The manuscript essd-2024-396 presents a dataset identifying historical compound dry and hot extreme events derived from ERA5 global meteorological data. The study's focus on compound events, which are more damaging than univariate extremes, is timely and valuable for the community. However, several issues require attention to enhance the dataset's reliability and utility.

Major Concerns:

1. Global Trend of Heat Extremes:
   
   The data analysis indicates a non-significant trend in heat extreme day numbers globally from 1970 to 2022. This finding contradicts numerous studies showing that heatwaves have become more frequent and severe over time. This discrepancy should be thoroughly investigated, as it undermines the reliability of the dataset.
2. Data & Methodology:
   
   a. The dataset relies exclusively on ERA5 data. The authors should include a literature review demonstrating that ERA5 is widely accepted for historical drought and heat stress analyses.
   
   b. The use of the 1% threshold for defining "extreme" events requires justification through references to relevant literature.
   
   c. The parameterization G=0.5Rn for ground heat flux is uncommon as this ratio is typically associated with vegetation cover. Now the impact from the surface cover is missing. This choice should be explained or supported with references.
3. Seasonal Detrending:
   
   The proposed methodology lacks seasonal detrending, a standard preprocessing step in drought and heat analyses. Without removing seasonal cycles, anomalies are compared to absolute values rather than seasonal baselines. For example, warmer days in spring might qualify as heat stress even if their absolute temperatures are lower than those in summer. Similarly, seasonal cycles in PEI could influence water stress results. This methodological issue weakens the robustness of the findings and should be addressed.
4. Omission and Commission Errors:
   
   The authors conducted a qualitative literature survey of extreme events captured or missed by the dataset. This evaluation is commendable but could be improved by quantitatively summarizing omission and commission errors. These statistics should also be briefly mentioned in the abstract for clarity.
5. Global Trend Mapping:
   
   Figure 6 presents trend analyses across continents. A pixelwise global trend map would provide a more detailed spatial representation and is strongly recommended.
6. Intercomparison with Other Indices:
   
   The dataset should be compared with drought and heat indices from other sources over a long time span to validate its reliability.

Additional Comments:

• Data Citation: ESSD requires the data URL and citation to be explicitly mentioned in the abstract.
• Figure 1: The terms "ET0" and "ETref" should be unified for consistency.
• Hourly ETref Calculation: Clarify why θ (daily mean temperature) is used instead of hourly temperature.
• Missing References: Two papers by Ima are cited but not included in the reference list.
• Figure 2: Clarify the difference between "no extreme" and "10th–90th percentile."
• Figure 3: Add a legend explaining the meaning of the additional colors.
• Table 2: Specify the units for area and volume.
• Data Accessibility: URLs for the data cubes are not accessible. Please ensure they are active and functional.