The manuscript has been significantly improved, but there are some points where it could still be improved for more clarity and readability. My comments are given below and some examples that the authors could consider to make the paper more understandable to readers.
COMMENT: In Introduction, the prediction of South Asian Monsoon using ENSO is problematic given their complex relationship in time domain and frequency domain. However, there have been new studies accounting for differences in spectral attributes which improve prediction performance using wavelet analysis. For example,
Jiang, Z., Sharma, A., & Johnson, F. (2020). Refining Predictor Spectral Representation Using Wavelet Theory for Improved Natural System Modeling. Water Resources Research, 56(3), e2019WR026962. doi:10.1029/2019wr026962
Authors may want to have a look and include some discussion in Introduction as a possible means of improving their assessment further through the latest refinements in wavelet methodology.
COMMENT1: The way to compute monthly anomaly = monthly – monthly climatology over a baseline period, so given different base period in most cases it won’t be uniformly up or down. Authors must have misunderstood something referring to Line 421-423:
“To remove the influence of the annual cycle, the time series was converted into anomaly time series by subtracting the 1871-2016 long-term mean for each month from the individual monthly values.”
COMMENT2: Authors focus on the skewness, but throughout there is not clear definition or quantification of skewness you used in this work. Only a paragraph discussion is given in the introduction (Line 370 to 382). I would suggest adding a description in the Method section.
COMMENT3: Section 4.2, you probably mess up with figure captions. Figure 4 shows the correlation while Figure 5 gives skewness. Same in Section 4.3. Also, I would suggest authors combine section 4.1 and 4.2 since they both discussed the relationship between the correlation and skewness.
COMMENT4: Section 4.3, I would suggest authors keep the x-axis labels of Figure 4 and 5 consistent with Figure 6 and 7. So readers can easily refer to each other. Also, the auto-bicoherence of Nino 3 and 3.4 are not shown in the main context or supporting information. However, one entire paragraph is discussed about this. I would suggest authors to add the results of Nino3 and 3.4 to both Figure 7 and 8.
COMMENT5: Section 4.4, the second paragraph is talking about Figure 8 not Figure 10 (There are many other places in the manuscript, e.g. Section 4.5). This might be due to the review process, but authors need to read through the paper and make sure the content and figure are associated with each other.
COMMENT6: Figure 12-15 now are not discussed in the revised manuscript, so it can be removed. Even though Table 1 is included in the end, it is not cited or discussed anywhere in the main context. A discussion should be added to clarify the difference among them.
1. Line 396: keep the numbering format consistent. 1) -> (1)
2. Where is abbreviation AIR in Data section?
3. Line 454: 3.1 Wavelet Analysis and hereafter
4. Line 464: Readers are referred to…
5. Line 588: Eq. (12)
6. Line 517: should be B_local(s1,s1) ?
7. Line 526: shoulde be phi_n(s1, s1) ?
8. Line 629: small capital w_F(t)
9. Figure 3: ylab: Nino 1+2
10. Line 688: it should be Nino 4 time series?
11. Line 713: should it be (Figure 4a and 4b)
12. Figure 10 and 11: The ylab is from 20N to 20S.
13. Line 1117: The R software link missing. These methods…