Weakening the Flicker Noise in GPS Vertical Coordinate Time Series Using Hybrid Approaches

Round 1

Reviewer 1 Report

Dear Authors

Your manuscript is quite interesting and touches a reasonable problem of GPS-based coordinate time series. However I have identified a small number of technical issues and a larger number of grammar/style problems which should be adressed in an updated version. I will start with the technical comments and proceed further with grammar issues/hints. Please note that my grammar hints are by no means exhaustive and a nother round of proof reading is recommended

A) Technical issues

1) At several occassions in the manuscript you use the term 'GPS series' or GPS time series. I recommend to state clerly in the begin if the coordinate series are just derived from GPS observations or they base on all GNSS systems observations (depending on capability of the receivers installed at your investigated 226 sites). Also clarify very early if you assess just 'Height component coordinates series' as I assume, or if your input time series comprise also the plane coordinate components. When studying your manuscript I assume you just refer to the vertical component ?

2) at least one graphic is missing showing initial raw time series and input time series to your investigations (corrected for jumps) for a few (2-3) typical sites

3) Add at the begin of chapter 2 one paragraph with introducing the term pink noise (or flicker noise) with some basic characteristics of flicker noise and its relation to frequency. This would be extremely helpful for readers not so involved in time series analysis. In this respect you should also explain in this paragraph why you provide the noise amplitudes in your paper in units

amplitude/f (power sqrt(4) = a/f(power 0.25) and not as usual in 1/f or for amplitudes in 1/sqrt(f) ?

4) You have shown impressing reduction rates (correction rates) of flicker noise. Besides a lot of percentage numbers it would be more interesting if you are able to extract from the denoised time series clear signals like annual or semiannual variations caused by e.g hydrology or glacial cycles. Show that (according to equation (1) this estimation of these signals is clearly improved after denoising of the time series

5) In chapter 4.3 I do not understand why you note that the largest differences in CR range between 14% and 28%, but the maximum is just 26.58%. How can the range go up to 28% when the max ist 26..?

B) Grammar

1) Abstract l12

here you note twice : 'year0.25'? do you mean power of 0.25 ?

2) same line; start a new sentence: 'This relates to a reduction of 86% after applying...'

3) 5 lines later

'.. and VMD&WD we can identify...'

4) Introduction, line 1

 '.. two decades, the Global...'

5) 4 lines later

'.. and a better understanding of surface...'

6) page 2, last sentence

do you mean ? 'Finally, the two hybrid approaches to reduce flicker noise were further assessed by means of analysing coordinate time series of 226 GPS stations from the...'

7) page 3, paragraph 2.1.1, line 2

'.. and removes the residual white noise...'

8) next line

'.. are the following [21]:'

9) chapter 2.1.3, lines 2,3

  do you mean? '.. IMFs, which are limited to a band in the ...'

10) page 3, chapter 2.2, line

again the question: are your investiagtions focusing just on height series of coordinate series at all ?

11) line 3

just delete the sentence 'We also discussed...'

12) 2 lines later

'We also introduce the Hausdorff...'

13) next paragarph

'.. we thus varied beta from...'

14) remove last sentence on page 3 'For the intensities...'

15) next sentence:

  'The amplitude of flicker noise of the denoised coordinate time series of the BJSH station achieves a minimum of 1.85mm/year (0.25) with beta is equal to 4. Therefore...'

16) next paragraph

'We conducted a test varying K from 3 to 11 following...'

17) next sentence

'.. of flicker noise of the denoised coordinate...'

18) next line

'.. different K are shown in Figure 1b.'

19) next line

'.. 6.14 mm /year (0,25). Therefore 4 was employed as an..'

20) next paragraph line 7

'.. time series ranges from 1.30mm ... but drops sharply to a ...'

21) 3 lines lates

sentence 'when the thresholding selection..' not understandable

-> re-phrase

22) 2 lines later

'.. is set to 6.'

23) 3 lines above Figure 1

'.. yields a smaller noise amplitude..'

24) next sentence

'Hence, we adopted ...

25) Graphs in Figure 1 are small and hard to view. Try to increase Figures

26) chapter 2.3, line 1

  'The two combined methods proposed...'

27) next line

'.. are performed in two steps..'

28) next line

'.. with the help of the Hausdorff...'

29) list item ii

'.. of the Hausdorff distance..'

30) list item iv

'.. is performed to..'

31) item vi

'.. The thresholded high-frequency...'

same problem in the last box of Figure 2

32) page 6, just after equation (1)

'.. the position at time t...'

33) 3 lines later

  '.. (k=2) variations are considered in this study, eps(t) is...'

34) chapter 3.1, line 3

explain what you mean with 'the termination dates of 19 and 200 stations'?

do you mean '19 of these 200' or anything else

35) next line

'.. The observation spans of the remaining 7 stations range from...'

36) 3 lines below figure 3

',, the 226 GPS time series a pre-processing...'

37) Chapter 4 , title

 typo -> 'Flicker'

38) line 1

'.. geographical distribution and..'

39) last lines of this paragraph

'... whereas 75 staions experience an amplitude of 20-25mm/yr. '

Just divide the sentence here,;

the term '19 and 8 stations were found for the amplitudes..' is not understandable-> re-phrase

do you mean that for 19 stations the amplitudes range between 10-15mm ??

40) next paragraph , line 11

'... for about 72.12% of the stations.'

41) end of this paragraph

'In detail, 138 stations show a flicker noise between 3-4mm/yr after denoising with CEEMD&WD, while 144 stations show a noise in this range after denoising with VMD&WD.'

42) last sentence page 8

'.. and 81.49% for WD, respectively. In order to compare...'

43) the next sentence is too long and hard to understand; Divide in at least 2 short sentences

44) last sentence this paragraph

'10-15mm/yr (0.25) comprises 19 stations, .. '

and so on-replace the word 'with' by 'comprises'

45) in the next paragraph you discuss the CRs, as well

'.. and are accompanied by more than 6% for standard deviation.'

What's the meaning . do you refer her to the standard variation of the CR?

46) Think about adding a table to support Figure 5 or to replace Figure 5 by a table; would be more clear

47) legend of Figure 5

'Flicker..'

48) chapter 4.3 / see also technical 5

line 8

'.. largest differences in CR for eight stations '

49) next line

'.. which includes a '

50) 3 lines later

'.. which are located in Sichuan...'

51) 4 lines later

re-phrase 'of 153 arising froma difference of 14-20%'

not clear

52) legend of left Figure 6

'Single method';

also vertical axis: 'gemethod' ???

53) chapter 5.1 , first paragraph

'As stated previously, the hybrid approaches were more efficient in removing flicker noise.'

54) next sentence

'.. of hybrid algorithms in the frequency domain.' 

Just one time 'Figure 7'

55) next paragraph, line 2

'.the power compared to CEEMD...'

56) 2 lines later

'.. flicker noise of about 1mm...'

57) at the end of this paragraph the meaning of 'and WD have distinct frequencies' is just unclear -> re-phrase

58) last pragraph , line 2

  '.. frequency signals of 3-7 cpy..      signals larger than 36cpy.'

59) chapter 5.2, line 1

IF you just analyze height time series than replace here

'Positioning time series' by 'height time series'

60) end of first paragraph

'.. adaptibility of the applied method in this section.'

61) 4 lines later

'.. all stations with CRs higher than..'

62) 8 lines later

'.. groups are higher, while...'

63) chapter 5.3 , last paragraph, line 4

'.. determined by the Hausdorff..'

same 4 lines later

64) chapter 6, line 4

'.. based on time series of 226 sites...'

65) next line

'The new methods CEEMD&WD..'
66) 4 lines later

'.. single method, the two hybrid algorithms reveal improvements...'

67) 2 lines later

'.. than 3 cpy in more comprehensive...'

68) last paragraph, 3 lines from bottom

whats the meaning of 'for replying to the complexity'?

just re-phrase

 

best regards

Author Response

Please see the attachment.

Author Response File: Author Response.docx

Reviewer 2 Report

It is of great importance to accurately remove noises in GPS height time series to improve SNR of weak signals for the study of vertical motion. In this study, authors propose a strategy of combining CEEMD or VMD and WD to reduce noises in GPS height time series, and verify the denoising effects of the proposed strategy. However, in my opinion, there are a couple of issues needed to be clarified and I suggest a minor revision before the manuscript can be accepted.

 

The major comments:

1) The determination of β and K plays an important role in the denoising process, and the appropriate values are beneficial to good denoising results. However, authors determine them only based on one single station, and the results are a little doubtful since this single station is not representative for the other stations because of different settings, such as monument types, observation environment, climate conditions, etc. I suggest authors carry out the similar experiments at more representative stations with different geographic locations to solve for more robust values of β, K and types of wavelet functions.

 

2) It’s very important to discriminate noises from signals according to characteristics of noises. In this manuscript, what’s the criterion of Hausdorff distance to separate pure noise modes and signal modes? Please detail more about this.

 

3) Authors compare the denoising effects of CEEMD&WD and VMD&WD with that of CEEMD and VMD, respectively (Figures 6 and 7). It’s also necessary to compare the denoising effects between CEEMD&WD and VMD&WD for better demonstration. I suggest authors revise the relevant plots and texts.

 

4) A careful proofreading is very necessary to correct some typos in the manuscript. For example,

a. Page 1, Line 12: “mm/year^0.25”?

b. Page 4, Line 17: “increases from 1.30 mm to 1.60 mm”?

c. Page 11, Line 7, “Figure 7”?

 

Author Response

Please see the attachment.

Author Response File: Author Response.docx

Round 2

Reviewer 1 Report

Dear Authors you have respected most of my comments in the revised version; from my point of view the manuscript fine now; Below is just a minor list of remaining grammar/style hints   1) Chapter 2.1.1 , line 2   '.. and to remove the residual...'   2) chapter 2.1.3 '.. limited to a band ...' 3) page 4, last paragraph before Figures 1, l11  '... noise decreases as the number of decomposition layers grows.' 4) Figure 1 legend 'The variation...' 5) Figure 2 legend   '.. methods for denoisinf GPS...' 6) page 7, chapter 3.1 , second sentence   'Among these, tracking data of 19 stations is available until September 2019, while for 200 more stations observations could be retrieved until December 2020,   corresponding to...' 7) chapter 4.1  In the First sentence the Figure number is missing 8) the same problem shows up in the first sentence of the second paragraph (page 9) Page 12 , first line   'As seen in and Table1' ??? 10) chapter 6 conclusions , 2 lines from bottom  '... In addition, to mitigate the complex...'   best regards

Author Response

Please see the attachment.

Author Response File: Author Response.pdf