Antarctic ice cover material balance inversion method and equipment based on prior information constraint

Abstract

The invention provides a prior information constraint-based Antarctic ice cover material balance inversion method and device, and the method comprises the steps: obtaining satellite height measurement data, and extracting an elevation parameter of an Antarctic ice cover region; preprocessing the gravity satellite data; performing inversion material balance of physical priori constraint, including dividing the Antarctic ice cover into Mascon units which are geographically aligned with the ice flow basin, constructing a regularization constraint matrix of space differentiation based on elevation variation variance of satellite altimetry data, dynamically optimizing regularization parameters in combination with generalized cross validation criterion, and solving mass change; and outputting the Antarctic ice cover material balance result. According to the method, regularization is carried out by using the uncertainty difference of the quantized area of the height measurement data, so that the inversion precision and the spatial resolution are remarkably improved, and GIA model errors and data noise interference are effectively inhibited.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of polar remote sensing monitoring and geodesy, and particularly relates to a high-precision inversion technical scheme for Antarctic ice sheet mass balance by using satellite altimetry data as prior constraints, which realizes accurate quantification of ice sheet mass change by fusing gravity satellite observation and laser altimetry satellite data. BACKGROUND

[0002] The Antarctic ice sheet, as the largest freshwater storage on Earth, its mass balance change directly affects the global sea level rise and climate system stability. In the past three decades, the melting of the Antarctic ice sheet has led to an accelerated global sea level rise, which poses a serious threat to low-lying coastal areas and island nations. Accurate monitoring of Antarctic ice sheet mass balance has important scientific significance for predicting future sea level rise and developing response strategies.

[0003] Currently, the international community mainly relies on two types of satellite technologies to monitor ice sheet changes: gravity satellites (such as GRACE / GRACE-FO) and laser altimetry satellites (such as ICESat / ICESat-2). Gravity satellites measure the change in the Earth's gravity field to invert the mass change, and its basic principle is to express the Earth's gravity field as a spherical harmonic coefficient expansion. The low-order terms (l≤30) reflect the large-scale mass distribution, and the high-order terms represent the local changes. However, this method has significant limitations: limited by the spatial resolution of about 300 km, it is difficult to capture the fine changes in key areas such as the ice shelf edge; high-order spherical harmonic coefficients are easily disturbed by measurement noise, even if Gaussian filtering (filter radius usually needs to be ≥200 km) is used, the details will still be lost; more seriously, it relies on the Glacial Isostatic Adjustment (GIA) model to correct the crustal rebound effect, and the existing GIA model (such as ICE-6G_D) has larger errors in the Antarctic region, resulting in systematic bias in the mass inversion results.

[0004] Laser altimetry satellites provide a new perspective for ice sheet monitoring by directly measuring surface elevation changes, with the advantage of sub-meter vertical accuracy and about 70 m along-track resolution. However, this method faces a fundamental challenge: the conversion of elevation change to mass change requires the assumption of snow density, while the spatial difference of Antarctic snow density is significant (from 300 kg / m3 for fresh snow to 830 kg / m3

[0005] To improve the resolution, the academic community has developed Mascon (mass block) inversion method. The method divides the Antarctic into several mass blocks and directly inverts the changes of each mass block. However, when a high-resolution Mascon (1°x1° or smaller) is used, the coefficient matrix A presents a serious ill-conditioning - a small observation noise can cause the solution to oscillate dramatically. The traditional solution is to introduce Tikhonov regularization, but the regularization matrix R is mostly an identity matrix or an empirical spatial smoothing constraint, which lacks physical basis. Such "mathematically driven" regularization can stabilize the numerical solution, but at the cost of sacrificing the authenticity.

[0006] In this context, the present application proposes a new technology for Antarctic ice sheet mass balance inversion based on prior information constraint. SUMMARY

[0007] In order to overcome the problems of the prior art, the present application proposes an innovative idea of using satellite altimetry data to construct physical prior constraints. This scheme breaks through the limitations of traditional single data source, effectively makes up for the shortcomings of existing methods in spatial resolution, model dependency and physical authenticity by fusing the complementary information of gravity field change and surface elevation change, and provides new generation technical support for Antarctic mass balance monitoring.

[0008] The present application proposes an Antarctic ice sheet mass balance inversion method based on prior information constraint, comprising the following processes: Satellite altimetry data is obtained, including extracting the elevation parameters of the Antarctic ice sheet region; The gravity satellite data is preprocessed; The inversion mass balance of physical prior constraint is performed, including dividing the Antarctic ice sheet into Mascon units consistent with the geography of the ice flow basin, constructing a spatially differentiated regularization constraint matrix based on the elevation change variance of the satellite altimetry data, dynamically optimizing the regularization parameter combined with the generalized cross-validation criterion, and solving the mass change; the Mascon represents a mass block; The Antarctic ice sheet mass balance result is output.

[0009] Moreover, the elevation parameters of the Antarctic ice sheet region include longitude, latitude, elevation and time, and the extracted elevation parameters of the Antarctic ice sheet region are used to construct the elevation change time series function within each Mascon unit and calculate the elevation change variance as the prior information for mass balance inversion.

[0010] Moreover, the preprocessing of the gravity satellite data includes truncating the spherical harmonic coefficient order, implementing low-order term correction, Gaussian filtering and glacier equilibrium adjustment correction.

[0011] Moreover, the construction of the spatially differentiated regularization constraint matrix adopts the following implementation manner, The elevation change variance of each Mascon unit is calculated according to the satellite altimetry data; convert the variance of the elevation change into regularization constraint weights, wherein weak constraint weights are given to the coastal glacier flow area and strong constraint weights are given to the Antarctic inland stable area; generate a diagonal regularization constraint matrix based on the weights to realize physical coupling of the ice sheet dynamics characteristics and the mathematical constraints.

[0012] Moreover, the dynamic optimization of the regularization parameter includes constructing a generalized cross-validation function, and iteratively calculating in a preset interval through a segmentation search algorithm. The time-varying characteristics of the gravity satellite observation noise are dynamically tracked, and the regularization parameter corresponding to the minimum generalized cross-validation function value is taken as the optimal solution.

[0013] Moreover, when the Mascon unit is divided, the unit boundary is divided according to the ice flow velocity gradient and the bedrock topography mutation characteristics, so that the unit spatial resolution is not greater than a preset threshold, and the boundary is aligned with the ice flow basin geography.

[0014] Moreover, the output of the Antarctic ice sheet mass balance result includes defining a regional indicator function to represent the geographical boundary, calculating the mass contribution of each Mascon unit through spherical harmonic expansion, and generating the mass balance spatiotemporal distribution and regional statistical time series.

[0015] In another aspect, the present application also provides an electronic device, including a memory, a processor, and a computer program stored on the memory and executable on the processor, wherein the processor implements the edge computing-based federated filtering data fusion method as described above when executing the program.

[0016] In another aspect, the present application also provides a non-transitory computer readable storage medium having a computer program stored thereon, wherein the computer program is executed by a processor to implement the edge computing-based federated filtering data fusion method as described above.

[0017] In another aspect, the present application also provides a computer program product, including a computer program, wherein the computer program is executed by a processor to implement the edge computing-based federated filtering data fusion method as described above.

[0018] The satellite gravity data-based ice sheet mass balance estimation method provided by the present application can effectively reduce the uncertainty caused by leakage by introducing satellite altimetry physical prior constraints, and improve the reliability of the ice sheet mass balance change result.

[0019] The present application scheme is simple and convenient to implement, and has strong practicability, solves the problems of low practicability and inconvenience in actual application in related technologies, can improve the ice sheet mass balance calculation accuracy, and has important scientific significance. BRIEF DESCRIPTION OF DRAWINGS

[0020] Figure 1A flowchart of an embodiment of the present application; Figure 2 A schematic diagram of Mascon distribution and elevation change prior information value of an embodiment of the present application; Figure 3 A result of the distribution of the Antarctic ice sheet mass balance change rate from 2002.4 to 2023.12 of an embodiment of the present application. DETAILED DESCRIPTION

[0021] The technical solutions of the present application are specifically described below in combination with the drawings and embodiments.

[0022] The present application provides a high-precision Antarctic ice sheet mass balance inversion method using satellite altimetry data as prior constraints. In the existing GRACE gravity field inversion technology based on the Mascon model, uniform constraints or empirical regularization methods are usually used to suppress noise. Although such solutions can solve the problem of ill-conditioned observation equations, they ignore the differences in physical characteristics of mass changes in different regions of the Antarctic ice sheet, resulting in excessive smoothing of the rapid mass loss signal in the coastal dynamic zone and the drowning of the weak change signal in the inland stable zone by noise.

[0023] The present application breaks through the limitations of existing technology and creatively introduces a satellite altimetry physical prior constraint mechanism and a generalized cross-validation dynamic optimization algorithm (see Figure 1 System flowchart), which realizes a leap in precision through three core innovations: first, by establishing a physically mechanism-driven prior constraint matrix, the elevation change variance obtained from satellite altimetry data such as ICESat-2 / CryoSat-2 is converted into spatially differentiated regularization constraint weights, with weak constraint weights assigned to coastal glacier flow zones (such as the Pine Island Glacier) and strong constraint weights applied to the Antarctic inland stable zone (such as Dome A), realizing the physical coupling of ice sheet dynamics and mathematical constraints; second, in solving the regularization equation, the traditional empirical threshold setting is completely abandoned, and an adaptive optimization function is constructed based on the generalized cross-validation criterion (GCV), which automatically locks the optimal regularization strength within the interval by dynamically tracking the time-varying characteristics of GRACE observation noise; third, according to the ice flow velocity field and bedrock topography, the Antarctic ice sheet is divided into multiple uniform Mascon units, with the unit boundaries highly consistent with the ice flow basins, effectively extracting the mass balance of the target region (see Figure 2 Mascon distribution map).

[0024] The Antarctic ice sheet mass balance inversion method based on prior information constraint provided by the application comprises the following steps: satellite altimetry data extraction, obtaining the spatial and temporal information of ice sheet surface elevation; GRACE gravity satellite data processing, including coefficient truncation, Gaussian filtering, low-order term correction and ice sheet equilibrium adjustment (GIA) correction; dividing Mascon units based on Antarctic ice flow characteristics and constructing the spherical harmonic coefficient base function matrix thereof; calculating the elevation change variance in each Mascon unit based on the satellite altimetry data, and constructing a physical prior constraint matrix representing the mass change uncertainty; performing mass balance inversion, modeling the gravity field change as a linear combination of the mass change of Mascon units, introducing the physical prior constraint matrix to construct an improved regularization observation equation; performing generalized cross-validation criterion (GCV) dynamic optimization of the regularization parameter, and solving the observation equation to obtain the mass change of each Mascon unit; and performing mass balance result output to generate high-resolution spatial and temporal distribution maps and statistical time series. The application uses altimetry data to quantify regional uncertainty differences (weak constraint along the coast / strong constraint in the inland) for regularization, significantly improves the inversion accuracy and spatial resolution (about 100 kilometers), and effectively suppresses the GIA model error and data noise interference.

[0025] Referring to Figure 1 , the embodiment provides a high-precision Antarctic ice sheet mass balance inversion method using satellite altimetry data as prior constraints, comprising the following steps: Step 1, satellite altimetry data extraction, including extracting longitude, latitude, elevation value and time: obtaining satellite altimetry data covering the Antarctic ice sheet region, analyzing the geographic spatial information layer thereof, and extracting the longitude, latitude, elevation value and time stamp of each observation point; In specific implementation, the satellite altimetry data can be derived from multiple satellite altimetry missions, and it is recommended to extract elevation change information with a spatial resolution of ≤2 kilometers.

[0026] The embodiment preferably uses satellite altimetry products based on NASA, obtains satellite altimetry raw data files (NC format) from the NASA data distribution center, and automatically analyzes the geographic spatial information layer thereof; takes the Antarctic ice sheet as the research region, extracts the longitude ( ), latitude ( ), elevation ( ), time ( ) and other parameters of all elevations in the ice sheet, and uses the longitude, latitude, elevation and time to construct the elevation change time series function in each Mascon unit and calculate the elevation change variance as prior information for mass balance inversion:

[0027] wherein, is the mean elevation, is the elevation at time i, is the total number of time.

[0028] Step 2, processing of GRACE satellite data, including truncation of coefficients, correction of Gaussian filtering, correction of low-order terms, correction of ice mass balance adjustment; In specific implementation, the GRACE satellite data can be processed.

[0029] It is preferred to use the GRACE Level-2 monthly gravity field model (RL06.2 version) published by the Center for Space Research (CSR) of the University of Texas at Austin, which contains completely normalized spherical harmonic coefficients Clm 、 Slm ( l is the order, m is the number of times). The following operations are performed on the spherical harmonic coefficients of the GRACE Level-2 time-varying gravity field model: Truncate the spherical harmonic coefficients to order l≤60; apply low-order term correction, correct the errors of C10, C11, S11, C20 and C30 terms using satellite laser ranging (SLR) data; use Gaussian filtering with a radius of 150 km to suppress strip noise; subtract the ice mass balance adjustment (GIA) effect predicted by the ICE-6G_D model to generate corrected gravity field change data.

[0030] After truncating the original spherical harmonic coefficients to 60 orders to filter out high-frequency noise components with a wavelength less than 150 kilometers, the satellite laser ranging database is called to correct the center of mass offset and the first-order term missing problem, and the low-precision C20 term data is replaced simultaneously. And implement Gaussian filtering, effectively suppress the strip-shaped artifacts and improve the signal fidelity, finally subtract the ice mass balance adjustment effect predicted by the ICE-6G_D model.

[0031] The embodiment further proposes a preferred implementation of step 2, which includes the following sub-steps, Step 2.1, truncate the GRACE data to 60 orders: After receiving the original spherical harmonic coefficients ( Clm , Slm ) from the GRACE Level-2 data center, the order truncation operation needs to be performed first. High-order spherical harmonic coefficients (usually l >60) mainly contain satellite measurement noise, atmospheric disturbance error and unmodeled tidal effects and other interference components, and the signal-to-noise ratio is significantly reduced. In order to suppress the influence of high-order noise on the Antarctic ice sheet signal, the spherical harmonic coefficients of the Level-2 time-varying gravity field model are truncated to 60 orders:

[0032] wherein where Cnmis the truncated spherical harmonic coefficient, and the dimension of the truncated coefficient matrix is 61x121 = 60, m ∈ [-60, 60], is the truncated spherical harmonic coefficient.

[0033] Step 2.2. Low-order term correction for GRACE data: The GRACE data product is fixed in the Earth-Centered Earth-Fixed (ECEF) reference frame, and the C 10, C 11, S 11 are forced to zero. However, the actual Earth Center of Mass (CM) will be displaced due to the mass redistribution caused by ice sheet melting, so the true CM offset is recovered using the Satellite Laser Ranging (SLR) product. The C20 and C30 terms are greatly affected by instrument errors, so the high-precision solution of the satellite orbit perturbation SLR is used for correction.

[0034] Step 2.3. Gaussian filtering correction for GRACE data: After truncating the spherical harmonic data, since the noise mainly appears in the high-frequency part, and the low-frequency component represents a more stable signal, it is necessary to perform filtering processing when analyzing the GRACE data, effectively removing the noise and retaining the useful signal. Therefore, the embodiment preferably uses a 150 km radius Gaussian filter to suppress high-order term errors:

[0035] where, is the initial weight coefficient, is the first-order weight coefficient, is the l order weight coefficient, l is the order number, is a natural constant, is a scale parameter.

[0036] The filtering radius r = 150 km corresponds to the scale parameter b = ln2 / (1-cos( r / Re )) = 3.47, and Re is the average radius of the Earth.

[0037] Step 2.4. Glacier isostatic adjustment correction for GRACE data: The mantle viscoelastic response triggered by ice sheet melting since the Last Glacial Maximum (LGM) has produced a persistent upward trend in the gravity field in Antarctica, which must be separated from the observed signal. The embodiment preferably uses the ICE-6G_D model to subtract the predicted GIA signal (long-term crustal rebound signal):

[0038] wherein, is the corrected spherical harmonic coefficient variation, is the observed and pre-processed spherical harmonic coefficient variation, is the spherical harmonic coefficient predicted by the glacier mass balance adjustment model, is the time, is the time interval.

[0039] Step 3, using Mascon method based on prior information constraint to solve the mass balance inversion: solving the regularized observation equation and optimizing the parameters The present application proposes to divide the Antarctic region into a plurality of Mascon units, to construct a basis function matrix through spherical harmonic analysis, and to convert the spatial distribution characteristics of each Mascon into spectral domain representation. The gravity field change observed by GRACE is decomposed into a linear combination of the mass change of each Mascon unit, and an observation equation is established. The change variance of satellite altimetry data is innovatively introduced to construct a physical prior constraint matrix, which quantitatively characterizes the uncertainty of the mass change in each region. The scaling factor is solved through an improved regularization equation, and the generalized cross-validation criterion is used to dynamically optimize the regularization parameter, so as to realize the automatic balance of noise suppression and signal preservation. The contribution of each Mascon unit to the total mass change is calculated by defining a regional indicator function to clearly define the geographical boundary, and the high-resolution mass balance spatiotemporal distribution is output.

[0040] Further, it is preferred that the Mascon unit division is based on the ice flow velocity gradient and the bedrock topography mutation characteristics, and the unit spatial resolution is ≤100 km, so as to ensure that the boundary is aligned with the geography of the ice flow basin.

[0041] The embodiment further proposes a preferred implementation manner of step 3, which includes the following sub-steps, Step 3.1, based on the MEaSUREs ice flow velocity field and the BEDMAP2 bedrock topography data, the Antarctic ice sheet is divided into a plurality of Mascon units matched with the ice flow basin boundary.

[0042] Specifically, first, based on the MEaSUREs ice flow velocity field and the BEDMAP2 bedrock topography data, the Antarctic ice sheet is divided into a plurality of Mascon units with a resolution of about 100 km, and the unit boundary is consistent with the geography of the ice flow basin, as shown in Figure 2 Each Mascon unit is defined as 1 within the block and 0 in other regions around the world, which assumes that each Mascon has a uniform mass distribution equivalent to 1 cm of equivalent water height.

[0043] The spherical harmonic function matrix A of each Mascon unit is constructed, and the elements are generated by the following spherical area integral formula, which is calculated by the spherical harmonic coefficients of each mass block. In the embodiment, each Mascon is converted into 60-order truncated spherical harmonic coefficients:

[0044] wherein, is the equatorial radius of the earth, is the average density of the earth, is the load Love number, is the mass change area density function, is the colatitude, is the longitude, l is the order, is the degree, is the completely normalized associated Legendre function. The expression converts the spatial distribution characteristics of each Mascon into a spectral domain representation through spherical area integration, and establishes a mathematical basis for subsequent inversion.

[0045] All Mascon units are combined to generate the design matrix A.

[0046] The gravity field change is decomposed into a linear combination of the mass changes of each Mascon unit, and the corresponding observation equation is established as:

[0047] wherein, is the spherical harmonic coefficient form of the Mascon, is defined as a scaling factor, that is, the optimal solution vector estimated, is the GRACE spherical harmonic coefficient at time t, is the vector residual.

[0048] Step 3.2, construct a regularization constraint solving framework, and iteratively solve the optimal regularization parameter.

[0049] The regularization constraint solving is implemented by introducing a physical prior constraint matrix R constructed by the variance of satellite altimetry data, which quantitatively represents the uncertainty of the mass change in each region. The improved regularization equation is solved, and the generalized cross-validation criterion is used to dynamically optimize the regularization parameter.

[0050] The physical prior constraint is constructed, and the regularization inversion uses the variance of satellite altimetry data as prior information, which specifically includes extracting the height change time series of each Mascon unit based on step 1 (t=1,…,T, T is the total time length), calculating the space-time variance of each Mascon unit, and generating a diagonal regularization matrix , realize regional physical property difference constraint, give weak constraint weight in coastal glacier flow area, give strong constraint weight in Antarctic inland stable area, that is, generate diagonal type physical priori constraint matrix:

[0051] wherein the normalization factor , is the total number of Mascon units, is the Mascon unit label, is the Mascon unit variance, is the regularization constraint matrix.

[0052] Regularization dynamic solution, including obtaining the optimal solution by minimizing the regularization objective function :

[0053] wherein, is the mass change parameter vector to be solved, is the design matrix, is the observation vector, is the regularization parameter, is the regularization constraint matrix Analyze the mass change by the improved regularization equation, and the analytical solution is as follows:

[0054] wherein, is the estimated optimal solution vector, is the transpose of the design matrix.

[0055] Wherein the selection of the regularization parameter , too small cause weak regularization effect, and the solution may be dominated by noise, resulting in instability or false signal; too large may cause the solution to be too smooth, losing the real signal. Therefore, the application further proposes to use the generalized cross-validation method (GCV) for iterative optimization, that is, the regularization parameter is dynamically optimized by minimizing the generalized cross-validation function. Dynamic parameter optimization adopts a segmentation search algorithm, and the global optimal solution is automatically locked by calculating the curvature change rate of the GCV function .

[0056] That is, the following iteration is performed: 1) Calculate the GCV function:

[0057] wherein, is the value of the generalized cross-validation function, is the regularization parameter, For the i-th observation, Let n be the model prediction value for the i-th observation, where i is the observation index and n is the total number of observations. Let H be the trace of the hat matrix. This is the hat matrix.

[0058] 2) Update the regularization parameters: Using a segmentation search algorithm in the interval [ α min, α Iterative optimization within the [max] (typically [10⁻¹⁰, 10⁻²]) involves partitioning all values ​​within the search range and iteratively selecting the optimal parameters. in, α min is the lower limit of the search interval. α `max` is the upper limit of the search interval. 3) Optimal decision In the interval [ α min, α [max] Select the minimum GCV value. As the optimal regularization parameter Step 3.3: Calculate and output the optimized mass balance result based on the optimal parameters:

[0059] in, This is the optimized solution vector. The optimal regularization parameters are selected using the GCV method. This is the observation vector.

[0060] Step 4: Output the mass balance results, including the spatiotemporal distribution and regional statistical time series.

[0061] This step is used to perform statistical analysis on changes in material balance and generate a spatiotemporal distribution product of material balance.

[0062] The quality change output of the embodiment is implemented as follows: Define region indicator function Characterize the target boundary and calculate the mass contribution of each Mascon using spherical harmonic expansion. :

[0063] in, The mass change of the Mascon element at time t. The radius of the Earth's equator. For area indicator functions, This represents the (equivalent) change in mass per unit area of ​​the Earth's surface at time t and position (λ,φ). a regional indicator function a spherical harmonic coefficient, a mass change field represented by a (normalized) spherical harmonic coefficient observed by GRACE at time t, Ω represents an integral region, lmax represents a maximum order of spherical harmonic expansion, l represents a spherical harmonic order, and m represents a spherical harmonic number.

[0064] Using the mass balance result of each Mascon calculated, a spatial distribution map is generated, as shown in Figure 3 and a statistical time series is output.

[0065] In the mass balance inversion process using the present application, the main inversion results are mass balance time series and spatial distribution. The current international mainstream products are CSR (Center for Space Research at the University of Texas at Austin), JPL (Jet Propulsion Laboratory), and GSFC (Goddard Space Flight Center). The present application realizes high precision and high reliability of the inversion time series through the spatial differentiation constraint mechanism constructed by satellite altimetry prior information and the dynamic optimization algorithm of generalized cross-validation. Specifically, in the typical inversion experiment from 2002 to 2023, the present application selects the Antarctic ice sheet region (East Antarctica, West Antarctica, and the Antarctic Peninsula) and compares and analyzes the time series with the CSR, JPL, and GSFC products. The statistical indicators (unit: Gt per year) of the mass balance time series are shown in Table 1.

[0066] Table 1 Mass balance inversion trend statistics

[0067] As can be seen from Table 1, the inversion results of the present application in the key regions of the Antarctic ice sheet are highly consistent with the international mainstream GRACE products. The West Antarctica mass loss trend (-129.36 Gt / a) is in the same scientific recognized rapid change interval as CSR (-135.06 Gt / a) and GSFC (-136.06 Gt / a); the Antarctic Peninsula change (-11.76 Gt / a) is more closely consistent with CSR (-11.87 Gt / a) and JPL (-12.11 Gt / a). This trend consistency across agencies and multiple products fully proves that the inversion scheme of the present application has reached an international advanced level, and its spatial distribution characteristics are highly consistent with the prediction of the dynamics model of the Antarctic ice flow system. Therefore, the present application not only achieves an international leading level in mass balance inversion accuracy, but also has strong adaptability, reduces the dependence on artificial parameters, and has other comprehensive advantages.

[0068] In specific implementation, the method provided by the technical scheme of the present application can be automatically run by a computer software technology, and the system device of the method, such as a computer readable storage medium storing the corresponding computer program of the technical scheme of the present application and a computer device including the corresponding computer program, should also be within the protection scope of the present application.

[0069] The following examples describe the electronic device provided by the present application, and the electronic device described below can be correspondingly referred to the federated filtering data fusion method based on edge computing described above.

[0070] The electronic device can include a processor, a communications interface, a memory and a communications bus, wherein the processor, the communications interface and the memory complete mutual communication through the communications bus. The processor can call the logical instructions in the memory to execute the federated filtering data fusion method based on edge computing, mainly including the software processing part in the above steps.

[0071] In addition, the logical instructions in the memory described above can be implemented in the form of a software function unit and sold or used as an independent product, and can be stored in a computer readable storage medium. Based on such understanding, the technical scheme of the present application essentially or the part that contributes to the prior art or part of the technical scheme can be embodied in the form of a software product, and the computer software product stored in a storage medium includes a plurality of instructions for causing a computer device (which can be a personal computer, a server or a network device, etc.) to execute all or part of the steps of the method described in the various embodiments of the present application. The foregoing storage medium includes a U disk, a mobile hard disk, a read-only memory (ROM), a random access memory (RAM), a magnetic disk or an optical disk and various program code storage media.

[0072] On the other hand, the embodiments of the present application also provide a computer program product, which includes a computer program, the computer program can be stored on a non-transitory computer readable storage medium, and when the computer program is executed by a processor, the computer can execute the software processing part in the federated filtering data fusion method based on edge computing provided by the above-mentioned methods.

[0073] In another aspect, the embodiments of the present application also provide a non-transitory computer readable storage medium, which stores a computer program, and when the computer program is executed by a processor, the software processing part in the federated filtering data fusion method based on edge computing provided by the above-mentioned methods is implemented.

[0074] In some possible embodiments, a high-precision inversion system for Antarctic ice sheet mass balance with satellite altimetry data as prior constraints is provided, comprising the following modules, The first module is used for satellite altimetry data extraction, including longitude, latitude, elevation value and time extraction. The module obtains satellite altimetry raw data files (NC format) from the NASA data distribution center, and automatically parses the geographic spatial information layer therein; The second module is used for GRACE data preprocessing, including coefficient truncation, Gaussian filtering, low-order term correction and ice sheet balance adjustment correction. The original spherical harmonic coefficients are subjected to 60-order truncation processing to filter out high-frequency noise components with a wavelength less than 150 kilometers. Subsequently, the satellite laser ranging database is called to correct the center of mass offset and the first-order item missing problem, and the low-precision C20 item data is replaced synchronously. Gaussian filtering is implemented to effectively suppress the strip-shaped artifacts and improve the signal fidelity, and finally the ice sheet balance adjustment effect predicted by the ICE-6G_D model is deducted; The third module is used for solving the regularization observation equation and optimizing the parameters, and the implementation is as follows: The Antarctic region is divided into a plurality of Mascon units, a base function matrix is constructed through spherical harmonic analysis, and the spatial distribution characteristics of each Mascon are converted into spectral domain representation. The gravity field change observed by GRACE is decomposed into a linear combination of the mass change of each Mascon unit, and an observation equation is established.

[0075] The change variance of satellite altimetry data is innovatively introduced to construct a physical prior constraint matrix, and the uncertainty of the mass change of each region is quantitatively characterized. The scaling factor is solved through an improved regularization equation, and the regularization parameter is dynamically optimized through the generalized cross-validation criterion to realize the automatic balance of noise suppression and signal preservation. The contribution of each Mascon unit to the total mass change is calculated by defining a region indicator function to explicitly define the geographical boundary, and a high-resolution mass balance spatiotemporal distribution is output The fourth module is used for statistical analysis of the mass balance change to generate a mass balance spatiotemporal distribution product.

[0076] Finally, it should be noted that: the above embodiments are only used to illustrate the technical solutions of the present application, and not to limit them; although the present application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that: it can still modify the technical solutions recorded in the foregoing embodiments, or make equivalent replacement for part of the technical features; and these modifications or replacements do not make the essence of the corresponding technical solutions deviate from the spirit and scope of the technical solutions of the embodiments of the present application.

Claims

1. An Antarctic ice sheet mass balance inversion method based on prior information constraint, characterized in that, The method comprises the following steps: acquiring satellite altimetry data, including extracting elevation parameters of the Antarctic ice sheet region; preprocessing gravity satellite data; performing inversion of physical prior constraints on mass balance, including dividing the Antarctic ice sheet into Mascon units consistent with the geography of ice flow basins, constructing a spatially differentiated regularization constraint matrix based on the variance of elevation change of satellite altimetry data, dynamically optimizing the regularization parameter in combination with a generalized cross-validation criterion, and solving the mass change; the Mascon represents a mass block; outputting the mass balance result of the Antarctic ice sheet.

2. The method of claim 1, wherein the method is characterized by: The elevation parameters of the Antarctic ice sheet region include longitude, latitude, elevation, and time, and the extracted elevation parameters of the Antarctic ice sheet region are used to construct an elevation change time series function within each Mascon unit and calculate the variance of elevation change as prior information for mass balance inversion.

3. The method of claim 1, wherein the method is characterized by: The preprocessing of gravity satellite data includes truncating the order of spherical harmonic coefficients, implementing low-order term correction, Gaussian filtering, and glacier equilibrium adjustment correction.

4. The method of claim 1, wherein the method is characterized by: The construction of the spatially differentiated regularization constraint matrix is implemented in the following manner, calculating the variance of elevation change of each Mascon unit based on satellite altimetry data; converting the variance of elevation change into regularization constraint weights, wherein weak constraint weights are assigned to the coastal ice flow area, and strong constraint weights are assigned to the Antarctic inland stable area; generating a diagonal regularization constraint matrix based on the weights to realize physical coupling of the dynamics of the ice sheet and mathematical constraints.

5. The method of claim 1, wherein: The dynamic optimization of the regularization parameter includes constructing a generalized cross-validation function and iteratively calculating it in a preset interval through a segmentation search algorithm; dynamically tracking the time-varying characteristics of gravity satellite observation noise, and taking the regularization parameter corresponding to the minimum generalized cross-validation function value as the optimal solution.

6. The method of claim 1, wherein: When dividing the Mascon units, the unit boundaries are divided according to the ice flow velocity gradient and the abrupt features of bedrock topography, so that the spatial resolution of the units is not greater than a preset threshold, and the boundaries are aligned with the geography of the ice flow basin.

7. The method of claim 1, wherein: The output of the mass balance result of the Antarctic ice sheet includes defining a regional indicator function to represent the geographical boundaries, calculating the mass contribution of each Mascon unit through spherical harmonic expansion, and generating the spatiotemporal distribution of mass balance and the regional statistical time series.

8. An electronic device comprising a memory, a processor, and a computer program stored on the memory and executable on the processor, characterized in that: The processor executes the program to implement the method for inversion of mass balance of the Antarctic ice sheet based on prior information constraints according to any one of claims 1 to 7. 9.A non-transitory computer-readable storage medium having stored thereon a computer program. The computer program is executed by the processor to implement the method for inversion of mass balance of the Antarctic ice sheet based on prior information constraints according to any one of claims 1 to 7.

10. A computer program product comprising a computer program, characterized in that: The computer program is executed by the processor to implement the method for inversion of mass balance of the Antarctic ice sheet based on prior information constraints according to any one of claims 1 to 7.

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