the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 24 Sep 2026
Hydrological Memory Regulates River Basin Recovery from Climate Extremes: Evidence from China’s Major River Basins
Abstract. Hydrological memory from climate extremes depends not only on disturbance magnitude but also on the persistence of antecedent basin storage. This study developed a Hydrological Memory Framework (HMF) to quantify basin-scale hydrological memory and assess its influence on resilience across eight major river basins in China during 1981–2025. Hydrological memory was estimated using the Catchment Forgetting Curve (CFC), while drought and flood recovery were evaluated from standardized hydrological anomalies. Principal Component Analysis, Random Forest regression, generalized additive models, and mixed-effects modelling were used to identify environmental controls and quantify the memory–resilience relationship. Hydrological memory varied markedly among basins, from less than 3 years in the humid Yangtze and Pearl basins to approximately 5–6 years in the arid Heihe and Tarim basins. Recovery time increased strongly with memory duration (R² = 0.81, p < 0.001), and drought recovery was generally two to three times longer than flood recovery. Mixed-effects modelling confirmed hydrological memory as the dominant predictor of recovery time (β = 0.68, p < 0.001), with the full model explaining 84% of the observed variability. Random Forest analysis identified groundwater storage (28.4%), climatic aridity (22.7%), soil moisture persistence (17.9%), and basin elevation (12.6%) as the principal controls on memory. The results show that antecedent storage exerts a measurable control on post-extreme recovery and basin resilience. The HMF provides a process-based basis for identifying vulnerable basins and improving climate-adaptive water resources management.
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Status: open (until 05 Nov 2026)
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RC1: 'Comment on egusphere-2026-5097', Anonymous Referee #1, 06 Oct 2026
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AC1: 'Reply on RC1', Muhammad Touseef, 06 Oct 2026
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Response 1:
We thank the reviewer for this important comment. We agree that antecedent runoff may contain hydrological-state information that is not fully represented by antecedent humidity-index anomalies. To address this, we revised the model to an autoregressive distributed-lag formulation that includes (q'_{t-1}) together with current and lagged humidity anomalies. This allows us to separate persistence inherited from the previous runoff state from the climatic-memory signal represented by the lag coefficients. The Catchment Forgetting Curve is now derived from the conditional climatic-lag coefficients, and the revised model is compared with the original formulation using model fit, information criteria, prediction error, and residual diagnostics. The Methods section has been updated accordingly, and the interpretation of the CFC has been clarified as the persistence of antecedent climatic forcing after accounting for autoregressive hydrological persistence.
Response 2:
We thank the reviewer for this important comment. We agree that using the humidity index \(H=P/PET\) imposes a predefined relationship between precipitation and potential evapotranspiration and does not allow their separate effects on runoff to be identified. Our rationale for using \(H\) was to provide a physically interpretable measure of water supply relative to atmospheric demand across basins with contrasting climates. To address this concern, we also tested an alternative formulation in which precipitation and potential evapotranspiration were included separately as lagged predictors, together with the autoregressive runoff term. The two formulations were compared using model fit, predictive performance, and residual diagnostics. The Methods section has been revised accordingly, and the humidity index is now interpreted explicitly as an integrated hydroclimatic forcing metric rather than as a substitute for the independent effects of precipitation and potential evapotranspiration.
Response 3:We thank the reviewer for this important comment. We agree that defining the forgetting timescale solely from a fixed cumulative threshold may not provide an objective basis for lag selection. To strengthen the analysis, we revised the lag-selection procedure by comparing candidate models across a range of lag lengths using information criteria (AIC and BIC), predictive cross-validation, and the statistical relevance of lagged terms. The preferred lag structure was selected from the model that provided the best balance between goodness of fit and parsimony, while residual diagnostics were used to confirm that no substantial temporal structure remained unexplained. The 90% cumulative threshold is now used only to summarize the effective memory timescale from the selected lag structure rather than to determine model order itself. We also evaluated sensitivity using 80%, 90%, and 95% cumulative thresholds to assess the robustness of the estimated Catchment Forgetting Curve timescale. The Methods section has been revised accordingly to clarify the distinction between objective lag selection and threshold-based interpretation of memory duration.Response 4:We thank the reviewer for this important observation. We agree that the individual lag coefficients are not expected to decrease monotonically with increasing lag because delayed groundwater contributions, storage thresholds, snowmelt, regulation, and other processes can generate non-monotonic responses. We have therefore clarified that the Catchment Forgetting Curve does not assume monotonic decay of the raw \(\beta_k\) coefficients. Instead, the cumulative curve is constructed from the normalized absolute contribution of statistically supported lag coefficients, so that it represents the cumulative fraction of total antecedent climatic influence accounted for through time rather than a strictly monotonic physical response function. To demonstrate this explicitly, we now present the basin-specific lag-coefficient patterns with uncertainty intervals and discuss cases where delayed or secondary peaks occur. We also evaluated the robustness of the derived memory timescale using alternative lag selections and cumulative thresholds. The manuscript has been revised to distinguish clearly between the potentially non-monotonic lag-response structure and the cumulative memory metric used to summarize the duration of antecedent climatic influence.Response 5:We thank the reviewer for emphasizing this important point. We agree that the reliability of the Catchment Forgetting Curve depends directly on the statistical performance of the underlying lag-regression model. We have therefore expanded the model evaluation to report goodness-of-fit statistics, confidence intervals for regression coefficients, significance of lagged terms, and residual diagnostics for each basin. In addition, out-of-sample predictive performance was assessed using cross-validation to evaluate whether the selected lag structure generalizes beyond the calibration period. Residual autocorrelation, heteroscedasticity, and normality were also examined to ensure that key regression assumptions were not violated. These results are now summarized in the revised manuscript and supplementary material, allowing the robustness of the inferred forgetting curves to be assessed directly. The interpretation of hydrological memory has also been revised to reflect model uncertainty, particularly where lag coefficients are weakly constrained.Citation: https://doi.org/10.5194/egusphere-2026-5097-AC1
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AC1: 'Reply on RC1', Muhammad Touseef, 06 Oct 2026
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The derivation of the “catchment forgetting curve” based on the lag-regression model described in Eq. (6) is questionable and requires stronger theoretical and statistical justification.
Eq. (6) relates the annual runoff anomaly solely to the contemporaneous and antecedent anomalies of the humidity index, defined as the ratio of precipitation to potential evapotranspiration (PET). However, runoff in year t may depend not only on Ht and its antecedent values, but also strongly on antecedent hydrological states. In particular, qt-1 may contain important information on catchment storage and hydrological memory that cannot necessarily be represented by antecedent H alone. The omission of autoregressive runoff terms therefore requires justification. The authors should examine whether an autoregressive or distributed-lag formulation provides a more appropriate representation of catchment memory.
The formulation based on (H=P/PET) imposes a particular relationship between runoff, precipitation, and PET before the regression is performed. Consequently, the separate effects of precipitation and PET cannot be independently identified by this model. The authors should provide a physical justification for representing climatic forcing exclusively through H, rather than considering precipitation and PET separately or testing alternative model formulations.
The procedure used to determine the lag length, and hence the timescale of the “catchment forgetting curve,” appears somewhat arbitrary. The manuscript seems to determine the model order according to a fixed cumulative percentage (e.g., 90%), but this does not ensure that the included lagged predictors are statistically meaningful or that the selected model is optimal. A more objective model-selection procedure should be considered, for example using AIC/BIC, cross-validation, statistical significance of lagged terms, or other established lag-selection methods. The sensitivity of the estimated forgetting timescale to the selected threshold should also be evaluated.
The construction of the forgetting curve appears to implicitly assume that the absolute magnitude of the lag-regression coefficients decreases progressively with increasing lag. However, there is no theoretical or statistical guarantee that beta_k will decrease monotonically with lag k. Catchment responses may exhibit non-monotonic lag structures because of seasonality, delayed groundwater contributions, storage thresholds, and other hydrological processes. Therefore, simply accumulating regression coefficients sequentially according to lag order may not necessarily provide a robust measure of hydrological memory. The authors need demonstrate the actual lag-coefficient patterns and justify why the proposed cumulative formulation can reasonably be interpreted as a “forgetting curve.”
The lag-regression model is the basis of this study, yet its performance and robustness are not reported in the paper. This is important because the estimated forgetting curve and all subsequent analyses depend directly on the reliability of this model. Model performance statistics, uncertainty in the regression coefficients, statistical significance of the lagged terms, residual diagnostics, and preferably out-of-sample validation should be provided. Without such information, it is difficult to assess whether the derived forgetting curves represent meaningful catchment memory or are partly artifacts of the adopted regression formulation.