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35 pages, 12090 KB  
Article
Multidimensional Copula-Based Assessment, Propagation, and Prediction of Drought in the Lower Songhua River Basin
by Yusu Zhao, Tao Liu, Zijun Wang, Xihao Huang, Yingna Sun and Changlei Dai
Hydrology 2025, 12(11), 287; https://doi.org/10.3390/hydrology12110287 (registering DOI) - 31 Oct 2025
Abstract
As global climate change intensifies, understanding drought mechanisms is crucial for managing water resources and agriculture. This study employs the Standardized Precipitation–Actual Evapotranspiration Index (SPAEI), Standardized Runoff Index (SRI), and Standardized Soil Moisture Index (SSMI) to analyze meteorological, hydrological, and agricultural droughts in [...] Read more.
As global climate change intensifies, understanding drought mechanisms is crucial for managing water resources and agriculture. This study employs the Standardized Precipitation–Actual Evapotranspiration Index (SPAEI), Standardized Runoff Index (SRI), and Standardized Soil Moisture Index (SSMI) to analyze meteorological, hydrological, and agricultural droughts in the lower Songhua River basin. The PLUS model was used to predict future land types, with model accuracy validated using four evaluation metrics. The projected land cover was integrated with CMIP6 data into the SWAT model to simulate future runoff, which was used to calculate future SRI. Drought events were extracted using run theory, while drought occurrence probability and return period were calculated via a Copula-based joint distribution model. Bayesian conditional probability was employed to explore propagation mechanisms. The results indicate a significant increase in multidimensional drought risk, particularly when the cumulative frequency of univariate droughts reaches 25%, 50%, or 75%. Although increased duration and intensity enhance the likelihood of combined droughts, extremely high values cause a decline in joint probability under “OR” and “AND” conditions. Under different climate scenarios, the recurrence intervals of meteorological, hydrological, and agricultural droughts in the lower reaches of the Songhua River exhibit increased sensitivity with severity, demonstrating consistent propagation patterns across the meteorological–hydrological–agricultural system. Meteorological drought was found to propagate to hydrological and agricultural drought within ~6.00 months and ~3.67 months, respectively, with severity amplifying this effect. Propagation thresholds between drought types decreased with increasing intensity. This study combined SWAT and CMIP6 models with PLUS-based land-use scenarios, highlighting that land-use changes significantly influence spatiotemporal drought patterns. Model validation (Kappa = 0.83, OA = 0.92) confirmed robust predictive accuracy. Overall, this study proposes a multidimensional drought risk model integrating Copula and Bayesian networks, offering valuable insights for drought management under climate change. Full article
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29 pages, 4176 KB  
Article
Distinct Pollution Profiles and Spatio-Temporal Dynamics in Adjacent Ramsar Lakes (Algeria): An Integrated Assessment and High-Resolution Mapping for Targeted Conservation
by Ines Houhamdi, Leila Bouaguel, Laid Bouchaala, Nedjoud Grara, Mouslim Bara, Agnieszka Szparaga and Moussa Houhamdi
Processes 2025, 13(11), 3466; https://doi.org/10.3390/pr13113466 - 28 Oct 2025
Viewed by 252
Abstract
This study provides the first integrated spatio-temporal assessment of water quality in Lakes Tonga and Oubeira, two adjacent Ramsar-designated wetlands within El Kala National Park (Algeria). The objective was to identify major pollution sources and inform targeted conservation strategies. Physico-chemical, microbiological, and heavy [...] Read more.
This study provides the first integrated spatio-temporal assessment of water quality in Lakes Tonga and Oubeira, two adjacent Ramsar-designated wetlands within El Kala National Park (Algeria). The objective was to identify major pollution sources and inform targeted conservation strategies. Physico-chemical, microbiological, and heavy metal analyses were performed on water samples collected monthly over one year (September 2022–August 2023) from two sites per lake. Applying robust statistical analyses (ANOVA, Kruskal–Wallis, PCA, boxplots) and high-resolution spatial mapping, we revealed significant spatio-temporal heterogeneity and distinct pollution profiles between the two lakes. Specifically, Lake Tonga exhibited higher concentrations of organic and bacterial pollutants, likely linked to agricultural runoff and domestic discharge, while Lake Oubeira was characterized by elevated heavy metal concentrations and higher mineralization. The calculated Water Quality Index (WQI) classified the water quality of both lakes predominantly as “Moderate”, with punctual “Poor” quality episodes. Numerous parameters consistently exceeded water quality standards, indicating substantial ecological and health risks. Spatial distribution maps clearly pinpointed pollution hotspots, guiding lake-specific management measures. These findings underscore the urgent need for differentiated, targeted management interventions and an integrated, multidisciplinary approach for the effective conservation of these valuable wetland ecosystems. Full article
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17 pages, 8801 KB  
Article
Bioavailability, Ecological Risk, and Microbial Response of Rare Earth Elements in Sediments of the Remediated Yitong River: An Integrated DGT and Multi-Parameter Assessment
by Yu Zhong, Chanchan Wu, Jiayi E, Yangguang Gu, Hai Chi and Xinglin Du
Microorganisms 2025, 13(11), 2443; https://doi.org/10.3390/microorganisms13112443 - 24 Oct 2025
Viewed by 316
Abstract
The expanding use of rare earth elements (REEs) in high-tech industrials has increased their environmental release, raising concerns about their ecological risks. This study employed the Diffusive Gradients in Thin Films (DGT) technique to assess REE bioavailability, spatial distribution, and ecological risks of [...] Read more.
The expanding use of rare earth elements (REEs) in high-tech industrials has increased their environmental release, raising concerns about their ecological risks. This study employed the Diffusive Gradients in Thin Films (DGT) technique to assess REE bioavailability, spatial distribution, and ecological risks of REEs in sediments of the Yitong River, a historically polluted urban river in Changchun, China. Sediment characteristics (organic matter, pH, salinity), nutrient dynamics (N, P), and metal concentrations (Fe, Mn, As, etc.) were analyzed alongside REEs to evaluate their interactions and environmental drivers. Results revealed that REE concentrations (0.453–1.687 μg L−1) were dominated by light REEs (50.1%), with levels an order of magnitude lower than heavily industrialized regions. Ecological risk quotients (RQ) for individual REEs were below thresholds (RQ < 1), indicating negligible immediate risks, though spatial trends suggested urban runoff influences. Probabilistic risk assessment integrating DGT data and species sensitivity distributions (SSD) estimated a low combined toxic probability (2.26%) for REEs and nutrients. Microbial community analysis revealed correlations between specific bacterial (e.g., Clostridium, Dechloromonas) and fungal genera (e.g., Pseudeurotium) with metals and REEs, highlighting microbial sensitivity to pollutant shifts. This study provides a multidimensional framework linking REE bioavailability, sediment geochemistry, and microbial ecology, offering insights for managing REE contamination in urban riverine systems. Full article
(This article belongs to the Section Environmental Microbiology)
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19 pages, 6351 KB  
Article
Spatio-Temporal Variations in Soil Organic Carbon Stocks in Different Erosion Zones of Cultivated Land in Northeast China Under Future Climate Change Conditions
by Shuai Wang, Xinyu Zhang, Qianlai Zhuang, Zijiao Yang, Zicheng Wang, Chen Li and Xinxin Jin
Agronomy 2025, 15(11), 2459; https://doi.org/10.3390/agronomy15112459 - 22 Oct 2025
Viewed by 367
Abstract
Soil organic carbon (SOC) plays a critical role in the global carbon cycle and serves as a sensitive indicator of climate change impacts, with its dynamics significantly influencing regional ecological security and sustainable development. This study focuses on the Songnen Plain in Northeast [...] Read more.
Soil organic carbon (SOC) plays a critical role in the global carbon cycle and serves as a sensitive indicator of climate change impacts, with its dynamics significantly influencing regional ecological security and sustainable development. This study focuses on the Songnen Plain in Northeast China—a key black soil agricultural region increasingly affected by water erosion, primarily through surface runoff and rill formation on gently sloping cultivated land. We aim to investigate the spatiotemporal dynamics of SOC stocks across different cultivated land erosion zones under projected future climate change scenarios. To quantify current and future SOC stocks, we applied a boosted regression tree (BRT) model based on 130 topsoil samples (0–30 cm) and eight environmental variables representing topographic and climatic conditions. The model demonstrated strong predictive performance through 10-fold cross-validation, yielding high R2 and Lin’s concordance correlation coefficient (LCCC) values, as well as low mean absolute error (MAE) and root mean square error (RMSE). Key drivers of SOC stock spatial variation were identified as mean annual temperature, elevation, and slope aspect. Using a space-for-time substitution approach, we projected SOC stocks under the SSP245 and SSP585 climate scenarios for the 2050s and 2090s. Results indicate a decline of 177.66 Tg C (SSP245) and 186.44 Tg C (SSP585) by the 2050s relative to 2023 levels. By the 2090s, SOC losses under SSP245 and SSP585 are projected to reach 2.84% and 1.41%, respectively, highlighting divergent carbon dynamics under varying emission pathways. Spatially, SOC stocks were predominantly located in areas of slight (67%) and light (22%) water erosion, underscoring the linkage between erosion intensity and carbon distribution. This study underscores the importance of incorporating both climate and anthropogenic influences in SOC assessments. The resulting high-resolution SOC distribution map provides a scientific basis for targeted ecological restoration, black soil conservation, and sustainable land management in the Songnen Plain, thereby supporting regional climate resilience and China’s “dual carbon” goals. These insights also contribute to global efforts in enhancing soil carbon sequestration and achieving carbon neutrality goals. Full article
(This article belongs to the Section Agroecology Innovation: Achieving System Resilience)
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30 pages, 15268 KB  
Article
Multi-Objective Two-Layer Robust Optimisation Model for Water Resource Allocation in the Basin: A Case Study of Yellow River Basin, China
by Danyang Di, Hao Hu, Shikun Duan, Qi Shi, Huiliang Wang and Lizhong Xiao
Water 2025, 17(20), 3009; https://doi.org/10.3390/w17203009 - 20 Oct 2025
Viewed by 326
Abstract
The continuous growth of the social economy and the accelerated urbanisation process have led to a rising increase in the demand for water resources in river basins. The uneven temporal and spatial distribution of water resources has further exacerbated the contradiction between supply [...] Read more.
The continuous growth of the social economy and the accelerated urbanisation process have led to a rising increase in the demand for water resources in river basins. The uneven temporal and spatial distribution of water resources has further exacerbated the contradiction between supply and demand. The traditional extensive water resource allocation model is no longer suitable for the diverse demands of sustainable development in river basins. Therefore, there is an urgent demand to determine how to reconcile the supply and demand of water resources in river basins to achieve a rational allocation. Taking the Yellow River Basin as an example, an optimal water allocation framework based on multi-objective robust optimisation method was proposed in this study. A robust constraint boundary conditions for the industrial, agricultural, construction and service, ecological, and social water demand were selected from the perspective of the economy–society–ecology nexus. Then, Latin hypercube sampling was adopted to modify the Monte Carlo method to improve the dispersion of sampling values for quantifying the uncertainty of water allocation parameters. Furthermore, a multi-dimensional spatial equilibrium optimal allocation combining adjustable robust optimisation and multi-objective optimisation was established. Finally, a multi-objective particle swarm optimisation algorithm based on a crossover operator was constructed to obtain the Pareto-optimal solution for multi-dimensional spatial equilibrium optimal allocation. The primary findings were as follows: (1) Parameter uncertainty had a significant effect on the provincial/regional revenues of water resources but has no obvious effect on basin revenue. (2) The uncertainty in runoff and parameters had a significant influence on decisions for optimal water allocation. The optimal volume of water purchased by different provinces (regions) varied greatly under different scenarios. Full article
(This article belongs to the Section Water Resources Management, Policy and Governance)
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19 pages, 5819 KB  
Article
Research on Driving Forces of Spatiotemporal Patterns in Cotton Cultivation Considering Spatial Heterogeneity
by Meng Du, Deyu Shen, Xun Yang, Fenfang Lin, Chunfa Wu and Dongyan Zhang
Agriculture 2025, 15(20), 2163; https://doi.org/10.3390/agriculture15202163 - 18 Oct 2025
Viewed by 202
Abstract
Cotton is increasingly important in global development. The exploration of drivers of spatiotemporal patterns for cotton planting, considering spatial heterogeneity, is essential for optimizing its distribution and supporting sustainable production. This study combined the locally explained stratified heterogeneity (LESH) model with geographically weighted [...] Read more.
Cotton is increasingly important in global development. The exploration of drivers of spatiotemporal patterns for cotton planting, considering spatial heterogeneity, is essential for optimizing its distribution and supporting sustainable production. This study combined the locally explained stratified heterogeneity (LESH) model with geographically weighted regression (GWR) to investigate the factors shaping cotton-planting patterns in the northern slope of the Tianshan Mountains (NSTM), China, from 2000 to 2020. Cotton distribution was derived from long-term Landsat image series, and its expansion showed an average annual growth rate of 2.10 × 103 km2, with intensive cultivation primarily distributed across the central and western counties. The dominant drivers of cotton distribution were elevation (ELE), sunshine duration (SD), slope (SLO), temperature (TEM), runoff (RO), and gross domestic product (GDP). ELE explained about 40% of the spatial heterogeneity. SD showed a declining influence, SLO remained stable, TEM increased in importance, and GDP exhibited a progressive upward trend, although weaker. Moreover, nonlinear weakening interactions, especially between ELE and other factors, as well as between socio-economic and climatic variables, substantially enhanced explanatory power. These findings highlight the significance of accounting for spatial heterogeneity and factor interactions in guiding the spatial optimization and sustainable management of cotton cultivation. Full article
(This article belongs to the Section Artificial Intelligence and Digital Agriculture)
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16 pages, 1699 KB  
Technical Note
Synthetic Hydrograph Estimation for Ungauged Basins: Exploring the Role of Statistical Distributions
by Dan Ianculescu and Cristian Gabriel Anghel
Stats 2025, 8(4), 100; https://doi.org/10.3390/stats8040100 - 17 Oct 2025
Viewed by 581
Abstract
The use of probability distribution functions in deriving synthetic hydrographs has become a robust method for modeling the response of watersheds to precipitation events. This approach leverages statistical distributions to capture the temporal structure of runoff processes, providing a flexible framework for estimating [...] Read more.
The use of probability distribution functions in deriving synthetic hydrographs has become a robust method for modeling the response of watersheds to precipitation events. This approach leverages statistical distributions to capture the temporal structure of runoff processes, providing a flexible framework for estimating peak discharge, time to peak, and hydrograph shape. The present study explores the application of various probability distributions in constructing synthetic hydrographs. The research evaluates parameter estimation techniques, analyzing their influence on hydrograph accuracy. The results highlight the strengths and limitations of each distribution in capturing key hydrological characteristics, offering insights into the suitability of certain probability distribution functions under varying watershed conditions. The study concludes that the approach based on the Cadariu rational function enhances the adaptability and precision of synthetic hydrograph models, thereby supporting flood forecasting and watershed management. Full article
(This article belongs to the Special Issue Robust Statistics in Action II)
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18 pages, 4431 KB  
Article
Simulation and Parameter Law of HEC-HMS for Multi-Source Flood in Arid Region Based on Three-Dimensional Classification Criteria: A Case Study of Manas River Basin
by Jiaming Tu and Changlu Qiao
Water 2025, 17(20), 2952; https://doi.org/10.3390/w17202952 - 14 Oct 2025
Viewed by 334
Abstract
(1) Background: Aiming at low-accuracy and unclear parameter differentiation of snowmelt ice melting, rainstorm and mixed flood simulation in Northwest Chinese arid inland river basins, this study aimed to improve complex flood simulation ability and support arid area flood prediction via HEC-HMS model [...] Read more.
(1) Background: Aiming at low-accuracy and unclear parameter differentiation of snowmelt ice melting, rainstorm and mixed flood simulation in Northwest Chinese arid inland river basins, this study aimed to improve complex flood simulation ability and support arid area flood prediction via HEC-HMS model optimization and classification standard innovation. (2) Method: A distributed HEC-HMS model was built using topography, soil and land use data. A “meteorology, hydrology, underlying surface” flood classification method was developed, and runoff generation-concentration parameters were calibrated via trial-and-error and Latin hypercube sampling for 36 historical floods (12 each type) to verify model applicability. (3) Result: The classification accuracy reached 92%. All three flood types met simulation standards: flood peak and runoff depth error ≤ ±20%, peak time error < 3 h, average NSE = 0.76 (snowmelt: 0.82, rainstorm: 0.76, mixed: 0.70). Parameters showed gradient differences: snowmelt (CN = 65, Ia = 20 mm, k = 0.3), rainstorm (CN = 80, Ia = 10 mm, k = 0.5), mixed (parameters in between). (4) Conclusions: After parameter optimization, the HEC-HMS model is suitable for multi-source flood simulation in arid areas, and the revealed parameter laws provide a quantitative basis for flood forecasting in similar basins. Full article
(This article belongs to the Section Hydrology)
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23 pages, 10835 KB  
Article
Evaluation of Post-Fire Treatments (Erosion Barriers) on Vegetation Recovery Using RPAS and Sentinel-2 Time-Series Imagery
by Fernando Pérez-Cabello, Carlos Baroja-Saenz, Raquel Montorio and Jorge Angás-Pajas
Remote Sens. 2025, 17(20), 3422; https://doi.org/10.3390/rs17203422 - 13 Oct 2025
Viewed by 369
Abstract
Post-fire soil and vegetation changes can intensify erosion and sediment yield by altering the factors controlling the runoff–infiltration balance. Erosion barriers (EBs) are widely used in hydrological and forest restoration to mitigate erosion, reduce sediment transport, and promote vegetation recovery. However, precise spatial [...] Read more.
Post-fire soil and vegetation changes can intensify erosion and sediment yield by altering the factors controlling the runoff–infiltration balance. Erosion barriers (EBs) are widely used in hydrological and forest restoration to mitigate erosion, reduce sediment transport, and promote vegetation recovery. However, precise spatial assessments of their effectiveness remain scarce, requiring validation through operational methodologies. This study evaluates the impact of EB on post-fire vegetation recovery at two temporal and spatial scales: (1) Remotely Piloted Aircraft System (RPAS) imagery, acquired at high spatial resolution but limited to a single acquisition date coinciding with the field flight. These data were captured using a MicaSense RedEdge-MX multispectral camera and an RGB optical sensor (SODA), from which NDVI and vegetation height were derived through aerial photogrammetry and digital surface models (DSMs). (2) Sentinel-2 satellite imagery, offering coarser spatial resolution but enabling multi-temporal analysis, through NDVI time series spanning four consecutive years. The study was conducted in the area of the Luna Fire (northern Spain), which burned in July 2015. A paired sampling design compared upstream and downstream areas of burned wood stacks and control sites using NDVI values and vegetation height. Results showed slightly higher NDVI values (0.45) upstream of the EB (p < 0.05), while vegetation height was, on average, ~8 cm lower than in control sites (p > 0.05). Sentinel-2 analysis revealed significant differences in NDVI distributions between treatments (p < 0.05), although mean values were similar (~0.32), both showing positive trends over four years. This study offers indirect insight into the functioning and effectiveness of EB in post-fire recovery. The findings highlight the need for continued monitoring of treated areas to better understand environmental responses over time and to inform more effective land management strategies. Full article
(This article belongs to the Special Issue Remote Sensing for Risk Assessment, Monitoring and Recovery of Fires)
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26 pages, 7079 KB  
Article
Hydrological Response Analysis Using Remote Sensing and Cloud Computing: Insights from the Chalakudy River Basin, Kerala
by Gudihalli Munivenkatappa Rajesh, Sajeena Shaharudeen, Fahdah Falah Ben Hasher and Mohamed Zhran
Water 2025, 17(19), 2869; https://doi.org/10.3390/w17192869 - 1 Oct 2025
Viewed by 548
Abstract
Hydrological modeling is critical for assessing water availability and guiding sustainable resource management, particularly in monsoon-dependent, data-scarce basins such as the Chalakudy River Basin (CRB) in Kerala, India. This study integrated the Soil Conservation Service Curve Number (SCS-CN) method within the Google Earth [...] Read more.
Hydrological modeling is critical for assessing water availability and guiding sustainable resource management, particularly in monsoon-dependent, data-scarce basins such as the Chalakudy River Basin (CRB) in Kerala, India. This study integrated the Soil Conservation Service Curve Number (SCS-CN) method within the Google Earth Engine (GEE) platform, making novel use of multi-source, open access datasets (CHIRPS precipitation, MODIS land cover and evapotranspiration, and OpenLand soil data) to estimate spatially distributed long-term runoff (2001–2023). Model calibration against observed runoff showed strong performance (NSE = 0.86, KGE = 0.81, R2 = 0.83, RMSE = 29.37 mm and ME = 13.48 mm), validating the approach. Over 75% of annual runoff occurs during the southwest monsoon (June–September), with July alone contributing 220.7 mm. Seasonal assessments highlighted monsoonal excesses and dry-season deficits, while water balance correlated strongly with rainfall (r = 0.93) and runoff (r = 0.94) but negatively with evapotranspiration (r = –0.87). Time-series analysis indicated a slight rise in rainfall, a decline in evapotranspiration, and a marginal improvement in water balance, implying gradual enhancement of regional water availability. Spatial analysis revealed a west–east gradient in precipitation, evapotranspiration, and water balance, producing surpluses in lowlands and deficits in highlands. These findings underscore the potential of cloud-based hydrological modeling to capture spatiotemporal dynamics of hydrological variables and support climate-resilient water management in monsoon-driven and data-scarce river basins. Full article
(This article belongs to the Section Hydrology)
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15 pages, 1519 KB  
Article
Heavy Metal Mobilization in Urban Stormwater Runoff from Residential, Commercial, and Industrial Zones
by Amber Hatter, Daniel P. Heintzelman, Megan Heminghaus, Jonathan Foglein, Mahbubur Meenar and Eli K. Moore
Pollutants 2025, 5(4), 32; https://doi.org/10.3390/pollutants5040032 - 30 Sep 2025
Viewed by 490
Abstract
Increased precipitation and extreme weather due to climate change can remobilize recent and legacy environmental contaminants from soil, sediment, and sewage overflows. Heavy metals are naturally distributed in Earth’s crust, but anthropogenic activity has resulted in concentrated emissions of toxic heavy metals and [...] Read more.
Increased precipitation and extreme weather due to climate change can remobilize recent and legacy environmental contaminants from soil, sediment, and sewage overflows. Heavy metals are naturally distributed in Earth’s crust, but anthropogenic activity has resulted in concentrated emissions of toxic heavy metals and deposition in surrounding communities. Cities around the world are burdened with heavy metal pollution from past and present industrial activity. The city of Camden, NJ, represents a valuable case study of climate impacts on heavy metal mobilization in stormwater runoff due to similar legacy and present-day industrial pollution that has taken place in Camden and in many other cities. Various studies have shown that lead (Pb) and other toxic heavy metals have been emitted in Camden due to historic and recent industrial activity, and deposited in nearby soils and on impervious surfaces. However, it is not known if these heavy metals can be mobilized in urban stormwater, particularly after periods of high precipitation. In this study, Camden, NJ stormwater was collected from streets and parks after heavy rain events in the winter and spring for analysis with inductively coupled plasma-mass spectrometry (ICP-MS) to identify lead (Pb), mercury (Hg), cadmium (Cd), and arsenic (As). Lead was by far the most abundant of the four target elements in stormwater samples followed by Hg, Cd, and As. The locations with the highest Pb concentrations, up to 686.5 ppb, were flooded allies and streets between commercial and residential areas. The highest concentrations of Hg (up to 11.53 ppb, orders of magnitude lower than Pb) were found in partially flooded streets and ditches. Lead stormwater concentrations exceed EPA safe drinking levels at the majority of analyzed locations, and Hg stormwater concentrations exceed EPA safe drinking levels at all analyzed locations. While stormwater is not generally ingested, dermal contact and hand-to-mouth behavior by children are potential routes of exposure. Heavy metal concentrations were lower in stormwater collected from parks and restored areas of Camden, indicating that these areas have a lower heavy metal exposure risk. This study shows that heavy metal pollution can be mobilized in stormwater runoff, resulting in elevated exposure risk in industrial cities. Full article
(This article belongs to the Section Water Pollution)
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26 pages, 4609 KB  
Article
Coupling a Physically Based Hydrological Model with a Modified Transformer for Long-Sequence Runoff and Peak-Flow Prediction
by Yicheng Gu, Bing Yan, Siru Wang, Zhao Cai and Hongwei Liu
Sustainability 2025, 17(19), 8618; https://doi.org/10.3390/su17198618 - 25 Sep 2025
Viewed by 939
Abstract
Climate change and human activities are intensifying the hydrologic cycle and increasing extreme events, challenging accurate prediction. This study builds on the Transformer architecture by introducing a sliding time window and runoff classification mechanism, enabling high-precision long-term runoff forecasting and significantly improving the [...] Read more.
Climate change and human activities are intensifying the hydrologic cycle and increasing extreme events, challenging accurate prediction. This study builds on the Transformer architecture by introducing a sliding time window and runoff classification mechanism, enabling high-precision long-term runoff forecasting and significantly improving the simulation of extreme floods. However, the generalization ability of data-driven models remains limited in non-stationary environments. To address this issue, we further propose a hybrid framework that couples the process-based GBHM with the enhanced Transformer via bias correction. This fusion leverages the strengths of both models: the process-based model explicitly captures topographic heterogeneity, the spatial distribution of meteorological forcings, and their temporal variability, while the data-driven model excels at uncovering latent relationships among hydrological variables. The results demonstrate that the coupled model significantly outperforms traditional approaches in peak-flow prediction and exhibits superior robustness and generalizability under changing environmental conditions. Full article
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57 pages, 12419 KB  
Article
The Learning Rate Is Not a Constant: Sandwich-Adjusted Markov Chain Monte Carlo Simulation
by Jasper A. Vrugt and Cees G. H. Diks
Entropy 2025, 27(10), 999; https://doi.org/10.3390/e27100999 - 25 Sep 2025
Viewed by 564
Abstract
A fundamental limitation of maximum likelihood and Bayesian methods under model misspecification is that the asymptotic covariance matrix of the pseudo-true parameter vector θ* is not the inverse of the Fisher information, but rather the sandwich covariance matrix [...] Read more.
A fundamental limitation of maximum likelihood and Bayesian methods under model misspecification is that the asymptotic covariance matrix of the pseudo-true parameter vector θ* is not the inverse of the Fisher information, but rather the sandwich covariance matrix 1nA*1B*1A*1, where A* and B* are the sensitivity and variability matrices, respectively, evaluated at θ* for training data record ω1,,ωn. This paper makes three contributions. First, we review existing approaches to robust posterior sampling, including the open-faced sandwich adjustment and magnitude- and curvature-adjusted Markov chain Monte Carlo (MCMC) simulation. Second, we introduce a new sandwich-adjusted MCMC method. Unlike existing approaches that rely on arbitrary matrix square roots, eigendecompositions or a single scaling factor applied uniformly across the parameter space, our method employs a parameter-dependent learning rate λ(θ) that enables direction-specific tempering of the likelihood. This allows the sampler to capture directional asymmetries in the sandwich distribution, particularly under model misspecification or in small-sample regimes, and yields credible regions that remain valid when standard Bayesian inference underestimates uncertainty. Third, we propose information-theoretic diagnostics for quantifying model misspecification, including a strictly proper divergence score and scalar summaries based on the Frobenius norm, Earth mover’s distance, and the Herfindahl index. These principled diagnostics complement residual-based metrics for model evaluation by directly assessing the degree of misalignment between the sensitivity and variability matrices, A* and B*. Applications to two parametric distributions and a rainfall-runoff case study with the Xinanjiang watershed model show that conventional Bayesian methods systematically underestimate uncertainty, while the proposed method yields asymptotically valid and robust uncertainty estimates. Together, these findings advocate for sandwich-based adjustments in Bayesian practice and workflows. Full article
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27 pages, 9431 KB  
Article
Improved Monthly Frequency Method Based on Copula Functions for Studying Ecological Flow in the Hailang River Basin, Northeast China
by Zijun Wang, Yusu Zhao, Jian Shang, Yuanming Wang, Changlei Dai and Enzhong Li
Atmosphere 2025, 16(9), 1110; https://doi.org/10.3390/atmos16091110 - 22 Sep 2025
Viewed by 486
Abstract
Climate change has intensified extreme hydrological events in cold regions, threatening the stability of river ecosystems. The traditional monthly frequency method for calculating ecological flow assumes equal guarantee rates across all months, overlooking the complex nonlinear dependencies between interannual and intermonthly flows. This [...] Read more.
Climate change has intensified extreme hydrological events in cold regions, threatening the stability of river ecosystems. The traditional monthly frequency method for calculating ecological flow assumes equal guarantee rates across all months, overlooking the complex nonlinear dependencies between interannual and intermonthly flows. This approach may result in flow values for certain months during low-flow years exceeding those of corresponding months in high-flow years, failing to align with actual hydrological patterns. This study integrates Copula functions with the monthly frequency method to establish an improved ecological flow calculation framework, accurately characterizing the statistical correlation between interannual and intermonthly flow variability. The Hailang River basin in Northeast China was selected as the study area. First, the SWAT model was employed to simulate natural runoff processes from 1956 to 1965. The calibration phase demonstrated excellent performance (R2 = 0.84, NSE = 0.83), and the validation phase also met standards (R2 = 0.82, NSE = 0.81). The improved method selected optimal Copula functions for each month through rigorous statistical tests (AIC, BIC, RMSE, and K-S test), establishing joint probability distributions for annual and monthly average flows. The results indicate that different Copula types better align with monthly hydrological seasonal characteristics: Gaussian Copula suits February, May, and July; t-Copula suits August; Clayton Copula from September to December; Gumbel Copula for January, March, April, and June. Through conditional probability relationships (P(X0≥x0, 90%) = 0.9), the monthly guarantee rate range determined by the improved method spans 81.83% to 90.08%, significantly outperforming the uniform 90% guarantee rate employed by traditional methods. Verification using the Tennant method confirmed that ecological flows throughout the year met “excellent” or higher standards. Ecological flows exhibited pronounced seasonal variation, ranging from 6.2 m3/s during winter to spring to 96.93 m3/s during summer to autumn, providing scientific basis for basin-scale ecological water management. This study establishes a reliable methodological framework for ecological flow management in cold-region rivers. Full article
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26 pages, 12189 KB  
Article
ESA-MDN: An Ensemble Self-Attention Enhanced Mixture Density Framework for UAV Multispectral Water Quality Parameter Retrieval
by Xiaonan Yang, Jiansheng Wang, Yi Jing, Songjia Zhang, Dexin Sun and Qingli Li
Remote Sens. 2025, 17(18), 3202; https://doi.org/10.3390/rs17183202 - 17 Sep 2025
Cited by 1 | Viewed by 481
Abstract
Urban rivers, as crucial components of ecosystems, serve multiple functions, including flood control, drainage, and landscape services. However, with the acceleration of urbanization, factors such as industrial wastewater discharge, domestic sewage leakage, and surface runoff pollution have led to increasingly severe degradation of [...] Read more.
Urban rivers, as crucial components of ecosystems, serve multiple functions, including flood control, drainage, and landscape services. However, with the acceleration of urbanization, factors such as industrial wastewater discharge, domestic sewage leakage, and surface runoff pollution have led to increasingly severe degradation of water quality in urban rivers. Unmanned aerial vehicle (UAV) remote sensing technology, with its sub-meter spatial resolution and operational flexibility, demonstrates significant advantages in the detailed monitoring of complex urban water systems. This study proposes an Ensemble Self-Attention Enhanced Mixture Density Network (ESA-MDN), which integrate an ensemble learning framework with a mixture density network and incorporates a self-attention mechanism for feature enhancement. This approach better captures the nonlinear relationships between water quality parameters and remote sensing features, achieving high-precision modeling of water quality parameter distributions. The resulting spatiotemporal distribution maps provide valuable support for pollution source identification and management decision making. The model successfully retrieved five water quality parameters, Chl-a, TSS, COD, TP, and DO, and validation metrics such as R2, RMSE, MAE, MSE, MAPE, bias, and slope were utilized. Key metrics for the ESA-MDN test set were as follows: Chl-a (R2 = 0.98, RMSE = 0.31), TSS (R2 = 0.93, RMSE = 0.27), COD (R2 = 0.93, RMSE = 0.39), TP (R2 = 0.99, RMSE = 0.02), and DO (R2 = 0.88, RMSE = 0.1). The results indicated that ESA-MDN can effectively extract water quality parameters from multispectral remote sensing data, with the generated spatiotemporal water quality distribution maps providing crucial support for pollution source identification and emergency response decision making. Full article
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