Empirical Orthogonal Function Analysis and Modeling of Global Tropospheric Delay Spherical Harmonic Coefficients
Abstract
:1. Introduction
2. Data
2.1. ERA-5 Data
2.2. Global Tropospheric Delay SH Coefficients Set
3. Construction of the EOF-Based Model
3.1. Empirical Orthogonal Function and Analysis
3.1.1. EOF Method
3.1.2. Timing Characteristics of Ai(h)
3.2. EGtrop Model Construction
4. Results
4.1. Global Tropospheric Delay SH Coefficients Set Validation
4.2. Verification of SH Coefficient for EGtrop Model
4.3. Verification of the Tropospheric Delay for EGtrop Model
5. Conclusions
- 1.
- This study adopts a spherical harmonic function to fit the tropospheric delay calculated with global ERA-5 meteorological data at each time, and an SH coefficients dataset is obtained in the calculation, which is convenient for EOF decomposition and formula fitting. It is verified that the SH_set yield a good accuracy (ERA-5 ZTD, Bias: −1.0 × 10−4 cm; RMSE: 1.97 cm; IGS ZTD, Bias: 0.08 cm; RMSE: 2.6 cm), indicating the feasibility and reliability of this strategy, which provides a reference for near-real-time model products.
- 2.
- Based on the analysis of the SH_set data from 2015 to 2019, it is found that the spherical harmonic coefficients exhibit a certain periodic variation. Based on this phenomenon, this study implements the EOF method and trigonometric functions to establish an SH coefficients model for the SH_set data called EGtrop and combines it with the spherical harmonic function to complete the establishment of the global tropospheric delay model. The results indicate that the accuracy of the new model is higher than that of GPT2w and UNB3m on the different reference data. In addition, through verification of the model accuracy, it is found that the EGtrop model is applicable not only at the global scale but also at the regional scale, and this model yields the advantage of local enhancement.
- 3.
- Compared to GGOS tropospheric delay grid data, the SH_set proposed in this study experiences a slight loss of accuracy, but it greatly reduces the number of parameters and is more convenient for users.
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
Appendix A
References
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EOF Mode | 1 | 2 | 3 | 4 | 5 | 6 |
---|---|---|---|---|---|---|
Variances (%) | 99.9503 | 0.0184 | 0.0040 | 0.0031 | 0.0029 | 0.0014 |
Cumulative var. (%) | 99.9503 | 99.9687 | 99.9727 | 99.9758 | 99.9787 | 99.9801 |
Year | Bias [cm] | RMSE [cm] | ||||
---|---|---|---|---|---|---|
Min | Max | Mean | Min | Max | Mean | |
2015 | −5.78 | 4.03 | −1.1 × 10−4 | 0.38 | 6.64 | 1.98 |
2016 | −5.97 | 3.78 | −1.0 × 10−4 | 0.40 | 6.91 | 2.01 |
2017 | −5.99 | 3.79 | −1.1 × 10−4 | 0.39 | 6.79 | 1.93 |
2018 | −6.28 | 3.72 | −1.1 × 10−4 | 0.41 | 7.01 | 1.97 |
2019 | −6.00 | 3.73 | −1.1 × 10−4 | 0.42 | 6.74 | 1.96 |
Mean | −1.0 × 10−4 | 1.97 |
Bias [cm] | RMSE [cm] | |||||
---|---|---|---|---|---|---|
Min | Max | Mean | Min | Max | Mean | |
EGtrop | −10.84 | 6.04 | −0.25 | 1.06 | 11.69 | 3.79 |
GPT2w | −9.20 | 16.11 | −1.02 | 1.19 | 15.79 | 4.32 |
UNB3m | −13.28 | 17.32 | 3.11 | 1.06 | 17.72 | 6.60 |
Data | Area | Error [cm] | Asia | Europe | Oceania | Africa | North America | South America | Antarctica | |
---|---|---|---|---|---|---|---|---|---|---|
Model | ||||||||||
IGS ZTD | EGtrop | Bias | 1.73 | −0.27 | 2.93 | 0.36 | 1.33 | 0.90 | 1.05 | |
RMSE | 4.97 | 3.14 | 3.66 | 3.09 | 3.98 | 4.09 | 3.36 | |||
GPT2w | Bias | −0.11 | −0.33 | 0.17 | 0.41 | −0.30 | 1.01 | 0.02 | ||
RMSE | 4.55 | 3.37 | 3.53 | 3.05 | 4.04 | 4.19 | 2.45 | |||
UNB3m | Bias | −1.11 | −2.44 | 4.44 | 2.30 | 2.19 | 0.51 | 8.70 | ||
RMSE | 6.29 | 4.32 | 6.27 | 4.82 | 5.28 | 5.44 | 9.48 | |||
Radiosonde ZTD | EEtrop | Bias | 0.89 | 0.06 | 3.24 | −0.27 | 1.33 | −0.52 | 0.96 | |
RMSE | 3.69 | 3.54 | 3.89 | 3.74 | 4.02 | 4.36 | 2.66 | |||
GPT2w | Bias | −0.95 | 0.72 | 2.38 | −0.23 | −0.41 | −0.32 | −0.13 | ||
RMSE | 3.49 | 3.52 | 3.20 | 3.59 | 3.88 | 4.43 | 2.64 | |||
UNB3m | Bias | −0.10 | −0.42 | 8.70 | 5.22 | 0.63 | −0.60 | 9.00 | ||
RMSE | 3.65 | 4.03 | 9.21 | 7.44 | 4.22 | 6.35 | 9.57 |
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Ma, Y.; Liu, H.; Xu, G.; Lu, Z. Empirical Orthogonal Function Analysis and Modeling of Global Tropospheric Delay Spherical Harmonic Coefficients. Remote Sens. 2021, 13, 4385. https://doi.org/10.3390/rs13214385
Ma Y, Liu H, Xu G, Lu Z. Empirical Orthogonal Function Analysis and Modeling of Global Tropospheric Delay Spherical Harmonic Coefficients. Remote Sensing. 2021; 13(21):4385. https://doi.org/10.3390/rs13214385
Chicago/Turabian StyleMa, Yongchao, Hang Liu, Guochang Xu, and Zhiping Lu. 2021. "Empirical Orthogonal Function Analysis and Modeling of Global Tropospheric Delay Spherical Harmonic Coefficients" Remote Sensing 13, no. 21: 4385. https://doi.org/10.3390/rs13214385