Three-dimensional wind field inversion method and device for space-borne conical scanning Doppler radar

Abstract

The application provides a kind of spaceborne conical scanning Doppler radar three-dimensional wind field inversion method and device, the method comprises: the radar observation strip area is divided into multiple sub-blocks, and there is area overlap between adjacent sub-blocks, and the horizontal wind field of each height layer is parameterized in each sub-block with piecewise continuity variation assumption;Variational method is used to obtain the optimal horizontal wind field parameter of each height layer in each sub-block, and the horizontal wind field in each sub-block is determined according to the optimal horizontal wind field parameter, the horizontal wind field of the corresponding position of each sub-block in the overlapping area is linearly weighted and fused to obtain the final horizontal wind field;The horizontal divergence is calculated according to the optimal horizontal wind field parameter of each height layer in each sub-block, and the vertical wind field is obtained by integrating the horizontal divergence in the height direction using the atmospheric mass conservation equation, and the vertical wind field of the corresponding position of each sub-block in the overlapping area is linearly weighted and fused to obtain the final vertical wind field.The application realizes the continuous and robust three-dimensional wind field inversion of spaceborne conical scanning Doppler radar.

Description

Technical Field

[0001] This invention relates to the field of meteorological forecasting technology, and in particular to a method and apparatus for three-dimensional wind field inversion using a spaceborne conical scanning Doppler radar. Background Technology

[0002] To obtain global horizontal wind information within clouds, scholars have recently proposed the concept of using spaceborne conical scanning radar. By rotating the radar, the front and rear beams intersect at certain points, forming multi-view observations to obtain the orthogonal components of the wind field (such as...). Figure 1 As shown in the figure, this makes it possible to invert the entire wind field from the radial wind. However, since this radar is still a conceptual radar, there is a lack of mature wind field inversion methods.

[0003] However, wind field inversion is a classic problem in meteorological radar, especially ground-based radar, and methods such as single-radar inversion and dual / Doppler inversion have been developed. VAD (Velocity–Azimuth Display) can invert radial velocity azimuth scan observations at one or more elevation angles using a single radar, and invert wind direction, descent velocity, divergence / deformation profiles through harmonic fitting. This method requires the assumption that the wind field is homogeneous or exhibits only linear variation within the azimuth scan range. The applicability of this assumption decreases significantly with increasing scan radius. Spaceborne radar orbital altitudes generally exceed 500 km, and the horizontal diameter of the conical scan reaches 800 km, exceeding the scale of many weather systems; therefore, the assumption of homogeneous or linearly varying wind fields has a large error, making it difficult to achieve accurate wind field inversion using the VAD method.

[0004] Ground-based dual / Doppler wind field inversion is based on radial wind observations from two or more radars in the same observation area. The horizontal wind component at the intersection point is obtained by solving a simplified horizontal-radial wind mapping equation. Ground-based radars can invert high spatial resolution three-dimensional wind fields through dense volumetric scanning networks at multiple elevation angles. Spaceborne conical scanning radars, situated on a moving platform, can acquire observations of the orthogonal components of the wind field in the same area using beams from both the front and rear sides in a short time. However, due to the high speed of the moving platform and single elevation angle, the intersection points of Doppler observations with suitable intersection angles are sparsely distributed. This results in the classical dual-Doppler wind field inversion method only obtaining sparse point wind fields. Furthermore, the vertical airflow significantly affects the inversion accuracy due to the large elevation angle of the spaceborne radar.

[0005] The three-dimensional wind field inversion problem of spaceborne conical scanning Doppler radar is an underdetermined problem, and the main difficulties include:

[0006] 1. Applicability of inversion under ultra-large spatial scale and significantly non-uniform wind field

[0007] In situations where spaceborne radar observations often cover hundreds of kilometers and target systems are frequently non-uniform or nonlinear, the first challenge in inversion is how to improve the assumption of "uniform or low-order variation" relied upon by VAD-type methods to adapt to strong shear, strong convection, and rapidly evolving fields.

[0008] 2. The sparsity and uneven distribution of multi-view intersection points caused by spaceborne conical scanning method

[0009] During operation, the forward and backward beams of a spaceborne conical scanning radar intersect to form orthogonal components of the wind field for multi-view observation. However, due to the high operating speed, the intervals between the same azimuth trajectory lines reach tens of kilometers (the specific interval depends on the satellite's operating speed and the radar's conical scanning period). Therefore, the intersection points are relatively sparse and unevenly distributed (becoming denser from the nadir point towards both sides). Simultaneously, the intersection angles corresponding to the intersection points also differ at different distances from the nadir point (decreasing towards both sides). These characteristics lead to significant differences in orthogonal wind field observation information in different regions, representing the second major challenge in the inversion process.

[0010] 3. Horizontal and vertical information aliasing under the geometry of spaceborne high elevation angle observation

[0011] The observed radial velocity is a coupling quantity of horizontal wind velocity, vertical velocity, and particle falling velocity. The observation beam of a spaceborne conical scanning radar is generally at a large angle to the zenith (30-50 degrees). At this angle, the horizontal and vertical winds may have roughly equal contributions to the radial velocity. The third challenge in the inversion is how to collaboratively estimate the contributions of these two components when their information is mixed, reduce the influence of vertical component contamination on the estimation of the inverted wind vector (especially the horizontal wind), and make the wind vector stable and solvable under underdetermined conditions. Summary of the Invention

[0012] This invention provides a method and apparatus for three-dimensional wind field inversion using a spaceborne conical scanning Doppler radar, which addresses three major challenges in the prior art: (a) extremely large observation coverage and significant wind field non-uniformity; (b) sparse and unevenly distributed intersection points at multiple angles on the front and rear sides; and (c) the overlapping of horizontal wind, vertical wind, and particle terminal velocity under large elevation angle geometry. It realizes a set of overlapping block continuity constraint optimization inversion method to perform continuous and robust three-dimensional wind field reconstruction.

[0013] This invention provides a method for inverting three-dimensional wind fields using a spaceborne conical scanning Doppler radar, comprising:

[0014] The radar observation strip area is divided into multiple sub-blocks, with regional overlap between adjacent sub-blocks. Within each sub-block, the horizontal wind field at each altitude layer is parameterized based on the assumption of piecewise continuous variation.

[0015] The optimal horizontal wind field parameters of each height layer in each sub-block are obtained by using a variational method. The horizontal wind field in each sub-block is determined based on the optimal horizontal wind field parameters. The horizontal wind fields of corresponding positions in each sub-block in the overlapping area are linearly weighted and fused to obtain the final horizontal wind field.

[0016] The horizontal divergence is calculated based on the optimal horizontal wind field parameters at each height level within each sub-block. The vertical wind field is obtained by integrating the horizontal divergence in the height direction using the atmospheric mass conservation equation. The vertical wind fields at corresponding positions in each sub-block within the overlapping region are then linearly weighted and fused to obtain the final vertical wind field.

[0017] According to the present invention, a three-dimensional wind field inversion method for spaceborne conical scanning Doppler radar is provided. The inversion is performed in the satellite orbit coordinate system, where the direction parallel to the satellite's orbital direction is denoted as x-direction, the direction perpendicular to the satellite's orbital direction is y-direction, and the left side of the orbital direction is positive. The horizontal wind field at each altitude level is parameterized in each sub-block using the following linear transformation formula:

[0018] ;

[0019]

[0020] Where x and y are the distances of the observation point relative to the starting point of the sub-block in the x and y directions, respectively. , For corresponding wind speed; and It is the wind speed at the starting point within each sub-block. and They are respectively The average linear rate of change in the x and y directions, and They are respectively The average linear rate of change in the x and y directions, and the horizontal wind field parameters are: , , , , and .

[0021] According to the present invention, a three-dimensional wind field inversion method for spaceborne conical scanning Doppler radar is provided, which uses a variational method to obtain the optimal horizontal wind field parameters at each height layer within each sub-block. Its cost function is:

[0022]

[0023] in, Let be the total cost function. For observations, this represents the difference between the observed radial velocity and the radial velocity calculated based on the parameterized wind field. The background term represents the difference between wind field parameters and statistical characteristic parameters. To control background items Relative to the observation term The weight.

[0024] According to the present invention, a three-dimensional wind field inversion method for spaceborne conical scanning Doppler radar is provided, and the formula for the observation term is as follows:

[0025]

[0026] in, The number of effective observation points; This is a vector of horizontal wind field parameters. ; For the first One radial velocity observation, To correspond to the equivalent radial velocity, , The average falling velocity of the hydrogel; This represents the observation error of the radial velocity; For the first The coefficient vector corresponding to each radial velocity observation , , ; and These are the elevation angle of the radar beam relative to the horizontal plane and the azimuth angle relative to the y-direction, respectively.

[0027] The formula for the background item is:

[0028]

[0029] in, For the first A horizontal wind field parameter and The first The expected value and standard deviation of each horizontal wind field parameter.

[0030] According to the present invention, a three-dimensional wind field inversion method for spaceborne conical scanning Doppler radar is provided, which uses a variational method to obtain the optimal horizontal wind field parameters at each altitude layer within each sub-block, including:

[0031] In the process of inversion using variational methods, the L-BFGS-B method is used for iterative solution to obtain the optimal horizontal wind field parameters of each height layer in each sub-block, so as to minimize the cost function.

[0032] According to the present invention, a three-dimensional wind field inversion method for spaceborne conical scanning Doppler radar is provided, which calculates the horizontal divergence based on the optimal horizontal wind field parameters of each height layer within each sub-block using the following formula:

[0033]

[0034] in, For the kth height layer Horizontal divergence.

[0035] According to the present invention, a three-dimensional wind field inversion method for spaceborne conical scanning Doppler radar is provided, which obtains the vertical wind field by integrating the horizontal divergence in the height direction using the atmospheric mass conservation equation using the following formula:

[0036]

[0037] in, Let be the vertical velocity of the k-th height layer. For reference height, These are the boundary conditions at the corresponding height.

[0038] According to the present invention, a three-dimensional wind field inversion method for spaceborne conical scanning Doppler radar, in addition to linearly weighting and fusing the horizontal and vertical wind fields at corresponding positions of each sub-block in the overlapping region to obtain the final inversion result of the entire inversion region, also includes:

[0039] The final horizontal wind field projection is converted into a geographic wind field.

[0040] The present invention also provides a spaceborne conical scanning Doppler radar three-dimensional wind field inversion device, comprising:

[0041] The parameterization module is used to divide the radar observation strip area into multiple sub-blocks, with regional overlap between adjacent sub-blocks. Within each sub-block, the horizontal wind field at each height layer is parameterized based on the assumption of piecewise continuous variation.

[0042] The first calculation module is used to obtain the optimal horizontal wind field parameters of each height layer in each sub-block using a variational method, determine the horizontal wind field in each sub-block based on the optimal horizontal wind field parameters, and perform linear weighted fusion of the horizontal wind fields at corresponding positions of each sub-block in the overlapping area to obtain the final horizontal wind field.

[0043] The second calculation module is used to calculate the horizontal divergence based on the optimal horizontal wind field parameters of each height layer in each sub-block, and to obtain the vertical wind field by integrating the horizontal divergence in the height direction using the atmospheric mass conservation equation. The vertical wind fields at corresponding positions of each sub-block in the overlapping area are linearly weighted and fused to obtain the final vertical wind field.

[0044] The present invention also provides an electronic device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the program to implement the three-dimensional wind field inversion method of spaceborne conical scanning Doppler radar as described above.

[0045] The present invention also provides a non-transitory computer-readable storage medium storing a computer program thereon, which, when executed by a processor, implements the three-dimensional wind field inversion method of spaceborne conical scanning Doppler radar as described above.

[0046] The present invention also provides a computer program product, including a computer program that, when executed by a processor, implements the three-dimensional wind field inversion method of spaceborne conical scanning Doppler radar as described above.

[0047] The spaceborne conical scanning Doppler radar three-dimensional wind field inversion method and apparatus provided by this invention have the following main advantages:

[0048] 1. Overcoming the limitations of "sparse / uneven intersection points," significantly expanding the invertible region. Existing spaceborne conical scan multi-view methods largely rely on the geometric intersection points of the front / back beams, resulting in an extremely limited invertible region when intersection points are sparse or the included angle degenerates. This invention, through overlapping block division, linear continuity parameterization, and variational joint solution, describes the entire wind field within a sub-block using a small number of parameters, uniformly incorporating all radial velocities within that block (including observations at non-intersection points) into the cost function. This expands the problem from "only solvable at intersection points" to "solvable across the entire region." Therefore, under the same observation conditions, the spatial coverage of the three-dimensional wind field in this invention is significantly higher than that of inversion methods based solely on intersection points.

[0049] 2. Adapting to ultra-large spatial scales and significantly non-uniform wind fields, balancing accuracy and robustness. Ground-based VADs and their variants rely on assumptions of uniformity or low-order variation, resulting in significant errors at spaceborne scales of hundreds of kilometers and under conditions of strong convection / wind shear. This invention employs a locally linear + overlapping block approach: within each sub-block, the wind field is only required to be approximately linear at a scale of tens of kilometers, while overlapping and weighting ensure continuity between blocks. This avoids making overly strong global linear assumptions over the entire observation strip, while utilizing multi-block stacking to characterize more complex non-uniform and nonlinear structures, ensuring that the inversion still possesses good physical rationality and numerical stability at strong shear, strong convection, and strip scales.

[0050] 3. Explicitly process the terminal velocity of falling particles to reduce horizontal / vertical wind aliasing at high angles of elevation. Traditional methods often correlate vertical velocity w with falling velocity. Incorporate it into an "effective vertical velocity", or ignore it entirely. In spaceborne high-elevation-angle geometry, this severely contaminates horizontal wind inversion. This invention estimates horizontal wind using information such as radar reflectivity factors. Before horizontal wind inversion, it is first subtracted from radial velocity. Furthermore, the vertical velocity w is solved uniformly through mass conservation integrals. This significantly reduces the systematic influence of particle falling velocity on the inversion of horizontal and vertical winds, improves the reliability of inversion in areas of heavy precipitation and high-altitude ice crystals, and effectively addresses the shortcomings of existing technologies in the third challenge.

[0051] 4. Overlapping segmentation and linear weighted fusion ensure overall wind field continuity and smoothness. Traditionally, simply stitching together independent inversion results from different regions easily leads to obvious "seams" and discontinuities at the boundaries. This invention sets 20%–50% overlap bands between sub-blocks and applies linear weights (such as bilinear weights) to multiple solutions within the overlapping regions based on spatial location. When necessary, overlap consistency can also be incorporated into the cost function to form soft constraints. This ensures smooth transitions at the strip scale and overall continuity while maintaining local adaptability, avoiding pseudo-gradients and numerical oscillations caused by simple stitching.

[0052] 5. Pixel-level uncertainty estimation is provided, facilitating quality control and data assimilation. Within the linear quadratic variational framework of this invention, the Hessian matrix can be directly used to estimate the parameter covariance, and then the error propagation formula can be used to obtain the value for each grid point. , Uncertainties in wind speed and direction. Compared to traditional methods that only provide wind vectors without error information, this invention can output voxel-level error estimates and quality indicators, facilitating subsequent data assimilation using an "error-weighted" approach to absorb observations. It also allows users to filter high-confidence areas based on uncertainty, improving the security and reliability of business applications.

[0053] 6. The computational load is controllable, easily implemented in parallel, and highly feasible in engineering. This invention inverts only six linear parameters within each sub-block, with a convex quadratic cost function that can be solved using efficient algorithms such as L-BFGS-B or least squares. Most computational steps between sub-blocks can be performed in parallel, with limited information exchange only occurring during overlap fusion or consistency constraints. Therefore, compared to global optimization methods that require direct solution of the 3D wind field on a large-scale grid across the entire domain, this invention offers advantages such as moderate computational load, modular implementation, and ease of deployment on parallel computing platforms while maintaining inversion accuracy. It is suitable for the large-scale, near-real-time operational processing needs of spaceborne missions.

[0054] 7. Highly adaptable; parameters and structure can be flexibly adjusted according to the task. The block size, overlap ratio, and background weight of this invention... Error statistics and other parameters can be optimized and configured according to mission requirements (such as stratiform clouds / convective clouds, different orbital altitudes, and scanning modes). Furthermore, the linear assumption can be extended to higher-order forms such as piecewise splines. Compared to traditional algorithms with relatively rigid structures, this invention offers better scalability and adjustability, facilitating its application across different spaceborne platforms and operational systems. Attached Figure Description

[0055] To more clearly illustrate the technical solutions in this invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of this invention. For those skilled in the art, other drawings can be obtained from these drawings without creative effort.

[0056] Figure 1 This is a schematic diagram of the footprint line (arc) and radar position (straight line) of a spaceborne conical scanning radar provided by existing technology. The same color represents the same time.

[0057] Figure 2 This is a flowchart illustrating the three-dimensional wind field inversion method for spaceborne conical scanning Doppler radar provided by the present invention.

[0058] Figure 3 This is a schematic diagram of the simulation and solution results of a certain height layer in the three-dimensional wind field inversion method of spaceborne conical scanning Doppler radar provided by the present invention;

[0059] Figure 4 This is a schematic diagram of the structure of the spaceborne conical scanning Doppler radar three-dimensional wind field inversion method device provided by the present invention. Detailed Implementation

[0060] To make the objectives, technical solutions, and advantages of this invention clearer, the technical solutions of this invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of this invention. All other embodiments obtained by those skilled in the art based on the embodiments of this invention without creative effort are within the scope of protection of this invention.

[0061] The following is combined Figure 2 The present invention describes a method for inverting three-dimensional wind fields using a spaceborne conical scanning Doppler radar, comprising:

[0062] Step 201: Divide the radar observation strip area into multiple sub-blocks, with regional overlap between adjacent sub-blocks. Within each sub-block, parameterize the horizontal wind field at each height level based on the assumption of piecewise continuous variation.

[0063] Step 202: Use variational methods to obtain the optimal horizontal wind field parameters of each height layer in each sub-block, determine the horizontal wind field in each sub-block based on the optimal horizontal wind field parameters, and perform linear weighted fusion of the horizontal wind fields at corresponding positions of each sub-block in the overlapping area to obtain the final horizontal wind field.

[0064] Step 203: Calculate the horizontal divergence based on the optimal horizontal wind field parameters of each height layer in each sub-block, and use the atmospheric mass conservation equation to integrate the horizontal divergence in the height direction to obtain the vertical wind field. Then, perform linear weighted fusion of the vertical wind fields at corresponding positions of each sub-block in the overlapping area to obtain the final vertical wind field.

[0065] The inversion area is horizontally divided into blocks, and the continuity of horizontal wind field changes within each block is considered. The block size is selected based on a trade-off between parameters such as the footprint radius, movement speed, and scanning speed of the pin-mounted conical scanning Doppler radar: if the block is too large, the uncertainty of subsequent continuity assumptions will increase significantly; if the block is too small, the number of multi-view radial wind observations within the area will be too small or the coverage area will be too small, increasing the uncertainty of the inversion.

[0066] Regarding the segmentation strategy, this embodiment adopts an overlapping segmentation method: except for the outermost region, each sub-block is partially spatially superimposed (e.g., 20%-50%) with adjacent sub-blocks in the front-back and left-right directions. If the same spatial point is covered by multiple sub-blocks, its wind field inversion result is obtained by linearly weighting the results of these sub-blocks according to their spatial relative positions (e.g., bilinear weighting can be used). This overlapping and weighting method ensures the overall continuity and smooth transition of the wind field between different regions. On the other hand, compared with the simple linear assumption of a single large region, it can more effectively characterize the spatially non-uniform and nonlinear wind field structure, solving the first difficulty of inversion.

[0067] Regarding the block size, in this embodiment, the length of the sub-block selected along the x-direction is approximately equal to the radar's movement distance within one scan cycle, and the length of the sub-block selected along the y-direction is approximately 2 / 3 of that along the x-direction. Each sub-block is spatially superimposed on its adjacent sub-blocks by 50% in both the front-back and left-right directions. These parameters can be adjusted to suit specific tasks. For example, in a stratiform cloud system, where the spatial consistency of the wind field is enhanced, the sub-blocks can be enlarged to ensure sufficient data within each sub-block.

[0068] For a given observation height within each sub-block, the optimal horizontal wind field parameters are solved using a variational method. After obtaining the horizontal wind field parameters for each sub-block and each altitude layer, the vertical velocity is integrally inverted using the atmospheric mass conservation equation.

[0069] This embodiment provides a set of overlapping block continuity constraint optimization inversion method: the radar observation strip area is divided into horizontal sub-blocks (blocks) with overlapping bands, the wind field is parameterized in each sub-block with the assumption of piecewise continuity change, and the wind field is inverted by jointly using the sparse and irregularly distributed multi-view observations from the front and rear sides in the optimization framework. Adjacent sub-blocks are combined in the overlapping band through consistency constraints to achieve continuous and robust three-dimensional wind field reconstruction.

[0070] Based on the above embodiments, this embodiment assumes that the horizontal wind field at each altitude changes continuously within the inversion block, and uses a few parameters to parameterize the horizontal wind field within the block. This embodiment mainly considers the linear assumption, that is, it assumes that the wind speed u parallel to the satellite's direction of motion (x-direction) and the wind speed v perpendicular to the satellite's direction of motion (y-direction) (positive along the left side of the orbital direction) satisfy:

[0071] ;

[0072]

[0073] Where x and y are the distances of the observation point relative to the starting point of the sub-block in the x and y directions, respectively. , For corresponding wind speed; and It is the wind speed at the starting point within each sub-block. and They are respectively The average linear rate of change in the x and y directions, and They are respectively The average linear rate of change in the x and y directions, and the horizontal wind field parameters are: , , , , and .

[0074] Based on the above embodiments, in this embodiment, for a certain observation height within each sub-block, the variational method is used to comprehensively utilize the optimal solution for the horizontal wind field parameters ( , , , , , Its cost function is:

[0075]

[0076] in, Let be the total cost function. For observation terms, it represents the difference between the observed radial velocity and the radial velocity calculated based on the parameterized wind field (observation operator). The background term represents the difference between wind field parameters and statistical characteristic parameters. To control background items Relative to the observation term The weighting, empirically taken Magnitude (generally taken as 0-) (between). When A value of 0 indicates that the background term is not used; otherwise, both the background and observations are used to constrain the inverted wind field.

[0077] Under normal circumstances, the radar beam elevation angle and azimuth The radial velocity component of the point with respect to the horizontal velocity / Vertical velocity component and the falling speed of the uniform concrete The complete operator can be represented as:

[0078]

[0079] For spaceborne radar inversion, the radial velocity observation points are relatively sparse. In the horizontal inversion, w is not explicitly inverted, but is determined by the subsequent mass conservation integral.

[0080] Cost function observation term representation At each valid observation point, parameterized , The difference between the calculated radial velocity and the actual observation is as follows:

[0081]

[0082] The average falling velocity of the water-soluble material is estimated using information such as radar reflectivity factor and temperature at each observation point. For ease of calculation, an equivalent radial velocity for particle falling is constructed. :

[0083]

[0084] The observation terms are:

[0085]

[0086] Background items The difference between wind field parameters and statistical characteristic parameters is expressed as:

[0087]

[0088] in, , , , , , Let be the expected value of the wind field parameters. , , , , , The corresponding standard deviations. These parameters can be obtained by using numerical models to perform ensemble simulations of specific systems or regions and then statistically analyzing them.

[0089] Based on the above embodiments, the cost function in this embodiment can also be represented in vector form, and the total cost function... Regarding the horizontal wind field parameter vector It is a convex quadratic function. Let the th... The coefficient vector corresponding to each radial velocity observation for:

[0090]

[0091] in, , At this point, the radial velocity given by the parameterized wind field can be written as:

[0092]

[0093] The formula for the observation term is:

[0094]

[0095] The formula for the background item is:

[0096]

[0097] in, Let k be the horizontal wind field parameter. and The first The expected value and standard deviation of each horizontal wind field parameter.

[0098] Based on the above embodiments, this embodiment uses a variational method to obtain the optimal horizontal wind field parameters at each height level within each sub-block, including:

[0099] In the process of inversion using variational methods, the L-BFGS-B method is used for iterative solution to obtain the optimal horizontal wind field parameters of each height layer in each sub-block, so as to minimize the cost function.

[0100] The variational inversion process is the process of minimizing the cost function. In this embodiment, the L-BFGS-B method is used for iterative solution. The solution process requires the gradient of the cost function with respect to the solution variables (usually called state variables).

[0101] As can be seen from the simplified cost function, the observation equation is linear with respect to the parameters, and both the observation and background terms are quadratic. Therefore, the total cost function is a convex quadratic function with respect to the parameters, which is essentially equivalent to a linear least squares problem with the background term introduced. Its gradient is an affine function with respect to the parameters (a vector composed of multiple linear functions).

[0102] The gradient of the observation term is:

[0103] The gradient of the background term is:

[0104] thereby:

[0105]

[0106] During optimization inversion, the L-BFGS-B algorithm constructs an approximation of the Hessian inverse matrix in each iteration using the current gradient and a finite amount of historical iteration information, thereby determining the search direction. It updates the algorithm while satisfying the linear search condition and incorporating parameter boundary constraints (e.g., limiting wind speed or gradient to a reasonable physical range). Since the cost function in this embodiment is a convex quadratic form, L-BFGS-B typically converges to the global optimum within a relatively small number of iterations. When no boundary constraints are imposed on x, the problem can be equivalently rewritten as (regularized) linear least squares and solved directly using normal equations or methods such as QR / SVD.

[0107] By using partitioned optimal inversion, all observation data within a region can be used simultaneously for optimal inversion of the regional wind field. The inversion is no longer limited to intersection points, effectively expanding the region and making effective use of observation information, thus effectively solving the second difficulty of inversion. At the same time, by utilizing the continuous characteristics of horizontal wind, the influence of the aliasing of horizontal and vertical wind and the terminal velocity of falling particles on the inversion is avoided in single-point solutions, effectively solving the third difficulty of inversion.

[0108] Based on the above embodiments, this embodiment obtains the horizontal wind field parameters for each sub-block and each altitude layer. Next, the vertical velocity was integrally inverted using the atmospheric mass conservation equation. Since the aforementioned processing has already explicitly subtracted... The contribution to the radial velocity is therefore obtained from the divergence integral. This corresponds to the vertical motion of air itself. For simplicity, we assume that the density in the analysis region changes only with height, satisfying an approximately divergence-free (or uncompressible) condition, then we have:

[0109] in, For the horizontal wind component, This represents the vertical velocity of the air.

[0110] For each sub-block, each height layer Based on the aforementioned linear assumption, the horizontal divergence of this height layer can be directly obtained:

[0111]

[0112] in, For the kth height layer Horizontal divergence.

[0113] Based on the above embodiments, the following can be obtained from the mass conservation equation in this embodiment:

[0114]

[0115] Integrating along the height direction yields the vertical velocity at any height:

[0116]

[0117] in, Let the vertical velocity be the velocity at the k-th height level. For reference height, These are the boundary conditions at the corresponding height.

[0118] Considering the top-down scanning method of spaceborne radar, this embodiment adopts a top-down integration method: for the troposphere and below, the top layer of the analysis area is typically taken. As a reference height. Assuming (If the vertical motion of the upper atmosphere is relatively small, or if a small background value is given by the numerical model), then:

[0119]

[0120] In practical calculations, the height direction is discretized into several layers. , record The horizontal divergence of the layer is The grid spacing is Then the top-down integral can be implemented in discrete form as follows:

[0121] ;

[0122] ;

[0123] in, The average of the divergence between the upper and lower layers can be taken to improve numerical stability. This allows the vertical velocity profile to be obtained layer by layer at each horizontal grid point. .

[0124] Within the overlapping block framework, the calculation of vertical velocity is consistent with that of horizontal wind field; that is, within each sub-block, the corresponding vertical velocity is first calculated using the horizontal wind parameters of that sub-block. And integrate using the method described above to obtain the block content. For the same grid point located within the overlapping region of multiple sub-blocks, its vertical velocity is also weighted and superimposed according to the aforementioned bilinear (or other linear) weights to ensure the continuity and smooth transition of vertical velocity between different sub-blocks. Through the above-mentioned mass conservation integral method, this embodiment further obtains a dynamically consistent vertical wind field based on the inverted continuous horizontal wind field, realizing the complete reconstruction of the three-dimensional wind vector field.

[0125] Meanwhile, since the vertical velocity is obtained by the divergence integral of the horizontal wind field, compared with the single-point solution that directly separates w from the particle's final velocity in the radial velocity, it more robustly reduces the influence of the overlap of horizontal wind, vertical wind, and final velocity on the vertical wind field estimation under large elevation angle geometry, thus effectively addressing the third difficulty of inversion.

[0126] Based on the above embodiments, this embodiment performs linear weighted fusion of the horizontal and vertical wind fields at corresponding positions of each sub-block in the overlapping area to obtain the final inversion result of the entire inversion area.

[0127] Meanwhile, the embodiments defined , In the orbital system (along and across orbits), the wind field in the geographic system needs to be obtained through conversion, i.e. (Eastward wind speed component is positive) (Wind speed component with a positive northward orientation) or wind speed Wind direction (relative to due north on Earth).

[0128] Define a satellite orbital heading angle as It is the azimuth angle of the satellite's ground trajectory at that point, defined as the angle rotated clockwise from due north to the direction of the satellite's motion. At this point, the rotational relationship between the wind field in the orbital system and the geographic system is:

[0129]

[0130]

[0131] The wind speed is constant during rotation, and... , The relationship is:

[0132]

[0133] To calculate the meteorological wind direction angle (the direction from which the wind blows) with true north as 0 and clockwise as positive, we can first calculate the angle of the wind vector relative to the orbital coordinate system (starting from the satellite's direction of motion, rotating counterclockwise to the direction the wind vector points; denoted in radians):

[0134]

[0135] Then add the satellite's heading angle. This gives us the "direction of travel" (the direction the wind blows) relative to true north in the geography system:

[0136]

[0137] Add (Corresponding to 180°) and converted to 0-2 (Corresponding to 0-360°) Obtain wind direction (where the wind is coming from):

[0138]

[0139] Based on the above embodiments, this embodiment can simultaneously estimate the inversion error during the inversion: the error covariance matrix of the observed wind field parameters can be obtained from the inverse of the Hessian in variational inversion. Find the second derivative and multiply by the global scaling factor 1 / 2 to obtain the Hessian matrix:

[0140]

[0141] in, The covariance matrix of the parameter estimation is approximately:

[0142]

[0143] Further based on the horizontal wind field , The parameterized relations can be written in matrix form.

[0144]

[0145]

[0146] in

[0147]

[0148]

[0149] At this point, the grid point Upper horizontal wind field ( and Uncertainty (variance) can be obtained using the error propagation formula:

[0150]

[0151] The covariance between the two components is

[0152]

[0153] The corresponding error covariance matrix is ​​expressed as follows

[0154]

[0155] Furthermore, horizontal wind speed Uncertainty can be achieved through in Perform first-order linearized propagation, corresponding to the Jacobian equation:

[0156]

[0157]

[0158] so The variance is approximately:

[0159] ;

[0160] Right now:

[0161] ;

[0162] Similarly, wind direction The uncertainty is mainly related to the formula. Regarding (other parameters are constants), perform first-order error propagation on it:

[0163]

[0164] (that is) The variance of ) is:

[0165]

[0166] in, The unit is radians, multiplied by Obtain the degree unit.

[0167] Depend on As can be seen from the formula, the inversion error is affected by the observation, background field, and The combined influence of. In the observations, It includes multiple factors such as radial velocity observation error, quantity, and the azimuth / elevation angle of the location:

[0168] 1) Under the same conditions, the number of effective radial velocity observations within the sub-block The more, The eigenvalues ​​increase overall, and the inversion error roughly follows the formula. The regularity decreases;

[0169] 2) For the horizontal wind component, the radial velocity is related to... , Sensitivity and Proportional, the closer the elevation angle is to horizontal ( The larger the elevation angle, the smaller the inversion error; when the elevation angle is too large, the constraint on the horizontal wind weakens and the uncertainty increases.

[0170] 3) The more uniform the azimuth distribution, the closer the angle between the front and rear beams is to orthogonality. The closer the matrix is ​​to isotropic, the larger its minimum eigenvalue and the better the inversion conditions. If the azimuth angle is concentrated in a narrow sector, the matrix tends to be ill-conditioned, some wind components are almost negligible, and the inversion error is significantly amplified.

[0171] 4) For parameterizations that include horizontal gradients, in addition to the number of observations and azimuth angle, the spatial distribution of observation points within the sub-block also directly affects the parameterization. When the observation points are sufficiently dispersed within a region, the constraint on the gradient is stronger, and its uncertainty is less than that when the observations are concentrated in a small region.

[0172] After calculating the inversion error at each point using the above method, this error is also output as part of the product. This not only outputs the inversion result but also allows for further quantification of its error characteristics. Furthermore, this embodiment also sets an error threshold; when… or If the standard deviation exceeds the threshold (e.g., 4 m / s), the wind field at the corresponding point will no longer be output.

[0173] Since the spaceborne conical scanning radar is still in the experimental stage, the following explanation is based on the forward modeling results of numerical simulation. This embodiment selects the high-resolution numerical forecast results of Typhoon Soulik in 2023 (horizontal grid spacing of 3 km) as the "true value scenario" to extract temperature and three-dimensional wind vectors. The characteristics of different water-soluble particle distributions were used to simulate a spaceborne conical scanning Doppler radar. The simulated orbit had a semi-major axis of 6878 km, an eccentricity of 0, and an orbital inclination of 65 degrees. The radar wavelength was 94 GHz (W-band), the beamwidth was 0.11 degrees, the range was 500 meters, the conical scanning distance from the zenith was 38 degrees, and the scanning speed was 10 revolutions per minute. The radar observed a typhoon near 111 degrees east longitude and 22 degrees north latitude, at which time the satellite's orbital altitude was approximately 501 km and its moving speed was approximately 7.4 km / s.

[0174] An analysis grid was constructed in the orbital coordinate system: the grid spacing was 45 km in both the along-track (x) and across-track (y) directions. Horizontal partitioning was performed on the plane according to a partitioning strategy, with overlapping zones set.

[0175] Length of track sub-block The satellite's ground displacement (45 km) is taken as the distance within one scan cycle; the length of the trans-orbit sub-block. Except for the edges, adjacent sub-blocks overlap by about 50% in the front / back and left / right directions.

[0176] For each altitude level and each sub-block, the horizontal wind component of the orbital system is calculated using the aforementioned general method of "linear continuity assumption + variational cost function". , Parameterization. And observations are made using the effective radial velocities of all falling sub-blocks. As input to the observations, construct the corresponding cost function. For the sake of simplicity, Set to 0. In implementation, the vector form and gradient expression given earlier are directly reused, and the L-BFGS-B algorithm is used for solving. , The initial values ​​are all 0 m / s. , , , The processing speed is 0 m / (s km). The optimal convergence condition is that the change in the relative objective function is less than 0. or gradient norm less than m / s, maximum number of iterations 100.

[0177] Find the optimal parameters for each sub-block Then, restore it to the grid within the sub-block. , Field. Grid points located in the overlapping areas of multiple sub-blocks are fused using bilinear weighting based on the distance between the sub-block centers to obtain the continuous orbital horizontal wind field over the entire observation strip.

[0178] At each height level, based on the sub-block parameters Calculate the horizontal divergence and perform weighted fusion in the overlapping region to obtain a continuous strip within the strip range. Field. Then, the mass conservation equation is applied in the height direction. Integrating from top to bottom, with the top-level boundary conditions taken as follows: (Or take the minimum value of the model field) to obtain the vertical air velocity at each altitude level. The marginal regions can be fused with the model background field according to weights to avoid anomalous oscillations in unobserved areas.

[0179] Finally, using the known orbital heading angle, the orbital wind field is determined. Rotate to the geography system to get east and west winds. and north and south winds The horizontal wind speed and wind direction angle (0° north, positive clockwise) are calculated. The error estimation section directly uses the aforementioned Hessian and error propagation formulas, providing the error for each grid point. , , And the uncertainty of wind speed and wind direction.

[0180] Figure 3 This is a schematic diagram of the simulation results at an altitude of approximately 6.9 kilometers in this embodiment, where: Figure 3 (a) shows the true wind field based on numerical simulation (wind speed coloring and wind feather diagram); Figure 3 (b) shows the radial velocity field generated by radar geometry based on this. The black dashed line is the satellite orbit line. It can be seen that the observation is distributed in a strip along the orbit. The intersection of the front and rear beams is relatively sparse near the orbit, while it is obviously dense in the two sides. Figure 3 (c) shows the horizontal wind speed and wind vector field (wind plume) obtained by inversion using the method of this invention and projected onto geographic coordinates. The intersection angle of the front and rear beam scans within 100 km of the orbit is too small and the inversion error is large, so it is not output. Figure 3 In the middle (d), the numerical simulation true values ​​and the inversion parameters are compared.

[0181] from Figure 3 It can be seen that in both dense and sparse regions of the intersection points of the front and rear beams, the method of this invention can provide a continuous and smooth horizontal wind vector field. The principal-scale wind direction is consistent with the true numerical value, indicating that the overlapping block-variational joint inversion can effectively overcome the limitation of "only intersection points can be solved". In regions with very few intersection points on both sides of the strip, the inverted wind field does not show obvious noise amplification or broken structure. In the typhoon eyewall, the spatial distribution of the inverted wind vector also has good consistency with the true field. The quantitative assessment shows a correlation coefficient of about 0.98 and a root mean square error of 1.8 m / s, both of which indicate that the inversion has high accuracy and robustness.

[0182] This embodiment verifies the feasibility and effectiveness of the present invention under spaceborne conical scanning geometry. This is achieved by adjusting sub-block size, overlap ratio, background weight, and... The parameterized form can achieve similar results at different orbital altitudes and observation modes, and those skilled in the art can make various equivalent improvements to the present invention accordingly.

[0183] The following describes the spaceborne conical scanning Doppler radar three-dimensional wind field inversion device provided by the present invention. The spaceborne conical scanning Doppler radar three-dimensional wind field inversion device described below can be referred to in correspondence with the spaceborne conical scanning Doppler radar three-dimensional wind field inversion method described above.

[0184] like Figure 4As shown, the device includes a parameterization module 401, a first calculation module 402, and a second calculation module 403, wherein:

[0185] The parameterization module 401 is used to divide the radar observation strip area into multiple sub-blocks, with regional overlap between adjacent sub-blocks. Within each sub-block, the horizontal wind field at each height layer is parameterized based on the assumption of piecewise continuous variation.

[0186] The first calculation module 402 is used to obtain the optimal horizontal wind field parameters of each height layer in each sub-block using a variational method, determine the horizontal wind field in each sub-block according to the optimal horizontal wind field parameters, and perform linear weighted fusion of the horizontal wind fields at the corresponding positions of each sub-block in the overlapping area to obtain the final horizontal wind field.

[0187] The second calculation module 403 is used to calculate the horizontal divergence based on the optimal horizontal wind field parameters of each height layer in each sub-block, and to obtain the vertical wind field by integrating the horizontal divergence in the height direction using the atmospheric mass conservation equation. The vertical wind fields at corresponding positions of each sub-block in the overlapping area are linearly weighted and fused to obtain the final vertical wind field.

[0188] This embodiment provides a set of overlapping block continuity constraint optimization inversion method: the radar observation strip area is divided into horizontal sub-blocks (blocks) with overlapping bands, the wind field is parameterized in each sub-block with the assumption of piecewise continuity change, and the wind field is inverted by jointly using the sparse and irregularly distributed multi-view observations from the front and rear sides in the optimization framework. Adjacent sub-blocks are combined in the overlapping band through consistency constraints to achieve continuous and robust three-dimensional wind field reconstruction.

[0189] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for inverting three-dimensional wind fields using a spaceborne conical scanning Doppler radar, characterized in that, include: The radar observation strip area is divided into multiple sub-blocks, with regional overlap between adjacent sub-blocks. Within each sub-block, the horizontal wind field at each altitude layer is parameterized based on the assumption of piecewise continuous variation. The optimal horizontal wind field parameters of each height layer in each sub-block are obtained by using a variational method. The horizontal wind field in each sub-block is determined based on the optimal horizontal wind field parameters. The horizontal wind fields of corresponding positions in each sub-block in the overlapping area are linearly weighted and fused to obtain the final horizontal wind field. The horizontal divergence is calculated based on the optimal horizontal wind field parameters of each height layer in each sub-block. The vertical wind field is obtained by integrating the horizontal divergence in the height direction using the atmospheric mass conservation equation. The vertical wind fields of corresponding positions in each sub-block in the overlapping area are linearly weighted and fused to obtain the final vertical wind field. The inversion is performed in the satellite orbit coordinate system, where the x-direction is parallel to the satellite's orbital direction, the y-direction is perpendicular to the satellite's orbital direction, and the left side of the orbital direction is positive. The horizontal wind field at each altitude level is parameterized in each sub-block using the following linear transformation formula: ； ； Where x and y are the distances of the observation point relative to the starting point of the sub-block in the x and y directions, respectively. , For corresponding wind speed; and It is the wind speed at the starting point within each sub-block. and They are respectively The average linear rate of change in the x and y directions, and They are respectively The average linear rate of change in the x and y directions, and the horizontal wind field parameters are: , , , , and ; The optimal horizontal wind field parameters at each height level within each sub-block are obtained using a variational method, with the following cost function: ； in, Let be the total cost function. For observations, this represents the difference between the observed radial velocity and the radial velocity calculated based on the parameterized wind field. The background term represents the difference between wind field parameters and statistical characteristic parameters. To control background items Relative to the observation term The weight.

2. The method for inverting three-dimensional wind fields using spaceborne conical scanning Doppler radar according to claim 1, characterized in that, The formula for the observation term is: ； in, The number of effective observation points; This is the horizontal wind field parameter vector. ; For the first One radial velocity observation, To correspond to the equivalent radial velocity, , The average falling velocity of the hydrogel; This represents the observation error of the radial velocity; For the first The coefficient vector corresponding to each radial velocity observation , , , and The first Two components of horizontal wind at each observation point , Geometric coefficients projected onto the radar line-of-sight direction. and The first Each observation point is relative to the starting point of this sub-block. and displacement in the y direction; and These are the elevation angle of the radar beam relative to the horizontal plane and the azimuth angle relative to the y-direction, respectively. The formula for the background item is: ； in, For the first A horizontal wind field parameter and The first The expected value and standard deviation of each horizontal wind field parameter.

3. The method for inverting three-dimensional wind fields using spaceborne conical scanning Doppler radar according to claim 1, characterized in that, The optimal horizontal wind field parameters at each height level within each sub-block are obtained using variational methods, including: In the process of inversion using variational methods, the L-BFGS-B method is used for iterative solution to obtain the optimal horizontal wind field parameters of each height layer in each sub-block, so as to minimize the cost function.

4. The method for inverting three-dimensional wind fields using spaceborne conical scanning Doppler radar according to claim 1, characterized in that, The horizontal divergence is calculated using the following formula based on the optimal horizontal wind field parameters at each height level within each sub-block: ； in, Indicated on the horizontal coordinate And vertically towards the first Floor height Horizontal divergence at that point for At height The average linear rate of change in the x-direction at point X. for At height The average linear rate of change in the y-direction.

5. The method for inverting three-dimensional wind fields using spaceborne conical scanning Doppler radar according to claim 4, characterized in that, The vertical wind field is obtained by integrating the horizontal divergence along the height direction using the atmospheric mass conservation equation as follows: ； in, Let the vertical velocity be the velocity at the k-th height level. For reference height, For the boundary conditions at the corresponding height, For the k-th height layer, It is a temporary height variable in the integral.

6. The method for inverting three-dimensional wind fields using a spaceborne conical scanning Doppler radar according to any one of claims 1-5, characterized in that, The final inversion result of the entire inversion area is obtained by linearly weighting and fusing the horizontal and vertical wind fields at corresponding locations in each sub-block of the overlapping region, and also includes: The final horizontal wind field projection is converted into a geographic wind field.

7. A spaceborne conical scanning Doppler radar three-dimensional wind field inversion device, characterized in that, The method for inverting three-dimensional wind fields using a spaceborne conical scanning Doppler radar as described in any one of claims 1-6 includes: The parameterization module is used to divide the radar observation strip area into multiple sub-blocks, with regional overlap between adjacent sub-blocks. Within each sub-block, the horizontal wind field at each height layer is parameterized based on the assumption of piecewise continuous variation. The first calculation module is used to obtain the optimal horizontal wind field parameters of each height layer in each sub-block using a variational method, determine the horizontal wind field in each sub-block based on the optimal horizontal wind field parameters, and perform linear weighted fusion of the horizontal wind fields at corresponding positions of each sub-block in the overlapping area to obtain the final horizontal wind field. The second calculation module is used to calculate the horizontal divergence based on the optimal horizontal wind field parameters of each height layer in each sub-block, and to obtain the vertical wind field by integrating the horizontal divergence in the height direction using the atmospheric mass conservation equation. The vertical wind fields at corresponding positions of each sub-block in the overlapping area are linearly weighted and fused to obtain the final vertical wind field.

8. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the program, it implements the three-dimensional wind field inversion method of spaceborne conical scanning Doppler radar as described in any one of claims 1 to 6.

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