AbstractStudy region and rationale: The case study focuses on two hydrological stations on the lower Tisza River (Serbia and Hungary), located on a large lowland river stream strongly influenced by the downstream Novi Bečej reservoir (Serbia), where backwater effects and long-term hydraulic variability pose significant challenges for accurate flow estimation.Methods and dataConventional approaches that assume a stable stage-flow relationship fail to capture rating curve complexity. To address these limitations, this study introduces a joint machine learning (ML)–copula framework in which ML-based rating models are developed and verified on measured data and stochastically generated synthetic stage-flow pairs using a Gumbel copula. The framework integrates traditional power-law regression with Support Vector Regression (SVR), Multilayer Perceptron (MLP), and Kolmogorov–Arnold Networks (KAN), and evaluates uncertainty through confidence intervals and performance metrics (MAE, RMSE, MAPE, R², PICP).Main results and conclusionsML models outperform classical power regression across low, mean, and high flows, with SVR, MLP, and KAN achieving RMSE ≈ 78–163 m³ /s compared to RMSE ≈ 80–173 m³ /s for power regression. Under synthetic Gumbel-generated datasets, KAN maintains performance comparable to SVR (RMSE ≈ 129–212 m³/s) and preserves stable behavior across flow regimes, avoiding the underprediction observed in MLP. Consequently, KAN demonstrates the robustness necessary for adaptive stage-flow rating curve estimation under changing hydraulic conditions.

Water quality modeling is essential for the management and operational control of water distribution systems (WDSs). The dynamic nature of these systems increases uncertainty about the permanent state of the network; therefore, conventional models are often insufficient to predict their behavior. In this study, a comprehensive literature review on water quality modeling in offline and online conditions, including classical models and real-time applications, is presented. The objective of this work is to classify and analyze these methodologies, identify knowledge gaps, and suggest directions for future research. The classification is divided into four categories: contaminant event detection, monitoring, contaminant source identification, and water quality simulation. The findings suggest that only approximately 20% of the articles analyzed address real-time applications. Consequently, there is a pressing need to strengthen the development of systems that integrate modeling, prediction, and control mechanisms to enhance water quality management.

Inflow and infiltration (I&I) in urban sewer networks increase both the delivery loads and overflow risks, thereby compromising environmental safety. While sensor-based detection of I&I is promising, a key limitation in most current applications is their reliance on fixed, isolated detection thresholds derived from individual sensors. This approach prevents the synthesis of information from multiple sensors and inherently limits the detectability of I&I events. To bridge this gap, this study introduces a novel topology-derived flow inference (TDFI) method that quantifies the pipe-specific minimum detectable I&I flow by synthesizing data from upstream sensors in sewer networks. Based on this method, a new detection threshold metric is formulated for sensor placement strategy (SPS) optimization, accompanied by an efficient Sequential Backward Selection (SBS) approach that deterministically constructs hierarchical sensor subsets through an iterative removal of the least-contributing sensors. Evaluation across three case studies (one synthetic and two real-life) demonstrates that the TDFI-based optimization framework identifies robust SPSs, leading to significantly improved overall detection performance for minor I&I events. A key finding is that prioritizing sensor density in high building-density areas significantly enhances overall detection performance. Comparative analysis shows that SBS achieved performance close to that of the DE-based optimizer while providing deterministic layouts under various budgets, offering a computationally efficient complementary approach. The core contribution of this study is to propose a topology-informed framework for SPS optimization in support of I&I detection, integrating upstream flow inference to maximize the detection capability of sensor layouts.

Biofilms in drinking water distribution systems (DWDS) challenge water quality, infrastructure and public health. Current monitoring methods often disrupt biofilms or lack spatial coverage. This study explores two novel, non-intrusive techniques to measure biofilm thickness: one based on heat resistance, the other on changes in hydraulic residence time. Experiments were conducted in a lab-scale DWDS simulator replicating realistic pipe conditions. Both methods were evaluated against traditional destructive sampling to assess accuracy. Results show that the residence time method yields consistent, reliable estimates closely matching physical samples, while the heat resistance approach shows greater variability and requires refinement. Sensitivity analyses further demonstrate that the residence time method is more robust under varying operational conditions. These findings highlight its potential for field deployment, offering a scalable and minimally invasive solution for real-time biofilm monitoring. This advancement could support improved water quality management through targeted interventions in actual DWDS environments.

Simulating urban drainage hydraulics is computationally demanding, limiting its application in tasks that require real-time or repeated simulations. Graph Neural Networks (GNNs) are promising metamodels, but the effect of their internal components and transferability potential remain underexplored. This study addresses these gaps through two main contributions: (1) a systematic evaluation of key architectural components, including graph layer type, processor depth, and prediction window with links to physical transport dynamics; and (2) transferability experiments across domains (across two distinct drainage networks) and tasks (from head to flow prediction). As case studies, we selected two combined sewer networks in The Netherlands that differ in their hydraulic dynamics. We find that metamodels with moderate depth and a ten-step prediction window achieve high accuracy (RMSE of 2–5 cm for hydraulic heads and 0.02 m³/s for flowrates). They also reach speed-ups of up to four orders of magnitude higher compared to the physics-based model, SWMM, when executing parallel simulations in GPU. Based on our two case studies, we find that pre-trained metamodels with full fine-tuning effectively adapt to a new task within the same domain, whereas cross-domain transfer requires appropriate normalization and fine-tuning. Furthermore, joint training on both case studies enables the metamodel to capture representations of both systems, suggesting potential for more general applicability. These findings demonstrate that metamodel architecture can reflect physical system behavior and offer practical guidance for building fast, accurate, and generalizable GNN-based metamodels—establishing a foundation for their use in applications such as uncertainty analysis, design optimization, and nowcasting.

Storm-driven runoff scours accumulated sediments within stormwater drainage systems, transporting multi-source pollutants (including pathogens) into surface water through stormwater overflows, thereby elevating contamination risks in the recipient. Chlorine-based disinfection of overflowed stormwater applied in related storage tanks mitigates these risks before release. This study reveals that chlorophenylacetonitriles (CPANs), which are formed during the disinfection process, exhibit toxicity levels higher than conventional trihalomethanes and haloacetonitriles. Laboratory analyses conducted in this work demonstrated that sewer sediments — not runoff or stormwater — are the dominant precursor source for CPAN formation during overflow disinfection. Source apportionment further identified a robust linear correlation (R² = 0.95) between sediment indole concentrations (0.093–0.91 μg/g) and CPAN formation, experimentally confirming for the first time that indole is a critical precursor. Laboratory experiments also uncovered the presence of monochloroindoles in indole chlorination, a novel class of aromatic nitrogenous disinfection byproducts (DBPs). In addition, density functional theory calculations demonstrated that monochloroindole formation has lower activation energy barriers compared to CPAN pathways, resulting in new molecular-level insights into their preferential transformation. Given that indole serves as a shared precursor for both highly toxic CPANs and even more ecotoxic monochloroindoles, this study emphasizes the urgent need for sewer sediment management to mitigate the ecological and human health risks associated with these highly toxic nitrogenous DBPs.

The illicit connections between sewage and stormwater pipes result in the discharge of untreated sewage into receiving rivers, posing significant odor and health hazards. While thioethers are recognized as key odorants in sewage systems, their distribution in stormwater systems remain poorly characterized. This study analyzed 12 types of thioethers in stormwater pipes sampled at 21 sites in China. Advanced analytical techniques, including Mantel analysis and Structural Equation Modeling, were employed to examine the relationships between overlying water properties, sediment microbial characteristics, and thioether concentrations. Results showed that sediment thioether loads (36.77 ± 50.14 μg S/m; range: 7.24–99.96 μg S/m) were substantially higher than those in the overlying water (12.02 ± 42.52 μg S/m; range: 0.03–92.76 μg S/m), highlighting sediment as a critical pollution reservoir. Dissolved oxygen, NH₃-N, and terrestrial-derived dissolved organic nitrogen were identified as key factors shaping sediment microbiome composition, particularly fermentative, sulfate-reducing, and denitrifying bacteria, which in turn drives thioether formation. Specifically, dominant compounds like dimethyl disulfide and dimethyl trisulfide were found to be produced through the anaerobic fermentation of methionine and redox conversion of methanethiol, as well as the anaerobic fermentation of cysteine and methylation of polysulfides. Humic substances could facilitate methanethiol redox conversion and polysulfide methylation by serving as methyl donors and enhancing electron transfer efficiency. Additionally, NH₃-N may promote microbial metabolism by providing amino groups essential for the synthesis of metabolic precursors. Therefore, effective mitigation of odorous thioethers in stormwater systems necessitates integrated strategies targeting both sulfur-containing organic precursors and nitrogen-rich pollutants.

Biofilms in drinking water distribution systems (DWDS) pose a critical challenge to water quality. If left unchecked, they can compromise the biological stability of delivered water and ultimately public health. Existing biofilm sensing techniques primarily focus on metabolic or genetic indicators of activity, often using local and destructive methods. While rich in information, such data are difficult to apply in developing practical biofilm growth models. Biofilm thickness, however, is a more representative and scalable metric for this purpose. Yet, limited research exists on non-invasive thickness sensing in DWDS. This study introduces two non-destructive methods for measuring biofilm thickness by leveraging changes in heat resistance and residence time. Heat resistance was evaluated using ambient and water temperature measurements, while residence time was assessed with a conservative tracer. Both techniques were tested in the Slimer experimental setup (50 m long, 13.2 mm diameter PVCp pipe) under realistic hydraulic conditions. Results showed a strong correlation between biofilm thickness and residence time drift, indicating flow disturbance as a reliable indicator of biofouling. In contrast, heat resistance sensing exhibited considerable natural variability, limiting its analytic value. The findings highlight residence time analysis as a promising, non-invasive approach for estimating biofilm thickness. This method offers continuous, non-destructive monitoring, enabling early detection of biofilm-related anomalies and providing valuable input for both laboratory and field applications aimed at enhancing DWDS resilience.

Addressing water scarcity requires significant attention to reducing water footprint (WF) related to food consumption. Since individuals' dietary behavior is largely influenced by their demographic and anthropometric attributes, it is crucial to identify individuals who have a high dietary WF and prioritize them as the focus of policies. Several studies analyzing the driving factors behind dietary WF exist but have multiple limitations. These include the statistical models with rather modest performances, lack of rigorous sensitivity analysis/feature importance (FI) analysis, and lack of generalization ability. Here, we developed a novel ML-based framework for analyzing the driving forces behind dietary WF. The framework incorporated three machine learning (ML) models (Extra-Trees (ET), Histogram-based Gradient Boosting (HGB), and eXtreme Gradient Boosting (XGB)) and an ML explanation approach Shapley Additive exPlanations (SHAP). This framework was applied to a case study on Chinese inhabitants. The derived results validated the proposed framework and demonstrated ML's superiority over conventional statistical methods. XGB was identified as the optimal model as it effectively captured the variability in the data and showed good generalization performance. The FI analysis for XGB revealed the most influential features on dietary WF, with income level, urbanization level, education level, and gender emerging as the top four features in descending order. Through the subsequent SHAP dependence analysis, the priority groups for dietary WF reduction interventions were identified as high-income residents, urban residents, highly educated residents, and male residents. In light of these findings and their underlying causes, the paper concluded with a set of policy recommendations.

Accurate calibration of hydraulic models of water distribution systems (WDSs) is essential for reliable simulations. After eliminating gross errors, including those in estimated demands, pipe roughness coefficients (PRCs) are the most often used calibration parameters. Although numerous PRC calibration methods exist to ensure model simulations align well with field observations, they typically assume error-free pressure gauge elevations and overlook the compensatory interactions between elevation errors and PRC uncertainties. This often results in biased PRC calibration outcomes. To overcome this limitation, this paper introduces a novel framework that decouples elevation errors by minimizing the standard deviation of pressure residual time series, rather than relying on traditional residual minimization techniques. Additionally, a clustering-based data preprocessing approach is employed to reduce the impact of uncertain nodal demands and measurement noise. Tests on three benchmark networks demonstrate that the proposed method accurately calibrates PRCs, even when accounting for elevation inaccuracies, nodal demand uncertainties and measurement noise simultaneously. This establishes a new paradigm that leverages the statistical characteristics of residual time series to enable error-decoupled model calibration. Crucially, the method also quantifies pressure gauge elevation errors through post-calibration residual analysis, eliminating the need for costly field surveys. This advancement is particularly valuable for regions with missing or erroneous elevation data, significantly improving WDS calibration practices.

Urban drainage network models (UDNMs) have been widely used to facilitate flood management. Typically, a UDNM is developed using data from Geographic Information Systems (GIS), and hence it consists of many short pipes and connection nodes or manholes. To improve modeling efficiency, a GIS-based model is generally skeletonized by removing many elements. However, there has been surprisingly a lack of knowledge on to what extent such skeletonization can affect the model's simulation accuracy, resulting in uncertainty in flood risk estimation. This paper makes the first attempt to quantitatively evaluate multidimensional impacts of different skeletonization levels on hydraulic properties of UDNMs. This goal is achieved by a new evaluation framework comprising of eight existing and new metrics that make use of hydrographs, main pipe hydraulics and flood distribution properties. A real-life UDNM is used to illustrate the new framework under various rainfall conditions and different skeletonization levels. The new framework is also used to compare the performance of two compensation methods in mitigating impacts caused by model skeletonization. Results obtained show that: (a) model skeletonization can significantly affect the magnitude of peak flow at the outfall, with a maximum overestimation of up to 20%, (b) hydraulics in main pipes can also be affected by model skeletonization with the maximum flow increasing up to 35%, and (c) model skeletonization may significantly alter the flood distribution properties which has been largely ignored in past studies. These findings provide guidance for UDNM skeletonization, where their associated impacts should be aware in engineering practice.

Transportation of non-Newtonian fluids (NNFs) through pipelines is a cornerstone of modern infrastructure. While the laminar and transitional flows have been extensively studied, the turbulent behavior of NNFs remains poorly understood. This study investigates large-scale pipe-loop experiments on clay–water slurries, spanning Reynolds numbers (Formula presented) in a 100-mm diameter facility. Using non-invasive ultrasound velocity profiling (UVP) together with wall shear stress measurements, we characterize flows ranging from weakly to highly non-Newtonian conditions with concentrations up to 19%(w/w). The experiments show that the transition to the log-law region is delayed and the log-law intercept shifts upward with increasing concentration, reflecting the redistribution of stresses as shear-thinning and yield effects become more pronounced. To further interpret these findings, the experimental observations were compared with established modeling approaches. Semi-empirical correlations exhibited intermediate performance (mean absolute error, MAE, up to 0.55 Pa for wall shear stress and 0.15 m/s for velocity), while the Launder–Spalding wall function performed worst due to its assumption of constant viscosity (MAE ≈ 1.48 Pa and 0.08 m/s). In contrast, the rheology-based wall function achieved the most reliable predictions, with minimal deviations from experiments (MAE ≈ 0.20 Pa for wall shear stress and 0.06 m/s for velocity). Overall, this work provides a comprehensive experimental and modeling assessment of turbulent non-Newtonian pipe flow at an industrial scale, yielding new insights into flow physics and establishing a valuable reference for future experimental and computational studies.

This chapter presents a detailed description of the circularity and efficiency assessment methods to be used in the context of resource recovery solutions in the water sector. The resource recovery solutions are meant to produce multiple benefits, such as increased resource efficiency and decreased negative environmental impact, among others. The solutions need to be assessed and compared using a comprehensive set of criteria and indicators. This report discusses key concepts, explains methods, and briefly presents a spreadsheet tool developed for conducting the assessment. Some key concepts, such as circular bioeconomy and efficiency, are first introduced. Several resources may be recovered from the water sector, and thus, commonly recovered resources are classified. This is followed by an expansion of the scope of the material circularity indicator, a prevalent assessment method. This is done to apply the MCI to the resources relevant to the water sector. Equations for the resource categories are developed and presented. Efficiency is then defined as a ratio between the benefits and costs of a resource recovery solution. Two categories of cost indicators are introduced, followed by three categories of benefit indicators. By combining different cost and benefit indicators, several indicators such as simple material efficiency, service unit-based energy efficiency, and service unit ecoefficiency can be created. Circularity and efficiency assessment methods are explained with simple examples, and screenshots from the spreadsheet assessment tool are presented. Lastly, the assessment method is demonstrated on a real-life case study located in Italy. The case study involves reuse of treated wastewater (TW) for irrigation. The newly developed circularity and efficiency methods demonstrate the improvements in the circularity and efficiency resulting from TW irrigation reuse, along with pointing to the most crucial factors to be considered for such cases.

This review explores recent advancements in modeling the flow behavior of Herschel-Bulkley (HB) fluids in pipes, discussing theoretical, semi-empirical, computational, and experimental methods. While the laminar flow of non-Newtonian HB fluids can be effectively modeled using first-principle physics, significant challenges remain in turbulent and transitional flow regimes. Existing turbulence models, though widely used, may not always fully align with experimental data, often requiring further validation or complex mathematical tuning, leading to higher computational costs. Further, the transition to turbulence in HB fluids is influenced by shear-thinning and yield stress, yet current models often fail to account for this delayed transition. Consequently, stability and Reynolds number-based transition models can exhibit inconsistencies, limiting their broader applicability. Progress is further hindered by limited experimental studies, constrained by resolution, attenuation, cost, and material combinations. Inaccuracies in rheological modeling—due to inappropriate shear rate ranges, curve-fitting techniques, or simplifying assumptions such as homogeneity and non-elasticity—further complicate flow predictions. Through this review, we delve deeper into the state-of-the-art modeling of HB fluids, highlighting progress and these challenges. Addressing these limitations requires advanced experimental and numerical studies, particularly for near-wall measurements, to better capture flow complexities and improve model predictions. This could also facilitate the development of data-driven approaches and operational envelopes that define their validity thresholds. Future research should also prioritize the independent effects of yield stress and shear-thinning properties while considering material attributes and settling phenomena in non-Newtonian suspensions. Ultimately, these advancements will enable more accurate flow predictions and practical solutions for industrial applications.

Supervised deep learning methods have been widely employed to detect floating macroplastic litter (>5 mm) in (fresh)water bodies. However, few studies used them to quantify floating litter fluxes in rivers with wide cross-sections, that is important for pollution assessment. Additionally, commonly used supervised learning (SL) models rely on extensive labeled data, that is time-consuming and expensive to obtain. Moreover, regardless of the model type, current deep learning models for litter detection usually fail to correctly identify small litter items. To overcome these issues, we propose a semi-supervised learning (SSL)-based framework combined with Slicing Aided Hyper Inference (SAHI) for quantifying cross-sectional floating litter fluxes in rivers. The framework includes four steps: (a) collecting camera images of river surfaces from multiple locations across the river, (b) developing a robust litter detection model using SSL, (c) applying this model with SAHI to detect litter items in images, and (d) post-processing the detection results to quantify fluxes. The SSL method involves: (i) self-supervised pre-training of a ResNet50 on a large amount of unlabeled data, and (ii) supervised fine-tuning of a Faster R-CNN with the ResNet50 backbone on a limited amount of labeled data. We evaluated the in-domain detection performance of SSL models with varying pre-training epochs and pre-training dataset sizes, using images from waterways of The Netherlands, Indonesia and Vietnam, that were used for model pre-training and fine-tuning. Additionally, we assessed the zero-shot out-of-domain detection performance of SSL models and litter flux quantification performance of the proposed framework on a Vietnam case study, that was not used for model development. We benchmarked our results against the SL methods and human visual counting. The results show that SSL models benefit from longer pre-training time and larger pre-training dataset, achieving an in-domain F1-score increase of 0.2 and a zero-shot out-of-domain increase of up to 0.14, over baseline SL benchmarks. Furthermore, the SAHI method correctly identifies 45 additional small litter items (areas < 1,000 cm2), improving the F1-score by up to 0.19, compared to the results obtained without SAHI. The flux measurement results indicate that the SSL-based framework substantially underestimates fluxes by a factor of 3–4 compared to human measurements, due to missed detections of transparent litter items and items entrapped in water hyacinths. However, it estimates nearly twice the fluxes of the baseline SL-based framework, aligning more closely with human measurements. These findings highlight the potential of SSL-based framework to enhance litter flux measurement. Scaling it with broader datasets could significantly advance global-scale litter monitoring systems.

There is a trend towards decentralized source separation (DSS) for wastewater treatment and resource recovery. An assessment framework is required to assess whether implementing a DSS treatment over a conventional centralized one is advantageous. This framework needs to account for the performance of the wastewater treatment plant (WWTP) and the effect that resource recovery has on closely-linked sectors such as food and energy production. A framework is lacking that covers the economic dimension, the circularity, the nature reciprocity of resource recovery and that can be applied to real-life cases. A novel WFE framework has been developed here to compare a conventional centralized and a DSS-based WWTP. This novel WFE framework contains assessment methods that are reproducible, and applicable to real-life cases. It also accounts for the local climatic conditions that determine irrigation water requirements. The comparison results revealed that the need to construct new DSS infrastructure leads to a lower economic efficiency of water treatment. Further, chemical-intensive treatment reduces the DSS's material resource circularity and efficiency. Using heat pumps increases the energy use of the DSS WWTP, causing a reduction in water treatment energy efficiency. However, the advantages of DSS show up in the freshwater and nutrient efficiency of food production as well as in the energy self-sufficiency of the WWTP. The novel WFE framework contains indicators specific to water treatment and the food production sectors to improve inter-sectoral communication. Also, including the nature reciprocity assessment can help demonstrate the issue with treated wastewater discharge, especially in arid regions with low stream flows. It can potentially help improve the acceptance of treated wastewater-based reuse. To conclude, the novel framework helps to assess real-life case studies in a more integrated and holistic way. It can help make decisions related to decentralization and source separation by simultaneously considering the water treatment, energy production, and food production sectors.

The effective environmental management of combined sewer systems requires reliable estimation of discharge and pollutant loads conveyed at the outlet during rainstorms. This study investigates how, with a lumped modelling approach, it is possible to reproduce the quality characteristics of discharged water, provided that high temporal resolution experimental data of pollutant concentrations are available. The methodology is applied to the combined sewer of a real urban drainage network where a continuous high resolution monitoring campaign of water quality and quantity has been carried out at an overflow structure location near the outlet of the drainage system. The lumped modelling approach has been implemented in the Storm Water Management Model (SWMM) with hydrological parameters estimated from cartographic information, based on recently proposed methodology that allows reliably simulating the storm hydrographs without model calibration. A semi-distributed model has been also developed using the SWMM with hydrologic parameters randomly sampled to fit the measured hydrographs of different training and validation data. The results obtained show that the uncalibrated lumped model simulates the observed hydrographs with similar performance as with the semi-distributed model (i.e., the normalized Nash-Sutcliff efficiency index of the validation set is 0.753 for the uncalibrated lumped model and 0.765 for the best-performing sampled parameter set of the semi-distributed model). The water quality parameters describing the build-up and wash-off of total dissolved solids (TDS) in a lumped model have been calibrated too, as well as those describing the mixing and consumption of dissolved oxygen (DO). The results show that a lumped modelling approach can reproduce the water quality dynamics in a combined sewer system, representing a promising tool for effective environmental management. However, event-specific calibrated parameter values have been obtained in some cases, which require further investigation and still limit the general applicability of the obtained results, thus confirming that setting up a reliable model requires water quality measurements.