Review of the manuscript “Cross-scale causal information flow from El Niño Southern Oscillation to precipitation in eastern China” by Yasir Latif , Kaiyu Fan, Geli Wang and Milan Paluš.

Authors present original research on the link between ENSO states and/or quasi-oscillatory (QO) ENSO components and QO Chinese-river-basins precipitation components obtained by a wavelet approach. Authors use an information-theoretic approach to establish causal links and optimal delays between ENSO and precipitation. They also estimate statistical significance causality thresholds using means over surrogates preserving the spectrum. The method and results are interesting and susceptible of development and generalization by using other possible atmospheric-oceanic indexes as drivers of precipitation. The material of the manuscript is acceptable for publication after the adjustment of several points that can improve much better the presented research.

Major points:

Fig. 2 A color bar for the orography height must be included. Add in the maps the location of local precipitation stations used in manuscript.

Fig. 4a. The ENSO time-series (or a proxy of that) is plotted (black curve) with indication of positive, negative, and neutral ENSO states. However, it is the ONI (lines 117-120) that is used to discriminate ENSO states. From the graph the cross of +0.5 and -0.5 to determine ENSO phases is not well suited. Change the graph accordingly with the chosen criterium of ENSO phases.

Line 171. The formula of the transfer-entropy (TE) (eq. 9) is proposed by Wibral et al. (2013) as a CMI in the case of SPO (Self Prediction Optimality) of Y states prior to the forecast delay tau. This is a very conservative estimate of TE since the SPO may be never reached with TE of eq.9 being underestimated. Authors shall comment on this.  

Line 188. The Z statistics use Id and Is. Id is the CMI value estimated from the studied data, Is is the mean for 100 realizations of the surrogate data. What formula is used for Id and Is? Are formulas 8 or 9 used? Give an example used in the manuscript.

Line 202-205. Conditional means of precipitation, given the phase of ENSO CCWT component (or the ENSO state) are computed on a grid basis. However on Figs. 8c,d and Fig 9c,d the values are overlapped over the grid cells. Figures must be redone precisely.

Line 220. What authors conclude from the histogram of Fig.5c?

Fig. 5 Authors compute: The conditional mutual information measuring the causal influence of ENSO states on

precipitation characterized by the EASMI-ZQY index (solid blue line) and causality in the opposite direction (dashed black line). What exact formulas authors use? (Eqs 8,9?). What are the embedding dimensions used? Be precise about X and Y in this case. By opposite direction, what authors mean? X, Y are swapped? Give a mathematical expression in the method section. Authors use certain precipitation stations. What was the criterium of choice? Explain. The values of significance values (red thresholds9 on panels a) and d) are not very well explained how they are computed. Explain it in detail in the method section.

Fig. 5 In this figure the authors choose a point in the North where the ENSO states does not discriminate significantly the precipitation (see crosses in Figs. 7b,d). However in the South region (Yangtze River basin) it is apparent the existence of locations where ENSO states have an important role on precipitation. Authors should add the equivalent of Figs. 5a,b,c for a particular significant location in the South.

Figure 6 presents the Z score of a certain CMI (eq. 7) between the instantaneous amplitudes of the CCWT of El-Niño and of the precipitation.  Which is the value of lag tau used? Clarify. Values presented in Fig. 6 depend on tau. Explain.

Fig. 6 uses values for 6 stations but the geographical coordinates are not given. Provide them in a Table in the data section and point them in the first maps.

Figure 7. Authors present the effects of two causal mechanisms. Concerning the effect of oscillatory components of ENSO, only results for the 6-year component are presented in a map. Since the QB component is also relevant in the annual cycle of precipitation, authors shall conceive a map (similar to Fig. 7a,c) giving the representativeness of such link.

Conclusion: Authors say: ‘physical mechanisms explaining the observed cross-scale information transfers are yet to be established, the uncovered causal relations’. Can authors elaborate a little bit more here,

Minor points:

Line 53. After the work of Jajcay et al. (2018), it is worth citing the work of Pires et al. (2021) which also studies the interactions between quasi-oscillatory ENSO components and the role of triadic resonances and synchronization in the explanation of super El-Niños.

Pires C.A. and Hannachi A. (2021) Bispectral analysis of nonlinear interaction, predictability and stochastic modelling with application to ENSO, Tellus A: Dynamic Meteorology and Oceanography, 73:1, 1-30, DOI: 10.1080/16000870.2020.1866393

Eq. (1) time t is missing in the complex exponential.

Line 127:  Delete ‘sigma t =’

The use of red color for the rivers is not ideal since the color bar includes red in several figures. Suggestion: use black.