Numerical method of moments for solute transport in a nonstationary flow field conditioned on hydraulic conductivity and head measurements

The unconditional stochastic studies on groundwater flow and solute transport in a nonstationary conductivity field show that the standard deviations of the hydraulic head and solute flux are very large in comparison with their mean values (Zhang et al. in Water Resour Res 36:2107–2120, 2000; Wu et al. in J Hydrol 275:208–228, 2003; Hu et al. in Adv Water Resour 26:513–531, 2003). In this study, we develop a numerical method of moments conditioning on measurements of hydraulic conductivity and head to reduce the variances of the head and the solute flux. A Lagrangian perturbation method is applied to develop the framework for solute transport in a nonstationary flow field. Since analytically derived moments equations are too complicated to solve analytically, a numerical finite difference method is implemented to obtain the solutions. Instead of using an unconditional conductivity field as an input to calculate groundwater velocity, we combine a geostatistical method and a method of moment for flow to conditionally simulate the distributions of head and velocity based on the measurements of hydraulic conductivity and head at some points. The developed theory is applied in several case studies to investigate the influences of the measurements of hydraulic conductivity and/or the hydraulic head on the variances of the predictive head and the solute flux in nonstationary flow fields. The study results show that the conditional calculation will significantly reduce the head variance. Since the hydraulic head measurement points are treated as the interior boundary (Dirichlet boundary) conditions, conditioning on both the hydraulic conductivity and the head measurements is much better than conditioning only on conductivity measurements for reduction of head variance. However, for solute flux, variance reduction by the conditional study is not so significant.     

A dripper-TDR method for in situ determination of hydraulic conductivity and chemical transport properties of surface soils

Field determined hydraulic and chemical transport properties can be useful for the protection of groundwater resources from land-applied chemicals. Most field methods to determine flow and transport parameters are either time or energy consuming and/or they provide a single measurement for a given time period. In this study, we present a dripper-TDR field method that allows measurement of hydraulic conductivity and chemical transport parameters at multiple field locations within a short time period. Specifically, the dripper-TDR determines saturated hydraulic conductivity (K_s), macroscopic capillary length (λ_c), immobile water fraction (θ_im/θ), mass exchange coefficient (α) and dispersion coefficient (D_m). Multiple dripper lines were positioned over five crop rows in a field. Background and step solutions were applied through drippers to determine surface hydraulic conductivity parameters at 44 locations and surface transport properties at 38 locations. The hydraulic conductivity parameters (K_s, λ_c) were determined by application of three discharge rates from the drippers and measurements of the resultant steady-state flux densities at the soil surface beneath each dripper. Time domain reflectometry (TDR) was used to measure the bulk electrical conductivity of the soil during steady infiltration of a salt solution. Breakthrough curves (BTCs) for all sites were determined from the TDR measurements. The K_s and λ_c values were found to be lognormally distributed with average values of 31.4 cm h⁻¹ and 6.0 cm, respectively. BTC analysis produced chemical properties, θ_im/θ, α, and D_m with average values of 0.23, 0.0036 h⁻¹, and 1220 cm² h⁻¹, respectively. The estimated values of the flow and transport parameters were found to be within the ranges of values reported by previous studies conducted at nearby field locations. The dripper TDR method is a rapid and useful technique for in situ measurements of hydraulic conductivity and solute transport properties. The measurements reported in this study give clear evidence to the occurrence of non-equilibrium water and chemical movement in surface soil. The method allows for quantification of non-equilibrium model parameters and preferential flow. Quantifying the parameters is a necessary step toward determining the influences of surface properties on infiltration, runoff, and vadose zone transport.     

Simulation of field‐scale water flow and bromide transport in a cracked clay soil

Single domain models may seriously underestimate leaching of nutrients and pesticides to groundwater in clay soils with shrinkage cracks. Various two‐domain models have been developed, either empirical or physically based, which take into account the effects of cracks on water flow and solute transport. This paper presents a model concept that uses the clay shrinkage characteristics to derive crack volume and crack depth under transient field conditions. The concept has been developed to simulate field average behaviour of a field with cracks, rather than flow and transport at a small plot. Water flow and solute transport are described with basic physics, which allow process and scenario analysis. The model concept is part of the more general agrohydrological model SWAP, and is applied to a field experiment on a cracked clay soil, at which water flow and bromide transport were measured during 572 days. A single domain model was not able to mimic the field‐average water flow and solute transport. Incorporation of the crack concept considerably improved the simulation of water content and bromide leaching to the groundwater. Still deviations existed between the measured and simulated bromide concentration profiles. The model did not reproduce the observed bromide retardation in the top layer and the high bromide dispersion resulting from water infiltration at various soil depths. A sensitivity analysis showed that the amounts of bromide leached were especially sensitive to the saturated hydraulic conductivity of the top layer, the solute transfer from the soil matrix to crack water flow and the mean residence time of rapid drainage. The shrinkage characteristic and the soil hydraulic properties of the clay matrix showed a low sensitivity. Copyright © 2000 John Wiley & Sons, Ltd.     

Characterizing heterogeneous soil water flow and solute transport using information measures

Heterogeneous water flow and solute transport in soils are an important phenomenon and difficult to be characterized. The objectives of this study were to investigate the heterogeneity of solute transport related to heterogeneous soil water flow using dye infiltration experiments, and to characterize heterogeneous water flow and solute transport in soils using the information theory. Field experiments of dye infiltration were performed in four plots. Various information measures were applied to characterize information content and complexity of water flow and solute transport in soils. Information contents and complexities of the maximum and apparent infiltration depths, and the mean and standard deviation of concentrations in the vertical direction of the plots were calculated. More heterogeneous processes of soil water flow and transport result in higher information/complexity values. The probability distributions of mean concentration were similar to those of the corresponding apparent infiltration depths for the plots, indicating that heterogeneity of dye concentrations was closely related to that of soil water flow. However, the range of information entropy and complexity of the water flow sequences was much narrower than that of the sequences of the concentrations. The results suggested that the transport processes were more heterogeneous than the water flow processes. Compared with the probability distributions of flow parameters, the information measures appeared to be a more versatile tool to describe flow and transport heterogeneities in soils.     

Bulk density effects on soil hydrologic and thermal characteristics: A numerical investigation

Soil bulk density (ρ_b) is commonly treated as static in studies of land surface dynamics. Magnitudes of errors associated with this assumption are largely unknown. Our objectives were to (a) quantify ρ_b effects on soil hydrologic and thermal properties and (b) evaluate effects of ρ_b on surface energy balance and heat and water transfer. We evaluated 6 soil properties, volumetric heat capacity, thermal conductivity, soil thermal diffusivity, water retention characteristics, hydraulic conductivity, and vapour diffusivity, over a range of ρ_b, using a combination of 6 models. Thermal conductivity, water retention, hydraulic conductivity, and vapour diffusivity were most sensitive to ρ_b, each changing by fractions greater than the associated fractional changes in ρ_b. A 10% change in ρ_b led to 10–11% change in thermal conductivity, 6–11% change in saturated and residual water content, 49–54% change in saturated hydraulic conductivity, and 80% change in vapour diffusivity. Subsequently, 3 field seasons were simulated with a numerical model (HYDRUS‐1D) for a range of ρ_b values. When ρ_b increased 25% (from 1.2 to 1.5 Mg m^?3), soil temperature variation decreased by 2.1 °C in shallow layers and increased by 1 °C in subsurface layers. Surface water content differed by 0.02 m³ m^?3 for various ρ_b values during drying events but differences mostly disappeared in the subsurface. Matric potential varied by >100 m of water. Surface energy balance showed clear trends with ρ_b. Latent heat flux decreased 6%, sensible heat flux increased 9%, and magnitude of ground heat flux varied by 18% (with a 25% ρ_b increase). Transient ρ_b impacted surface conditions and fluxes, and clearly, it warrants consideration in field and modelling investigations.     

Contaminant transport in a small deformation aquitard affected by the delayed drainage phenomenon

This paper presents a formulation accounting for the effect of delayed drainage phenomenon (DDP) on the breakthrough of contaminant flux in an aquitard, by considering the movement of soil particles, porosity variation, hydraulic head variation, and transient flow during the consolidation. The water flow equation in an aquitard was based on the Terzaghi's consolidation theory, and the contaminant transport equation was derived on the basis of the mass balance law. Two cases were used to illustrate the effect of DDP on the contaminant transport in an aquitard of small deformation. It is found that the breakthrough time of contaminant in an aquitard is very long, which is mainly ascribed to the low permeability of aquitard and sorption of soil particles. It is also found that the increase of depletion, which is in general induced by the increase of thickness and specific storativity and the decrease of hydraulic conductivity, enhances the impact of DDP on the contaminant transport in an aquitard. A larger delay index (τ₀) of DDP gives a greater delay breakthrough time (DBT) of solute transport in an aquitard, which controls the difference of the breakthrough time of contaminant transport in aquitards with and without the occurrence of DDP. For the cases where advection plays a dominant role during the process of solute transport, τ₀ is almost linearly correlated with DBT, and the ratio of DBT over the breakthrough time without consideration of DDP also approximately shows a linear relationship with the ratio of specific storativity to porosity, given a fixed drawdown in the adjacent aquifer with the sorption being ignored.     

双探针型海底热流计的结构优化

本文在现有海底热流探针制作技术条件下,首先建立了脉冲式双探针海底测量单元的有限元数值模型,模拟获得多组参数下的温度-时间数据,作为“实测”数据,再用脉冲加热有限长线热源(PFLS)模型求解待测介质热导率及其相对误差上限(RE_λ-UL),并以RE_λ-UL最小为原则,对双探针热流计的结构进行优化.结果表明:(1)在不同探针脉冲强度(q)、温度测量误差(ΔT_m)和探针长度(L)组合下,都存在最佳探针间距(Best_r),使得RE_λ-UL降到最低;(2)随着q增大或ΔT_m减小,Best_r逐渐增大;(3)当q、ΔT_m及探针半径(a)都给定时,Best_r与探针长度(L)呈线性正相关;(4)当a=1.0 mm,且q、ΔT_m分别取为628.0~1100.0 J·m^-1、0.5~1.0 mK,若L在20.0~42.0 mm之间时,则Best_r在18.0~30.0 mm之间,此时介质热导率相对误差上限可控制在5.5%以内,同时测量温度可在6 min内达到最大值,即脉冲加热开始后,温度测量只需约7 min,便可满足介质热导率的求解,这比目前常用的Lister型热流计所需海底测量时间缩短8 min左右.     

Using time‐domain reflectometry to characterize shallow solute transport in an oak woodland hillslope in northern California,USA

The natural heterogeneity of water and solute movement in hillslope soils makes it difficult to accurately characterize the transport of surface‐applied pollutants without first gathering spatially distributed hydrological data. This study examined the application of time‐domain reflectometry (TDR) to measure solute transport in hillslopes. Three different plot designs were used to examine the transport of a conservative tracer in the first 50 cm of a moderately sloping soil. In the first plot, which was designed to examine spatial variability in vertical transport in a 1·2 m² plot, a single probe per meter was found to adequately characterize vertical solute travel times. In addition, a dye and excavation study in this plot revealed lateral preferential flow in small macropores and a transport pattern where solute is focused vertically into preferential flow pathways. The bypass flow delivers solute deeper in the soil, where lateral flow occurs. The second plot, designed to capture both vertical and lateral flow, provided additional evidence confirming the flow patterns identified in the excavation of the first plot. The third plot was designed to examine lateral flow and once again preferential flow of the tracer was observed. In one instance rapid solute transport in this plot was estimated to occur in as little as 3% of the available pore space. Finally, it was demonstrated that the soil anisotropy, although partially responsible for lateral subsurface transport, may also homogenize the transport response across the hillslope by decreasing vertical solute spreading. Copyright © 2002 John Wiley & Sons, Ltd.     

Thermal conductivity in a vadose zone: A novel spectral solution and application by the implication of significant coherence of thermal condition in the shallow soil water layer

In the context of the heterogeneity in the unsaturated or vadose zone, accurately representing the analytical mechanisms and in-situ water content within the soil layer poses a significant challenge. Particularly in shallow layers, thermal conditions exhibit rapid changes in response to evolving surface temperatures. This study proposes a hypothesis suggesting that the in situ heat mechanism may notably impact the soil water layer. The research introduces an innovative approach to theoretically uncover thermal conditions, including soil temperature, soil temperature gradients, and heat flux, within the shallow Quaternary gravel layer at various depths through spectral analysis of temporal observations. The study presents a stochastic inverse solution to estimate thermal conductivity by leveraging spectral analysis of soil heat flux and temperature gradients. The findings reveal that thermal conditions exhibit the most prominent periodic fluctuations during the diurnal process over a 24-hour cycle. The soil temperature gradients and heat flux measurements at depths of 0.1, 0.3, 0.6, and 1.2 m demonstrate their ability to capture changes in soil temperature and air temperature to a certain extent within the frequency domain. Furthermore, the analysis highlights the intrinsic uncertainty and sensitivity of estimating thermal conductivity in heterogeneous soil environments. The wide variability observed in thermal conductivity values, coupled with their dependence on soil type and environmental conditions, underscores the need for careful consideration of these factors in future studies and modeling efforts. Applying the derived inverse spectral solution allows for determining thermal conductivity throughout the soil-water system across depths ranging from 0.1 to 1.2 m. As a result, this research demonstrates the feasibility and practicality of assessing the thermal conductivity of the soil layer in conjunction with heat flux and temperature gradients through spectral analysis.     

Effects of Coal Gangue Content on Water Movement and Solute Transport in a China Loess Plateau Soil

The mining industry has grown strongly in China in recent decades, resulting in large amounts of coal gangues, which cause water and soil pollution, soil erosion, and various other environmental problems. They are often used in reclamation projects in attempts to restore land damaged by mining, hence they are frequently present (in widely varying proportions) in the topsoil in areas around mines. Their presence can strongly affect key soil variables, including its bulk density, structure, water retention, water movement, and solute transport rates. In the study presented here, the effects of gangue contents on infiltration, saturated hydraulic conductivity, and solute transport parameters of a Chinese Loess plateau soil were examined. The results show that infiltration rates and saturated hydraulic conductivity decreased with increasing gangue content. The Peck–Watson equation modeled these relationships well, but Bouwer–Rice equations provided poorer matches with the acquired data. Cumulative infiltration over time was described well by both the Philip equation and Kostiakov equation. Both the simplified convection–dispersion equation and a two‐region model described the solute transport processes well. In addition, the dispersion increased, while both the Peclet number and mobile water fraction decreased, with increases in gangue contents.     

A 3D ERT study of solute transport in a large experimental tank

A high resolution, cross-borehole, 3D electrical resistivity tomography (ERT) study of solute transport was conducted in a large experimental tank. ERT voxels comprising the time sequence of electrical images were converted into a 3D array of ERT estimated fluid conductivity breakthrough curves and compared with direct measurements of fluid conductivity breakthrough made in wells. The 3D ERT images of solute transport behaviour were also compared with predictions based on a 3D finite-element, coupled flow and transport model, accounting for gravity induced flow caused by concentration differences.The tank (dimensions 185×245×186 cm) was filled with medium sand, with a gravel channel and a fine sand layer installed. This heterogeneous system was designed to complicate solute transport behaviour relative to a homogeneous sand tank, and to thus provide a challenging but insightful analysis of the ability of 3D ERT to resolve transport phenomena. Four ERT arrays and 20 piezometers were installed during filling. A NaCl tracer (conductivity 1.34 S/m) was injected and intensively monitored with 3D ERT and direct sampling of fluid chemistry in piezometers.We converted the bulk conductivity estimate for 250 voxels in the ERT imaged volume into ERT estimated voxel fluid conductivity by assuming that matrix conduction in the tank is negligible. In general, the ERT voxel response is in reasonable agreement with the shape of fluid conductivity breakthrough observed in six wells in which direct measurements of fluid conductivity were made. However, discrepancies occur, particularly at early times, which we attribute to differences between the scale of the image voxels and the fluid conductivity measurement, measurement errors mapped into the electrical inversion and artificial image roughness resulting from the inversion.ERT images revealed the 3D tracer distribution at 15 times after tracer injection. The general pattern and timing of solute breakthrough observed with ERT agreed with that predicted from the flow/transport modelling. However, the ERT images indicate a vertical component of tracer transport and preferential flow paths in the medium sand. We attribute this to transient vertical gradients established during tracer injection, and heterogeneity caused by sorting of the sand resulting from the filling procedure. In this study, ERT provided a unique dataset of 250 voxel breakthrough curves in 1.04 m³. The use of 3D ERT to generate an array of densely sampled estimated fluid conductivity breakthrough curves is a potentially powerful tool for quantifying solute transport processes.     

Sediment and solute transport on soil slope under simultaneous influence of rainfall impact and scouring flow

Soil erosion and nutrient losses with surface runoff in the loess plateau in China cause severe soil quality degradation and water pollution. It is driven by both rainfall impact and runoff flow that usually take place simultaneously during a rainfall event. However, the interactive effect of these two processes on soil erosion has received limited attention. The objectives of this study were to better understand the mechanism of soil erosion, solute transport in runoff, and hydraulic characteristics of flow under the simultaneous influence of rainfall and shallow clear‐water flow scouring. Laboratory flume experiments with three rainfall intensities (0, 60, and 120 mm h⁻¹) and four scouring inflow rates (10, 20, 30, and 40 l min⁻¹) were conducted to evaluate their interactive effect on runoff. Results indicate that both rainfall intensity and scouring inflow rate play important roles on runoff formation, soil erosion, and solute transport in the surface runoff. A rainfall splash and water scouring interactive effect on the transport of sediment and solute in runoff were observed at the rainfall intensity of 60 mm h⁻¹ and scouring inflow rates of 20 l min⁻¹. Cumulative sediment mass loss (Ms) was found to be a linear function of cumulative runoff volume (Wr) for each treatment. Solute transport was also affected by both rainfall intensity and scouring inflow rate, and the decrease in bromide concentration in the runoff with time fitted to a power function well. Reynolds number (Re) was a key hydraulic parameter to determine erodability on loess slopes. The Darcy–Weisbach friction coefficients (f) decreased with the Reynolds numbers (Re), and the average soil and water loss rate (M_l) increased with the Reynolds numbers (Re) on loess slope for both scenarios with or without rainfall impact. Copyright © 2010 John Wiley & Sons, Ltd.     

How Does Subsurface Characterization Affect Simulations of Hyporheic Exchange?

We investigated the role of increasingly well‐constrained geologic structures in the subsurface (i.e., subsurface architecture) in predicting streambed flux and hyporheic residence time distribution (RTD) for a headwater stream. Five subsurface realizations with increasingly resolved lithological boundaries were simulated in which model geometries were based on increasing information about flow and transport using soil and geologic maps, surface observations, probing to depth to refusal, seismic refraction, electrical resistivity (ER) imaging of subsurface architecture, and time‐lapse ER imaging during a solute tracer study. Particle tracking was used to generate RTDs for each model run. We demonstrate how improved characterization of complex lithological boundaries and calibration of porosity and hydraulic conductivity affect model prediction of hyporheic flow and transport. Models using hydraulic conductivity calibrated using transient ER data yield estimates of streambed flux that are three orders of magnitude larger than uncalibrated models using estimated values for hydraulic conductivity based on values published for nearby hillslopes (10^?4 vs. 10^?7 m²/s, respectively). Median residence times for uncalibrated and calibrated models are 10³ and 10⁰ h, respectively. Increasingly well‐resolved subsurface architectures yield wider hyporheic RTDs, indicative of more complex hyporheic flowpath networks and potentially important to biogeochemical cycling. The use of ER imaging to monitor solute tracers informs subsurface structure not apparent from other techniques, and helps to define transport properties of the subsurface (i.e., hydraulic conductivity). Results of this study demonstrate the value of geophysical measurements to more realistically simulate flow and transport along hyporheic flowpaths.     

Water and solute movement in a coarse-textured water-repellent field soil

Unstable water flow in water-repellent unsaturated soils can significantly affect the processes of infiltration and soil water redistribution. A field experiment was carried out to study the effect of water-repellency on water and bromide movement in a coarse-textured soil in the southwestern part of The Netherlands. The field data were analyzed using a relatively simple numerical model based on the standard Richards' equation for unsaturated water flow and the Fickian-based convection-dispersion equation for solute transport. Water-repellency was accounted for by multiplying the water content and the unsaturated hydraulic conductivity of the soil with F, a factor equal to the volumetric fraction of soil occupied by preferential flow paths resulting from the unstable flow process. The good comparison of simulated and measured bromide concentrations suggests that the model provides a viable method for simulating unstable water flow in water-repellent soils.     

Characterising deep vadose zone water movement and solute transport under typical irrigated cropland in the North China Plain

Understanding the dynamics and mechanisms of soil water movement and solute transport is essential for accurately estimating recharge rates and evaluating the impacts of agricultural activities on groundwater resources. In a thick vadose zone (0–15 m) under irrigated cropland in the piedmont region of the North China Plain, soil water content, matric potential, and solute concentrations were measured. Based on these data, the dynamics of soil water and solutes were analysed to investigate the mechanisms of soil water and solute transport. The study showed that the 0–15‐m vadose zone can be divided into three layers: an infiltration and evaporation layer (0–2 m), an unsteady infiltration layer (2–6 m), and a quasi‐steady infiltration layer (6–15 m). The chloride, nitrate, and sulphate concentrations all showed greater variations in the upper soil layer (0–1 m) compared to values in the deep vadose zone (below 2 m). The average concentrations of these three anions in the deep vadose zone varied insignificantly with depth and approached values of 125, 242, and 116 mg/L. The accumulated chloride, sulphate, and nitrate were 2,179 ± 113, 1,760 ± 383, and 4,074 ± 421 kg/ha, respectively. The soil water potential and solute concentrations indicated that uniform flow and preferential flow both occurred in the deep vadose zone, and uniform flow was the dominant mechanism of soil water movement in this study. The piston‐like flow velocity of solute transport was 1.14 m per year, and the average value of calculated leached nitrate nitrogen was 107 kg/ha?year below the root zone. The results can be used to better understand recharge processes and improve groundwater resources management.     

A novel platform to evaluate the dampening of water and solute transport in an experimental channel under unsteady flow conditions

This paper presents a novel platform to study the dampening of water and solute transport in an experimental channel under unsteady flow conditions, where literature data are scarce. We address the question about what could be the smallest size of experimental platform that is useful for research, project studies, and teaching activities and that allows to do rational experiments characterized by small space occupation, short experimental duration, high measurement precision, high quality and reproducible experimental curves, low water and energy consumption, and the possibility to test a large variety of hydrograph scenarios. Whereas large scale hydraulic laboratories have focused their studies on sediment transport, our platform deals with solute transport. The objectives of our study are (a) building a platform that allows to do rational experiments, (b) enriching the lack of experimental data concerning water and solute transport under unsteady state conditions, and (c) studying the dampening of water and solute transport. We studied solute transport in a channel with lateral gain and lateral loss under different experimental configurations, and we show how the same lateral loss flow event can lead to different lateral loss mass repartitions under different configurations. In order to characterize water and solute dampening between the input and the output of the channel, we calculate dampening ratios based on peak coordinates of time flow curves and time mass curves and that express the decrease of peak amplitude and the increase of peak occurrence time between the input and output curves. Finally, we use a solute transport model coupling the diffusive wave equation for water transfer and the advection–diffusion equation for solute transport in order to simulate the experimental data. The simulations are quite good with a Nash–Sutcliffe efficiency NSE > 0.98 for water transfer and 0.84 < NSE < 0.97 for solute transport. This platform could serve hydrological modellers because it offers a variety of measured parameters (flow, water height, and solute concentration), at a fine time step under unsteady flow conditions.     

The effect of non divergence-free velocity fields on field scale ground water solute transport

Solute plume subjected to field scale hydraulic conductivity heterogeneity shows a large dispersion/macrodispersion, which is the manifestation of existing fields scale heterogeneity on the solute plume. On the other hand, due to the scarcity of hydraulic conductivity measurements at field scale, hydraulic conductivity heterogeneity can only be defined statistically, which makes the hydraulic conductivity a random variable/function. Random hydraulic conductivity as a parameter in flow equation makes the pore flow velocity also random and the ground water solute transport equation is a stochastic differential equation now. In this study, the ensemble average of stochastic ground water solute transport equation is taken by the cumulant expansion method in order to upscale the laboratory scale transport equation to field scale by assuming pore flow velocity is a non stationary, non divergence-free and unsteady random function of space and time. Besides the stochastic explanation of macrodispersion and the velocity correction term obtained by Kavvas and Karakas (J Hydrol 179:321–351, 1996) before a new velocity correction term, which is a function of mean pore flow velocity divergence, is obtained in this study due to strict second order cumulant expansion (without omitting any term after the expansion) performed. The significance of the new velocity correction term is investigated on a one dimensional transport problem driven by a density dependent flow field.     

A quasi three-dimensional model for flow and transport in unsaturated and saturated zones: 1. Implementation of the quasi two-dimensional case

A quasi three-dimensional (QUASI 3-D) model is presented for simulating the subsurface water flow and solute transport in the unsaturated and in the saturated zones of soil. The model is based on the assumptions of vertical flow in the unsaturated zone and essentially horizontal groundwater flow. The 1-D Richards equation for the unsaturated zone is coupled at the phreatic surface with the 2-D flow equation for the saturated zone. The latter was obtained by averaging 3-D flow equation in the saturated zone over the aquifer thickness. Unlike the Boussinesq equation for a leaky-phreatic aquifer, the developed model does not contain a storage term with specific yield and a source term for natural replenishment. Instead it includes a water flux term at the phreatic surface through which the Richards equation is linked with the groundwater flow equation. The vertical water flux in the saturated zone is evaluated on the basis of the fluid mass balance equation while the horizontal fluxes, in that equation, are prescribed by Darcy law. A 3-D transport equation is used to simulate the solute migration. A numerical algorithm to solve the problem for the general quasi 3-D case was developed. The developed methodology was exemplified for the quasi 2-D cross-sectional case (QUASI2D). Simulations for three synthetic problems demonstrate good agreement between the results obtained by QUASI2D and two fully 2-D flow and transport codes (SUTRA and 2DSOIL). Yet, simulations with the QUASI2D code were several times faster than those by the SUTRA and the 2DSOIL codes.     

A Flux Detection Probe to Quantify Dynamic Groundwater-Surface Water Exchange in the Hyporheic Zone

A new probe was designed to quantify groundwater-surface water exchange in the hyporheic zone under dynamic stage condition. Current methods focus on either vertical pore water velocity or Darcy flux measurements. Both parameters must be understood to evaluate residence time and mass flux of constituents. Furthermore, most instruments are not well suited for monitoring instantaneous velocity or flux under dynamic exchange conditions. For this reason, the flux detection probe (FDP) was designed that employs electrogeophysical measurements to estimate in situ sediment porosity, which can be used to convert pore water velocity to Darcy flux. Dynamic pore water velocity is obtained by monitoring fluid conductivity and temperature along the FDP probe. Pressure sensors deployed at the top and bottom of the probe provide the additional information necessary to estimate vertical permeability. This study focuses on the use of a geophysical method to estimate pore water velocity, porosity, and permeability within a controlled soil column where simulated river water displaces simulated groundwater. The difference between probe derived and theoretical pore water velocity using natural tracers such as electrical conductivity and temperature was −4.9 and 3.9% for downward flow and 1.1 and 12.8% for upward flow, respectively. The difference in porosity calculated from mass and volume packed in the soil column and probe measure porosity ranged between −3.2% and 1.5%. Also, the calculated hydraulic conductivity differed from probe derived values by −8.9%.     

Effect of anisotropy on solute transport in degraded fen peat soils

Peat soils are heterogeneous, anisotropic porous media. Compared to mineral soils, there is still limited understanding of physical and solute transport properties of fen peat soils. In this study, we aimed to explore the effect of soil anisotropy on solute transport in degraded fen peat. Undisturbed soil cores, taken in vertical and horizontal direction, were collected from one drained and one restored fen peatland both in a comparable state of soil degradation. Saturated hydraulic conductivity (K _s) and chemical properties of peat were determined for all soil cores. Miscible displacement experiments were conducted under saturated steady state conditions using potassium bromide as a conservative tracer. The results showed that (1) the K _s in vertical direction (K _sv) was significantly higher than that in horizontal direction (K_sh), indicating that K _s of degraded fen peat behaves anisotropically; (2) pronounced preferential flow occurred in vertical direction with a higher immobile water fraction and a higher pore water velocity; (3) the 5% arrival time (a proxy for the strength of preferential flow) was affected by soil anisotropy as well as study site. A strong correlation was found between 5% arrival time and dispersivity, K _s and mobile water fraction; (4) phosphate release was observed from drained peat only. The impact of soil heterogeneity on phosphate leaching was more pronounced than soil anisotropy. The soil core with the strongest preferential flow released the highest amount of phosphate. We conclude that soil anisotropy is crucial in peatland hydrology but additional research is required to fully understand anisotropy effects on solute transport.