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Understanding streamflow generation at the catchment scale requires quantifying how different components of the system are linked, and how they respond to meteorological forcing. Here we present a proof‐of‐concept study characterizing and quantifying dynamic linkages between precipitation, groundwater recharge, and streamflow using a data‐driven nonlinear deconvolution and demixing approach, Ensemble Rainfall‐Runoff Analysis (ERRA). Streamflow in our mesoscale, intensively farmed test catchment is flashy, but occurs at time lags that are too long to be plausibly attributed to overland flow. Instead, ERRA's estimates of the impulse responses of groundwater recharge to precipitation, and of streamflow to groundwater recharge, imply that this intermittent streamflow is primarily driven by precipitation infiltrating to recharge groundwater, followed by discharge of groundwater to streamflow. ERRA reveals that streamflow increases nonlinearly with increasing precipitation intensity or groundwater recharge, and exhibits almost no response to precipitation or recharge rates of less than 10 mm d−1. Groundwater recharge is both nonlinear, increasing more‐than‐proportionally with precipitation intensity, and nonstationary, increasing with antecedent wetness. Simulations with the infiltration model Hydrus‐1D can reproduce the observed water table time series reasonably well (NSE = 0.70). However, ERRA shows that the model's impulse response is inconsistent with the real‐world impulse response estimated from measured precipitation and groundwater recharge, illustrating that conventional goodness‐of‐fit statistics can be weak tests of model realism. Thus, our proof‐of‐concept study demonstrates how impulse responses estimated by ERRA can help clarify linkages between precipitation and streamflow at the catchment scale, quantify nonlinearity and nonstationarity in hydrologic processes, and critically evaluate simulation models. Key Points Nonlinear and nonstationary behaviors of streamflow and groundwater recharge are quantified using Ensemble Rainfall‐Runoff Analysis (ERRA) Subsurface processes, rather than overland flow, generate episodic streamflow in an intensively farmed catchment ERRA can help evaluate model realism by comparing the characteristic impulse responses of models with those of real‐world systems

This study shows that cloud seeding should be planned by considering the dam reservoir characteristics as well as the dam basin characteristics. First, the collection efficiency of increased rainfall by cloud seeding is compared for three dam basins (Boryeong Dam, Yongdam Dam, and Namgang Dam basins) located in the western part of the Korean Peninsula. Second, the additional runoff volumes in those three basins from cloud seeding are compared with each other. Finally, the change in water supply capacity is evaluated by considering the dam reservoir operation and planned water supply. In this study, cloud seeding is simulated using the WRF−ARW model, and, additionally, four different rainfall data generated by considering the scenarios of a rainfall increase of 5, 10, 15, and 20% are used for more practical evaluation. The results in this study show that the situation in Boryeong Dam basin is better than in the other two dam basins. More active cloud seeding is necessary in the Yongdam Dam and Namgang Dam basins. However, it has also been found that cloud seeding alone cannot solve the water supply problems in those two dam basins. The above findings also indicate that cloud seeding should be carefully planned. It can vary dam-by-dam. Cloud seeding might be effective every season in one dam, but only in Spring in another dam basin, while in other dams, summer or fall season might be the best option. The target increase of rainfall is also an important issue. Just a mild increase could be better in one dam, but it can be important to secure much more rainfall in other dams. Even though the three dams considered in this study are located in practically the same climatic zone, the conditions required for cloud seeding differ completely.

Soil water storage properties, which are affected by land management practices, alter the water balance and flow regimes in watersheds; thus, it is highly plausible to clarify the influence of such management practices on the water storage condition by analyzing the long-term variations in discharge. In this study, the changes in soil water storage characteristics of the Ogouchi Dam watershed, which had undergone intensive forest management through the decades, were investigated using two approaches. Reported results from the rainfall–runoff correlation analysis show a gradual and steady increase in the soil water storage capacity at weaker continuous-rainfall events, i.e., uninterrupted wet days accumulating less than 70 mm. Meanwhile, the second approach utilizing the parameter calibration in the SWAT discharge model illustrated a constant trend in the runoff potential and the high possibility of a steady improvement in the soil available water capacity. Overall, the established decadal trends were able to prove the capability of sustainable forest management, i.e., thinning, regeneration cutting, multi-layer planting, deer-prevention fences, and earth-retaining fences (lined felled trees), in improving the water conservation function of the catchment.

Under global warming, according to results obtained from offline drought indices driven by projections of general circulation models (GCMs), future droughts in China will worsen but the results are not consistent. We analyzed changes in droughts covering the entire hydrologic cycle using outputs of GCMs of the 6th Coupled Model Intercomparison Project (CMIP6) for SSP2-4.5 and SSP5-8.5 climate scenarios, and compared the results with that of popular, offline drought indices [the self-calibrating Palmer Drought Severity Index (scPDSI), Standardized Precipitation Evapotranspiration Index (SPEI) and Standardized Precipitation Actual Evapotranspiration Index (SPAEI)]. Among meteorological, agricultural, and hydrological drought indices tested under both SSP scenarios, the results obtained from SPAEI and scPDSI agree better with univariate drought indices than SPEI. scPDSI generally agrees well with agricultural droughts (Standardized Soil Moisture Index with the surface soil moisture content; SSIS). Future droughts estimated using soil moisture analysis are more widespread than that from precipitation and runoff analysis in humid regions of South China by the end of the twenty-first century. In arid northwestern China and Inner Mongolia, drought areas and severity based on scPDSI and SSIS forced with the SSP scenarios show obvious decreasing trends, in contrast to increasing trends projected in South China. Trends projected using SPEI contradict those projected by other drought indices in non-humid regions. Therefore, selecting appropriate drought indices is crucial in project representative future droughts and provides meaningful information needed to achieve effective regional drought mitigation strategies under climate warming impact.

Spatial rainfall patterns exert a key control on the catchment-scale hydrologic response. Despite recent advances in radar-based rainfall sensing, rainfall observation remains a challenge, particularly in mountain environments. This paper analyzes the importance of high-density rainfall observations for a 13.4 km2 catchment located in the Swiss Alps, where rainfall events were monitored during 3 summer months using a network of 12 low-cost, drop-counting rain gauges. We developed a data-based analysis framework to assess the importance of high-density rainfall observations to help predict the hydrological response. The framework involves the definition of spatial rainfall distribution metrics based on hydrological and geomorphological considerations and a regression analysis of how these metrics explain the hydrologic response in terms of runoff coefficient and lag time. The gained insights on dominant predictors are then used to investigate the optimal rain gauge network density for predicting the streamflow response metrics, including an extensive test of the effect of down-sampled rain gauge networks and an event-based rainfall–runoff model to evaluate the resulting optimal rain gauge network configuration. The analysis unravels that, besides rainfall amount and intensity, the rainfall distance from the outlet along the stream network is a key spatial rainfall metric. This result calls for more detailed observations of stream network expansions and the parameterization of along-stream processes in rainfall–runoff models. In addition, despite the small spatial scale of this case study, the results show that an accurate representation of the rainfall field (with at least three rain gauges) is of prime importance for capturing the key characteristics of the hydrologic response in terms of generated runoff volumes and delay for the studied catchment (0.22 rain gauges per square kilometer). The potential of the developed rainfall monitoring and analysis framework for rainfall–runoff analysis in small catchments remains to be fully unraveled in future studies, potentially also including urban catchments.

Double-peak hydrographs are widely observed in diverse hydrological settings, but their implications for our understanding of runoff generation remain unclear. Previous studies of double-peak hydrographs in the extensively instrumented Weierbach catchment have linked the first peak to event water and the second, delayed and broader peak to pre-event water. Here we use ensemble rainfall-runoff analysis (ERRA) to quantify how precipitation intensity and antecedent wetness influence groundwater recharge and double-peak runoff generation at the Weierbach catchment (Luxembourg). The spiky first peak can be attributed to a rapid response directly linking precipitation to streamflow via near-surface flowpaths. Relative to this first peak, the second peak is delayed (peaking ∼ 1.5 d after rain falls), lower (∼1/3 the height of the first peak), and broader (declining to nearly zero in ∼ 10 d), and can be attributed to a groundwater-mediated pathway that links precipitation, groundwater recharge, and streamflow. The sum of these two runoff responses quantitatively approximates the whole-catchment runoff response. Under wet conditions (here defined as antecedent water table depth ≤1.66 m), the first peak increases nonlinearly (particularly at precipitation intensities above 2 mm h−1) and the second peak becomes higher, narrower, and earlier with increasing precipitation intensity. Under dry conditions (here defined as antecedent water table depth >1.66 m), the first peak increases nonlinearly with precipitation intensity (particularly above 4 mm h−1), and groundwater recharge also responds to precipitation, but no clear second peak occurs regardless of precipitation intensity. The lack of a second peak under dry conditions plausibly arises from groundwater loss to evapotranspiration and from limited connectivity between groundwater and the stream, rather than from a lack of groundwater recharge. Almost no runoff response occurs at precipitation intensities below ∼ 0.8 mm h−1 under wet conditions and ∼ 1.5 mm h−1 under dry conditions. Above a precipitation-related threshold that initiates the first peak and a catchment wetness threshold that initiates the second peak, higher precipitation intensities amplify the first peak nonlinearly and trigger a larger and quicker second peak.

A classical approach to understanding hydrological behavior is the unit hydrograph and its many variants, but these often assume linearity (runoff response is proportional to effective precipitation), stationarity (runoff response to a given unit of rainfall is identical, regardless of when it falls), and spatial homogeneity (runoff response depends only on spatially averaged precipitation). In the real world, by contrast, runoff response is typically nonlinear, nonstationary, and spatially heterogeneous. Quantifying this nonlinearity, nonstationarity, and spatial heterogeneity is essential to unraveling the mechanisms and subsurface properties controlling hydrological behavior. Here, I present proof-of-concept demonstrations illustrating how nonlinear, nonstationary, and spatially heterogeneous rainfall–runoff behavior can be quantified, directly from data, using ensemble rainfall–runoff analysis (ERRA), a data-driven, model-independent method for quantifying rainfall–runoff relationships across a spectrum of time lags. I show how ERRA uses nonlinear deconvolution to quantify how catchments' runoff responses vary with precipitation intensity and to estimate their precipitation-weighted runoff response distributions. I further illustrate how ERRA combines nonlinear deconvolution with de-mixing techniques to reveal how runoff response depends jointly on precipitation intensity and nonstationary ambient conditions, including antecedent wetness and vapor pressure deficit. I demonstrate how ERRA's de-mixing techniques can be used to quantify spatially heterogeneous runoff responses in different parts of a catchment, even if those subcatchments are not separately gauged. I also illustrate how ERRA's broken-stick deconvolution capabilities can be used to quantify multiscale runoff responses that combine hydrograph peaks lasting for hours and recessions lasting for weeks, well beyond the average spacing between storms. ERRA can unscramble these multiple effects on runoff response even if they are overprinted on each other through time and even if they are corrupted by autoregressive moving average (ARMA) noise. Results from this approach may be informative for catchment characterization, process understanding, and model–data comparisons; they may also lead to a better understanding of storage dynamics and landscape-scale connectivity. An R script is provided to perform the necessary calculations, including uncertainty analysis.

Pristine peatlands are believed to play an important role in regulating hydrological extremes because they can act as reservoirs for rainwater and release it gradually during dry periods. Rewetting of drained peatlands has therefore been considered an important strategy to reduce the catastrophic effects of flooding. With the anticipation of more frequent extreme rainfall events in the future due to a changing global climate, the importance of peatland rewetting in flood mitigation becomes even more important. To date, however, empirical data showing that rewetting of drained peatlands actually restores their hydrological function similar to pristine peatlands are largely lacking, particularly for boreal fens. To assess whether peatland rewetting can mitigate flooding from extreme rainfall events and ensure water security in a future climate, we measured event-based runoff responses before and after rewetting using a BACI approach (before–after and control–impact) within a replicated, catchment-scale study at the Trollberget Experimental Area in northern Sweden. High-resolution hydrological field observations, including groundwater level (GWL), discharge, and rainfall data, were collected over 4 years, allowing us to detect and analyze 17 rainfall-runoff events before and 30 events after rewetting. We found that the rewetted sites experienced an increase in the GWL following rewetting and that this was consistently observed across all distances from the blocked ditch within the peatland. Our rainfall-runoff analysis revealed that rewetting significantly decreased peak flow and the runoff coefficient and reduced the overall flashiness of hydrographs, making the rewetted sites function more like the pristine control peatland. However, “lag time”, which was already similar to pristine conditions, was pushed farther away from pristine conditions following rewetting. Yet, our results showed that the effectiveness of ditch blocking in flood moderation was strongly influenced by the initial condition and the catchment percentage of restoration, as one of our two rewetted peatlands did not show significant change, attributed to it being already similar to the pristine site, suggesting less treatment effect, and the other catchment, with higher restoration percentage, had a better response to treatment. In summary, our findings suggest that peatland rewetting has the potential to mitigate flood responses; however, further research over a longer time period is needed, as peat properties and the peatland vegetation will develop and change over time.

Understanding the factors that influence catchment runoff response is essential for effective water resource management. Runoff response to precipitation can vary significantly, depending on the dynamics of hillslope water storage and release and on the transmission of hydrological signals through the channel network. Here, we use ensemble rainfall–runoff analysis (ERRA) to characterize the runoff response of 189 Iranian catchments with diverse landscapes and climates. ERRA quantifies the increase in lagged streamflow attributable to each unit of additional precipitation, while accounting for nonlinearities in catchment behavior. Peak runoff response, as quantified by ERRA across Iran, is higher in more humid climates, in steeper and smaller catchments, and in catchments with shallower water tables. The direction and approximate magnitude of these effects persist after correlations among the drivers (e.g., deeper water tables are more common in more arid regions) are accounted for. These findings highlight the importance of catchment attributes in shaping runoff behavior, particularly in arid and semi-arid regions, where climatic variability and groundwater dynamics are crucial factors in sustainable water resource management and effective flood risk mitigation.

Most hydrological phenomena have stochastic behaviour; therefore, the theory of statistics and probability usually uses to describe and analyse them. Rainfall and runoff are two hydrological phenomena, described with different characteristics, e.g., volume, peak flow, and time base (runoff), and intensity, duration and depth (rainfall). In the current study, we used the copula functions for multivariate modelling of rainfall and runoff characteristics. To do this, the performance of 10 different copulas was examined in a multivariate analysis of rainfall and runoff characteristics measured in Kasilian basin located in northeastern Iran during a 37-yr period (1984–2020). The rainfall characteristics, including intensity, duration, and depth for 562 recorded rainfall events for the Kasilian basin at intervals of 15–30 min were extracted for rainfall–runoff analysis. Then, the rainfall histograms and flood hydrographs were drawn, and rainfall characteristics (i.e., depth, duration, and intensity) and runoff characteristics (i.e., peak discharge, peak discharge time, time base, flood volume, the width flood hydrograph at 50 and 75% of peak discharge ( W 50 and W 75)) were extracted. In the next step, the univariate distributions with best fitness on every studied rainfall and runoff characteristics were determined. The results demonstrated that the GEV has the best fitness on all studied rainfall and runoff characteristics. Also, the Joe copula had the best fitness for joining the duration and depth of rainfall, as well as the intensity and depth of rainfall, and the Gumbel–Barnett and Farlie–Gumbel–Morgenstern were in the following ranks. Then the multivariate probability and return period were computed in two states of ‘AND’ and ‘OR’. It was demonstrated that in the ‘AND’ mode, the joint return period for a rainfall depth of 60 mm and rainfall intensity of 60 mm/h is less than 20 years, while for the same rainfall depth and intensity values, in the ‘OR’ mode, the joint return period is obtained about 6 years. Research Highlights Multivariate probabilistic rainfall–runoff model created using copula functions. The GEV distribution had the best fitness on all studied rainfall and runoff characteristics. The Joe copula had the best fitness for joining the duration and depth of rainfall, as well as the intensity and depth of rainfall. The difference between standard return periods and Kendall return periods increases with increasing the probability level.