Please take account of the following comments in revising your manuscript which I will then look through again. [These are the same as the "referee" comments that you may see.]
Yours sincerely
John Huthnance

(Abstract)
Line 14. “rates” -> “values”?
Line 15. “temporarily” (spelling).
Lines 19-20. “. . the number N of look-ahead time steps, and . .”
Line 20. I Googled “computational complexity”. I think the number of operations (which is what you count) is one aspect of computational complexity but might be better described as number of operations.

(1 Introduction)
Lines 55, 426, 430 (and maybe other places) “noise” not “noises”.
Line 60. Something missing at “. . is [Chelton . .”
Line 63. Omit “following”

(2.1 Input data)
Line 118. “detection, . .”
Line 120. Omit “to”
Line 127. “territories” -> “areas”. [You said you would use “areas”. “territory” suggests land, not sea. Especially, if “. . and boundaries” then “areas” is the word. “areas and boundaries” might be “territories” on land; “domains” is the mathematical word.

(3.1 Overview of GEM)
Line 205. “. . In addition to eddy area and boundary, . . input, the critical values of area ratio rc and N. See section 5.2 . . .” (duplication of “input”).

(3.2 Map link)
Line 210. Maybe “territory” -> “domain”
Lines 217, 218, 219, 226. Maybe likewise “territories” -> “domains”. For all these “area” is also possible but less precise.
Line 221. “B2 only had partial similarity”. B1 is discussed but not B2. Also not obvious in figure.
Lines 237-238. I think you need to say here, how the values of r1 and r2 decide whether it is T1 or T2. See lines 262-263 for how r2 determines T1; this should be at line 238.
Line 274. “(section 3.4)”
Line 275. “. . similar, and 2) the earliest day. Rule 1 . .” (i.e. omit “first” twice, it is confusing).
Lines 276, 282. “E1” -> “Ed1”.
Line 283. “. . as the following Ed2, Ed3 respectively.” ?

(3.3 Track tree)
Lines 304, 305. Again you should say how the values of r1 and r2 decide whether it is “first type” or “second type”.

(4.1 Eddy tracks)
Lines 356-357. “Eddy C1 . . trajectory is the longest”. This is a good reason for choosing it as the only example; it has the best chance of showing any problem! You should say this and also that you did actually look at many others.
Line 371. “it” – not clear what this refers to.

(5.2 Impact of variations of parameters)
Lines 447-448. Maybe better “To discuss the impact of the GEM critical value rc and look-ahead time N, we carry out . . 2012. The number of eddies”
Line 474. “O-W” needs defining here (bring definition from lines 498-9).
Line 474 “sensitive”. What is sensitive to what? I think you perhaps mean that “suitable rc depends on whether it is O-W or SLA identification”.
Line 481. “to though”. This does not make sense and I cannot say what you do mean!
Lines 496-497. Better “comparison of eddies identified by different methods, since the eddy detection algorithms differ a lot from each other.” ?

Figure 4. This is OK on my screen but had dark infill when I printed it; please check.
Figure 6. There is no illustration of T1.
Line 692. “. . (b) There are four similarity types . .”

Dear Authors
Thank-you for your amendments. I have looked again carefully (in the absence of other referee comments) and here follow some more recommended changes for you to include. Line numbers are as in your latest “clean” version “4”. Please check carefully that my suggested changes keep to your intended meaning. Also there will be copy editing which will make changes to detailed use of English; again you should please check carefully that the copy-editing changes keep to your intended meaning.
Yours sincerely
John Huthnance

(Abstract)
Line 11. “The Genealogical . . (GEM) presented here is an efficient . .”
Lines 16-17. “. . Second, for tracking when an eddy splits, GEM uses both “parent” (the original eddy) and “child” (eddy split from parent) and the dynamic processes . .”
Line 18. “Additionally, a new look-ahead approach . .”
Line 21. I do not like “time complexity” either! I think you just mean “number of computing operations” which can be more simply stated as “computer time” or “runtime” as on line 103 [the unit of time would be the time for one computer operation]. See also lines 68, 96(twice), 103, 273, 320, 322, 324, 325, 327, 329, 549 (and perhaps other places).

(Introduction)
Line 70. “. . motion of an eddy. . .”
Line 82. “. . risk of missing an eddy . .”
Line 84. “. . may arise from two or more eddies (at time step k-1)”
Line 97. “. . where L denotes the number of pixels . .”
Line 103. “runtime. Results . .”

(2.2 Eddy identification)
Line 123. “. . identified as multinuclear . .”
Line 150. I think cyclonic eddies have lowered sea-surface, i.e. SLA < 0, etc. So “. . SLA < -3 cm for cyclonic eddies and SLA > 3 cm for anticyclonic . .”
Line 153. Omit “those”

(2.3 Eddy segmentation . .)
Line 156. “. . eddies. Different”

(3.2.1 Eddy similarity)
Lines 233-234. “. . When we apply GEM . . Pacific Ocean (section 4.1), we choose . .”
Lines 235-242. In figure 6(a) the subscripts (1,2,3,4) in E1, . . E4 are very small. I suggest you use E1, E2, E3, E4 (no subscripts) in the figure and in the text here.
Lines 245-249 and Figure 6a. The description seems to correspond to rc about 0.4 or less. E.g. S12/S1 < ½ and with rc = 2/3 this would be case T2 not T3. Also S13 ~ ½ and with rc = 2/3 this would be case T0 not T2. You might find it easier to say rc = 0.3 than to re-draw the figure but re-drawing for rc = 2/3 would be less confusing for the reader.
Lines 246-247. “. . different relationship (“splitting”, marked as T2 in Fig. 6b). . .”

(3.2.2 Eddy Look-ahead)
Lines 259-260. “. . procedure. Examples for a given eddy . .”
Line 263. “. . In the middle row, eddy Ec1 has two”
Line 265. “In the lower row, eddy Ec1 has T2 . .and T3 . . (respectively Ec2, Ec3)”. [E1 -> Ec1] But in the figure Ec2 and Ec3 are the other way round! Better to change the figure so Ec2 <-> T2 and Ec3 <-> T3.

(3.3.1 Eddy branch)
Lines 299-300. “. . high for the record of eddy C to be appended to either parent. There might be . .”

(3.4 Runtime (?!))
Line 329. “. . much less than . .”

(4.1 Eddy tracks)
Line 362. “trajectory from . .”
Line 371. “. . application of our similarity vector . .”
Line 373. “. . application of the similarity vector . .”
Line 374. “. . as a scalar . .”

(4.2 Eddy merging and splitting)
Line 386. “. . (Fig. 5) . .”
Line 387. “. . location south of B1 and B2 . .”
Lines 388-389. “. . After that, eddy B2 merged into eddy B3 . . eddies B1 and B3 eventually merged . .”
Line 395. Omit “which is”. [A general point; “which” must follow immediately after the item it refers to. So here the meaning is clearer without “which”.]
Line 397. “. . eddies (A1, A2; B1, B2, B3) are anticyclonic, they have clockwise rotation and orbits, like point vortices”

(4.3 Census)
Line 403. “. . Figure 12 and are similar . .”
Lines 417-418. I do not see “high frequency of merging and splitting” in the “eddy desert” in Figure 12. It might just be “high frequency” relative to the number of eddies but that is not enough to explain the lack of eddies.
Lines 419-420. “. . may be due to eddies being too small to be detected or to eddy lifetimes being too short . .” [You cannot have a “fact” about eddies that you do not know about.]
Lines 423-425. “. . regardless of eddy polarizations . . splitting events increase approximately linearly with eddy lifetime. However, merging and splitting events are more frequent for anticyclonic eddies than for cyclonic eddies.” Please note that there is duplication with the figure caption lines 744-745. I think this is better here because it is interpretation not explanation of the figure.

(5.1 Data noise)
Line 435. “As a sensitivity test . .”
Line 441. “. . even when it is small. It might . .”

(5.2 Impact of variations . .)
Lines 456-457. These numbers of splitting and merging events do not agree with figure 15b. Perhaps 121220 and 120612 respectively?
Lines 465-466. “. . reasonable. On the one hand, . . .we know there is error (~10%) in calculating eddy area since . .consideration. . .”
Lines 469-470. “. . N=1 and N=2 have respectively 95.5% and 98% . .for N=4. To reduce . .”
Line 473. Omit “of”
Line 474. “. . independent of MEI . .”
Line 475. “. . in eddy identification. . .”
Lines 475-476. “. . is more sensitive . . than is SLA-based GEM, since . .”
Line 477. “. . independent of N, . .”
Line 478. “. . too large, eddies may move too far so that eddy”
Line 479. “constraint”

(5.3 Impact of eddy boundary)
Lines 488-491. “Different identification methods may give different eddy boundaries, although the eddy centre is relatively robust. Eddy area S is sensitive to eddy boundary but it is difficult to compare directly the influence of eddy boundary differences that result from identification method choice. However, the area ratio . .” [I have rearranged these lines. I have also omitted the sentence about “indirect way”; it does not seem to help.]
Line 497. “However, such a sensitivity test . . values used in the same”
Line 505. “. . eddy boundary differences resulting from using . .”

(5.4 Future research)
Line 513. “Eddies identified by using algorithms without watershed segmentation can also be tracked ..”
Lines 516-517. “. . because most merging/splitting occurred between eddies more than a certain distance apart. This weak interaction . .” [I am not sure about “more” but assume this from “weak” interaction. If the eddies need to be close for merging/splitting then “less” not “more”].
Line 524. “. . physical quantities (. .”
Line 527. “. . other than simple estimation from identification.”
Line 539. Omit “on those problems”
Lines 551-552. “. . and in “eddy deserts”. . .” This was not obvious to me (seem comment on lines 417-418).

(Figures and captions)
Line 664. July 26 to August 3.
Figure 4. In figure, “territory” -> “domain”
Figure 5b. Add “B2” eddy label.
Figure 6a. See comment on lines 235-242. The subscripts (1,2,3,4) in E1, . . E4 are very small. I suggest you use E1, E2, E3, E4 (no subscripts) in the figure here and in the text.
Lines 744-745. See comment on lines 423-425. Repetition! I think these two sentences are interpretation, should be in the text and are not needed here.