the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 17 Oct 2023
Extraction of periodic signals in GNSS vertical coordinate time series using adaptive Ensemble Empirical Modal Decomposition method
Weiwei Li
Jing Guo
Abstract. Ensemble Empirical Mode Decomposition (EEMD) has been widely used in the data analysis. Adaptive EEMD further improves computational efficiency through the adaptability in the white noise amplitude and set average number. However, its effectiveness of the periodic signal extraction in Global Navigation Satellite System (GNSS) coordinate time series regarding on the inevitable missing data and offsets issues have not been comprehensively validated. It is verified with 5- year time series through 300 simulations for each case. The results show that high accuracy could reach for the overall random missing rate below 15 % and avoiding consecutive missing epochs exceeding 30. Meanwhile, offsets should be corrected in advance regardless of their magnitudes. The analysis of vertical component of 13 stations within the Australian Global Sea Level Observing System (GLOSS) monitoring network, demonstrates the advantage in revealing the time-varying characteristics of periodic signals. From the perspectives of correlation coefficients, power spectral density (PSD) indices and signal noise ratio (SNR), the means for adaptive EEMD are 0.36, -0.18 and 0.48, respectively, while for least squares (LS), they are 0.27, -0.50 and 0.23. Meanwhile, significance test of the residuals further substantiate the effectiveness in periodic signal extraction, which shows there is no annual signal remained. Also, the longer the series, the higher accuracy of extracted periodic signal is reasonable concluded via the significance test. Furthermore, the time-varying periodic characteristics is more conducive to analyze the driving factors. Overall, the application of adaptive EEMD could achieve high accuracy in analyzing GNSS time series, but it should be based on the proper dealing with missing data and offsets.
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Weiwei Li and Jing Guo
Status: open (until 19 Dec 2023)
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RC1: 'Comment on npg-2023-23', Anonymous Referee #1, 19 Nov 2023
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Dear Editor and authors,
"Extraction of periodic signals in GNSS vertical coordinate time series using adaptive Ensemble Empirical Modal Decomposition method" is an interesting investigation about the reliability of GNSS measurement in case of sparse and continuous missing data and anomalies due to gaps (antropic dispacements, antenna failures) and other spurius contributions to the time series. Authors apply the empirical modal decomposition technique to fit data and compare their results with others methods such as least square fit. They conclude that EMD has higher ability to model GNSS time series.
I agree with authors about the potentiality of EMD and I think that the manuscript may deserve publication in Nonlinear Processes in Geophysics after revision needed to improve the main text, especially abstract and introduction; add some tests to strengthen their conclusions and to amend some minor mistakes.
I kindly ask authors to solve the following issues:
1. The abstract and introduction are not clear enough: too limited introduction to the concept of EMD, GNSS data etc. Moreover, some sentences are obscure and in few cases there are grammar mistakes. Can the authors add background for the reader, be more inclusive in the references they include and amend errors? Follow my point-by-point notes in the attached pdf file.
2. Some transient trends in GNSS time series are not connected with seasonal trends, but they also may include other contributions such as
- tectonic effects such as afterslip. I know authors investigate signals of GNSS stations in Australia and surrounding regions, but I think that at least a short discussion about this topic should be added; moreover, I suggest to check whether some remote signal can be identified or not. In Australia large earthquakes do not occur, but along the surrounding subduction zones even M9+ earthquakes take place, producing long-term rearrangement of stress at even large distances (I know this because of my direct expertise).
Check, for instance, Blewitt, G., Kreemer, C., Hammond, W. C., Plag, H.-P., Stein, S., & Okal, E. (2006). Rapid determination of earthquake magnitude using GPS for tsunami warning systems Geophysical Research Letters, 33, L11309. https://doi.org/10.1029/2006GL026145
- both solid and ocean tides can impact on GNSS time series, check, for instance, Zaccagnino, D., Vespe, F., & Doglioni, C. (2020). Tidal modulation of plate motions. Earth-science reviews, 205, 103179. and Ide, S., & Tanaka, Y. (2014). Controls on plate motion by oscillating tidal stress: Evidence from deep tremors in western Japan. Geophysical Research Letters, 41(11), 3842-3850.
Can the author add a short discussion about these topics?
3. Subfigures should be highlighted using letters (such as A, B; C)
4. To prove that EMD works better than other techniques, a test should be done in addition to the already performed one. For instance, at least RMSE or Chi Squared of fits in Figure 8.
I also attach the revised pdf version of authors' manuscript with listed minor suggestions, requests and corrections.
Thanks for your work!
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RC2: 'Comment on npg-2023-23', Anonymous Referee #2, 27 Nov 2023
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This paper examines applications of Empirical Modal Decomposition (EMD) to extract periodic components and level offsets in daily vertical GPS time series. The EMD method is initially focused on the analysis of signals that are either a mixture of harmonic oscillations with different periods, such as the length of day (LOD) series, or non-stationary signals with smoothly varying amplitudes and frequencies, such as the probing signal of a bat. The main disadvantage of EMD is that it requires the construction of the upper and lower envelopes based on the position points of local extrema, through which approximating curves are drawn using 3rd order splines. Therefore, the method begins to work unstably if local extrema are poorly defined, for example, when the signal contains relatively long plateaus of constant values or inclusions of short-lived waves of small amplitude and short period (intermittency). To overcome these difficulties, the author of the method (Huang) proposed an approach of averaging multiple EMD decompositions, each of which adds independent white noise of small amplitude.
Adding noise creates auxiliary local extrema, which regularizes the determination of the Intrinsic Mode Functions sequence, and their subsequent averaging sharply reduces the influence of white noise due to their independence. This approach was called Ensemble Empirical Mode Decomposition (EEMD) and is what is applied to the data analysis in the paper. The authors used the further modification of the method, which was developed to fill missing values in series - Iterative EEMD.
In general, the work represents a qualified application of a set of EMD methods that have been developed to date in the direction of time series analysis. Examples of application to real GPS data at 13 stations in Australia are given.
As minor comments, we would like the authors to present their thoughts regarding the processing of not only vertical GPS data, but also horizontal components. As is known, horizontal components almost always contain strong trends reflecting slow movements of tectonic plates. It would be interesting to read about how the authors would highlight harmonic components against the background of strong trends. With the exception of simple preliminary elimination of the general trend with subsequent analysis of the remainder.
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Citation: https://doi.org/10.5194/npg-2023-23-RC2
Weiwei Li and Jing Guo
Weiwei Li and Jing Guo
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