Effect of mineral reactions on the hydraulic properties of unsaturated soils: Model development and application

The selective radius shift model was used to relate changes in mineral volume due to precipitation/dissolution reactions to changes in hydraulic properties affecting flow in porous media. The model accounts for (i) precipitation/dissolution taking place only in the water-filled part of the pore space and further that (ii) the amount of mineral precipitation/dissolution within a pore depends on the local pore volume. The pore bundle concept was used to connect pore-scale changes to macroscopic soil hydraulic properties. Precipitation/dissolution induces changes in the pore radii of water-filled pores and, consequently, in the effective porosity. In a time step of the numerical model, mineral reactions lead to a discontinuous pore-size distribution because only the water-filled pores are affected. The pore-size distribution is converted back to a soil moisture characteristic function to which a new water retention curve is fitted under physically plausible constraints. The model equations were derived for the commonly used van Genuchten/Mualem hydraulic properties. Together with a mixed-form solution of Richards’ equation for aqueous phase flow, the model was implemented into the geochemical modelling framework PHREEQC, thereby making available PHREEQC’s comprehensive geochemical reactions. Example applications include kinetic halite dissolution and calcite precipitation as a consequence of cation exchange. These applications showed marked changes in the soil’s hydraulic properties due to mineral precipitation/dissolution and the dependency of these changes on water contents. The simulations also revealed the strong influence of the degree of saturation on the development of the saturated hydraulic conductivity through its quadratic dependency on the van Genuchten parameter α. Furthermore, it was shown that the unsaturated hydraulic conductivity at fixed reduced water content can even increase during precipitation due to changes in the pore-size distribution.     

Selenium transport and transformation modelling in soil columns and ground water contamination prediction

Selenium transport and transformation were simulated in a soil column. A one‐dimensional dynamic mathematical and computer model is formulated to simulate, selenate, selenite, selenomethionine, organic selenium, and gaseous selenium. This computer model is based on the mass balance equation, including convective transport, dispersive transport, surface adsorption, oxidation and reduction, volatilization, chemical and biological transformation. The mathematical solution is obtained by the finite difference implicit method. The model was verified by comparison of model results with experimental measurements and also using mass balance calculations in each time step of calculation. For example after 4 days of simulation, the simulated value of adsorbed selenate for depth of 20 cm is 0·2 µmol kg^?1 and the measured value is 0·25 µmol kg^?1. Therefore simulated results are in good agreement with measured values. With this study and its results the distribution of various forms of selenium in soil column to ground water table can be predicted. Copyright © 2008 John Wiley & Sons, Ltd.     

Multi-functional heat pulse probe measurements of coupled vadose zone flow and transport

Simultaneous measurement of coupled water, heat, and solute transport in unsaturated porous media is made possible with the multi-functional heat pulse probe (MFHPP). The probe combines a heat pulse technique for estimating soil heat properties, water flux, and water content with a Wenner array measurement of bulk soil electrical conductivity (EC_bulk). To evaluate the MFHPP, we conducted controlled steady-state flow experiments in a sand column for a wide range of water saturations, flow velocities, and solute concentrations. Flow and transport processes were monitored continuously using the MFHPP. Experimental data were analyzed by inverse modeling of simultaneous water, heat, and solute transport using an adapted HYDRUS-2D model. Various optimization scenarios yielded simultaneous estimation of thermal, solute, and hydraulic parameters and variables, including thermal conductivity, volumetric water content, water flux, and thermal and solute dispersivities. We conclude that the MFHPP holds great promise as an excellent instrument for the continuous monitoring and characterization of the vadose zone.     

On the temporal resolution of mass balance models for soluble chemicals in soils

A daily step model of chemical mass balance in the topsoil is presented and validated at the three experimental sites in Europe, and subsequently applied to perform two distinct numerical experiments. First, an experiment was run using hypothetic soluble chemicals with half‐lives ranging from 10^?1 to 10⁴, with a range of representative European climate and soil properties, assuming uniform constant emissions of the chemicals throughout the year. Chemical mass in soil from the daily step model calculations can be surrogated by the monthly step model consistently parameterized in terms of absolute values, patterns and inter‐monthly variability with decreasing accuracy at higher chemical half‐lives. Leaching fluxes can be also surrogated by the monthly step calculation, although with higher errors. Runoff is correct in the order of magnitude, but it shows only a weak correlation with the monthly mean of the daily model output. For leaching and runoff, the accuracy depends mainly on soil properties. Variability is well reproduced for both leaching and runoff. The second experiment represented a pulse emission of chemicals discharged on a single day in a 12‐month period. Results from the annual average mass of chemicals in the soil, annual runoff and leaching fluxes from the daily step model were compared with the results obtained from the experiment assuming constant‐removal rates for the year. The two values are within a factor of 10 for half‐lives longer than 10 days; therefore, it is possible to emulate the daily step model with a simple constant‐removal rate model for screening‐level assessment. The experiments suggest that simpler schemes may be a practical screening‐level approximation of detailed daily step models for both continuous and pulse emissions, two cases providing extreme bounds of variation to real world emissions. Copyright © 2010 John Wiley & Sons, Ltd.     

Stochastic modelling of groundwater flow and solute transport in aquifers

This paper presents an introductory overview of recently developed stochastic theories for tackling spatial variability problems in predicting groundwater flow and solute transport. Advantages and limitations of the theories are discussed. Lastly, strategies based on the stochastic approaches to predict solute transport in aquifers are recommended.     

Water flow and solute transport model of potentially toxic elements through unsaturated zone at regional wellfield Kosnica

The objective of this work was to build a prognostic water flow model and potentially toxic elements (lead, cadmium, zinc) transport model in the unsaturated zone. Research was conducted in the catchment area of Kosnica regional wellfield, where the unsaturated zone is characterised by Fluvisol. Lower sorption capacities were determined in the first horizons for all three potentially toxic elements. Correlation coefficient of the measured and simulated values of tracer concentration is 0.58 for the AC horizon and 0.84 for the 2C/C1 horizon. Based on calibrated water flow and transport parameters, a prognostic water flow model and potentially toxic elements (lead, cadmium, zinc) transport model in the unsaturated zone was built. In case of an accidental spill of potentially toxic elements with concentrations of 1000 mg/l, the risk of contamination of the aquifer is present. Copyright © 2016 John Wiley & Sons, Ltd.     

Mobility of major ions and nutrients in the unsaturated zone during paddy cultivation: a field study and solute transport modelling approach

Study of the movement of water and solute within soil profiles is important for a number of reasons. Accumulation of prominent contaminants from agricultural chemicals in the unsaturated zone over the years is a major concern in many parts of the world. As a result, the unsaturated zone has been a subject of great research interest during the past decade. Hence, an intensive field study was conducted in a part of Palar and Cheyyar river basins to understand the variation of major ions and nutrients in the soil zone during paddy cultivation. The chloride and nitrate data were used to model the movement of these chemicals in the unsaturated zone using the HYDRUS‐2D model. The field study shows that fertilizer application and irrigation return flow increases the major ions and nutrients concentration in the unsaturated zone. Further, the nutrient concentrations are regulated by plant uptake, fertilizer application and infiltration rate. Additionally, denitrification and soil mineralization processes also regulate the nitrogen concentration in the unsaturated zone. The solute transport modelling study concluded that the simulated results match reasonably with the observed trends. Simulated concentrations of chloride and nitrate for a 5‐year period indicate that the concentrations of these ions fluctuate in a cyclic manner (from 60 to 68 mg l^?1 and from 3·4 to 3·5 mg l^?1 respectively in groundwater) with no upward and downward trend. The influence of excessive fertilizer application on groundwater was also modelled. The model predicts an increase of about 17 mg l^?1 of chloride and 2·3 mg l^?1 of nitrogen in the groundwater of this area when the application of fertilizers is doubled. The model indicates that the present level of use of agrochemicals is no threat to the groundwater quality. Copyright © 2007 John Wiley & Sons, Ltd.     

Coupled inverse modelling of groundwater flow and mass transport and the worth of concentration data

This paper presents the extension of the self-calibrating method to the coupled inverse modelling of groundwater flow and mass transport. The method generates equally likely solutions to the inverse problem that display the variability as observed in the field and are not affected by a linearisation of the state equations. Conditioning to the state variables is measured by an objective function including, among others, the mismatch between the simulated and measured concentrations. Conditioning is achieved by minimising the objective function by gradient-based methods. The gradient contains the partial derivatives of the objective function with respect to: log conductivities, log storativities, prescribed heads at boundaries, retardation coefficients and mass sources. The derivatives of the objective function with respect to log conductivity are the most cumbersome and need the most CPU-time to be evaluated. For this reason, to compute this derivative only advective transport is considered. The gradient is calculated by the adjoint-state method. The method is demonstrated in a controlled, synthetic study, in which the worth of concentration data is analysed. It is shown that concentration data are essential to improve transport predictions and also help to improve aquifer characterisation and flow predictions, especially in the upstream part of the aquifer, even in the case that a considerable amount of other experimental data like conductivities and heads are available. Besides, conditioning to concentration data reduces the ensemble variances of estimated transmissivity, hydraulic head and concentration.     

Assessment of radionuclide transport uncertainty in the unsaturated zone of Yucca Mountain

The present study assesses the uncertainty of flow and radionuclide transport in the unsaturated zone at Yucca Mountain using a Monte Carlo method. Matrix permeability, porosity, and sorption coefficient are considered random. Different from previous studies that assume distributions of the parameters, the distributions are determined in this study by applying comprehensive transformations and rigorous statistics to on-site measurements of the parameters. The distribution of permeability is further adjusted based on model calibration results. Correlation between matrix permeability and porosity is incorporated using the Latin Hypercube Sampling method. After conducting 200 Monte Carlo simulations of three-dimensional unsaturated flow and radionuclide transport for conservative and reactive tracers, the mean, variances, and 5th, 50th, and 95th percentiles for quantities of interest (e.g., matrix liquid saturation and water potential) are evaluated. The mean and 50th percentile are used as the mean predictions, and their associated predictive uncertainties are measured by the variances and the 5th and 95th percentiles (also known as uncertainty bounds). The mean predictions of matrix liquid saturation and water potential are in reasonable agreement with corresponding measurements. The uncertainty bounds include a large portion of the measurements, suggesting that the data variability can be partially explained by parameter uncertainty. The study illustrates propagation of predictive uncertainty of percolation flux, increasing downward from repository horizon to water table. Statistics from the breakthrough curves indicate that transport of the reactive tracer is delayed significantly by the sorption process, and prediction on the reactive tracer is of greater uncertainty than on the conservative tracer because randomness in the sorption coefficient increases the prediction uncertainty. Uncertainty in radionuclide transport is related to uncertainty in the percolation flux, suggesting that reducing the former entails reduction in the latter.     

Catchment‐scale conceptual modelling of water and solute transport in the dual flow system of the karst critical zone

Hydrological and hydrochemical processes in the critical zone of karst environments are controlled by the fracture‐conduit network. Modelling hydrological and hydrochemical dynamics in such heterogeneous hydrogeological settings remains a research challenge. In this study, water and solute transport in the dual flow system of the karst critical zone were investigated in a 73.5‐km² catchment in southwest China. We developed a dual reservoir conceptual run‐off model combined with an autoregressive and moving average model with algorithms to assess dissolution rates in the “fast flow” and “slow flow” systems. This model was applied to 3 catchments with typical karst critical zone architectures, to show how flow exchange between fracture and conduit networks changes in relation to catchment storage dynamics. The flux of bidirectional water and solute exchange between the fissure and conduit system increases from the headwaters to the outfall due to the large area of the developed conduits and low hydraulic gradient in the lower catchment. Rainfall amounts have a significant influence on partitioning the relative proportions of flow and solutes derived from different sources reaching the underground outlet. The effect of rainfall on catchment function is modulated by the structure of the karst critical zone (e.g., epikarst and sinkholes). Thin epikarst and well‐developed sinkholes in the headwaters divert more surface water (younger water) into the underground channel network, leading to a higher fraction of rainfall recharge into the fast flow system and total outflow. Also, the contribution of carbonate weathering to mass export is also higher in the headwaters due to the infiltration of younger water with low solute concentrations through sinkholes.     

Lateral water flux in the unsaturated zone: A mechanism for the formation of spatial soil heterogeneity in a headwater catchment

Measurements of soil water potential and water table fluctuations suggest that morphologically distinct soils in a headwater catchment at the Hubbard Brook Experimental Forest in New Hampshire formed as a result of variations in saturated and unsaturated hydrologic fluxes in the mineral soil. Previous work showed that each group of these soils had distinct water table fluctuations in response to precipitation; however, observed variations in soil morphology also occurred above the maximum height of observed saturation. Variations in unsaturated fluxes have been hypothesized to explain differences in soil horizon thickness and presence/absence of specific horizons but have not been explicitly investigated. We examined tensiometer and shallow groundwater well records to identify differences in unsaturated water fluxes among podzols that show distinct morphological and chemical differences. The lack of vertical hydraulic gradients at the study sites suggests that lateral unsaturated flow occurs in several of the soil units. We propose that the variations in soil horizon thickness and presence/absence observed at the site are due in part to slope‐parallel water flux in the unsaturated portion of the solum. In addition, unsaturated flow may be involved in the translocation of spodic material that primes those areas to contribute water with distinct chemistry to the stream network and represents a potential source/sink of organometallic compounds in the landscape.     

Estimating water balance components in irrigated agriculture using a combined approach of soil moisture and energy balance monitoring,and numerical modelling

Information on water balance components such as evapotranspiration and groundwater recharge are crucial for water management. Due to differences in physical conditions, but also due to limited budgets, there is not one universal best practice, but a wide range of different methods with specific advantages and disadvantages. In this study, we propose an approach to quantify actual evapotranspiration, groundwater recharge and water inflow, i.e. precipitation and irrigation, that considers the specific conditions of irrigated agriculture in warm, arid environments. This approach does not require direct measurements of precipitation or irrigation quantities and is therefore suitable for sites with an uncertain data basis. For this purpose, we combine soil moisture and energy balance monitoring, remote sensing data analysis and numerical modelling using Hydrus. Energy balance data and routine weather data serve to estimate ET₀. Surface reflectance data from satellite images (Sentinel-2) are used to derive leaf area indices, which help to partition ET₀ into energy limited evaporation and transpiration. Subsequently, first approximations of water inflow are derived based on observed soil moisture changes. These inflow estimates are used in a series of forward simulations that produce initial estimates of drainage and ET_act, which in turn help improve the estimate of water inflow. Finally, the improved inflow estimates are incorporated into the model and then a parameter optimization is performed using the observed soil moisture as the reference figure. Forward simulations with calibrated soil parameters result in final estimates for ET_act and groundwater recharge. The presented method is applied to an agricultural test site with a crop rotation of cotton and wheat in Punjab, Pakistan. The final model results, with an RMSE of 2.2% in volumetric water content, suggest a cumulative ET_act and groundwater recharge of 769 and 297 mm over a period of 281 days, respectively. The total estimated water inflow accounts for 946 mm, of which 77% originates from irrigation.     

Sensitivity of soil parameters in unsaturated zone modelling and the relation between effective,laboratory and in situ estimates

Simulation of soil moisture content requires effective soil hydraulic parameters that are valid at the modelling scale. This study investigates how these parameters can be estimated by inverse modelling using soil moisture measurements at 25 locations at three different depths (at the surface, at 30 and 60 cm depth) on an 80 by 20 m hillslope. The study presents two global sensitivity analyses to investigate the sensitivity in simulated soil moisture content of the different hydraulic parameters used in a one‐dimensional unsaturated zone model based on Richards' equation. For estimation of the effective parameters the shuffled complex evolution algorithm is applied. These estimated parameters are compared to their measured laboratory and in situ equivalents. Soil hydraulic functions were estimated in the laboratory on 100 cm³ undisturbed soil cores collected at 115 locations situated in two horizons in three profile pits along the hillslope. Furthermore, in situ field saturated hydraulic conductivity was estimated at 120 locations using single‐ring pressure infiltrometer measurements. The sensitivity analysis of 13 soil physical parameters (saturated hydraulic conductivity (K_s), saturated moisture content (θ_s), residual moisture content (θ_r), inverse of the air‐entry value (α), van Genuchten shape parameter (n), Averjanov shape parameter (N) for both horizons, and depth (d) from surface to B horizon) in a two‐layer single column model showed that the parameter N is the least sensitive parameter. K_s of both horizons, θ_s of the A horizon and d were found to be the most sensitive parameters. Distributions over all locations of the effective parameters and the distributions of the estimated soil physical parameters from the undisturbed soil samples and the single‐ring pressure infiltrometer estimates were found significantly different at a 5% level for all parameters except for α of the A horizon and K_s and θ_s of the B horizon. Different reasons are discussed to explain these large differences. Copyright © 2004 John Wiley & Sons, Ltd.     

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.     

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.     

The role of rainfall temporal and spatial averaging in seasonal simulations of the terrestrial water balance

The partitioning of rainfall into surface runoff and infiltration influences many other aspects of the hydrologic cycle including evapotranspiration, deep drainage and soil moisture. This partitioning is an instantaneous non-linear process that is strongly dependent on rainfall rate, soil moisture and soil hydraulic properties. Though all rainfall datasets involve some degree of spatial or temporal averaging, it is not understood how this averaging affects simulated partitioning and the land surface water balance across a wide range of soil and climate types. We used a one-dimensional physics-based model of the near-surface unsaturated zone to compare the effects of different rainfall discretization (5-min point-scale; hourly point-scale; hourly 0.125° gridded) on the simulated partitioning of rainfall for many locations across the United States. Coarser temporal resolution rainfall data underpredicted seasonal surface runoff for all soil types except those with very high infiltration capacities (i.e., sand, loamy sand). Soils with intermediate infiltration capacities (i.e., loam, sandy loam) were the most affected, with less than half of the expected surface runoff produced in most soil types when the gridded rainfall dataset was used as input. The impact of averaging on the water balance was less extreme but non-negligible, with the hourly point-scale predictions exhibiting median evapotranspiration, drainage and soil moisture values within 10% of those predicted using the higher resolution 5-min rainfall. Water balance impacts were greater using the gridded hourly dataset, with average underpredictions of ET up to 27% in fine-grained soils. The results suggest that “hyperresolution” modelling at continental to global scales may produce inaccurate predictions if there is not parallel effort to produce higher resolution precipitation inputs or sub-grid precipitation parameterizations.     

Retracted and replaced: A modelling study of hyporheic exchange pattern and the sequence,size, and spacing of stream bedforms in mountain stream networks,Oregon, USA

This article has been retracted and replaced. See Retraction and Replacement Notice DOI: 10.1002/hyp.6350 Studies of hyporheic exchange flows have identified physical features of channels that control exchange flow at the channel unit scale, namely slope breaks in the longitudinal profile of streams that generate subsurface head distributions. We recently completed a field study that suggested channel unit spacing in stream longitudinal profiles can be used to predict the spacing between zones of upwelling (flux of hyporheic water into the stream) and downwelling (flux of stream water into the hyporheic zone) in the beds of mountain streams. Here, we use two‐dimensional groundwater flow and particle tracking models to simulate vertical and longitudinal hyporheic exchange along the longitudinal axis of stream flow in second‐, third‐, and fourth‐order mountain stream reaches. Modelling allowed us to (1) represent visually the effect that the shape of the longitudinal profile has on the flow net beneath streambeds; (2) isolate channel unit sequence and spacing as individual factors controlling the depth that stream water penetrates the hyporheic zone and the length of upwelling and downwelling zones; (3) evaluate the degree to which the effects of regular patterns in bedform size and sequence are masked by irregularities in real streams. We simulated hyporheic exchange in two sets of idealized stream reaches and one set of observed stream reaches. Idealized profiles were constructed using regression equations relating channel form to basin area. The size and length of channel units (step size, pool length, etc.) increased with increasing stream order. Simulations of hyporheic exchange flows in these reaches suggested that upwelling lengths increased (from 2·7 m to 7·6 m), and downwelling lengths increased (from 2·9 m to 6·0 m) with increase in stream order from second to fourth order. Step spacing in the idealized reaches increased from 5·3 m to 13·7 m as stream size increased from second to fourth order. Simulated upwelling lengths increased from 4·3 m in second‐order streams to 9·7 m in fourth‐order streams with a POOL–RIFFLE–STEP channel unit sequence, and increased from 2·5 m to 6·1 m from second‐ to fourth‐order streams with a POOL–STEP–RIFFLE channel unit sequence. Downwelling lengths also increased with stream order in these idealized channels. Our results suggest that channel unit spacing, size, and sequence are all important in determining hyporheic exchange patterns of upwelling and downwelling. Though irregularities in the size and spacing of bedforms caused flow nets to be much more complex in surveyed stream reaches than in idealized stream reaches, similar trends emerged relating the average geomorphic wavelength to the average hyporheic wavelength in both surveyed and idealized reaches. Copyright © 2005 John Wiley & Sons, Ltd.