CN113962056A - Method for improving accuracy of water reserve change of GRACE land - Google Patents

Method for improving accuracy of water reserve change of GRACE land Download PDF

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CN113962056A
CN113962056A CN202110450205.XA CN202110450205A CN113962056A CN 113962056 A CN113962056 A CN 113962056A CN 202110450205 A CN202110450205 A CN 202110450205A CN 113962056 A CN113962056 A CN 113962056A
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coefficient
grace
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郑伟
尹文杰
杨帅
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China Academy of Space Technology CAST
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Abstract

The invention discloses a method for improving the accuracy of the change of the water reserves of GRACE land, which comprises the following steps: obtaining land water reserves delta h (theta, lambda) from the hydrological model, and determining a spherical harmonic coefficient cosine term C corresponding to the delta h (theta, lambda)lmAnd a sine term Slm(ii) a To ClmAnd SlmPerforming de-banding filtering and Gaussian smoothing filtering to obtain the filtered spherical harmonic coefficient cosine term
Figure DDA0003038420270000011
And sine term
Figure DDA0003038420270000012
Based on
Figure DDA0003038420270000013
And
Figure DDA0003038420270000014
obtaining filtered land water reserves delta eta (theta, lambda); determining time sequence data deltah corresponding to deltah (theta, lambda) in t time sequencei(t), time-series data Δ η corresponding to the time-series of t Δ η (θ, λ)i(t); according to Δ hi(t) and Δ ηi(t), resolving to obtain a decision coefficient weighting scale factor; and correcting leakage errors in the process of inverting the land water reserves by the GRACE data according to the decision coefficient weighting scale factors, and recovering real hydrological signals so as to improve the accuracy of the change of the land water reserves of the GRACE.

Description

Method for improving accuracy of water reserve change of GRACE land
Technical Field
The invention belongs to the cross technical field of satellite gravimetry, hydrology and the like, and particularly relates to a method for improving the accuracy of the change of the water reserves of GRACE land.
Background
Since 2002 gravity Recovery and Climate experiment GRACE (gravity Recovery and Climate experiment) satellite transmission, the GRACE satellite provides a new means for observing earth time-varying gravity field signals with high precision. At present, the GRACE satellite has been widely used in many fields of research such as change of terrestrial Water reserves tws (terrestial Water storage), glacier change and mass balance thereof, global average ocean mass change, earthquake, and the like.
Based on the theory of Wahr et al, the change in mass of the earth's surface can be obtained by using GRACE spherical harmonic coefficient solution inversion. However, spherical harmonic coefficients contain both random errors that increase with the coefficient order and systematic errors associated with the system. Therefore, spatial smoothing filtering (such as gaussian smoothing filtering, wiener filtering, etc.) and de-banding filtering (the de-banding method of Swenson and Wahr (2006), the P4M6 method of Chen et al (2009), etc.) have been proposed in succession by many researchers. These filtering methods also change the true physical signal while eliminating the effect of errors. Experimental simulations by Chen et al (2015) show that the leakage error generated by truncation and smoothing for 300km can reach 80.95Gt/yr (measured-150.00 Gt/yr, simulated-69.05 Gt/yr) in the south China; jin and zuo (2015) studies showed that 42.4% of the glaring island glacier mass loss signals were due to leakage errors, which were corrected to increase glacier melting rate from-15.58 ± 0.93Gt/yr2 to-26.19 ± 1.67Gt/yr 2. Therefore, leakage error is a main limiting factor in the quality variation of the Grace inversion, and correcting leakage error is crucial to improving the accuracy of inversion results.
Currently, the recovery method commonly used for the leakage error of the GRACE data includes: (1) scale factor method SF (scaling factor). The calculation process is simple, Long and the like (2015) utilize the scale factors obtained by the global hydrological model PCR-GLOBWB to recover the signal loss of the water reserve change of the Yangtze river basin, and the method has important value for improving the accuracy of the water reserve change of the research area; huang et al (2019) performed sensitivity analysis on a scale factor leakage error correction method based on different global hydrological models, and evaluated the water reserve change in southwest of China. The scale factor method relies on a prior hydrological model, which has been widely applied to the leakage of prior information for error correction of the GRACE data, but has some disadvantages, such as incomplete surface and ground water representation components and no consideration of human activity effects. (2) Iterative recovery method FM (forward modeling). The method is mainly constrained by the original observed value of the GRACE, a prior model is not needed, Chen and the like (2014) recover the north-west northwest India long-term groundwater change by using an iterative recovery method, and the newly estimated water reserve change trend reflects the iterative recovery method, so that the leakage error in the GRACE estimation can be effectively reduced; wuyunlong et al (2015) can effectively recover initial signals of water reserve change in black river basin based on an iterative recovery method, reduce leakage errors and improve the spatial resolution effect of water reserve change. The iterative recovery method is relatively complex in calculation process, and a signal recovery insufficiency or excessive recovery phenomenon may exist in a partial region.
Disclosure of Invention
The technical problem of the invention is solved: the method overcomes the defects of the prior art, provides a method for improving the accuracy of the change of the water reserves of the GRACE land, constructs a novel Scale Factor Determination Coefficient Weighted Average Correction method NSFCM (New Scale Factor Determination Coefficient Weighted Average Correction method), fully considers the information of various model Scale factors, and can effectively improve the accuracy of the change of the water reserves of the GRACE land compared with the traditional Scale Factor method and an iteration recovery method.
In order to solve the technical problem, the invention discloses a method for improving the accuracy of the change of the water reserve of the land of GRACE, which comprises the following steps:
obtaining land water reserves delta h (theta, lambda) from the hydrological model, and determining a spherical harmonic coefficient cosine term C corresponding to the delta h (theta, lambda)lmAnd a sine term Slm(ii) a Wherein θ represents the remaining latitude, and λ represents the longitude;
to ClmAnd SlmPerforming de-banding filtering and GaussianSmoothing the filtering process to obtain the cosine term of the spherical harmonic coefficient after filtering
Figure BDA0003038420250000021
And sine term
Figure BDA0003038420250000022
Based on
Figure BDA0003038420250000023
And
Figure BDA0003038420250000024
obtaining filtered land water reserves delta eta (theta, lambda);
determining time sequence data deltah corresponding to deltah (theta, lambda) in t time sequencei(t), time-series data Δ η corresponding to the time-series of t Δ η (θ, λ)i(t)；
According to Δ hi(t) and Δ ηi(t), resolving to obtain a decision coefficient weighting scale factor;
and correcting leakage errors in the process of inverting the land water reserves by the GRACE data according to the decision coefficient weighting scale factors, and recovering real hydrological signals so as to improve the accuracy of the change of the land water reserves of the GRACE.
In the method for improving the accuracy of the change of the terrestrial water reserves of the GRACE, the cosine term C of the spherical harmonic coefficient corresponding to the delta h (theta, lambda) is determined by the following formula (1)lmAnd a sine term Slm：
Figure BDA0003038420250000031
Where ρ iswDenotes the density of water, a denotes the mean radius of the earth, ρaveWhich represents the average density of the earth,
Figure BDA0003038420250000032
expressing the normalized associated Legendre function, l the order of the spherical harmonic coefficient solution inversion, m the number of times of the spherical harmonic coefficient solution inversion, klThe load lux number of order l is shown.
In the method for improving the accuracy of the change of the water reserves of the GRACE land, the step C is carried outlmAnd SlmPerforming de-banding filtering and Gaussian smoothing filtering to obtain the filtered spherical harmonic coefficient cosine term
Figure BDA0003038420250000033
And sine term
Figure BDA0003038420250000034
The method comprises the following steps:
according to the following formulae (2) and (3), to ClmAnd SlmPerforming de-banding filtering processing to obtain spherical harmonic coefficient cosine item after de-banding filtering
Figure BDA0003038420250000035
And sine term
Figure BDA0003038420250000036
Figure BDA0003038420250000037
Figure BDA0003038420250000038
Wherein w is the width of the sliding window, e is the natural logarithm, max () represents the maximum value, and Q is the de-banding filter coefficient; de-banding n for odd terms is the odd term in the order l, and the even terms are the same;
according to the following formulae (4) and (5)
Figure BDA0003038420250000039
And
Figure BDA00030384202500000310
performing Gaussian smoothing filtering to obtain spherical harmonic coefficient cosine term after Gaussian filtering
Figure BDA00030384202500000311
And sine term
Figure BDA00030384202500000312
Figure BDA0003038420250000041
Figure BDA0003038420250000042
Wherein r represents a Gaussian smoothing radius, W0Representing initial order Gaussian smoothing weights, Wl-1、WlAnd Wl+1And respectively represent Gaussian smoothing weights of order l-1, order l and order l +1, wherein l is 0,1,2,3 … 60.
In the method for improving accuracy of the change of the terrestrial water reserve of the GRACE, the terrestrial water reserve Δ η (θ, λ) after filtering is obtained by the following formula (6):
Figure BDA0003038420250000043
in the method for improving the accuracy of the change of the water reserves of the land of GRACE, the change is carried out according to delta hi(t) and Δ ηi(t) solving to obtain a decision coefficient weighting scale factor, comprising:
according to Δ hi(t) and Δ ηi(t), resolving to obtain a scale factor K based on a least square principle;
according to Δ hi(t) obtaining the coefficient of determination R by calculation2；
According to the scale factor K and the decision coefficient R2And calculating to obtain a decision coefficient weighting scale factor NSFCM-SF.
In the method for improving accuracy of the change of the water reserves of the terrestrial sites of the GraCE, the scale factor K is obtained by calculation according to the following formula (7):
Figure BDA0003038420250000044
where N represents the number of time series, and i represents the ith time series.
In the method for improving the accuracy of the change of the water reserves of the land of GRACE, the change is carried out according to delta hi(t) obtaining the coefficient of determination R by calculation2The method comprises the following steps:
according to Δ hi(t) determining fitted land water reserves
Figure BDA0003038420250000045
Average of land and water reserves
Figure BDA0003038420250000046
The coefficient of determination R is obtained by calculation using the following formula (8)2：
Figure BDA0003038420250000051
In the method for improving the accuracy of the change of the water reserves of the terrestrial sites of the GRACE, the determination coefficient weighting scale factor NSFCM-SF is obtained by calculation and calculation according to the following formula (9):
Figure BDA0003038420250000052
wherein n represents the number of scale factor models, j represents the jth scale factor model, KjRepresents the scale factor corresponding to the jth scale factor model,
Figure BDA0003038420250000053
and represents a determination coefficient corresponding to the jth scale factor model.
The invention has the following advantages:
the invention discloses a method for improving the accuracy of the change of the terrestrial water reserves of GRACE, which adopts a weighting technology based on decision coefficients, utilizes terrestrial water reserve data of various hydrological models to simulate signal loss caused by a filtering process during the inversion of the GRACE data, calculates scale factors before and after filtering of the terrestrial water reserve data of the various hydrological models by a least square method, and weights the scale factors of the hydrological models based on the decision coefficients generated by simulation to obtain novel scale factors. Novel scale factor synthesizes the land water reserves information of multiple hydrological models, and the signal loss that the filtering process when more accurate reflection GRACE data inversion caused utilizes novel scale factor to correct the leakage error of GRACE data inversion land water reserves change in-process, can effectively resume real hydrological signal to improve GRACE land water reserves change accuracy.
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FIG. 1 is a flow chart illustrating steps of a method for improving the accuracy of GRACE land water reserve changes in an embodiment of the present invention;
FIG. 2 is a schematic diagram of a Yangtze river basin location and its altitude according to an embodiment of the present invention;
FIG. 3 is a schematic diagram of changes in TWS spatial distribution trend of Yangtze river basin calculated by a GLDAS-NOAH model in an embodiment of the present invention;
FIG. 4 is a schematic diagram of scale factors of Yangtze river basin calculated by different models in the embodiment of the present invention;
FIG. 5 is a diagram illustrating an embodiment of an iterative recovery method for recovering a GRACE quality variation signal;
FIG. 6 is a schematic diagram illustrating spatial distribution trends of different recovery methods for Yangtze river basin according to an embodiment of the present invention;
FIG. 7 is a schematic diagram of the TWS time series recovered by different leakage error correction methods in the Yangtze river basin according to an embodiment of the present invention;
FIG. 8 is a schematic diagram of the annual amplitude and long-term trend of TWS recovered by different leakage error recovery methods in the Yangtze river basin in an embodiment of the present invention; wherein, fig. 8(a) is the annual amplitude, fig. 8(b) is the long-term trend;
FIG. 9 is a schematic diagram of a TWS time series for a Yangtze river sub-basin in an embodiment of the present invention; wherein, fig. 9(a) is the upper reaches of the Yangtze river, and fig. 9(b) is the middle and lower reaches of the Yangtze river;
FIG. 10 is a schematic illustration of a time series of Yangtze river basin precipitation and TWS in accordance with an embodiment of the present invention; wherein, fig. 10(a) is a Yangtze river basin, fig. 10(b) is the upper reaches of the Yangtze river, and fig. 10(c) is the middle and lower reaches of the Yangtze river;
fig. 11 is a schematic diagram of annual precipitation anomaly in the Yangtze river basin in an embodiment of the invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the embodiments of the present invention will be described in detail with reference to the accompanying drawings.
The invention discloses a method for improving the accuracy of the change of the water reserves of GRACE land, which mainly comprises the following steps: (1) converting the hydrological grid data into spherical harmonic data; (2) de-banding filtering and Gaussian smoothing filtering; (3) converting the spherical harmonic coefficient into grid data; (4) calculating a scale factor based on a least square principle; (5) calculating a model decision coefficient; (6) the scale factors are weighted based on the decision coefficient.
As shown in fig. 1, in this embodiment, the method for improving accuracy of change of the terrestrial water reserves of the GRACE includes:
step 101, obtaining land water reserves delta h (theta, lambda) from a hydrological model, and determining a spherical harmonic coefficient cosine term C corresponding to the delta h (theta, lambda)lmAnd a sine term Slm。
In the present embodiment, the spherical harmonic coefficient cosine term C corresponding to Δ h (θ, λ) can be determined by the following formula (1)lmAnd a sine term Slm：
Figure BDA0003038420250000071
Where θ represents the remaining latitude, λ represents the longitude, ρwDenotes the density of water, a denotes the mean radius of the earth, ρaveWhich represents the average density of the earth,
Figure BDA0003038420250000072
expressing the normalized associated Legendre function, l the order of the spherical harmonic coefficient solution inversion, m the number of times of the spherical harmonic coefficient solution inversion, klThe load lux number of order l is shown.
Step 102, for ClmAnd SlmPerforming de-banding filtering and Gaussian smoothing filtering to obtain the filtered spherical harmonic coefficient cosine term
Figure BDA0003038420250000073
And sine term
Figure BDA0003038420250000074
In this embodiment, in order to maintain the same filtering as the GRACE data processing, Swenson de-banding filtering and gaussian smoothing filtering of 300km are used.
Preferably, the de-banding filtering generally adopts a quadratic polynomial filtering window with the width w and the l order as the center, and the relation between the width w of the sliding window and the degree m of the spherical harmonic coefficient is as follows:
Figure BDA0003038420250000075
that is, C can be prepared according to the following formulas (2) and (3)lmAnd SlmPerforming de-banding filtering processing to obtain spherical harmonic coefficient cosine item after de-banding filtering
Figure BDA0003038420250000076
And sine term
Figure BDA0003038420250000077
Figure BDA0003038420250000078
Figure BDA0003038420250000079
Wherein e is a natural logarithm, max () represents a maximum value, and Q is a de-banding filter coefficient; and de-banding n for the odd terms is the odd term in the order l, and the even terms are the same.
Preferably, the gaussian smoothing filtering refers to a method for giving different weights to spherical harmonic coefficients of different orders, so as to reduce the high-order term error of the GRACE data. Can be prepared according to the following formulas (4) and (5)
Figure BDA00030384202500000710
And
Figure BDA00030384202500000711
performing Gaussian smoothing filtering to obtain spherical harmonic coefficient cosine term after Gaussian filtering
Figure BDA00030384202500000712
And sine term
Figure BDA0003038420250000081
Figure BDA0003038420250000082
Figure BDA0003038420250000083
Wherein r represents a Gaussian smoothing radius, W0Representing initial order Gaussian smoothing weights, Wl-1、WlAnd Wl+1And respectively represent Gaussian smoothing weights of order l-1, order l and order l +1, wherein l is 0,1,2,3 … 60.
Step 103, based on
Figure BDA0003038420250000084
And
Figure BDA0003038420250000085
and obtaining the filtered land water reserves delta eta (theta, lambda).
In this embodiment, the method can be used for
Figure BDA0003038420250000086
And
Figure BDA0003038420250000087
converted into grid data, i.e., by the following formula (6), filtered land water reserves Δ η (θ, λ) are obtained:
Figure BDA0003038420250000088
step 104, determining time series data Δ h corresponding to the time series t of Δ h (θ, λ)i(t), time-series data Δ η corresponding to the time-series of t Δ η (θ, λ)i(t)。
Step 105, according to the delta hi(t) and Δ ηiAnd (t) calculating to obtain a decision coefficient weighting scale factor.
In this embodiment, the specific implementation of step 105 is as follows:
a) according to Δ hi(t) and Δ ηiAnd (t) calculating to obtain a scale factor K based on the least square principle.
For any grid point, the unfiltered land water reserve corresponding to the time sequence t is delta hi(t) filtered land water reserve Δ ηi(t), by the least squares principle, has:
Figure BDA0003038420250000089
where N represents the number of time series, and i represents the ith time series.
b) According to Δ hi(t) obtaining the coefficient of determination R by calculation2。
The decision coefficient is a statistical indicator for reflecting the regression fitting degree of the regression model, and can be defined as the ratio of the discrete degree of the fitting value of the independent variable in the sample regression model to the real value thereof. For any grid point, the coefficient R is determined2The specific calculation of (a) is as follows:
according to Δ hi(t) determining fitted land water reserves
Figure BDA0003038420250000091
Average of land and water reserves
Figure BDA0003038420250000092
The coefficient of determination R is obtained by calculation using the following formula (8)2：
Figure BDA0003038420250000093
c) According to the scale factor K and the decision coefficient R2And calculating to obtain a decision coefficient weighting scale factor NSFCM-SF.
Based on a scale factor K and a decision coefficient R2The formula of the obtained novel scale factor decision coefficient weighted average correction method is as follows:
Figure BDA0003038420250000094
wherein n represents the number of scale factor models, j represents the jth scale factor model, KjRepresents the scale factor corresponding to the jth scale factor model,
Figure BDA0003038420250000095
and represents a determination coefficient corresponding to the jth scale factor model.
And 106, correcting leakage errors of the GRACE data in the land water reserve change inversion process according to the decision coefficient weighting scale factors, and recovering real hydrological signals so as to improve the accuracy of the GRACE land water reserve change.
In summary, the present invention utilizes the model to determine the Weighted scaling Factor of the Coefficient for the first time, and constructs a novel Weighted Average Correction Method (NSFCM) for determining the Coefficient of the scaling Factor. The novel scale factor decision coefficient weighted average correction method fully considers the information of various model scale factors, and can improve the accuracy of the change of the water reserves of the GRACE land compared with the traditional scale factor method and the iterative recovery method.
On the basis of the above embodiments, a specific example is described below.
1. Study area and data
1.1 area of investigation
The Yangtze river basin is located in the south of China, the longitude and latitude ranges are 85-122 degrees E and 24-36 degrees N, 19 provinces, cities and autonomous regions are spanned in the west, middle and east of China, and the position and the altitude of the Yangtze river basin are shown in figure 2. The annual average precipitation of the Yangtze river basin is 1067mm, the spatial distribution is not uniform, and about 70-90% of the annual average precipitation is concentrated in 5-10 months. The main stream of Yangtze river is above Yichang and is the upper stream of Yangtze river, and the area of drainage basin is 100 km2The area of the river basin is 68 km with the area from Yichang to the lake outlet being midstream of Yangtze river2The area of the river basin is 12 km with the area from the lake outlet to the sea inlet of the Yangtze river being the lower reaches of the Yangtze river2. Given that the area of the flow field downstream of the Yangtze river is small, the inversion result may have large uncertainty when the GRACE data is applied to the area smaller than the GRACE resolution. Therefore, the present invention refers to the middle and lower reaches of the Yangtze river as the middle and lower reaches of the Yangtze river, as shown by the dotted line east in FIG. 2, and the dotted line west as the upper reaches of the Yangtze river.
1.2 GRACE data
The data used by the present invention includes two mesh data products: CSR-grid and CSR-M (CSR Mascon). The CSR-grid data was obtained based on RL05 spherical harmonics of the united states university of texas Space Research Center (CSR), the united states Jet Propulsion Laboratory (JPL), and the german boltzmann earth science Research Center (GFZ), with data of 60 th order maximum, time span ranging from 4 months to 2017 months in 2002, and monthly grid data representing mass changes from the average 12 months in 2004 to 2009. C of GRACE20C of value ratio Satellite Laser Ranging (SLR)20The value has more uncertainty, therefore, C with SLR20Coefficient solution replacing C of GRACE20And (4) the coefficient. The first order term is estimated using the method of Swenson et al (2008) and applied to geocentric correction. Glacier equilibrium Adjustment (GIA) correction was performed based on the model of Geruo et al (2012). To reduce the month of GRACEThe data is processed by de-banding according to the related error of the south-north direction banding in the figure. In addition, the data also applied 300km gaussian smoothing filtering to suppress higher order random errors in the spherical harmonic coefficients.
CSR-M data is solved based on Level-1B data without applying any smoothing or de-banding filtering. Thus, the CSR-M data is used without further processing. The CSR-M data set is not tailored to a specific application and is applicable to all scientific fields of interest, such as oceanography, land surface hydrology, frozen circles, etc. Studies have shown that CSR-M data solutions are suitable for restoring mass redistribution for different mass sources in the global and large watershed scales (greater than about 3 ° × 3 °), while spherical harmonic coefficient solutions are superior to CSR-M data solutions on smaller or local scales when effectively processed.
1.3 hydrological data
The Global Land Assimilation System hydrological model (GLDAS) was developed by the united states aviation administration and the united states marine and atmospheric administration. The model outputs various parameters (soil temperature and soil moisture, evaporation capacity, surface runoff and the like) and hydrological variables of the land surface through land surface modeling and data assimilation technology. The GLDAS data used by the invention comprises four land surface models NOAH, CLM, MOS and VIC, the spatial resolution of the data is 1 degree multiplied by 1 degree, the time resolution is 1 month, and the selected data time range is consistent with GRACE data. The GLDAS model has soil moisture with different depths, 3 layers of VIC simulation are carried out, and the maximum depth is 1.90 m; NOAH simulated 4 layers with a maximum depth of 2.00 m; CLM simulates 10 layers, and the maximum depth is 3.43 m; the MOS simulates 3 layers, and the maximum depth is 3.50 m. According to the model, soil moisture, snow water equivalent and total canopy water storage amount are considered when the TWS is calculated, and the data average value of 1 month to 12 months in 2004 is deducted from data average value of 12 months in 2009 every month to obtain the TWS relative change.
1.4 precipitation data
The Chinese ground precipitation monthly data set is based on the latest China ground station precipitation data specially compiled for the basic data of the national weather center. The data is subjected to spatial interpolation by using a thin disc spline method, so that Chinese rainfall month value lattice point data with the resolution of 0.5 degrees multiplied by 0.5 degrees from 1961 to date are generated, and the data ranges are 72-136 degrees E and 18-54 degrees N. The time range of the data selected by the invention is 4 months to 2017 months and is consistent with the time range of GRACE data.
2. Verification of novel scale factor decision coefficient weighted average correction method
2.1 data processing
2.1.1 Signal attenuation by truncation and Filtering
The method for processing the GRACE spherical harmonic coefficient truncation and the de-banding and Gaussian smoothing filter causes leakage errors of the GRACE inversion result, and the method mainly comprises two conditions: (1) when the signal in the research area is strong and the surrounding signal is weak, the signal in the research area leaks out of the research area after the spherical harmonic coefficient is truncated and filtered, and the area is controlled by an external leakage error, which is called an external leakage error; (2) when the signal in the research area is weak and the surrounding signal is strong, the spherical harmonic coefficient is truncated and filtered, and the surrounding signal leaks into the research area, which indicates that the area is controlled by the internal leakage error, and is called the internal leakage error.
The method uses a GLDAS-NOAH hydrological model to calculate TWS space distribution trend change, deducts data outside a Yangtze river basin of a research area, and simulates external leakage errors caused by truncation and filtering of spherical harmonic coefficients of the Yangtze river basin. Fig. 3(a) shows the trend of spatial distribution of TWS in the Yangtze river basin calculated from the GLDAS-NOAH data between 4 and 2017 months in 2002. The data in fig. 3(a) is spherical-harmonic expanded and truncated to order 60, and the result is shown in fig. 3 (b). FIG. 3(c) and FIG. 3(d) are obtained by Gaussian smoothing filtering at 300km and 500km, respectively. It can be seen that the value of the region a1 in fig. 3(a) ranges from 0.50 to 1.00cm/yr, the value of the region a2 in fig. 3(b) ranges from 0.25 to 0.50cm/yr, the value of the region A3 in fig. 3(c) ranges from 0.25 to 0.30cm/yr, the value of the region a4 in fig. 3(d) ranges from 0.10 to 0.15cm/yr, and signals are continuously diffused from the red region labeled a1 → a2 → A3 → a4 to the surroundings, and the TWS spatial distribution trend of the region is continuously reduced. The signal is diffused to the periphery after the spherical harmonic coefficient expansion and truncation, and is further attenuated after the Gaussian smoothing filtration, and the larger the Gaussian smoothing radius is, the stronger the signal loss is.
In order to evaluate the external leakage error effect of truncation and filtering, the average trend change of the region in the Yangtze river flow domain is respectively calculated for comparative analysis, and the trend change loss Rate is defined as:
Rate＝(NOAH-Model)/NOAH
wherein, NOAH is the average regional trend of the GLDAS-NOAH hydrological Model, and the Model is the average regional trend of the GLDAS-NOAH hydrological Model after filtering.
Calculating the average regional trend of the Yangtze river basin to be 0.08cm/yr by using the initial data; after spherical harmonic expansion and truncation to 60-order, the average trend of the region without Gaussian smoothing is 0.07cm/yr, which is 12% of the loss of the initial data signal; after spherical harmonic expansion and truncation to 60 orders, the average trend of the area subjected to 300km Gaussian smoothing is 0.06cm/yr, and the loss is 25% relative to the initial data signal; the average trend of the region subjected to Gaussian smoothing of 500km after spherical harmonic expansion and truncation to order 60 was 0.05cm/yr, which is a 37% loss with respect to the initial data signal. These data also verify the signal attenuation caused by truncation and filtering. Therefore, the signal loss caused by truncation and filtering of the recovered GRACE data has important significance for utilizing the GRACE spherical harmonic data to invert the study area quality change.
2.1.2 Scale factor model
The invention uses four hydrological models of GLDAS and a scale factor model calculated by CSR-M, and the novel scale factor model obtained based on the novel scale factor decision coefficient weighted average correction method is shown in figure 4 (a). As shown in fig. 4(b), 4(d), 4(e) and 4(f), the global hydrological model CLM, MOS, NOAH and VIC data are applied to all grid points at 1 ° × 1 ° based on equation (5), and the off-boundary data are subtracted to obtain the scale factor for the meshing of the Yangtze river basin. To compare the scale factor results, the present invention uses the CLM4.0 scale factor provided by the official, preserving the CLM4.0 scale factor with the data in the Yangtze river basin region as shown in fig. 4 (c). The scale factors CLM-SF (fig. 4(b)), MOS-SF (fig. 4(d)), NOAH-SF (fig. 4(e)), and VIC-SF (fig. 4(f)) are spatially distributed similarly, and the spatial distribution of NSFCM-SF (fig. 4(a)) and CLM4.0-SF (fig. 4(c)) downstream of the Yangtze river is significantly different compared to fig. 4(b), fig. 4(d), fig. 4(e), and fig. 4 (f). These differences also reflect differences in the spatial distribution of different model TWS data due to different composition considerations for different hydrologic model data.
Although the scale factors of different models show obvious difference and spatial heterogeneity, the spatial distribution of the scale factor grid values of different models is basically larger than 1, which indicates that the analog signals of Yangtze river basin are mainly controlled by external leakage errors and need to be corrected by using the scale factors larger than 1. The method utilizes scale factors of different models to calculate space average scale factors in the Yangtze river basin, wherein the space average scale factors of the Yangtze river basin are all larger than 1, the CLM4.0-SF space average scale factor is the largest (1.42), the MOS-SF space average scale factor is the smallest (1.30), and the space average scale factor reflects the influence on annual amplitude and long-term trend of a correction result to a certain extent.
2.1.3 iterative recovery method
The iterative recovery method is proposed by Chen and the like for the first time, and is widely applied to the GRACE data leakage error correction after improvement. The iterative recovery method comprises the following specific steps: (1) on each grid point of the 1 ° × 1 ° grid (fig. 5(b)), the initial mass change rate is the mass change rate of the GRACE (fig. 5 (a)). (2) The forward model mass change rate (fig. 5(c)) was obtained by performing spherical harmonic expansion from the 1 ° × 1 ° gridded model mass change rate (fig. 5(b)) of step (1), and truncating the spherical harmonic coefficients to 60 th order, setting the coefficients of 0 th order and 1 st order to 0, and then applying gaussian smoothing filtering of 300 km. (3) On each grid point, the difference between the initial GRACE mass change rate (fig. 5(a)) and the forward model mass change rate (fig. 5(c)) is multiplied by 1.20 and added back to the 1 ° × 1 ° gridded model mass change rate (fig. 5(b)), and step (2) is performed as a new model mass change rate, and the process is repeated. Successive iterations yield an increase in the consistency between the forward model mass change rate and the initial GRACE mass change rate (fig. 5(a) and 5 (c)). (4) When the difference between the initial GRACE quality change rate (FIG. 5(a)) and the forward model quality change rate (FIG. 5(c)) is less than a certain threshold or iterated a certain number of times, the iteration is stopped.
After iteration is carried out for 60 times, the obtained spherical harmonic signals are converted into grid signals, namely, the signal results recovered by the iterative recovery method (fig. 5(b)), and the spherical harmonic signals are compared with the signal results recovered by the iterative recovery method (fig. 5(a)) and the signal results recovered by the iterative recovery method (fig. 5(c)) to find that the spherical harmonic signals have stronger consistency and the difference value between the spherical harmonic signals (fig. 5(d)) is smaller (the color bar value is-0.10 cm/yr). Therefore, the resulting signal recovered by the iterative recovery method is considered to be authentic.
2.2 novel Scale factor decision coefficient weighted average correction method comparative analysis
1.2.1 contrastive analysis of spatial distribution trend of water reserve change in Yangtze river basin
The time-varying signal of the corrected GRACE data obtained by the method of the scale factor calculated according to the GLDAS hydrological model, the scale factor calculated by the novel scale factor determining coefficient weighted average correction method, the CLM4.0 scale factor provided by the official part and the iterative recovery method is shown in FIG. 6. It can be seen that the scale factor method and the iterative recovery method have significantly enhanced correction results compared to the spatial distribution trend signal of the CSR-grid inversion result (fig. 6(e)), especially in the middle and downstream of the Yangtze river.
In order to further compare recovery results of different leakage error correction methods, the CSR-M data correction result is used as a real signal of CSR-grid data. Compared with the spatial distribution Trend of the CSR-M data, the recovery result spatial distribution Trend of the different leakage error correction methods has the advantages that NSFCM-Trend (figure 6(a)), CLM-Trend (figure 6(B)), MOS-Trend (figure 6(g)), NOAH-Trend (figure 6(h)) and VIC-Trend (figure 6(i)) are consistent with CSR-M-Trend (figure 6(d)), and CLM4.0-Trend (figure 6(c)) marked region B is obviously excessive in recovery phenomenon compared with CSR-M-Trend (figure 6 (d)). The FM-Trend (FIG. 6(f)) marked region C is obviously inferior to the CSR-M-Trend (FIG. 6(d)) in signal recovery. The method also calculates the regional average trend of the recovery results of different leakage error correction methods of the Yangtze river basin. The region average Trend can obtain that CSR-M-Trend is maximum, CSR-grid-Trend is minimum, and the NSFCM-Trend region average Trend is larger than the region average Trend of the scale factor correction result calculated by the GLDAS model, but smaller than the CLM4.0-Trend and FM-Trend region average Trend. In conclusion, the NSFCM-Trend avoids the phenomena of incomplete signal recovery and excessive signal recovery of FM-Trend and CLM4.0-Trend, and the average Trend of the NSFCM-Trend area is better than that of the GLDAS hydrological model scale factor correction result.
2.2.2 comparative analysis of time series of water reserves in Yangtze river basin
Fig. 7 shows a time series of water reserve change obtained by different leakage error correction method recovery results of Yangtze river basin. Compared with CSR-grid data and CSR-M data, the recovery results of different leakage error correction methods are better in year-round phase consistency, but year-round amplitudes are obviously different, which shows that the scale factor method and the iterative recovery method mainly change the year-round amplitudes of the water reserve change time sequence, and have smaller influence on the year-round phases of the water reserve time sequence. In order to further compare the difference of the recovery results of different leakage error correction methods, the annual amplitude and the long-term trend of the time series of the water reserve change of the Yangtze river basin are calculated by the method disclosed by the invention and are shown in FIG. 8.
Fig. 8 shows the long-term trend and the annual amplitude of the water storage change recovered by different leakage error correction methods in the Yangtze river basin, and the annual amplitude and the long-term trend of the CSR-grid data can be obtained to be at a lower level, so that a signal leakage phenomenon exists. After leakage error correction, annual amplitude and long-term trend are enhanced, and signal leakage is recovered to a certain degree. In the annual amplitude, the CSR-M data and the FM method correction result are close to the CSR-grid data, and the GLDAS hydrological model scale factor correction result is obviously larger than the CSR-grid data. This may be because the TWS modeled by the GRACE raw observation data is insensitive on a fine spatial scale, while CSR-M and CSR-grid are product data, mainly constrained by the GRACE satellite raw observation data, so the FM method recovery annually has a small amplitude; the GLDAS hydrological model simulates the TWS most widely varying on a sub-seasonal and seasonal time scale, so the scale factor calculated from the model simulated TWS optimizes the annual amplitude. In the long-term trend, CSR-M data is the largest (0.41 + -0.07 cm/yr), TWS-CLM4.0 data (0.38 + -0.11 cm/yr), TWS-FM (0.37 + -0.09 cm/yr) and TWS-NSFCM (0.34 + -0.10 cm/yr) are better. The scale factor correction results calculated by the GLDAS hydrological model underestimate the long-term trend, which may be related to insufficient TWS simulated by the GLDAS hydrological model, which only considers soil moisture, snow water equivalent and total canopy water storage, wherein the soil moisture factor is large, the MOS simulated soil moisture depth (3.50m) is equivalent to the CLM simulated soil moisture depth (3.43m), and therefore the long-term trend is large, and the VIC and NOAH simulated soil moisture depths are equivalent (1.90m and 2.00m), but the VIC corrected long-term trend is good, which may be related to the snow water equivalent and total canopy water storage parameters.
3. Application of novel scale factor decision coefficient weighted average correction method
3.1 contrastive analysis of the change in water reserves in the Yangtze river sub-basin
The method has the advantages that the spatial distribution trend of the scale factor correction result calculated by combining the NSFCM-SF scale factors with the GLDAS hydrological model is avoided, and the phenomenon that the spatial distribution trend of the CLM4.0-SF and FM correction results is uneven is avoided. On the long-term trend, the NSFCM-SF scale factor correction result is lower than CLM4.0-SF and FM, but is better than the long-term trend calculated by the GLDAS hydrological model correction result, and on the annual amplitude, the NSFCM-SF scale factor correction result is obviously better than the FM and CSR-M results. In general, the present invention is discussed below primarily in the context of NSFCM-SF scale factor correction. And (3) selecting a CSR-M, CSR-grid model and a TWS-NSFCM model, and further analyzing the correction result of the NSFCM-SF in the Yangtze river sub-basin (the upper stream of the Yangtze river and the middle and lower stream of the Yangtze river).
FIG. 9 shows the water reserves time series for the Changjiang river sub-basin CSR-M, CSR-grid and TWS-NSFCM models. As can be seen in FIG. 9, the annual TWS-NSFCM amplitudes upstream and mid-downstream of the Yangtze river are significantly better than the results of the CSR-grid and CSR-M. The time series downstream in the Yangtze river is more complex and seasonal TWS changes are greater than upstream in the Yangtze river, which may be related to seasonal surface water storage changes downstream in the Yangtze river. The long-term trend of the CSR-grid at the upper reaches of the Yangtze river is 0.09cm/yr, the long-term trend of the TWS-NSFCM is 0.13cm/yr after being corrected by the NSFCM-SF scale factor, the long-term trend is improved by 44%, the long-term trend of the TWS-grid at the middle and lower reaches of the Yangtze river is 0.44cm/yr, the long-term trend of the TWS-NSFCM is 0.61cm/yr after being corrected by the NSFCM-SF scale factor, the long-term trend is improved by 39%, and the water storage quantity rising trend of the Yangtze river basin is mainly concentrated at the middle and lower reaches of the Yangtze river.
3.2 comparison of precipitation in Yangtze river basin with Water reserve Change
The time series of the correction result based on the NSFCM-SF scale factor is compared with precipitation month data of the national weather center, as shown in FIG. 9. It can be seen that rainfall in the Yangtze river basin and the sub-basins is mainly concentrated in 5-10 months, when the rainfall is obviously increased, the change of the TWS-NSFCM water reserve is obviously increased, and the rainfall data is delayed for 1-2 months. The change of the precipitation data is consistent with the change of the TWS-NSFCM water reserves, which indicates that the precipitation is the main reason of the change of the water reserves of the Yangtze river basin. The water storage capacity and the precipitation of the Yangtze river basin and the sub-basin both show rising trends in the year 4-2007 1, the rising trend of the water storage capacity of the Yangtze river basin is 0.33cm/yr, the rising trend of the precipitation is 0.06cm/yr, the rising trend of the water storage capacity of the upper reaches of the Yangtze river is 0.10cm/yr, the rising trend of the precipitation is 0.03cm/yr, the rising trend of the water storage capacity of the middle and lower reaches of the Yangtze river is 0.63cm/yr, the rising trend of the precipitation is 0.10cm/yr, the rising trend of the precipitation is mainly concentrated in the middle and lower reaches of the Yangtze river, the characteristic is consistent with the characteristic that the rising trend of the water storage capacity of the Yangtze river basin is mainly concentrated in the middle and lower reaches of the Yangtze river, and the fact that the precipitation is the main reason of the change of the water storage capacity of the Yangtze river basin is further verified. The invention also calculates the annual precipitation anomaly of the Yangtze river basin as shown in fig. 11, and the year of incomplete precipitation data is not discussed because the precipitation data in 2010, 2011 and 2015 are incomplete. As can be seen from fig. 11, precipitation was near or below the multi-year average for most years, but precipitation was significantly higher than the multi-year average for 2012, 2014 and 2016, which may be related to global warming and frequent climatic extremes (e.g., el nino, etc.) in recent years. With reference to fig. 10, in the years with more precipitation, the annual change of the TWS-NSFCM water storage amount is significantly increased, so that the annual change characteristics of the TWS-NSFCM water storage amount in the Yangtze river basin are consistent with the annual change rule of precipitation.
Although the present invention has been described with reference to the preferred embodiments, it is not intended to limit the present invention, and those skilled in the art can make variations and modifications of the present invention without departing from the spirit and scope of the present invention by using the methods and technical contents disclosed above.
Those skilled in the art will appreciate that the invention may be practiced without these specific details.

Claims (8)

1. A method for improving the accuracy of the change of the water reserves of the land of GRACE is characterized by comprising the following steps:
obtaining land water reserves delta h (theta, lambda) from the hydrological model, and determining a spherical harmonic coefficient cosine term C corresponding to the delta h (theta, lambda)lmAnd a sine term Slm(ii) a Wherein θ represents the remaining latitude, and λ represents the longitude;
to ClmAnd SlmPerforming de-banding filtering and Gaussian smoothing filtering to obtain the filtered spherical harmonic coefficient cosine term
Figure FDA0003038420240000011
And sine term
Figure FDA0003038420240000012
Based on
Figure FDA0003038420240000013
And
Figure FDA0003038420240000014
obtaining filtered land water reserves delta eta (theta, lambda);
determining time sequence data deltah corresponding to deltah (theta, lambda) in t time sequencei(t), time-series data Δ η corresponding to the time-series of t Δ η (θ, λ)i(t)；
According to Δ hi(t) and Δ ηi(t), resolving to obtain a decision coefficient weighting scale factor;
and correcting leakage errors in the process of inverting the land water reserves by the GRACE data according to the decision coefficient weighting scale factors, and recovering real hydrological signals so as to improve the accuracy of the change of the land water reserves of the GRACE.
2. The method of claim 1, wherein determining the ball corresponding to Δ h (θ, λ) is performed by the following equation (1)Harmonic coefficient cosine term ClmAnd a sine term Slm：
Figure FDA0003038420240000015
Where ρ iswDenotes the density of water, a denotes the mean radius of the earth, ρaveWhich represents the average density of the earth,
Figure FDA0003038420240000016
expressing the normalized associated Legendre function, l the order of the spherical harmonic coefficient solution inversion, m the number of times of the spherical harmonic coefficient solution inversion, klThe load lux number of order l is shown.
3. The method of claim 2, wherein C is addedlmAnd SlmPerforming de-banding filtering and Gaussian smoothing filtering to obtain the filtered spherical harmonic coefficient cosine term
Figure FDA0003038420240000017
And sine term
Figure FDA0003038420240000018
The method comprises the following steps:
according to the following formulae (2) and (3), to ClmAnd SlmPerforming de-banding filtering processing to obtain spherical harmonic coefficient cosine item after de-banding filtering
Figure FDA0003038420240000019
And sine term
Figure FDA00030384202400000110
Figure FDA0003038420240000021
Figure FDA0003038420240000022
Wherein w is the width of the sliding window, e is the natural logarithm, max () represents the maximum value, and Q is the de-banding filter coefficient; de-banding n for odd terms is the odd term in the order l, and the even terms are the same;
according to the following formulae (4) and (5)
Figure FDA0003038420240000023
And
Figure FDA0003038420240000024
performing Gaussian smoothing filtering to obtain spherical harmonic coefficient cosine term after Gaussian filtering
Figure FDA0003038420240000025
And sine term
Figure FDA0003038420240000026
Figure FDA0003038420240000027
Figure FDA0003038420240000028
Wherein r represents a Gaussian smoothing radius, W0Representing initial order Gaussian smoothing weights, Wl-1、WlAnd Wl+1And respectively represent Gaussian smoothing weights of order l-1, order l and order l +1, wherein l is 0,1,2,3 … 60.
4. A method for improving the accuracy of terrestrial water reserve variation of GRACE as defined in claim 3, wherein the filtered terrestrial water reserve Δ η (θ, λ) is obtained by the following formula (6):
Figure FDA0003038420240000029
5. the method of claim 1, wherein the accuracy of the change in terrestrial water reserves of GRACE is improved in terms of Δ hi(t) and Δ ηi(t) solving to obtain a decision coefficient weighting scale factor, comprising:
according to Δ hi(t) and Δ ηi(t), resolving to obtain a scale factor K based on a least square principle;
according to Δ hi(t) obtaining the coefficient of determination R by calculation2；
According to the scale factor K and the decision coefficient R2And calculating to obtain a decision coefficient weighting scale factor NSFCM-SF.
6. The method of claim 5, wherein the scale factor K is obtained by calculating according to the following equation (7):
Figure FDA0003038420240000031
where N represents the number of time series, and i represents the ith time series.
7. The method of improving GRACE land water reserves accuracy of claim 6, wherein the method is based on Δ hi(t) obtaining the coefficient of determination R by calculation2The method comprises the following steps:
according to Δ hi(t) determining fitted land water reserves
Figure FDA0003038420240000032
Average of land and water reserves
Figure FDA0003038420240000033
The coefficient of determination R is obtained by calculation using the following formula (8)2：
Figure FDA0003038420240000034
8. The method of claim 7, wherein the determination coefficient weighting scale factor NSFCM-SF is obtained by solving the following equation (9):
Figure FDA0003038420240000035
wherein n represents the number of scale factor models, j represents the jth scale factor model, KjRepresents the scale factor corresponding to the jth scale factor model,
Figure FDA0003038420240000036
and represents a determination coefficient corresponding to the jth scale factor model.
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Cited By (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN115630686A (en) * 2022-10-11 2023-01-20 首都师范大学 Method for recovering land water reserve abnormity from satellite gravity data by machine learning
CN115712982A (en) * 2022-10-18 2023-02-24 首都师范大学 Satellite gravity collaborative forward modeling method for inverting regional underground water level change
CN117152629A (en) * 2023-08-23 2023-12-01 武汉大学 Method and system for filling gravity vacancy data of drainage basin scale time-varying satellite

Cited By (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN115630686A (en) * 2022-10-11 2023-01-20 首都师范大学 Method for recovering land water reserve abnormity from satellite gravity data by machine learning
CN115712982A (en) * 2022-10-18 2023-02-24 首都师范大学 Satellite gravity collaborative forward modeling method for inverting regional underground water level change
CN117152629A (en) * 2023-08-23 2023-12-01 武汉大学 Method and system for filling gravity vacancy data of drainage basin scale time-varying satellite
CN117152629B (en) * 2023-08-23 2024-03-22 武汉大学 Method and system for filling gravity vacancy data of drainage basin scale time-varying satellite

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