Detailed comments could be found in the supplement.

Based on the China daily-scale meteorological drought index, this manuscript revealed a double-logarithmic relationship between drought duration and occurrence frequency, and proposed that a single parameter can characterize this nonlinear feature. The findings provide quantitative evidence for water resource management, agricultural planning, and drought disaster prevention and mitigation. The following issues need to be corrected.

General comments

1. Page3: The manuscript mentions “Qinghai-Tibet Plateau (gray area in Fig. 1) region isnot included in our study due to sparse station data”, and “the selected stations distribute in most regions of China except Hainan and Taiwan”. However, the impact of such exclusion on the representativeness of conclusions at the national scale was not discussed.
2. Page4: Formula (2) uses log2 instead of natural logarithm or common logarithm. There is no justification for selecting base 2. It is recommended to briefly explain the rationale for this choice in the text or to uniformly use natural logarithm.
3. Page12: The article states that parameter k/bcan independently characterize the relationship between drought duration and occurrence frequency (page 8), but Figure 5a shows a highly linear correlation between k and b (R²=0.95). This does not imply that k itself contains all information, but rather indicates a strong linear relationship between the two. It is recommended to phrase more cautiously as “in practical applications, k can be used alone for regional comparisons.”
4. Page12: In practical drought management, mild and frequent short-duration droughts have significantly different socioeconomic impacts compared to rare long-duration droughts. It is recommended to supplement the conclusions or discussion with the implications of these findings in this regard.

Text and Formatting Issues

1. Page 2, line 35: “Generally, drought events occur on various time scales, including inter-decadal(Xu et al., 2017), inter-annua(e. g. Wang et al, 2018; Zhang et al, 2020)”  
2. → “inter-annua”should be “inter-annual”.
3. Page 2, line 45: “As it can be seen, droughts occurring on different time scales...”  
4. → is recommended changeto be “Thus, droughts occurring on different time scales...”.
5. Page 9, Figure 7: The title is written as “Distribution of parameter k (a) and the relationship... (a)”   → The second "(a)" should be corrected to "(b)", and Figure 7b is described as Figure 7b in the main text but lacks a title. It is recommended to maintain consistency.
6. Page13-14: Some references include DOI, while others do not. It is recommended to standardize the format or complete the DOI information for all references.

The manuscript targets to find the observed relationship between the duration and occurrence frequency of droughts in China. Generally, the study is very focused on that region, it would be very helpful to put this in context with droughts in other regions of the world. As it is not a new finding that longer droughts occur more frequent and that it has regional differences depending on the climate of the region. These results are not new and I struggle a bit with finding what is new as it does not reveal any new features and is unclear how it can be used.

The authors base their study on a daily index that they briefly discuss the derivation and discusses the concept of flash droughts which seems like an impossibility to me.  The main result of the study is the fitting of a double-logarithmic function for the combination of frequency and duration of the drought periods. As one of the motivations are these flash droughts, how can this research help with that?  

Is the derived function well-constrained and in what range is it valid? In Figure 7b, the frequency curve seems to not approach zero rather flatten at a constant value, what does that do to the overall distribution?

The discussion section of the manuscript is extremely short and does not enlighten the reader on how more specifically this can be used, in what way, uncertainties, limitations, differences to other index used in other areas of the world etc.