Method for atmospheric reduction considering terrain and three-dimensional density distribution in geoid determination, electronic device and storage medium

Abstract

This invention belongs to the field of geodesy technology, specifically providing a rigorous method, electronic device, and storage medium for atmospheric reduction in geoid determination that takes into account topography and three-dimensional density distribution. The method includes constructing a global three-dimensional atmospheric density model; establishing a precise calculation model of atmospheric effects; and determining the impact of atmospheric reduction on the geoid. This invention proposes a rigorous atmospheric mass adjustment scheme using the generalized Helmert condensation method; it constructs a global three-dimensional atmospheric density model using actual atmospheric data and establishes a precise calculation model of atmospheric effects in conjunction with a global digital elevation model; and it employs a high-precision gravity forward modeling algorithm based on spherical prisms and thin-layer spherical units, taking into account the effects of Earth's curvature, to accurately calculate the direct atmospheric effects, major indirect atmospheric effects, and minor indirect atmospheric effects.

Description

Technical Field

[0001] This invention belongs to the field of geodetic surveying technology and relates to a rigorous atmospheric reduction method that takes into account topography and three-dimensional density distribution in geoid determination, as well as electronic equipment and storage medium. Background Technology

[0002] The theoretical and methodological foundation for geoid determination lies in geodetic boundary value theory and potential field theory. One of the key issues is how to accurately handle the influence of external masses on the geoid, requiring topographic and atmospheric reduction. In existing technologies, topographic reduction typically employs residual topographic modeling and the second type of Helmert condensation. The residual topographic modeling method is used for quasi-geoid calculations within the Molodensky framework; the second type of Helmert condensation is primarily used for geoid calculations within the Stokes framework, and has also been introduced into the Molodensky framework in recent years.

[0003] Atmospheric corrections currently primarily employ the IAG (International Association of Geodesy) method. This method calculates the corresponding atmospheric corrections by removing the effects of actual and normal atmospheric mass from measured and normal gravity, respectively; that is, the atmospheric correction is the difference between normal and actual atmospheric gravity. However, this method neglects the following fact during the calculation: 1) There is a difference between the actual atmospheric mass and the normal atmospheric mass. Simply removing the two different masses may cause a difference between the actual Earth mass after mass adjustment and the reference ellipsoid mass, resulting in a systematic bias in the calculated geoid model. 2) The atmospheric density model used in this method is the USSA1976 (US Standard Atmosphere 1976) model. This model only considers the density distribution of the atmosphere in the radial direction, and the radial density distribution is consistent at all locations. However, the actual atmospheric density also varies with different horizontal locations. 3) This method approximates the ground as an ellipsoid or even a sphere in the process of calculating atmospheric effects, but in reality, there are topographical undulations at the interface between the atmosphere and the Earth's surface; 4) This method can only calculate the direct impact of atmospheric mass adjustments on gravity, but it cannot calculate the major indirect impact on gravitational potential or the minor indirect impact on gravity. In summary, the traditional IAG method has theoretical and technical shortcomings.

[0004] Currently, the international community has proposed the strategic goal of establishing a "geoid with 1-centimeter accuracy," which places higher demands on the fine processing of topography and air quality. Given the current abundance of research on rigorous topographic quality processing but scarcity of research on rigorous air quality processing, there is an urgent need in this field to propose more rigorous air quality processing techniques for geoid determination. Summary of the Invention

[0005] This invention aims to provide a rigorous atmospheric reduction method for determining the geoid, taking into account topography and three-dimensional density distribution, for calculating the impact of atmospheric quality adjustments on the determination of the geoid.

[0006] This invention provides a rigorous atmospheric reduction method for determining the geoid that takes into account topography and three-dimensional density distribution, comprising the following steps: Step 1: Calculate the atmospheric density and elevation of all grid points in each model layer of the global reanalysis grid dataset of the ERA-Interim or ERA5 model layer provided by ECMWF to obtain a global three-dimensional atmospheric density model. Step 2: Using a global three-dimensional atmospheric density model, analyze the radial direction of each grid cell. The atmospheric density and elevation provided by each grid point are used to obtain the atmospheric density and elevation at preset dense interpolation points in the same radial direction, thereby determining the atmospheric mass distribution model. Based on the atmospheric mass distribution model, atmospheric mass is discretized to obtain a series of discretized spherical prisms; Based on the spatial geometric position information of each spherical prism, determine the interpolation point located within each spherical prism. Based on the atmospheric density and elevation provided by the interpolation points within each spherical prism, a cubic polynomial density function varying with respect to elevation along the radial direction for each spherical prism is determined using least-squares fitting. ; The cubic polynomial density function with respect to elevation After transformation, we obtain the cubic polynomial density function of the geocentric radial vector in spherical coordinates. ; Based on an atmospheric mass distribution model, a discretized spherical prism, and a cubic polynomial density function with respect to the geocentric radius. All in the radial direction of each grid A series of spherical prisms are compressed and condensed radially into the selected condensation layer, resulting in a series of spherical thin-layer units with the same horizontal dimensions as the spherical prisms. Step 3: Based on a series of spherical prisms and a series of spherical thin-layer units, the corresponding high-precision gravity forward modeling algorithm is used to calculate the gravitational effect of the actual atmospheric mass and atmospheric condensation layer on ground points, as well as the gravitational potential effect of the actual atmospheric mass and atmospheric condensation layer on geoid points, and finally determine the direct, main, and secondary indirect effects of the dense atmosphere. The main indirect effects of the dense atmosphere are removed from the calculated adjusted geoid to determine the actual geoid.

[0007] Furthermore, the ERA-Interim model layer global reanalysis grid dataset contains global grid data for 60 model layers; The ERA5 model layer global reanalysis grid dataset contains global grid data for 137 model layers.

[0008] Furthermore, both the ERA-Interim and ERA5 model layer global reanalysis grid datasets contain a single layer of surface gravity potential. The natural logarithm of surface pressure And the temperature of all grid points on all model layers. and humidity .

[0009] Furthermore, the specific process of obtaining the global three-dimensional atmospheric density model is as follows: Download all ERA-Interim or ERA5 model layer global reanalysis grid datasets for the selected time period from the ECMWF website to obtain the raw data; the raw data includes surface gravity potential data for one layer of grid. The natural logarithm of surface pressure And the temperature of all grid points on all model layers. and humidity ; The raw data are averaged to obtain the average surface potential and average surface pressure representing the selected time period. Average temperature and average humidity ; Based on average surface pressure Calculate the atmospheric density of each grid point in the model layer. ; Based on mean surface gravity potential Calculate the elevation of each grid point in the model layer. .

[0010] Furthermore, the atmospheric density of each grid point in the model layer is calculated. The specific process is as follows: Calculate the pressure at each grid point in the model layer. ; pressure The expression is as follows: ; in, Represented as the model layer number, and 1 represents the model layer grid data furthest from the Earth's surface. Represented as the model layer grid data closest to the Earth's surface; and Represented as corresponding to the first The pressure of two half-model layer grid points in a model layer; Pressure of half-model grid points The expression is as follows: ; in, Represented as an index number, and , and These are all coefficients used to define the vertical coordinates and can be obtained from the ECMWF website; Expressed as average surface pressure; Calculate the atmospheric density of each grid point in the model layer. ; Atmospheric density The expression is as follows: ; ; ; in, Expressed as the gas constant for dry air, Represented as virtual temperature, J It is represented as joules. kg Expressed in kilograms, It is expressed in Kelvin (Celsius).

[0011] Furthermore, the elevation of each grid point in the model layer is calculated. The specific process is as follows: Let the gravitational potentials of two adjacent half-model layer grid points in each model layer be respectively and ; but and The expression relating the gravitational potentials between them is as follows: ; Furthermore, the gravity potential of any half-model layer grid point The expression is as follows: ; in, Represented as model layer number, Represented as located at the th Pressure of the grid points in the semi-model layer below the model layer Represented as located at the th Pressure of the grid points in the half-model layer above the model layer; Furthermore, the gravity potential of each grid point in the model layer The expression is as follows: ; ; Calculate the gravity potential of each grid point in the model layer. The expression is as follows: ; ; in, Represented as Gravity at latitude mean sea level Represented as the transmission coefficient; Calculate the elevation of each grid point in the model layer. The expression is as follows: ; in, It is represented as the co-latitude of each grid point in the same model layer.

[0012] Furthermore, the specific process of step three is as follows: Using a high-precision gravity forward modeling algorithm based on spherical prisms whose density varies radially as a cubic polynomial function, the relationship between each spherical prism and the ground point is calculated. The gravitational effects are superimposed to obtain the actual atmospheric gravitational effects that need to be removed. ; Actual atmospheric gravitational effects Extending downwards to the geoid Point mapping point The extension value is equivalent to the actual atmospheric mass at [value missing]. Gravitational effect of a point ; Furthermore, calculate the pairs of each spherical prism. The gravitational potential effect at a point is obtained by superimposing the gravitational potential effects at that point to obtain the actual atmospheric gravitational potential effect. ; Using a high-precision gravity forward modeling algorithm based on spherical thin-layer elements with constant surface density, the relationship between each spherical thin-layer element and the ground point is calculated. The gravitational effects are superimposed to obtain the atmospheric condensate gravitational effects that need to be compensated. ; gravitational effects of atmospheric condensation layer Extending downwards to the geoid The extension value of a point is equivalent to the atmospheric condensation layer at that point. Gravitational effect of a point ; Furthermore, the pair of each spherical thin-layer element is calculated. The gravitational potential effect of a point is obtained by superimposing the gravitational potential effect of the atmospheric condensate layer. ; based on and Calculate ground points The dense atmosphere directly affects ; based on and Calculate the projection points of the geoid The dense atmosphere has a secondary indirect influence and geoid projection points The dense atmosphere mainly has an indirect impact ; Will Remove the calculated adjusted geoid from the actual geoid.

[0013] As a further aspect of the present invention, the present invention also provides an electronic device, including a memory, one or more processes, and one or more programs stored in the memory, said one or more programs including instructions for executing a rigorous atmospheric reduction method for geoid determination that takes into account topography and three-dimensional density distribution as described above.

[0014] As a further aspect of the present invention, the present invention also provides a storage medium comprising one or more programs executable by one or more processors of an electronic device, the one or more programs comprising instructions for executing a rigorous atmospheric reduction method for geoid determination that takes into account topography and three-dimensional density distribution as described above.

[0015] Compared with the prior art, the present invention has the following beneficial effects: (1) To address the shortcomings of existing atmospheric methods used in geoid determination, such as insufficient rigor in atmospheric quality adjustment schemes, imprecise atmospheric influence calculation models, and inaccurate atmospheric influence calculations, this invention proposes a rigorous atmospheric quality adjustment scheme using the generalized Helmert condensation method. A global three-dimensional atmospheric density model is constructed using actual atmospheric data, and a precise atmospheric influence calculation model is established in conjunction with the global digital elevation model. A high-precision gravity forward modeling algorithm based on spherical prisms and thin-layer spherical units, taking into account the influence of Earth's curvature, is used to accurately calculate the direct atmospheric influence, major indirect atmospheric influence, and minor indirect atmospheric influence. Compared to the traditional IAG method, this invention systematically improves upon the design of the atmospheric quality adjustment scheme, the construction of the atmospheric influence calculation model, and the calculation of atmospheric influence, enabling more reasonable and effective adjustment of atmospheric quality in geoid determination, thereby improving the accuracy of geoid modeling. This invention can provide technical support for determining geoids with a precision of 1 cm, is applicable to the field of geodesy and mapping engineering, and has significant practical value.

[0016] (2) This invention proposes an atmospheric mass adjustment scheme using the generalized Helmert condensation method. On the one hand, it ensures that the actual total mass of the Earth remains unchanged, and on the other hand, it no longer condenses the actual atmospheric mass into a fixed spherical layer (such as the geoid) or the Earth's center, making the method more flexible.

[0017] (3) The present invention uses more realistic atmospheric density information, taking into account not only the change of atmospheric density in the radial direction but also its change in the lateral direction, which is closer to the real situation at the theoretical level.

[0018] (4) In constructing the atmospheric impact calculation model, this invention considers the undulating shape of the lower atmospheric boundary (i.e., topography) rather than simplifying it to an ellipsoid or sphere, making the model closer to reality. In addition, a spherical prism is used to discretize the atmospheric mass, which takes into account the influence of the Earth's curvature. A rigorous process is also used in the compression and condensation step to obtain reliable density information of the condensation layer.

[0019] (5) This invention employs a high-precision gravity forward modeling algorithm based on a spherical prism whose density varies radially as a cubic polynomial function, which can accurately calculate the gravitational and gravitational potential effects caused by the actual atmospheric mass. In addition, it also employs a high-precision gravity forward modeling algorithm based on a spherical thin-layer unit with constant surface density, which can accurately calculate the gravitational and gravitational potential effects caused by the atmospheric condensation layer.

[0020] (6) The present invention can provide the direct and secondary indirect atmospheric effects on gravity caused by atmospheric mass removal and compensation, as well as the main indirect atmospheric effects on the gravitational potential, while the IAG method can only provide the direct atmospheric effects on gravity.

[0021] In addition to the objectives, features, and advantages described above, the present invention has other objectives, features, and advantages. The invention will now be described in further detail with reference to the figures. Attached Figure Description

[0022] The accompanying drawings, which form part of this application, are used to provide a further understanding of the invention. The illustrative embodiments of the invention and their descriptions are used to explain the invention and do not constitute an undue limitation of the invention. In the drawings: Figure 1 This is a flowchart illustrating a rigorous atmospheric reduction method that takes into account topography and three-dimensional density distribution in determining the geoid according to Embodiment 1 of the present invention. Figure 2 This is a flowchart illustrating step one in Embodiment 1 of the present invention; Figure 3 This is a flowchart illustrating step two in Embodiment 1 of the present invention; Figure 4 This is a flowchart illustrating step three in Embodiment 1 of the present invention; Figure 5(a) shows the calculations performed using the ECMWF ERA-Interim model layer global reanalysis grid dataset in the experimental example of this invention. Schematic diagram of radial distribution of atmospheric density at a point; Figure 5(b) shows the calculations performed using the ECMWF ERA-Interim model layer global reanalysis grid dataset in the experimental example of this invention. Schematic diagram of radial distribution of atmospheric density at a point; Figure 5(c) shows the calculations performed using the ECMWF ERA-Interim model layer global reanalysis grid dataset in the experimental example of this invention. Schematic diagram of radial distribution of atmospheric density at a point; Figure 6 This is a schematic diagram of an atmospheric quality adjustment scheme using the generalized Helmert condensation method in the experimental examples of this invention; Figure 7 The global surface area calculated in the experimental examples of this invention. A high-resolution schematic diagram illustrating the direct impact of the atmosphere (the atmospheric condensation layer is located on the geoid). Figure 8 The global surface area calculated in the experimental examples of this invention. A high-resolution schematic diagram of the direct impact of the atmosphere (the atmospheric condensation layer is located on a sphere 1 m below the geoid); Figure 9 The global surface area calculated in the experimental examples of this invention. A high-resolution schematic diagram of the direct effects of the atmosphere (the atmospheric condensation layer is located on a sphere 1 km below the geoid); Figure 10The global surface area calculated in the experimental examples of this invention. A high-resolution schematic diagram of the direct effects of the atmosphere (the atmospheric condensation layer is located on a sphere 10 km below the geoid); Figure 11 The global surface area calculated in the experimental examples of this invention. A high-resolution diagram illustrating the direct impact of the atmosphere (atmospheric mass compressed and condensed to the Earth's core); Figure 12 The global surface area calculated in the experimental examples of this invention. Schematic diagram of the direct impact of IAG resolution on the atmosphere. Detailed Implementation

[0023] To make the above-mentioned objects, features, and advantages of the present invention clearer and easier to understand, the specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings. It should be noted that the accompanying drawings of the present invention are all in a simplified form and use non-precise proportions, and are only used to facilitate and clearly illustrate the implementation of the present invention.

[0024] Example 1: This embodiment proposes a rigorous atmospheric reduction method for determining the geoid, taking into account topography and three-dimensional density distribution. This method calculates the impact of atmospheric quality adjustments on geoid determination, primarily comprising three categories: the direct effect (DE) on gravity, the primary indirect effect (PIE) on gravitational potential, and the secondary indirect effect (SIE) on gravity. For achieving the above technical objectives, see [link to relevant documentation]. Figures 1 to 4 As shown, this invention proposes a rigorous atmospheric reduction method for determining the geoid that takes into account topography and three-dimensional density distribution, including the following steps: Step 1: Construct a global three-dimensional atmospheric density model based on the ERA-Interim or ERA5 model layer global reanalysis grid dataset provided by ECMWF (European Centre for Medium-Range Weather Forecasts).

[0025] Preferably, the ERA-Interim model layer global reanalysis grid dataset contains 60 model layer global grid data, covering the atmospheric space from near the Earth's surface to approximately 60 km above sea level; The ERA5 model layer global reanalysis grid dataset contains 137 model layer global grid data, covering atmospheric space from near the Earth's surface to approximately 80 km above sea level.

[0026] More preferably, both the ERA-Interim and ERA5 model layer global reanalysis grid datasets contain one layer of surface gravity potential. The natural logarithm of surface pressure And the temperature of all grid points on all model layers. and humidity .

[0027] The preferred method for constructing a global three-dimensional atmospheric density model based on the global reanalysis grid dataset of the ERA-Interim or ERA5 model layer is as follows: The atmospheric density and elevation of each grid point in the global reanalysis grid dataset of the ERA-Interim or ERA5 model layer are calculated to obtain a global three-dimensional atmospheric density model. The specific construction steps are as follows: Step 1.1: Download all ERA-Interim or ERA5 model layer global reanalysis grid datasets for the selected time period from the ECMWF website to obtain the raw data; the raw data includes the surface gravity potential of one grid layer. The natural logarithm of surface pressure And the temperature of all grid points on all model layers. and humidity ; Step 1.2: Averaging the raw data to obtain the average surface potential and average surface pressure representing the selected time period. Average temperature and average humidity ; Step 1.3: Calculate the pressure at each grid point in the model layer. ; pressure The expression is as follows: ; in, Represented as the model layer number, and 1 represents the model layer grid data furthest from the Earth's surface. Represented as the model layer grid data closest to the Earth's surface; and Represented as corresponding to the first The pressure of two half-model layer grid points in a model layer; Pressure of half-model grid points The expression is as follows: ; in, Represented as an index number, and , and These are all coefficients used to define the vertical coordinates and can be obtained from the ECMWF website; Expressed as average surface pressure; Step 1.4: Calculate the atmospheric density of each grid point in the model layer. ; Atmospheric density The expression is as follows: ; ; ; in, Expressed as the gas constant for dry air, Represented as virtual temperature, J It is represented as joules. kg Expressed in kilograms, It is expressed in Kelvin (Celsius).

[0028] Step 1.5: Calculate the gravitational potential of each grid point in the model layer. ; The specific process is as follows: Let the gravitational potentials of two adjacent half-model layer grid points in each model layer be respectively and ; but and The expression relating the gravitational potentials between them is as follows: ; Furthermore, the gravity potential of any half-model layer grid point The expression is as follows: ; in, Represented as model layer number, Represented as located at the th Pressure of the grid points in the semi-model layer below the model layer Represented as located at the th Pressure of the grid points in the half-model layer above the model layer; Furthermore, the gravity potential of each grid point in the model layer The expression is as follows: ; ; Step 1.6: Calculate the gravity potential height of each grid point in the model layer. , Represented as the transmission coefficient; Gravity The expression is as follows: ; ; in, Represented as Gravity at sea level at latitude mean.

[0029] Step 1.7: Calculate the elevation of each grid point in the model layer. ; Elevation The expression is as follows: ; in, It is represented as the co-latitude of each grid point in the same model layer.

[0030] The global three-dimensional atmospheric density model constructed through the above steps is a multi-layer grid model that can provide information on the distribution of atmospheric density along the radial and lateral directions.

[0031] Step 2: Based on the global three-dimensional atmospheric density model, construct a precise calculation model of atmospheric effects.

[0032] Preferably, the precise calculation model of atmospheric impacts includes two parts: constructing a precise calculation model of actual atmospheric impacts and constructing a precise calculation model of atmospheric condensation layer impacts.

[0033] Further preferred, the atmospheric condensation layer necessary for constructing a precise calculation model of the influence of the atmospheric condensation layer is a thin layer of surface mass obtained by radially compressing and condensing the actual atmospheric mass onto the geoid or a spherical surface inside it. The specific construction steps are as follows: Step 2.1: Using the topographic information provided by the Global Digital Elevation Model (BDMM) as the lower atmospheric boundary, and taking a plane 60 km or 80 km above sea level as the upper atmospheric boundary, the radial direction of each grid cell in the global three-dimensional atmospheric density model is used. The atmospheric density and elevation provided by each grid point are used to obtain the atmospheric density and elevation at preset dense interpolation points in the same radial direction, thereby determining the atmospheric mass distribution model. Step 2.2: Based on the atmospheric mass distribution model, the atmospheric mass is stratified from the lower boundary upwards to obtain... One spherical shell layer; among which... Except for the first layer, which has unequal heights due to its lower boundary being topography, all other layers are of equal height. Step 2.3: Based on the resolution of the global digital elevation model, divide the atmospheric mass of each spherical shell layer into multiple spherical prisms of equal horizontal size; and except for the spherical prisms in the first layer, whose radial dimensions are inconsistent, the spherical prisms in the same layer in the other layers have the same radial dimensions. Step 2.4: Based on the spatial geometric position information of each spherical prism, determine the interpolation point located within it; Based on the atmospheric density and elevation provided by the interpolation points within each spherical prism, a cubic polynomial density function varying with respect to elevation along the radial direction for each spherical prism is determined using least-squares fitting. ; cubic polynomial density function for elevation The expression is as follows: ; ; in, Let the elevation be expressed as the elevation of any point within the spherical prism. This represents the elevation of the lower surface of the spherical prism. This represents the elevation of the upper surface of the spherical prism. Represented as the order of a polynomial, Represented as corresponding to The density coefficient of the order.

[0034] Since the coordinate system used in actual atmospheric impact calculations is a spherical coordinate system, it is necessary to convert the cubic polynomial density function with respect to elevation. After transformation, we obtain the cubic polynomial density function of the geocentric radial vector in spherical coordinates. ; Regarding the cubic polynomial density function of the geocentric radial direction The expression is as follows: ; ; ; ; ; in, Let the radius be the geocentric radius at any point within the spherical prism. Expressed as the Earth's average radius, It is represented by the geocentric radius of the lower surface of the spherical prism. It is represented by the geocentric radius of the upper surface of the spherical prism. Represented as corresponding to The coefficients of a polynomial of order 1; Preferred, corresponding to polynomial coefficients of order The expression is as follows: ; ; ; ; ; in, Represented as coefficients of a 0th-order polynomial. Represented as coefficients of a first-order polynomial. Represented as coefficients of a second-order polynomial. Represented as coefficients of a third-order polynomial. Represented as the 0th order density coefficient, Represented as the first-order density coefficient, Represented as second-order density coefficients, It is represented as the third-order density coefficient.

[0035] Step 2.5: Based on the aforementioned atmospheric mass distribution model and the discretized spherical prism and its cubic polynomial density function, the first... All grids in the radial direction A series of spherical prisms are compressed and agglomerated radially into the selected agglomerated layer, resulting in a first layer with horizontal dimensions consistent with the spherical prisms. The areal density of a spherical thin-layer unit is determined based on the principle of constant total mass. ; areal density The expression is as follows: ; in, Represented as the first The radial direction of the grid corresponds to the first The coefficients of the cubic polynomial of a spherical prism Represented as the first The geocentric radius of the lower surface of a spherical prism Represented as the first The geocentric radius of the upper surface of a spherical prism Represented as the geocentric radial of the condensate, under the spherical approximation Value less than or equal to the Earth's average radius .

[0036] Step 3: Based on a series of spherical prisms and a series of spherical thin-layer units, calculate the effects of the dense atmosphere using the corresponding high-precision gravity forward modeling algorithm.

[0037] Specifically, the calculation of rigorous atmospheric effects includes the gravitational effect of the actual atmospheric mass on ground points and its gravitational potential effect on the projection points on the geoid, as well as the gravitational effect of the atmospheric condensate layer on ground points and its gravitational potential effect on the projection points on the geoid.

[0038] The preferred steps for calculating the effects of a tight atmosphere are as follows: Step 3.1: Using a high-precision gravity forward modeling algorithm based on a spherical prism whose density varies radially as a cubic polynomial function, calculate the relationship between each spherical prism and the ground point. The gravitational effects are superimposed to obtain the actual atmospheric gravitational effects that need to be removed. ; Actual atmospheric gravitational effects The expression is as follows: ; ; ; in, Represented as a partial differential operator; It is expressed as the gravitational constant; Represented as corresponding to the first The cubic polynomial density function of a spherical prism; and They are respectively represented as calculation points Integral points within a spherical prism The spherical coordinates, namely geocentric radius, latitude, and longitude; Represented as calculation point With integration points The Euclidean distance between them; Represented as calculation point With integration points The spherical distance between them; , and Represented as the first The longitude range, latitude range, and geocentric radius range of a spherical prism; Represented as calculation point The actual atmospheric gravitational potential effect, superscript This is referred to as the Real Atmosphere.

[0039] It should be noted that if... Extending downwards to the geoid Point mapping point Its extension value is equivalent to the actual atmospheric mass at , Gravitational effect of a point ; Actual air quality at Gravitational effect of a point and gravitational potential effect The expression is as follows: ; ; ; ; in, and They are respectively represented as calculation points Integral points within a spherical prism The spherical coordinates, namely geocentric radius, latitude, and longitude; Represented as calculation point With integration points The Euclidean distance between them; Represented as calculation point With integration points The spherical distance between them; Represented as calculation point The actual atmospheric gravitational potential effect.

[0040] Step 3.2: Using a high-precision gravity forward modeling algorithm based on spherical thin-layer elements with constant surface density, calculate the relationship between each spherical thin-layer element and the ground point. The gravitational effects are superimposed to obtain the atmospheric condensate gravitational effects that need to be compensated. ; Atmospheric condensation layer gravitational effect The expression is as follows: ; ; in, and Represented as the first The latitude and longitude range of each spherical thin-layer unit; Represented as calculation point Integration point within the spherical thin-layer unit Euclidean distance between them; superscript This is referred to as the condensed atmosphere.

[0041] If we consider the gravitational effect of the atmospheric condensate layer Extending downwards to the geoid The point, whose extension value is equivalent to the atmospheric condensate layer at... Gravitational effect of a point ; Atmospheric condensation layer Gravitational effect of a point and gravitational potential effect The expression is as follows: ; ; .

[0042] Step 3.3: Calculate ground points The dense atmosphere directly affects ; ground point The dense atmosphere directly affects The expression is as follows: .

[0043] In actual geoid calculations, this effect needs to be incorporated into the ground gravity anomaly to obtain the ground Helmert gravity anomaly after adjusting for atmospheric mass.

[0044] Step 3.4: Calculate the geoid projection points The dense atmosphere has a secondary indirect influence ; Geoid projection point The dense atmosphere has a secondary indirect influence The expression is as follows: .

[0045] In actual geoid calculations, this effect needs to be removed from the Helmert gravity anomaly extended to the geoid in order to obtain the adjusted Helmert gravity anomaly on the geoid.

[0046] Step 3.5: Calculate the geoid projection points The dense atmosphere mainly has an indirect impact ; The main indirect effects of a dense atmosphere The expression is as follows: ; in, This is represented as normal gravity on the reference ellipsoid.

[0047] In determining the actual geoid, this influence needs to be removed from the calculated adjusted geoid in order to determine the actual geoid.

[0048] Experimental example: Download the 2007-2016 ten-year monthly average EAR-Interim model layer global reanalysis grid dataset from the ECMWF official website. The required atmospheric parameters are surface gravity potential, natural logarithm of surface pressure, temperature, and humidity.

[0049] Each dataset contains atmospheric parameters for 60 model layers (i.e., 60 grid layers, extending from the Earth's surface to approximately 60 km above sea level, with each layer having a resolution of [resolution missing]). ), parameters for each atmospheric layer include Each grid point contains the atmospheric density and elevation of the point after constructing the global three-dimensional atmospheric density model. Therefore, the atmospheric density and elevation provided by the 60 grid points in the same radial direction describe the distribution variation of atmospheric density along the radial direction, while the grid points of each layer provide the distribution variation of atmospheric density along the lateral direction.

[0050] To verify the effectiveness of the global three-dimensional atmospheric density model construction method, this experimental example downloaded the 2000 monthly average EAR-Interim model layer global reanalysis grid data and calculated the values ​​at three points ( ; ; The radial density distribution at each point was measured for each month and compared with the radial density calculated by the USSA1976 model. The radial density at the three points varied with the seasons and location, and differed from the values ​​in the USSA1976 model. Furthermore, it was found that the near-surface atmospheric density in high-latitude regions (see Figure 5(a)) was greater than that in mid-latitude regions (see Figure 5(b)) and equatorial regions (see Figure 5(c)) due to lower temperatures, which is consistent with actual conditions.

[0051] The foundation for establishing a precise calculation model of atmospheric impacts lies in determining an atmospheric quality adjustment scheme, i.e., how to remove and compensate for atmospheric mass. The scheme described in this embodiment is an atmospheric quality adjustment scheme employing the generalized Helmert condensation method, such as... Figure 6 As shown, the actual atmospheric mass is first removed, then compressed and condensed radially onto the geoid or a spherical surface within it, resulting in an atmospheric condensation layer with the same mass as the actual atmosphere, ensuring that the Earth's total mass remains unchanged after atmospheric mass adjustment. Based on this, a precise calculation model of atmospheric impacts is constructed, comprising two parts: a precise calculation model of the actual atmospheric impacts and a precise calculation model of the atmospheric condensation layer impacts. The specific construction steps are as follows: ① Using downsampling The terrain provided by the high-resolution ETOPO1 model is used as the lower atmospheric boundary, and a plane 60 km above sea level is taken as the upper atmospheric boundary. The atmospheric density and elevation information provided by 60 grid points in the radial direction of each grid in the global three-dimensional atmospheric density model are used to obtain the atmospheric density and elevation at 1000 preset interpolation points in the same radial direction, thereby determining the atmospheric mass distribution model. ② Based on the atmospheric mass distribution model, the atmospheric mass is divided into 6 layers from the lower boundary upwards. The height range of each layer is [0, 10 km), [10, 20 km), [20, 30 km), [30, 40 km), [40, 50 km), [50, 60 km]. Except for the first layer, which is a spherical shell layer with unequal height due to the terrain at its lower boundary, the other layers are spherical shell layers with equal height. ③ Based on the resolution of the ETOPO1 model, the atmospheric mass of each spherical shell layer is divided into horizontal dimensions. The spherical prisms, except for those in the first layer which have inconsistent radial dimensions, have the same radial dimension of 10 km in all other layers. ④ Determine the interpolation point located within each spherical prism based on its spatial geometric position information; Based on the atmospheric density and elevation information provided by the interpolation points within each spherical prism, a cubic polynomial density function of elevation varying radially for each spherical prism is determined using least-squares fitting. ; The cubic polynomial density function with respect to elevation After transformation, we obtain the cubic polynomial density function of the geocentric radial vector in spherical coordinates. .

[0052] ⑤ Based on the aforementioned atmospheric mass distribution model and the discretized spherical prism and its cubic polynomial density function, the th... All six spherical prisms in the radial direction of the grid are compressed and agglomerated into the selected agglomerated layer, resulting in the first layer with the same horizontal dimensions as the spherical prisms. The areal density of a spherical thin-layer unit is determined based on the principle of constant total mass. .

[0053] The calculation of the effects of a tight atmosphere includes the gravitational effect of the actual atmospheric mass on ground points and its gravitational potential effect on the projection points on the geoid, as well as the gravitational effect of the atmospheric condensate layer on ground points and its gravitational potential effect on the projection points on the geoid. Based on the above discretized series of spherical prisms representing the actual atmospheric mass distribution and a series of spherical thin-layer units representing the atmospheric condensate layer mass distribution, the specific steps for calculating the effects of a tight atmosphere using the corresponding high-precision gravity forward modeling algorithm are as follows: Using a high-precision gravity forward modeling algorithm based on spherical prisms whose density varies radially as a cubic polynomial function, the relationship between each spherical prism and the ground point is calculated. The gravitational effects are superimposed to obtain the actual atmospheric gravitational effects that need to be removed. ; Actual atmospheric gravitational effects Extending downwards to the geoid Point mapping point Its extension value is equivalent to the actual atmospheric mass at , Gravitational effect of a point .

[0054] Using a high-precision gravity forward modeling algorithm based on spherical thin-layer elements with constant surface density, the relationship between each spherical thin-layer element and the ground point is calculated. The gravitational effects are superimposed to obtain the atmospheric condensate gravitational effects that need to be compensated. ; gravitational effects of atmospheric condensation layer Extending downwards to the geoid The point, whose extension value is equivalent to the atmospheric condensate layer at... Gravitational effect of a point ; Calculate ground points The dense atmosphere directly affects ; In actual geoid calculations, this effect needs to be incorporated into the ground gravity anomaly to obtain the ground Helmert gravity anomaly after adjusting for atmospheric mass.

[0055] In this embodiment, the atmospheric condensation layer was placed on the geoid, on a sphere 1 m below the geoid, on a sphere 1 km below the geoid, on a sphere 10 km below the geoid, and the entire atmospheric mass was condensed to the Earth's core. Based on the aforementioned precise atmospheric influence calculation model and high-precision gravity forward modeling algorithm, the corresponding global surface condensation was calculated. The resolution is rigorously calculated to determine the direct atmospheric effects, and these are compared with the direct atmospheric effects calculated by the traditional IAG method. Figures 7-12 As shown. The calculation formula for the IAG method is as follows: ; in, The unit is mGal; h The elevation of the calculated point is shown in meters (m). Table 1 also provides statistical information on various direct atmospheric influences. Figures 7-12 As shown in Table 1, the direct influence of a tight atmosphere varies with the location of the condensate layer. When the condensate layer is located on the geoid ( Figure 7Due to the singularity of the gravitational force at the estimated surface point of the condensate layer, the direct atmospheric effects at the ocean surface differ significantly from those obtained using other condensate layer locations. However, the direct atmospheric effects at the land surface are relatively similar for all dense atmospheres. This problem can be addressed by placing the condensate layer below the geoid. When the condensate layer is located 1 m, 1 km, and 10 km below the geoid on the sphere (…),… Figures 8-10 The calculated direct effects of the dense atmosphere are very close. However, when all atmospheric mass is compressed and condensed at the Earth's core ( Figure 11 The calculated direct effects of the tight atmosphere differ from the three cases mentioned above. This indicates that the selection of the condensation layer location significantly impacts the calculation of the direct effects of the tight atmosphere. Furthermore, all the direct effects of the tight atmosphere calculated in this embodiment differ significantly from the direct effects of the IAG atmosphere, directly reflecting the tightening process.

[0056] Table 1: Statistics on the direct impacts of the tight atmosphere and the IAG atmosphere at different condensation layer locations (unit: mGal)

[0057] Calculate the projection points of the geoid The dense atmosphere has a secondary indirect influence ; In actual geoid calculations, this effect needs to be removed from the Helmert gravity anomaly extended to the geoid in order to obtain the adjusted Helmert gravity anomaly on the geoid.

[0058] Calculate the projection points of the geoid The dense atmosphere mainly has an indirect impact ; In determining the actual geoid, this influence needs to be removed from the calculated adjusted geoid in order to determine the actual geoid.

[0059] This embodiment calculates the main indirect effects of the tight atmosphere based on the five condensation layer locations mentioned above, and the statistical information is shown in Table 2. Since the IAG method cannot provide indirect atmospheric effects, they are not compared in this table. Table 2 shows that the main indirect effects of the tight atmosphere obtained by condensing atmospheric mass to the Earth's core differ significantly from the results obtained using the other four condensation layer locations. Combined with the aforementioned results of the direct effects of the tight atmosphere, it can be inferred that this method of atmospheric mass adjustment is not suitable. It should be noted that the results obtained using the condensation layer located on the geoid and on spheres 1 m, 1 km, and 10 km below it are basically consistent. This is because the gravitational potential at the estimated points on the surface of the condensation layer does not exhibit singularity. Combined with the aforementioned results of the direct atmospheric effects, it can be inferred that the results obtained by placing the condensation layer on spheres 1 m, 1 km, and 10 km below the geoid are reliable.

[0060] Table 2: Statistics on the main indirect influences of the tight atmosphere at different condensation layer locations (unit: cm)

[0061] Example 2: As a further embodiment of the present invention, the present invention also provides an electronic device, comprising: One or more processors; Storage device for storing one or more programs; When the one or more programs are executed by the one or more processors, the one or more processors implement the aforementioned method.

[0062] In practical use, users can interact with servers, which are also electronic devices, via a network to receive or send messages. Terminal devices are generally various electronic devices equipped with a display and used through a human-computer interface, including but not limited to smartphones, tablets, laptops, and desktop computers. Various specific application software can be installed on these terminal devices as needed, including but not limited to web browsers, instant messaging software, social media platforms, and shopping apps.

[0063] Furthermore, the server is a network server used to provide various services, such as a backend server that provides corresponding calculation services for atmospheric parameters transmitted from terminal devices, so as to realize the processing of the rigorous atmospheric reduction method that takes into account topography and three-dimensional density distribution in the determination of geoid, calculate the direct, main and secondary indirect effects of the rigorous atmosphere, and return the final results to the terminal devices.

[0064] Example 3: As a further embodiment of the present invention, the present invention also provides a storage medium including one or more programs executable by one or more processors of an electronic device, the one or more programs including instructions for executing a rigorous atmospheric reduction method for geoid determination that takes into account topography and three-dimensional density distribution as described above.

[0065] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A rigorous atmospheric reduction method for determining the geoid that takes into account topography and three-dimensional density distribution, characterized in that, Includes the following steps: Step 1: Calculate the atmospheric density and elevation of all grid points in each model layer of the global reanalysis grid dataset of the ERA-Interim or ERA5 model layer provided by ECMWF to obtain a global three-dimensional atmospheric density model. Step 2: Using a global three-dimensional atmospheric density model, analyze the radial direction of each grid cell. The atmospheric density and elevation provided by each grid point are used to obtain the atmospheric density and elevation at preset dense interpolation points in the same radial direction, thereby determining the atmospheric mass distribution model. Based on the atmospheric mass distribution model, atmospheric mass is discretized to obtain a series of discretized spherical prisms; Based on the spatial geometric position information of each spherical prism, determine the interpolation point located within each spherical prism. Based on the atmospheric density and elevation provided by the interpolation points within each spherical prism, a cubic polynomial density function varying with respect to elevation along the radial direction for each spherical prism is determined using least-squares fitting. ; The cubic polynomial density function with respect to elevation After transformation, we obtain the cubic polynomial density function of the geocentric radial vector in spherical coordinates. ; Based on an atmospheric mass distribution model, a discretized spherical prism, and a cubic polynomial density function with respect to the geocentric radius. All in the radial direction of each grid A series of spherical prisms are compressed and condensed radially into the selected condensation layer, resulting in a series of spherical thin-layer units with the same horizontal dimensions as the spherical prisms. Step 3: Based on a series of spherical prisms and a series of spherical thin-layer units, the corresponding high-precision gravity forward modeling algorithm is used to calculate the gravitational effect of the actual atmospheric mass and atmospheric condensation layer on ground points, as well as the gravitational potential effect of the actual atmospheric mass and atmospheric condensation layer on geoid points, and finally determine the direct, main, and secondary indirect effects of the dense atmosphere. The main indirect effects of the dense atmosphere are removed from the calculated adjusted geoid to determine the actual geoid.

2. The rigorous atmospheric reduction method for determining the geoid that takes into account topography and three-dimensional density distribution as described in claim 1, characterized in that, The ERA-Interim model layer global reanalysis grid dataset contains global grid data for 60 model layers; The ERA5 model layer global reanalysis grid dataset contains global grid data for 137 model layers.

3. The rigorous atmospheric reduction method for determining the geoid based on topography and three-dimensional density distribution as described in claim 2, characterized in that, The global reanalysis grid datasets of both the ERA-Interim and ERA5 models contain surface gravity potentials from one grid layer. The natural logarithm of surface pressure And the temperature of all grid points on all model layers. and humidity .

4. The rigorous atmospheric reduction method for determining the geoid based on topography and three-dimensional density distribution as described in claim 3, characterized in that... The specific process for obtaining the global three-dimensional atmospheric density model is as follows: Download all ERA-Interim or ERA5 model layer global reanalysis grid datasets for the selected time period from the ECMWF website to obtain the raw data; the raw data includes surface gravity potential data for one layer of grid. The natural logarithm of surface pressure And the temperature of all grid points on all model layers. and humidity ; The raw data are averaged to obtain the average surface potential and average surface pressure representing the selected time period. Average temperature and average humidity ; Based on average surface pressure Calculate the atmospheric density of each grid point in the model layer. ; Based on mean surface gravity potential Calculate the elevation of each grid point in the model layer. .

5. The rigorous atmospheric reduction method for determining the geoid based on topography and three-dimensional density distribution as described in claim 4, characterized in that, Calculate the atmospheric density of each grid point in the model layer. The specific process is as follows: Calculate the pressure at each grid point in the model layer. ; pressure The expression is as follows: ； in, Represented as the model layer number, and 1 represents the model layer grid data furthest from the Earth's surface. Represented as the model layer grid data closest to the Earth's surface; and Represented as corresponding to the first The pressure of two half-model layer grid points in a model layer; Pressure of half-model grid points The expression is as follows: ； in, Represented as an index number, and , and All are represented as coefficients used to define the vertical coordinate; Expressed as average surface pressure; Calculate the atmospheric density of each grid point in the model layer. ; Atmospheric density The expression is as follows: ； ； ； in, Expressed as the gas constant for dry air, Represented as virtual temperature, J It is represented as joules. kg Expressed in kilograms, It is expressed in Kelvin (Celsius).

6. The rigorous atmospheric reduction method for determining the geoid based on topography and three-dimensional density distribution as described in claim 5, characterized in that... Calculate the elevation of each grid point in the model layer. The specific process is as follows: Let the gravitational potentials of two adjacent half-model layer grid points in each model layer be respectively and ; but and The expression relating the gravitational potentials between them is as follows: ； Furthermore, the gravity potential of any half-model layer grid point The expression is as follows: ； in, Represented as model layer number, Represented as located at the th Pressure of the grid points in the semi-model layer below the model layer Represented as located at the th Pressure of the grid points in the half-model layer above the model layer; Furthermore, the gravity potential of each grid point in the model layer The expression is as follows: ； ； Calculate the gravity potential of each grid point in the model layer. The expression is as follows: ； ； in, Represented as Gravity at latitude mean sea level Represented as the transmission coefficient; Calculate the elevation of each grid point in the model layer. The expression is as follows: ； in, It is represented as the co-latitude of each grid point in the same model layer.

7. The rigorous atmospheric reduction method for determining the geoid that takes into account topography and three-dimensional density distribution according to any one of claims 1-6, characterized in that, The specific process of step three is as follows: Using a high-precision gravity forward modeling algorithm based on spherical prisms whose density varies radially as a cubic polynomial function, the relationship between each spherical prism and the ground point is calculated. The gravitational effects are superimposed to obtain the actual atmospheric gravitational effects that need to be removed. ; Actual atmospheric gravitational effects Extending downwards to the geoid Point mapping point The extension value is equivalent to the actual atmospheric mass at [value missing]. Gravitational effect of a point ; Furthermore, calculate the pairs of each spherical prism. The gravitational potential effect at a point is obtained by superimposing the gravitational potential effects at that point to obtain the actual atmospheric gravitational potential effect. ; Using a high-precision gravity forward modeling algorithm based on spherical thin-layer elements with constant surface density, the relationship between each spherical thin-layer element and the ground point is calculated. The gravitational effects are superimposed to obtain the atmospheric condensate gravitational effects that need to be compensated. ; gravitational effects of atmospheric condensation layer Extending downwards to the geoid The extension value of a point is equivalent to the atmospheric condensation layer at that point. Gravitational effect of a point ; Furthermore, the pair of each spherical thin-layer element is calculated. The gravitational potential effect of a point is obtained by superimposing the gravitational potential effect of the atmospheric condensate layer. ; based on and Calculate ground points The dense atmosphere directly affects ; based on and Calculate the projection points of the geoid The dense atmosphere has a secondary indirect influence and geoid projection points The dense atmosphere mainly has an indirect impact ; Will Remove the calculated adjusted geoid from the actual geoid.

8. An electronic device, characterized in that, It includes a memory, one or more processes, and one or more programs stored in the memory, the one or more programs including instructions for executing a rigorous atmospheric reduction method for geoid determination that takes into account topography and three-dimensional density distribution as described in any one of claims 1-7.

9. A storage medium, characterized in that, Includes one or more programs executable by one or more processors of an electronic device, the one or more programs including instructions for executing a rigorous atmospheric reduction method for geoid determination that takes into account topography and three-dimensional density distribution as described in any one of claims 1-7.

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