Understanding the Common-Mode Error in Array GPS Displacement Fields: Insights from Taiwan’s Atmospheric Mass Loading

In our study, we explored the common-mode error (CME) in GPS displacement fields across Taiwan, uncovering its significant correlation with atmospheric mass loading (AML). By analyzing 10 years of GPS data from 47 stations, we found that up to 90% of CME variations in the vertical component can be attributed to AML. These findings enhance our understanding of systematic errors in GPS data and offer pathways to improving the precision of geophysical measurements.

Introduction

In the field of geophysics, the precision of Global Positioning System (GPS) data is paramount for understanding a wide range of Earth processes, from fault motion detection to postseismic deformation. However, systematic errors, particularly the common-mode error (CME), can obscure these insights. In our study, titled “What Causes the Common‐Mode Error in Array GPS Displacement Fields: Case Study for Taiwan in Relation to Atmospheric Mass Loading,” we delved into the origins of CME using a dense network of GPS stations in Taiwan. Our findings not only shed light on the sources of CME but also underscore the significant role of atmospheric mass loading (AML) in influencing GPS measurements.

Background

Common-mode errors are systematic errors in GPS data that exhibit strong spatial coherence across a network of stations. These errors, if not properly accounted for, can contaminate the interpretation of geophysical phenomena. Previous studies have suggested that these errors might be influenced by various environmental factors, including atmospheric, hydrological, and oceanic loads. However, the specific contributions of these factors, particularly atmospheric mass loading, had not been fully quantified until now.

Methodology

To investigate the origin of CME, we analyzed 10 years of GPS data from 47 selected stations across Taiwan. The data was meticulously processed to ensure high quality, with particular attention given to the vertical, north, and east components of the displacement fields.

Empirical Orthogonal Function (EOF) Analysis

We employed the Empirical Orthogonal Function (EOF) analysis, a robust technique akin to principal component analysis (PCA), to extract the CME from the GPS displacement data. This method allowed us to segregate the CME as the leading mode, which represents the most significant spatially coherent signal across the network.

Atmospheric Mass Loading (AML) Data

The AML data was obtained from the NASA Goddard Space Flight Center, providing detailed displacement fields for Taiwan. This data was critical in evaluating the impact of AML on the GPS measurements. By correlating the extracted CME with the AML data, we sought to understand the degree to which AML contributes to the observed errors in GPS displacement fields.

(a) Topographical map of Taiwan showing 392 GPS stations (gray circles) and 47 selected stations (colored circles). The selected stations’ colors represent vertical component cross-correlation values with reference station SHJU (magenta star). AML displacement data is retrieved at station TAIW (white square). (b) Time-variable standard deviation of GPS residuals (top) and calculated AML displacements at TAIW (bottom). Vertical: red, north: green, east: blue. (Source: Kumar et al. 2020)

Results

Our analysis revealed several key findings:

CME Extraction and Correlation with AML

The EOF analysis showed that the first mode, which represents the CME, captured 56% of the variance in the vertical component of the GPS data. Notably, we found a significant correlation between the CME and AML residuals, particularly in the vertical component, with a correlation coefficient (ρ) of 0.43. This strong correlation indicates that AML plays a substantial role in influencing the CME, especially on a monthly timescale.

EOF modes of the GPS residuals (Kumar et. al. 2020)

Regression Analysis

Further regression analysis between the CME and AML residuals revealed an admittance factor of 0.93, suggesting that up to 90% of the CME variations can be attributed to AML in the vertical component. This finding is crucial as it quantifies the impact of AML on CME and provides a pathway to correcting for these errors in GPS data.

Discussion

The implications of our findings are significant for the geophysical community. By establishing a strong link between AML and CME, our study provides a framework for improving the accuracy of GPS data analysis. The results suggest that by accounting for AML, we can significantly reduce the CME in GPS displacement fields, leading to more precise measurements of Earth’s processes.

However, our study also highlights certain limitations. The AML data used in this study, while comprehensive, has a spatial resolution limit that may affect the precision of the correlation with GPS data. Additionally, our focus on the vertical component leaves room for further exploration of the horizontal components and their relation to other environmental factors.

Conclusion

In conclusion, our study demonstrates that atmospheric mass loading is a significant contributor to the common-mode error in GPS displacement fields in Taiwan. By applying EOF analysis and correlating the results with AML data, we have provided a detailed understanding of the sources of CME. These insights are invaluable for enhancing the precision of GPS-based geophysical studies and offer a pathway to mitigating the impact of CME in future research.

As we continue to refine our understanding of these errors, the potential applications of this research extend beyond Taiwan, offering implications for GPS networks worldwide.

References

For readers interested in exploring the detailed methodology and results of our study, the original paper can be accessed here. We also encourage readers to review the supporting literature cited throughout this post, including key studies on GPS data processing and atmospheric mass loading.

Kumar, U., Chao, B. F., & Chang, E. T.-Y. Y. (2020). What Causes the Common‐Mode Error in Array GPS Displacement Fields: Case Study for Taiwan in Relation to Atmospheric Mass Loading. Earth and Space Science, 0–2. https://doi.org/10.1029/2020ea001159
Utpal Kumar
Utpal Kumar

Geophysicist | Geodesist | Seismologist | Open-source Developer
I am a geophysicist with a background in computational geophysics, currently working as a postdoctoral researcher at UC Berkeley. My research focuses on seismic data analysis, structural health monitoring, and understanding deep Earth structures. I have had the opportunity to work on diverse projects, from investigating building characteristics using smartphone data to developing 3D models of the Earth's mantle beneath the Yellowstone hotspot.

In addition to my research, I have experience in cloud computing, high-performance computing, and single-board computers, which I have applied in various projects. This includes working with platforms like AWS, GCP, Linode, DigitalOcean, as well as supercomputing environments such as STAMPEDE2, ANVIL, Savio and PERLMUTTER (and CORI). My work involves developing innovative solutions for structural health monitoring and advancing real-time seismic response analysis. I am committed to applying these skills to further research in computational seismology and structural health monitoring.

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