Assessing summertime hydrological cycle acceleration through drought indices

Sabin, Matthew Walter; Bjarke, Nels R.; Livneh, Ben

doi:10.5194/egusphere-2026-2895

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https://doi.org/10.5194/egusphere-2026-2895

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18 Jun 2026

| 18 Jun 2026

Status: this preprint is open for discussion and under review for Hydrology and Earth System Sciences (HESS).

Assessing summertime hydrological cycle acceleration through drought indices

Matthew Walter Sabin, Nels R. Bjarke, and Ben Livneh

Abstract. The rate (or velocity) of the hydrological cycle affects water availability for agriculture, energy production, and planning for droughts or floods. Therefore, acceleration in the velocity of the hydrological cycle is likely to impact multiple hydrological domains and management practices. Previous work has primarily studied hydrological cycle velocity and acceleration through the lens of flux magnitudes and their change. Motivated to expand this definition to characterize temporal coupling between stages in the hydrological cycle, we introduce a novel definition of hydrological cycle velocity and acceleration derived from the concept of drought propagation. We define the hydrological cycle velocity as the response time between the 1-month Standardized Precipitation Index (SPI) and the 1-month Standardized Soil Moisture Index (SSI) and define acceleration as the change in response time between an early time period and a late period. Using gridded reanalysis data over the conterminous United States (CONUS) from 1951–2020, we analyzed the summer period (June, July, August) to minimize the lagging-effects of cold-season processes. Response times exceeded 100 days in southwestern CONUS (indicating a slower hydrological cycle velocity), but were substantially shorter elsewhere, 10–20 days, indicating a faster hydrological cycle velocity. A Random Forest variable importance analysis revealed strong negative associations of response time and mean annual flux magnitudes, with higher precipitation and evaporation associated with shorter response times. Regarding potential acceleration between an earlier (1951–1985) and later (1986–2020) period, 48.47 % of reanalysis grid cells experienced a deceleration (lengthening of response time) of their local summer hydrological cycle, while 39.32 % of grid cells experienced an acceleration (shortening of response time). However, a false detection rate correction found a lack of robust field significance (a_FDR=0.05), a finding reinforced by a regional decadal trend analysis. By framing hydrological cycle acceleration in terms of propagation of meteorological anomalies to land surface anomalies, we expand the conceptual basis for diagnosing changes in the hydrological cycle.

Received: 20 May 2026 – Discussion started: 18 Jun 2026

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Matthew Walter Sabin, Nels R. Bjarke, and Ben Livneh

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RC1:
'Comment on egusphere-2026-2895', Anonymous Referee #1, 16 Sep 2026 reply
This manuscript proposes a new framing of hydrological-cycle acceleration based on the lag that maximizes the correlation between the 30-day Standardized Precipitation Index and the 30-day Standardized Soil Moisture Index. The approach is applied to ERA5-Land over CONUS for 1951-2020. The authors characterize the spatial distribution of this response time, use random forests to examine associated hydroclimatic variables, and compare response times between 1951-1985 and 1986-2020. They find longer response times in the western and southwestern United States, shorter response times in the eastern United States, and no grid cells with statistically significant temporal changes after false-discovery-rate correction.
The manuscript has several strengths. The research question is timely, the distinction between flux intensification and temporal coupling is potentially useful, and the long record and continental-scale application are valuable. The use of spatially blocked cross-validation and multiple-testing correction also strengthens the analysis. The authors also appropriately acknowledge several limitations, such as the occurrence of broad or multiple correlation peaks in the western United States.
However, the central metric has not yet been shown to be a robust measure of hydrological-cycle velocity or acceleration. The maximum-correlation lag is sensitive to the accumulation scale, temporal autocorrelation, switching between competing correlation peaks, precipitation and soil-water storage from earlier seasons, and the structure of ERA5-Land and changes in the underlying observing system. The bootstrap analysis also does not fully account for uncertainty in the selected lag or in both comparison periods. I therefore recommend major revision.

Major Comments:

Physical interpretation of the SPI-SSI lag as “hydrological-cycle velocity.” The manuscript equates a shorter SPI-SSI lag with a faster hydrological cycle, yet Sect. 4.1 explains the spatial pattern through wetting-drydown asymmetry and the persistence of soil-moisture anomalies. This suggests that the metric may be strongly influenced by soil-moisture memory and land-surface persistence rather than representing hydrological-cycle velocity in a broader physical sense. The authors should either strengthen the justification for this interpretation or reframe the metric more cautiously as a precipitation-soil-moisture coupling or propagation timescale. As written, the velocity and acceleration terminology appears broader than what the metric directly supports.

Novelty relative to recent drought-propagation research. The manuscript presents changing SPI-SSI response times as a novel characterization of hydrological-cycle acceleration, but closely related response-time analyses already exist. In particular, Liu et al. (2026, HESS, 30, 2775–2795) quantified meteorological-to-agricultural drought response times using standardized precipitation and soil-moisture indices, multiple datasets, correlation- and event-based propagation metrics, and 30-year moving windows. I recommend discussing this study, clarifying the specific novelty of the present metric and study design, and explaining the different conclusions regarding temporal change.

Liu, Y., Hu, T., Yang, J., & Yu, L. (2026). Understanding meteorological, runoff, and agricultural drought propagation and their influencing factors in an ensemble of multiple datasets. Hydrology and Earth System Sciences, 30(9), 2775-2795.

Robustness of the maximum-correlation response time. Figure 7 shows the Southwest response time shifting from 234 to 14 days because relatively small changes in correlation alter which of two competing peaks is selected. The authors acknowledge that broad or multiple peaks occur across the West and Southwest, meaning that apparent acceleration or deceleration may reflect peak switching rather than a physical shift in response timing. I recommend introducing a robustness criterion, such as minimum peak prominence, a minimum difference in correlation between the dominant and secondary peaks, the bootstrap probability of selecting the same peak, or restriction of the analysis to cells with one clearly dominant peak. The domain-wide percentages of acceleration and deceleration should then be recalculated or de-emphasized, as they currently combine robust and potentially unstable response-time estimates.

Bootstrap and significance testing. For the early-late comparison, only the early period is resampled and the observed late-period lag is compared against the early-period bootstrap distribution. This omits the sampling uncertainty in the late-period estimate, particularly consequential where the selected peak can switch. Both periods should be resampled, and the early-late difference should be calculated for each bootstrap replicate. The authors should also justify applying a 90-observation block after restricting the series to JJA and report sensitivity to block length. Given that only 1,000 resamples are used before FDR correction across many grid cells, the minimum attainable p-value and the ability to detect plausible changes should also be reported.

Dependence on a single model-based product and changes in data quality over time. ERA5-Land soil moisture is produced by H-TESSEL without direct soil-moisture assimilation, so the spatial response pattern and wetting-drying behavior may partly reflect the land model rather than observed hydrological dynamics. The manuscript also notes lower confidence in precipitation before 1979; the early period is mostly pre-1979, whereas the late period is entirely post-1979. The authors should test the main spatial pattern and the sign of change using an independent product based on a different land model or observation source and conduct a post-1979 sensitivity analysis. If this is not feasible, the conclusions should be explicitly limited to ERA5-Land.

Framing of the RF analysis: associations, not drivers. The RF explains the spatial distribution of the full-period (1951-2020) response time, and the dominant predictors (annual and summer precipitation, evaporation, etc.) largely follow the broad east-west aridity gradient, which itself closely resembles the spatial pattern of the response-time metric. Spatially blocked cross-validation reduces dependence between nearby training and test locations, but a high R² does not by itself demonstrate that the RF has identified physical controls rather than recovering this large-scale climatological structure.

The results should be framed as spatial associations rather than "drivers" or causal influences. For example, “higher precipitation results in shorter response times” should be revised to “higher precipitation is associated with shorter predicted response times.” The interpretation of permutation importance should also note that importance is assigned to manually selected representatives of correlated clusters and therefore cannot be attributed uniquely to an individual variable. Partial-dependence plots can also be misleading when predictors are strongly correlated because they may average predictions over combinations that are rare or absent in the data.

A baseline comparison using precipitation, aridity, or climate region alone together with residual maps or a leave-one-region-out test would show whether the RF adds information beyond the dominant climatological gradient. Reporting uncertainty across spatial folds and the sensitivity to the blocking and clustering choices would further support the importance rankings.

The RF does not explain the acceleration. 4.3 states that attempts to model the change in response time had insufficient predictive skill. Because the temporal change is the manuscript's central question, this should be stated prominently in the Results and Discussion rather than only in the Limitations. The manuscript should conclude explicitly that the RF characterizes the static spatial pattern of response time but does not identify the mechanisms controlling its temporal change.

Cold-season influence despite restricting SSI to JJA. Although the analysis uses only JJA soil moisture to minimize frozen-soil and snow effects, testing SPI lags up to 300 days explicitly includes precipitation from the preceding autumn, winter, and spring. The long western response times may therefore reflect snow accumulation and melt, seasonal soil-water carryover, or re-emergence of earlier anomalies rather than slow summertime propagation. I recommend testing sensitivity to a shorter lag range, such as 0-90 days, and comparing snow-dominated and rain-dominated regions. Unless these influences can be separated, the metric should be described more cautiously as the summer soil-moisture response to antecedent precipitation rather than the velocity of the summertime hydrological cycle.

Drought-index construction. Several index choices require stronger justification or sensitivity testing. First, SSI is derived using a two-parameter gamma distribution, although soil moisture is bounded and may not be gamma-distributed across all climates and seasons. Please provide goodness-of-fit diagnostics and test an empirical or alternative formulation. Second, SPI-30 is selected partly because it produces substantially more identifiable non-zero peaks than SPI-90. Because accumulation scale directly affects both peak prominence and estimated response time, the authors should demonstrate that the main conclusions are robust to this choice or explicitly limit their interpretation to SPI-30. Finally, the analysis combines positive and negative anomalies even though the proposed mechanism relies on asymmetric wetting and drying dynamics; response times should therefore be compared separately for wet and dry anomalies, or this choice should be more clearly justified. Using a common climatology for both periods is reasonable for comparability, but the authors should explain the fixed-reference approach and justify extending the fitting period to 2023 when the response-time analysis ends in 2020.

Minor Comments:

Title: Remove the period at the end.

SPI-30 and SPI-90 statistics. The mean and median response times reported in Sect. 3.1 appear to be assigned to SPI-30 and SPI-90 in the opposite order from the Discussion and Fig. S1. Please verify and correct them.

Reporting precision. Consider rounding the reported grid-cell percentages to one decimal place. Two decimal places are unnecessary given the spatial dependence among grid cells and uncertainty in the response-time estimates.

Figure 6 panel labels. The Southwest panel is labeled "(b)" in the embedded figure text; it should be "(h)" per the caption.

Figure 7. In Figure 7 and the associated text, verify whether the Southwest peak is 234 or 243 days and remove the extra closing parenthesis in the caption.

Equation numbering. The text refers to "Equation 2" (RT = S/P) but no Equation 1 is presented.

Analysis period. Use the analysis period consistently throughout; the manuscript alternates between 1950-2020 and 1951-2020.

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Citation: https://doi.org/10.5194/egusphere-2026-2895-RC1

Matthew Walter Sabin, Nels R. Bjarke, and Ben Livneh

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Code and outputs for assessing summertime hydrological cycle acceleration through drought indices. Matthew Sabin, Ben Livneh, and Nels Bjarke https://doi.org/10.5281/zenodo.20277374

Matthew Walter Sabin, Nels R. Bjarke, and Ben Livneh

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Short summary

As the climate changes, the water cycle is expected intensify and accelerate. We introduce a metric to measure water cycle velocity and acceleration that tracks how quickly rainfall anomalies propagate into soil moisture anomalies. Despite expectations of acceleration across the United States from 1951–2020, we found no robust statistical speedup or slowdown. This suggests that climate change signals may not yet have manifested into this aspect of the water cycle.


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