# Inverted Algorithm of Terrestrial Water-Storage Anomalies Based on Machine Learning Combined with Load Model and Its Application in Southwest China

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## Abstract

**:**

^{2}) are equal to 0.76 and 0.65, respectively; the values of PCC and R

^{2}between MLLIM and GLDAS solutions are equal to 0.79 and 0.65. Compared with the traditional GPS inversion, the MLLIM improves PCC and R

^{2}by 8.85% and 7.99% on average, which indicates that the MLLIM can improve the accuracy of TWSA inversion more than the traditional GPS method. Third, this study applies the MLLIM to invert the TWSA in each province of southwest China and combines the precipitation to analyze the change of TWSA in each province. The results are as follows: (1) The spatial distribution of TWSA and precipitation is coincident, which is highlighted in southwest Yunnan and southeast Guangxi; (2) this study compares TWSA of MLLIM with GRACE and GLDAS solutions in each province, which indicates that the maximum value of PCC is as high as 0.86 and 0.94, respectively, which indicates the MLLIM can be used to invert the TWSA in the regions with sparse GPS stations. The TWSA based on the MLLIM can be used to fill the vacancy between GRACE and GRACE-FO.

## 1. Introduction

**U**) [18,19,20,21]. The elastic response is especially presented in the deformation of U direction, which can be established using the model of load–deformation [22,23,24]. The response of crustal loading can be measured by numerous observation methods, such as GPS [25], InSAR [26], and VLBI [27], etc. GPS can observe the crustal displacement with the virtues of efficiency, accuracy, and all weather [28]. Furthermore, the crustal movement observation network of China (CMONOC) has been established for 9 years, which can measure crustal displacement in China [29]. Previous studies have used this data to analyze geophysical phenomena in typical regions of China, such as Southern China [19], the North China Plain [29,30], and Sichuan province [31], etc. However, the uneven spatial distribution of GPS greatly limits its application to analyze geophysical phenomena [32,33,34]. The GPS stations are concentrated in Sichuan and Yunnan provinces [35]. It has become a hotpot to simulate the crustal deformation on the unobserved regions. Specifically, the unobserved regions represent that the 1°×1° grid does not contain the GPS station.

## 2. Materials and Methods

#### 2.1. Materials

#### 2.1.1. GPS Solutions

#### 2.1.2. GRACE Solutions

^{3}kg/m

^{3}; ${\rho}_{w}$ denotes the density of the water that equals 10

^{3}kg/m

^{3}; ${h}_{l}$ and ${k}_{l}$ represent the Love numbers; ${W}_{l}$ denotes the kernel function of Gaussian smoothing; ${\overline{P}}_{l,m}$ denotes the Legendre functions; $\Delta {C}_{lm}$ and $\Delta {S}_{lm}$ represent the spherical harmonic coefficient of Earth gravity field.

#### 2.1.3. Products of GLDAS and ERA 5

#### 2.2. Methods

#### 2.2.1. Random Forest

_{t}(x) denotes each tree’s simulated result of RF; T represents the number of spanning trees for RF; N denotes the number of the GPS stations.

#### 2.2.2. Inversion of TWSA Using Crustal Load–Deformation

_{n}denotes the Legendre polynomials; G represents the constant of Newton’s universal gravitation; R denotes the radius of the Earth; h

_{n}represents the Love’s number; g denotes the constant of the acceleration for the gravity; The deduction of the ${\mathsf{\Gamma}}_{n}$ is shown as follows [46]:

#### 2.2.3. Construction of the MLLIM

#### 2.3. Evaluation Index

^{2}) [58], respectively, as follows:

^{2}is also called the coefficient of determination, which can explain the variation degree according to the independent variables. The value of R

^{2}is between 0 and 1, and the larger it is, the better the fitting effect.

## 3. Results

#### 3.1. Inversion of the TWSA Based on the MLLIM

#### 3.2. Comparison with Traditional Method of GPS Inversion

#### 3.3. Comparison with GRACE

^{2}equal 0.76 and 0.65. Hence, compared with the traditional GPS inverted method, the MLLIM improves the PCC and R

^{2}by 7.98% and 9.30% on average.

#### 3.4. Comparison with the GLDAS Solutions

^{2}between the MLLIM and GLDAS solution are 0.79 and 0.64, respectively. Furthermore, compared with the traditional GPS inverted method, the MLLIM improves the PCC and R

^{2}by 9.72% and 6.67% on average, respectively.

## 4. Discussion

## 5. Conclusions

- (1)
- To increase the inverted accuracy for TWSA, the MLLIM is constructed using RF and the crustal load model. To simulate the crustal displacement in unobserved grids, the sequences of temperature and atmospheric pressure are used as the input data, and the GPS vertical sequence is used as the output data. Thus, the unobserved grids’ crustal deformation can be simulated based on the MLLIM. Furthermore, all the corrected crustal sequences are employed as the input data for the crustal load model; specifically, the corrected sequences include the GPS vertical sequences and the simulated sequences.
- (2)
- To verify the reliability of the MLLIM, the results of traditional GPS inverted method (without adding the simulated crustal deformation), GRACE, and GLDAS are used to compare with the TWSA based on the MLLIM. The compared results show that this inverted method can detect the raised region of annual amplitude in Yunnan, central Sichuan, and Guangxi provinces, and is consistent with the results of GRACE Mascon and GLDAS. However, the traditional GPS inverted method loses this characteristic signals due to the fitting of inversion (Figure 8d–f). From the comparison with GRACE, the values of PCC with GRACE and GRACE-FO equal 0.91 and 0.88, and the values of R
^{2}equal 0.76 and 0.65, respectively. The MLLIM improves PCC and R^{2}by 7.98% and 9.30% than traditional method, respectively. From the comparison with GLDAS, the values of PCC and R^{2}equal 0.79 and 0.64, respectively, it improves PCC and R^{2}by 9.72% and 6.67% compared with the traditional method, respectively. On the whole, compared with the traditional GPS inverted method, the MLLIM effectively improves the accuracy of TWSA inversion. - (3)
- The data of precipitation is combined to analyze the relationship between the TWSA and the rainfall. We apply the MLLIM to derive the TWSA in the five provinces, and the results indicate that the precipitation in Yunnan and Guangxi is significantly higher than other provinces. Meanwhile, the spatial distribution characteristics of TWSA is consistent with the precipitation in southwest China. From the comparison with GRACE and GLDAS solutions, the maximum PCC values equal 0.86 and 0.94, respectively. The above conclusions show that the TWSA can be inverted accurately based on the MLLIM in the region where the distribution of GPS stations is uneven.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**The information of GPS stations in southwest China. (

**a**) The location of study region (red region) in China; (

**b**) The distribution of the GPS stations (Green points); (

**c**) The use of land over southwest China; (

**d**) The relationship between the unobserved grids (G1-G87) and the GPS stations (red points).

**Figure 2.**The sequences of vertical deformation (orange line), temperature (blue line), and atmospheric pressure (green line) on the GPS stations of SCPZ (

**a**), SCXJ (

**b**), YNMJ (

**c**), and YNML (

**d**), respectively.

**Figure 3.**The relationship between the vertical deformation and center distance of disks with different mass and radius.

**Figure 6.**The regressed result of crustal deformation in the unobserved grids, taking G36 and G43 as an example.

**Figure 8.**(

**a**–

**c**) and (

**d**–

**f**) shows the annual, semi-annual, and periodic items of the new and traditional methods, respectively.

**Figure 9.**The compared result of GRACE, showing in the average fitting sequence (

**a**), annual (

**b**), semi-annual (

**c**) and periodic items (

**d**) of GRACE, and scatter figure (

**e**).

**Figure 10.**The compared result of GLDAS solutions, showing in the average fitting sequence (

**a**), annual (

**b**), semi-annual (

**c**) and periodic items (

**d**) of GLDAS, and scatter figure (

**e**).

**Figure 11.**The comparison with precipitation in each province; (

**a**–

**d**) show the spatial distribution of the total precipitation; (

**f**–

**J**) describe the result of GPS, GRACE, GLDAS solutions, and precipitation in each province.

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**MDPI and ACS Style**

Shen, Y.; Zheng, W.; Yin, W.; Xu, A.; Zhu, H.; Yang, S.; Su, K.
Inverted Algorithm of Terrestrial Water-Storage Anomalies Based on Machine Learning Combined with Load Model and Its Application in Southwest China. *Remote Sens.* **2021**, *13*, 3358.
https://doi.org/10.3390/rs13173358

**AMA Style**

Shen Y, Zheng W, Yin W, Xu A, Zhu H, Yang S, Su K.
Inverted Algorithm of Terrestrial Water-Storage Anomalies Based on Machine Learning Combined with Load Model and Its Application in Southwest China. *Remote Sensing*. 2021; 13(17):3358.
https://doi.org/10.3390/rs13173358

**Chicago/Turabian Style**

Shen, Yifan, Wei Zheng, Wenjie Yin, Aigong Xu, Huizhong Zhu, Shuai Yang, and Kai Su.
2021. "Inverted Algorithm of Terrestrial Water-Storage Anomalies Based on Machine Learning Combined with Load Model and Its Application in Southwest China" *Remote Sensing* 13, no. 17: 3358.
https://doi.org/10.3390/rs13173358