CN112083453A - A tropospheric chromatography method involving water vapor spatiotemporal parameters - Google Patents

Abstract

The invention provides a tropospheric tomography method involving water vapor spatiotemporal parameters. In the method, the wet refractive index varies with spatial position and its value is obtained by weighted sum and interpolation of eight nodes of the voxel where it is located, and inverse distance weighting is adopted in the horizontal direction. For interpolation, exponential interpolation is used in the vertical direction, and the parameters required by the interpolation method are obtained according to the real-time estimation of the tomographic wet refractive index field. On the basis of the existing parameterized tomography model, the invention improves the tomographic modeling accuracy by refining the interpolation method of the parameterized tomography model. Especially when the grid division is large or the water vapor space changes drastically, the improved parameterization method proposed in the present invention can construct a tropospheric tomography model more accurately.

Description

A tropospheric chromatography method involving water vapor spatiotemporal parameters

technical field

The invention relates to the field of geophysics, in particular to a tropochromatographic method involving water vapor spatiotemporal parameters.

Background technique

The troposphere is the layer of atmosphere closest to the earth's surface and the densest layer of the earth's atmosphere, containing about 75% of the mass of the entire atmosphere, as well as almost all water vapor and aerosols. The tropospheric tomography is based on the inversion calculation of the wet delay information obtained by the ray scanning, and reconstructs the three-dimensional image of the distribution law of the wet refractive index in the measured troposphere. Among them, wet delay means that when the electromagnetic wave signal passes through the troposphere, its signal is refracted by water vapor and bent, the propagation path becomes longer than the geometric distance, and the propagation speed becomes slower, which is called the delay of atmospheric water vapor to the electromagnetic wave signal.

Water vapor is an important part of the earth's atmosphere, and it plays a vital role in many fields such as weather dynamics, atmospheric environmental science, surveying and mapping science and technology, and hydrology. Although the water vapor content in the atmosphere is only 0.1-3% of the total, it is the most active component in the atmosphere. The occurrence of many weather changes and natural disasters is directly related to the water vapor content and its transport in the atmosphere, so atmospheric water vapor plays a key role in weather forecasting and climate change. The water vapor in the atmosphere is mainly concentrated in the troposphere, and its highly dynamic and rapidly changing characteristics make it a very difficult task to accurately and timely obtain the water vapor distribution with high spatial and temporal resolution. Ground-based GNSS (Global Navigation Satellite System) tomography technology can reconstruct high-precision atmospheric water vapor fields, and has incomparable advantages over many traditional water vapor detection methods.

Using the densely intertwined SWD (Slant Wet Delay) data over the region obtained from the ground-based GNSS observation network, combined with tomography technology, the regional three-dimensional water vapor field can be reconstructed. The commonly used tomographic modeling method uses voxels as the minimum cutting unit, discretizes the inversion area into small grids, and then uses the SWD data to calculate the wet refractive index in each grid. In traditional tomographic model research, it is assumed that the water vapor distribution in a single grid is uniform and constant, but when the water vapor changes strongly in space or the grid range is large, this assumption is unreasonable, resulting in large model errors. In this regard, some scholars have proposed a numerical integration parameterization method, which uses different interpolation algorithms to obtain the wet refractive index of any point in the grid, and uses the numerical integration algorithm to discretize the wet delay of the oblique path. In this method, the parameter to be determined is the wet refractive index of each grid vertex, which overcomes the unreasonable assumption that the water vapor distribution in the cell grid is uniform and unchanged in traditional tomographic modeling, and the number of parameters to be determined does not vary. obviously increase. The numerical integration parameterization method is the key to constructing a high spatial resolution tomographic model, and this method can better invert the inversion layer of the water vapor profile, indicating that its mathematical model is more reasonable. However, the bilinear/spline interpolation used in the existing parametric models does not consider the physical characteristics of the temporal and spatial variation of water vapor, resulting in an inaccurate water vapor interpolation method. It is necessary to conduct in-depth research and improve the method.

That is to say, the existing tropospheric tomographic modeling methods can be basically divided into two categories: one is a non-parametric model, in which the water vapor in each voxel in the tomographic period is considered to be uniformly distributed. The other type is the parametric model, in which the water vapor in each voxel in the tomographic period changes with the spatial position.

Among them, the non-parametric model discretizes the troposphere space into multiple voxels and assumes a constant and uniform distribution of the wet refractive index within each voxel. The advantage is that there are relatively few parameters involved in modeling and the operation is simple. However, when the grid division is large or extreme weather conditions occur, it will cause modeling errors that cannot be ignored.

The parametric model also discretizes the troposphere space into multiple voxels, but the wet refractive index in each voxel varies with the spatial position, and the wet refractive index at any point is determined by the eight nodes of the voxel (as shown in Figure 1, N The eight nodes ₁ to N ₈ ) are obtained by horizontal and vertical interpolation. It can solve the adverse effects of unreasonable mesh division, and at the same time ensure the calculation efficiency.

But in practice, water vapor varies greatly in space, especially in the vertical direction or under extreme weather conditions, which can cause model errors that cannot be ignored for non-parametric models. A finer meshing can mitigate the adverse effects of this unreasonable assumption, but it will increase computational efficiency and the constraints between voxels will also affect the results. The parametric model can solve the adverse effects caused by unreasonable meshing, while ensuring the computational efficiency. The wet refractive index of any point in the parametric model is obtained by horizontal and vertical interpolation of the eight nodes of the voxel. However, the existing interpolation methods (such as linear interpolation, cubic spline interpolation) do not take into account the spatiotemporal parameters of water vapor, resulting in insufficient modeling accuracy. When the grid division is large or the water vapor space changes drastically, the inversion error is large, which limits the application of tropospheric tomography to a certain extent.

In order to solve the above problems and establish a more accurate parametric tropospheric tomography model, there is a need in the art for an improved tropospheric tomography method.

SUMMARY OF THE INVENTION

Based on the parameterized tropospheric tomography model, the present invention develops an improved tropospheric tomography parameterization method for the problem of insufficient accuracy of its interpolation method. In this method, the wet refractive index varies with spatial position and its value is determined by The eight-node weighted summation and interpolation of , adopt inverse distance weighted interpolation in the horizontal direction, and use exponential interpolation in the vertical direction, and the parameters required by the interpolation method are obtained according to the real-time estimation of the tomographic wet refractive index field. The parametric tropospheric tomography model is refined to overcome the defect that water vapor spatiotemporal parameters are not considered in previous modeling.

That is to say, the present invention provides a tropospheric tomography method involving water vapor spatiotemporal parameters. In the method, the wet refractive index varies with spatial position and its value is obtained by weighted summation and interpolation of the eight nodes of the voxel. The horizontal direction Inverse distance weighted interpolation is adopted, and exponential interpolation is adopted in the vertical direction, and the parameters required by the interpolation method are obtained according to the real-time estimation of the tomographic wet refractive index field.

In the present invention, the spatiotemporal parameters of water vapor are involved, that is, its time parameters and spatial parameters, wherein the spatial parameters of water vapor include the interpolation of its horizontal and vertical directions, and the time parameters of water vapor are obtained because the parameters are obtained according to the transformation of time. Dynamically different estimates.

In a specific embodiment, during tropospheric tomography, vertical interpolation is performed first and then horizontal interpolation is performed, or horizontal interpolation is performed first and then vertical interpolation is performed. Preferably, horizontal interpolation is performed first and then vertical interpolation is performed. This simplifies the calculation.

In a specific embodiment,

Along the ray path from the GNSS satellite to the receiver, the relationship between SWD and the wet refractive index N _w can be expressed as:

SWD=∫ _l N _w d _l (1)

In the tomographic model, the reconstruction space is discretized into multiple voxels, where l is the oblique path in the SWD; the vertical layer division method considering the water vapor distribution is as shown in Equation 2:

where h _i is the height of the top layer of the i-th layer; n is the total number of vertical layers; h _min is the height of the bottom layer of the tomographic study area; h _max is the height of the top layer of the tomographic study area; The sounding profile data is obtained by fitting with Equation 6;

In the parametric model, the wet index of refraction in each voxel varies with position, and the wet index of refraction at any point in the voxel is determined by the weighted sum of the wet index values of the eight nodes N ₁ to N ₈ of the voxel , so that the SWD is expressed as the integral of the wet refractive index at the voxel node, and the Newton-Kertz method is used to solve the integral; the wet refractive index N _W integral of the five equidistant points P ₁ -P ₅ on the oblique path 1 can be Expressed in the following way:

where D _P1P5 is the intercept of P ₁ to P ₅ , P ₁ , P ₂ , P ₃ , P ₄ , P ₅ are five equidistant points, and the wet refractive index of point P _k is composed of 8 individuals from N ₁ to N ₈ The wet refractive index value of the prime node is determined by interpolation;

The parametric modeling method considering the spatiotemporal distribution of water vapor is shown in Equation 5, and the wet refractive index of P _k can be vertically interpolated with points V ₁ and V ₂ :

Among them, V ₁ is a point on the same height plane as N ₁ -N ₄ , V ₂ is a point on the same height plane as N ₅ -N ₈ , and V ₁ , V ₂ and P _k are on the same line On the vertical line; k is any integer selected from 1 to 5, and h _Pk is the height of the point P _k ;

where the parameter α can be estimated from the following equation:

where h ₀ refers to the height of the lower surface of the voxel, and _hi refers to the height of any point in the voxel. Equation 6 takes into account the exponential variation of water vapor with vertical height;

To take into account the temporal variation of water vapor, use the tomographic profile of the previous period to estimate the α of each voxel in the current period;

Additionally, the wet refractive index values for V ₁ and V ₂ are calculated using inverse distance-weighted interpolation:

where i is 1 or 2, where d _j is the distance between _Vi and N _j , and _Vi and N _j are on the same height plane; u is the power of the distance, and N _j is the voxel surface where _Vi is located The 4 surrounding nodes of ; N _w (N _j ) is the wet refractive index value of the 4 surrounding nodes on the surface of the voxel where V _j is located;

In order to improve the modeling accuracy, the u value of each vertical layer is estimated in each period using the tomographic results of the previous period.

In a specific embodiment, all SWDs during modeling are collected to establish a linear system between the SWD and the wet refractive index field:

y=Ax (8)

where y is the vector of SWD observations, x is the unknown parameter vector containing the wet refractive index of all voxel nodes, and A is the design matrix consisting of the x contributions of the SWD.

In a specific implementation, since equation 8 usually has an ill-posed problem, horizontal and vertical constraints are added to make the equation full rank, and then the least squares method is used to solve x.

Advantages of the present invention:

On the basis of the existing parameterized tomography model, the invention improves the tomographic modeling accuracy by refining the interpolation method of the parameterized tomography model. In the past, the interpolation method of parametric tropospheric tomography model usually adopts linear interpolation or spline interpolation, and does not consider the spatial and temporal distribution characteristics of water vapor, especially when the grid division is large or the water vapor space changes drastically, the inversion error is large, but the present invention The proposed improved parametric method can construct a tropospheric tomography model more accurately. For example, in practical case applications, the inversion accuracy of the new parametric method provided by the present invention is higher than that of the non-parametric method and the traditional parametric method, respectively. 54% and 10%. Based on a large number of comparative analyses, it is known that the parametric tomographic model proposed by the present invention considering the temporal and spatial distribution of water vapor can significantly improve the tomographic solution accuracy compared with the traditional model. Therefore, the present invention can effectively make up for the defects of the traditional model, and determine the wet refractive index field structure more accurately.

Description of drawings

FIG. 1 is a schematic diagram of discretization of a tropospheric tomography model provided by the present invention.

Figure 2 shows the RMS error (Figure a) and relative RMS error (Figure b) of the nonparametric model (Tomo-I), the traditional parametric model (Tomo-II) and the parametric model (Tomo-III) provided by the present invention Comparison chart.

Fig. 3 is the RMS distribution diagram of ERA5 and the non-parametric model (Fig. 3a), the traditional parametric model (Fig. 3b) and the improved parametric model provided by the present invention (Fig. 3c).

Detailed ways

According to the spatial variation characteristics of water vapor, the invention obtains the wet refractive index at any point in the troposphere space by weighting and summing the eight nodes of the voxel where it is located. The horizontal direction adopts inverse distance weighted interpolation, and the vertical direction adopts exponential interpolation. The required parameters are obtained according to the dynamic estimation of the tomographic wet refractive index field, which overcomes the defect that the water vapor spatiotemporal parameters are not considered in the previous modeling, and refines the parametric tropospheric tomography model. The principle and process are as follows:

Along the ray path from the GNSS satellite to the receiver, the relationship between SWD and the wet refractive index N _w can be expressed as:

SWD=∫ _l N _w d _l (1)

As shown in Figure 1, l is the oblique path in SWD. The tomography technique can invert the spatial distribution of the wet refractive index based on the spatially interwoven SWD from all directions within the tomographic period. Usually tomographic models must discretize the reconstruction space into multiple voxels (see Figure 1). In the previous grid division, the vertical stratification was determined artificially, and the vertical distribution of water vapor was not considered. The present invention proposes a vertical layer division method considering water vapor distribution:

where h _i is the height of the top layer of the i-th layer; n is the total number of vertical layers; h _min is the height of the bottom layer of the tomographic study area; h _max is the height of the top layer of the tomographic study area; The sounding profile data are obtained by fitting with Equation 6. Historical sounding profile data are publicly available data that can be easily obtained.

In traditional nonparametric methods, it is assumed that the water vapor in each voxel is constant and uniformly distributed during the modeling period. Therefore, each SWD can be viewed as the sum of all segments along the ray path traversing those voxels, so equation (1) can be approximated as:

指的是体素i中的湿折射率，d_i是体素i的SWD射线路径的截距。where i refers to voxel i, n is the number of voxels traversed by the SWD,

refers to the wet refractive index in voxel _i , and di is the intercept of the SWD ray path for voxel i.

In parametric models (both prior art and the present invention), the wet index of refraction within each voxel varies with position. The wet index of refraction at any point within a voxel is determined by a weighted sum of the wet index values of the 8 nodes of that voxel, such that SWD is expressed as the integral of the wet index of refraction at the voxel node. Since an analytical solution to the integral cannot be obtained in most cases, the Newton-Kertz method is used to solve the integral. As shown in Figure 1, the integral of the wet refractive index (ie, _NW ) along P1-P5 can be expressed as:

where D _P1P5 is the intercept of P ₁ to P ₅ , and P ₁ , P ₂ , P ₃ , P ₄ , and P ₅ are five equally spaced points. The wet index of refraction at point _Pk is determined by interpolating the wet index values of the ₈ voxel nodes (ie, N1, _N2 , . . . , _N8 ).

In previous studies, the interpolation method usually adopts linear interpolation or spline interpolation, and does not consider the spatial and temporal distribution characteristics of water vapor. When the grid division is large or the water vapor space changes drastically, the inversion error is large, which limits the application of tropospheric tomography to a certain extent.

To this end, the present invention proposes a parametric modeling method that takes into account the spatial and temporal distribution of water vapor. Taking point _P3 as _an example, its wet refractive index can be interpolated vertically with points V1 and V2 _:

where the parameter α can be estimated from the following equation:

Among them, h ₀ refers to the height of the lower surface of the voxel, and _hi refers to the height of any point in the voxel. Equation (6) takes into account the exponential variation of water vapor with the vertical height. To account for temporal changes in water vapor, the tomographic profiles of the previous period were used to estimate α for each voxel in the current period. Additionally, the wet refractive index values for V ₁ and V ₂ are calculated using inverse distance-weighted interpolation:

where i is 1 or 2, and V _i is V ₁ and V ₂ in Equation 5. where d _j is the distance between _Vi and N _j , and _Vi and N _j are on the same plane. u is the power of distance, and _Nj refers to the four surrounding nodes on the surface of the voxel where _Vi is located. N _w (N _j ) (j=1, 2, 3, 4) is the wet refractive index value of the four surrounding nodes of the voxel surface where _Vi is located. In order to improve the modeling accuracy, the u value of each vertical layer is estimated in each period using the tomographic results of the previous period.

Collecting all SWDs during modeling, a linear system between the SWD and the wet refractive index field can be established:

y=Ax (8)

where y is the vector of SWD observations, x is the unknown parameter vector containing the wet refractive index of all voxel nodes, and A is the design matrix consisting of the x contributions of the SWD. Since equation (8) usually has ill-posed problems, additional horizontal and vertical constraints are required to make the equation full rank, and then the least squares method can be used to solve x.

The case of FIG. 2 shows that the improved parametric model proposed by the present invention can significantly improve the accuracy of the tomographic water vapor field. FIG. 2 shows a graph comparing the RMS error and relative RMS error with height for the nonparametric model (Tomo-I), the traditional parametric model (Tomo-II) and the improved parametric model of the present invention (Tomo-III). Compared with the other two models, the improved parametric model can significantly improve the tomographic accuracy, and its RMS error gradually decreases with height. In terms of relative RMS error, the improved parametric model increases from 8% in the lowest layer to 443% in the highest layer. Compared with the nonparametric model (blue) and the traditional parametric model (pink), the accuracy of the wet refractive index value inversion by the improved parametric model is greatly improved. In Figures 2a and 2b, from right to left are the curves of the nonparametric model (Tomo-I), the traditional parametric model (Tomo-II) and the improved parametric model of the present invention (Tomo-III).

Figure 3 shows the comparison of the chromatographic wet refractive index with the ERA5 reanalysis data. Figure 3(a) shows the comparison results of ERA5 and non-parametric models, Figure 3(b) shows the comparison results of ERA5 and traditional parametric models, and Figure 3(c) shows the comparison results of ERA5 and improved parametric models . Obviously, both the nonparametric model and the traditional parametric model have large deviations from the ERA5 reanalysis data. The RMS errors of the three methods, Tomo-I, Tomo-II and Tomo-III, vary in the range of 7.0 to 16.8 mm/km, 5.9 to 15.8 mm/km and 6.0 to 11.0 mm/km, respectively. For the improved parametric model of the present invention, the RMS error values in most areas are less than 10 mm/km, which is in high consistency with the ERA5 reanalysis data. Overall, the inversion accuracy of the water vapor field obtained by the improved parametric model is 17% and 8% higher than that of the non-parametric model and the traditional parametric model, respectively.

The above content is a further detailed description of the present invention in conjunction with specific preferred embodiments, and it cannot be considered that the specific implementation of the present invention is limited to these descriptions. For those of ordinary skill in the technical field to which the present invention pertains, without departing from the concept of the present invention, some simple deductions and substitutions can also be made, all of which should be regarded as belonging to the protection scope of the present invention.

Claims (5)

1. A tropospheric tomography method related to water vapor spatiotemporal parameters, in the method, the wet refractive index varies with spatial position and its value is obtained by the weighted sum and interpolation of eight nodes of the voxel where it is located, and the horizontal direction adopts the inverse distance weighted inner Interpolation, exponential interpolation is used in the vertical direction, and the parameters required by the interpolation method are obtained according to the real-time estimation of the tomographic wet refractive index field. 2. tropospheric tomography method according to claim 1, is characterized in that, during tropospheric tomography, first vertical direction interpolation and then horizontal direction interpolation or first horizontal direction interpolation and then vertical direction interpolation, preferably first horizontal direction interpolation Interpolate vertically after interpolation. 3. tropochromatographic method according to claim 1 and 2, is characterized in that, Along the ray path from the GNSS satellite to the receiver, the relationship between SWD and the wet refractive index N _w can be expressed as: SWD=∫ _l N _w d _l (1) In the tomographic model, the reconstruction space is discretized into multiple voxels, where l is the oblique path in the SWD; the vertical layer division method considering the water vapor distribution is as shown in Equation 2:

where h _i is the height of the top layer of the i-th layer; n is the total number of vertical layers; h _min is the height of the bottom layer of the tomographic study area; h _max is the height of the top layer of the tomographic study area; The sounding profile data is obtained by fitting with Equation 6; In the parametric model, the wet index of refraction in each voxel varies with position, and the wet index of refraction at any point in the voxel is determined by the weighted sum of the wet index values of the eight nodes N ₁ to N ₈ of the voxel , so that SWD is expressed as the integral of the wet refractive index at the voxel node. Specifically, the Newton-Kertz method is used to solve the integral; the wet refractive index N _W integral of five equally spaced points P ₁ -P ₅ along the inclined path l can be Expressed in the following way:

where D _P1P5 is the intercept from P ₁ to P ₅ , P ₁ , P ₂ , P ₃ , P ₄ , P ₅ are five equidistant points, and the wet refractive index of point Pk is composed of 8 voxels from N ₁ to N ₈ The wet refractive index value of the node is determined by interpolation; The parametric modeling method considering the spatiotemporal distribution of water vapor is shown in Equation 5, and the wet refractive index of P _k can be vertically interpolated with points V ₁ and V ₂ :

Among them, V ₁ is a point on the same height plane as N ₁ -N ₄ , V ₂ is a point on the same height plane as N ₅ -N ₈ , and V ₁ , V ₂ and P _k are on the same line On the vertical line; k is any integer selected from 1 to 5, and h _Pk is the height of the Pk point; where the parameter α can be estimated from the following equation:

where h ₀ refers to the height of the lower surface of the voxel, and _hi refers to the height of any point in the voxel. Equation 6 takes into account the exponential variation of water vapor with vertical height; To take into account the temporal variation of water vapor, use the tomographic profile of the previous period to estimate the α of each voxel in the current period; Additionally, the wet refractive index values for V ₁ and V ₂ are calculated using inverse distance-weighted interpolation:

where i is 1 or 2, where d _j is the distance between _Vi and N _j , and _Vi and N _j are on the same height plane; u is the power of the distance, and N _j is the voxel surface where _Vi is located The 4 surrounding nodes of ; N _w (N _j ) is the wet refractive index value of the 4 surrounding nodes on the surface of the voxel where V _j is located; In order to improve the modeling accuracy, the u value of each vertical layer is estimated in each period using the tomographic results of the previous period. 4. The tropospheric tomography method according to claim 3, wherein all SWDs during modeling are collected to establish a linear system between the SWD and the wet refractive index field: y=Ax (8) where y is the vector of SWD observations, x is the unknown parameter vector containing the wet refractive index of all voxel nodes, and A is the design matrix consisting of the x contributions of the SWD. 5. The tropospheric tomography method according to claim 4, characterized in that, since equation 8 usually has an ill-posed problem, horizontal and vertical constraints are added to make the equation full rank, and then the least squares method is used to solve x.

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