Dear Authors.
Thank-you for your revised manuscript. I still have trouble with some of your statements about (non) stationarity and especially nonlinearity as detailed in “Comments” below. Referee 1 (Huang) also commented on this and I think you have not yet addressed all his comments. He also asked for a comparison with the results of EMD-BPNN (his point 1) and demonstration that there is a mode mixing problem with EMD (his point 2); you respond to these points in your response but in the revised paper I do not see either of what is asked for. Also at the end of your response to referee 2 you say “We have stated some factors affecting the SST prediction in the revised manuscript” but I do not see any more about this in the revised manuscript. Hence I am still asking for “minor” revision and wish to see the manuscript again myself. Please also note that all comments will be available when any final version is published and readers will be able to see how you have addressed them.
Yours sincerely
John Huthnance

Comments
Line 9. Please delete “novel” (Referee 1)
Lines 48-49. “. . the nonlinear and non-stationary characteristics are obvious.” You have not yet defined “non-linear”! The definition is in lines 51-52: “the change of the output is not proportional to the change of the input”. To claim “nonlinear” you need evidence that the SST is not proportional to its “input” – what is the input? I agree the SST is “non-stationary” but not because of “high randomness” so not “due to” (line 47).
Line 56. “deterministic” here but “high randomness” in line 48. Which?
Line 56. “non-linear” needs evidence.
Line 56. “non-stationary” – I agree but you have not justified this.
Line 59. You imply that the trend is orthogonal; Referee 1 objected. Maybe “. . obtain several periodic signals orthogonal to each other and a trend.”
Line 59. Are the EMD IMFs in fact orthogonal? Lines 87-88 “decomposing it via EMD . . . In contrast to the EEMD method, the CEEMD also ensures that the IMF set is quasi-complete and orthogonal. . .” suggests EMD IMFs are not orthogonal.
Lines 59-60. You can delete “the method can decompose the stronger nonlinear and non-stationary signals”; it is repeated in line 62.
Line 67. What is “essential modal function”? Please define it. If you mean “IMF”, say “IMF”.
Lines 72-73. These need to make clear the difference between EEMD and CEEMD. What is the difference between the EEMD “white noise” and the CEEMD “set of noise signals”?
Lines 83-84. “can effectively reduce the non-stationarity of the time-series data”. Surely the non-stationarity has to remain somewhere in the IMFs and RES?
Lines 57-90 overall need to be properly organised as a logical sequence, EMD then EEMD then CEEMD, to avoid repetition (e.g. lines 72-73 and 74-76 describe the same thing, EEMD), clarify the differences and exactly what is orthogonal.
Lines 130-131. “. . then each IMFi is reconstructed to obtain the predicted value of SSTA.” I think you mean “. . then the IMFi are recombined to obtain the predicted value of SSTA.” You already have each IMFi (line 130) so each IMFi does not need to be “reconstructed”.
Line 141. “still exhibit strong nonlinearity and non-stationarity”. Some non-stationarity can be seen in figure 3, e.g. sub-periods with larger and longer-period variance, but it would help if you said what non-stationarity the reader is supposed to see. Figure 3 cannot show nonlinear dependence on the input since we do not know the input.
Line 142. “the non-stationary and nonlinear properties are less”. Again, how do we see non-stationary properties? The figure cannot show nonlinear properties since we do not know the input.
Line 144. “. . As the non-stationarity of each IMFi is gradually reduced, . .” I think you mean “. . As the non-stationarity of IMFi decreases with increasing i, . .”
Lines 156-157. “. . and the order of magnitude is 10^-3.” This can be deleted (unnecessary) and is not an accurate description of 0.0035°C.
Line 166. Delete “nonlinearities and” unless you can show non-linear dependence on an input.
Line 166. “eight” -> “seven”; the eighth series is RES which is definitely non-stationary!
Line 177. “. . and the order of magnitude is 10^-17.” This can be deleted (unnecessary) and is not an accurate description of 6.10×10^-17°C.
Lines 223, 225. Delete “nonlinearity” unless you can show non-linear dependence on an input.

Lines 225, 226. “since” (line 225) implies that these two lines are related. How?
Line 226. Do the “12 nodes” correspond to 12 months in the year?
Line 234. N = 12? Please be explicit.
Lines 240-241. To have “error (Max ERR) of the first decomposition component IMF1” you have to have “true” 2017 values for IMF1 as well as the predicted values. You need to say how you obtain the “true” values of IMF1. It seems to imply that you did the decomposition for 1982-2017 as well as for 1982-2016. Likewise for the other IMFi and RES. I guess the IMFs for these two decomposition periods differ in 1982-2016, although perhaps very little for IMF1 until the very end of 2016.

Tables 1 and 2. The format of the values in any row should be the same for max/min/mean ERR and for RMSE.
Table 1 row RES. RMSE has to be greater than mean ERR. Also Mean ERR is too small; (Min ERR x 11 + Max ERR) / 12 exceeds Mean ERR.
Line 248. Delete “nonlinearity and” unless you can show non-linear dependence on an input.
Lines 273, 274. Please state a criterion for “satisfactory” and do not change it for CCEMD. At present you imply 0.3°C for EEMD and 0.1°C for CCEMD. And include the “°C”.
Lines 281-283. Better “The correlation coefficient between the prediction values based on the CEEMD-BPNN model and observations is 0.97 indicating a significance level of 0.001. The result . . 2017 was predicted”
Lines 286-287. Better “. . Table 3 shows that prediction results of the hybrid CEEMD and BPNN model are much better than with the EEMD-BPNN . .”
Line 288. Delete “and nonlinear” unless you can show non-linear dependence on an input.
Line 303. You can omit “respectively” (unnecessary).
Line 307. “. . components (IMF1, . .”
Line 308. Justify or omit “strong nonlinearity and non-stationarity. As the nonlinearity gradually decreases”
Line 310. Better “. . preliminary, based . .”

Dear Authors
Thank-you for revisions. I am sorry that I still think there should be some improvements and I would like to see your manuscript once more.

Line 25. Better “. . data of the individual IMFs. A case study . .”
Line 38. Better “. . 2019b) and dynamic processes”
Line 40. I do not understand “reflects”. Maybe “e.g.” or “and”?
Line 47. “. . randomness and irregularity of the . .”
Line 47 “high randomness” and line 55 “deterministic” are contradictory. You have to delete one of these.
Line 74. “component” – do you mean “IMF”?
Lines 76-77. These are about EEMD. Merge them in at lines 69-70.
Lines 86-87. This sentence is about EEMD. Merge it in at lines 69-70.
Then lines 78-85 and 87-91 about CCEMD are brought together but you will need to remove duplication.
Line 85. Do you mean “. . can effectively confine the impact of the time-series non-stationarity to the trending component and ??, which helps . .”. If you can recombine the components to the original time series, then all the non-stationarity must remain in the components somewhere – where (replace the ?? above)?

Line 119. You need to define SSTA – i.e. anomaly relative to what?
Line 181. Better “reduced compared with that of the EEMD algorithm.”
Lines 221-222. “observation results of 12 months in 2017 are used to compare and analyze with the prediction results.” But you need to say how you go from the 2017 observations to the IMF1, IMF2, . . IMF7 for 2017 with which you compare the predicted IMF1, IMF2, . . IMF7.
Line 273. “. . less than 0.3°C). The . .” You must be consistent about what is “satisfactory”. If ERR > 0.1°C is not satisfactory for CEEMD, as you imply, then 0.1°C < ERR < 0.3°C is not satisfactory for EEMD. I suggest for line 274 “. . satisfactory; ERR exceeds 0.1 °C only in October, . .”

Dear Authors
Thank-you for your revisions. I am now asking for some “Technical corrections” after which your manuscript should go through the Copernicus/Ocean Science production system for publication. There is still one “serious” comment below !!(lines 222-223)!! about how you obtain “actual” IMFi for 2017. You need to explain this to satisfy the overall scientific principle that another scientist should be able to repeat what you have done. Readers will be able to see my comment and how you respond to it. Please also note that your final manuscript will be copy-edited and you should check that the copy-edited version keeps your intended meaning. Thank-you for publishing in Ocean Science.
Yours sincerely
John Huthnance

Technical corrections
Line 55. Better “. . system with non-stationary time series . .”
Lines 66-67. Better “. . modal functions (IMFs) to lose their physical meaning. The problem is manifested as either . .”
Line 76. Can omit “for EEMD”
Lines 81-82. This sentence duplicates lines 75-76; can be omitted.
Line 83. This sentence duplicates line 79; can be omitted.
Thus from line 80 to 84: “. . reconstruction of the input signal. In contrast to the EEMD method, the CEEMD also ensures that the IMF set is quasi-complete and orthogonal. The CEEMD is a computationally expensive algorithm . .”. I don’t think this loses any information.
Line 85. “had” -> “have”.

Line 102 (or 118). Definition of SSTA. You still need to say what “average” SSTA departs from. I guess from the small values that a January SSTA (for example) is obtained by subtracting the average of all Januarys, and likewise for other months. You need to state this clearly.
Line 119. Better omit “it can be found”
Figure 1 and line 122 (figure caption). At any place, there is only one value of SST for the 35 years. You can omit “annual”!
Line 176. “very” -> “much”.

!!Lines 222-223. In figure 8 and table 1 you compare the predicted IMFi with the “actual results of 12 months in 2017”. Of course there are actual SSTA in 2017, but how do you obtain “actual” IMFi for the comparison in figure 8? You must explain this. At present the reader has no information to try to repeat what you did.!!

Line 306. “. .and IMF3). SST prediction . .”
Lines 309-310. “. . In a follow-up . . is the focus.”