We selected three hydro-climatically distinct watersheds in southwestern China to represent a spectrum of mountain hazard environments (Fig. 2; detailed physiographic characteristics are provided in Appendix B and Table B1). These three basins were purposefully selected to cover a diverse range of hydro-climatic conditions (semi-arid to humid) and geomorphic types (loess plateau to steep tectonic valleys), allowing for a robust comparative analysis of SMM drivers across contrasting mountain terrains.

Dali River Basin (DRB). Semi-Arid Erosion-Prone System. Located on the Chinese Loess Plateau (3906 km2), the DRB features steep loess terrain (avg. slope 17°) and highly erodible soils (silt > 60 %). The climate is semi-arid continental, with precipitation highly concentrated in summer storms (> 70 % from May to September), leading to persistent soil moisture deficits and severe erosion rates (Liu et al., 2023; Zhang et al., 2023).

Despite the large difference in basin area (ARB: 11 150 km2 vs. JJR: 48.6 km2), a scale-matching sensitivity analysis (Appendix H) confirms that the observed differences in soil moisture memory between basins reflect intrinsic hydrological and landscape characteristics rather than artifacts of spatial averaging or domain size.

We constructed a dataset comprising 12 static and dynamic covariates (Table 1) alongside daily soil moisture (SM) data (1 km resolution) for 2003–2022. These covariates were selected based on an extensive literature review of soil moisture drivers (Rahmati et al., 2024; Seneviratne et al., 2010), prioritizing variables that are (1) widely recognized as key controls on SMM (topography, soil properties, meteorology, vegetation), (2) frequently used in prior multi-scale SMM studies, and (3) available at consistent spatial and temporal resolution with high reliability across the study region.

Soil Moisture Dataset. We utilized the all-weather 1 km daily soil moisture (SM) product developed by Song et al. (2022). This dataset employs a machine learning-based spatiotemporal reconstruction framework to generate seamless high-resolution estimates by downscaling and fusing coarse-resolution passive microwave observations (AMSR-E/2) with high-resolution optical/thermal land surface parameters (MODIS) and meteorological forcing (ERA5-Land), using a random forest algorithm trained on extensive ground observations.

Static variables (e.g., soil texture, TWI) represent basin physiography, while dynamic variables (e.g., precipitation, NDVI) capture climate-vegetation interactions. All data were resampled to a uniform 1 km grid. Preprocessing included linear interpolation for short gaps (≤ 3 d), outlier removal, and stationarity checks using the Augmented Dickey-Fuller test (details in Appendix C).

To characterize the multi-scale persistence of soil moisture, we employed two complementary spectral techniques that quantify long-range temporal correlations. Power Spectrum Analysis (PSA) identifies memory strength across frequency domains, while Detrended Fluctuation Analysis (DFA-2) detects the timescales over which memory persists. Both methods are robust to non-stationarity and can distinguish genuine long-term correlations from short-term noise or trends (Kantelhardt et al., 2006; Zhu et al., 2010).

Given the 20-year record length (2003–2022), statistical limitations exist for resolving low-frequency dynamics. Following established guidelines requiring N≥ 3T for robust spectral estimation (Ghannam et al., 2016; Percival and Walden, 1993), we distinguish between two regimes: 1.

Reliable Spectral Window (T≤ 7 years). Timescales up to T=N/3≈ 6.7 years (rounded to 7 years) can be reliably estimated, as our record contains at least three complete cycles.

Power Spectral Analysis (PSA). PSA decomposes a time series into its constituent frequencies, estimating how variance (power) is distributed across them. The relationship follows a power law: S(f)∼fβ, where S(f) is the spectral power at frequency f, and β is the spectral exponent. A higher β indicates that low-frequency (long-term) variations dominate the signal, implying stronger soil moisture memory. In this study, β values within the Reliable Spectral Window (seasonal to ∼ 7 years) quantify interannual persistence, while those in the Low-Frequency Background (> 7 years) indicate quasi-static mean-state stability.

We defined the “persistence horizon” as the range of timescales over which α≥ 0.9, indicating strong long-range memory approaching scale-invariant behavior. In this study, persistence horizon is used as the operational measure of memory length, specifically denoting the temporal range where significant long-range memory (α≥ 0.9) is maintained. This threshold follows established criteria in hydroclimatic memory studies (Zhang et al., 2025; Zhu et al., 2010). Physically, it represents the temporal window over which antecedent moisture conditions influence the current state – a critical parameter for hazard preconditioning. Persistence horizons extending beyond 7 years reflect slow-changing baseline conditions rather than event-scale memory. Detailed formulations and significance testing are provided in Appendix A.

For clarity, key terms are defined as follows:

Soil Moisture Memory (SMM). The tendency of soil moisture anomalies to persist over time following wetting or drying events. SMM is quantified by the spectral exponent β (memory strength) and fluctuation exponent α (memory timescale).

To determine the hierarchical importance of environmental predictors, we utilized the Boruta feature selection algorithm wrapped around a Random Forest regressor. Boruta is an all-relevant feature selection method that creates randomized “shadow” copies of original predictors (permuted versions with no real relationship to the target) and iteratively compares the importance of each real predictor against the best-performing shadow variable. Predictors that consistently outperform shadow variables are retained as relevant, while others are rejected (Kursa et al., 2010). Boruta was selected because it (1) captures non-linear relationships inherent in soil–vegetation–atmosphere systems, (2) handles collinearity among predictors without requiring prior variable removal, and (3) provides statistically validated importance rankings by comparing against a null model.

Given that SMM is a temporal statistic derived from time series, while landscape attributes are spatially heterogeneous, we constructed a spatial attribution framework to link these dimensions, quantifying how driver importance shifts across different temporal aggregation windows (monthly to decadal). Specifically, the temporal memory metric for each pixel (e.g., spectral exponent β) serves as the spatial response variable, regressed against spatially distributed predictors: 1.

Static variables. Landscape properties constant over the study period (e.g., soil texture, slope, TWI).

This framework quantifies how spatial heterogeneity in static and dynamic boundary conditions correlates with temporal persistence of soil moisture. Feature importance was validated using spatial block cross-validation to account for spatial autocorrelation (details in Appendix D).

The “Space-for-Time” framework leverages spatial heterogeneity across the three watersheds as a substitute for long-term temporal observations at a single site, an approach widely adopted in ecological and hydrological studies (Pickett, 1989). However, this approach identifies statistical associations rather than causal relationships. The Boruta-RF algorithm ranks predictors by their capacity to explain spatial variance in temporal memory metrics, but cannot distinguish between direct causal drivers, proxy variables, or feedback responses. Therefore, associations should be interpreted as indicative of likely controls rather than confirmed causal mechanisms (McColl et al., 2017; Seneviratne et al., 2010).

Additionally, physical collinearity inherent in mountain landscapes – often described by the catena concept of co-evolved soil-topography relationships (i.e., steep upper slopes have thin, sandy, fast-draining soils while gentle lower slopes accumulate thick, clay-rich, water-retaining soils; Anderson, 2005) – means that high importance scores for both Slope and Clay content (Sect. 3.3) likely reflect coupled landscape structure rather than independent effects.

To address these limitations, we (1) interpret associations through established hydrological theory (e.g., linear reservoir models; Sect. 4.1) to provide mechanistic plausibility, and (2) conduct partial correlation analysis controlling for topographic variables (Appendix G) to assess robustness against landscape confounding. This framework generates testable hypotheses about SMM predictors rather than confirming causal mechanisms, which would require controlled experiments beyond the scope of this study.

Power spectrum analysis revealed scale-dependent characteristics of soil moisture memory (SMM) across the three basins (Fig. 3). Quantitative interpretations focus on the Reliable Spectral Window (≤ 7 years), while longer timescales reflect quasi-stationary moisture regimes.

In Fig. 3, the x-axis represents frequency (cycles per year, logarithmic scale) and the y-axis represents spectral power S(f) (log-transformed). The spectral exponent β corresponds to the negative slope of the fitted line: higher β indicates variance concentrated at low frequencies, implying strong memory, while lower β indicates high-frequency dominance characteristic of weak memory. Shaded bands represent 95 % confidence intervals. Three key patterns emerge: (1) intra-annual contrasts between wet and dry seasons, (2) systematic decline in memory strength with increasing timescale, and (3) inter-basin differences reflecting contrasting hydro-climatic regimes. For seasonal classification, the rainy and dry seasons are defined based on local precipitation regimes: the Dali River Basin (DRB) rainy season spans July to September (dry season: October–June), while both the Anning River Basin (ARB) and Jiangjia Ravine (JJR) share a rainy season from May to October (dry season: November–April).

Intra-annual patterns: Analysis compared individual months with integrated seasonal periods (Fig. 3a-1, b-1, and c-1) (Detailed definitions and analytical methods are provided in Appendix D). This revealed asymmetric patterns: memory during individual rainy season months was consistently weaker than the integrated rainy season, whereas individual dry season months showed stronger memory than the dry season aggregate. For example, in the ARB, the integrated rainy season yielded β = 2.190 ± 0.101, while individual rainy months averaged β = 2.179 ± 0.095; conversely, individual dry season months (β = 2.698 ± 0.121) exceeded the integrated dry season (β = 1.643 ± 0.051).

Interannual patterns: SMM declined progressively at longer timescales. Within the reliable window, the hierarchical trend follows β(1-year) > β(5-year). Beyond 7 years, metrics stabilized, capturing the basin's static storage baseline (Fig. 3a-2, b-2, and c-2).

In the Dali River Basin (DRB), full rainy season memory (β = 2.392 ± 0.105) was significantly stronger than the initial month (June, β = 1.889 ± 0.098), indicating pronounced long-range persistence where cumulative monsoon rainfall progressively builds hydrological inertia (Rahmati et al., 2024). Conversely, integrated dry season memory (β = 1.028 ± 0.075) was weaker than October (β = 2.378 ± 0.112) (Fig. 3a-1), reflecting residual moisture persisting into early autumn before rapid depletion. At interannual scales, SMM declined from β = 1.355 ± 0.089 (1-year) to β = 1.000 ± 0.081 (20-year) (Fig. 3a-2), indicating limited carryover beyond a few years. For erosion hazards, antecedent moisture from preceding weeks to months – rather than years – is most relevant for modulating soil erodibility (Ran et al., 2012). We explain the rationale for selecting June and October in Appendix B.

In the Anning River Basin (ARB), integrated rainy season memory (β = 2.190 ± 0.101) was slightly stronger than May (β = 2.179 ± 0.095), peaking in October (β = 2.698 ± 0.121) (Fig. 3b-1). High β values reflect strong persistence driven by accumulated monsoon precipitation and the buffering capacity of deep forest soils (Bogaard and Greco, 2018). At interannual scales, the ARB exhibited the highest SMM among basins (mean β = 1.468 ± 0.084), decreasing from 1.964 ± 0.096 (1-year) to 1.265 ± 0.074 (20-year) (Fig. 3b-2). This sustained multi-year memory suggests wet years can progressively elevate baseline pore pressures, potentially lowering landslide triggering thresholds (Cui et al., 2025).

In Jiangjia Ravine (JJR), SMM peaked during the rainy season (May: β = 2.492 ± 0.114; full rainy season: β = 2.629 ± 0.118) and weakened during the dry season (November: β = 1.733 ± 0.085; full dry season: β = 1.404 ± 0.076) (Fig. 3c-1). This strong seasonal contrast reflects rapid hydrological response: frequent monsoon rainfall maintains elevated moisture and strong autocorrelation, while steep terrain promotes quick drainage during dry periods. At interannual scales, JJR exhibited intermediate SMM – stronger than DRB but weaker than ARB – with β decreasing from 1.654 ± 0.090 (1-year) to 1.191 ± 0.073 (20-year) (Fig. 3c-2). For debris flow hazards, antecedent wetness from preceding days to weeks within the rainy season is critical (Wei et al., 2025), whereas inter-annual carryover is less pronounced than in the forest-buffered ARB.

In summary, SMM is consistently stronger in rainy seasons than in individual months and weakens progressively toward a climate-driven baseline. The ARB shows the strongest overall memory, highlighting how basin characteristics shape persistence beyond short-term weather effects – with clear relevance for multi-scale hazard prediction.

Building on the PSA results, we quantified persistence horizons using DFA-2. While β characterizes overall memory strength, the fluctuation exponent α identifies specific timescales where memory is strongest (α≥ 0.9). All reported α values in this range were statistically significant (p < 0.01) based on phase-randomization surrogate testing (see Appendix A).

Figure 4 presents DFA-2 results organized by basin (rows: a = DRB, b = ARB, c = JJR) and timescale (columns: left = seasonal, right = inter-annual). Solid lines show how α varies with window size s; labeled time windows (e.g., “236–728 d”) indicate persistence horizons where α≥ 0.9.

In the Dali River Basin (DRB), persistence was short during the early rainy season (24–30 d in June) but extended substantially through the full rainy season (41–122 d); October exhibited negligible persistence, with α falling below the 0.9 threshold (Fig. 4a-1). This indicates rapid decay of moisture anomalies due to intense evaporative drying following monsoon withdrawal. During the dry season, persistence increased to 61–95 d, reflecting conditions where moisture decay is governed primarily by intrinsic drainage properties rather than evaporative demand (Seneviratne et al., 2010). At interannual scales, persistence horizons increased from 31–73 d (1-year) to 174–429 d (20-year), peaking between 10 and 15 years (Fig. 4a-2). This pattern is consistent with deeper-layer memory and reduced influence of high-frequency atmospheric forcing at longer timescales (Rahmati et al., 2024).

The Anning River Basin (ARB) exhibited the longest persistence horizons across all temporal scales (p < 0.05). At the monthly scale, persistence ranged from 17–31 d in May to 25–31 d in October, increasing markedly at the seasonal scale – reaching 37–184 d during the rainy season and 47–76 d during the dry season (Fig. 4b-1). At interannual scales, persistence horizons rose sharply from 40–71 d (1-year) to 236–728 d (20-year) (Fig. 4b-2). This extended memory implies that the basin's soil moisture state integrates cumulative effects of multi-year climate variability rather than responding solely to individual storm events. Consequently, a sequence of wet years progressively saturates deep soil layers, elevating background pore pressures – a critical factor for landslide susceptibility assessment.

In Jiangjia Ravine (JJR), rainy season persistence was the shortest among the three basins (18–31 d in May; 33–91 d when aggregated), indicating rapid response to precipitation inputs (Fig. 4c-1). This 2–4 week persistence horizon defines the critical “look-back window” for debris flow early warning (Pan et al., 2018; Wicki et al., 2020). In contrast, dry season persistence (60–125 d) was longer, reflecting reduced evaporative demand when rainfall ceases. At interannual scales, persistence horizons remained stable, ranging from 78–171 d (1-year) to 129–367 d (20-year) (Fig. 4c-2), suggesting that intrinsic drainage characteristics impose a consistent upper bound on moisture retention regardless of climatic variability.

Persistence horizons vary markedly across basins: longest in ARB (months to years), shortest in JJR during the rainy season (2–4 weeks), and intermediate in DRB. These time windows define practical “look-back” periods for anticipating different mountain hazards, from short-term debris flows to longer-term landslide preconditioning.

The Boruta Random Forest Algorithm identified statistical associations between environmental variables and SMM across multiple timescales (Fig. 5). Variables were classified as “confirmed” (Z-score significantly exceeds shadow maximum, p < 0.01), “tentative” (borderline significance), or “rejected.” Bootstrap resampling (n = 1000) confirmed that top predictors at each scale maintained significance across > 95 % of iterations.

Monthly to seasonal scales: June – the onset of the rainy season – showed no distinct dominant predictor. However, when the entire rainy season (June–September) was considered, relative humidity (rhu), NDVI, actual evaporation (AE), and 2 m air temperature (T2m) emerged as the strongest predictors of SMM spatial patterns. During the dry season (October-May), NDVI, AE, rhu, and T2m maintained strong associations with SMM, whereas precipitation and wind speed exhibited limited predictive power, reflecting the transition from moisture-limited to energy-limited evapotranspiration regimes.

Annual to decadal scales: The pattern of associations underwent progressive transition. The cumulative importance of atmospheric variables (Precipitation, Wind Speed, T2m, rhu) declined from 62 % at the monthly scale to 34 % at the 10-year scale, while soil texture variables (Sand, Silt, Clay) increased from 12 % to 38 % (Fig. 5). At annual scales, precipitation and wind speed declined in importance as temporal averaging smoothed their high-frequency variability. By the 5-year scale, these climatic variables were excluded from significant predictors, leaving NDVI, rhu, AE, and T2m as dominant variables. Over decadal timescales (10–20 years), associations of NDVI, rhu, and T2m with SMM further intensified.

Static factors: The relative importance of static factors also varied with timescale (Fig. 5b). During June and the rainy season, bulk density (ρb) and aspect (Asp) showed the strongest associations. At annual scales, topographic associations (TWI) strengthened. However, over longer timescales, pedological factors became increasingly prominent.

Scale-transition threshold: Quantitative analysis revealed a distinct structural break at the 5-year scale (Table 2). At the 1-year scale, TWI showed the strongest association (28.7 %), consistent with topography-driven lateral water redistribution. At the 5-year scale, TWI importance declined (to 13.5 %), with the hierarchy shifting to Soil Texture and Slope (∼ 19 %). This threshold reflects a fundamental shift from event-scale hydraulic connectivity (“Fast-Response Regime”) to long-term pedological storage control (“Background-Storage Regime”) (Blöschl and Sivapalan, 1995; Western et al., 2004).

Methodological considerations: These associations do not establish causal relationships. The Boruta-RF algorithm identifies variables with strong predictive power but cannot distinguish between direct causal drivers, proxy variables, or bidirectional feedbacks. For instance, the strong NDVI–SMM association at decadal scales may reflect vegetation's influence on soil hydraulic properties, soil moisture's constraint on vegetation growth, or both. Mechanistic interpretation is discussed in Sect. 4.1. Partial correlation analysis controlling for topographic variables (Appendix G) indicated that soil texture maintained significant associations with decadal-scale SMM (partial r = 0.43, p < 0.01) after accounting for slope and TWI, though effect size was reduced compared to raw correlation (r = 0.61), suggesting approximately 30 % of the apparent association may be attributable to topographic confounding.

Short-term memory is driven primarily by weather and vegetation factors, whereas beyond ∼ 5 years, soil texture and topography become dominant. This scale-dependent shift from dynamic to static control marks a fundamental transition in SMM mechanisms – essential for developing timescale-appropriate hazard models.

To address basin-specific memory characteristics relevant to mountain hazards, we synthesized SMM properties and dominant controls across the three watersheds. Key metrics – spectral exponent (β), DFA-2 predictive period, and the top three driving factors – at monthly, annual, and decadal scales are summarized in Table 3. Complete Boruta and Random Forest results for the ARB and JJR are provided in Appendix F (Figs. F1–F4).

This comparative synthesis revealed several key patterns. Among the three basins, the Anning River Basin (ARB) exhibited the strongest long-term memory and longest predictive periods across interannual to multi-year scales. Its drivers were dominated by climatic and vegetation variables (T2m, NDVI, rhu) even at multi-year scales, reflecting the profound influence of dense forest cover and stable mountain-valley climate on prolonging soil water residence time.

In contrast, the Jiangjia Ravine (JJR), characterized by steep slopes and high drainage density, showed the most rapid response to precipitation inputs and the shortest predictive periods during the rainy season. Topographic control (TWI) was dominant across almost all scales, underscoring the role of rapid hydrological redistribution in this debris-flow-prone catchment.

The Dali River Basin (DRB) presented an intermediate case in memory length but was distinctive in its driver dynamics: a clear scale-dependent transition from atmospheric variables (rhu) at monthly scales to static landscape properties (soil texture and topography) at multi-year scales. This transition reflects the basin's semi-arid loessal environment, where intrinsic soil water-holding capacity and terrain ultimately govern long-term moisture availability.

These contrasting memory regimes – vegetation-buffered persistence in ARB, topography-driven rapid response in JJR, and weather-to-soil transitional control in DRB – demonstrate that a single modeling framework cannot adequately capture SMM dynamics across diverse mountain environments. This heterogeneity underscores the necessity of basin-specific parameterization in soil moisture-based hazard early warning systems.

Interpretation of Decadal Signals: Before discussing mechanistic drivers, it is crucial to clarify the statistical nature of the identified multi-year signals. Given the 20-year record length, the persistence horizons detected at the decadal scale (> 7 years) should not be interpreted as verifiable oscillatory cycles, which would require multiple realizations. Instead, these signals reflect a stable baseline state – a low-frequency background governed by persistent climatic trends and the basin's intrinsic buffering capacity. Therefore, the term “Decadal Memory” used hereafter refers to the system's inertia in responding to these slow-varying boundary conditions, not to a self-sustaining oscillation.

With this clarification, the identified transition in driver dominance at approximately the 5-year scale marks a fundamental mechanistic shift: from event-driven hydraulic responses to long-term equilibrium storage governed by landscape properties.

Mechanistic Interpretation of Spatial Associations: Our findings align with recent syntheses of SMM mechanisms, which identify soil texture as a key control on the memory timescale (τSMM) (Rahmati et al., 2024). Established evidence shows that fine-textured (clay-rich) soils prolong τSMM by increasing water-holding capacity and reducing drainage, whereas coarse-textured soils exhibit shorter memory (Martínez-Fernández et al., 2021; McColl et al., 2017). Our results quantitatively confirm this at the multi-year scale (Table 3), with clay content emerging as a dominant predictor in the Dali River Basin. This agreement underscores the role of soil hydraulic properties (e.g., reduced saturated hydraulic conductivity, Ksat) in acting as a low-pass filter, as conceptualized in linear reservoir theory (Salvucci and Entekhabi, 1994).

Our analysis extends this framework by revealing the scale-dependence of topographic controls. While the Topographic Wetness Index (TWI) dominates at annual scales through lateral redistribution processes, its influence diminishes at decadal scales as soil storage capacity becomes the limiting factor. Although topography's influence on SMM variability is recognized (e.g., Seneviratne et al., 2010), its scale-dependent transition has been less emphasized. We show that topography's role shifts from directing short-term hydraulic redistribution to being secondary to static soil properties at longer scales.

Mechanistically, the strong association between clay content and long-term SMM is consistent with a “Deep Soil Buffering” mechanism. High clay content reduces hydraulic diffusivity and Ksat, increasing the characteristic response time of the soil column (Van Genuchten, 1980). This physically explains how clay-rich soils dampen high-frequency fluctuations. Similarly, TWI dominance reflects sustained lateral recharge in convergent valleys, which decouples local storage from vertical evaporation demand (Western et al., 2004).

Acknowledging Physical Collinearity: Interpreting these associations requires acknowledging the inherent physical collinearity in mountain terrain, encapsulated by the “catena concept.” Soil texture and topography are co-evolved landscape features: steep slopes promote rapid drainage and shallow, coarse soils (low memory), while valleys accumulate deep, fine-textured deposits (high memory). Thus, the high importance of both slope and clay (Fig. 6) likely reflects this coupled landscape structure. Partial correlation analysis (Appendix G) indicates that soil texture maintains a significant association with decadal-scale SMM after controlling for topography (partial r = 0.43, p < 0.01). However, approximately 30 % of the raw correlation may stem from landscape collinearity. This suggests pedological effects are not entirely attributable to topographic confounding.

The Dual Role of Vegetation Across Timescales: Our results reveal that vegetation exerts contrasting, scale-dependent influences on SMM, consistent with ecohydrological theory (Rodriguez-Iturbe et al., 1999).

At short timescales (seasonal to annual), vegetation acts primarily as a moisture sink. Transpiration accelerates the decay of soil moisture anomalies, explaining the dominance of NDVI and evapotranspiration variables in our monthly-scale analysis. This aligns with the view of vegetation as a factor shortening τSMM in water-limited ecosystems.

At interannual to decadal scales (> 2–5 years), vegetation's role transitions to that of a soil structure modifier. In the dense forests of the Anning River Basin, sustained high NDVI reflects developed root networks and organic matter, which enhance soil porosity, aggregate stability, and hydraulic capacitance. These improvements increase the soil's moisture retention capacity, thereby extending the memory timescale.

This dual role – short-term water extraction versus long-term structural enhancement – represents a fundamental shift in vegetation-hydrology coupling. However, we caution against interpreting the strong statistical link between NDVI and decadal-scale SMM as unidirectional causality. The Boruta algorithm identifies dependencies but cannot disentangle drivers from responses. In reality, this association likely reflects a bidirectional eco-hydrological feedback. Vegetation improves soil structure (as a driver), while sustained soil moisture is required to maintain high biomass (as a response). Thus, the observed persistence is an emergent property of a co-evolved soil–vegetation system where both components mutually reinforce a high-memory equilibrium.

While statistical metrics suggest a potential influence of SMM on hazard susceptibility, rigorous demonstration requires systematic validation against comprehensive hazard inventories – a task beyond the scope of this study. Here, we present a single-event case study as a conceptual illustration, acknowledging that one event cannot establish general causality or predictive skill. We focus on the Jiangjia Ravine (JJR), a well-documented debris-flow-prone catchment where antecedent wetness is recognized as a key preconditioning factor. This example aligns with broader literature on SMM's role in preconditioning extreme events (Rahmati et al., 2024), but remains illustrative rather than predictive.

To conceptualize this physical coupling, Fig. 7 illustrates the multi-scale interaction between SMM and slope stability. At the slope scale (Fig. 7a), failure is instantaneous, governed by pore-pressure thresholds. In contrast, SMM operates at the basin scale (Fig. 7b), defining a slowly varying “background loading” state. The key mechanism (Fig. 7c) is that elevated antecedent soil moisture modulates the effective rainfall threshold (Icrit) required for triggering localized failures, thereby increasing hazard probability.

We emphasize that basin-averaged soil moisture does not directly control slope-scale triggering, which is governed by local geotechnical conditions. Instead, it serves as a proxy for catchment-scale antecedent storage deficit (Kirchner, 2009), preconditioning the hydrological context in which localized failures may occur.

Applying this framework to a real-world event, Fig. 8 reconstructs the soil moisture trajectory preceding the 10 July 2007 debris flow. Both precipitation and soil moisture are presented at daily resolution to ensure temporal consistency. The watershed experienced a distinct “pre-wetting” phase throughout June, with basin-scale soil moisture maintaining elevated levels for over 10 d. This duration falls within the reliable rainy-season persistence horizon identified in our DFA-2 analysis (18–31 d; Fig. 4c-1), suggesting sufficient hydrological inertia to carry antecedent wetness across the inter-storm period. When the 29 mm rainfall trigger occurred on July 10, it acted on compromised storage capacity rather than a dry baseline. We hypothesize that persistent June wetness contributed to lowering the effective rainfall threshold for instability. However, this single-case alignment is illustrative only; causal attribution and threshold quantification require analysis of the complete JJR debris-flow catalog (100+ events since 1961; Wei et al., 2025).

This interpretation is supported by the broader persistence characteristics observed in the JJR (Fig. 4c), though basin-averaged metrics smooth out slope-scale heterogeneity and cannot substitute for detailed local measurements or failure-plane modeling.

We caution that this example illustrates the “Temporal Bridge” hypothesis but does not demonstrate predictive capability. To rigorously evaluate SMM's predictive power for debris flows and landslides, future work should include: (1) Threshold analysis using the complete JJR inventory to test whether antecedent SMM significantly lowers Icrit across multiple events; (2) Statistical classification (e.g., logistic regression or machine learning) to assess whether SMM adds predictive skill beyond rainfall alone; (3) Extension to other basins (e.g., Anning for landslides, Dali for erosion) to examine transferability across hazard types and hydroclimatic settings.

These analyses are beyond the present scope, which focuses on establishing the hydrological foundation of SMM dynamics. Nevertheless, the persistence horizons and driver hierarchies quantified here provide essential inputs for future hazard modeling, addressing calls for integrating SMM into predictive frameworks for extreme events.

While this study provides a novel framework for understanding SMM, two limitations regarding spatiotemporal scales must be acknowledged.

First, spatial scale mismatch. An inherent discrepancy exists between our 1 km gridded soil moisture data and the localized shear zones where slope failures initiate (10¹–10² m scale). In complex terrain such as the Jiangjia Ravine, spatial averaging across a 1 km pixel acts as a low-pass filter, smoothing rapid, localized drainage events. According to the spatial variance scaling function (Crow et al., 2012), aggregating from point-scale to 1 km resolution can reduce signal variance by approximately 63 % (assuming a correlation length λ≈ 500 m). Consequently, the persistence horizons calculated here (e.g., 78–171 d for JJR) likely overestimate point-scale geotechnical reality.

However, this “inflated” memory is precisely what makes the 1 km metric valuable: rather than pinpointing specific gully failures, it quantifies the average antecedent condition of the entire hillslope system. This basin-scale metric serves as a proxy for “Catchment Storage Deficit” (Kirchner, 2009), distinguishing slowly evolving background criticality – how close the basin is to saturation excess – from rapid, slope-scale triggering thresholds governed by local geotechnical defects.

A related concern is the disparity in basin size (JJR: ∼ 49 km2 vs. ARB: ∼ 11 150 km2), which raises the question: is the stronger memory observed in ARB merely an artifact of spatial averaging over a larger domain? To address this, we conducted a scale-matching sensitivity analysis (Appendix H), randomly sampling 1000 sub-regions from the ARB, each matching JJR's size (49 pixels). Results showed that these small ARB sub-regions still exhibit significantly stronger memory (mean β≈ 1.48) than the JJR (β≈ 1.39), confirming that inter-basin differences reflect genuine hydrological contrasts (e.g., deeper soils, denser vegetation) rather than scaling artifacts. In summary, the scale-matching sensitivity analysis (Appendix H) confirmed that the stronger memory observed in the ARB reflects genuine hydrological contrasts rather than basin size artifacts.

Second, temporal duration constraints. The 20-year dataset (2003–2022) imposes statistical constraints on decadal-scale memory estimation. Robust spectral estimation typically requires record length (N) significantly exceeding the period of interest (T), with N≥ 3T as a common threshold. Therefore, while our analysis identifies trends extending to 20 years, quantitative persistence horizons beyond approximately 7 years (N/3) must be interpreted with caution.

These long-term signals likely capture a hybrid of intrinsic deep-soil buffering and external low-frequency climatic trends (e.g., secular shifts in precipitation regimes). Although mathematically indistinguishable in a short record, both mechanisms contribute to background preconditioning for hazards. Future studies utilizing extended satellite records (e.g., ESA-CCI, SMAP) will be essential to validate these long-term memory estimates.

Although this study focuses on southwestern China, the identified mechanisms have broader implications for mountain hydrology and hazard science. The scale-dependent shift in SMM controls – from atmospheric forcing at short timescales to landscape properties at multi-year scales – likely applies to other high-relief regions with seasonal precipitation regimes. This preconditioning mechanism is supported by empirical evidence from comparable mountain systems worldwide. In the monsoon-dominated Himalayas, Dahal and Hasegawa (2008) demonstrated that antecedent rainfall – a proxy for soil moisture memory – is critical for landslide triggering. Similarly, research in the European Alps (Wicki et al., 2020) and Italian Apennines (Brocca et al., 2012; Ponziani et al., 2012) has linked landslide susceptibility to antecedent soil wetness, confirming that soil moisture persistence critically influences slope stability. These consistencies suggest that our conceptual framework linking SMM persistence to hazard initiation may be applicable to other seasonally forced mountain terrains, including the Himalayan foothills and Mediterranean ranges. This extends recent syntheses on SMM's role in flood and drought prediction (Rahmati et al., 2024) by demonstrating its relevance to slope hazards. Nevertheless, direct transferability of specific parameters (e.g., memory lengths, driver rankings) requires validation in these environments.