An Adaptive Constraint Method for Determining Global Mass Changes Using Gravity Satellite Data

Abstract

This application relates to an adaptive constraint method for determining global mass change using gravity satellite data. First, a noisy global mass change signal is obtained using gravity satellite observation data and a background force model. An initial constraint matrix is ​​constructed using zero-order Tikhonov regularization to obtain the initial constraint solution for global mass change. Second, considering land-sea signal leakage, strong and weak signal constraint matrices are used to calculate the strong and weak signals of global mass change, respectively. Adding the strong and weak signals yields the complete global mass change signal. Finally, considering land signal leakage, the root mean square (RMS) value of the obtained complete global mass change signal is used as prior information to construct a leakage error correction constraint matrix to solve for the leakage error-corrected global mass change signal.

Description

Technical Field

[0001] This invention relates to the field of satellite gravity measurement applications, and more specifically to an adaptive constraint method for determining global mass changes using gravity satellite data. Background Technology

[0002] Mass migration changes in the Earth system monitored by gravity satellites are typically expressed as monthly mean time-varying gravity field models or Mascon models. Influenced by factors such as instrument noise levels, background model accuracy, and non-modeling errors, the calculated global mass changes exhibit severe "strip" noise in the north-south direction of the airspace, obscuring the true geophysical signal. Common noise reduction methods include Gaussian smoothing and prior information constraint methods. Gaussian smoothing reduces the weighting of higher-order spherical harmonic coefficients with significant noise, decreasing errors in shortwave components and achieving noise reduction. Prior information constraint methods are mainly used to solve Mascon models, and currently widely adopted constraint methods include regularized smoothing constraints, spatiotemporal constraint equations, and prior physical information constraints. However, existing constraint methods can lead to problems such as unclear physical meaning of prior information or distortion of constraint information, resulting in the calculated global mass changes being contaminated by prior information and failing to accurately reflect the monthly global mass changes.

[0003] Because the signal strength of global surface mass change varies, with strong periodic variations in the Amazon basin and strong long-term variations in Greenland and Antarctica, the long-term variations caused by groundwater over-extraction in areas such as the North China Plain, the Mississippi River basin in the United States, and northern India are relatively weak. Using uniform constraint parameters for solving this problem presents the following issues: if the constraint parameters are weak, the weak global mass change signal can be preserved, but it will be significantly affected by striping errors; if the constraint parameters are strong, while the influence of striping errors can be reduced, the weak mass change signal will be over-constrained.

[0004] To eliminate land-sea signal leakage errors when calculating global mass change signals, current techniques retain the RMS value of the land signal constant while setting a uniform maximum RMS value for the ocean signal. This is based on the assumption that the maximum RMS value of the mass change signal in the sea areas near Greenland and the Antarctic ice sheet, where mass changes are significant, does not exceed 4 cm. Therefore, the maximum monthly RMS value of the ocean signal, except in seismic areas and enclosed sea areas, is uniformly set to 4 cm. However, ocean mass is not constant over the long term. Setting a uniform maximum RMS value for the ocean mass change signal every month is inappropriate; variations in the ocean mass signal need to be considered. Summary of the Invention

[0005] The purpose of this invention is to provide an adaptive constraint method for determining global mass changes using gravity satellite data, in order to solve the problems mentioned in the background art.

[0006] To achieve the above objectives, the present invention adopts the following technical solution:

[0007] An adaptive constraint method for determining global mass change using gravity satellite data includes the following steps:

[0008] S1: Constructing the initial constraint matrix: Obtain the noisy global mass change signal using gravity satellite observation data and background force model, and then construct the initial constraint matrix using zero-order Tikhonov regularization technique to obtain the initial constraint solution for global mass change;

[0009] S2: Land-Sea Signal Leakage Constraints: Strong and weak signals of global mass change are calculated using strong and weak signal constraint matrices, respectively. The complete global mass change signal is obtained by adding the strong and weak signals. The initial constraint solution of global mass change calculated in step S1 is used as prior information and combined with land-sea information to construct the strong signal constraint matrix. The weak signal constraint matrix is ​​constructed as follows:

[0010] (1) Calculate the initial constraint solution for the global mass change for each month using the method in step S1, and fit the global mass change signal using the following formula:

[0011]

[0012] Where y(t) is the global mass change signal corresponding to time t, C is the fitting constant term, B is the long-term trend term, and A is the interannual amplitude. ε represents the interannual phase; ε represents the residual.

[0013] (2) Using the calculated fitting constant term C, long-term trend term B, interannual amplitude A, and interannual phase Fit the monthly global mass change values, then subtract the fitted values ​​from the initial constraint solution, and use the difference as prior information. Combine this with land and sea information to construct a weak signal constraint matrix.

[0014] S3: Land signal leakage constraint: Using the root mean square (RMS) value of the complete global mass change signal obtained in step S2 as prior information, construct a constraint matrix to process the leakage of the global mass change signal, so as to solve the global mass change signal after leakage error correction.

[0015] A further technical solution of this application: the initial constraint matrix in step S1 is set as the identity matrix.

[0016] A further technical solution of this application: In step S2, the land and sea information construction method is to keep the root mean square value (RMS) of the land signal unchanged, and set the maximum value of the root mean square value (RMS) of the ocean signal as a certain threshold, with different thresholds for different months.

[0017] A further technical solution of this application: the threshold is determined by 85% of the total root mean square (RMS) value of the ocean signal for the current month.

[0018] Compared with the prior art, the present invention can achieve at least the following beneficial effects:

[0019] 1. The initial constraint matrix is ​​constructed using the zero-order Tikhonov regularization technique to solve for the initial constraint value of global mass change. This initial constraint value contains all the spectral information of mass change, has a clear physical meaning, and does not contain or depend on external geophysical signals.

[0020] 2. The strong signal and weak signal of global mass change are calculated using the strong signal constraint matrix and the weak signal constraint matrix respectively. The strong signal and the weak signal are added together to obtain the complete signal of global mass change. This avoids the problem of insufficient constraint of the strong signal of mass change due to strip noise or over-constraint of the weak signal of mass change caused by using uniform constraint information.

[0021] 3. When dealing with land and sea signal leakage, the long-term changes in ocean quality are accurately considered. The maximum RMS value of the ocean signal is set as a uniform threshold, but the threshold changes with the overall intensity of the ocean signal each month. The dynamic determination of the threshold can adapt to the long-term changes in ocean quality. The land signal in the strong signal constraint matrix and the weak signal constraint matrix is ​​integrated with the global quality change signal of the current month. That is, the strong signal constraint matrix and the weak signal constraint matrix are time-varying and can be best matched with the global quality change signal of the current month.

[0022] 4. The adaptive constraint model also considers the leakage problem of land signals. It uses the RMS of the complete signal of global quality change as prior information to construct a constraint matrix to process the leakage of global quality change signal, so as to solve the global quality change signal after leakage error correction, thus solving the problem of difficult correction of land signal leakage. Attached Figure Description

[0023] Figure 1 The process for constructing an adaptive constraint model;

[0024] Figure 2 Comparison of global mass change results (a) and spherical harmonic results (b) with zero-order Tikhonov regularization constraints, global mass change in April 2015 in equivalent water height form (unit: mm), spherical harmonic results are 96th order CSR-RL06 spherical harmonic models with 300km Gaussian filtering;

[0025] Figure 3Comparison of long-term trends and annual amplitudes of global mass change results with zero-order Tikhonov regularization constraints (a and b) with 96th-order CSR-RL06 spherical harmonic results (c and d) from April 2002 to August 2016;

[0026] Figure 4 For statistical analysis of ocean signals, (a) represents the percentage of global ocean signals whose maximum RMS value does not exceed 80mm, 70mm, 60mm, 50mm, 40mm, 30mm, 20mm, and 10mm in each month; (b) represents the RMS values ​​corresponding to the 95th, 90th, 85th, 80th, 75th, 70th, 65th, and 60th percentiles in each month. The values ​​in parentheses in the legend represent the average for all months. Figure 5 The RMS of global mass change and its constraint results are shown in April 2015 as an example. (a) represents the prior RMS for constructing the constraint matrix of the strong signal, (c) represents the constraint solution of the strong signal, (d) represents the prior RMS for constructing the constraint matrix of the weak signal, and (d) represents the constraint solution of the weak signal. Note that the color scale range is inconsistent.

[0027] Figure 6 The global quality change signal before and after land signal constraint (taking April 2015 as an example) is (a) the global quality change before signal leakage correction (i.e. the sum of strong and weak signals in the second step), and (b) the global quality change after signal leakage correction (the final global quality change result calculated in this paper).

[0028] Figure 7 Comparison of geoid step errors;

[0029] Figure 8 This represents the long-term trend of global quality changes from April 2002 to August 2016.

[0030] Figure 9 This represents the amplitude of the global mass change signal from April 2002 to August 2016. Detailed Implementation

[0031] The specific embodiments of the present invention will be described in further detail below with reference to the accompanying drawings and examples. The following examples are for illustrative purposes only and are not intended to limit the scope of the invention.

[0032] The specific steps of this method are as follows:

[0033] Step 1: Construct the initial constraint matrix

[0034] Noisy global mass change signals were obtained using gravity satellite observation data and a background force model. Zero-order Tikhonov regularization was employed to construct an initial constraint matrix and solve for the initial constraint values ​​of global mass change. To better constrain mass changes in the polar ice cap regions, a post-ice rebound model was used to subtract the long-term trend term of post-ice rebound. The initial constraint matrix was set as the identity matrix, and the initial constraint results of global mass change were calculated based on the initial constraint matrix. The optimal regularization parameter was α1, which is less affected by striping errors. Figure 2 As shown, the results are comparable to those of the spherical harmonic coefficient model after using a 300km Gaussian filter, both exhibiting significant signal leakage issues.

[0035] Step 2: Constraining Signal Leakage on Land and Sea

[0036] To better mitigate the impact of striping errors and preserve the weak signal of global mass change as much as possible, we calculate the strong and weak signals of global mass change using the strong signal constraint matrix and the weak signal constraint matrix, respectively. Adding the strong and weak signals yields the complete signal of global mass change. The specific steps are as follows:

[0037] (1) Calculate the fitted value of the monthly global mass change. The initial constraint solution for the monthly global mass change is calculated using the method from step one, and the global mass change signal is fitted using the following formula:

[0038]

[0039] Where y(t) is the global mass change signal corresponding to time t, C is the fitting constant term, B is the long-term trend term, and A is the interannual amplitude. ε represents the interannual phase; ε represents the residual.

[0040] The long-term trends and interannual amplitudes of the initial constraint solution for global mass change from April 2002 to August 2016 and the 96th-order spherical harmonic solution of the CSR-RL06 sphere harmonic solution from the University of Texas Space Research Center are shown in the figure. Figure 3 As shown, the two are generally consistent, but due to differences in data processing details, there are some differences in some regions such as Greenland.

[0041] (2) Constructing strong and weak signal constraint matrices for monthly global mass changes. The initial constraint solution for global mass changes calculated in step one is used as prior information to construct the strong signal constraint matrix. The calculated fitting constant term C, long-term trend term B, interannual amplitude A, and interannual phase are then used. Fit the monthly global mass change values, then subtract the fitted values ​​from the initial constraint solution, and use the difference as prior information to construct a weak signal constraint matrix.

[0042] When constructing the strong and weak signal constraint matrices, land-sea constraint equations are used to eliminate land-sea signal leakage errors. Over the long term, ocean mass is not constant, and variations in ocean mass signals need to be considered. We perform statistical analysis on the ocean component of the initial constraint solution for global mass changes. Figure 4 (a) shows the percentage of ocean signals with an RMS value not exceeding a certain threshold. For example, ocean signals with an RMS value not exceeding 40 mm account for approximately 85% of the total ocean signals, but this percentage fluctuates across different months. Simultaneously, we statistically analyzed the magnitude of the RMS value corresponding to ocean signals not exceeding a certain percentage (e.g., ...). Figure 5 (b) The RMS mean of the overall signal, which accounts for 85%, is approximately 40 mm. The RMS value varies across different months for the same percentage. Since our reference average epoch is 2010.0, the signal strength increases with distance from the reference epoch, reflecting the long-term variation in global ocean quality. Through calculation and analysis, we set the maximum value of the ocean signal RMS as a threshold, but the threshold is not fixed for different months. It is determined by 85% of the total RMS value of the ocean signal for that month (e.g., ...). Figure 4 (b) shows. Meanwhile, in order to preserve some marine geophysical signals, we do not process marine seismic areas and (semi-)enclosed marine areas, and the RMS of these areas remains unchanged.

[0043] (3) Adding the strong signal and the weak signal yields the complete global mass change signal. An example of constructing the strong signal constraint matrix, the weak signal constraint matrix, the prior RMS of global mass change, and their constraint results is shown below. Figure 5 As shown.

[0044] Step 3: Land Signal Leakage Constraints

[0045] When using the complete global mass change signal obtained in the second step, we applied constraint corrections to signal leakage between land and sea. However, signal leakage in the land region remained significant. Experimental analysis revealed that land signal leakage correction could still be achieved through constraint correction. Using the RMS value of the complete global mass change signal obtained in the second step as prior information, we constructed a leakage error correction constraint matrix to solve for the leakage error-corrected global mass change signal. At this point, no further land-sea constraint processing was applied to the complete global mass change signal. The solution obtained using the constructed leakage error correction constraint matrix is ​​the leakage error-corrected global mass change signal.

[0046] Global mass changes before and after leakage error correction are as follows: Figure 6 As shown, Figure 6 (a) is the sum of the strong and weak signals in the second step. Figure 6 (b) is based on Figure 6(a) The solution results of the constraint matrix constructed based on prior information. It can be seen that in Greenland, Antarctica, North America, Tianshan Mountains, Pamir Plateau, North China Plain and Caspian Sea, after leakage error correction, the signal leakage in these areas is significantly improved, and the signal strength is also enhanced.

[0047] The above steps construct a constraint matrix to solve for global mass change. Since the prior information required for constructing the constraint matrix in each step does not include external geophysical signals, and the global RMS is provided by the observation signals from gravity satellites themselves, with each month's constraint matrix constructed from the satellite observation signals for that month, this method can adaptively construct the constraint matrix appropriately according to the intensity and spatial distribution of the time-varying signals for that month when constructing the constraint matrix to solve for global mass change. Figure 1 The steps shown in the diagram calculate global mass change, separating strong and weak signals. This allows for the use of optimal regularization parameters, avoiding over- or under-constraint of the signals, and also effectively addresses the issue of land signal leakage.

[0048] Example

[0049] Based on the aforementioned adaptive constraint method, PMA-final, monthly global mass variation signals from April 2002 to August 2016 were calculated using Gravity Recovery and Climate Experiment (GRACE) Level-1B data. The calculated global mass variation was compared with that calculated by other models. The spatial signal was converted to 120th-order spectral domain spherical harmonic potential coefficients through spherical harmonic analysis, and the geoid step error was calculated. Taking April 2002 as an example, the geoid step errors of each model are as follows: Figure 7 As shown. The models used for comparison are the Mascon model released by the University of Texas Space Research Center (CSR), Jet Propulsion Laboratory (JPL), and Goddard Flight Control Center (GSFC), and the 96th-order RL06 time-varying gravity field model released by the University of Texas Space Research Center (CSR).

[0050] Comparative Example 1

[0051] Using the CSR-RL06 model, the other steps are the same as in the example.

[0052] Comparative Example 2

[0053] Using the CSR MASCON RL06.2 model, the other steps are the same as in the example.

[0054] Comparative Example 3

[0055] Using the JPL MASCON RL06.1M model, the other steps are the same as in the example.

[0056] Comparative Example 4

[0057] Using the GSFC MASCON model, the other steps are the same as in the example.

[0058] Comparative Example 5

[0059] The global mass change, calculated based on the initial constraint matrix, is known as PMA-Tikh, with the other steps being the same as in the embodiment.

[0060] Comparative Example 6

[0061] The global quality change is calculated based on the initial constraint matrix and land-sea signal leakage constraints, i.e. using PMA-sum, with other steps being the same as in the example.

[0062] from Figure 7 It can be seen that, compared with the unfiltered spherical harmonic coefficients, the constrained Mascon model and the results calculated by the above constraint methods show significant improvement in higher-order noise. The global mass change calculated using the zero-order Tikhonov constraint exhibits rapid signal attenuation after the 10th order. The results using the adaptive constraint method show good consistency with the Mascon models published by CSR, JPL, and GSFC across the entire spectral domain, especially the final global mass change after leakage error correction, which is basically consistent with CSR Mascon. The long-term trend of global mass change from April 2002 to August 2016 calculated by the above adaptive constraint method (e.g., ...) Figure 8 (as shown) and the interannual amplitude of global mass change (as shown) Figure 9 (As shown) The results are compared with those of CSR, JPL, and GSFCMascon from the same period. Overall, the results calculated by the various methods show good consistency with... Figure 3 Compared to the long-term trend of the 96th-order spherical harmonic potential coefficient model in (c), the model calculated using this method has a smaller signal leakage error than the Mascon model and is largely unaffected by striping errors. Of course, due to inconsistencies in the specific parameter settings used by different institutions to calculate global mass change, differences still exist in local areas, such as inland Greenland, parts of the Caspian Sea region, and the Sumatra earthquake zone. Simultaneously, we compared the interannual amplitude of the global mass change signal from each model (e.g., Figure 9 and Figure 3 As shown in the figure, the signal amplitudes of each model have good overall consistency.

[0063] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. An adaptive constraint method for determining global mass variations using gravity satellite data, characterized in that, The method comprises the following steps: S1: constructing an initial constraint matrix: obtaining a global mass change signal containing noise by using gravity satellite observation data and a background force model, and then constructing an initial constraint matrix by using a zero-order Tikhonov regularization technique to obtain an initial constrained solution of the global mass change; S2: land-sea signal leakage constraint: calculating a global mass change signal strong signal and a global mass change signal weak signal by using a strong signal constraint matrix and a weak signal constraint matrix, respectively, and adding the strong signal and the weak signal to obtain a complete global mass change signal; wherein the initial constrained solution of the global mass change calculated in step S1 is used as prior information and combined with land-sea information to construct the strong signal constraint matrix, and the weak signal constraint matrix is constructed as follows: (1) calculating the initial constrained solution of the global mass change of each month by using the method of step S1, and fitting the global mass change signal by using the following formula: wherein y(t) is the global quality change signal corresponding to time t, C is a constant term for fitting, B is a long-term trend term, A is an interannual amplitude, is an interannual phase; and ε is a residual. (2) using the calculated fitting constant term C, long-term trend term B, interannual amplitude A, and interannual phase The fitted value of the global mass change of each month is fitted, and then the fitted value is subtracted from the initial constraint solution, and the difference is taken as prior information and combined with land and sea information to construct a weak signal constraint matrix; S3: land signal leakage constraint: using the root mean square (RMS) value of the complete global mass change signal obtained in step S2 as prior information to construct a leakage error correction constraint matrix to solve the global mass change signal after leakage error correction.

2. The method of claim 1, wherein, The initial constraint matrix in step S1 is set as a unit matrix.

3. The method of claim 1, wherein, In step S2, the land-sea information construction method is to keep the root mean square (RMS) value of the land signal unchanged, and set the maximum value of the root mean square (RMS) value of the ocean signal as a certain threshold, and the threshold is different for different months.

4. The method of claim 3, wherein, The threshold is determined by 85% of the overall root mean square (RMS) value of the ocean signal of the month.

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