GNSS-based water vapor gradient calculation method

Abstract

The embodiment of the invention provides a GNSS (Global Navigation Satellite System)-based water vapor gradient calculation method. Relates to the meteorological data processing field. The method comprises the following steps: calculating south-north / east-west horizontal gradient oblique path delay according to site information of a GNSS observation station in a research area and a troposphere delay formula; respectively converting the south-north / east-west horizontal gradient oblique path delay into corresponding south-north / east-west oblique path water vapor increment according to the water vapor conversion factor; projecting the south-north / east-west inclined path water vapor increment to the horizontal direction according to the geometric elevation angle to obtain a south-north / east-west water vapor gradient in the horizontal direction; obtaining the horizontal projection distance of the observation station according to the geometric elevation angle and the troposphere top height; calculating a unit distance south-north / east-west water vapor gradient component according to the horizontal south-north / east-west water vapor gradient and the horizontal projection distance of the observation station; and calculating a water vapor gradient value according to the water vapor gradient component. Therefore, the problem that the horizontal gradient delay range is not clear is solved, and non-uniform water vapor information in the north-south direction and the east-west direction of the unit distance can be accurately described.

Description

Technical Field

[0001] The present disclosure relates to the field of meteorological data processing, and in particular to a method for calculating water vapor gradient based on GNSS. Background Art

[0002] Water vapor is the most abundant greenhouse gas on Earth and one of the most active components in the atmosphere. It participates in processes such as water energy cycle, condensation, cloud formation and precipitation. It changes rapidly in time and space and is highly heterogeneous. The water vapor gradient (WVG) can reflect the local asymmetry of water vapor in the atmosphere. Extreme weather such as heavy precipitation, typhoons and storms are often accompanied by strong spatial changes in water vapor, resulting in a large water vapor gradient. Obtaining atmospheric water vapor gradient information is of great significance for severe weather warning and forecasting.

[0003] Existing water vapor detection technologies mainly include sounding, microwave radiometers, satellite remote sensing, etc. Sounding is a traditional water vapor detection method that provides reliable water vapor information, but it is observed twice a day with low temporal resolution, which is not conducive to water vapor observation of extreme events. Microwave radiometers provide reliable water vapor observations at sea, but due to the complex reflectivity on land, the accuracy is relatively low. Satellite-based infrared radiometers can only provide water vapor information under clear sky conditions, while extreme weather is often accompanied by the formation of clouds and rain. Therefore, these water vapor detection methods are subject to many restrictions in the study of extreme weather events.

[0004] The Global Navigation Satellite System (GNSS) has the characteristics of low cost, high precision, high temporal and spatial resolution, and all-weather operation in obtaining water vapor, making it an important means of water vapor detection. Ground-based GNSS has been used by the World Meteorological Organization (WMO) as the primary observation object for measuring precipitable water in the entire atmosphere. It is also widely used as a tool to evaluate the accuracy of other water vapor detection methods and a reference for numerical forecast models. In recent years, with the rapid development of GNSS systems and their successful applications in various fields, the ground-based GNSS station network has been greatly expanded, providing high temporal and spatial resolution water vapor information, laying the foundation for studying the water vapor gradient and changing characteristics of extreme weather events.

[0005] Most GNSS observations use double-difference network solutions and precise single-point positioning methods to estimate tropospheric delay in real time or quasi-real time. Precipitable water vapor (PWV) is obtained by inverting the wet delay in the tropospheric delay. Common atmospheric delay processing software includes GAMIT, GIPSY-OASIS, GSTAR, etc. While solving and obtaining PWV, the GNSS processing software can also obtain the horizontal tropospheric gradient (HTG) information (unit: mm) of the zenith tropospheric delay at each station. The horizontal gradient of delay is due to the asymmetric distribution of the tropospheric atmosphere in spatial orientation, which causes the delay of satellite signals in the tropospheric atmosphere to be different in different propagation path directions, divided into north-south and east-west directions, mainly due to the uneven distribution of water vapor in the atmosphere. In order to more accurately simulate the delay of satellite signal tropospheric propagation path, it is necessary to consider the change of the horizontal gradient delay of the tropospheric atmosphere. However, this delayed horizontal gradient is not a gradient in the meteorological sense. It only represents the delayed superposition of atmospheric asymmetry in the north-south and east-west directions at the measuring station. It does not clearly define the range of horizontal gradient delay, that is, the north-south and east-west gradient delay information generated within a unit distance (unit: mm / km), and the water vapor gradient caused by the north-south and east-west gradient delay within a unit distance (unit: mm / km). Therefore, the horizontal gradient delay cannot meet the precision needs of the meteorological industry, restricting its application in extreme weather events. Summary of the invention

[0006] The present invention provides a GNSS-based water vapor gradient calculation method, device, equipment and storage medium.

[0007] According to a first aspect of the present disclosure, a GNSS-based water vapor gradient calculation method is provided.

[0008] The method includes:

[0009] Collect the site information of GNSS stations in the study area, and solve the horizontal gradient slant path delay in the north-south and east-west directions based on the site information and the tropospheric delay formula;

[0010] According to the water vapor conversion factor, the horizontal gradient oblique path delay in the north-south direction is converted into the water vapor increment in the north-south direction, and the horizontal gradient oblique path delay in the east-west direction is converted into the water vapor increment in the east-west direction;

[0011] The water vapor increments of the oblique paths in the north-south and east-west directions are projected to the horizontal direction according to the geometric altitude angle to obtain the north-south and east-west water vapor gradients in the horizontal direction; wherein the geometric altitude angle is expressed as the angle between the propagation path of the signal from the satellite to the station receiver and the zenith direction passing through the station receiver;

[0012] Determine the height of the tropopause according to the latitude range of the study area; obtain the projection distance of the GNSS station in the horizontal direction according to the geometric altitude angle and the tropopause height;

[0013] According to the north-south and east-west water vapor gradients in the horizontal direction and the projection distance of the GNSS station in the horizontal direction, the north-south and east-west water vapor gradient components per unit distance are calculated; according to the north-south and east-west water vapor gradient components per unit distance, the water vapor gradient value is calculated.

[0014] In some implementations of the first aspect, the tropospheric delay formula is expressed as:

[0015]

[0016] in, represents the total tropospheric delay of the signal from satellite s to station receiver r at time t; the subscript apr represents the value obtained based on the prior model; Δρ apr,r represents the total tropospheric delay value obtained based on the prior model; f represents the projection function of the horizontal gradient slant path delay; Represents the geometric altitude angle; is the projection function of the horizontal gradient slant path delay with respect to the geometric altitude angle; represents a projection function that converts the total tropospheric delay value obtained based on the prior model into the slant path delay corresponding to the geometric altitude angle; Represents the projection function Partial derivatives with respect to geometric altitude angle; represents the azimuth of the satellite s relative to the station receiver r; represents the cosine of the azimuth of the satellite s relative to the station receiver r; represents the sine value of the azimuth of the satellite s relative to the station receiver r; Δ h ρ r (t) represents the zenith direction delay through the station receiver at time t; Δ N ρ r (t) represents the delay change of horizontal gradient in the north-south direction at time t; Δ E ρ r (t) represents the delay change of horizontal gradient in the east-west direction at time t.

[0017] In some implementable embodiments of the first aspect, calculating the north-south and east-west horizontal gradient slant path delays according to the site information and the tropospheric delay formula includes:

[0018] The horizontal gradient slant path delay SD in the north-south direction is obtained using the tropospheric delay formula according to the station information. N and the east-west horizontal gradient oblique path delay SDE ;in,

[0019]

[0020]

[0021] In some possible implementations of the first aspect, Calculated by the following formula:

[0022]

[0023] in, represents the sine value of the geometric altitude angle, Represents the tangent value of the geometric altitude angle; C represents a constant.

[0024] In some implementations of the first aspect, the horizontal gradient slant path delay in the north-south direction is converted into the water vapor increment of the north-south direction slant path, and the horizontal gradient slant path delay in the east-west direction is converted into the water vapor increment of the east-west direction slant path according to the water vapor conversion factor through the following conversion formula:

[0025]

[0026] Where ∏ is the water vapor conversion factor, ΔSW N is the water vapor increment along the oblique path in the north-south direction, ΔSW E It is the water vapor increment along the oblique path in the east-west direction.

[0027] In some implementations of the first aspect, the water vapor increments of the oblique paths in the north-south and east-west directions are projected to the horizontal direction according to the geometric altitude angle by the following formula to obtain the north-south and east-west water vapor gradients in the horizontal direction:

[0028]

[0029] in, Indicates the cosine value of the geometric altitude angle, HG N represents the north-south water vapor gradient in the horizontal direction, HG E Represents the east-west water vapor gradient in the horizontal direction.

[0030] In some implementations of the first aspect, the projection distance of the GNSS station in the horizontal direction is obtained according to the geometric altitude angle and the tropopause height by the following formula:

[0031]

[0032] Among them, D level Indicates the projection distance of the GNSS station in the horizontal direction, H trop is the height of the tropopause, Indicates the tangent value of the geometric altitude angle.

[0033] In some implementations of the first aspect, the water vapor gradient components in the north-south and east-west directions per unit distance are calculated according to the north-south and east-west water vapor gradients in the horizontal direction and the projection distance of the GNSS station in the horizontal direction by the following formula:

[0034]

[0035] Among them, WG N Represents the water vapor gradient component in the north-south direction per unit distance, WG E Represents the water vapor gradient component in the east-west direction per unit distance.

[0036] In some implementations of the first aspect, the water vapor gradient value is calculated according to the water vapor gradient components in the north-south and east-west directions of the unit distance by the following formula:

[0037]

[0038] Where WVG is the water vapor gradient value.

[0039] According to a second aspect of the present disclosure, a GNSS-based water vapor gradient calculation device is provided.

[0040] The device includes:

[0041] The horizontal gradient slant path delay calculation module is used to collect the site information of the GNSS stations in the study area, and calculate the horizontal gradient slant path delay in the north-south and east-west directions according to the site information and the tropospheric delay formula;

[0042] The oblique path water vapor increment acquisition module is used to convert the oblique path delay of the north-south horizontal gradient into the oblique path water vapor increment in the north-south direction, and convert the oblique path delay of the east-west horizontal gradient into the oblique path water vapor increment in the east-west direction according to the water vapor conversion factor;

[0043] A horizontal water vapor gradient acquisition module is used to project the water vapor increments of the oblique paths in the north-south and east-west directions to the horizontal direction according to the geometric altitude angle, so as to acquire the north-south and east-west water vapor gradients in the horizontal direction; wherein the geometric altitude angle is expressed as the angle between the propagation path of the signal from the satellite to the station receiver and the zenith direction passing through the station receiver;

[0044] The station horizontal projection distance acquisition module is used to determine the tropopause height according to the latitude range of the study area; and to obtain the GNSS station horizontal projection distance according to the geometric altitude angle and the tropopause height;

[0045] The water vapor gradient calculation module is used to calculate the water vapor gradient components in the north-south and east-west directions per unit distance according to the north-south and east-west water vapor gradients in the horizontal direction and the projection distance of the GNSS station in the horizontal direction; and calculate the water vapor gradient value according to the water vapor gradient components in the north-south and east-west directions per unit distance.

[0046] According to a third aspect of the present disclosure, an electronic device is provided. The electronic device includes: at least one processor; and a memory connected to the at least one processor in communication; the memory stores instructions executable by the at least one processor, and the instructions are executed by the at least one processor so that the at least one processor can perform the method described above.

[0047] According to a fourth aspect of the present disclosure, a non-transitory computer-readable storage medium storing computer instructions is provided, where the computer instructions are used to cause a computer to execute the method as described above.

[0048] In the present disclosure, the site information of the GNSS stations in the study area is collected, and the horizontal gradient oblique path delay in the north-south and east-west directions is solved according to the site information and the tropospheric delay formula; the horizontal gradient oblique path delay in the north-south direction is converted into the water vapor increment of the oblique path in the north-south direction according to the water vapor conversion factor, and the horizontal gradient oblique path delay in the east-west direction is converted into the water vapor increment of the oblique path in the east-west direction; the water vapor increment of the oblique path in the north-south and east-west directions is projected to the horizontal direction according to the geometric altitude angle to obtain the north-south and east-west water vapor gradients in the horizontal direction; the tropopause height is determined according to the latitude range of the study area; the projection distance of the GNSS station in the horizontal direction is obtained according to the geometric altitude angle and the tropopause height; the north-south and east-west water vapor gradient components per unit distance are calculated according to the north-south and east-west water vapor gradients in the horizontal direction and the projection distance of the GNSS station in the horizontal direction; the water vapor gradient value is calculated according to the north-south and east-west water vapor gradient components per unit distance. In this way, the problem of unclear horizontal gradient delay range is solved, and the description of the uneven water vapor information in the north-south and east-west directions within the unit distance is more accurate, which is suitable for extreme weather.

[0049] It should be understood that the contents described in the summary of the invention are not intended to limit the key or important features of the embodiments of the present disclosure, nor are they intended to limit the scope of the present disclosure. Other features of the present disclosure will become easily understood through the following description. BRIEF DESCRIPTION OF THE DRAWINGS

[0050] The above and other features, advantages and aspects of the embodiments of the present disclosure will become more apparent with reference to the following detailed description in conjunction with the accompanying drawings. The accompanying drawings are used to better understand the present solution and do not constitute a limitation of the present disclosure. In the accompanying drawings, the same or similar reference numerals represent the same or similar elements, among which:

[0051] Figure 1A flow chart of a GNSS-based water vapor gradient calculation method provided in an embodiment of the present disclosure is shown;

[0052] Figure 2 A schematic diagram of a GNSS water vapor gradient calculation principle provided by an embodiment of the present disclosure is shown;

[0053] Figure 3 A water vapor gradient spatial distribution diagram obtained by a GNSS water vapor gradient calculation method provided in an embodiment of the present disclosure is shown;

[0054] Figure 4 A structural diagram of a GNSS-based water vapor gradient calculation device provided in an embodiment of the present disclosure is shown;

[0055] Figure 5 A block diagram of an exemplary electronic device capable of implementing an embodiment of the present disclosure is shown. DETAILED DESCRIPTION

[0056] In order to make the purpose, technical solution and advantages of the embodiments of the present disclosure clearer, the technical solution in the embodiments of the present disclosure will be clearly and completely described below in conjunction with the drawings in the embodiments of the present disclosure. Obviously, the described embodiments are part of the embodiments of the present disclosure, not all of the embodiments. Based on the embodiments in the present disclosure, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present disclosure.

[0057] In addition, the term "and / or" in this article is only a description of the association relationship between the associated objects, indicating that there can be three relationships. For example, A and / or B can represent: A exists alone, A and B exist at the same time, and B exists alone. In addition, the character " / " in this article generally indicates that the associated objects before and after are in an "or" relationship.

[0058] In response to the problems in the background technology, the embodiments of the present disclosure provide a method and device for calculating water vapor gradient based on GNSS. Specifically, the site information of the GNSS stations in the study area is collected, and the horizontal gradient oblique path delays in the north-south and east-west directions are solved according to the site information and the tropospheric delay formula; the horizontal gradient oblique path delays in the north-south direction are converted into the water vapor increment of the north-south oblique path according to the water vapor conversion factor, and the horizontal gradient oblique path delays in the east-west direction are converted into the water vapor increment of the east-west oblique path; the water vapor increments of the north-south and east-west oblique paths are projected to the horizontal direction according to the geometric altitude angle to obtain the north-south and east-west water vapor gradients in the horizontal direction; the tropopause height is determined according to the latitude range of the study area; the projection distance of the GNSS station in the horizontal direction is obtained according to the geometric altitude angle and the tropopause height; the north-south and east-west water vapor gradient components per unit distance are calculated according to the north-south and east-west water vapor gradients in the horizontal direction and the projection distance of the GNSS station in the horizontal direction; the water vapor gradient value is calculated according to the north-south and east-west water vapor gradient components per unit distance. In this way, the problem of unclear horizontal gradient delay range is solved, and the description of water vapor inhomogeneity information in the north-south and east-west directions within a unit distance is more accurate, which is suitable for extreme weather.

[0059] The GNSS water vapor gradient calculation method and device provided by the embodiments of the present disclosure are described in detail below with reference to the accompanying drawings through specific embodiments.

[0060] Figure 1 A flow chart of a GNSS water vapor gradient method provided by an embodiment of the present disclosure is shown. The method 100 includes the following steps:

[0061] S110, collecting site information of GNSS stations in the study area, and solving the horizontal gradient slant path delay in the north-south and east-west directions according to the site information and the tropospheric delay formula.

[0062] In some embodiments, the site information includes observation data, meteorological data, and precise ephemeris data.

[0063] In some embodiments, since the total tropospheric delay maps the delays on all GNSS signal propagation paths to the zenith direction of the station, its value can only reflect the average total delay information in the zenith direction of the station;

[0064] The tropospheric slant delay reflects the delay information in different directions and contains the vertical profile information of water vapor. Therefore, using the slant delay to calculate the water vapor gradient can better meet the precision requirements of the meteorological industry.

[0065] In some embodiments, since the derivation of the projection function of the horizontal gradient slant path delay is based on the assumption of atmospheric horizontal symmetry, in order to obtain higher accuracy, the use of low altitude angle observations requires consideration of changes in the atmospheric horizontal gradient delay. Therefore, the tropospheric slant path delay can be divided into various in-line items and various anisotropies, wherein the various in-line items are the slant path zenith delays of the measuring station, and the various anisotropies are the effects of azimuth asymmetry on the atmospheric delay.

[0066] Furthermore, the zenith direction of the projection function is usually tilted at an angle (β) to represent the change in horizontal gradient delay, such as Figure 2 As shown, the direction with the smallest tropospheric delay after tilting is The zenith direction is Z, and the signal is relative to The altitude angles of and Z are expressed as and z, the altitude angle corresponding to the direction where the tropospheric delay of the signal from the satellite to the station receiver is the smallest The angle between the propagation path of the same signal from the satellite to the station receiver and the zenith direction passing through the station receiver There is the following relationship between them:

[0067]

[0068] Among them, x r is the coordinate value of the measuring station in the x direction, y r is the coordinate value of the measuring station in the y direction, is the azimuth of the station receiver r relative to the satellite s, is the cosine of the azimuth of the station receiver r relative to the satellite s, is the sine of the azimuth of the station receiver r relative to the satellite s.

[0069] In some embodiments, the tropospheric delay formula based on the horizontal gradient change is expressed as:

[0070]

[0071] in, represents the total tropospheric delay of the signal from satellite s to station receiver r at time t; the subscript apr represents the value obtained based on the prior model; Δρ apr,r represents the total tropospheric delay value obtained based on the prior model; f represents the projection function of the horizontal gradient slant path delay; Represents the geometric altitude angle; is the projection function of the horizontal gradient slant path delay with respect to the geometric altitude angle; represents a projection function that converts the total tropospheric delay value obtained based on the prior model into the slant path delay corresponding to the geometric altitude angle; Represents the projection function Partial derivatives with respect to geometric altitude angle; represents the azimuth of the satellite s relative to the station receiver r; represents the cosine of the azimuth of the satellite s relative to the station receiver r; represents the sine value of the azimuth of the satellite s relative to the station receiver r; Δ h ρ r (t) represents the zenith direction delay through the station receiver at time t; Δ N ρ r (t) represents the delay change of horizontal gradient in the north-south direction at time t; Δ E ρ r (t) represents the delay change of horizontal gradient in the east-west direction at time t.

[0072] In some embodiments, the atmospheric horizontal gradient delay change is achieved by increasing Δ N ρ r (t) and Δ E ρ r (t) is implemented with two parameters.

[0073] In some embodiments, calculating the north-south and east-west horizontal gradient slant path delays according to the site information and the tropospheric delay formula includes:

[0074] The horizontal gradient slant path delay SD in the north-south direction is obtained using the tropospheric delay formula according to the station information. N and the east-west horizontal gradient oblique path delay SD E ;in,

[0075]

[0076]

[0077] In some embodiments, the GNSS atmospheric delay processing software can solve the horizontal gradient slant path delay according to the station information and the tropospheric delay formula based on the horizontal gradient change, but the projection functions selected by different GNSS atmospheric delay processing software are slightly different. Taking the projection function used by the GAMIT atmospheric delay processing software as an example, the projection function is expressed as:

[0078]

[0079] in, represents the sine value of the geometric altitude angle, Indicates the tangent value of the geometric altitude angle; C represents a constant; generally speaking, C is 0.003;

[0080] Furthermore, the data that can be obtained using the GNSS atmospheric delay processing software include:

[0081] Total tropospheric delay in the zenith direction (unit: mm), air pressure (unit: hPa), temperature (unit: ℃), relative humidity (unit: %), atmospheric precipitable water (unit: mm), atmospheric precipitable water formal error (unit: mm), total tropospheric delay formal error in the zenith direction (unit: mm), north-south horizontal gradient slant path delay (unit: mm), north-south horizontal gradient formal error (unit: mm), east-west horizontal gradient slant path delay (unit: mm), east-west horizontal gradient formal error (unit: mm), and the quality control codes corresponding to the above data.

[0082] In some embodiments, the estimation is performed using a linear segmentation method. It can also be expressed as:

[0083]

[0084] Among them, a, b, and c are all mapping coefficients;

[0085] Furthermore, combined with and The relationship between and , the tropospheric delay formula based on horizontal gradient changes, and the linear segmentation method According to the calculation formula, when β = 40″, the atmospheric horizontal gradient will cause a delay of about 15 cm to the satellite signal with a geometric altitude angle of 3°.

[0086] S120, converting the north-south horizontal gradient slant path delay into the north-south slant path water vapor increment according to the water vapor conversion factor, and converting the east-west horizontal gradient slant path delay into the east-west slant path water vapor increment.

[0087] In some embodiments, the horizontal gradient slant path delay includes dry horizontal gradient delay and wet horizontal gradient delay. The dry horizontal gradient delay is mainly caused by the horizontal distribution gradient of the atmosphere and atmospheric temperature, and its temporal and spatial variations are relatively stable. The wet horizontal gradient delay is mainly caused by the horizontal distribution gradient of atmospheric water vapor, and its temporal and spatial variations are relatively large, and it accounts for a large proportion of the horizontal gradient delay. Since the dry horizontal gradient delay is numerically much smaller than the wet horizontal gradient delay, the influence of the dry horizontal gradient is ignored, and the horizontal gradient slant path delay is approximated as the wet horizontal gradient delay.

[0088] In some embodiments, the north-south horizontal gradient slant path delay is converted to the north-south slant path water vapor increment, and the east-west horizontal gradient slant path delay is converted to the east-west slant path water vapor increment according to the water vapor conversion factor through the following conversion formula:

[0089]

[0090] Where ∏ is the water vapor conversion factor, ΔSW N is the water vapor increment along the oblique path in the north-south direction, ΔSW E is the water vapor increment along the oblique path in the east-west direction;

[0091] The water vapor conversion factor is calculated using the following formula:

[0092]

[0093] T m is the weighted average temperature in K, ρ w is the density of liquid water, which is 1000kg / m 3 ; R v is the gas constant of water vapor, which is 461.518 J / kg·K; k′2 and k3 are both experimental constants of atmospheric refractive index, which are 16.52 K / hPa and 3.776×105 K2 / hPa respectively;

[0094] Furthermore, T m The Bevis linear regression model is used to determine the expression:

[0095] T m =d+m·T s

[0096] d and m are model coefficients, with values ​​of 70.2 and 0.72 respectively. s is the ground temperature at the measuring station, in K.

[0097] In some embodiments, the oblique path water vapor increment represents the difference between north and south water vapor or the difference between east and west water vapor at the geometric altitude angle.

[0098] S130, projecting the water vapor increments in the north-south and east-west oblique paths to the horizontal direction according to the geometric altitude angle to obtain the north-south and east-west water vapor gradients in the horizontal direction; wherein the geometric altitude angle is represented by the angle between the propagation path of the signal from the satellite to the station receiver and the zenith direction passing through the station receiver.

[0099] In some embodiments, the water vapor increments of the oblique paths in the north-south and east-west directions are projected to the horizontal direction according to the geometric altitude angle by the following formula to obtain the north-south and east-west water vapor gradients in the horizontal direction:

[0100]

[0101] in, Indicates the cosine value of the geometric altitude angle, HG N represents the north-south water vapor gradient in the horizontal direction, HG E Represents the east-west water vapor gradient in the horizontal direction.

[0102] S140, determining the height of the tropopause according to the latitude range of the study area; and obtaining the projection distance of the GNSS station in the horizontal direction according to the geometric altitude angle and the height of the tropopause.

[0103] In some embodiments, determining the tropopause height according to the latitude range of the research area includes:

[0104] The latitude range of the study area is less than 24°N, and the tropopause height is 17km; the latitude range of the study area is between 24°N and 30°N, and the tropopause height is 16km; the latitude range of the study area is between 30°N and 32°N, and the tropopause height is 15km; the latitude range of the study area is between 32°N and 35°N, and the tropopause height is 14km; the latitude range of the study area is between 35°N and 40°N, and the tropopause height is 16km. °N, the tropopause height is 13km; the latitude range of the study area is between 40°N and 42°N, the tropopause height is 12km; the latitude range of the study area is between 42°N and 45°N, the tropopause height is 11km; the latitude range of the study area is between 45°N and 48°N, the tropopause height is 10.5km; the latitude range of the study area is greater than 48°N, the tropopause height is 10km.

[0105] In some embodiments, the projection distance of the GNSS station in the horizontal direction is obtained according to the geometric altitude angle and the tropopause height by the following formula:

[0106]

[0107] Among them, D level Indicates the projection distance of the GNSS station in the horizontal direction, H trop is the height of the tropopause, Indicates the tangent value of the geometric altitude angle.

[0108] S150, calculating the north-south and east-west water vapor gradient components per unit distance according to the north-south and east-west water vapor gradients in the horizontal direction and the projection distance of the GNSS station in the horizontal direction; calculating the water vapor gradient value according to the north-south and east-west water vapor gradient components per unit distance.

[0109] In some embodiments, the water vapor gradient components in the north-south and east-west directions per unit distance are calculated according to the north-south and east-west water vapor gradients in the horizontal direction and the projection distance of the GNSS station in the horizontal direction by the following formula:

[0110]

[0111] Among them, WG NRepresents the water vapor gradient component in the north-south direction per unit distance, WG E Represents the water vapor gradient component in the east-west direction per unit distance.

[0112] In some embodiments, the water vapor gradient value is calculated according to the water vapor gradient components in the north-south and east-west directions of the unit distance by the following formula:

[0113]

[0114] Among them, WVG is the water vapor gradient value; the water vapor gradient value is the total water vapor gradient within a unit distance.

[0115] In some embodiments, for extreme rainstorm weather, the above method can realize the visualization of water vapor convergence area, and can observe the magnitude and direction of water vapor gradient, providing a reference for rainstorm warning / forecast;

[0116] For typhoon weather, the temporal and spatial variation characteristics of the water vapor gradient size and direction are obtained through the above method to characterize the typhoon path and the affected area of ​​the typhoon;

[0117] For weather where an air mass front may occur (such as the Yunnan-Guizhou quasi-stationary front and the South China quasi-stationary front), the water vapor gradient calculated by the above method is used to determine whether an air mass front has appeared. If the water vapor gradient is in the same direction for a long time and the gradient is large, it indicates that an air mass front has appeared.

[0118] For weather where atmospheric rivers occur, since the boundary of the atmospheric river has a large water vapor gradient, the boundary information of the atmospheric river is judged based on the size and direction of the water vapor gradient obtained using the above method.

[0119] The above is an introduction to the method embodiment. The following further illustrates the scheme of the present disclosure by adopting a specific embodiment of the method.

[0120] Taking the rare rainstorm in Beijing-Tianjin-Hebei in July 2023 as an example, the research time is 14:00 on July 29, 2023, and the area of ​​longitude 105°E-135°E and latitude 30°N-50°N is selected as the research area. The GNSS stations in the Beijing-Tianjin-Hebei region are densely distributed. The site information of the stations in this area is collected. Based on the site information, the GAMIT atmospheric delay processing software (a type of GNSS atmospheric delay processing software) is used to solve the horizontal gradient slant path delay in the north-south and east-west directions according to the tropospheric delay formula. Since the north-south horizontal gradient delay and the east-west horizontal gradient delay are small near the zenith (ie f=1), the GAMIT atmospheric delay processing software adjusts the geometric altitude angle to 10° (such as Figure 2 As shown in Figure 2, when the altitude angle is 10°, the RMS of the gradient observed by VLBI is about 5 mm, and the default a priori constraint is 30 mm. According to the water vapor conversion factor, the horizontal gradient oblique path in the north-south direction is delayed by SDN Converted to the oblique path water vapor increment ΔSW in the north-south direction N , delaying the horizontal gradient oblique path in the east-west direction by SD E Converted to the oblique path water vapor increment ΔSW in the east-west direction E ; Based on the altitude angle of 10°, the water vapor increment along the oblique path in the north-south direction is projected to the horizontal direction to obtain the north-south water vapor gradient in the horizontal direction, and the water vapor increment along the oblique path in the east-west direction is projected to the horizontal direction to obtain the east-west water vapor gradient in the horizontal direction; the tropopause height H is determined according to the latitude range of the study area trop ;like Figure 2 As shown, based on the altitude angle of 10° and the tropopause height H trop Get the projection distance D of the measuring station in the horizontal direction level ; Finally, using the north-south water vapor gradient and projection distance D in the horizontal direction level Calculate the north-south water vapor gradient component per unit distance, using the east-west water vapor gradient in the horizontal direction and the projection distance D level Calculate the water vapor gradient component in the east-west direction per unit distance; calculate the total water vapor gradient per unit distance based on the water vapor gradient component in the north-south direction per unit distance and the water vapor gradient component in the east-west direction per unit distance;

[0121] According to the above calculation results, the spatial distribution map of water vapor gradient is drawn, such as Figure 3 As shown in the figure, the rainbow bar represents the water vapor gradient value, and its value range is 200×10 5 ~400×10 5 mm / Km, the arrows point to areas with higher water vapor content. There is strong water vapor convergence in the Beijing-Tianjin-Hebei region. The longer the arrows and the darker the colors on the graph, the greater the water vapor gradient.

[0122] According to the embodiment of the present disclosure, the site information of the GNSS station in the study area is collected, and the horizontal gradient oblique path delay in the north-south and east-west directions is solved according to the site information and the tropospheric delay formula; the horizontal gradient oblique path delay in the north-south direction is converted into the water vapor increment of the oblique path in the north-south direction according to the water vapor conversion factor, and the horizontal gradient oblique path delay in the east-west direction is converted into the water vapor increment of the oblique path in the east-west direction; the water vapor increment of the oblique path in the north-south and east-west directions is projected to the horizontal direction according to the geometric altitude angle to obtain the north-south and east-west water vapor gradients in the horizontal direction; the tropopause height is determined according to the latitude range of the study area; the projection distance of the GNSS station in the horizontal direction is obtained according to the geometric altitude angle and the tropopause height; the north-south and east-west water vapor gradient components per unit distance are calculated according to the north-south and east-west water vapor gradients in the horizontal direction and the projection distance of the GNSS station in the horizontal direction; the water vapor gradient value is calculated according to the north-south and east-west water vapor gradient components per unit distance. In this way, the problem of unclear horizontal gradient delay range is solved, and the description of the uneven water vapor information in the north-south and east-west directions within the unit distance is more accurate, which is suitable for extreme weather.

[0123] It should be noted that, for the aforementioned method embodiments, for the sake of simplicity, they are all described as a series of action combinations, but those skilled in the art should be aware that the present disclosure is not limited by the order of the actions described, because according to the present disclosure, certain steps can be performed in other orders or simultaneously. Secondly, those skilled in the art should also be aware that the embodiments described in the specification are all optional embodiments, and the actions and modules involved are not necessarily required by the present disclosure.

[0124] The above is an introduction to the method embodiment. The following is a further explanation of the scheme disclosed in the present invention through an apparatus embodiment.

[0125] Figure 4 The structure diagram of a GNSS-based water vapor gradient calculation device provided by an embodiment of the present disclosure is shown. The device 400 includes:

[0126] The horizontal gradient slant path delay calculation module 410 is used to collect the site information of the GNSS measurement stations in the study area, and calculate the horizontal gradient slant path delay in the north-south and east-west directions according to the site information and the tropospheric delay formula.

[0127] In some embodiments, module 410 is specifically configured to:

[0128] The tropospheric delay formula is expressed as:

[0129]

[0130] in, represents the total tropospheric delay of the signal from satellite s to station receiver r at time t; the subscript apr represents the value obtained based on the prior model; Δρ apr,r represents the total tropospheric delay value obtained based on the prior model; f represents the projection function of the horizontal gradient slant path delay; Represents the geometric altitude angle; is the projection function of the horizontal gradient slant path delay with respect to the geometric altitude angle; represents a projection function that converts the total tropospheric delay value obtained based on the prior model into the slant path delay corresponding to the geometric altitude angle; Represents the projection function Partial derivatives with respect to geometric altitude angle; represents the azimuth of the satellite s relative to the station receiver r; represents the cosine of the azimuth of the satellite s relative to the station receiver r; represents the sine value of the azimuth of the satellite s relative to the station receiver r; Δ h ρ r (t) represents the zenith direction delay through the station receiver at time t; Δ N ρ r (t) represents the delay change of horizontal gradient in the north-south direction at time t; Δ E ρ r (t) represents the delay change of horizontal gradient in the east-west direction at time t.

[0131] In some embodiments, module 410 is further configured to:

[0132] The horizontal gradient slant path delay in the north-south and east-west directions is calculated based on the site information and the tropospheric delay formula, including:

[0133] The horizontal gradient slant path delay SD in the north-south direction is obtained using the tropospheric delay formula according to the station information. N and the east-west horizontal gradient oblique path delay SD E ;in,

[0134]

[0135]

[0136] In some embodiments, module 410 is further configured to:

[0137] Calculated by the following formula:

[0138]

[0139] in, represents the sine value of the geometric altitude angle, Represents the tangent value of the geometric altitude angle; C represents a constant.

[0140] The oblique path water vapor increment acquisition module 420 is used to convert the north-south horizontal gradient oblique path delay into the north-south oblique path water vapor increment, and convert the east-west horizontal gradient oblique path delay into the east-west oblique path water vapor increment according to the water vapor conversion factor.

[0141] In some embodiments, module 420 is specifically configured to:

[0142] The following conversion formula is used to convert the north-south horizontal gradient slant path delay into the north-south slant path water vapor increment, and the east-west horizontal gradient slant path delay into the east-west slant path water vapor increment according to the water vapor conversion factor:

[0143]

[0144] Where ∏ is the water vapor conversion factor, ΔSW N is the water vapor increment along the oblique path in the north-south direction, ΔSW E It is the water vapor increment along the oblique path in the east-west direction.

[0145] The horizontal water vapor gradient acquisition module 430 is used to project the water vapor increments of the north-south and east-west oblique paths to the horizontal direction according to the geometric altitude angle, so as to obtain the north-south and east-west water vapor gradients in the horizontal direction; wherein the geometric altitude angle is expressed as the angle between the propagation path of the signal from the satellite to the station receiver and the zenith direction passing through the station receiver.

[0146] In some embodiments, module 430 is specifically configured to:

[0147] The following formula is used to project the water vapor increment of the north-south and east-west oblique paths to the horizontal direction according to the geometric altitude angle to obtain the north-south and east-west water vapor gradients in the horizontal direction:

[0148]

[0149] in, Indicates the cosine value of the geometric altitude angle, HG N represents the north-south water vapor gradient in the horizontal direction, HG E Represents the east-west water vapor gradient in the horizontal direction.

[0150] The station horizontal projection distance acquisition module 440 is used to determine the tropopause height according to the latitude range of the study area; and to acquire the horizontal projection distance of the GNSS station according to the geometric altitude angle and the tropopause height.

[0151] In some embodiments, module 440 is specifically configured to:

[0152] The projection distance of the GNSS station in the horizontal direction is obtained according to the geometric altitude angle and the tropopause height through the following formula:

[0153]

[0154] Among them, D level Indicates the projection distance of the GNSS station in the horizontal direction, H trop is the height of the tropopause, Indicates the tangent value of the geometric altitude angle.

[0155] The water vapor gradient calculation module 450 is used to calculate the north-south and east-west water vapor gradient components per unit distance according to the north-south and east-west water vapor gradients in the horizontal direction and the projection distance of the GNSS station in the horizontal direction; and calculate the water vapor gradient value according to the north-south and east-west water vapor gradient components per unit distance.

[0156] In some embodiments, module 450 is specifically configured to:

[0157] The water vapor gradient components in the north-south and east-west directions per unit distance are calculated by the following formula according to the north-south and east-west water vapor gradients in the horizontal direction and the projection distance of the GNSS station in the horizontal direction:

[0158]

[0159] Among them, WG N Represents the water vapor gradient component in the north-south direction per unit distance, WG E Represents the water vapor gradient component in the east-west direction per unit distance.

[0160] In some embodiments, module 450 is further configured to:

[0161] The water vapor gradient value is calculated according to the water vapor gradient components in the north-south and east-west directions of the unit distance using the following formula:

[0162]

[0163] Where WVG is the water vapor gradient value.

[0164] Understandably, Figure 4 Each module / unit in the detection device 400 shown has the function of implementing each step in the detection method 100 provided in the embodiment of the present disclosure and can achieve its corresponding technical effect. For the sake of brevity, it will not be repeated here.

[0165] Figure 5A block diagram of an exemplary electronic device capable of implementing an embodiment of the present disclosure is shown. Electronic device 500 is intended to represent various forms of digital computers, such as laptop computers, desktop computers, workstations, personal digital assistants, servers, blade servers, mainframe computers, and other suitable computers. Electronic device 500 may also represent various forms of mobile devices, such as personal digital processing, cellular phones, smart phones, wearable devices, and other similar computing devices. The components shown herein, their connections and relationships, and their functions are merely examples and are not intended to limit the implementation of the present disclosure described and / or required herein.

[0166] like Figure 5 As shown, the electronic device 500 includes a computing unit 501, which can perform various appropriate actions and processes according to a computer program stored in a read-only memory (ROM) 502 or a computer program loaded from a storage unit 508 into a random access memory (RAM) 503. In the RAM 503, various programs and data required for the operation of the electronic device 500 can also be stored. The computing unit 501, the ROM 502, and the RAM 503 are connected to each other via a bus 504. An I / O interface 505 is also connected to the bus 504.

[0167] Multiple components in the electronic device 500 are connected to the I / O interface 505, including: an input unit 506, such as a keyboard, a mouse, etc.; an output unit 507, such as various types of displays, speakers, etc.; a storage unit 508, such as a disk, an optical disk, etc.; and a communication unit 509, such as a network card, a modem, a wireless communication transceiver, etc. The communication unit 509 allows the electronic device 500 to exchange information / data with other devices through a computer network such as the Internet and / or various telecommunication networks.

[0168] The computing unit 501 may be a variety of general and / or special processing components with processing and computing capabilities. Some examples of the computing unit 501 include, but are not limited to, a central processing unit (CPU), a graphics processing unit (GPU), various dedicated artificial intelligence (AI) computing chips, various computing units running machine learning model algorithms, digital signal processors (DSPs), and any appropriate processors, controllers, microcontrollers, etc. The computing unit 501 performs the various methods and processes described above, such as method 100. For example, in some embodiments, the method 100 may be implemented as a computer software program, which is tangibly contained in a machine-readable medium, such as a storage unit 508. In some embodiments, part or all of the computer program may be loaded and / or installed on the electronic device 500 via ROM 502 and / or communication unit 509. When the computer program is loaded into RAM 503 and executed by the computing unit 501, one or more steps of the method 100 described above may be performed. Alternatively, in other embodiments, the computing unit 501 may be configured to perform the method 100 in any other appropriate manner (e.g., by means of firmware).

[0169] Various implementations of the systems and techniques described above herein can be implemented in digital electronic circuit systems, integrated circuit systems, field programmable gate arrays (FPGAs), application specific integrated circuits (ASICs), application specific standard products (ASSPs), systems on chips (SOCs), load programmable logic devices (CPLDs), computer hardware, firmware, software, and / or combinations thereof. These various implementations can include: being implemented in one or more computer programs that can be executed and / or interpreted on a programmable system including at least one programmable processor, which can be a special purpose or general purpose programmable processor that can receive data and instructions from a storage system, at least one input device, and at least one output device, and transmit data and instructions to the storage system, the at least one input device, and the at least one output device.

[0170] The program code for implementing the method of the present disclosure may be written in any combination of one or more programming languages. These program codes may be provided to a processor or controller of a general-purpose computer, a special-purpose computer, or other programmable data processing device, so that the program code, when executed by the processor or controller, enables the functions / operations specified in the flow chart and / or block diagram to be implemented. The program code may be executed entirely on the machine, partially on the machine, partially on the machine and partially on a remote machine as a stand-alone software package, or entirely on a remote machine or server.

[0171] In the context of the present disclosure, a machine-readable medium may be a tangible medium that may contain or store a program for use by or in conjunction with an instruction execution system, device, or equipment. A machine-readable medium may be a machine-readable signal medium or a machine-readable storage medium. A machine-readable medium may include, but is not limited to, an electronic, magnetic, optical, electromagnetic, infrared, or semiconductor system, device, or equipment, or any suitable combination of the foregoing. A more specific example of a machine-readable storage medium may include an electrical connection based on one or more lines, a portable computer disk, a hard disk, a random access memory (RAM), a read-only memory (ROM), an erasable programmable read-only memory (EPROM or flash memory), an optical fiber, a portable compact disk read-only memory (CD-ROM), an optical storage device, a magnetic storage device, or any suitable combination of the foregoing.

[0172] It should be noted that the present disclosure also provides a non-transitory computer-readable storage medium storing computer instructions, wherein the computer instructions are used to enable a computer to execute method 100 and achieve the corresponding technical effect achieved by executing the method in the embodiment of the present disclosure. For the sake of concise description, they are not repeated here.

[0173] To provide interaction with a user, the systems and techniques described herein can be implemented on a computer having: a display device for displaying information to the user; and a keyboard and a pointing device (e.g., a mouse or trackball) through which the user can provide input to the computer. Other types of devices can also be used to provide interaction with the user; for example, the feedback provided to the user can be any form of sensory feedback (e.g., visual feedback, auditory feedback, or tactile feedback); and input from the user can be received in any form (including acoustic input, voice input, or tactile input).

[0174] The systems and techniques described herein may be implemented in a computing system that includes back-end components (e.g., as a data server), or a computing system that includes middleware components (e.g., an application server), or a computing system that includes front-end components (e.g., a user computer with a graphical user interface or a web browser through which a user can interact with implementations of the systems and techniques described herein), or a computing system that includes any combination of such back-end components, middleware components, or front-end components. The components of the system may be interconnected by any form or medium of digital data communication (e.g., a communication network). Examples of communication networks include: a local area network (LAN), a wide area network (WAN), and the Internet.

[0175] A computer system may include a client and a server. The client and the server are generally remote from each other and usually interact through a communication network. The relationship of client and server is generated by computer programs running on respective computers and having a client-server relationship with each other. The server may be a cloud server, a server of a distributed system, or a server combined with a blockchain.

[0176] It should be understood that the various forms of processes shown above can be used to reorder, add or delete steps. For example, the steps recorded in this disclosure can be executed in parallel, sequentially or in different orders, as long as the desired results of the technical solutions disclosed in this disclosure can be achieved, and this document does not limit this.

[0177] The above specific implementations do not constitute a limitation on the protection scope of the present disclosure. It should be understood by those skilled in the art that various modifications, combinations, sub-combinations and substitutions can be made according to design requirements and other factors. Any modification, equivalent substitution and improvement made within the spirit and principle of the present disclosure shall be included in the protection scope of the present disclosure.

Claims

1. A method for calculating water vapor gradient based on GNSS, characterized in that: include: Collect the site information of GNSS stations in the study area, and solve the horizontal gradient slant path delay in the north-south and east-west directions based on the site information and the tropospheric delay formula; According to the water vapor conversion factor, the horizontal gradient oblique path delay in the north-south direction is converted into the water vapor increment in the north-south direction, and the horizontal gradient oblique path delay in the east-west direction is converted into the water vapor increment in the east-west direction; The water vapor increments of the oblique paths in the north-south and east-west directions are projected to the horizontal direction according to the geometric altitude angle to obtain the north-south and east-west water vapor gradients in the horizontal direction; wherein the geometric altitude angle is expressed as the angle between the propagation path of the signal from the satellite to the station receiver and the zenith direction passing through the station receiver; Determine the height of the tropopause according to the latitude range of the study area; obtain the projection distance of the GNSS station in the horizontal direction according to the geometric altitude angle and the tropopause height; According to the north-south and east-west water vapor gradients in the horizontal direction and the projection distance of the GNSS station in the horizontal direction, the north-south and east-west water vapor gradient components per unit distance are calculated; according to the north-south and east-west water vapor gradient components per unit distance, the water vapor gradient value is calculated.

2. The method according to claim 1, characterized in that The tropospheric delay formula is expressed as: in, represents the total tropospheric delay of the signal from satellite s to station receiver r at time t; the subscript apr represents the value obtained based on the prior model; Δρ apr,r represents the total tropospheric delay value obtained based on the prior model; f represents the projection function of the horizontal gradient slant path delay; Indicates the geometric altitude angle; is the projection function of the horizontal gradient slant path delay with respect to the geometric altitude angle; represents a projection function that converts the total tropospheric delay value obtained based on the prior model into the slant path delay corresponding to the geometric altitude angle; Represents the projection function Partial derivatives with respect to geometric altitude angle; represents the azimuth of the satellite s relative to the station receiver r; represents the cosine of the azimuth of the satellite s relative to the station receiver r; represents the sine value of the azimuth of the satellite s relative to the station receiver r; Δ h ρ r (t) represents the zenith direction delay through the station receiver at time t; Δ N ρ r (t) represents the delay change of horizontal gradient in the north-south direction at time t; Δ E ρ r (t) represents the delay change of horizontal gradient in the east-west direction at time t.

3. The method according to claim 2, characterized in that The calculating the north-south and east-west horizontal gradient slant path delays according to the site information and the tropospheric delay formula includes: The horizontal gradient slant path delay SD in the north-south direction is obtained using the tropospheric delay formula according to the station information. N and the east-west horizontal gradient oblique path delay SD E ;in, 4. The method according to claim 3, characterized in that Said Calculated by the following formula: in, represents the sine value of the geometric altitude angle, Represents the tangent value of the geometric altitude angle; C represents a constant.

5. The method according to claim 4, characterized in that The following conversion formula is used to convert the north-south horizontal gradient slant path delay into the north-south slant path water vapor increment, and the east-west horizontal gradient slant path delay into the east-west slant path water vapor increment according to the water vapor conversion factor: Where ∏ is the water vapor conversion factor, ΔSW N is the water vapor increment along the oblique path in the north-south direction, ΔSW E It is the water vapor increment along the oblique path in the east-west direction.

6. The method according to claim 5, characterized in that The following formula is used to project the water vapor increment of the north-south and east-west oblique paths to the horizontal direction according to the geometric altitude angle to obtain the north-south and east-west water vapor gradients in the horizontal direction: in, Indicates the cosine value of the geometric altitude angle, HG N represents the north-south water vapor gradient in the horizontal direction, HG E Represents the east-west water vapor gradient in the horizontal direction.

7. The method according to claim 6, characterized in that The projection distance of the GNSS station in the horizontal direction is obtained according to the geometric altitude angle and the tropopause height through the following formula: Among them, D level Indicates the projection distance of the GNSS station in the horizontal direction, H trop is the height of the tropopause, Indicates the tangent value of the geometric altitude angle.

8. The method according to claim 7, characterized in that The water vapor gradient components in the north-south and east-west directions per unit distance are calculated by the following formula according to the north-south and east-west water vapor gradients in the horizontal direction and the projection distance of the GNSS station in the horizontal direction: Among them, WG N Represents the water vapor gradient component in the north-south direction per unit distance, WG E Represents the water vapor gradient component in the east-west direction per unit distance.

9. The method according to claim 8, characterized in that The water vapor gradient value is calculated according to the water vapor gradient components in the north-south and east-west directions of the unit distance using the following formula: Where WVG is the water vapor gradient value.

10. A GNSS-based water vapor gradient calculation device, characterized in that: include: The horizontal gradient slant path delay calculation module is used to collect the site information of the GNSS stations in the study area, and calculate the horizontal gradient slant path delay in the north-south and east-west directions according to the site information and the tropospheric delay formula; The oblique path water vapor increment acquisition module is used to convert the oblique path delay of the north-south horizontal gradient into the oblique path water vapor increment in the north-south direction, and convert the oblique path delay of the east-west horizontal gradient into the oblique path water vapor increment in the east-west direction according to the water vapor conversion factor; A horizontal water vapor gradient acquisition module is used to project the water vapor increments of the oblique paths in the north-south and east-west directions to the horizontal direction according to the geometric altitude angle, so as to acquire the north-south and east-west water vapor gradients in the horizontal direction; wherein the geometric altitude angle is expressed as the angle between the propagation path of the signal from the satellite to the station receiver and the zenith direction passing through the station receiver; The station horizontal projection distance acquisition module is used to determine the tropopause height according to the latitude range of the study area; and to obtain the GNSS station horizontal projection distance according to the geometric altitude angle and the tropopause height; The water vapor gradient calculation module is used to calculate the water vapor gradient components in the north-south and east-west directions per unit distance according to the north-south and east-west water vapor gradients in the horizontal direction and the projection distance of the GNSS station in the horizontal direction; and calculate the water vapor gradient value according to the water vapor gradient components in the north-south and east-west directions per unit distance.

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