Runoff Model Research Articles (Page 1)

Flash floods in urban and karst environments present major modeling challenges due to their complex hydrodynamics, characterized by a rapid urban runoff response and a delayed slower karst groundwater response. This study explores the use of artificial neural networks ANN (multilayer perceptron in particular) to predict flash floods at the downstream of the Las River in Toulon (France). The Las River is fed in a larger proportion by the nearby karst springs and in a smaller proportion by the urban drainage network. In this study, we propose an ensemble modeling strategy to address the system’s double hydrological regime. The initial step was to identify rainfall events in the six-year hydrometeorological database and classify them according to their karst contributions. Two specialized models: urban runoff model (UM) and karst model (KM) were trained solely on each event type (urban runoff and karst events). These models were combined by two methods in an attempt model all events, disregarding of their event type: the first approach was to combine the outputs of the specialized models in an ANN called output combination model (OM), the second approach was to combine the structures of the specialized models and retraining the model parameters called structure combination model (SM). A third more “basic” approach, called bulk model (BM), was to optimize the ANN by selecting the inputs with the best performance improvements. As expected, the specialized models (UM and KM) performed the best on the cross-validation sets and on the test sets on their respective event types but failed to generalize across regimes. The OM was the most robust ensemble strategy across all event types with consistent accuracy on predicting both urban runoff and karst flood events. The BM was better on the karst events while having worst performance on karst events and the SM was the least accurate model. These findings confirm the added value of combining specialized ANNs to model complex hydrological systems. In addition, selecting the right inputs to the models has a bigger impact on the model’s performance than choosing its structure by changing its hyperparameters.

Abstract. Long short-term memory (LSTM) networks have shown strong performance in rainfall–runoff modeling, often surpassing conventional hydrological models in benchmark studies. However, recent studies raise questions about their ability to extrapolate, particularly under extreme conditions that exceed the range of their training data. This study examines the performance of a stand-alone LSTM trained on 196 catchments in Switzerland when subjected to synthetic design precipitation events of increasing intensity and varying duration. The model's response is compared to that of a hybrid model – a model that combines conceptual hydrological approaches with the LSTM – and evaluated against hydrological process understanding. Our study reiterates that the stand-alone LSTM is not capable of predicting discharge values above a theoretical limit (which we have calculated for this study to be 73 mm d−1), and we show that this limit is below the maximum value of 183 mm d−1 in the training data. Furthermore, the LSTM exhibits a concave runoff response under extreme precipitation, indicating that event runoff coefficients decrease with increasing design precipitation – a phenomenon not observed in the hybrid model used as a benchmark. We show that saturation of the LSTM cell states alone does not fully account for this characteristic behavior, as the LSTM does not reach full saturation, particularly for the 1 d events. Instead, its gating structures prevent new information about the current extreme precipitation from being incorporated into the cell states. Adjusting the LSTM architecture, for instance, by increasing the number of hidden states and/or using a larger, more diverse training dataset, can help mitigate the problem. However, these adjustments do not guarantee improved extrapolation performance, and the LSTM continues to predict values below the range of the training data or show unfeasible runoff responses during the 1 d design experiments. Despite these shortcomings, our findings highlight the inherent potential of stand-alone LSTMs to capture complex hydrometeorological relationships. We argue that more robust training strategies and model configurations could address the observed limitations, preserving the promise of stand-alone LSTMs for rainfall–runoff modeling.

To address the stochasticity, time-varying characteristics, and nonlinear dynamics of runoff series, this research proposes a novel deep learning architecture, BWDformer, based on wavelet decomposition and dynamic feature fusion, to enhance the precision of streamflow forecasting. Based on Informer, the model innovatively integrates wavelet decomposition, a dynamic feature fusion module (DFF), and Bayesian optimization to address the limitations of conventional deep learning models in multi-scale feature integration, long-term dependency capture, and dynamic feature adjustment. Specifically, wavelet decomposition is first applied to extract multi-scale features through adaptive time windows, accurately capturing short-term fluctuations, seasonal variations, and long-term trends in runoff data. Then, based on DFF, the feature weights are dynamically adjusted using the attention mechanism to optimize the feature combination, thereby enhancing the model’s ability to analyze complex runoff sequences. Finally, Bayesian optimization is used to efficiently search for hyperparameters, significantly improving the model’s training efficiency. To verify the model’s effectiveness, this study tested it at four hydrological stations: Hongshanhe, Manwan, Baihe, and Tangnaihai. The results show that BWDformer significantly outperforms benchmark models, such as CNN, LSTM, Transformer, and Informer, in terms of MAE, RMSE, R, NSE, and KGE. For example, in Hongshanhe, the MAE is 0.1921, a decrease of 18.82% compared to CNN (0.2366), 4.65% compared to LSTM (0.2014), 15.63% compared to Transformer (0.2277), and 7.87% compared to Informer (0.2086). RMSE decreased by 25.46% compared to CNN, KGE was 0.9651, increased by 18.51% compared to Transformer (0.8143), and increased by 13.43% compared to Informer (0.8506). In Baihe, the MAE is 228.6971 m ³/s, a decrease of about 2.35% compared to CNN (243.0662), and the R value reaches 0.9998, an increase of 4.26% compared to CNN (0.9591). NSE is 0.9972, an increase of 18.73% compared to Transformer (0.8398), KGE is 0.9934, an increase of 9.79% compared to Informer (0.9048). These results verify the excellent performance of BWDformer in improving prediction accuracy, robustness, and practicality.Supplementary InformationThe online version contains supplementary material available at 10.1038/s41598-025-21007-4.

Abstract. This study explores the ability of global reanalyses to simulate catchment hydrology at the European scale using a conceptual rainfall–runoff model. We used two reanalyses, NOAA 20CR and ERA-20C, to simulate daily streamflows for over 2000 catchments since the 1840s. Our findings show that both reanalyses perform well, particularly for mean flows, with simulation performance improving as catchment size increases, though challenges remain for Mediterranean and snow-dominated regions. Additionally, the study highlights significant multi-decadal variations in streamflow, revealing alternating wet and dry periods across Europe. These findings provide valuable insights into long-term hydrological trends and offer a useful framework for understanding future changes in both water resources and hydrological extremes, such as floods, under climate variability.

Abstract. Assessing the transport behaviour of microbes in surface water–groundwater systems is important to prevent contamination of drinking-water resources by pathogens. While wellhead protection area (WHPA) delineation is predominantly based on dye injection tests and advective transport modelling, size exclusion of colloid-sized microbes from the smaller and usually less conductive pore spaces causes a faster breakthrough and thus faster apparent transport of microbes compared to that of solutes. To provide a tool for better assessment of the differences between solute and microbial transport in surface water–groundwater systems, here, we present the implementation of a dual-permeability, two-site kinetic deposition formulation for microbial transport in the integrated surface–subsurface hydrological model HydroGeoSphere (HGS). The implementation considers attachment, detachment, and inactivation of microbes in both permeability regions and allows for multispecies transport. The dual-permeability, two-site kinetic deposition implementation in HGS was verified against an analytical solution for dual-permeability colloid transport. The suitability of the model for microbial transport in integrated surface–subsurface hydrological settings at the wellfield or small headwater catchment scale is demonstrated by two illustrative examples. The first example is a benchmark for integrated rainfall–runoff and streamflow generation modelling to which we added microbial transport from a conceptual manure application, demonstrating the novelty of explicit and coupled microbial and solute transport simulations in an integrated surface–subsurface hydrological scenario. The second example is a multi-tracer flow and transport study of an idealized alluvial riverbank filtration site, in which we simulate in parallel the transport of reactive microbes, conservative 4He, and reactive 222Rn, demonstrating the assessment of mixing ratios, tracer breakthrough curves, and travel times in an integrated manner via multiple approaches. The developed simulation tool represents the first integrated surface–subsurface hydrological simulator for reactive solute and microbial transport and marks an important advancement to unlock and quantify governing microbial transport processes in coupled surface water–groundwater settings. It enables meaningful WHPA delineation and risk assessments of riverbank filtration sites with respect to microbial contamination even under situations of extreme hydrological and microbial stress, such as flood events.

Given significant water scarcity events in the recent past, water resources management in the Piracicaba River Basin, São Paulo, Brazil, has intensified the adoption of complex measures to meet the population’s water supply demands. This study presents a methodology to optimize reservoir water release while adhering to restrictive rules, aiming to also conserve water. A rainfall–runoff model was utilized alongside a hydrological routing model, incorporating meteorological forecasts for simulation over ten consecutive years. The results demonstrated significant water savings when comparing the optimization scenario with the actual reservoir operation during the same period. The applied methodology reduced water releases up to 66% in comparison to the observed scenario. Overall, the study introduces tools to improve reservoir operation with computational techniques, enriching local water resources management, water security, and decision-making processes, ensuring water security for the São Paulo Metropolitan Region, the most populous region in Brazil.

Improving runoff modelling through strengthened snowmelt and glacier module enhances runoff attribution in a large watershed in Central Asia

Hybrid runoff model improves daily peak flow simulation in arid and semi-arid basins

Soil hydraulic conductivity and root distribution represent two important parameters toward the engineering applications, ranging from quantification of hydrological and geotechnical processes (e.g., water runoff, shallow landslides) to agricultural management and forestry practices. To investigate the relationship among these soil parameters, two study areas located in Italy (Garfagnana, Tuscany) and Switzerland (Zollikofen, Bern) were selected. Root Area Ratio (RAR) and soil saturated hydraulic conductivity (Ks) data were collected through the application of the trench method and the constant hydraulic head (Aardwark permeameter) and falling-head methods, respectively. Results highlight that Root Area Ratio concentrates in the first soil layers and decreases sharply following deeper layers. Root Area Ratio and soil saturated hydraulic conductivity show positive linear correlation that depends on the forest station. Our results support the hypothesis that the presence of roots represent a key factor in preferential infiltration and, therefore, hydrological models applied for the runoff modelling, slope stability and soil erosion can be improved considering the spatial distribution of roots derived by field measurement and/or remote sensing data.

Changes in the Ob River sediment runoff caused by current climatic and socio-economic changes in Russian Federation have a multidirectional character in the middle and lower courses of the watercourse. According to meteorological observations, the air temperature in the studied region increased by 2 °C, and annual precipitation layers by more than 80 mm/yr, while the area of agricultural land in the middle reaches of the river decreased by 40% compared to the period before 1990. A decrease in acreage in the catchment area of the middle stream caused a three-fold decrease in sediment runoff during the high water period, while the activation of thermal erosion processes in the lower reaches led to a two-fold increase in sediment runoff during the same period. As a result of water and sediment runoff modeling according to climate forecasts, it was found that by the end of the 21st century, the average annual water runoff of the Ob River for the RCP 2.6 scenario increases by 20% relative to the period 1991–2020, while sediment runoff almost does not change. At the same time, the RCP 8.5 scenario provides a decrease in water and sediment runoff.

Abstract Flood control reservoir design requires estimating the total storable water volume or the maximum allowable discharge. This study proposes a novel Generalized Semi‐Analytical Approach (GS‐AA) to identify the maximum outlet discharge a flood control reservoir can handle for a specific return period. The approach exploits the analytical expression of Flow Duration Reduction (FDR) curves and combines them with an optimization algorithm to find the critical hydrograph and, thus, the hydrograph providing the maximum outlet discharge from the reservoir. The approach models the runoff process of the basin upstream of the reservoir, allowing users to choose any runoff model (RM). The proposed approach shows faster computational times than a fully numerical procedure, enabling potential users to explore and compare multiple reservoir configurations easily. Moreover, this approach addresses flow data limitation issues that prevent FDR curve derivation by correlating them to Intensity Duration Frequency curve parameters, expanding the potential applicability of the procedure in ungauged basins. Finally, results demonstrated the functionality of the procedure regardless of the chosen RM, offering widespread flexibility for users. The proposed GS‐AA is a robust and adaptable tool for design and verification purposes to improve flood management strategies.

A three-parameter runoff probability model for long-slope croplands in the black soil region of Northeast China

Revisiting overland runoff modeling: Mixed flows and pseudo-kinematic waves

Abstract Extreme floods pose escalating risks in a changing climate, yet forecasting remains challenging due to peak flow underestimation and high uncertainty. We introduce diffusion‐based runoff model (DRUM), a probabilistic deep learning (DL) approach that advances extreme flood forecasting across representative basins in the contiguous United States. DRUM outperforms state‐of‐the‐art benchmarks, enhancing nowcasting skill for the top 1‰ of flows in 72.3% of studied basins. Under operational scenarios, DRUM extends reliable lead times by nearly a full day for 20‐ and 50‐year floods. When evaluated with measured precipitation, an ideal condition, recall improves by 0.3–0.4 and the early warning window extends by 2.3 days for 50‐year floods. The enhancement potential varies regionally, with precipitation‐driven flood zones in the eastern and northwestern US benefiting most, gaining 3–7 days in lead time. These findings highlight the transformative potential of diffusion models as a cutting‐edge generative AI technique for advancing hydrology and broader Earth system sciences.

Accurate flood forecasting is of critical importance for flood control and disaster mitigation. This study focuses on the upper basin of the Juma River and employs the China Flash Flood Hydrological Model (CNFF) to calibrate model parameters using three specific runoff generation models implemented within the CNFF platform: the Xin’anjiang three-source saturation-excess runoff model, the vertical mixed runoff model, and the Dahuofang model. These models, respectively, represent three distinct physical runoff mechanisms—saturation-excess, vertical mixing, and infiltration-excess. The primary scientific objective is to systematically compare the flood forecasting accuracy of these models and to identify the most suitable one for flood forecasting in this basin. The results indicate that the overall forecasting accuracy of the Xin’anjiang model is superior to that of the vertical mixed runoff model and the Dahuofang model. The absolute value of the relative error in peak discharge and the relative error in mean runoff depth simulated by the Xin’anjiang model are 6.8 and 10.7%, respectively. The absolute value of the mean peak arrival time error is 0.47 h, and the average Nash-Sutcliffe efficiency coefficient is 0.69. The Xin’anjiang model demonstrated superior performance, achieving an average Nash-Sutcliffe Efficiency (NSE) approximately 0.21 higher than the other models across the evaluated events. When flood discharge is high and exhibits a single-peak pattern, the simulation performance of all runoff models improves. Overall, the Xin’anjiang model achieves a Class B accuracy level in flood simulation for the upper Juma River basin. These findings provide a reference for hydrological simulation, flood forecasting, and early warning in the upper Juma River basin.

Reliable gridded precipitation products (GPPs) are essential for effective hydrological simulations, particularly in mountainous regions with limited ground-based observations. This study evaluates the performance of two widely used GPPs, CHIRPS and ERA5, in estimating precipitation and supporting runoff generation using the Soil and Water Assessment Tool (SWAT) across three headwater catchments (Sill, Drava and Isel) in the Austrian Alps from 1991 to 2018. The region’s complex topography and climatic variability present a rigorous test for GPP application. The evaluation methods combined point-to-point comparisons with gauge observations and assessments of generated runoff and runoff trends at annual, seasonal and monthly scales. CHIRPS showed a lower precipitation error (RMAE = 25%) and generated more consistent runoff results (RMAE = 12%), particularly in smaller catchments, whereas ERA5 showed higher spatial consistency but higher overall precipitation bias (RMAE = 37%). Although both datasets successfully reproduced the seasonal runoff regime, CHIRPS outperformed ERA5 in trend detection and monthly runoff estimates. Both GPPs systematically overestimate annual and seasonal precipitation amounts, especially at lower elevations and during the cold season. The results highlight the critical influence of GPP spatial resolution and its alignment with catchment morphology on model performance. While both products are viable alternatives to observed precipitation, CHIRPS is recommended for hydrological modelling in smaller, topographically complex alpine catchments due to its higher spatial resolution. Despite its higher precipitation bias, ERA5’s superior correlation with observations suggests strong potential for improved model performance if bias correction techniques are applied. The findings emphasize the importance of selecting GPPs based on the scale and geomorphological and climatic conditions of the study area.

The water regime in Pakistan’s northern region has experienced significant changes regarding hydrological extremes like floods because of climate change. Coupling hydrological models with remote sensing data can be valuable for flow simulation in data-scarce regions. This study focused on simulating the snow- and glacier-melt runoff using the snowmelt runoff model (SRM) in the Gilgit and Kachura River Basins of the upper Indus basin (UIB). The SRM was applied by coupling it with in situ and improved cloud-free MODIS snow and glacier composite satellite data (MOYDGL06) to simulate the flow under current and future climate scenarios. The SRM showed significant results: the Nash–Sutcliffe coefficient (NSE) for the calibration and validation period was between 0.93 and 0.97, and the difference in volume (between the simulated and observed flow) was in the range of −1.5 to 2.8% for both catchments. The flow tends to increase by 0.3–10.8% for both regions (with a higher increase in Gilgit) under mid- and late-21st-century climate scenarios. The Gilgit Basin’s higher hydrological sensitivity to climate change, compared to the Kachura Basin, stems from its lower mean elevation, seasonal snow dominance, and greater temperature-induced melt exposure. This study concludes that the simple temperature-based models, such as the SRM, coupled with improved satellite snow cover data, are reliable in simulating the current and future flows from the data-scarce mountainous catchments of Pakistan. The outcomes are valuable and can be used to anticipate and lessen any threat of flooding to the local community and the environment under the changing climate. This study may support flood assessment and mapping models in future flood risk reduction plans.

Makassar City, a fast-growing urban center in Eastern Indonesia, is highly vulnerable to flooding due to a combination of extreme rainfall, urban expansion, sedimentation, and a limited flood management system. This study investigates the main contributors to flooding in Makassar, based on the city’s extreme flood event in January 2019 and evaluates the effectiveness of the Bili-Bili Reservoir in mitigating flood impacts through integrated hydrologic–hydrodynamic modeling. A combination of HEC-HMS and HEC-RAS 2D was used to simulate the rainfall runoff processes and model flood inundation. GSMaP satellite rainfall data, land cover, soil type, and topographic information (FABDEM + river cross-section) were integrated into the model. Additional terrain data from OSM-B highlights urban areas characterized by dense building development. The validation process was conducted by comparing the modeling output against the inundation maps provided by the local government. Scenario simulations with 20-year return period (Q20) discharges from the Tallo River, Jenelata River, and Bili-Bili Reservoir outflow were used to assess their individual and combined impacts on flooding. Findings indicate that the Tallo River is the dominant contributor to flooding, while reservoir releases and Jenelata River inflow triggered additional inundation in downstream areas. The Bili-Bili Reservoir reduced upstream flooding but was less effective under high-inflow conditions. Discrepancies between model results and reported flood extents in several districts suggest other contributing mechanisms, including urban drainage inadequacies. This study’s findings emphasize the need for more targeted flood mitigation strategies, underscoring the importance of optimizing reservoir operations, managing sedimentation, and exploring storage interventions within Makassar City’s river system to strengthen urban flood resilience.

As global water scarcity becomes more acute, cross-basin water diversion projects, such as the South-to-North Water Diversion Project in China, need scientific risk assessment methods to ensure sustainable water allocation. This study proposes a coupling analysis framework based on Copula-Bayesian, which fills the gap in the systematic risk research of large-scale water transfer projects. By constructing a joint annual runoff distribution model for the Yangtze River and Yellow River, combined with mutation point detection, periodicity analysis (Morlet wavelet) and frequency statistics of boom-bust encounter, the characteristics of hydrological variability under climate change were systematically evaluated. The risk of water diversion under different scenarios is quantified by using Bayesian network for probabilistic reasoning. The results showed that: (1) During 1959–2023, three abrupt runoff points were detected in both the Yangtze River basin (YTB) and the Yellow River basin (YRB), with periodicism of 27/17/11 years and 12/27/29 years, respectively. The runoff of the lower Yellow River showed a significant downward trend (− 1.2%/ decade, p < 0.05). (2) The occurrence probability of extreme flood and ebb synchronous events is less than 5%, while the overall distribution of asynchronous and synchronous events is balanced (45–55%), indicating that the risk of water transfer is generally controllable; (3) The four-level water diversion risk scenario (optimal to most unfavorable) is identified through probability simulation, showing that the low-risk operation probability of the project under current conditions is 68%. This study innovatively combines statistical hydrological models with risk simulation to provide decision support for inter-basin collaborative water resources management in the context of climate change.

Abstract High‐resolution measurements of soil surface flow velocity are critical for advancing the calibration and validation of physically based runoff and erosion models, yet such data remain scarce, particularly under field conditions. This study demonstrates the application and feasibility of particle tracking velocimetry (PTV) for capturing spatially distributed flow velocities during artificial rainfall simulations on agricultural plots. Combined with structure from motion (SfM) for topographic change detection, PTV enables detailed, non‐invasive measurements of surface flow patterns at millimetre to centimetre scales. Two process‐based models were applied and compared against these flow velocity observations. We further analysed the influence of digital elevation model (DEM) resolution on flow simulations, revealing that while average velocities remained relatively stable, spatial flow patterns and rill formation were strongly dependent on resolution. Model comparisons showed that dynamic surface updates better reflected observed flow patterns compared to a static approach. Measured flow velocities from PTV show slight variation from model outputs, due to scale and the nature of measurement. Our results position PTV as a powerful tool for future soil erosion research, enabling spatially resolved flow velocity estimation, improved validation of hydrodynamic processes, and more physically meaningful model parameterisation. This study provides a proof of concept for in‐field PTV during rainfall simulations on small agricultural scales and for integrating high‐resolution optical measurements into process‐based runoff and erosion modelling workflows.