Method for estimating top-of-atmosphere radiance based on high-orbit satellite sensors

Abstract

This invention relates to a method for estimating the radiant energy emitted from the top of the atmosphere based on high-orbit satellite sensors. The method calculates the radiance of the radiant energy emitted from the top of the atmosphere using the following formula: where F is the radiance of the radiant energy emitted from the top of the atmosphere, and E... m Ω represents the energy emitted from the top of the atmosphere received by high-orbit satellite sensors. e To obtain the solid angle of observation of the top of the atmosphere by a high-orbit satellite sensor, the solid angle can be solved using a complete elliptic integral of the third kind. A rectangular coordinate system based on the solid angle is then constructed to calculate the boundary curve of the observation field of view. The corresponding geocentric and geofixed coordinates are obtained through a coordinate transformation matrix. This invention can accurately estimate the emitted energy from the top of the atmosphere, providing support for related research.

Description

Technical Field

[0001] This invention relates to a method for estimating the energy emitted from the top of the Earth's atmosphere based on high-orbit satellite sensors, and belongs to the field of Earth observation. Background Technology

[0002] High-orbit satellites refer to satellites with orbital altitudes higher than geostationary orbits, as well as the Moon, a natural satellite. They are commonly used in research fields such as deep space navigation, asteroid defense, space weather detection, and astronomy, and also have broad application prospects in Earth observation. The atmospheric top radiation outgoing energy of this invention refers to the long-wave radiation energy emitted by the Earth within the field of view observed by remote sensing sensors. Accurate measurement of this energy is beneficial for determining the important boundary condition of global change models regarding whether the Earth's radiation energy is balanced. By carrying sensors on high-orbit satellites, the Earth can be treated as a point-like radiation source, observing the radiation outgoing energy from the atmospheric top within the entire field of view. This allows for answering the question of whether the Earth's radiation energy input to the atmospheric top is greater than its output, deepening our understanding of changes in the entire Earth-atmosphere system. However, such a technology has not yet been discovered.

[0003] Given the aforementioned requirements for observation geometry and high-precision calculations, the Earth ellipsoid model will significantly impact the accuracy of the estimation results. Because traditional spaceborne platforms are limited by their low orbits, small observation ranges, and relatively singular observation angles, the methods used by corresponding sensors to observe and estimate the energy emitted from the top of the atmosphere within the field of view cannot be directly applied to high-orbit satellites. Therefore, it is necessary to develop new methods for estimating the energy emitted from the top of the atmosphere within the field of view based on observations from high-orbit satellite sensors.

[0004] Since the observation field of view is almost the entire hemisphere of the Earth, the Earth's ellipsoid will have a significant impact on energy estimation. The design of high-orbit satellite orbits is not limited to running along longitude and latitude lines. In fact, the lunar base platform is a highly elliptical orbit with varying orbital inclination and observation distance. In this case, the influence of the Earth's shape on energy estimation will become more complicated. Summary of the Invention

[0005] The purpose of this invention is to provide a method for estimating the energy emitted from the top of the Earth's atmosphere based on high-orbit satellite sensors, in order to meet the corresponding requirements.

[0006] The technical solution of this invention is: a method for estimating the radiant energy emitted from the top of the atmosphere based on high-orbit satellite sensors, which calculates the radiance of the radiant energy emitted from the top of the atmosphere (hemispherical scale) according to the following formula:

[0007]

[0008] Where F is the radiance of the energy emitted from the top of the atmosphere, and E m Ω represents the energy emitted from the top of the atmosphere received by high-orbit satellite sensors.e This is the solid angle of observation of the top of the atmosphere (which can be considered as an ellipsoid) by a high-orbit satellite sensor.

[0009] Preferably, the Earth shape model adopts the WGS-84 (or WGS84) ellipsoid (Earth ellipsoid).

[0010] Preferably, the top of the atmosphere is an atmospheric top ellipsoid, which is an ellipsoid formed by an atmosphere of equal thickness on the Earth's ellipsoid.

[0011] Preferably, the atmospheric thickness (or the height of the top of the atmosphere above the ground / geodetic reference surface) is set to 20 km.

[0012] Furthermore, high-orbit satellites can serve as Earth observation platforms above geostationary orbit, such as a 380,000 km lunar-based Earth observation platform or a Sun-Earth Lagrange point 1 platform satellite.

[0013] Furthermore, the solid angle of observation of the top of the atmosphere by the high-orbit satellite sensor can be calculated using the following formula:

[0014]

[0015] or,

[0016]

[0017] Where S is the observation field surface (or surface area) of the high-orbit satellite sensor at the top of the atmosphere, r is the position vector from any point / corresponding point on the observation field surface of the high-orbit satellite sensor at the top of the atmosphere to the high-orbit satellite sensor (real-time position), ds is the integral infinitesimal vector on surface S (direction is the surface normal), L is the boundary curve of the observation field surface of the high-orbit satellite sensor at the top of the atmosphere (can be regarded as a spatial ellipse), and (x1, y1, z1) is the observation field surface (surface area) of the high-orbit satellite sensor at the top of the atmosphere. The coordinates of any point in the observation solid angle in a rectangular coordinate system. This rectangular coordinate system uses the observation position (sensor position) as its origin, with coordinate axes X1, Y1, and Z1. The Z1 axis points towards the boundary of the observation field of view (spatial ellipse), and the base plane (X1Y1 plane) is parallel to the observation range plane (the plane containing the boundary curve of the observation field of view surface). The X1 axis is parallel to the major axis of the observation field of view boundary, and the Y1 axis is parallel to the minor axis of the observation field of view boundary. e and b e Let L be the major and minor semi-axis of the ellipse L.

[0018] Furthermore, the coordinate transformation between the geocentric coordinate system (x, y, z) and the rectangular coordinate system (x1, y1, z1) based on the observed solid angle can be performed based on the following formula:

[0019] [x1y1z1]T=[R][xyz] T

[0020] Where [R] is the coordinate transformation matrix,

[0021]

[0022]

[0023] (x m ,y m ,z m ) represents the coordinates of the high-orbit satellite sensor (real-time position) in the geocentric (rectangular) coordinate system, where a and b are the equatorial radius (or major radius) and polar radius (or minor radius) of the ellipsoid at the top of the atmosphere, respectively.

[0024] Furthermore, the boundary curve of the field of view of the high-orbit satellite sensor at the top of the atmosphere can be calculated using the following formula:

[0025]

[0026] in,

[0027]

[0028] The following equation can be solved using a complete elliptic integral of the third kind:

[0029]

[0030] Furthermore, the equatorial radius (or major radius) and polar radius (or minor radius) of the ellipsoid at the top of the atmosphere can be determined based on the following formula:

[0031] a = a0 + h, b = b0 + h

[0032] Where a0 is the Earth's equatorial radius, b0 is the Earth's polar axis radius, and h is the height of the top of the atmosphere.

[0033] Furthermore, the semi-major and semi-minor axes of the ellipse of the boundary curve of the field of view surface of the high-orbit satellite sensor for the top of the atmosphere can be determined based on the following formula:

[0034]

[0035]

[0036] in

[0037]

[0038]

[0039] This invention designs an algorithm based on the Earth ellipsoid model. Based on the overall observation data at the hemispherical scale and considering the complexity of the influence of the Earth ellipsoid on the observation, it calculates the observation solid angle based on the Earth ellipsoid, thereby determining the radiance of the emitted energy from the top of the atmosphere within the field of view.

[0040] This invention provides a solution to the unique problems faced by new observation platforms. It can calculate the radiance of the hemispherical atmospheric top radiation without having to subdivide the Earth's ellipsoid and iterate multiple times, thus avoiding tedious calculations and reducing computational complexity.

[0041] This invention calculates in the Earth-fixed coordinate system, with clear geometric meaning, and can provide a reliable estimate of the radiant energy emitted from the top of the atmosphere under the assumption of an Earth ellipsoid.

[0042] This invention is convenient and quick to implement, yields simple and direct results, and the derived formulas occupy very little memory. It has the advantages of high efficiency and speed, and can be applied to the field of Earth observation, providing corresponding support for related research and other related work. Attached Figure Description

[0043] Figure 1 Example of solid angle observation from a high-orbit satellite under an Earth ellipsoid model;

[0044] Figure 2 The annual variation curves of the ratio of solid angles calculated based on the assumptions of Earth ellipsoid and Earth sphere for lunar-based and Sun-Earth Lagrange high-orbit platforms;

[0045] Figure 3 The difference in Earth's radiation outgoing energy calculated based on the Earth ellipsoid assumption and the Earth sphere assumption at a lunar base platform of 380,000 km is given. Detailed Implementation

[0046] See Figures 1-3 Based on the relevant theories of geodesy and atmospheric radiometry, this invention obtains the position information of the sensor in the geocentric coordinate system through satellite orbit information, obtains the field of view of the sensor based on the Earth ellipsoid model, and determines the radiation output energy of the top of the Earth's atmosphere within the field of view by calculating the solid angle of the given Earth ellipsoid model.

[0047] Due to the great distance from Earth, almost the entire Earth hemisphere can be seen from high-orbit satellites above the geostationary orbit altitude. Therefore, the influence of the chosen Earth ellipsoid model on the estimation cannot be ignored. It is necessary to calculate the observation solid angle based on the Earth ellipsoid to obtain the radiant energy emitted from the top of the atmosphere within the field of view. The specific steps are as follows:

[0048] Step 1: Represent the Earth ellipsoid model.

[0049] The ellipsoid of the upper atmosphere (the Earth's ellipsoid plus the thickness of the atmosphere) can be expressed in the Earth-centered, Earth-fixed (Cartesian) coordinate system (ECEF) as:

[0050]

[0051] That is

[0052] The equation for the ellipsoid of the top of the atmosphere is:

[0053] or, Where a0 is the Earth's equatorial radius, b0 is the Earth's polar radius, h is the height of the top of the atmosphere, (x e ,y e ,z e (x,y,z) are the coordinates of the ellipsoid at the top of the atmosphere, a = a0 + h is the major radius of the ellipsoid at the top of the atmosphere (or the equatorial radius, which corresponds to the equatorial radius of the Earth's ellipsoid), and b = b0 + h is the minor radius of the ellipsoid at the top of the atmosphere (or the polar radius, which corresponds to the polar radius of the Earth's ellipsoid).

[0054] Under the current technological context, the Earth ellipsoid can be represented by the WGS84 ellipsoid, where a0 = 6378137 km, b0 = 6356752.3142 km, and e 2 =0.00669437999013(e 2 (This is the square of the first eccentricity of the Earth's ellipsoid). The height h of the top of the atmosphere can be set to 20 km.

[0055] Step 2: Solve for the analytical high-orbit satellite observation field of view.

[0056] For any point p in space involved by the high-orbit satellite (or point p, for example, any real-time location of the high-orbit satellite sensor), its position vector p ECEF [x] can be used p ,y p ,z p ] T It means that (x) p ,y p ,z p Let p be the rectangular coordinates (Geocentric coordinate system coordinates). ECEF Expressed as a function in the corresponding spherical coordinates (geocentric geodetic coordinate system):

[0057]

[0058] in,

[0059]

[0060] and θ p These are the geographic latitude and longitude coordinates of the sensor's nadir point, h. p The elevation (height) of the sensor.

[0061] Similarly, the position vector d of any point d on the Earth's ellipsoid. ECEF It can also be expressed as a function in the corresponding latitude, longitude, and altitude coordinate system:

[0062]

[0063] in,

[0064]

[0065] (x d ,y d ,z d Let d be the rectangular coordinates (Geocentric coordinate system coordinates). and θ d The latitude and longitude of point d are respectively, and h is the geographical coordinates of point d. d Let d be the elevation of point d.

[0066] The cosine f of the observed zenith angle can be expressed as a function of any point d on the Earth's ellipsoid and the sensor's position p, i.e.

[0067]

[0068] The condition for the boundary of the observation field of view can be f = 0, that is, the boundary of the observation field of view satisfies the following condition:

[0069]

[0070] Equation 6 shows that the observation range boundary can be expressed as a function of the sensor orbital altitude and the latitude and longitude of the nadir point, thus determining the analytical observation field of view boundary. Furthermore, this function indicates that the observation field of view boundary is a spatial ellipse; therefore, the formula for calculating the observation solid angle under the spherical assumption will not be applicable.

[0071] Step 3: Solve for the observed solid angle.

[0072] Solving the observation field boundary based on the Earth ellipsoid, according to the observation solid angle Ω e Definition,

[0073]

[0074] Where S is the area of ​​a unit sphere centered on the observation point, projected onto the field of view of the high-orbit satellite sensor at the top of the atmosphere; r is the position vector of the infinitesimal element (or integral infinitesimal element) on the unit sphere; and ds is the vector of the infinitesimal element on the unit sphere (direction is the surface normal).

[0075] Equation 7 can be expressed in the form of (x1, y1, z1) Cartesian coordinates based on the observed solid angle:

[0076]

[0077] Where L is the boundary curve of the observation field of view surface of the high-orbit satellite sensor at the top of the atmosphere (which can be regarded as a spatial ellipse), and (x1, y1, z1) are the coordinates of any point on the observation field of view surface of the high-orbit satellite sensor at the top of the atmosphere in rectangular coordinates based on the observation solid angle. The rectangular coordinate system based on the observation solid angle refers to a coordinate system with the observation position (sensor position) as the origin, and its coordinate axes are represented by X1, Y1, and Z1 respectively. The direction of the Z1 axis is towards the boundary of the observation field of view (spatial ellipse), the base plane (X1Y1 plane) is parallel to the observation range plane (the plane where the boundary curve of the observation field of view surface is located), and the direction of the X1 axis is parallel to the major axis direction of the observation field of view boundary, and the direction of the Y1 axis is parallel to the minor axis direction of the observation field of view boundary.

[0078] Using the third complete elliptic integral, we get:

[0079]

[0080] Among them, the third complete elliptic integral formula is: θ is the integration angle of the complete elliptic integral, and ε and k are the elliptic integral parameters. a e and b e For the major and minor semi-axis of the observation field boundary, z1 is equal to the distance from the sensor to the plane where the observation field is located.

[0081] Therefore, the observation solid angle based on the Earth ellipsoid was solved by integrating the boundary of the observation field of view.

[0082] For position coordinates (Geocentric coordinate system coordinates) as (x m ,y m ,z m For any high-orbit satellite sensor m, considering the geometric relationship between the Earth's ellipsoid and the high-orbit observation platform, the boundary of its observation field of view is a spatial ellipse, which can be expressed as the following equation. In other words, its observation field of view boundary L at the top of the atmosphere is a curve defined by the following equations (set of equations):

[0083]

[0084] As can be seen from the formula for the observation solid angle, it is necessary to derive the parametric equation of the spatial ellipse in order to calculate the observation solid angle. Therefore, it is essential to transform the spatial ellipse in the geocentric coordinate system to a planar ellipse in rectangular coordinates based on the observation solid angle.

[0085] Let the two vectors n1 and n2 be:

[0086]

[0087]

[0088] The transformation matrix for the two vectors n1 and n2 is as follows:

[0089]

[0090] in

[0091]

[0092] The transformation relationship between the two coordinate systems is: [x1y1z1] T =[R][xyz] T

[0093] Therefore, the spatial ellipse can be expressed as:

[0094]

[0095] The parametric equations of this spatial ellipse are further obtained as follows:

[0096]

[0097] Where t is the parameter in the above parametric equation, taking values ​​in the range [0, 2π], and x1(t), y1(t), and z1(t) are the corresponding coordinates x, y, and z of the spatial ellipse (the boundary curve of the observation field surface) in the observation solid angle coordinate system (a rectangular coordinate system based on the observation solid angle). Therefore, the parametric equation can be written as:

[0098]

[0099] Obtain the major semi-axis a e and short half-axis b e :

[0100]

[0101]

[0102] in

[0103]

[0104] Step 4: Calculate the hemispherical scale atmospheric top radiation radiance based on the energy received from the observation field of view by the high-orbit sensor.

[0105] Let the energy received by the sensor be E. mThe radiance F of the energy emitted from the top of the atmosphere on a hemispherical scale can be written as:

[0106]

[0107] This invention realizes the estimation of the radiance of the Earth's atmosphere top radiation based on high-orbit satellite observations. The calculation is simple, efficient, reliable, and easy to use. It has significant advantages in terms of reliability, stability, and computational efficiency. The realization of high-orbit satellite platforms such as lunar-based Earth observation platforms and the Sun-Earth Lagrange L1 point platform has spurred the demand for estimation of hemispherical-scale atmosphere top radiation emission energy in this field. Therefore, it has broad application prospects in the field of Earth observation.

[0108] All coordinate systems involved in this invention can follow the right-hand rule, that is, all can adopt a right-hand coordinate system.

[0109] Unless otherwise specified, the preferred and optional technical means disclosed in this invention can be arbitrarily combined to form several different specific embodiments when one preferred or optional technical means is a further limitation of another technical means.

Claims

1. A method for estimating atmospheric top radiation emission energy based on high-orbit satellite sensors, characterized in that... The radiance of the emitted energy from the top of the atmosphere is calculated using the following formula: , in, The radiance of the energy emitted from the top of the atmosphere. This refers to the energy emitted from the top of the atmosphere received by high-orbit satellite sensors. The solid angle of observation of the top of the atmosphere by a high-orbit satellite sensor; The solid angle of observation of the top of the atmosphere by a high-orbit satellite sensor is calculated using the following formula: ， or, ， in, This represents the projection of the observation field of view of a high-orbit satellite sensor onto a unit spherical area centered on the observation point. Let be the position vector of a infinitesimal element on the unit sphere. Let be a infinitesimal vector on the unit sphere. The boundary curve of the field of view of the upper atmosphere observed by a high-orbit satellite sensor. The coordinates of the observation field of view of the top of the atmosphere by a high-orbit satellite sensor are in a Cartesian coordinate system based on the observation solid angle. This Cartesian coordinate system is defined with the observation position as the origin, and its coordinate axes are respectively... express, The axis is oriented towards the boundary of the observation field of view, and the base plane is parallel to the plane of the observation range. The axial direction is parallel to the major axis of the observation field of view boundary. The axial direction is parallel to the minor axis direction of the observation field of view boundary. and They are respectively The major and minor semi-axis of the ellipse; The coordinates in the Earth-centered and Earth-fixed coordinate system are determined based on the following formula: z) to coordinates in a rectangular coordinate system based on the observed solid angle ( Coordinate transformation between: in, This is the coordinate transformation matrix. ( ( ) represents the coordinates of the high-orbit satellite sensor in the geocentric-ground-fixed coordinate system. and These are the equatorial radius and polar axis radius of the ellipsoid at the top of the atmosphere, respectively.

2. The method for estimating atmospheric top radiation emission energy based on high-orbit satellite sensors as described in claim 1, characterized in that... The Earth shape model uses the WGS-84 ellipsoid.

3. The method for estimating atmospheric top radiation emission energy based on high-orbit satellite sensors as described in claim 1, characterized in that... The top of the atmosphere is represented by the top of the atmosphere ellipsoid, which is an ellipsoid formed by an atmosphere of equal thickness on the Earth's ellipsoid.

4. The method for estimating atmospheric top radiation emission energy based on high-orbit satellite sensors as described in claim 1, characterized in that... High-orbit satellites are Earth observation platforms that are higher than geostationary orbit.

5. The method for estimating atmospheric top radiation emission energy based on high-orbit satellite sensors as described in claim 1, characterized in that... The boundary curve of the field of view of the high-orbit satellite sensor at the top of the atmosphere is calculated using the following formula: 。 6. The method for estimating atmospheric top radiation emission energy based on high-orbit satellite sensors as described in claim 1, characterized in that... Solve the following equation using a complete elliptic integral of the third kind: 。 7. The method for estimating atmospheric top radiation emission energy based on high-orbit satellite sensors as described in claim 1, characterized in that... The equatorial radius and polar radius of the ellipsoid at the top of the atmosphere are determined based on the following formula: ， ， in, The radius of the Earth's equator. The radius of the Earth's polar axis. This refers to the height of the top of the atmosphere.

8. The method for estimating atmospheric top radiation emission energy based on high-orbit satellite sensors as described in claim 1, characterized in that... The semi-major axis of the ellipse that defines the boundary curve of the field of view surface of the high-orbit satellite sensor observing the top of the atmosphere is determined based on the following formula. and short half shaft : ； ； in ( ( ) represents the coordinates of the high-orbit satellite sensor in the geocentric-ground-fixed coordinate system. and These are the equatorial radius and polar axis radius of the ellipsoid at the top of the atmosphere, respectively.

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