Thank you for your very positive evaluation.

1. First, it appears that the evaluation throughout the paper relies on the correlation coefficient of the entire time series of SPEI and soil moisture. The increment in the correlation coefficient is almost less than 0.1, even if statistically significant. Since drought indices are typically used to identify and quantify drought events, I suggest the authors evaluate the skill of their improved SPEI index in detecting and quantifying extreme events rather than the dynamics of the entire time series.

Response: Thank you for the great suggestion. Our study primarily aims to assess the overall improvement in predicting of temporal variations in drought indices and soil moisture. While the absolute increment in correlation appears modest, the percentage change is quite significant, around 25-30%. Despite the small average increase, local improvements are notable (as shown in Figure 4). We acknowledge the importance of capturing the extreme events in future studies and will add this to our discussion.

1. Secondly, I observed that many Ga and Gs parameters (in Table 1) have been used to incorporate features of aerodynamic and surface conductance. I wonder if substantial uncertainty arises from these prescribed parameters. In other words, does the subpar performance of the improved SPEI index in non-forest ecosystems relate to larger uncertainties in parameters for grassland, shrubland, or cropland compared to the forest?

Response: We agree that the uncertainties in the Ga and Gs parameters can potentially affect the results. For example, the better performance of the tall crop reference ET compared to the Land Cover approaches for the non-forest ecosystems suggests inaccuracies in the Gs or Ga parameters, given the similar big-leaf model. We will compare the Gs and Ga between tall crop and the Land Cover approaches in the discussion section and note that parameter uncertainty merits further exploration in future research.

1. Thirdly, the improved SPEI exhibits better performance in humid regions, which aligns with expectations given the energy-limited water availability dynamics. However, in arid regions where water availability is more supply-dependent, the adjustment to PET has no significant effects and the uncertainty in precipitation data may be crucial. The authors may elaborate on this point in the manuscript.

Response: Thank you for pointing out the influence of aridity on our results. We will elaborate on this point in Figure 5 and in section 6.2, discussing the differential impacts in humid and arid regions.

1. Specific comment: Figure 2: It is unclear whether the correlation between soil moisture and SPEI reflects temporal or spatial variability or includes both signals. Additionally, please clarify what the white dots within each bar represent.

Response: The correlation reflects spatially averaged temporal variability between SM and SPEI. The white dots indicate the average difference in correlations between the four methods and the reference method (Table A1). We will clarify this in the legend of Figure 2.

Thank you for your very positive evaluation.

1. A more detailed description of the "two-source model" in Section 3.3 would be beneficial. The manuscript does not clearly articulate the relationship between this model, Equation (13), and the improved vegetation characteristics described in Section 3.2. The statement "We adopt the same parameterizations detailed in Zhou et al. (2006)" is too vague. It would be valuable to elaborate on how these parameter improvements are integrated into your PET method.

Response: Thank you for the suggestion. We will add detailed explanations about the two-source model in section 3 and clarify the parameter improvements for different models.

1. The manuscript estimates PET over 1981–2017. This timeframe should be explicitly mentioned in Sections 2 and 3, such as "PET is estimated over 1981–2017 using [specific methodology]."

Response: We will ensure to clearly mention the timeframe in Sections 2 and 3.

1. Clarify whether PET calculations are based on monthly or daily scale meteorological inputs. The application of land surface ancillary data in your equations, such as the usage of "black- sky and white-sky albedo," is not clearly explained. For instance, how is albedo factored into the net radiation calculations in your equations?

Response: PET calculations are based on daily meteorological inputs, which will be clarified in section 2.1. Regarding the processing of GLASS albedo: we resample the 8-day albedo product to a daily resolution, average the black- and white-sky albedos, and implement gap-filling for missing data using the average of adjacent years. We will add this detail in Section 2.3.

1. On L121, you mention obtaining "canopy height data from a global tree height dataset at 1- km for 2005 using spaceborne lidar." It seems not clear how this dataset is used in your study? You also state that "As canopy height and frictional velocity are rarely measured continuously for each grid, we use a simple look-up table approach to provide roughness parameters." These statements seem contradictory and need clarification.

Response: We acknowledge the confusion and will clarify the combined usage of global tree height dataset and the literature values for roughness parameters in L195.

1. Section 3.1 lists different PET methods, most of which are derived from the Penman equation. Including the derivation process in the supplementary material and schematic figures illustrating the differences between these methods (e.g., big leaf models vs. two-source models) would enhance understanding. This suggestion is optional if it's difficult to implement.

Response: Thank you for the suggestion. We could include detailed derivations of the PET equations in section 3.1 and SW approach in section 3.3 in the Appendix for better understanding.

1. In Section 3.3.3, clarify the role of Gstmax in previous PET methods or equations mentioned earlier.

Response: I assume you meant Section 3.2.2. We will clarify the difference between Gstmax (used in actual ET estimate) and Gs (used in potential ET estimate).

1. While many surface vegetation characteristics are included to improve PET estimations, some easily accessible characteristics are not utilized. Global canopy vegetation height data (https://www.nature.com/articles/s41559-023-02206-6), which could be employed in Ga estimation, is now available. Other datasets like the 1k datasets (https://essd.copernicus.org/preprints/essd-2023-242/) may also be valuable for your study.

Response: Thanks for the recommendations. These datasets are useful for future improvements of our approach.

1. A recent study "Sun, S., Bi, Z., Xiao, J., et al." (2023) considers comprehensive parameters for improved PET estimation. If detailed consideration of vegetation characteristics is a novelty of your study, please explicitly explain its advantages compared to this study. Alternatively, if your focus is more on comparing different PET methods with limited vegetation considerations, clarify this in your introduction and discussion.
2. Compare your PET estimations with reference datasets, such as Sun et al. (2023).

Response: Thanks for pointing out this new study focusing on the Shuttleworth-Wallace model. We will compare our estimates with this study in the discussion.

1. Appendix A contains important information leading to the results in Section 5.1. Mentioning this in your method sections would prevent sudden introduction of these comparisons in the results. Some sentences around L280 could be moved to the method section.

Response: We will move some sentences to the methods section to ensure a smoother transition to the results.

1. Move Figure A1 to the results section. The results section should feature PET estimations before transitioning to SPEI comparisons (starting in Figure 2).

Response: Thanks for the suggestion. Since the first set of pilot methods in Figure A1 are not exactly the same as Figure 3 and can potentially cause some confusion, we will consider reorganizing the figures, for example, a new figure with PET estimations that better aligns with Figure 3, or moving current Figure 2 to Appendix.

1. Incorporate multiple soil moisture datasets in your comparison to account for the significant uncertainties among different soil moisture data.

Response: The ESA CCI SM v4 dataset is chosen for its widely accepted data quality, which is achieved by combining multiple single-sensor active and passive microwave soil moisture products to minimize uncertainty. We will expand on the section 2.2 to discuss data reliability and uncertainty based on studies such as Gruber et al. (2019) for a more comprehensive understanding of the data accuracy. https://essd.copernicus.org/articles/11/717/2019/.

1. On L329, introduce the full name 'LC-Kelliher' before its abbreviation. LC is "land cover” as detailed in the table of Figure 3. Please check the manuscript for any potential similar issues.

Response: We will ensure all the abbreviations are introduced before being used and are consistent throughout the manuscript.

1. On L61, provide examples of "conventional PET methods" versus non-conventional methods for clearer understanding. Regarding the statement "The vegetation control on transpiration is often neglected," comment on the impact of plant hydraulics on potential transpiration estimation, referencing relevant studies (e.g., https://agupubs.onlinelibrary.wiley.com/doi/full/10.1029/2018MS001500).

Response: In the line mentioned, we differentiate between “conventional” PET methods, which often assume no or simple universal vegetation control on transpiration, and “non-conventional” methods that account for vegetation control based on specific conditions. For instance, conventional methods that are often used in SPEI include the Thornthwaite and Hargreaves-Samani equations, as well as the Penman open water or Reference crop ET formulas. The “unconventional” methods in this study do not refer to the land surface models or dynamic vegetation models, which normally have representations of the transpiration process including plant hydraulics.