A total of 2 553 834 rainfall–runoff events occurring between 1950 and 2020 across 6603 catchments have been identified through the simulation conducted with a conceptual hydrological model. The mean value of each connectivity indicator across all events is determined, and its spatial pattern of the multi-year average is illustrated in Fig. 3. Given the uneven spatial distribution of catchments across regions and climate zones, median values are adopted for group-level comparisons to mitigate the influence of unequal sample sizes and outliers. For the runoff coefficient (Fig. 3a–c), the dry climates are found to exhibit the lowest value, with a median of 0.15, indicating minimal loss in this hydrological transformation process. In contrast, the wet and snow climate zones show notably higher median values of 0.25 and 0.33, respectively, indicating a lower loss in the transformation process. It is also interesting that the highest values are found in western North America (WNA) and northwestern North America (NWN), with a median higher than 0.3, while the lowest values are found in eastern Australia (EAU), northeastern South America (NES), and southern Australia (SAU), with a median lower than 0.15.

However, in terms of the runoff intensity as shown in Fig. 3d–f, the highest value can be found in the dry climate zones, with a median of 11.3 mmd-1, signifying a rapid transformation rate from precipitation to runoff. In contrast, the wet and snow climate zones are found to have relatively lower median values of 8.6 and 8.5 mmd-1, respectively, indicating a slower transformation rate. From the spatial distribution, the highest median runoff intensity (exceeding 12 mmd-1) are found in the eastern Australia (EAU), northeastern South America (NES), and northern Australia (NAU) In contrast, the lowest median values (below 6.5 mmd-1) are concentrated in northern Europe (NEU), northwestern North America (NWN), and Mediterranean (MED). It should be noted that the spatial pattern of the runoff coefficient is inconsistent with that of the runoff intensity. For instance, NWN exhibits a relatively high runoff coefficient of 0.3, yet its runoff intensity is comparatively low at 6.5 mmd-1.

In terms of the runoff efficiency as shown in Fig. 3g–i, which is the product of the runoff coefficient and runoff intensity, its relatively high values are found in snow climates with a median of 2.41 mmd-1, while lower values are found in both wet (median =1.75 mmd-1) and dry (median =1.51 mmd-1) climates, indicating a balance between runoff coefficient and runoff intensity. Besides, its spatial distribution differs from that of the runoff coefficient and the runoff intensity. The highest median runoff efficiency values (exceeding 2.5 mmd-1) are found in western North America (WNA), eastern North America (ENA), and southeastern South America (SES), indicating a higher level of comprehensive connectivity for runoff generation, and consequently, a greater potential for flood generation. In contrast, the lowest median runoff efficiency values (below 1.35 mmd-1) are found in southern Australia (SAU), northern Europe (NEU), and northeastern South America (NES), indicating a lower level of comprehensive connectivity for runoff generation.

An interpretable machine-learning framework combining RF and ALE is subsequently employed to systematically investigate the key drivers governing the spatial heterogeneity of the process connectivity indicators. A total of 21 catchment attributes serve as input variables into the RF model to predict each of the process connectivity metrics. The cross-validated R2 values for the RF models are presented in Figs. S4–S6 in the Supplement. Generally, the RF model demonstrates robust predictive performance, achieving a mean R2 over 0.8 for all process connectivity indicators under 10-fold cross-validation. Figure 4 illustrates the ALE interpretable results of each indicator. For the runoff coefficient as shown in Fig. 4a, the aridity shows the greatest impact, followed by mean annual precipitation, organic carbon content in soil, fraction of snow, and seasonality of precipitation. For the runoff intensity as shown in Fig. 4b, the mean annual precipitation has the greatest impact, followed by the mean actual evapotranspiration, the average duration of high precipitation, and the frequency of high precipitation days. For the runoff efficiency as shown in Fig. 4c, the mean annual precipitation shows the greatest impact, followed by the frequency of high precipitation days, seasonality of precipitation, fraction of snow, and pasture extent. It can be noted that climate attributes dominate the impacts on all connectivity metrics, contributing 63.2 %, 89.6 %, and 79.3 % to the runoff coefficient, runoff intensity, and runoff efficiency, respectively.

Figure 5 depicts the long-term trends of process connectivity spanning from 1950 to 2020. For the runoff coefficient as shown in Fig. 5a–c, the increasing trends are observed across the majority of catchments in both dry and wet climate zones, with a median relative Sen's slope of 0.6 % per decade and 0.3 % per decade, respectively. In contrast, the majority of catchments in snow climates exhibit declining trends, with a median relative Sen's slope of -0.2 % per decade. The high increasing trends are mainly located in the Amazon (AMZ; 1.6 % per decade), northern Australia (NAU, 1.2 % per decade), central North America (CNA; 1.2 % per decade), southeastern South America (SES, 1.1 % per decade), and northeastern South America (NES, 1.0 % per decade). Meanwhile, significant decreasing trends are mainly observed in the Mediterranean (MED, -1.0 % per decade) and western North America (WNA, -0.6 % per decade). For the runoff intensity (Fig. 5e and f), the spatial distribution of long-term trends matches that of the runoff coefficient, with the high increasing trends in the AMZ (2.6 % per decade), SES (2.0 % per decade), NES (1.9 % per decade), NAU (1.8 % per decade) and CNA (1.4 % per decade), and the high decreasing trends in WNA (-0.9 % per decade) and MED (-0.7 % per decade). This indicates that long-term trends of the transformation ratio (i.e., runoff coefficient) and the transformation rate (i.e., runoff intensity) from precipitation to runoff show great synergy, meaning that regions with a higher transformation ratio may simultaneously experience a faster transformation rate under climate change. For runoff efficiency as shown in Fig. 5g–i, the high increasing trends also lie in the AMZ (3.4 % per decade), SES (2.5 % per decade), CNA (2.3 % per decade), NAU (1.8 % per decade), and NES (3.0 % per decade), and the high decreasing trends are also in the WNA (-1.5 % per decade) and MED (-0.9 % per decade), with the magnitude of change exceeding that of both runoff coefficient and runoff intensity.

Overall, the hotspots of increasing process connectivity for runoff generation under climate change are the Amazon, southeastern South America, central North America, northern Australia, and northeastern South America. In these regions, a larger proportion of rainfall is transformed to runoff at a faster rate, typically accompanied by greater event runoff volumes and higher peak discharges, thereby elevating the potential for flood generation. By contrast, the hotspots of decreasing process connectivity are western North America and the Mediterranean, with relatively lower potential for flood generation.

By examining the variations in process connectivity indicators across events grouped by peak discharge quantile ranges (Figs. S7–S9 in the Supplement), we find that these connectivity indicators increase consistently with increasing discharge quantiles, demonstrating a robust positive association between the runoff generation process connectivity and the event peak discharges. To highlight the contrast between the extreme conditions, we further quantified the fold-change in the connectivity indicators across peak-discharge quantile ranges, specifically the ratios of values in the highest range (i.e., 80–100th percentile) to those in the lowest range (i.e., 0–20th percentile), as shown in Fig. 6. Across all catchments, the runoff coefficient, runoff intensity, and runoff efficiency associated with events in the high peak discharge quantiles range are 3, 4, and 11 times those for low peak discharge quantile range, respectively. For the runoff coefficient (Fig. 6a–c), the highest fold-change ratios are found in the dry climate zones, with a median value of 5.4. In contrast, wet and snow climate zones exhibit relatively lower values, with a median value of 3.5 and 2.7, respectively. Spatially, the high values are found in EAU, NAU, CNA, and SAU, with a median value of 6.6, 4.8, 4.1, and 4.1, respectively, while the low values are found in NEN, NWN, and AMZ, with a median value of 1.6, 1.9, and 2.5. For the runoff intensity and runoff efficiency as shown in Fig. 6d–i, the spatial distribution is similar to that of the runoff coefficient, with the high values in EAU (17.1 for runoff intensity; 87.3 for runoff efficiency), NAU (11.5; 46.5), CNA (8.0; 27.5), and SAU (6.7; 21.9), and low values in NEN (2.3; 2.9), NWN (2,2; 3.6), and AMZ (1.9; 3.6) for both indicators. Furthermore, the highest fold-change ratios are found in the dry climate zones, where runoff intensity and runoff efficiency reach 10.7 and 54.4 folds, respectively, suggesting the significant nonlinear response of runoff processes to peak discharge.

To investigate how precipitation intensity influences runoff efficiency, we adopt a power function to fit event-based data for each individual catchment, with model parameters calibrated by the least squares method. A representative fitting example is illustrated in Fig. S10 in the Supplement, while the overall fitting performance across all catchments is summarized in Fig. S11 in the Supplement, with a mean R2 of 0.37. The spatial distributions of the two fitted parameters RE₁₀, defined as the runoff efficiency under a unit precipitation intensity of 10 mmd-1, and m, representing the sensitivity of runoff efficiency to changes in precipitation intensity, are illustrated in Fig. 7. The regional statistical summaries for these parameters are provided in Table 3. For the parameter RE₁₀ (Fig. 7a–c), its spatial distribution closely aligns well with that of multi-year average runoff efficiency (Fig. 4c). Dry climate zones exhibit relatively lower values, with a median of 1.9 mmd-1, whereas wet and snow climate zones show higher median values of 2.8 and 3.8 mmd-1, respectively. Regionally, the highest values (i.e., 3.9 mmd-1) are found in NEN and WNA, whereas the lowest values (0.9 mmd-1) are found in EAU. For the parameter m (Fig. 7d–f), the highest median value of 1.65 is found in the dry climate zones, while wet and snow climate zones exhibit relatively lower median values of 1.17 and 1.05, respectively. Thus, dry climate zones exhibit relatively high RE₁₀ values that are associated with high sensitivity, whereas wet and snow climate zones show relatively low RE₁₀ values that are associated with low sensitivity. Regionally, the highest sensitivity values are found in EAU (1.88) and NAU (1.70), while the lowest are found in MED (0.67) and NEN (0.72).

Through an interpretable machine learning approach, we revealed the factors driving the spatial variability of the process connectivity indicators across the globe (Fig. 4). For the runoff coefficient (RC), the dominant factors are aridity and mean annual precipitation. This finding aligns with previous regional investigations, which demonstrated that mean runoff coefficients are primarily governed by climatic factors, particularly the multi-year average of precipitation and the ratio of evapotranspiration to precipitation (Merz and Blöschl, 2009; Merz et al., 2006). Thus the climatic water–energy balance largely determines the average fraction of precipitation that transforms into runoff, consistent with the classical Budyko framework that a higher climatic aridity index increases the evaporative fraction (E/P) and reduces the runoff coefficient, leading to low runoff coefficients in dry areas and higher runoff coefficients in wet areas (Liang et al., 2015; Cheng et al., 2025; Cavalcante et al., 2019). It is worth highlighting that snow-dominated catchments exhibit the highest multi-year mean RC, which is likely attributed to the generally lower evaporative losses and the reduced infiltration capacity in frozen or near-saturated soils (Lundberg et al., 2016). This finding is further supported by the importance of snow fraction in explaining spatial RC variations (Fig. 4a). For the runoff intensity (RI), however, average duration and frequency of high-precipitation events show strong impacts, suggesting that shorter and/or more frequent intense precipitation events tend to generate more temporally concentrated runoff events with shorter ΔtR and consequently higher RI values. For the runoff efficiency (RE), the dominant factors are the multi-year average of precipitation, frequency of high-precipitation events, and seasonality of precipitation, indicating the rationality of this integrated connectivity metric that can capture both quantity and speed dimensions of runoff generation processes. In terms of categorical attributions, the explainable machine learning reveals that climate-related attributes account for a substantial portion of the cross-catchment variability in RC, RI and RE, suggesting that climatic water–energy availability acts as a first-order constraint on long-term runoff-generation connectivity at the global scale, while landscape characteristics (e.g., topography, soils and land cover) exert potentially region-specific regulatory effects. This finding is consistent with previous large-sample research on the dominant role of climate attributes in runoff generation processes (Kuentz et al., 2017; Jehn et al., 2020). It is also important to note that the strong climate gradients inherent in global datasets may mask subtler (yet process-relevant) controls from soils and geology characteristics that are frequently emphasized in field-based studies on the connectivity of the runoff generation process (Tromp-Van Meerveld and Mcdonnell, 2006).

By analysing long-term trends of the process connectivity indicators for runoff generation over 1950–2020, we identified several hotspots (Fig. 5). In general, trends in the RC and RI are highly coherent across most catchments worldwide, with regions experiencing increases in runoff transformation ratios tending to exhibit simultaneous increases in transformation intensity, and vice versa. Under the changing climate, the Amazon, southeastern and northeastern South America, central North America, and northern Australia exhibit pronounced increases in process connectivity. This might be attributed to the increases in occurrence frequency and magnitude of extreme precipitation events, which result in a greater fraction of precipitation being rapidly transformed into runoff (Donat et al., 2016; Harp and Horton, 2022). The increasing connectivity brings larger event runoff volumes and higher peak discharges, and thus causes a greater potential for flood generation. In contrast, the decreasing trends in runoff generation connectivity are found in western North America and the Mediterranean, which might be attributed to the reduction of total precipitation and enhanced evaporation. Thus, there are drier soils, lower runoff coefficients, and weaker runoff intensity, and consequently a reduction in average potential for flood generation (Zhan et al., 2019). It is important to note that a lower connectivity does not guarantee complete safety, as extreme events can still occur unexpectedly (Yan et al., 2025). Overall, the trends of the runoff generation connectivity offer a process-based perspective on acceleration or deceleration of the global hydrological cycle and reveal how the spatial pattern of potential for flood generation evolves in response to climate change.

At the event scale, we developed an empirical power-law model that quantifies the linkage between precipitation intensity and runoff efficiency. Characterized by its simplicity and flexibility, this two-parameter model effectively captures how runoff-generation connectivity evolves in response to precipitation intensity from weak to strong events. Across all catchments, the mean coefficient of determination is around 0.37, indicating that precipitation intensity alone can explain a substantial portion of the variability in runoff efficiency. Cross-climate analyses reveal that dry catchments exhibit a low baseline runoff efficiency per unit precipitation intensity (RE₁₀), while exhibiting the highest sensitivity parameter m (Fig. 7c and f). This pattern implies that strong evaporation and infiltration losses keep low runoff-generation connectivity under ordinary storms, whereas sufficiently intense events can temporarily exceed the soil infiltration capacity, causing the amount and intensity of runoff to increase sharply and leading to an amplification effect to precipitation intensity (m>1). In contrast, wet catchments exhibit high baseline RE₁₀ but low values for the sensitivity parameter m. Even small to moderate storm events in these hydrologically saturated regions generate a relatively large fraction of runoff, and further increases in precipitation intensity might not translate into proportional gains in runoff efficiency. This contrast reflects the fundamental differences in runoff-generation mechanisms: runoff generation in dry catchments is typically dominated by the infiltration-excess runoff with clear intensity thresholds, whereas it is more prone to saturation-excess runoff in wet catchments, where near-saturated soils allow even modest storms to produce runoff, leading to high baseline efficiency but much smoother changes with intensity. As the precipitation regime is projected to change under future climates (Song et al., 2024; Liu et al., 2024), regional empirical relationships between precipitation intensity and runoff efficiency provide a practical way for assessing shifts in runoff-generation connectivity, with potential applicability across the globe.

Our results show that at the multi-year mean scale, RE predominantly reflects a trade-off between RC and RI spatially. Specifically, under long-term average hydrological conditions, catchments with high RC tend to exhibit relatively low RI, and vice versa (Fig. 3). This contrast highlights the long-term regulatory role of climatic conditions in shaping the process connectivity for runoff generation, that is, water-abundant conditions tend to “win by quantity”, whereas water-limited conditions “win by rate”, revealing a fundamental compensatory balance between RC and RI. Besides, at the event scale, RE exhibits a strongly nonlinear response to meteorological forcing within a given catchment, particularly marked by a pronounced amplification with increasing precipitation intensity. Specifically, our analysis reveals that RE increases nonlinearly with the intensity of individual precipitation events, where high-intensity storms produce substantially greater RE values compared with low-intensity events (Fig. 7). Such behaviour is difficult to detect in long-term averages, where the effects of individual events with varying intensities are smoothed out over time. This nonlinear amplification indicates that, during heavy storms, both the ratio and the rate of precipitation to runoff transformation increase simultaneously and substantially, owing to the threshold effect inherent in the precipitation–runoff process (Zhang et al., 2021). More precipitation could be transformed into runoff at a faster rate, causing a sharp increase in RE. Such threshold-triggered nonlinear responses in runoff generation have been reported in many previous studies (Detty and Mcguire, 2010; Mahmood and Vivoni, 2011; Willgoose and Perera, 2001). Moreover, it should be noted that the RE is an integrated connectivity indicator for runoff generation, and a given RE value can result from different combinations of RC and RI. For instance, a high RE may stem from a scenario of high RC and low RI, or, conversely, from a scenario of low RC paired with exceptionally high RI. This multiplicity of pathways highlights that RE is not determined by a single factor but emerges from the nonlinear integration of catchment-specific connectivity and infiltration processes. It is necessary to comprehensively use these indicators for characterising the connectivity of the runoff generation to improve our understanding of how the water cycle responds to the changing climate from a process perspective.

It is also important to acknowledge the limitations of our study. First, our analysis only relies on a single conceptual rainfall–runoff model with its own assumptions and simplifications, which may not be universally applicable across the diverse range of global catchments and introduces structural uncertainty (Parasuraman and Elshorbagy, 2008). Although parameter calibration and performance screening have already secured a reasonable level of accuracy, future work could be done for ensembling hydrological models to better capture runoff-generation processes and to enhance the robustness of the results (Solanki et al., 2025). Second, the selected catchments exhibit uneven spatial distribution across regions and climate zones, a limitation that could undermine the representativeness of data-sparse areas. Although median-based summaries can reduce the effects of uneven spatial distribution, interpretation of the regional results from these underrepresented areas should be cautious. More data from the available hydrological stations would enable more refined and robust regional analyses. Third, uncertainties also exist in the identification and matching of rainfall–runoff events. Runoff events are currently defined to end when simulated quickflow returns to zero, yet in humid catchments, slow recession and structural biases from baseflow separation and model simulation may prevent strict zero-flow conditions, potentially causing event splitting or merging. In addition, the 0.1 mmd-1 threshold employed to delineate rainfall events is an empirical truncation criterion that may alter event boundaries, especially under hydroclimatic extremes. Moreover, rainfall–runoff matching relies on the DCMA-based lag window and the assumption that the rainfall-event centroid falls within that window; this assumption may be violated by nonlinear responses, particularly for long-duration and low-intensity events, thereby introducing matching errors. These uncertainties potentially affect event-scale identification and matching to some degree, but are expected to be partially mitigated in our analysis of multi-event averages and large-scale spatial patterns. Finally, the empirical power-law relationship developed here does not exactly account for event total precipitation depth and antecedent soil moisture, which can influence runoff-generation connectivity by governing storage filling and the expansion of saturated contributing areas, particularly in wet catchments where saturation-excess runoff is more prevalent (Zhang et al., 2021). Two storms with similar precipitation intensities can produce significantly different runoff efficiencies. For instance, a storm following a prolonged dry period generally tends to produce lower efficiency compared to one occurring under wet antecedent conditions. Since future climate change is projected to alter both the distribution of precipitation characteristics and soil moisture conditions (Yao et al., 2025), the empirical relationship calibrated under current conditions is likely to become invalid under future climate scenarios. These acknowledged limitations and uncertainties will be addressed and mitigated in future work.