Influence of Boundary Condition Types on Unstable Density‐Dependent Flow

Boundary conditions are required to close the mathematical formulation of unstable density‐dependent flow systems. Proper implementation of boundary conditions, for both flow and transport equations, in numerical simulation are critical. In this paper, numerical simulations using the FEFLOW model are employed to study the influence of the different boundary conditions for unstable density‐dependent flow systems. A similar set up to the Elder problem is studied. It is well known that the numerical simulation results of the standard Elder problem are strongly dependent on spatial discretization. This work shows that for the cases where a solute mass flux boundary condition is employed instead of a specified concentration boundary condition at the solute source, the numerical simulation results do not vary between different convective solution modes (i.e., plume configurations) due to the spatial discretization. Also, the influence of various boundary condition types for nonsource boundaries was studied. It is shown that in addition to other factors such as spatial and temporal discretization, the forms of the solute transport equation such as divergent and convective forms as well as the type of boundary condition employed in the nonsource boundary conditions influence the convective solution mode in coarser meshes. On basis of the numerical experiments performed here, higher sensitivities regarding the numerical solution stability are observed for the Adams‐Bashford/Backward Trapezoidal time integration approach in comparison to the Euler‐Backward/Euler‐Forward time marching approach. The results of this study emphasize the significant consequences of boundary condition choice in the numerical modeling of unstable density‐dependent flow.     

Formulation of a new ocean salinity boundary condition and impact on the simulated climate of an oceanic general circulation model

The salinity boundary condition at the ocean surface plays an important role in the stability of long-term integrations of an oceanic general circulation model(OGCM) and in determining its equilibrium solutions.This study presents a new formulation of the salt flux calculation at the ocean surface based on physical processes of salt exchange at the air-sea interface.The formulation improves the commonly used virtual salt flux with constant reference salinity by allowing for spatial correlations between surface freshwater flux and sea-surface salinity while preserving the conservation of global salinity.The new boundary condition is implemented in the latest version of the National Key Laboratory of Numerical Modeling for Atmospheric Sciences and Geophysical Fluid Dynamics/Institute of Atmospheric Physics Climate Ocean Model version 2(LICOM2.0).The impact of the new boundary condition on the equilibrium simulations of the model is presented.It is shown that the new formulation leads to a stronger Atlantic meridional overturning circulation(AMOC) that is closer to observational estimates.It also slightly improves poleward heat transport by the oceans in both the Atlantic and the global oceans.     

Modelling the effects of land‐use change on water and salt delivery from a catchment affected by dryland salinity in south‐east Australia

A comprehensive framework for the assessment of water and salt balance for large catchments affected by dryland salinity is applied to the Boorowa River catchment (1550 km²), located in south‐eastern Australia. The framework comprised two models, each focusing on a different aspect and operating on a different scale. A quasi‐physical semi‐distributed model CATSALT was used to estimate runoff and salt fluxes from different source areas within the catchment. The effects of land use, climate, topography, soils and geology are included. A groundwater model FLOWTUBE was used to estimate the long‐term effects of land‐use change on groundwater discharge. Unlike conventional salinity studies that focus on groundwater alone, this study makes use of a new approach to explore surface and groundwater interactions with salt stores and the stream. Land‐use change scenarios based on increased perennial pasture and tree‐cover content of the vegetation, aimed at high leakage and saline discharge areas, are investigated. Likely downstream impacts of the reduction in flow and salt export are estimated. The water balance model was able to simulate both the daily observed stream flow and salt load at the catchment outlet for high and low flow conditions satisfactorily. Mean leakage rate of about 23·2 mm year^?1 under current land use for the Boorowa catchment was estimated. The corresponding mean runoff and salt export from the catchment were 89 382 ML year^?1 and 38 938 t year^?1, respectively. Investigation of various land‐use change scenarios indicates that changing annual pastures and cropping areas to perennial pastures is not likely to result in substantial improvement of water quality in the Boorowa River. A land‐use change of about 20% tree‐cover, specifically targeting high recharge and the saline discharge areas, would be needed to decrease stream salinity by 150 µS cm^?1 from its current level. Stream salinity reductions of about 20 µS cm^?1 in the main Lachlan River downstream of the confluence of the Boorowa River is predicted. The FLOWTUBE modelling within the Boorowa River catchment indicated that discharge areas under increased recharge conditions could re‐equilibrate in around 20 years for the catchment, and around 15 years for individual hillslopes. Copyright © 2004 John Wiley & Sons, Ltd.     

Hydrologic‐response‐driven sediment transport at a regional scale,process‐based simulation

Assessing hydrologically driven erosion at regional scales from a process‐based perspective presents a significant challenge. Most regional‐scale erosion assessments are based upon a simple steady‐state hydrology foundation. For this study, the sediment transport version of the physics‐based Integrated Hydrology Model (InHM), excited by synthetically generated rainfall, was employed to assess long‐term hydrologically driven erosion for a regional‐scale island boundary‐value problem. The spatiotemporal dynamics of runoff generation, erosion, and deposition are illustrated through saturation, water depth, velocity, and sediment concentration results. The simulations demonstrate that process‐based assessment for concept development is both feasible and tractable at regional spatial and human time scales. Copyright © 2011 John Wiley & Sons, Ltd.     

Use of caesium‐137 data to evaluate SHETRAN simulated long‐term erosion patterns in arable lands

The caesium‐137 method of quantifying soil erosion is used to provide field data for validating the capability of the SHETRAN modelling system for predicting long‐term (30‐year) erosion rates and their spatial variability. Simulations were carried out for two arable farm sites (area 3–5 ha) in central England for which average annual erosion rates of 6·5 and 10·4 t ha^?1 year^?1 had already been determined using caesium‐137 measurements. These rates were compared with a range of simulated values representing the uncertainty in model output derived from uncertainty in the evaluation of model parameters. A successful validation was achieved in that the simulation range contained the measured rate at both sites, whereas the spatial variability was reproduced excellently at one site and partially at the other. The results indicate that, as the caesium‐137 technique measures the erosion caused by all the processes acting at a site, it is relevant to hydrologically based models such as SHETRAN only if erosion by wind, agricultural activities and other processes not represented in the model are insignificant. The results also indicate a need to reduce the uncertainty in model parameter evaluation. More generally, the caesium‐137 technique is shown to provide field data that improve the severity of the validation procedure (accounting for internal as well as outlet conditions) and that add spatial variability to magnitude as a condition for identifying unrealistic parameter sets when seeking to reduce simulation uncertainty. Copyright © 2004 John Wiley & Sons, Ltd.     

Appropriate vertical discretization of Richards' equation for two‐dimensional watershed‐scale modelling

A number of watershed‐scale hydrological models include Richards' equation (RE) solutions, but the literature is sparse on information as to the appropriate application of RE at the watershed scale. In most published applications of RE in distributed watershed‐scale hydrological modelling, coarse vertical resolutions are used to decrease the computational burden. Compared to point‐ or field‐scale studies, application at the watershed scale is complicated by diverse runoff production mechanisms, groundwater effects on runoff production, runon phenomena and heterogeneous watershed characteristics. An essential element of the numerical solution of RE is that the solution converges as the spatial resolution increases. Spatial convergence studies can be used to identify the proper resolution that accurately describes the solution with maximum computational efficiency, when using physically realistic parameter values. In this study, spatial convergence studies are conducted using the two‐dimensional, distributed‐parameter, gridded surface subsurface hydrological analysis (GSSHA) model, which solves RE to simulate vadose zone fluxes. Tests to determine if the required discretization is strongly a function of dominant runoff production mechanism are conducted using data from two very different watersheds, the Hortonian Goodwin Creek Experimental Watershed and the non‐Hortonian Muddy Brook watershed. Total infiltration, stream flow and evapotranspiration for the entire simulation period are used to compute comparison statistics. The influences of upper and lower boundary conditions on the solution accuracy are also explored. Results indicate that to simulate hydrological fluxes accurately at both watersheds small vertical cell sizes, of the order of 1 cm, are required near the soil surface, but not throughout the soil column. The appropriate choice of approximations for calculating the near soil‐surface unsaturated hydraulic conductivity can yield modest increases in the required cell size. Results for both watersheds are quite similar, even though the soils and runoff production mechanisms differ greatly between the two catchments. Copyright © 2003 John Wiley & Sons, Ltd.     

Influences of climate,terrain and land cover on stream salinity in southeastern Australia,and implications for management through reforestation

Reforestation of cleared land has the potential to reduce groundwater recharge, salt mobilization and streamflow. Stream salinity change is the net result of changes in stream salt load and streamflow. The net effect of these changes varies spatially as a function of climate, terrain and land cover. Successful natural resource management requires methods to map the spatial variability of reforestation impacts. We investigated salinity data from 2000 bores and streamflow and salinity measurements from 27 catchments in the Goulburn–Broken region in southeast Australia to assess the main factors determining stream salinity and opportunities for management through reforestation. For groundwater systems of similar geology, relationships were found between average annual rainfall and groundwater salinity and between groundwater salinity and low‐flow salinity. Despite its simplicity, we found that the steady‐state component of a simple conceptual coupled water–salt mass balance model (BC2C) adequately explained the spatial variation in streamflow and salinity. The model results suggest the efficiency of afforestation to reduce stream salinity could be increased by more than an order of magnitude through spatial planning. However, appreciable reductions in stream salinity in large rivers through land cover change alone would still require reforestation on an unprecedented scale. Copyright © 2008 John Wiley & Sons, Ltd.     

Phast4Windows: A 3D Graphical User Interface for the Reactive‐Transport Simulator PHAST

Phast4Windows is a Windows® program for developing and running groundwater‐flow and reactive‐transport models with the PHAST simulator. This graphical user interface allows definition of grid‐independent spatial distributions of model properties—the porous media properties, the initial head and chemistry conditions, boundary conditions, and locations of wells, rivers, drains, and accounting zones—and other parameters necessary for a simulation. Spatial data can be defined without reference to a grid by drawing, by point‐by‐point definitions, or by importing files, including ArcInfo® shape and raster files. All definitions can be inspected, edited, deleted, moved, copied, and switched from hidden to visible through the data tree of the interface. Model features are visualized in the main panel of the interface, so that it is possible to zoom, pan, and rotate features in three dimensions (3D). PHAST simulates single phase, constant density, saturated groundwater flow under confined or unconfined conditions. Reactions among multiple solutes include mineral equilibria, cation exchange, surface complexation, solid solutions, and general kinetic reactions. The interface can be used to develop and run simple or complex models, and is ideal for use in the classroom, for analysis of laboratory column experiments, and for development of field‐scale simulations of geochemical processes and contaminant transport.     

Evaluating the effect of land use changes on soil erosion and sediment yield using a grid‐based distributed modelling approach

Processes of soil erosion and sediment transport are strongly influenced by land use changes so the modelling of land use changes is important with respect to the simulation of soil degradation and its on‐site and off‐site consequences. The reliability of simulation results from erosion models is circumscribed by considerable spatial variation in many parameters. However, most of the currently widely used erosion models at the mesoscale are semidistributed, which leads to difficulties in incorporating a high degree of spatial information, especially land use information, so that the effects of land use changes on soil erosion have hitherto not been investigated in detail using these models. In this article, a grid‐based distributed erosion and sediment transport model is introduced, which simulates the spatial pattern of erosion and deposition rates and sediment transport processes in river channels. In this model, land use affects soil erosion through altering soil loss and influencing sediment delivery. Simulated soil erosion for events recorded in 1989 and 1996 in the Lushi basin in China was analyzed by comparing it with historical land use maps. The results indicated that even relatively minor land use changes had a significant effect on regional soil erosion rates and sediment transport to rivers. The average erosion rate increased from 1989 to 1996, after the transformation of forest to farmland. The results of the study suggest that the proposed soil erosion model can be applied in similar river basins. Copyright © 2011 John Wiley & Sons, Ltd.     

Salinity and periodic inundation controls on the soil‐plant‐atmosphere continuum of gray mangroves

Salinity and periodic inundation are both known to have a major role in shaping the ecohydrology of mangroves through their controls on water uptake, photosynthesis, stomatal conductance, gas exchanges, and nutrient availability. Salinity, in particular, can be considered one of the main abiotic regulating factors for halophytes and salt‐tolerant species, due to its influence on water use patterns and growth rate. Ecohydrological literature has rarely focused on the effects of salinity on plant transpiration, based on the fact that the terrestrial plants mostly thrive in low‐saline, unsaturated soils where the role of osmotic potential can be considered negligible. However, the effect of salinity cannot be neglected in the case of tidal species like mangroves, which have to cope with hyperosmotic conditions and waterlogging. We introduce here a first‐order ecohydrological model of the soil/plant‐atmosphere continuum of Avicennia marina—also known as gray mangrove—a highly salt‐tolerant pioneer species able to adapt to hyperarid intertidal zones and characterized by unique morphological and ecophysiological traits. The A. marina's soil‐plant‐atmosphere continuum takes explicitly into account the role of water head, osmotic water potential, and water salinity in governing plant water fluxes. A. marina's transpiration is thus modeled as a function of salinity based on a simple parameterization of salt exclusion mechanisms at the root level and a modified Jarvis' expression accounting for the effects of salinity on stomatal conductance. Consistently with previous studies investigating the physiology of mangroves in response to different environmental drivers, our results highlight the major influence of salinity on mangrove transpiration when contrasted with other potential stressors such as waterlogging and water stress.     

PHT3D‐UZF: A Reactive Transport Model for Variably‐Saturated Porous Media

A modified version of the MODFLOW/MT3DMS‐based reactive transport model PHT3D was developed to extend current reactive transport capabilities to the variably‐saturated component of the subsurface system and incorporate diffusive reactive transport of gaseous species. Referred to as PHT3D‐UZF, this code incorporates flux terms calculated by MODFLOW's unsaturated‐zone flow (UZF1) package. A volume‐averaged approach similar to the method used in UZF‐MT3DMS was adopted. The PHREEQC‐based computation of chemical processes within PHT3D‐UZF in combination with the analytical solution method of UZF1 allows for comprehensive reactive transport investigations (i.e., biogeochemical transformations) that jointly involve saturated and unsaturated zone processes. Intended for regional‐scale applications, UZF1 simulates downward‐only flux within the unsaturated zone. The model was tested by comparing simulation results with those of existing numerical models. The comparison was performed for several benchmark problems that cover a range of important hydrological and reactive transport processes. A 2D simulation scenario was defined to illustrate the geochemical evolution following dewatering in a sandy acid sulfate soil environment. Other potential applications include the simulation of biogeochemical processes in variably‐saturated systems that track the transport and fate of agricultural pollutants, nutrients, natural and xenobiotic organic compounds and micropollutants such as pharmaceuticals, as well as the evolution of isotope patterns.     

交错网格高阶差分法三维弹性波数值模拟

本文应用交错网格高阶有限差分方法模拟弹性波在三维各向同性介质中的传播。采用时间上二阶、空间上高阶近似的交错网格高阶差分公式求解三维弹性波位移-应力方程,并在计算边界处应用基于傍轴近似法得到的三维弹性波方程吸收边界条件。在此基础上进行了三维盐丘地质模型的地震波传播数值模拟试算。试算结果表明该方法模拟精度高,在很大程度上减小了数值频散,绕射波更加丰富,而且适用于介质速度具有纵向变化和横向变化的情况。     

The response of a gravel‐bed river planform configuration to flow variations and bed reworking: a modelling study

A 2D depth‐averaged model has been developed for simulating water flow, sediment transport and morphological changes in gravel‐bed rivers. The model was validated with a series of laboratory experiments and then applied to the Nove reach of the Brenta River (Northern Italy) to assess its bed material transport, interpret channel response to a series of intensive flood events (R.I. ≈ 10 years) and provide a possible evolutionary scenario for the medium term. The study reach is 1400 m long with a mean slope of 0.0039 m m^?1. High‐resolution digital terrain models were produced combining LiDAR data with colour bathymetry techniques. Extensive field sedimentological surveys were also conducted for surface and subsurface material. Data were uploaded in the model and the passage of two consecutive high intensity floods was simulated. The model was run under several hypotheses of sediment supply: one considering substantial equilibrium between sediment input and transport capacity, and the others reducing the sediment supply. The sediment supply was then calibrated comparing channel morphological changes as observed in the field and calculated by the model. Annual bed material transport was assessed and compared with other techniques. Low‐frequency floods (R.I. ≈ 1.5 years) are expected to produce negligible changes in the channel while high floods may erode banks rather than further incising the channel bed. Location and distribution of erosion and deposition areas within the Nove reach were predicted with acceptable biases stemming from imperfections of the model and the specified initial, boundary and forcing conditions. A medium‐term evolutionary scenario simulation underlined the different response to and impact of a consecutive sequence of floods. Copyright © 2015 John Wiley & Sons, Ltd.     

Modelling long‐term contaminant migration in a catchment at fine spatial and temporal scales using the UP system

A method has been developed to simulate the long‐term migration of radionuclides in the near‐surface of a river catchment, following their release from a deep underground repository for radioactive waste. Previous (30‐year) simulations, conducted using the SHETRAN physically based modelling system, showed that long‐term (many decades) simulations are required to allow the system to reach steady state. Physically based, distributed models, such as SHETRAN, tend to be too computationally expensive for this task. Traditional lumped catchment‐scale models, on the other hand, do not give sufficiently detailed spatially distributed results. An intermediate approach to modelling has therefore been developed which allows flow and transport processes to be simulated with the spatial resolution normally associated with distributed models, whilst being computationally efficient.The approach involves constructing a lumped model in which the catchment is represented by a number of conceptual water storage compartments. The flow rates to and from these compartments are prescribed by functions that summarize the results from physically based distributed models run for a range of characteristic flow regimes. The physically based models used were, SHETRAN for the subsurface compartments, a particle tracking model for overland flow and an analytical model for channel routing. One important advantage of the method used in constructing the lumped model is that it makes down scaling possible, in the sense that fine‐scale information on the distributed hydrological regime, as simulated by the physically based distributed models, can be inferred from the variables in the lumped model that describe the hydrology at the catchment scale. A 250‐year flow simulation has been run and the down scaling process used to infer a 250‐year time‐series of three‐dimensional velocity fields for the subsurface of the catchment. This series was then used to drive a particle tracking simulation of contaminant migration. The concentration and spatial distribution of contaminants simulated by this model for the first 30 years were in close agreement with SHETRAN results. The remaining 220 years highlighted the fact that some of the most important transport pathways to the surface carry contaminants only very slowly so both the magnitude and spatial distribution of concentration in surface soils are not apparent over the shorter SHETRAN simulations. Copyright © 1999 John Wiley & Sons, Ltd.     

Groundwater temperature evolution in the subsurface urban heat island of Cologne,Germany

Long‐term heating of shallow urban aquifers is observed worldwide. Our measurements in the city of Cologne, Germany revealed that the groundwater temperatures found in the city centre are more than 5 K higher than the undisturbed background. To explore the role of groundwater flow for the development of subsurface urban heat islands, a numerical flow and heat transport model is set up, which describes the hydraulic conditions of Cologne and simulates the transient evolution of thermal anomalies in the urban ground. A main focus is on the influence of horizontal groundwater flow, groundwater recharge and trends in local ground warming. To examine heat transport in groundwater, a scenario consisting of a local hot spot with a length of 1 km of long‐term ground heating was set up in the centre of the city. Groundwater temperature‐depth profiles at upstream, central and downstream locations of this hot spot are inspected. The simulation results indicate that the main thermal transport mechanisms are long‐term vertical conductive heat input, horizontal advection and transverse dispersion. Groundwater recharge rates in the city are low (<100 mm a^?1) and thus do not significantly contribute to heat transport into the urban aquifer. With groundwater flow, local vertical temperature profiles become very complex and are hard to interpret, if local flow conditions and heat sources are not thoroughly known. Copyright © 2014 John Wiley & Sons, Ltd.     

Low‐Resolution Modeling of Dense Drainage Networks in Confining Layers

Groundwater‐surface water (GW‐SW) interaction in numerical groundwater flow models is generally simulated using a Cauchy boundary condition, which relates the flow between the surface water and the groundwater to the product of the head difference between the node and the surface water level, and a coefficient, often referred to as the “conductance.” Previous studies have shown that in models with a low grid resolution, the resistance to GW‐SW interaction below the surface water bed should often be accounted for in the parameterization of the conductance, in addition to the resistance across the surface water bed. Three conductance expressions that take this resistance into account were investigated: two that were presented by Mehl and Hill (2010) and the one that was presented by De Lange (1999). Their accuracy in low‐resolution models regarding salt and water fluxes to a dense drainage network in a confined aquifer system was determined. For a wide range of hydrogeological conditions, the influence of (1) variable groundwater density; (2) vertical grid discretization; and (3) simulation of both ditches and tile drains in a single model cell was investigated. The results indicate that the conductance expression of De Lange (1999) should be used in similar hydrogeological conditions as considered in this paper, as it is better taking into account the resistance to flow below the surface water bed. For the cases that were considered, the influence of variable groundwater density and vertical grid discretization on the accuracy of the conductance expression of De Lange (1999) is small.     

新疆艾比湖湿地土壤水盐空间变异性分析

为揭示艾比湖湿地土壤退化程度空间分布特征,在离艾比湖湖滨5~15 km,绕湖一周160 km范围内,以湖心质点为中心,将艾比湖划分为东北、东南、西南、西北4个区域,采用传统统计学和地统计学相结合的方法对表层(0~20 cm)土壤盐分、含水量与p H的空间分异特征进行研究.结果表明:绕湖一周不同区域的土壤盐分均属中等变异强度;土壤含水量在西北部属强变异性,而东北、东南和西南部均属中等变异强度;土壤p H在不同区域内均属弱变异强度.绕湖一周除西北部土壤盐分的半方差理论模型较符合球状模型外,其它区域土壤盐分、含水量和p H均符合高斯模型;受结构性因素影响,不同区域土壤盐分、含水量和p H均具有较强的空间相关性;西南部土壤盐分、含水量和p H的Moran's I系数比其它区域的波动大,表明空间相关性较强.艾比湖湿地常年大风、干旱、缺水及沙化盐化的自然因素与引水围堰、种植耐盐碱植物的人为活动造成了采样区表层土壤盐分、含水量和p H的空间分布多呈现不规则条带状格局.艾比湖湿地土壤以盐土为主,重度盐化土次之,土壤盐渍化日益严重.     

Hydrologic‐response simulations for the North Fork of Caspar Creek: second‐growth,clear‐cut,new‐growth,and cumulative watershed effect scenarios

This study demonstrates that comprehensive hydrologic‐response simulation can be a useful tool for studying cumulative watershed effects. The simulations reported here were conducted with the Integrated Hydrology Model (InHM). The location of the 473 ha study site is the North Fork of the Caspar Creek Experimental Watershed, near Fort Bragg, California. Existing information from a long‐term monitoring programme and new soil‐hydraulic property measurements made for this study were used to parameterize InHM. Long‐term continuous wet‐season simulations were conducted for the North Fork catchments and main stem for second‐growth, clear‐cut and new‐growth scenarios. The simulation results show that the increases and decreases, respectively, for throughfall and potential evapotranspiration related to clear‐cutting had quantifiable impacts on the simulated hydrologic response at both the catchment and watershed scales. Model performance was best for the new‐growth simulation scenarios. To improve upon the simulations reported here would require additional soil‐hydraulic property information from across the study area. Although principally focused on the integrated hydrologic response, the effort reported here demonstrates the potential for characterizing distributed responses with physics‐based simulation. The search for a comprehensive understanding of hydrologic response will require both data‐intensive discovery and concept‐development simulation, from both integrated and distributed perspectives. Copyright © 2013 John Wiley & Sons, Ltd.     

Three‐dimensional hydrodynamic and salinity transport modelling of Danshuei River estuarine system and adjacent coastal sea,Taiwan

A three‐dimensional, time‐dependent hydrodynamic and salinity model was applied to the Danshuei River estuarine system and adjacent coastal sea in Taiwan. The model forcing functions consist of tidal elevations along the open boundary and freshwater flows from the main stem and tributaries in the Danshuei River system. The bottom roughness height was calibrated and verified with model simulation of barotropic flow, and the turbulent diffusivities were calibrated through comparison of time‐series of salinity distributions. The overall model verification was achieved with comparisons of residual current and salinity distribution. The model simulation results are in qualitative agreement with the available field data. The model was then used to investigate the tidal current, residual current, and salinity patterns under the low freshwater flow condition in the modelling domain. The results reveal that the extensive intrusion of saline water imposes a significant baroclinic forcing and induces a strong residual circulation in the estuary. The downriver net velocity in the upper layer increases seaward despite the enlargement of the river cross‐section in that direction. Strong residual circulation can be found near the Kuan‐Du station. This may be the result of the deep bathymetric features there. Copyright © 2007 John Wiley & Sons, Ltd.