Potential Contributors to Common Mode Error in Array GPS Displacement Fields in Taiwan Island
Abstract
:1. Introduction
2. Methods and Data Processing
2.1. GNSS Data Processing
2.2. Principal Component Analysis
2.3. Independent Component Analysis
- Centralize and whiten the observed data.
- Choose an initial weight vector of unit norm .
- Update through .
- Normalize by .
- Return to step 3 if is not converged.
3. Results
3.1. Common Mode Error Extraction Using PCA/ICA
3.2. Noise Analysis of GNSS Coordinate Time Series
4. Discussion
4.1. Potential Geophysical Interpretation of the CME
4.2. Effect of Removing the CME
5. Conclusions
- Both PCA and ICA can effectively remove the CME. The average RMS of PCA and ICA in the U direction shifted from 6.47 mm to 5.58 mm and 5.40 mm, respectively, a decreased by approximately 14% and 17%. However, the CMEs of the two approaches reveal notable differences in their temporal and spatial characteristics. Figure 6 shows that the PCA separates only one CME and the ICA separates two CMEs. We therefore believe that PCA may eliminate the original site information, whereas ICA retains more original site information.
- There are notable differences in the ICA filtering effect between the east and west of Taiwan. The RMS reduction rate in the west is relatively large, whereas that in the east small, which is partially due to topography. There are many mountains on the eastern side of Taiwan and the stations are sparsely distributed, whereas the western side is relatively flat and the stations are relatively dense. Another explanation is the orogenic processes, as there is a topographic uplift in the eastern region and sinking in the southwest region due to groundwater extraction.
- To explore the possible geophysical sources of ICA’s CMEs, we compare the CMEs of ICA with the predicted average loading displacements caused by changes in the atmospheric and hydrological loadings. It is found that GPS_IC1 and ATML, and GPS_IC2 and LWS are consistent in terms of amplitude and characteristics. The correlation between GPS_IC1 and ATML is 0.55, and the correlation coefficient between GPS_IC2 and LWS is 0.40. This indicates that seasonal changes in Taiwan are related to the movement of water in addition to atmospheric pressure.
- We used Hector software to analyze the noise characteristics of the time series of all stations prior to filtering. The average spectral index shifted from -0.72 to -0.92, which indicates that the most suitable noise model in Taiwan is W + FN. Filtering can also effectively reduce PL noise. After filtering, PL noise is reduced by an average of approximately 28%. The average annual cycle item is also significantly reduced by approximately 60%. ICA filtration is more advantageous than PCA filtration. The noise sequence filtered by ICA and PCA at the GS39 station was analyzed to verify the above conclusions.
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
References
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Order of PCs | Individual Contribution Rate (%) | Cumulative Contribution Rate (%) |
---|---|---|
1 | 24.7 | 24.7 |
2 | 6.5 | 31.2 |
3 | 4.6 | 35.8 |
4 | 3.7 | 39.5 |
5 | 3.6 | 43.1 |
6 | 3.0 | 46.1 |
7 | 2.7 | 48.8 |
8 | 2.5 | 51.3 |
9 | 2.4 | 53.7 |
10 | 2.3 | 56.0 |
Method | RMS/mm | |
---|---|---|
Before | 6.47 | |
After | PCA | 5.58 |
ICA | 5.40 |
Sites | Annual Amplitude (mm) | Semi-Annual (mm) | PL Amplitude | WN Amplitude | ||||||
---|---|---|---|---|---|---|---|---|---|---|
Before | After | Before | After | Before | After | Before | After | Before | After | |
‘ANKN’ | 1.23 ± 0.33 | 0.70 ± 0.25 | 0.55 ± 0.25 | 0.50 ± 0.21 | 10.32 | 8.07 | 4.08 | 4.13 | −0.47 | −0.37 |
‘CHKU’ | 2.41 ± 0.31 | 0.40 ± 0.19 | 0.60 ± 0.23 | 0.39 ± 0.15 | 8.63 | 4.94 | 3.50 | 4.00 | −0.67 | −0.93 |
‘CHNT’ | 3.80 ± 0.83 | 2.80 ± 0.80 | 0.88 ± 0.45 | 0.77 ± 0.40 | 20.32 | 19.12 | 6.17 | 6.40 | −0.98 | −1.05 |
‘CLAN’ | 4.30 ± 1.00 | 2.39 ± 0.94 | 1.58 ± 0.65 | 1.35 ± 0.60 | 24.21 | 23.04 | 6.09 | 6.23 | −1.01 | −1.10 |
‘CTOU’ | 2.54 ± 0.45 | 0.67 ± 0.31 | 0.53 ± 0.26 | 0.59 ± 0.24 | 11.60 | 8.14 | 4.90 | 5.24 | −0.85 | −1.02 |
‘CWEN’ | 3.41 ± 0.37 | 0.69 ± 0.20 | 0.55 ± 0.25 | 0.44 ± 0.16 | 9.99 | 5.37 | 3.88 | 3.75 | −0.73 | −0.65 |
‘DAHU’ | 2.63 ± 0.45 | 1.58 ± 0.38 | 0.48 ± 0.25 | 0.50 ± 0.24 | 12.19 | 9.52 | 4.24 | 4.73 | −0.75 | −0.89 |
‘DOSH’ | 3.90 ± 0.38 | 0.36 ± 0.18 | 0.40 ± 0.21 | 0.35 ± 0.15 | 10.94 | 5.36 | 3.80 | 4.52 | −0.64 | −0.68 |
‘FLON’ | 2.76 ± 0.46 | 1.64 ± 0.42 | 1.58 ± 0.39 | 1.33 ± 0.36 | 15.33 | 14.31 | 0.00 | 0.01 | −0.45 | −0.43 |
‘FNGU’ | 2.76 ± 0.37 | 0.44 ± 0.21 | 0.85 ± 0.27 | 0.64 ± 0.17 | 9.52 | 4.60 | 4.26 | 4.40 | −0.82 | −1.25 |
‘GS15’ | 2.90 ± 0.29 | 0.91 ± 0.20 | 0.40 ± 0.19 | 0.31 ± 0.13 | 8.37 | 3.90 | 3.54 | 4.32 | −0.60 | −1.19 |
‘GS16’ | 2.18 ± 0.45 | 0.67 ± 0.31 | 0.63 ± 0.30 | 0.42 ± 0.21 | 12.38 | 9.58 | 5.43 | 5.57 | −0.73 | −0.70 |
‘GS21’ | 2.03 ± 0.36 | 0.82 ± 0.25 | 0.58 ± 0.24 | 0.37 ± 0.15 | 8.48 | 4.36 | 3.95 | 3.84 | −0.94 | −1.47 |
‘GS22’ | 2.63 ± 0.43 | 1.72 ± 0.33 | 0.49 ± 0.25 | 0.43 ± 0.20 | 10.89 | 7.58 | 3.73 | 4.00 | −0.85 | −0.99 |
‘GS31’ | 1.80 ± 0.40 | 2.04 ± 0.33 | 0.45 ± 0.23 | 0.30 ± 0.16 | 9.54 | 6.58 | 3.82 | 3.78 | −0.99 | −1.24 |
‘GS33’ | 2.86 ± 0.36 | 0.49 ± 0.23 | 0.58 ± 0.24 | 0.50 ± 0.17 | 8.59 | 4.68 | 4.44 | 4.42 | −0.93 | −1.37 |
‘GS39’ | 3.94 ± 0.33 | 1.32 ± 0.24 | 0.58 ± 0.24 | 0.42 ± 0.16 | 9.13 | 4.81 | 3.02 | 3.75 | −0.67 | −1.17 |
‘HUAL’ | 4.06 ± 0.57 | 1.38 ± 0.45 | 0.89 ± 0.38 | 0.51 ± 0.25 | 14.22 | 10.14 | 5.96 | 5.68 | −0.89 | −1.11 |
‘ILAN’ | 4.10 ± 0.70 | 2.35 ± 0.43 | 0.92 ± 0.41 | 0.47 ± 0.23 | 14.38 | 9.43 | 6.60 | 5.59 | −1.27 | −1.09 |
‘JHCI’ | 3.72 ± 0.32 | 0.63 ± 0.18 | 0.56 ± 0.24 | 0.57 ± 0.16 | 10.23 | 5.50 | 2.79 | 3.83 | −0.45 | −0.37 |
‘JONP’ | 3.17 ± 0.34 | 0.58 ± 0.18 | 0.51 ± 0.23 | 0.28 ± 0.13 | 9.75 | 4.45 | 3.83 | 4.26 | −0.63 | −0.76 |
‘JPEI’ | 3.05 ± 0.46 | 1.70 ± 0.43 | 0.60 ± 0.29 | 0.68 ± 0.29 | 12.07 | 10.31 | 6.14 | 6.43 | −0.78 | −0.94 |
‘JULI’ | 2.20 ± 0.32 | 0.83 ± 0.26 | 0.63 ± 0.25 | 0.57 ± 0.20 | 9.33 | 5.70 | 4.98 | 6.01 | −0.51 | −0.95 |
‘JUNA’ | 3.16 ± 0.41 | 0.83 ± 0.27 | 0.46 ± 0.23 | 0.32 ± 0.16 | 10.38 | 5.75 | 4.56 | 4.66 | −0.89 | −1.19 |
‘PAOL’ | 2.84 ± 0.47 | 0.65 ± 0.31 | 0.52 ± 0.27 | 0.50 ± 0.24 | 12.30 | 9.80 | 5.68 | 5.58 | −0.80 | −0.78 |
‘S101’ | 3.50 ± 0.37 | 1.78 ± 0.29 | 0.72 ± 0.28 | 0.57 ± 0.23 | 11.76 | 8.98 | 2.63 | 3.96 | −0.50 | −0.51 |
‘S106’ | 2.90 ± 0.36 | 0.50 ± 0.22 | 0.35 ± 0.18 | 0.29 ± 0.14 | 9.21 | 5.70 | 4.42 | 4.36 | −0.82 | −0.87 |
‘S170’ | 2.14 ± 0.33 | 0.43 ± 0.20 | 0.96 ± 0.26 | 0.66 ± 0.17 | 9.22 | 5.00 | 3.94 | 4.27 | −0.71 | −1.00 |
‘SFON’ | 3.58 ± 0.48 | 1.19 ± 0.38 | 0.52 ± 0.26 | 0.42 ± 0.21 | 11.43 | 8.74 | 5.12 | 5.10 | −0.92 | −1.00 |
‘SHAN’ | 0.79 ± 0.40 | 1.87 ± 0.44 | 0.84 ± 0.37 | 0.63 ± 0.29 | 14.82 | 11.21 | 4.70 | 5.28 | −0.75 | −0.85 |
‘SHJU’ | 2.97 ± 0.45 | 1.20 ± 0.30 | 0.84 ± 0.31 | 0.76 ± 0.21 | 11.27 | 6.04 | 4.56 | 4.80 | −0.92 | −1.26 |
‘SHMN’ | 1.67 ± 0.34 | 0.36 ± 0.19 | 0.85 ± 0.28 | 0.71 ± 0.24 | 11.85 | 10.08 | 0.03 | 0.02 | −0.36 | −0.28 |
‘SINY’ | 3.82 ± 0.49 | 0.50 ± 0.26 | 1.01 ± 0.36 | 0.76 ± 0.27 | 13.29 | 9.31 | 5.64 | 5.57 | −0.73 | −0.73 |
‘TACH’ | 2.85 ± 0.49 | 0.68 ± 0.33 | 0.44 ± 0.23 | 0.36 ± 0.19 | 11.92 | 8.04 | 4.06 | 4.15 | −0.98 | −1.34 |
‘TOFN’ | 2.51 ± 0.46 | 0.5 ± 0.26 | 0.59 ± 0.28 | 0.62 ± 0.24 | 11.58 | 8.50 | 4.07 | 4.15 | −0.91 | −0.98 |
‘TSIO’ | 1.85 ± 0.45 | 0.96 ± 0.39 | 1.11 ± 0.33 | 0.96 ± 0.29 | 11.60 | 9.61 | 4.26 | 4.60 | −0.86 | −1.04 |
‘VR01’ | 1.60 ± 0.42 | 0.86 ± 0.33 | 0.46 ± 0.23 | 0.31 ± 0.16 | 10.31 | 6.85 | 4.46 | 4.40 | −0.97 | −1.33 |
‘WANS’ | 3.33 ± 0.49 | 2.05 ± 0.40 | 0.77 ± 0.32 | 0.83 ± 0.29 | 11.98 | 9.71 | 5.33 | 5.12 | −0.95 | −0.96 |
‘WARO’ | 2.01 ± 0.44 | 0.96 ± 0.32 | 0.81 ± 0.33 | 0.38 ± 0.20 | 13.44 | 10.57 | 5.08 | 4.06 | −0.55 | −0.47 |
‘WUFN’ | 2.61 ± 0.28 | 0.95 ± 0.18 | 0.51 ± 0.21 | 0.25 ± 0.12 | 9.00 | 4.00 | 2.43 | 4.46 | −0.42 | −0.82 |
‘WUKU’ | 2.71 ± 1.07 | 2.65 ± 1.05 | 1.99 ± 0.78 | 1.95 ± 0.76 | 29.23 | 28.39 | 0.05 | 1.59 | −0.92 | −0.95 |
‘YENL’ | 2.31 ± 0.36 | 0.73 ± 0.29 | 0.42 ± 0.21 | 0.31 ± 0.16 | 9.71 | 6.73 | 5.21 | 5.62 | −0.70 | −1.05 |
‘YM03’ | 1.61 ± 0.51 | 1.80 ± 0.40 | 0.78 ± 0.35 | 0.94 ± 0.32 | 13.74 | 11.38 | 5.84 | 5.23 | −0.80 | −0.64 |
‘YM05’ | 2.68 ± 0.47 | 0.77 ± 0.34 | 0.85 ± 0.34 | 0.59 ± 0.26 | 12.98 | 9.91 | 3.95 | 4.51 | −0.72 | −0.83 |
Mean | 2.77 ± 0.45 | 1.12 ± 0.34 | 0.72 ± 0.30 | 0.59 ± 0.23 | 12.08 | 8.72 | 4.21 | 4.46 | −0.77 | −0.92 |
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Ma, X.; Liu, B.; Dai, W.; Kuang, C.; Xing, X. Potential Contributors to Common Mode Error in Array GPS Displacement Fields in Taiwan Island. Remote Sens. 2021, 13, 4221. https://doi.org/10.3390/rs13214221
Ma X, Liu B, Dai W, Kuang C, Xing X. Potential Contributors to Common Mode Error in Array GPS Displacement Fields in Taiwan Island. Remote Sensing. 2021; 13(21):4221. https://doi.org/10.3390/rs13214221
Chicago/Turabian StyleMa, Xiaojun, Bin Liu, Wujiao Dai, Cuilin Kuang, and Xuemin Xing. 2021. "Potential Contributors to Common Mode Error in Array GPS Displacement Fields in Taiwan Island" Remote Sensing 13, no. 21: 4221. https://doi.org/10.3390/rs13214221