A Novel Method for Analyzing the Spatiotemporal Characteristics of GNSS Time Series: A Case Study in Sichuan Province, China

Round 1

Reviewer 1 Report

The paper deals with the issue of crustal deformation monitoring from GNSS time-series in Sichuan Province. The paper is interesting and well written. I have the following questions.

1) The proposed functional models includes a constant, a linear trend, two main harmonics and possible discontinuities. However, given the complexity of the area, the observed GNSS time series can include a residual signal that should be modelled deterministically (e.g. by splines) or stocastically (e.g. by collocation). This is generally implemented in GNSS time-series analysis and it should be at least mentioned by citing some papers like:

Reguzzoni, M.; Rossi, L.; De Gaetani, C.I.; Caldera, S.; Barzaghi, R. GNSS-Based Dam Monitoring: The Application of a Statistical Approach for Time Series Analysis to a Case Study. Appl. Sci. 2022, 12, 9981. https://doi.org/10.3390/app12199981

2) You should mentioned that the asumption of homogeneous and isotropic random field is invoked when modelling variance/covariance functions in Section 2.4. Model (13) is commonly referred as an exponetial function and not a Gaussian-like function. Finally the positive definiteness of all these models should be verified by specifying the acceptable range of variation of the k parameters. This is mainly critical for model (14) that is not generally positive definite and therefore it is not a good option to model variance/covariance function.

3) When presenting the deformation spatial analysis (see Figure 7), it would be useful to show some interpolation of the deformations over the study area along the North, East and Up directions which might be computed for instance by a kriging approach.

Summarizing, I recommend publication of the manuscript after revision.

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Reviewer 2 Report

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