CN112083453A - Troposphere chromatography method related to water vapor space-time parameters - Google Patents

Troposphere chromatography method related to water vapor space-time parameters Download PDF

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CN112083453A
CN112083453A CN202010964909.4A CN202010964909A CN112083453A CN 112083453 A CN112083453 A CN 112083453A CN 202010964909 A CN202010964909 A CN 202010964909A CN 112083453 A CN112083453 A CN 112083453A
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陈必焰
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Abstract

The invention provides a troposphere chromatography method related to water vapor space-time parameters, wherein the wet refractive index changes along with the space position, the value of the wet refractive index is obtained by eight node weighted summation interpolation of the voxel, the horizontal direction adopts inverse distance weighted interpolation, the vertical direction adopts exponential interpolation, and the parameters required by the interpolation method are obtained by real-time estimation according to a chromatography wet refractive index field. On the basis of the existing parameterized chromatographic model, the invention improves the chromatographic modeling precision by a refined parameterized chromatographic model interpolation method. Particularly, when the gridding division is large or the change of the water vapor space is severe, the improved parameterization method provided by the invention can be used for constructing the troposphere chromatographic model more accurately.

Description

Troposphere chromatography method related to water vapor space-time parameters
Technical Field
The invention relates to the field of geophysical, in particular to a troposphere chromatography method relating to water vapor space-time parameters.
Background
The troposphere is the layer of atmosphere closest to the earth's surface and the most dense layer in the earth's atmosphere, containing approximately 75% by mass of the entire atmosphere, as well as almost all water vapor and aerosols. The troposphere chromatography is to carry out inversion calculation according to the wet delay information obtained by ray scanning and reconstruct a three-dimensional image of the distribution rule of the wet refractive index in the range of the measured troposphere. The wet delay refers to that when an electromagnetic wave signal passes through the troposphere, the signal is refracted by water vapor and is bent, the propagation path is longer than the geometric distance, and the propagation speed is accordingly slower, which is called as the delay of the atmospheric water vapor on the electromagnetic wave signal.
The water vapor is an important component of the earth atmosphere and plays a vital role in various fields such as a natural gas power system, atmospheric environment science, surveying and mapping science and technology, hydrology and the like. Although the water vapor content in the atmosphere only accounts for 0.1-3 percent of the total amount, the water vapor is the most active component in the atmosphere. Many weather changes and natural disasters are directly related to the content and migration of water vapor in the atmosphere, so that the atmospheric water vapor plays a critical role in weather forecast and weather changes. The water vapor in the atmosphere is mainly concentrated in the convection layer, and the high dynamic and rapid change characteristics of the water vapor make the accurate and timely acquisition of the water vapor distribution with high spatial and temporal resolution a very difficult task. The high-precision atmospheric water vapor field can be reconstructed by a ground-based GNSS (Global Navigation Satellite System) chromatography technology, and the method has the advantages that a plurality of traditional water vapor detection means have incomparable advantages.
The regional three-dimensional water vapor field can be reconstructed by utilizing the SWD (slope Wet Delay) data densely interwoven in the upper space of the region and combining with the chromatography technology. The commonly used tomographic modeling method is to take a voxel as a minimum cutting unit, discretize an inversion region into a small grid, and then use SWD data to calculate the wet refractive index in each grid. In traditional chromatographic model researches, the uniform and unchanged water vapor distribution in a single grid is assumed, but when the water vapor is strongly changed in space or the grid range is large, the assumption is not reasonable, and a large model error is caused. In contrast, some researchers have proposed a numerical integration parameterization method, which uses different interpolation algorithms to interpolate the wet refractive index of any point in the grid, and uses a numerical integration algorithm to discretize the wet delay of the inclined path. The parameters to be solved in the method are the wet refractive indexes of the vertexes of the grids, the unreasonable assumption that the water vapor distribution in the unit grids is uniform and unchanged in the traditional chromatographic modeling is overcome, and the number of the parameters to be solved is not obviously increased. The numerical integration parameterization method is the key for constructing the high-spatial-resolution chromatographic model, and the method can better invert the inverse increment of the water vapor profile, so that the mathematical model is more reasonable. However, the bilinear/spline interpolation adopted in the existing parameterized model does not take the physical characteristics of the water vapor space-time change into account, so that the water vapor interpolation method is not accurate enough, and the method needs to be researched and improved deeply.
That is, existing tropospheric tomography modeling methods can be basically divided into two categories: one type is a non-parametric model in which the water vapor in each voxel during the analysis period is considered to be uniformly distributed. The other is a parameterized model in which the water vapor in each voxel varies with spatial position over the analysis period.
Wherein the non-parametric model spatially discretizes the troposphere into a plurality of voxels and assumes a constant and uniform distribution of the wet refractive index within each voxel. The method has the advantages of relatively few parameters involved in modeling and simple operation. But when the grid partitioning is large or extreme weather conditions occur, modeling errors that cannot be ignored result.
The parameterized model also discretizes the troposphere into a plurality of voxels, but the wet refractive index in each voxel is changed according to the spatial position, and the wet refractive index at any point is formed by eight nodes (such as N in FIG. 1) of the voxel1～N8These eight nodes) are obtained via horizontal and vertical interpolation. Adverse effects caused by unreasonable grid division can be solved, and meanwhile, the calculation efficiency is ensured.
However, in practice, moisture varies greatly spatially, and in particular in the vertical direction or in extreme weather conditions, this can lead to model errors that cannot be ignored for non-parametric models. Finer mesh partitioning can mitigate the adverse effects of this unreasonable assumption, but it increases computational efficiency and inter-voxel constraints can also impact the results. The parameterized model can solve adverse effects caused by unreasonable grid division, and meanwhile, the calculation efficiency is guaranteed. The wet refractive index of any point in the parameterized model is obtained by performing horizontal and vertical interpolation on the eight nodes of the voxel. However, the existing interpolation methods (such as linear interpolation and cubic spline interpolation) do not take into account that the water vapor space-time parameters cause insufficient modeling precision. When the grid division is large or the change of the water vapor space is severe, the inversion error is large, and the application of troposphere chromatography is limited to a certain extent.
In order to solve the above problems and to build a more accurate parameterized tropospheric tomography model, there is a need in the art for an improved tropospheric tomography method.
Disclosure of Invention
The invention is based on a parameterized troposphere tomographic model, and develops an improved troposphere tomographic parameterization method aiming at the problem of insufficient accuracy of an interpolation method thereof. The defect that water vapor space-time parameters are not considered in the traditional modeling is overcome, and the parameterized troposphere chromatographic model is refined.
That is, the invention provides a troposphere tomography method related to water vapor space-time parameters, in the method, the wet refractive index changes along with the space position, the value of the wet refractive index is obtained by eight node weighted summation interpolation of the voxel, the horizontal direction adopts inverse distance weighted interpolation, the vertical direction adopts exponential interpolation, and the parameters required by the interpolation method are obtained by real-time estimation according to the chromatography wet refractive index field.
The present invention relates to the space-time parameters of water vapor, namely the time parameters and the space parameters thereof, wherein the space parameters of water vapor comprise the interpolation of the horizontal direction and the vertical direction thereof, and the time parameters of water vapor are dynamically different estimated values obtained according to the time transformation.
In a specific embodiment, during tropospheric tomography, vertical interpolation is performed followed by horizontal interpolation or horizontal interpolation is performed followed by vertical interpolation, preferably horizontal interpolation is performed followed by vertical interpolation. This may make the calculation more simplified.
In a particular embodiment of the method of the present invention,
SWD and Wet along the ray path from the GNSS satellite to the receiverRefractive index NwThe relationship between can be expressed as:
SWD＝∫l Nwdl (1)
discretizing the reconstructed space into a plurality of voxels in the tomographic model, wherein l is an oblique path in the SWD; the vertical layer division method considering the water vapor distribution is as follows:
Figure BDA0002681914740000031
wherein h isiThe ith layer top height; n is the total number of vertical layers; h isminIs the height of the lowest layer of the chromatographic study area; h ismaxIs the top level of the chromatographic study area; alpha is a water vapor vertical change parameter and can be obtained by fitting historical sounding profile data through a formula 6;
in the parameterized model, the wet refractive index in each voxel is changed along with the position, and the wet refractive index at any point in the voxel is formed by 8 nodes N of the voxel1To N8Such that SWD is expressed as an integral of the wet refractive index at the voxel node, the integral being solved, in particular, using newton's method; five equidistant points P along the inclined path 11-P5Wet refractive index NWThe integral can be expressed in the following way:
Figure BDA0002681914740000032
wherein DP1P5Is P1To P5Intercept of, P1，P2，P3，P4，P5Is five equidistant points, point PkWet refractive index of N1To N8The wet refractive index values of the 8 voxel nodes are determined by interpolation;
parameterized modeling method considering water vapor space-time distribution, see formula 5, PkCan be measured by point V1And V2Vertical interpolation:
Figure BDA0002681914740000033
wherein V1Is equal to N1～N4Points on the same level, V2Is equal to N5～N8Points on the same level, and V1、V2And PkThe points are positioned on the same vertical line; k is any integer selected from 1 to 5, hPkIs PkThe height of the point;
wherein the parameter α can be estimated from:
Figure BDA0002681914740000034
wherein h is0Refers to the height of the voxel lower surface, hiThe height of any point in a voxel is referred to, and the exponential change characteristic of water vapor along with the vertical height is considered in formula 6;
in order to take the change of water vapor time into consideration, the chromatographic profile of the previous time interval is used for estimating alpha of each voxel of the current time interval;
in addition, V1And V2Is calculated using inverse distance weighted interpolation:
Figure BDA0002681914740000041
wherein i is 1 or 2, wherein djIs ViAnd NjA distance between, ViAnd NjOn the same height plane; u is a power of the distance, NjIs referred to as V i4 surrounding nodes of the voxel surface; n is a radical ofw(Nj) Is VjWet refractive index values of 4 surrounding nodes of the surface of the voxel at which it is located;
in order to improve the modeling precision, the u value of each vertical layer is estimated in each time interval by using the chromatography result of the previous time interval.
In one specific embodiment, all SWDs during modeling are collected, establishing a linear system between the SWD and the wet 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 composed of the SWD's x contributions.
In one specific embodiment, since equation 8 generally has an ill-defined problem, horizontal and vertical constraints are added to make the equation full-rank, and then a least squares method is used to solve for x.
The invention has the advantages that:
on the basis of the existing parameterized chromatographic model, the invention improves the chromatographic modeling precision by a refined parameterized chromatographic model interpolation method. The traditional parameterized troposphere chromatographic model interpolation method usually adopts linear interpolation or spline interpolation, does not consider water vapor space-time distribution characteristics, and particularly has larger inversion error when grid division is larger or water vapor space change is severe, but the improved parameterized method provided by the invention can more accurately construct a troposphere chromatographic model, and for example, compared with a nonparametric method and a traditional parameterized method, the inversion accuracy of a new parameterized method provided by the invention is respectively improved by 54% and 10% in practical case application. Based on a large number of comparative analyses, the parameterized chromatographic model considering the water vapor space-time distribution provided by the invention can obviously improve the chromatographic resolution precision compared with the traditional model. Therefore, the method can effectively make up for the defects of the traditional model and determine the wet refractive index field structure more accurately.
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Fig. 1 is a schematic diagram of the discretization of a troposphere tomography model provided by the invention.
FIG. 2 is a graph of RMS error (graph a) versus relative RMS error (graph b) for a non-parametric model (Tomo-I), a conventional parametric model (Tomo-II), and a parametric model provided by the present invention (Tomo-III).
FIG. 3 is a RMS distribution plot of ERA5 versus a non-parametric model (FIG. 3a), a conventional parametric model (FIG. 3b), and an improved parametric model provided by the present invention (FIG. 3 c).
Detailed Description
According to the method, according to the water vapor space change characteristic, the wet refractive index of any point in the troposphere space is obtained by weighting and summing eight nodes of a voxel, the reverse distance weighted interpolation is adopted in the horizontal direction, the exponential interpolation is adopted in the vertical direction, and the required parameters in the interpolation method are obtained according to the chromatography wet refractive index field dynamic estimation, so that the defect that water vapor space-time parameters are not considered in the past modeling is overcome, and the parameterized troposphere chromatography model is refined. The principle and the process are as follows:
SWD and wet refractive index N along the GNSS satellite to receiver ray pathwThe relationship between can be expressed as:
SWD＝∫l Nwdl (1)
as shown in fig. 1, i is the diagonal path in the SWD. The tomographic technique can invert the spatial distribution of the wet refractive index based on the spatially interleaved SWD from each direction over the tomographic period. Typically, the tomographic model has to discretize the reconstruction space into a plurality of voxels (see fig. 1). In the prior art, vertical layering is artificially determined during grid division, and the vertical distribution of water vapor is not considered. The invention provides a vertical layer dividing method considering water vapor distribution, which comprises the following steps:
Figure BDA0002681914740000051
wherein h isiThe ith layer top height; n is the total number of vertical layers; h isminIs the height of the lowest layer of the chromatographic study area; h ismaxIs the top level of the chromatographic study area; alpha is a water vapor vertical variation parameter and can be obtained by fitting historical sounding profile data through a formula 6. Historical sounding profile data is public data that can be readily obtained.
In the traditional non-parametric approach, it is assumed that the water vapor within each voxel is constant and evenly distributed over the modeling period. Thus, each SWD can be viewed as the sum of all segments that pass through those voxels along the ray path, so equation (1) can be approximated as:
Figure BDA0002681914740000054
whereini refers to voxel i, n is the number of voxels traversed by the SWD,
Figure BDA0002681914740000052
refers to the wet refractive index, d, in voxel iiIs the intercept of the SWD ray path for voxel i.
In a parametric model (including the prior art and the present invention), the wet refractive index within each voxel is position dependent. The wet refractive index at any point within a voxel is determined by a weighted sum of the wet refractive index values of the 8 nodes of the voxel, such that SWD is expressed as the integral of the wet refractive index at the voxel node. Since an analytical solution for the integration cannot be obtained in most cases, newton's method is used to solve for the integration. As shown in FIG. 1, the wet refractive index (i.e., N) along P1-P5W) The integral can be expressed in the following way:
Figure BDA0002681914740000053
wherein DP1P5Is P1To P5Intercept of, P1，P2，P3，P4，P5Are five equidistant points. Point PkHas a wet refractive index of 8 voxel nodes (i.e., N)1，N2，…，N8) And (4) determining interpolation.
In the past research, the interpolation method usually adopts linear interpolation or spline interpolation, and does not consider the water vapor space-time distribution characteristic. When the grid division is large or the change of the water vapor space is severe, the inversion error is large, and the application of troposphere chromatography is limited to a certain extent.
The invention provides a parameterized modeling method considering water vapor space-time distribution. With P3For example, the wet refractive index may be represented by point V1And V2Vertical interpolation:
Figure BDA0002681914740000061
wherein the parameter α can be estimated from:
Figure BDA0002681914740000062
wherein h is0Refers to the height of the voxel lower surface, hiRefers to the height of any point within the voxel, and equation (6) takes into account the characteristic of the exponential change of water vapor with vertical height. To account for moisture time variations, the tomographic profile of the previous session is used to estimate α for each voxel of the current session. In addition, V1And V2Is calculated using inverse distance weighted interpolation:
Figure BDA0002681914740000063
wherein i is 1 or 2, ViI.e. V in formula 51And V2. Wherein d isjIs ViAnd NjA distance between, ViAnd NjOn the same plane. u is a power of the distance, NjIs referred to as V i4 surrounding nodes of the surface of the voxel. N is a radical ofw(Nj) (j-1, 2, 3, 4) is ViWet refractive index values of 4 surrounding nodes of the surface of the voxel at which it is located. In order to improve the modeling precision, the u value of each vertical layer is estimated in each time interval by using the chromatography result of the previous time interval.
Collecting all SWDs during modeling, a linear system between the SWD and the wet 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 composed of the SWD's x contributions. Because the equation (8) usually has an ill-defined problem, horizontal and vertical constraints are required to be added to make the equation of full rank, and then the least square method is used to solve x.
The case of fig. 2 shows that the improved parameterized model provided by the invention can significantly improve the accuracy of the chromatographic water vapor field. FIG. 2 shows a graph of RMS error versus relative RMS error as a function of height for a non-parametric model (Tomo-I), a conventional parametric model (Tomo-II), and an improved parametric model of the present invention (Tomo-III). Compared with the other two models, the improved parameterized model can obviously improve the chromatographic accuracy, and the RMS error of the improved parameterized model is gradually reduced along with the height. The improved parameterized model increases from 8% at the lowest level to 443% at the highest level in terms of relative RMS error. Compared with a non-parametric model (blue) and a traditional parametric model (pink), the accuracy of the wet refractive index value of the improved parametric model inversion is greatly improved. In fig. 2a and 2b, curves of the non-parametric model (Tomo-I), the conventional parametric model (Tomo-II) and the improved parametric model of the present invention (Tomo-III) are shown from right to left, respectively.
FIG. 3 shows the comparison of chromatographic wet refractive index with the ERA5 reanalyzed data. FIG. 3(a) shows the results of ERA5 compared to a non-parametric model, FIG. 3(b) shows the results of ERA5 compared to a conventional parametric model, and FIG. 3(c) shows the results of ERA5 compared to a modified parametric model. It is clear that both the non-parametric model and the conventional parametric model have large deviations from the data reanalyzed by ERA 5. The RMS error variation ranges of the three methods Tomo-I, Tomo-II and Tomo-III are respectively 7.0-16.8 mm/km, 5.9-15.8 mm/km and 6.0-11.0 mm/km. For the improved parameterized model of the invention, most regional RMS error values are less than 10mm/km, and the data is analyzed by ERA5 to show higher consistency. On the whole, the accuracy of the steam field inverted by the improved parameterized model is improved by 17% and 8% respectively compared with that of a nonparametric model and a traditional parametric model.
The foregoing is a more detailed description of the invention in connection with specific preferred embodiments and it is not intended that the invention be limited to these specific details. For those skilled in the art to which the invention pertains, several simple deductions and substitutions can be made without departing from the spirit of the invention, and all shall be considered as belonging to the protection scope of the invention.

Claims (5)

1. In the method, the wet refractive index changes along with the space position, the value of the wet refractive index is obtained by eight node weighted summation interpolation of the voxel, the horizontal direction adopts inverse distance weighted interpolation, the vertical direction adopts exponential interpolation, and the parameters required by the interpolation method are obtained by real-time estimation according to a chromatography wet refractive index field.
2. Tropospheric tomography method according to claim 1, characterized in that during tropospheric tomography, vertical interpolation followed by horizontal interpolation or horizontal interpolation followed by vertical interpolation, preferably horizontal interpolation followed by vertical interpolation.
3. Tropospheric chromatography method according to claim 1 or 2, characterized in that,
SWD and wet refractive index N along the GNSS satellite to receiver ray pathwThe relationship between can be expressed as:
SWD＝∫lNwdl (1)
discretizing the reconstructed space into a plurality of voxels in the tomographic model, wherein l is an oblique path in the SWD; the vertical layer division method considering the water vapor distribution is as follows:
Figure FDA0002681914730000011
wherein h isiThe ith layer top height; n is the total number of vertical layers; h isminIs the height of the lowest layer of the chromatographic study area; h ismaxIs the top level of the chromatographic study area; alpha is a water vapor vertical change parameter and can be obtained by fitting historical sounding profile data through a formula 6;
in the parameterized model, the wet refractive index in each voxel is changed along with the position, and the wet refractive index at any point in the voxel is formed by 8 nodes N of the voxel1To N8Such that SWD is expressed as an integral of the wet refractive index at the voxel node, the integral being solved, in particular, using newton's method; five equidistant points P along the inclined path l1-P5Wet refractive index NWThe integral can be expressed in the following way:
Figure FDA0002681914730000012
wherein DP1P5Is P1To P5Intercept of, P1,P2,P3,P4,P5Is five equidistant points, the wet refractive index of point Pk is from N1To N8The wet refractive index values of the 8 voxel nodes are determined by interpolation;
parameterized modeling method considering water vapor space-time distribution, see formula 5, PkCan be measured by point V1And V2Vertical interpolation:
Figure FDA0002681914730000013
wherein V1Is equal to N1～N4Points on the same level, V2Is equal to N5～N8Points on the same level, and V1、V2And PkThe points are positioned on the same vertical line; k is any integer selected from 1 to 5, hPkHeight of Pk point;
wherein the parameter α can be estimated from:
Figure FDA0002681914730000021
wherein h is0Refers to the height of the voxel lower surface, hiThe height of any point in a voxel is referred to, and the exponential change characteristic of water vapor along with the vertical height is considered in formula 6;
in order to take the change of water vapor time into consideration, the chromatographic profile of the previous time interval is used for estimating alpha of each voxel of the current time interval;
in addition, V1And V2Is calculated using inverse distance weighted interpolation:
Figure FDA0002681914730000022
wherein i is 1 or 2, wherein djIs ViAnd NjA distance between, ViAnd NjOn the same height plane; u is a power of the distance, NjIs referred to as Vi4 surrounding nodes of the voxel surface; n is a radical ofw(Nj) Is VjWet refractive index values of 4 surrounding nodes of the surface of the voxel at which it is located;
in order to improve the modeling precision, the u value of each vertical layer is estimated in each time interval by using the chromatography result of the previous time interval.
4. Tropospheric tomography method according to claim 3, characterized in that all SWDs during modeling are collected, establishing a linear system between SWD and 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 composed of the SWD's x contributions.
5. Tropospheric tomography method according to claim 4, characterized in that since equation 8 usually has ill-posed problems, then 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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夏朋飞 等: ""地基GPS联合COSMIC掩星数据的水汽三维层析研究"", 《武汉大学学报（信息科学版）》 *

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CN114357770A (en) * 2022-01-04 2022-04-15 中南大学 Troposphere chromatography method
CN114357770B (en) * 2022-01-04 2022-10-11 中南大学 Troposphere chromatography method
JP7127928B1 (en) * 2022-03-15 2022-08-30 日本電気株式会社 Water vapor observation method
WO2023175735A1 (en) * 2022-03-15 2023-09-21 日本電気株式会社 Water vapor observation method
CN115184967A (en) * 2022-09-14 2022-10-14 中国石油大学(华东) GNSS correction method for scanning water vapor data of microwave radiometer

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