method. This method can effectively address issues such as mismatched spatiotemporal resolution, over-parameterization, and discontinuous variation, thereby improving the accuracy and stability of Beidou / GNSS three-dimensional water vapor inversion.

Description

Technical Field

[0001] The present invention relates to the application of global navigation satellite system technology in the field of meteorology, and in particular to GNSS meteorology and numerical inversion technology, specifically a Beidou three-dimensional water vapor inversion method and system with variable resolution. Background Art

[0002] BeiDou / GNSS 3D water vapor inversion is an emerging method for monitoring 3D atmospheric water vapor content and virtually the only technology capable of directly obtaining 3D water vapor distribution. It holds broad application prospects in atmospheric science and meteorology. However, using BeiDou / GNSS to invert 3D water vapor often results in ill-posed basic observation equations due to poor station geometry (excessive concentration of signal rays in the zenith direction) and low terrain elevation differences (poor vertical differentiation). This leads to significant uncertainty in the stability of existing BeiDou 3D water vapor inversion methods, severely hindering their practical application in engineering applications.

[0003] Furthermore, existing BeiDou / GNSS 3D water vapor inversion techniques mostly use horizontal and vertical slices to divide the continuous tropospheric space into a finite number of grids and assume a uniform distribution of water vapor within each grid. This assumption has three drawbacks: First, the grid division is arbitrary and cannot fully represent the spatial distribution of water vapor. In fact, the water vapor distribution within the grid is not uniform; second, the discretization and parameterization of the grid leads to discontinuous water vapor variations, and local grids may experience sudden changes, which prevents the full utilization of spatial correlations; third, the spatial resolution of the grid does not match the resolution achievable by actual observations. The resolution is often set too high, exacerbating ill-conditioned problems and requiring strong constraints to solve them. Summary of the Invention

[0004] In response to the above-mentioned shortcomings of the existing Beidou three-dimensional water vapor inversion method, the present invention proposes a variable-resolution Beidou three-dimensional water vapor inversion method, which can effectively solve problems such as mismatch of spatiotemporal resolution, over-parameterization, and discontinuous changes, and improve the accuracy and stability of Beidou / GNSS three-dimensional water vapor inversion.

[0005] According to one aspect of the present invention, a variable-resolution Beidou three-dimensional water vapor inversion method is provided, comprising:

[0006] The continuous vertical space is sliced ​​using a horizontally parallel spherical surface, and the spherical cap harmonic function is used to characterize the water vapor field on each slice.

[0007] Assuming that there is no horizontal variation of wet refractive index at a given height layer, the wet delay outside the tomographic space is reconstructed by section continuation.

[0008] Based on the above assumptions, the wet refractive index at any point in the tomographic space is expressed by the linear interpolation of the wet refractive indexes at the corresponding positions of the two nearest sections;

[0009] The coefficients of the water vapor field represented by the spherical cap harmonics on the tangent plane are solved by the least square method based on the functional relationship between the wet delay and the wet refractive index of the oblique path.

[0010] As a further technical solution, the method further includes:

[0011] Based on the objective fact that the wet refractive index decreases to 0 with increasing altitude and the higher the altitude, the smaller the horizontal change of the wet refractive index, the following parameter reduction scheme with increasing altitude is proposed: the bottom layer uses a high-order spherical cap harmonic model to characterize the horizontal change of water vapor richness, the middle and high layers use a low-order spherical cap harmonic model to characterize the degraded horizontal change, and the altitude layer is set to use a constant to represent no horizontal change.

[0012] As a further technical solution, the set height layer is the height layer corresponding to the section with a wet refractive index less than 5 mm / km.

[0013] As a further technical solution, the wet delay outside the tomographic space is reconstructed by slice continuation, which also includes:

[0014] The effective ray passes through the lowest section without horizontal change, and the section plane above the lowest section without horizontal change is extended. The wet refractive index on the extended section plane of each layer is the same as the wet refractive index on the section plane, and then the wet refractive index of the spatial extension plane above the lowest section without horizontal change outside the tomographic space is obtained.

[0015] As a further technical solution, the refractive index of any point outside the tomographic space above the lowest slice without horizontal change is expressed by linear interpolation of the wet refractive index constants corresponding to the two most adjacent slices.

[0016] As a further technical solution, the method further includes:

[0017] The wet refractivity is calculated by numerical weather prediction model and used to solve the initial coefficients of the underlying spherical cap harmonic model as the initial value constraint equation.

[0018] According to one aspect of the present invention, a BeiDou 3D water vapor inversion system with variable resolution is provided, comprising:

[0019] The first main module is used to slice the continuous vertical space using a horizontally parallel spherical surface, and each slice is characterized by a spherical cap harmonic function to represent the water vapor field on the slice;

[0020] The second main module is used to reconstruct the wet delay outside the tomographic space by means of slice continuation, assuming that there is no horizontal variation of the wet refractive index at a set height layer;

[0021] The third main module is used to represent the wet refractive index of any point in the tomographic space by the linear interpolation of the wet refractive indexes at the corresponding positions of the two nearest sections based on the above assumptions;

[0022] The fourth main module is used to use the functional relationship between the oblique path wet delay and the wet refractive index to solve the coefficients of the spherical cap harmonic function on the tangent plane using the least squares method to represent the water vapor field.

[0023] According to one aspect of the present invention, a Beidou three-dimensional water vapor inversion device with variable resolution is provided, comprising a memory and a processor, wherein the memory stores program instructions executed by the processor, and the processor calls the program instructions to execute the Beidou three-dimensional water vapor inversion method with variable resolution.

[0024] According to one aspect of the present invention, a non-transitory computer-readable storage medium is provided, wherein the non-transitory computer-readable storage medium stores computer instructions, and the computer instructions enable the computer to execute the variable-resolution Beidou three-dimensional water vapor inversion method.

[0025] This paper provides a BeiDou / GNSS 3D water vapor inversion method based on a spherical cap harmonic model to express water vapor level changes and a vertical parameter reduction strategy. Compared with conventional methods (research methods based on grid division planes), this method has the following advantages:

[0026] (1) The over-parameterization and ill-posedness of the equations are effectively alleviated by fitting the horizontal variation of water vapor with spherical cap harmonic functions and decreasing the parameters layer by layer with height in the vertical direction. At the same time, since the height section with a wet refractive index less than 5 mm / km has no horizontal variation, the section continuation method is used to weaken the ill-posedness of the equations. This formally improves the geometric structure of the observation values ​​and mathematically improves the well-posedness of the observation equations, making the inversion results more stable and reliable.

[0027] (2) Using spherical cap harmonic function fitting instead of traditional grid division can obtain horizontally continuous water vapor fields. The resolution can be easily adjusted by adjusting the order of the spherical cap harmonic function to adapt the observations to the results. There is no need to impose horizontal constraints, which is an unconstrained solution method.

[0028] (3) High-resolution continuous mapping of water vapor values ​​in vertical space is achieved. Through high-precision interpolation methods, more detailed vertical distribution information of water vapor can be obtained than fixed stratification, which effectively overcomes the problem of information loss between altitude layers caused by traditional discrete sampling.

[0029] In summary, the present invention can be used to construct a more accurate and reliable three-dimensional water vapor model, thereby improving the accuracy and stability of Beidou / GNSS three-dimensional water vapor inversion while introducing minimal deviation. BRIEF DESCRIPTION OF THE DRAWINGS

[0030] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, a brief introduction will be given below to the drawings used in the embodiments or the description of the prior art. Obviously, the drawings described below are some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0031] Figure 1 A schematic flow chart of a BeiDou three-dimensional water vapor inversion method with variable resolution provided in an embodiment of the present invention.

[0032] Figure 2 A schematic diagram of a plane sliced ​​vertically in space by a horizontally parallel spherical surface represented by spherical cap harmonics provided in an embodiment of the present invention.

[0033] Figure 3 Schematic diagram of reconstructing wet delay outside the tomographic region by slice continuation according to an embodiment of the present invention. DETAILED DESCRIPTION

[0034] In order to make the purpose, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are 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 work are within the scope of protection of the present invention. In addition, the technical features in the various embodiments or single embodiments provided by the present invention are arbitrarily combined with each other to form a new technical solution. This combination is not restricted by the sequence of steps and / or structural composition mode, but must be based on the ability of ordinary technicians in this field to implement it. When the combination of technical solutions is contradictory or cannot be implemented, it should be deemed that this combination of technical solutions does not exist and is not within the scope of protection required by the present invention.

[0035] The purpose of the present invention is to provide a new Beidou three-dimensional water vapor inversion model construction method. This method solves the problems of mismatch between observation and result resolution, over-parameterization, and discontinuous changes in traditional methods by using spherical cap harmonic functions to fit the water vapor level changes on different horizontal slices and gradually decreasing the resolution with height in the vertical direction. The ultimate goal is to improve the ill-conditioned problem of the three-dimensional water vapor inversion equation, improve the accuracy and stability of the Beidou three-dimensional water vapor inversion results, and promote its engineering application.

[0036] See also Figure 1 To address the problems of poor satellite station geometry and over-parameterization in existing BeiDou 3D water vapor inversion technology, which lead to ill-conditioned inversion equations and discontinuous water vapor inversion results, the present invention proposes the following solutions:

[0037] (1) In response to the non-rigorous assumption that the previous Beidou 3D water vapor inversion model discretizes the continuous space into finite space voxels and assumes that the wet refractive index within the voxels is consistent, the embodiment of the present invention proposes an inversion model with horizontal space continuity, such as Figure 2 As shown in Figure 1, the model first uses a horizontally parallel spherical surface (i.e., a contour surface in a spherical coordinate system) to slice the continuous vertical space. A spherical cap harmonic function is used on each slice to characterize the water vapor field on that slice. The spherical cap harmonic function expression of the wet refractive index on the i-th slice is as follows:

[0038]

[0039] Where θ represents the spherical coordinate co-latitude of a point on the section, λ represents the spherical coordinate longitude of the point, i represents the i-th section (the corresponding elevation is H i ), is the radius of the Earth's surface; is a joint Legendre function of the first kind; and m are the order and degree of the spherical cap harmonic model, Yes integer subscript to sort by, is a real number, and ; is the highest order of the spherical cap harmonic model expansion, and is the coefficient of the model, which represents the amplitude of the harmonic. Step Subspherical cap harmonic model (model coefficient is and , which is also a parameter to be determined) to represent the height section H i The wet refractive index field on the surface of the object is expressed in this way. The wet refractive index field expressed in this way not only presents continuous changes in the horizontal direction, but also can reduce the problem of high correlation between parameters caused by over-parameterization of traditional discretization schemes.

[0040] (2) In response to the ill-posed equation problem faced by the traditional Beidou 3D water vapor inversion model, the embodiment of the present invention proposes a parameter reduction scheme with increasing altitude based on the objective fact that the wet refractive index decreases to 0 with increasing altitude and that the higher the altitude, the smaller the horizontal change of the wet refractive index. That is, the bottom layer uses a high-order spherical cap harmonic model to represent the horizontal change of rich water vapor, the middle and high layers use a low-order spherical cap harmonic model to represent the degraded horizontal change, and a certain altitude layer uses a constant to represent the absence of horizontal change. In actual operation, considering that the accuracy of the current Beidou 3D water vapor inversion technology is no more than 5 mm / km, it is possible to set the section with a wet refractive index less than 5 mm / km to have no horizontal change. This design can significantly reduce the number of useless parameters, solve parameter-related problems, and reduce the computational burden. On the other hand, it can also weaken the ill-posed equation problem.

[0041] In BeiDou three-dimensional water vapor tomography, the effective observation value refers to the ray passing through the top of the troposphere, which causes the effective ray of the tomography to be overly concentrated in the zenith direction (i.e., the ray altitude angle is too high), resulting in poor geometric structure, which is also the main reason for the ill-conditioning of the equation. In step (2), it is assumed that there is no horizontal change in the wet refractive index at a certain altitude layer, which makes it possible to use more low-altitude angle rays. At this time, the effective ray will become the ray passing through the lowest horizontal change-free section. Compared with passing through the top of the troposphere, the altitude will decrease, so the altitude angle of the available ray will also decrease, which is conducive to improving the geometric structure of the observation value. In this case, the wet delay outside the tomography space can be reconstructed by extending the section. The specific method is as follows: Figure 3 As shown, the solid line represents the tangent plane within the tomographic space, and the dashed line represents the tangent plane after extension outside the tomographic space. The effective ray exits from the lowest horizontally unchanged tangent plane (the jth tangent plane). The wet refractive index on the jth tangent plane has no horizontal variation, denoted by C1. The tangent planes above the jth tangent plane are extended. The wet refractive index on the kth tangent plane (k>j) is the same as that on the tangent plane, and is represented by a constant. This method can be used to determine the wet refractive index of the spatially extended planes above the lowest horizontally unchanged tangent plane outside the tomographic space. Figure 3 In the equation, C2 represents the wet refractive index on the j+1th tangent plane, and C2' represents the wet refractive index on the tangent plane after the tomographic space extension corresponding to the j+1th tangent plane.

[0042] (3) According to the above settings, any point in the tomographic space The wet refractive index can be expressed by the linear interpolation of the wet refractive index of the corresponding positions of the two nearest sections. Assuming that the nearest lower section of point P is the i-th layer and the nearest upper section is the j-th layer, the wet refractive index of point P can be expressed as:

[0043]

[0044] H represents any height in the tomographic space. Similarly, the refractive index of any point Q outside the tomographic space above the lowest horizontally invariant section can also be expressed by linear interpolation of the wet refractive index constants corresponding to the two nearest sections.

[0045] (4) The observation equation of BeiDou 3D water vapor tomography is to construct the functional relationship between the slant wet delay (SWD) and the wet refractive index (expressed by spherical cap harmonics). Theoretically, the above relationship can be obtained by integrating along the BeiDou signal ray:

[0046]

[0047] Where, is the path of the signal within the tomographic region, Indicates the path outside the chromatography region. In the actual construction of the equation, within the chromatography region, a certain differential step size can be used. Formula (2) is used to calculate the wet refractive index on the signal path, according to the azimuth and altitude angles of the ray Calculate the intersection of the ray and the horizontal section, and integrate piecewise between the sections In the space outside the tomographic region, since the effective rays defined in (3) are rays passing through the lowest section without horizontal change, the calculation method within the tomographic region can also be used outside the tomographic region, and finally the discretized formula (3) is obtained, thereby constructing the basic observation equation of the tomography, in which the unknown parameters are the coefficients of the spherical cap harmonic model of each section and the constant wet refractive index of the high-level section.

[0048] (5) During the equation solution process, since there are fewer bottom observations but more parameters, the wet refractivity can be calculated using a numerical weather forecast model and used to solve the initial coefficients of the bottom spherical cap harmonic model. This is used as the initial value constraint equation to solve. The zero constraint at the bottom and top layers can effectively suppress the ill-conditioned problem of the equation. Finally, the least squares method can be used to solve the equation coefficients. At this point, the wet refractivity at any point can be obtained by function calculation or linear interpolation.

[0049] The implementation of each embodiment of the present invention is based on programmed processing performed by a device with processor functionality. Therefore, in practical engineering, the technical solutions and functions of each embodiment of the present invention are encapsulated into various modules. Based on this reality, and in addition to the aforementioned embodiments, an embodiment of the present invention provides a variable-resolution Beidou 3D water vapor inversion system. This system is used to implement a variable-resolution Beidou 3D water vapor inversion method described in the aforementioned method embodiment.

[0050] The system includes: a first main module, which is used to slice the continuous vertical space using horizontally parallel spheres, and each slice is used to characterize the water vapor field on the slice using a spherical cap harmonic function; a second main module, which is used to assume that the wet refractive index at a set altitude layer has no horizontal change, and reconstruct the wet delay outside the tomographic space by extending the slice; a third main module, which is used to represent the wet refractive index of any point in the tomographic space by linear interpolation of the wet refractive indices at the corresponding positions of the two nearest slices based on the above assumption; and a fourth main module, which is used to utilize the functional relationship between the wet delay of the oblique path and the wet refractive index to solve the coefficient of the water vapor field characterized by the spherical cap harmonic function on the tangent plane using the least squares method.

[0051] The embodiment of the present invention provides a Beidou 3D water vapor inversion system with variable resolution. This system addresses the shortcomings of existing Beidou 3D water vapor inversion methods and adopts the aforementioned modules to effectively solve problems such as mismatch in spatiotemporal resolution, over-parameterization, and discontinuous changes, thereby improving the accuracy and stability of Beidou / GNSS 3D water vapor inversion.

[0052] It should be noted that the system embodiments provided by the present invention are not only used to implement the methods in the above-mentioned method embodiments, but also used to implement the methods in other method embodiments provided by the present invention. The only difference lies in the setting of corresponding functional modules, and the principles thereof are basically the same as the principles of the above-mentioned system embodiments provided by the present invention. As long as those skilled in the art refer to the specific technical solutions in other method embodiments on the basis of the above-mentioned system embodiments, obtain corresponding technical means and technical solutions composed of these technical means by combining technical features, and on the premise of ensuring the practicality of the technical solutions, improve the modules in the above-mentioned system embodiments to obtain corresponding system class embodiments for implementing the methods in other method class embodiments.

[0053] Based on the same inventive concept as the aforementioned embodiment, an embodiment of the present invention also provides a Beidou three-dimensional water vapor inversion device with variable resolution, comprising a memory and a processor, wherein the memory stores program instructions executed by the processor, and the processor calls the program instructions to execute the Beidou three-dimensional water vapor inversion method with variable resolution.

[0054] In an embodiment of the present invention, the memory may be a non-volatile memory, such as a hard disk drive (HDD) or a solid-state drive (SSD), or a volatile memory (volatile memory), such as a random-access memory (RAM). The memory is any other medium that can be used to carry or store desired program code in the form of instructions or data structures and can be accessed by a computer, but is not limited thereto. The memory in an embodiment of the present invention may also be a circuit or any other device that can implement a storage function, for storing program instructions and / or data.

[0055] In the embodiments of the present invention, the processor may be a general-purpose processor, a digital signal processor, an application-specific integrated circuit, a field-programmable gate array or other programmable logic device, a discrete gate or transistor logic device, or a discrete hardware component, and may implement or execute the methods, steps, and logic block diagrams disclosed in the embodiments of the present invention. A general-purpose processor may be a microprocessor or any conventional processor. The steps of the methods disclosed in the embodiments of the present invention may be directly implemented and executed by a hardware processor, or by a combination of hardware and software modules within the processor.

[0056] According to one aspect of the present disclosure, a non-transitory computer-readable storage medium is provided, wherein the non-transitory computer-readable storage medium stores computer instructions, and the computer instructions enable the computer to execute the variable-resolution Beidou three-dimensional water vapor inversion method, comprising:

[0057] The continuous vertical space is sliced ​​using a horizontally parallel spherical surface, and the spherical cap harmonic function is used to characterize the water vapor field on each slice.

[0058] Assuming that there is no horizontal variation of wet refractive index at a given height layer, the wet delay outside the tomographic space is reconstructed by section continuation.

[0059] Based on the above assumptions, the wet refractive index at any point in the tomographic space is expressed by the linear interpolation of the wet refractive indexes at the corresponding positions of the two nearest sections;

[0060] The coefficients of the water vapor field represented by the spherical cap harmonics on the tangent plane are solved by the least square method based on the functional relationship between the wet delay and the wet refractive index of the oblique path.

[0061] In summary, the present invention solves the problems of mismatch between observation and result resolution, over-parameterization, and discontinuous changes in traditional methods by using spherical cap harmonic functions to fit the horizontal changes of water vapor on different horizontal slices and decreasing the resolution layer by layer with height in the vertical direction. The ultimate goal is to improve the ill-posed problem of the three-dimensional water vapor inversion equation, improve the accuracy and stability of the Beidou three-dimensional water vapor inversion results, and promote its engineering application.

[0062] Unless otherwise specified, the above technologies are all known technologies.

[0063] The terms "including" and "having" and any variations thereof in the description and claims of the present invention and the above-mentioned drawings are intended to cover non-exclusive inclusions, for example, a process, method, system, product or apparatus that includes a series of steps or units is not necessarily limited to the steps or units explicitly listed, but may include other steps or units not explicitly listed or inherent to these processes, methods, products or apparatuses.

[0064] 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 aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or replace some or all of the technical features therein with equivalents. However, these modifications or replacements do not deviate the essence of the corresponding technical solutions from the technical solutions of the embodiments of the present invention.

Claims

1. A variable-resolution Beidou three-dimensional water vapor inversion method, characterized in that: include: The continuous vertical space is sliced ​​using a horizontally parallel spherical surface, and the spherical cap harmonic function is used to characterize the water vapor field on each slice. Assuming that there is no horizontal variation of wet refractive index at a given height layer, the wet delay outside the tomographic space is reconstructed by section continuation. Based on the above assumptions, the wet refractive index at any point in the tomographic space is expressed by the linear interpolation of the wet refractive indexes at the corresponding positions of the two nearest sections; The coefficients of the water vapor field represented by the spherical cap harmonics on the tangent plane are solved by the least square method based on the functional relationship between the wet delay and the wet refractive index of the oblique path.

2. The variable resolution BeiDou 3D water vapor inversion method according to claim 1, characterized in that: The method further comprises: Based on the objective fact that the wet refractive index decreases to 0 with increasing altitude and the higher the altitude, the smaller the horizontal change of the wet refractive index, the following parameter reduction scheme with increasing altitude is proposed: the bottom layer uses a high-order spherical cap harmonic model to characterize the horizontal change of water vapor richness, the middle and high layers use a low-order spherical cap harmonic model to characterize the degraded horizontal change, and the altitude layer is set to use a constant to represent no horizontal change.

3. The variable resolution BeiDou 3D water vapor inversion method according to claim 2, characterized in that: The set height layer is the height layer corresponding to the section with a wet refractive index less than 5 mm / km.

4. The variable resolution BeiDou 3D water vapor inversion method according to claim 2, characterized in that: Reconstructing wet delay outside the tomographic space by slice continuation, including: The effective ray passes through the lowest section without horizontal change, and the section plane above the lowest section without horizontal change is extended. The wet refractive index on the extended section plane of each layer is the same as the wet refractive index on the section plane, and then the wet refractive index of the spatial extension plane above the lowest section without horizontal change outside the tomographic space is obtained.

5. The variable resolution BeiDou 3D water vapor inversion method according to claim 1, characterized in that: The refractive index of any point outside the tomographic space above the lowest horizontal change section is expressed by the linear interpolation of the wet refractive index constants corresponding to the two nearest sections.

6. The variable resolution BeiDou 3D water vapor inversion method according to claim 1, characterized in that: The method further comprises: The wet refractivity is calculated by numerical weather prediction model and used to solve the initial coefficients of the underlying spherical cap harmonic model as the initial value constraint equation.

7. A BeiDou 3D water vapor inversion system with variable resolution, characterized by: include: The first main module is used to slice the continuous vertical space using a horizontally parallel spherical surface, and each slice is characterized by a spherical cap harmonic function to represent the water vapor field on the slice; The second main module is used to reconstruct the wet delay outside the tomographic space by means of slice continuation, assuming that there is no horizontal variation of the wet refractive index at a set height layer; The third main module is used to represent the wet refractive index of any point in the tomographic space by the linear interpolation of the wet refractive indexes at the corresponding positions of the two nearest sections based on the above assumptions; The fourth main module is used to use the functional relationship between the oblique path wet delay and the wet refractive index to solve the coefficients of the spherical cap harmonic function on the tangent plane using the least squares method to represent the water vapor field.

8. A BeiDou 3D water vapor inversion device with variable resolution, characterized by: It includes a memory and a processor, the memory stores program instructions executed by the processor, and the processor calls the program instructions to execute the Beidou three-dimensional water vapor inversion method with variable resolution as described in any one of claims 1 to 6.

9. A non-transitory computer-readable storage medium, characterized in that The non-transitory computer-readable storage medium stores computer instructions, and the computer instructions enable the computer to execute the variable-resolution Beidou three-dimensional water vapor inversion method described in any one of claims 1 to 6.

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