This paper presents a novel approach for handling the singular loads, i.e., H−1(Ω) loads, in the ℙ1 conforming virtual element method (VEM) using a meshfree function. While VEM can accurately and efficiently solve elliptic problems with loads in L2(Ω), its implicit construction of shape functions prevents it from addressing singular loads. Although this issue can be mitigated by computing VEM shape functions explicitly through companion operators, doing so requires decomposing polygonal meshes into multiple simplices, which is challenging, particularly for concave meshes and higher dimensional cases. On the other hand, the principle of VEM decomposition can be applied to meshfree functions, where the polynomial part contributes to the consistency term, and the non-polynomial part is approximated by the stability term. Consequently, we propose using the meshfree function as the VEM shape function, enabling the duality pairing with H−1(Ω) loads to be computed easily, while the calculation of the local VEM stiffness matrix remains unchanged. The partition of unity method, coupled with the Gaussian radial basis function (RBF), is used to construct the meshfree shape function, which is then tested on two cases. Good agreement between numerical and analytical solutions is observed in all cases, indicating the accuracy of the approach. Moreover, the model accuracy is found to be insensitive to the shape parameter of the Gaussian RBF, demonstrating its robustness.

The mimetic finite difference (MFD) method has shown great advantages over conventional numerical techniques in modeling seepage flows due to its capability of handling general polygonal and nonmatching meshes. In the MFD method, the representative hydraulic conductivity for each cell is normally computed from the cell-centered pressure; however, this approach is often found to yield unphysically slow infiltration fronts and even locking when the hydraulic conductivity is close to zero, which impedes its application to unsaturated seepage flows. To address this limitation, this study extends and generalizes the idea of using equivalent hydraulic conductivity computed from face-based values, which is widely used in the mixed finite element method (FEM), as the cell-average coefficient in the MFD method. New algorithms for assigning weights in the averaging process are proposed based on the Frobenius norm of the mimetic inner product matrix, which account for mesh shape effects and are therefore more appropriate for general polygonal meshes than the uniform weights adopted in mixed FEM. Three schemes analogous to geometric, arithmetic, and power averages are developed and tested using four sets of numerical experiments. While the results obtained using the proposed equivalent hydraulic conductivity are close to those from the arithmetic average with uniform weights for triangular meshes, the proposed approach is more accurate for polygonal meshes. In addition, using the proposed equivalent values-particularly the arithmetic and power means-in the MFD method consistently produces accurate results and avoids unphysical locking in all cases.

Saline lakes are hypersensitive to changes in their water balance and therefore show amplified responses to climatic and land-use changes in their catchment. Despite often dramatic ecological impacts, saline lakes rank low on policy agendas as they are assumed to support few ecosystem services and low levels of biodiversity. Here, we challenge this view and evaluate ecosystem services and threatened species in 85 saline lakes distributed across the globe. We show that saline lakes support, additionally to threatened aquatic biota, a diverse range of red-listed terrestrial species that contribute together with a large beta diversity to their conservation value. Further, our results highlight that saline lakes provide a number of culturally and economically important ecosystem services but several of them are 'hidden' and difficult to quantify. We conclude our analysis with best-practice recommendations for sustainable management of saline lakes. Their local adaptation and implementation will be key for safeguarding biodiversity and ecosystem services of these valuable and highly sensitive ecosystems.

Abstract This paper presents a numerical sediment transport model based on data from a series of experiments with flow hydrographs of varying lengths in a laboratory flume with a sand bed. The model was calibrated and validated using one flow hydrograph and then applied to other hydrographs. Digital flumes with different initial and boundary conditions were generated to assist numerical simulations and further explore additional scenarios, such as flow rates on the rising limb of the hydrograph, different sediment sizes, and longer hydrographs. Both numerical and experimental results demonstrate the influence of flow hydrograph duration on transport rates, which typically resulted in a counterclockwise hysteresis pattern. Different rising slopes of the flow rate had limited effects on the hysteresis pattern. Coarser sediment yielded lower transport rates, while finer particles led to increased transport rates, though neither caused appreciable changes to the hysteresis pattern. Limited sediment supply resulted in a change in hysteresis pattern from counterclockwise to figure-8. Longer hydrographs led to irregular hysteresis patterns due to the influence of bedforms that developed during peak flows.

The Lagrangian particle method (LPM) is a promising alternative to Eulerian grid-based methods for modeling advection-dominant transport, as it avoids numerical diffusion and oscillation. However, the most widely used LPM for subsurface solute transport—Smooth Particle Hydrodynamics (SPH)—typically requires a large number of particles for local numerical approximation due to its low order of consistency, making it computationally expensive. In addition, the conventional SPH method is prone to producing negative concentrations under anisotropic dispersion because of the unphysical dispersive flux computed by the model. To address these two issues, this study proposes a new LPM for solute transport simulation based on the generalized moving least squares (GMLS) method. In this approach, a GMLS-based finite difference method is developed for conservative solute transport, enabling efficient and accurate computation of the required higher-order derivatives. As a result, the proposed GMLS-LPM achieves improved representation of anisotropic dispersion and enhanced robustness in long-term predictions of complex subsurface solute transport. The effectiveness of GMLS-LPM is demonstrated through comparisons with two existing LPMs that employ the conventional SPH method and the finite particle method (FPM) in two anisotropic dispersion scenarios: one in homogeneous porous media and the other in heterogeneous porous media. Under similar CPU time, the GMLS-LPM significantly outperforms both SPH and FPM models. Even with randomly distributed particles, the GMLS-LPM maintains high accuracy and avoids unphysical negative concentrations, highlighting its strong potential as a particle-based model for solute transport.

High computational demand limits the applications of two-dimensional (2D) shallow water equation models for high resolution overland flow simulations, while one-dimensional (1D) models can achieve higher computing efficiency. This study applied a 1D hydrodynamic model to surrogate 2D models for overland flow simulations on complex 2D domains. With one dimension reduced, the surrogate model simulation would have acceptable accuracy with much higher computing efficiency. The surrogating is fulfilled through mimicking 2D models in mesh generations, so that the 1D channel network is generated in such a way that it geometrically covers the whole domain without overlapping and intersection, and hydrologically follows the steepest slopes. Several benchmark cases on 2D domains in both laboratory and field scales with complex geometry, where no 1D models have been ever applied, are used to compare the 1D and 2D model simulations. The comparisons demonstrate that the 1D model does have potentials to efficiently simulate overland flow on 2D complex domains with accuracy comparable to 2D models.

After the release of the ASCE Manuals and Reports on Engineering Practice (MOP) No. 150: Total Maximum Daily Load Development and Implementation: Models, Methods, and Resources in 2022, the EWRI TMDL Analysis and Modeling Task Committee (TC) continues its work to advance the state-of-the-practice in TMDL development and implementation planning and address emerging issues. The committee is documenting its work in a special collection of papers in the Journal of Environmental Engineering. This paper reports progresses on nine papers addressing various TMDL issues/topics: (1) watershed models to predict climate change impacts, (2) advanced surface water quality modeling, (3) integration of the climate assessment modules in TMDL models, (4) advances in watershed and receiving water models for simulating PFAS, (5) advances in modeling best management practices and green infrastructure for TMDL implementation planning, (6) harmful algae bloom predictive approaches, (7) incorporation of social aspects and stakeholder participations in TMDL modeling, (8) overcoming data scarcity, and (9) survey of TMDL community. All the papers except #6 have been authored by the TC members. Paper 6, an external paper submitted and accepted in the collection, replaces the committee paper on the topic as it overlaps and meets the committee objectives. The committee has plans to write more papers and summarize all in a book to be a guidance document supplementing the ASCE MOP 150.

This paper presents the parallelization of two widely used implicit numerical solvers for the solution of partial differential equations on structured meshes, namely, the ADI (Alternating-Direction Implicit) solver for tridiagonal linear systems and the SIP (Strongly Implicit Procedure) solver for the penta-diagonal systems. Both solvers were parallelized using CUDA (Computer Unified Device Architecture) Fortran on GPGPUs (General-Purpose Graphics Processing Units). The parallel ADI solver (P-ADI) is based on the Parallel Cyclic Reduction (PCR) algorithm, while the parallel SIP solver (P-SIP) uses the wave front method (WF) following a diagonal line calculation strategy. To map the solution schemes onto the hierarchical block-threads framework of the CUDA on the GPU, the P-ADI solver adopted two mapping methods, one block thread with iterations (OBM-it) and multi-block threads (MBMs), while the P-SIP solver also used two mappings, one conventional mapping using effective WF lines (WF-e) with matrix coefficients and solution variables defined on original computational mesh, and a newly proposed mapping using all WF mesh (WF-all), on which matrix coefficients and solution variables are defined. Both the P-ADI and the P-SIP have been integrated into a two-dimensional (2D) hydrodynamic model, the CCHE2D (Center of Computational Hydroscience and Engineering) model, developed by the National Center for Computational Hydroscience and Engineering at the University of Mississippi. This study for the first time compared these two parallel solvers and their efficiency using examples and applications in complex geometries, which can provide valuable guidance for future uses of these two parallel implicit solvers in computational fluids dynamics (CFD). Both parallel solvers demonstrated higher efficiency than their serial counterparts on the CPU (Central Processing Unit): 3.73~4.98 speedup ratio for flow simulations, and 2.166~3.648 speedup ratio for sediment transport simulations. In general, the P-ADI solver is faster than but not as stable as the P-SIP solver; and for the P-SIP solver, the newly developed mapping method WF-all significantly improved the conventional mapping method WF-e.

Conventionally two-dimensional (2D) models are used to simulate 2D overland flow with a non-overlapping 2D computational mesh. However, 2D models are not computationally efficient when applied to large domains. Due to their computing efficiency, one-dimensional (1D) models can be used to simulate 2D overland flows by replacing 2D computational meshes with 1D computational channel networks with topography described by closely-spaced transverse cross sections that fully cover the whole domain. Channel networks must enforce the basic physical laws of gravity-driven flows ensuring water flow paths converge and connect from high to low elevations. This manuscript presents a novel algorithm to generate channel networks following two principles, a geometric principle and a hydrologic principle. The geometric principle requires that the generated channel network covers the whole study domain without overlaps or intersections, while the hydrologic principle requires that the generated channel network follows the local steepest slope. Correspondingly, the proposed generation algorithm includes two main processes: (1) the extraction of channel network using a terrain slope-calculation-based delineation algorithm; and, (2) the generation of cross sections with varying channel widths determined by considering topographic complexity, the hydrological correctness, and computational requirements. The proposed cross section generation algorithm is described using several 2D geometrically complex domains at the laboratory scale, and is also applied to a natural watershed. An overflow simulation on a 2D domain with obliques walls using a 1D model demonstrated the effectiveness of the proposed generation algorithm for 1D channel networks of 1D model.

This paper presents a technical approach to link a watershed model and surface water quality model to study the effects of agricultural conservation practices on the water quality of a receiving water body. The AnnAGNPS watershed model was applied to simulate runoff and loads of sediment and nutrients into Beasley Lake. The simulated results were used as boundary conditions for CCHE-WQ water quality model to simulate the concentrations of water quality constituents in the oxbow lake. In this model, the interactions between sediment and water quality constituents were considered. This integrated modeling system can be used to simulate flow, sediment and nutrient processes in both the watershed and waterbody systematically. Two modeling were calibrated and validated using measured data in Beasley Lake Watershed. The validated modeling system was applied to analyze the effects of cropping and tillage systems on the water quality of the receiving water body.

This paper presents a technical approach to link a watershed model and surface water quality model to study the effects of agricultural conservation practices implemented in the upland watershed on the water quality of a receiving water body. The Annualized Agricultural Nonpoint Source Pollution (AnnAGNPS) watershed model was applied to simulate the runoff and loads of sediment and nutrients exported from upland watersheds. The effects of land use/land cover, soil properties, climate, agriculture management, etc. on the watershed loads were considered. The simulated results were used as boundary conditions for CCHE-WQ, a water quality model developed at the National Center for Computational Hydroscience and Engineering (NCCHE), to simulate the concentrations of water quality constituents in water bodies. In this model, the interactions between sediment and water quality constituents were considered, and the distributions of nutrients, chlorophyll and dissolved oxygen in the water body can be obtained. This integrated modeling system can be used to simulate flow, sediment and nutrient processes in both the watershed and waterbody systematically. This system was tested using Beasley Lake watershed in the Mississippi Delta. The water quality of the watershed was monitored by USDA-ARS, and the measured data was used to calibrate and validate the AnnAGNPS and CCHE-WQ models. The validated modeling system was applied to analyze the effects of conservation practices (reduced-tillage/no-tillage) on the water quality of the receiving water body. This research provides useful tools to analyze the impacts of upland watersheds on the water quality of the receiving water bodies.

Prepared by the Total Maximum Daily Load Analysis and Modeling Task Committee and sponsored by the Watershed Management Technical Committee of the Watershed Council of the Environmental and Water Resources Institute of ASCE

Enid Lake is one of the largest reservoirs located in Yazoo River Basin, the largest basin in the state of Mississippi. The lake was impounded by Enid Dam on the Yocona River in Yalobusha County and covers an area of 30 square kilometers. It provides significant natural and recreational resources. The soils in this region are highly erodible, resulting in a large amount of fine-grained cohesive sediment discharged into the lake. In this study, a 3D numerical model was developed to simulate the free surface hydrodynamics and transportation of cohesive sediment with a median diameter of 0.0025 to 0.003 mm in Enid Lake. Flow fields in the lake are generally induced by wind and upstream river inflow, and the sediment is also introduced from the inflow during storm events. The general processes of sediment flocculation and settling were considered in the model, and the erosion rate and deposition rate of cohesive sediment were calculated. In this model, the sediment simulation was coupled with flow simulation. In this research, remote sensing technology was applied to estimate the sediment concentration at the lake surface and provide validation data for numerical model simulation. The model results and remote sensing data help us to understand the transport, deposition and resuspension processes of cohesive sediment in large reservoirs due to wind-induced currents and upstream river flows.

The Bonnet Carre Spillway (BCS) was constructed from 1929 to 1936 to protect the city of New Orleans from the Mississippi River floods. When the water stage of the Mississippi River is over 5.18 m of flood stage, BCS will be opened to divert the excessive flood water into the Gulf of Mexico through Lake Pontchartrain. During these flood release events, large amounts of freshwater, sediment and nutrients were discharged into the lake and significantly affected its water quality and aquatic environment. A numerical model (CCHE2D) developed at the National Center for Computational Hydroscience and Engineering (NCCHE), the University of Mississippi, was applied to simulate the dynamic process of hydrodynamics and associated temporal and spatial distributions of sediment, salinity and phytoplankton in Lake Pontchartrain due to the BCS flood release events. Three events occurred in 1997, 2008 and 2011, representing the median, low, and high flood discharge cases, were selected for this study. The simulated results were compared with field measured data and satellite imageries obtained from USGS, US Army Crop of Engineers and NOAA, and good agreements were obtained. The effects of nutrients and suspended sediment on the growth of phytoplankton as well as the occurrence of algal bloom in the lake were analyzed. The processes of salinity recovery in the lake were also discussed. The results obtained from this research provide useful information for analyzing the impacts of flood release event on the aquatic ecosystems in Lake Pontchartrain.

In order to protect the city of New Orleans from the Mississippi River flooding, the Bonnet Carre Spillway (BCS) was constructed from 1929 to 1936 to divert flood water from the river into Lake Pontchartrain and then into the Gulf of Mexico. However, a BCS opening event causes a lot of environmental problems in the lake. This paper presents the application of a two-dimensional numerical model (CCHE2D), developed at the National Center for Computational Hydroscience and Engineering, for simulating the flow circulations, sediment transport, and salinity distribution in Lake Pontchartrain during the Bonnet Carre Spillway (BCS) is opened for flood release. When the spillway is opened for flood release, large amount of fresh water and sediment discharged from the Mississippi River into Lake Pontchartrain, and then into the Gulf of Mexico, causing significant increase of lake sediment concentration and decrease of lake salinity. The aquatic environment and fish habitat in the lake are greatly affected by the opening events. CCHE2D model was applied to simulate the flow, sediment, and salinity in Lake Pontchartrain during the recent BCS flood releases in 1997, 2008, and 2011. The simulated results were compared with field measured data and satellite imageries, and good agreements were obtained. The flow patterns, sediment concentrations, and salinities in the lake due to the three flood release events were discussed. In addition, the salinity recovery processes in the lake were also simulated. The simulation results provides useful information to evaluate the environmental impacts of the flood events on lake ecosystems.

Water quality models are critical tools for the development of total maximum daily loads (TMDLs) and for the evaluation of water quality management alternatives by stakeholders and state environmental protection agencies. Currently there is a large availability of water quality models that can be used to support TMDL studies, and the selection of a particular model requires a good understanding of the model limitations, capabilities, and data requirements. The ASCE/Environmental and Water Resources Institute (EWRI) TMDL Analysis and Modeling Task Committee was established in part to produce guidance documentation to help modelers to identify and implement existing modeling approaches to address some of the most important causes of water quality impairment in the United States, including eutrophication, toxic chemicals, and metals. This paper presents a review of existing mathematical models to evaluate eutrophication processes, including carbon and nutrient cycling, phytoplankton dynamics, and dissolved oxygen availability, as well as a review of mathematical models to simulate the fate and transport of toxic chemicals and mercury. The paper also discusses the main capabilities and limitations of 11 widely used water quality models in the United States. Modelers can use this information to support more informed model selections and to facilitate an effective and successful application of models in TMDL studies.

Studying water quality problems in natural aquatic environment with numerical models is a very effective approach. As a result, many numerical models have been developed and applied to simulate water quality constituents in rivers, lakes, and coastal waters. The observed water quality in an aquatic system is a result of many physical, chemical, and bio-chemical processes, parameters of a water quality model associated to these processes need to be calibrated. Phytoplankton is one of the most important components in the water quality simulation. Its growth rate is significantly affected by temperature, sun light, and nutrients; while the death rate is influenced by the temperature. More than ten parameters need to be calibrated for modeling phytoplankton kinetics. In this study, a water quality model CCHE_WQ, developed at the National Center for Computational Hydroscience and Engineering (NCCHE), was applied to simulate the phytoplankton (as chlorophyll a) in Pelahatchie Bay in Mississippi. The parameters such as saturation light intensity, light extinction coefficient, optimal temperature for the growth, half-saturation constants for nutrients, etc. were calibrated and statistical analysis was conducted to evaluate the performance of numerical model by using different parameters.

This paper presents a technical approach to link the watershed model and surface water quality model to study the effect of pollutant loads from upland watershed on the water quality of the receiving water body. The AnnAGNPS watershed model, developed at the USDA ARS, National Sedimentation Laboratory (NSL), is applied to simulate the loads of water, sediment, and nutrients from upland watersheds. In this model, the effects of land use/land cover, soil properties, climate, agriculture management, etc. on the watershed loads are considered. The computed results are used as boundary conditions for CCHE_WQ, a water quality model developed at the National Center for Computational Hydroscience and Engineering (NCCHE), to simulate the water quality concentration in water bodies. In this model, the effects of sediment on the water quality constituents are considered, and the distributions of nutrients, chlorophyll, and dissolved oxygen in the water body can be obtained. This technical approach is tested using Beasley Lake watershed in the Mississippi Delta as a study site. The lake water quality is monitored by NSL, and the measured data is used to calibrate and validate the numerical model. In this lake, sediment concentration is relatively high, so the sediment-associated water quality processes need to be taken into account. This research provides a useful tool to assess long term impacts of watershed nutrient and sediment loads on the water quality of the receiving water bodies.