This manuscript presents a statistical analysis of drought propagation from meteorological to hydrologic drought. This is certainly an important topic and fits within the scope of the journal. I have some major comments that need to be addressed before publication that relate to the lack of validation against drought observations, the suitability of what is considered a measure of hydrologic drought as well as the clarity in description of the methods.  

Major comments: 

Drought Definitions including Hydrologic Drought and Model Validation:

I have some major questions about the applicability of the method. For example, I tend to use SM percentiles or Evaporative Stress Index as drought indicators. In my world it is typical to estimate a distribution of values for a given time period (e.g. week of year and then to look at the percentile anomaly). Here is seems as if there is a single underlying distribution for the entire year (or season), which is then evaluated. I am just wondering how well the model actually represents something that is observable as drought. This could easily be validated by looking at observed conditions. The authors determine that there are differences between drought propagation between both models, but are the underlying models actually good models for real world drought conditions rather than good models for fitting a precipitation distribution. I am also a bit confused by the definition of hydrologic drought, which seems to be based on surface runoff from the Noah model. Typically hydrologic drought is assessed from gauged river runoff, while surface runoff is a temporary phenomenon occurring after strong precipitation events. I am not sure whether it makes sense to use the Noah gridded runoff as an indicator of hydrologic drought in the first place. How does this compare to for example river gauges? Again this could be validated against observations.  

Methods Description: 

In general I find that methods need to be described better for the reader to understand how exactly the models are formulated. It is for example not clear to me what specifically is meant by non-stationary model. Non stationary with respect to what (climate change trends, seasonal cycles, teleconnections) etc. 

Presentation and Interpretation

In general figures and tables should have captions that clearly help with interpretation of the information presented there. This should be accompanied by a description and interpretation of the figure content. 

Specific Comments

L22: "propagation thresholds in winter significantly increasing by 0.1-0.2" > it is unclear hear what these thresholds represent. I assume that is explained in the text, but with the abstract information alone it is to me not comprehensible. 

L31: "evolution from one drought to another is called drought propagation " > I would reformulate this because one can also think of spatial drought propagation where drought propagates from one region to another. I recommend to find a terminology that is less ambiguous

L98: "he annual mean temperature ranges from 1 to 11°C, and the monthly mean temperature ranges from 17 to 25°C. " > this requires explanation as the two ranges don't seem to go together unless one represents elevation changes and the other monthly mean average over the basin. In any case information about what is averaged over should be given. 

 

L105 :"With global climate change, drought disasters in the Luanhe River Basin are becoming increasingly frequent," >  the increasing frequency is not really apparent in the list of major drought events given in L108. Please explain. Also, one has to be careful here given that there have also been major changes in land-use and other conditions which would probably dominate economic losses rather than climate change. This is not to say that climate change is not contributing, but I don't think that the information presented supports climate change as a reason or even increasing frequency. 

L118 "https://disc.gsfc.nasa.gov/datasets/GLDAS_NOAH10_M_2.0/" > This link is no longer working. Given the absolute mess that the USA are currently experiencing. Rather than providing links dataset IDs should be used that identify datasets conclusively. 

L121: "https://daac.ornl.gov/" > not a dataset link but a link to a data center (see comment above) 

Figure 1: How are these sub-regions defined. Are these sub watersheds or corresponding to administrative/ municipal districts? For a propagation analysis, it would make sense to divide by subwatersheds rather than administrative divisions. 

Section3/ Figure 2: If the figure is shown at the beginning of the section it should be explained in the text right then and there. It is also not clear to me whether there is really a flow between Step 1 and Step 2 since both start from data rather than Step 2 using Step 1 outputs. This figure should be revised accordingly.  

Section 3.1: Given that Pearson correlation is a standard method, I don't think it needs to be explained in detail. It would increase conciseness and legibility of the manuscript to remove this section and to briefly mention it when the correlation is applied  

Section 3.2. If GAMLSS only applies to the non-stationary part it should be introduced as a subsection there. If not it is missing in Step 1 of figure 2. In all cases a better explanation is needed

3.2.1: This is the standard approach and one could think of whether this is needed, whereas the non-stationary part is new/ less commonly applied. So the focus on the methods should lie on that. 

3.2.2 Non-stationary model.

My expertise is in drought and not necessarily statistics. I feel that this section is too short and I have trouble understanding what specifically is different between the two models. How are "large-scale climate factors as covariates" included into the model. I feel that this requires quite a bit more explanation, since that is the novel/ core aspect of the manuscript. 

Right now in my limited and very likely incorrect understanding it seems to me that the non-stationary model represents different gamma distributions for 3 month seasons?  

L232: 'CI', AMO, ... > define these here clearly (and avoid exessive abbreviations) 

Figure 3: Correlation over which time period? Also please provide a clear in text explanation on how to read this figure. What are the main take-aways, I am currently struggling to understand the significance of this figure. So there seems to be a positive correlation between precipitation and a teleconnection) in May, which then flips to negative later in the year. Is there a specific reason to show AMO or is this just to give an example. If just an example than other plots should be shown in supplement. 

Table 2: Trends over which periods? 

Table 2 and 4: It would be good to provide a clear comparison of these model parameters to the non-stationary model parameters 

L268: This explanation should be in the figure caption of figure 4

 

L273: "quantile" > percentile?

Figure 4: I don't quite understand what the right column of the plot indicates. Please provide a clear explanation of what is shown and the significance. Does the right side indicate that the fitted gamma function for precipitation is able to reproduce the statistical distribution of precipitation? Also do you have a comment on the behavior of the fitted gamma functions at the extremes, which are obviously much harder to model with confidence (hence also the larger space of the CI lines). 

Figure 5:Runoff should have units of volume / time not mm. This figure also leads me to a major question about the definition of hydrological drought used here. 

I am stopping here with specific comments, because I have some major general comments that I think need to be addressed 

Technical

L11: "the law of drought propagation" > this seems like a language issue: "processes governing  drought propagation" ?

L12: meteorological factorS (?)

There is some editing needed on language and also punctuation and spacing. this should either be done during copy-editing or by the authors before the next submission. Examples include L52 [")h" --> ") h"] L61 (, -> .), ... 

L272: Fig 44 > Fig 4

L269: PERcentile?