the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 09 Oct 2025
Is earlier always better? A comparative assessment of rainfall replenishment timing for multiyear drought mitigation
Abstract. Multiyear droughts (MYDs) are recognized as severe drought events, with especially profound impacts on both human activities and ecosystems. However, the optimal rainfall replenishment timing (toptimal) for MYDs mitigation remains insufficiently understood. With that in mind, we conducted a retrospective analysis of historical MYDs based on the Palmer Drought Severity Index (PDSI) in China during 1961–2020, and the calibration period was set to 1961-1990. We performed a series of numerical experiments involving precipitation gradient increases for 351 selected MYDs, distributed across 199 grids (2°×2°), from 1991 to 2020, and developed a drought mitigation quantitative model (DMQM). In addition, a key coefficient (k) derived from DMQM was defined to quantify the mitigation efficiency, and toptimal was then identified as the timing corresponding to the maximum k (kmax). Overall, drought severity exhibits a nonlinear response to increased precipitation. kmax occurred most frequently in the first month of drought onset (t1), accounting for 58.79 % of all grids, while the second (t2) and third (t3) months were also non-negligible, accounting for 22.11% and 11.06 %, respectively. Compared to the humid river basins in southern China, the arid and semi-arid northern regions had a higher probability for k at t2 or t3 to exceed k at t1. Drought duration (DD) was identified as a key factor, as longer DD was associated with a greater likelihood of t2 or t3 being the toptimal, evidenced by R2 values of 0.526 and 0.578, respectively. These findings contribute to ensuring timely and regionally appropriate MYD mitigation strategies and interventions.
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Status: final response (author comments only)
- RC1: 'Comment on egusphere-2025-4213', Anonymous Referee #1, 09 Nov 2025
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RC2: 'Comment on egusphere-2025-4213', Anonymous Referee #2, 10 Nov 2025
General Comment
This manuscript investigates the role of precipitation timing on reducing the severity of multiyear droughts. The topic is generally well suited for this journal, and the objective clearly identified.
I found, however, a few major drawbacks that limit the scope of the proposed research:
- The term mitigation is, in my opinion, improperly used or, at least, not well described. The term mitigation is usually associated with anthropogenic action to reduce the impacts of a natural hazard. Here, terms such as “amelioration” or “alleviation” may be more appropriate. In general, the authors discuss about precipitation as it is usually done for irrigation in agricultural districts. While there are some similarities, precipitation over large areas cannot be discussed in the same terms. I suggest a deep revision of the text to avoid any confusion on the strategy discussed here.
- The focus on multiyear drought is never clearly explained nor justified. Why the analysis focuses specifically on multiyear drought and not on drought in general? What is the reasoning behind such choice?
- The issue of non-linear response is not well discussed in the probabilistic context of drought indicators. The fact that drought severity changes non-linearly with the usual indicators is a well know factor, well reflected by the commonly used classifications of drought indices. In this context, it is not possible to simply compare a unitary change in severity between events occurring at different severity levels, as (example) a change in SPI from 0 to -1 and from -1 to -2 have completely different probabilistic implications. I suggest the authors to carefully revisit their considerations on the “mitigation” efficiency by explicitly taking into account for these disparities.
- The terminology used in the paper is sometime rather confusing. Different terms are used to define the same quantities in different part of the paper (e.g., t_optimal, t_a, t_b, t_c, etc.).
Overall, while a recognize some potential in this research, I suggest a careful revision of the text before considering it for publication. I added some further specific comments below, in the hope that they will be useful to improve the quality of the manuscript.
Specific comments
L12. Remove “especially”.
L13. The concept of “optimal rainfall replenishment timing (T_optimal)” needs to be better established here.
L15. Calibration period. I suggest rewording.
L16. “351 MYD”. These are obviously not droughts, but cells under drought. Many of these cells are under the same MYD contemporarily. Please reword, as this statement seems to suggest that 351 MYD were observed in a period of only 60 years.
L17. Is the study period 1991-2020 or 1961-2020? The different periods are confusing.
L17-18. A key coefficient (k)… This does not clarify what “k” is.
L18. T_optimal should be a subscript.
L20. This sentence is not clear if you do not clarify what k is.
L24. T_optimal should be subscript.
L24-25. This sentence needs to be clarified, as it is not clear to me how these findings can be used for “intervention”.
L30. I was not able to check the reported number of “3000 deaths” in the US, beside the Science paper cited in the text. I suggest checking the source of this information.
L55. “three key dimensions”. Please reword, as the term “dimension” is misused here.
L55. “the lowest”. This is true only for indicator where droughts are negative. Please clarify (largest in absolute value).
L57. These are not indicators but rather drought features.
L60. “the four stages”. These stages have not been introduced yet.
L68-70. This sentence is misleading. A large numerical shift in anomalies (e.g., from 4 to 2) does not necessarily means a large change in drought conditions, as conditions still remains extreme. This is due to the non-linearity in the drought definition according to the indices, but not to a non-linear response of drought to precipitation. I think that this needs to be better clarified, as it has huge implications on your analyses.
L71. This example is incorrect, as a 1-unit change does not have the same physical and probabilistic meaning at, e.g., -1 or -4. Maybe I misunderstand your statement, and we are saying the same think, but changes in anomalies cannot be treated linearly but they need to account for the non-linearity.
Fig. 1. The term forcing is used without a proper definition.
L85. This concept is here introduced without a proper definition.
L90. Fig. 3 is cited before fig. 2.
L104. Remove and.
L105. Some additional details on the selection procedure are needed.
Fig. 2. Add region names instead of only numbers.
L121. “representative”. How?
L122. PIP is not well defined. Is it the value of the PDSI or the time?
L125-128. This paragraph is confusing, as it relies on several concepts not introduced yet.
Fig. 3. Many terms are not explained here (pr_mean, is it the long term of the mean of each month?), k_theoretical and k_actual.
L132. PDSI requires calilbration. How was this performed? Add details.
L135. Was the FAO-56 applied directly on monthly data? Clarify how, as daily data are previously discussed.
L138. How is G modelled?
L142. Why is the period 1961-1990 used for reference? If the analysis focuses on 1991-2020, why wasn’t this period (recommended by WMO) used instead.
L148. What is a “typical” MYD? Please clarify.
L149. Did you perform any pooling? A single month of interruption was enough to stop a MYD? Clarify
L151-152. These are not events, but drought periods for each given grid cells. Speaking about “at least 11” multiyear drought events in each basin over 30 years is misleading.
L164. “greater negative values”. Even if this is true, the relationship is not linear, and the same DS change may mean very different things depending on the conditions. As an example, if you use the corresponding probability rather than the standardize anomalies, the results will be very different. The “mitigation” effect should be independent from the way the metric is presented.
L166. I do not follow this logic. Maybe it is still a consequence of the misunderstanding on the meaning of a unitary change in DS. Please reword and clarify, ad this is a key assumption of your methodology.
Fig. 4a is the same as in Fig. 3. Avoid repeating the same plot multiple times.
L185. Why the absence of overlap between the baseline period and the experiment period is needed?
L194. Clarify the acronym. Also, why a theoretical model is needed? As seen later, this introduced some unneeded approximations. Cannot be the same analyses made on the empirically computed values Delta_DS and Delta_pr?
Eq. 3. As stated before, a change in DS can have different meaning depending on the severity itself. How did you account for that?
L209. The terms “actual” and “theoretical” are poorly explained. Is the former based on the empirical values and the latter on the model? If you have K_actual, why you should base your analysis on the theoretical?
Fig. 5. It is not clear to me how these plots were derived. Are these from eq. 6. Using which k? This section of the results and the previous methodology need to be restructured.
Fig. 6. Errors in the theoretical seem larger in the North-east, which is the same region where with several Kmax at month >= 2. Is there an effect of the error in the theoretical model in these results?
Fig. 7. Same as before. Most of the large differences seem to be in the north-east.
Fig. 8. Why reporting the map of the duration. Is this the median duration of the droughts (as in Table 1)? How are the probability plots made? Based on how many data? Is there any smoothing applied?
Table 1. Add the number of pixels for each basin, and also the DS.
L305. Why not DS? Is it possible that this result is just the effect of DS as mentioned before (not all the delta have the same effect, as they depend on DS itself).
L325. Some basins are just one pixel, or close to. How these values can be compared among basins?
L339. “precipitation-based drought mitigation”. What does this mean?
L355-356. How much of this result is due to the error in the theoretical values?
L366. This is not true everywhere in the world.
Citation: https://doi.org/10.5194/egusphere-2025-4213-RC2 -
RC3: 'Comment on egusphere-2025-4213', Anonymous Referee #3, 13 Nov 2025
This manuscript develops a Drought Mitigation Quantitative Model (DMQM) based on the Palmer Drought Severity Index (PDSI) and examines how the timing of rainfall increases influence drought mitigation efficiency. The research question is reasonable, and the modeling framework provides a structured way to evaluate drought mitigation sensitivity. The results have the potential to contribute to the understanding of drought mitigation processes and to inform strategic decisions regarding drought response planning.
At the same time, several conceptual assumptions underlying the framework require more explicit clarification to enhance the interpretability and generality of the findings. In particular, the reliance on a single drought index, the interpretation of the key coefficient (k), and the mechanisms driving regional differences in optimal rainfall replenishment timing require further discussion. Addressing these points would improve the clarity of the conceptual narrative and broaden the potential applicability of the DMQM. The specific issues are reported below:
- The model framework is built entirely on PDSI, yet standardized drought indices vary substantially in their input variables, water balance assumptions, and how auto-correlation processes are incorporated. Because PDSI embeds a two-layer soil moisture storage structure, the mitigation efficiency patterns derived here may reflect this structure rather than a general characteristic of drought mitigation. A discussion of whether similar outcomes would be expected when using SPI (precipitation based) or SPEI (precipitation and evapotranspiration based) would clarify the extent to which the coefficient k reflects a broader drought response characteristic compared with the behavior of a particular index formulation. Even a conceptual comparison would enhance confidence in the applicability of the framework.
- Standardized drought indices are designed to approximate a normal distribution, which can make them particularly sensitive to the treatment of tails and extremes in hydroclimatic data. Since the core results of DMQM concern changes in drought severity under incremental rainfall increases, it would be worthwhile to examine whether the statistical normalization process itself influences the magnitude of the estimated mitigation efficiency. A brief consideration of whether alternative representations that are less sensitive to extremes might produce similar mitigation patterns would help delineate the robustness of the conclusions.
- The coefficient k is positioned as a measure of mitigation efficiency, yet its physical interpretation remains implicit. Clarifying whether k should be understood primarily as an empirical sensitivity parameter or whether it reflects an underlying hydrological recovery rate would help readers understand how it should be compared across regions and timescales. Further elaboration on this point would strengthen the conceptual coherence of the framework. At the same time, the spatial patterns of k and the optimal rainfall replenishment timing suggest systematic regional differences, especially between northern and southern basins. These differences may reflect variations in climate seasonality, soil water storage capacity, and land-atmosphere feedbacks. A more detailed discussion of which factors are most likely to drive the observed spatial differences would improve the interpretability of the results. It would also help clarify the extent to which the framework may be transferable to regions with different hydroclimatic conditions.
Citation: https://doi.org/10.5194/egusphere-2025-4213-RC3
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Review of "Is earlier always better? A comparative assessment of rainfall replenishment timing for multiyear drought mitigation"
This is my first review of the paper. The paper addresses an interesting and potentially important question: how the timing of rainfall replenishment affects the mitigation of multiyear droughts (MYDs). The authors propose a “drought mitigation quantitative model” (DMQM) to quantify how increases in precipitation at different stages of a drought affect drought severity, using historical events in China (1961–2020). The topic is relevant to understanding drought recovery dynamics and could make a valuable contribution if presented more clearly and conceptually coherently.
However, in its current form, the manuscript suffers from major issues, which I report below:
1. The term mitigation is central to the paper but is never clearly or consistently defined.
Throughout the introduction and abstract, “drought mitigation” is used in the general sense of reducing drought impacts, which typically implies human or management intervention. Later, in Section 3.4, it becomes apparent that mitigation actually refers to the modelled reduction in drought severity (DS) resulting from hypothetical precipitation forcing in numerical experiments. In this way, readers are left uncertain whether the study concerns physical hydrological recovery, operational drought management, or synthetic model sensitivity.
I suggest defining drought mitigation explicitly in the introduction as a numerical or index-based construct (i.e., “the reduction in DS under hypothetical precipitation increases”). In practice, clarify early that no human intervention or feasible rainfall modification is implied. Terms such as index-based recovery or drought attenuation efficiency would be more accurate and less misleading.
This also impacts other terms. Indeed, the manuscript repeatedly refers to “precipitation-based drought mitigation” and “early intervention,” giving the impression that rainfall timing can be controlled or managed (e.g., through artificial replenishment). Yet, the study merely perturbs precipitation values in the PDSI model. This language conflates natural rainfall timing with anthropogenic mitigation, generating unnecessary conceptual ambiguity. I suggest rephrasing these expressions to reflect that the experiments involve idealized precipitation scenarios, not management interventions. For example: “The model explores how the timing of hypothetical precipitation increases affects index-based drought recovery.”
2. The central relationship of the DMQM model, that is, the DS rate equation, is introduced without theoretical justification or empirical testing. The exponential law is simply postulated at the beginning, not derived from data or hydrological reasoning. Consequently, the “goodness of fit” (R² > 0.9) is largely tautological, since k is defined within this same assumed functional form. I think that the auhtors, shall provide evidence that the exponential function is appropriate, or test alternative relationships (linear, logistic, power-law). Explain whether k has a physical interpretation (e.g., storage or recovery constant) or is purely a curve-fitting parameter. Without this, the DMQM remains a mathematical construct lacking process basis.
3. Although the analysis uses real meteorological data, the results remain statistical and abstract. The study would benefit from at least some discussion on what the “optimal timing” might mean in real hydrological terms, e.g., soil moisture recharge, vegetation response, or water resource management, instead of only index sensitivity. Otherwise, the practical implications of tₒptimal remain unclear.
4. While the paper contains extensive methodological detail, the presentation is overly technical and textually dense, often making it difficult to follow the main line of reasoning. Equations, parameters, and symbols are introduced in rapid succession without sufficient intuitive explanation, and transitions between conceptual discussion, mathematical derivation, and numerical experiments are often abrupt.
As a result, even readers with a strong hydrological background may struggle to understand the logical progression from the conceptual models (Section 3.4) to the construction of the DMQM and its application. The heavy use of notation (DS, DD, DI, DDP, PIP, k, t₁–t₈, toptimal) without repeated restatement of their physical meaning contributes to confusion. I strongly suggest providing a short, intuitive summary before or after key equations and reducing unnecessary algebraic detail or moving it to supplementary material and restating the physical meaning of variables (e.g., PIP, DDP, k) when they reappear in later sections.