The study proposes an integrated drought index (GTDI) that combines hazard-causing (SPEI) and hazard-bearing (SSMI) indices using game theory. The GTDI is compared with an entropy-based index (ETDI) and validated against LAI data in the Wei River Basin. The key findings are that GTDI outperforms single indices and ETDI in identifying droughts spatiotemporally, and can monitor changes in hazard-causing vs bearing impacts. Overall, the manuscript is well-written and the methodology appears sound. I have a few suggestions for improvement:

Major suggestion:

1. The novelty and significance of the GTDI should be highlighted more clearly in the Introduction. Discuss how it advances integrated drought indices beyond existing approaches like copula functions and entropy weighting. Articulate the unique advantages of using game theory.
2. The authors compare the GTDI with the ETDI, showing that the GTDI is more accurate. However, additional drought indices like the Standardized Compound Event Indicator (SCEI) and Standardized Dry and Hot Index (SDHI) (Hao et al., 2018, 2019; Wu et al., 2020) are constructed using similar approaches. Comparing the GTDI with these indices would provide readers with valuable insights into its performance relative to state-of-the-art methods in the field.
3. Comment on the sensitivity of GTDI to the choice of input indices. Would the results change meaningfully if indices other than SPEI and SSMI were used? Some discussion of generalizability would be useful.
4. The conclusion section could be more concise, focusing on the key findings and their implications.

Minor suggestions:

(Line 21-22) Include a brief description of the assessment method in the abstract.

(Line 24-25) Explain concisely in the abstract why the ETDI was used as a benchmark to demonstrate the GTDI's efficiency.

(Line 58-70) Consider condensing this paragraph to improve the paper's focus.

(Line 76-78) Rephrase this sentence for clarity.

(Line 80-81) Elaborate on why the mentioned indices struggle to distinguish between meteorological and agricultural drought influences and evaluate changes in regional patterns.

(Line 89-91) Copulas are an efficient tool for constructing drought indices, and the samples do not necessarily need to follow a specific probability density function. For example, empirical probability functions can effectively fit the samples. Consider modifying this paragraph accordingly.

(Line 136-137) Provide a rationale for using soil moisture data from the 0 to 10 cm surface layer, as agricultural drought indices often utilize soil moisture data from the root zone.

(Line 140-141) Include details on the resampling method used.

(Line 153-154) Explain the reasoning behind using SPEI-3 and SSMI-3.

(Line 206) Add a reference to support the statement.

(Line 246) Incorporate a duration threshold in the drought identification criteria.

General comments:

This study created a new integrated drought index (GTDI) by integrating SPEI and SSMI using the game theory method. The GTDI's usefulness in drought identification was evaluated through a case study in the Wei River Basin, and the effects of hazard-causing and hazard-bearing elements on drought episodes were discovered. Overall, this drought study falls within the scope of the NHESS journal and offers useful insights for recognizing and tracking drought hazards. However, the method and analysis in the manuscript are insufficient to support several of the authors' arguments, and the general presentation of the manuscript (including some images and discusses) requires improvement. I believe that this work requires certain revisions before it can be accepted for publication. My comments can be seen below.

Specific comments:

Abstract

Line 31-33, “This study surely serves as a helpful reference for the development of integrated drought indices as well as regional drought mitigation, prevention, and monitoring.” I am not convinced that the integrated drought index developed in this study has practical applications for “regional drought mitigation”. Please improve the phrasing in this statement.

1. 1. Introduction

Line 54, “with drought occurrences becoming more frequent, intense, and extended”, remove “occurrences”.

Line 89, change “has” to “had”.

Line 95, according to the statements in lines 82 to 84, “comprehensive” should be replaced by “integrated” or “composite”.

Line 99-101, provide the appropriate citations for “it has been revealed that the impacts of different factors on drought, such as hazard-causing and hazard-bearing, are changing …”.

1. Study area and data

Line 124-128, the precipitation and temperature conditions in the Wei River Basin are mentioned here, however there are no corresponding subfigures in Figure 1. Please include a matching regional distribution map of precipitation and temperature in Figure 1.

Line 134, add a citation for the DEM data.

Line 135, add a citation for the precipitation and temperature dataset.

Line 136, add a citation for GLDAS_NOAH025_3H_2.0 and GLDAS_NOAH025_3H_2.1.

Line 138, add a citation for GLOBMAP leaf area index dataset (Version 3).

1. Methodology

Line 145, please put the detailed calculation procedure for SPEI in a supplementary file.

Line 156, please put the detailed calculation procedure for SSMI in a supplementary file.

In Section 3.2, as a comparison to the GTDI index, the calculation process of the ETDI index needs to be explained in detail.

In Table 2, the value range for “moderate drought” is wrong and should be changed to “-1.5 < Index ≤ -1.0”.

Line 199-202, add the appropriate citations for the Pearson's correlation coefficients (PCC).

Line 210, "indexes" is used incorrectly and should be replaced by "indices".

Line 230-237, the method of using Leaf Area Index (LAI) data to access the performance of the drought indices is not clearly stated. Should the comparison be between the mean values of the LAI rather than the drought indices in arid and non-arid months?

Line 240, provide the appropriate citations for the Mann-Kendall (M-K) test.

Line 247-248, it is needed to explain in more detail how to identify drought through the drought index threshold and drought area threshold, and what are the specific identification criteria?

1. Results and Discussion

The manuscript calculated four drought indices: the SPEI, SSMI, ETDI, and GTDI, but except for the GTDI, the calculations of the other three drought indices are not reflected in the results section. It is suggested that the calculation results of the SPEI, SSMI, and ETDI be placed in a supplementary file.

Line 267-269, the findings from the final month of each season were used to depict drought conditions throughout the season; why not utilize a multi-month average?

In Figure 4, "PCC" can be marked above the legend on the right, and enlarge the names of the two drought indices in each row on the left.

Line 297, "worse" is inappropriately used to describe correlation coefficients (PCC) and should be replaced by "lower."

Line 314, "their" should be changed to "its".

Line 320-321, “to contrast the weight distribution of SPEI and SSMI in ...”, "allocation" may be more suitable than "distribution" here.

Line 328, "comprehensive" should be replaced by "integrated".

Line 343, “as a consequence of comparing GTDI and ETDI, it is discovered that …”, "is" should be changed to "was".

Line 344-345, “which is essentially congruent with the drought generation mechanism in this basin”: what is the drought generation mechanism in Wei River Basin? Please elaborate on this sentence better.

Figures 6 and 7 can be combined into one figure.

Line 371, “the soil moisture data used in this study is only 0 to 10cm of soil surface layer”, "is" should be changed to "are".

Figure 9 needs to be streamlined, as the year-month labeling is somewhat repetitive. It is suggested that the three drought indices be marked with only one year-month label under each drought event image.

Line 463-466, "In addition" and "Furthermore" are repeated, "in addition" can be removed.

1. Conclusions

Line 482, add " between “correlation” and “in”.

Line 492, the same as the comment for line 320-321, "allocation" may be more suitable than "distribution" here.

Line 511-513, the evolution trend of the GTDI is first presented in the results section, why don’t authors summarize the findings of this part in the first conclusion?

GTDI: a spatially variable weight drought combining two single-type indices SSMI and SPEI for drought hazard causing and bearing impacts changing. Authors claim that GTDI has a greatly high correlation with single-type drought indices (SPEI and SSMI) which is obvious because both indices are used to develop GTDI.

-This is not an individual validation of GTDI.

-Line 28: “GTDI exhibits the gaming feature” What are the features? The major question is how the author came up with this equation.

-Are there any sound criteria that support this form?

- The soil moisture dataset resolution is very high for a very course and a very small catchment means all the regions could exhibit similar values how do authors distinguish?

-What is the basis for classifying the GTDI? Line 194 “calculating approach of SSMI in this study is comparable to that of SPEI, while GTDI and ETDI are built on SSMI and SPEI” GTDI is using a weighted approach, and it may reflect different drought intensity/severity. Thus, the classification approach could not be straightforward.  

-How did authors build ETDI? Section 3.2 only shows the GTDI process.

-Temporal evaluation of GTDI is needed to present along SPEI and SSMI.

-Figure 3: The results are not meaningful. What scale is used for calculating drought with GTDI? Is this drought tendency mild, moderate, or extreme?

 -GTDI is developed to present an agricultural drought. Right? Individual verification is needed.

-The efficacy verification in Table 6 only presents some percentage numbers. Why choose these specific months, which period? GTDI is overestimating the drought ratio because this river basin has a very small area where seasonal drought happens. Moreover, Fig. 6 and 7 present what is beyond my understanding. What is the purpose of showing satellite image?

What do you mean fine, poor?

Fig. 9: it could be seen that drought is moderate in this basin, Thus authors are advised to expand the region for proper verification of GTDI.

Review

Understanding the response mechanisms of different vegetation types to drought is critical for the conservation and sustainable development of vegetation resources. Therefore, this study used the Standardized Precipitation Evapotranspiration Index (SPEI) and Vegetation Health Index (VHI) to analyze drought and vegetation changes, and to identify their dynamic characteristics and return periods. They analyzed the spatial characteristics of vegetation change and the cumulative and lagged effects of vegetation on drought. Furthermore, they selected representative influencers (air humidity, air temperature, evapotranspiration, precipitation, soil moisture, soil temperature) to identify scale effects between different climate factors and vegetation growth. They used the Bayesian Estimator of Abrupt Seasonal and Trend change (or Pixel-based Mann-Kendall analysis) to analyze the dynamic changes (or trend changes) in the VHI and SPEI. They used run theory to characterize the drought. The copula model was used to analyze the duration-severity-return period of drought events. Correlation analysis was used to analyze the response of vegetation condition to drought. The multiple wavelet coherence method was used to investigate the dependence of specific geophysical variables on the interdependent effects of multiple variables. Through this research, they uncovered the dynamic changes and responses between vegetation and drought in interior Mongolia. They also identified patterns of vegetation fluctuation during drought events and identified key climate factors that influence vegetation growth.

Comments

(1) In the introduction, it feels like it is repeatedly mentioned that drought threatens (adversely affects) vegetation growth. I think it would be better if the authors organized these related parts well.

(2) Section 3.2 describes the VHI used in this study. How was the weight set when calculating VHI? It would be better to have an explanation for this.

(3) In section 3.4, I would like to know if there is a specific reason why the authors chose to perform the Kolmogorov-Smirnov test.

(4) In Section 3.5.2, I would like to know why the Monte Carlo method was selected and used.

(5) In section 3.6, I think it would be better to add a rough description of what a black-box model is.

(6) In Section 4.1, is the data in Figure 3 meant to be VHI data? If this is VHI, VHI has values between 0 and 100, but here it is showing the value VHI × 0.01?

(7) In Figure 6 in Section 4.2, it would be better to add units for return period and drought duration.