Two-scale computational modelling of water flow in unsaturated soils containing irregular-shaped inclusions

The focus of this paper is two-dimensional computational modelling of water flow in unsaturated soils consisting of weakly conductive disconnected inclusions embedded in a highly conductive connected matrix. When the inclusions are small, a two-scale Richards’ equation-based model has been proposed in the literature taking the form of an equation with effective parameters governing the macroscopic flow coupled with a microscopic equation, defined at each point in the macroscopic domain, governing the flow in the inclusions. This paper is devoted to a number of advances in the numerical implementation of this model. Namely, by treating the micro-scale as a two-dimensional problem, our solution approach based on a control volume finite element method can be applied to irregular inclusion geometries, and, if necessary, modified to account for additional phenomena (e.g. imposing the macroscopic gradient on the micro-scale via a linear approximation of the macroscopic variable along the microscopic boundary). This is achieved with the help of an exponential integrator for advancing the solution in time. This time integration method completely avoids generation of the Jacobian matrix of the system and hence eases the computation when solving the two-scale model in a completely coupled manner. Numerical simulations are presented for a two-dimensional infiltration problem.

Concepts and dimensionality in modeling unsaturated water flow and solute transport

Many environmental studies require accurate simulation of water and solute fluxes in the unsaturated zone. This paper evaluates one- and multi-dimensional approaches for soil water flow as well as different spreading mechanisms to model solute behavior at different scales. For quantification of soil water fluxes,Richards equation has become the standard. Although current numerical codes show perfect water balances, the calculated soil water fluxes in case of head boundary conditions may depend largely on the method used for spatial averaging of the hydraulic conductivity. Atmospheric boundary conditions, especially in the case of phreatic groundwater levels fluctuating above and below a soil surface, require sophisticated solutions to ensure convergence. Concepts for flow in soils with macro pores and unstable wetting fronts are still in development. One-dimensional flow models are formulated to work with lumped parameters in order to account for the soil heterogeneity and preferential flow. They can be used at temporal and spatial scales that are of interest to water managers and policymakers. Multi-dimensional flow models are hampered by data and computation requirements.Their main strength is detailed analysis of typical multi-dimensional flow problems, including soil heterogeneity and preferential flow. Three physically based solute-transport concepts have been proposed to describe solute spreading during unsaturated flow: The stochastic-convective model (SCM), the convection-dispersion equation (CDE), and the fraction aladvection-dispersion equation (FADE). A less physical concept is the continuous-time random-walk process (CTRW). Of these, the SCM and the CDE are well established, and their strengths and weaknesses are identified. The FADE and the CTRW are more recent,and only a tentative strength weakness opportunity threat (SWOT)analysis can be presented at this time. We discuss the effect of the number of dimensions in a numerical model and the spacing between model nodes on solute spreading and the values of the solute-spreading parameters. In order to meet the increasing complexity of environmental problems, two approaches of model combination are used: Model integration and model coupling. Amain drawback of model integration is the complexity of there sulting code. Model coupling requires a systematic physical domain and model communication analysis. The setup and maintenance of a hydrologic framework for model coupling requires substantial resources, but on the other hand, contributions can be made by many research groups.

Efficient simulation of unsaturated flow in heterogeneous soils using an exponential integrator

- Provided a practical variable-stepsize implementation of the exponential Euler method (EEM). - Introduced a new second-order variant of the scheme that enables the local error to be estimated at the cost of a single additional function evaluation. - New EEM implementation outperformed sophisticated implementations of the backward differentiation formulae (BDF) of order 2 and was competitive with BDF of order 5 for moderate to high tolerances.

Catchment-scale modelling of flow and nutrient transport in the Chalk unsaturated zone

The unsaturated zone exerts a major control on the delivery of nutrients to Chalk streams, yet flow and transport processes in this complex, dual-porosity medium have remained controversial. A major challenge arises in characterising these processes, both at the detailed mechanistic level and at an appropriate level for inclusion within catchment-scale models for nutrient management. The lowland catchment research (LOCAR) programme in the UK has provided a unique set of comprehensively instrumented groundwater-dominated catchments. Of these, the Pang and Lambourn, tributaries of the Thames near Reading, have been a particular focus for research into subsurface processes and surface water-groundwater interactions. Data from LOCAR and other sources, along with a new dual permeability numerical model of the Chalk, have been used to explore the relative roles of matrix and fracture flow within the unsaturated zone and resolve conflicting hypotheses of response. From the improved understanding gained through these explorations, a parsimonious conceptualisation of the general response of flow and transport within the Chalk unsaturated zone was formulated. This paper summarises the modelling and data findings of these explorations, and describes the integration of the new simplified unsaturated zone representation with a catchment-scale model of nutrients (INCA), resulting in a new model for catchment-scale flow and transport within Chalk systems: INCA-Chalk. This model is applied to the Lambourn, and results, including hindcast and forecast simulations, are presented. These clearly illustrate the decadal time-scales that need to be considered in the context of nutrient management and the EU Water Framework Directive. (C) 2007 Elsevier B.V. All rights reserved.

Experimental modelling of coupled water flow and associated movements in swelling soils

Modelling of water flow and associated deformation in unsaturated reactive soils (shrinking/swelling soils) is important in many applications. The current paper presents a method to capture soil swelling deformation during water infiltration using Particle Image Velocimetry (PIV). The model soil material used is a commercially available bentonite. A swelling chamber was setup to determine the water content profile and extent of soil swelling. The test was run for 61 days, and during this time period, the soil underwent on average across its width swelling of about 26% of the height of the soil column. PIV analysis was able to determine the amount of swelling that occurred within the entire face of the soil box that was used for observations. The swelling was most apparent in the top layers with strains in most cases over 100%.

On the use of combined compact scheme for numerical solution of the two-layer oceanic shallow water equations

Many types of oceanic physical phenomena have a wide range in both space and time. In general, simplified models, such as shallow water model, are used to describe these oceanic motions. The shallow water equations are widely applied in various oceanic and atmospheric extents. By using the two-layer shallow water equations, the stratification effects can be considered too. In this research, the sixth-order combined compact method is investigated and numerically implemented as a high-order method to solve the two-layer shallow water equations. The second-order centered, fourth-order compact and sixth-order super compact finite difference methods are also used to spatial differencing of the equations. The first part of the present work is devoted to accuracy assessment of the sixth-order super compact finite difference method (SCFDM) and the sixth-order combined compact finite difference method (CCFDM) for spatial differencing of the linearized two-layer shallow water equations on the Arakawa's A-E and Randall's Z numerical grids. Two general discrete dispersion relations on different numerical grids, for inertia-gravity and Rossby waves, are derived. These general relations can be used for evaluation of the performance of any desired numerical scheme. For both inertia-gravity and Rossby waves, minimum error generally occurs on Z grid using either the sixth-order SCFDM or CCFDM methods. For the Randall's Z grid, the sixth-order CCFDM exhibits a substantial improvement , for the frequency of the barotropic and baroclinic modes of the linear inertia-gravity waves of the two layer shallow water model, over the sixth-order SCFDM. For the Rossby waves, the sixth-order SCFDM shows improvement, for the barotropic and baroclinic modes, over the sixth-order CCFDM method except on Arakawa's C grid. In the second part of the present work, the sixth-order CCFDM method is used to solve the one-layer and two-layer shallow water equations in their nonlinear form. In one-layer model with periodic boundaries, the performance of the methods for mass conservation is compared. The results show high accuracy of the sixth-order CCFDM method to simulate a complex flow field. Furthermore, to evaluate the performance of the method in a non-periodic domain the sixth-order CCFDM is applied to spatial differencing of vorticity-divergence-mass representation of one-layer shallow water equations to solve a wind-driven current problem with no-slip boundary conditions. The results show good agreement with published works. Finally, the performance of different schemes for spatial differencing of two-layer shallow water equations on Z grid with periodic boundaries is investigated. Results illustrate the high accuracy of combined compact method.

Spatial and temporal distribution of solute leaching in heterogeneous soils: analysis and application to multisampler lysimeter data

Accurate assessment of the fate of salts, nutrients, and pollutants in natural, heterogeneous soils requires a proper quantification of both spatial and temporal solute spreading during solute movement. The number of experiments with multisampler devices that measure solute leaching as a function of space and time is increasing. The breakthrough curve (BTC) can characterize the temporal aspect of solute leaching, and recently the spatial solute distribution curve (SSDC) was introduced to describe the spatial solute distribution. We combined and extended both concepts to develop a tool for the comprehensive analysis of the full spatio-temporal behavior of solute leaching. The sampling locations are ranked in order of descending amount of total leaching (defined as the cumulative leaching from an individual compartment at the end of the experiment), thus collapsing both spatial axes of the sampling plane into one. The leaching process can then be described by a curved surface that is a function of the single spatial coordinate and time. This leaching surface is scaled to integrate to unity, and termed S can efficiently represent data from multisampler solute transport experiments or simulation results from multidimensional solute transport models. The mathematical relationships between the scaled leaching surface S, the BTC, and the SSDC are established. Any desired characteristic of the leaching process can be derived from S. The analysis was applied to a chloride leaching experiment on a lysimeter with 300 drainage compartments of 25 cm2 each. The sandy soil monolith in the lysimeter exhibited fingered flow in the water-repellent top layer. The observed S demonstrated the absence of a sharp separation between fingers and dry areas, owing to diverging flow in the wettable soil below the fingers. Times-to-peak, maximum solute fluxes, and total leaching varied more in high-leaching than in low-leaching compartments. This suggests a stochastic–convective transport process in the high-flow streamtubes, while convection–dispersion is predominant in the low-flow areas. S can be viewed as a bivariate probability density function. Its marginal distributions are the BTC of all sampling locations combined, and the SSDC of cumulative solute leaching at the end of the experiment. The observed S cannot be represented by assuming complete independence between its marginal distributions, indicating that S contains information about the leaching process that cannot be derived from the combination of the BTC and the SSDC.

Fractal Behaviour and Irregularity of Wetting Fronts in Heterogeneous Porous Media

The wetting front is the zone where water invades and advances into an initially dry porous material and it plays a crucial role in solute transport through the unsaturated zone. Water is an essential part of the physiological process of all plants. Through water, necessary minerals are moved from the roots to the parts of the plants that require them. Water moves chemicals from one part of the plant to another. It is also required for photosynthesis, for metabolism and for transpiration. The leaching of chemicals by wetting fronts is influenced by two major factors, namely: the irregularity of the fronts and heterogeneity in the distribution of chemicals, both of which have been described by using fractal techniques. Soil structure can significantly modify infiltration rates and flow pathways in soils. Relations between features of soil structure and features of infiltration could be elucidated from the velocities and the structure of wetting fronts. When rainwater falls onto soil, it doesn?t just pool on surfaces. Water ?or another fluid- acts differently on porous surfaces. If the surface is permeable (porous) it seeps down through layers of soil, filling that layer to capacity. Once that layer is filled, it moves down into the next layer. In sandy soil, water moves quickly, while it moves much slower through clay soil. The movement of water through soil layers is called the the wetting front. Our research concerns the motion of a liquid into an initially dry porous medium. Our work presents a theoretical framework for studying the physical interplay between a stationary wetting front of fractal dimension D with different porous materials. The aim was to model the mass geometry interplay by using the fractal dimension D of a stationary wetting front. The plane corresponding to the image is divided in several squares (the minimum correspond to the pixel size) of size length ". We acknowledge the help of Prof. M. García Velarde and the facilities offered by the Pluri-Disciplinary Institute of the Complutense University of Madrid. We also acknowledge the help of European Community under project Multi-scale complex fluid flows and interfacial phenomena (PITN-GA-2008-214919). Thanks are also due to ERCOFTAC (PELNoT, SIG 14)

Comparison among monitoring strategies to assess water flow dynamic and soil hydraulic properties in agricultural soils

Irrigated agriculture is usually performed in semi-arid regions despite scarcity of water resources. Therefore, optimal irrigation management by monitoring the soil is essential, and assessing soil hydraulic properties and water flow dynamics is presented as a first measure. For this purpose, the control of volumetric water content, θ, and pressure head, h, is required. This study adopted two types of monitoring strategies in the same experimental plot to control θ and h in the vadose zone: i) non-automatic and more time-consuming; ii) automatic connected to a datalogger. Water flux was modelled with Hydrus-1D using the data collected from both acquisition strategies independently (3820 daily values for the automatic; less than 1000 for the non-automatic). Goodness-of-fit results reported a better adjustment in case of automatic sensors. Both model outputs adequately predicted the general trend of θ and h, but with slight differences in computed annual drainage (711 mm and 774 mm). Soil hydraulic properties were inversely estimated from both data acquisition systems. Major differences were obtained in the saturated volumetric water content, θs, and the n and α van Genuchten model shape parameters. Saturated hydraulic conductivity, Ks, shown lower variability with a coefficient of variation range from 0.13 to 0.24 for the soil layers defined. Soil hydraulic properties were better assessed through automatic data acquisition as data variability was lower and accuracy was higher.

Vinasse application to sugar cane fields. Effect on the unsaturated zone and groundwater at Valle del Cauca (Colombia)

Extensive application of vinasse, a subproduct from sugar cane plantations for bioethanol production, is currently taking place as a source of nutrients that forms part of agricultural management in different agroclimatic regions. Liquid vinasse composition is characterised by high variability of organic compounds and major ions, acid pH (4.7), high TDS concentration (117,416–599,400 mg L− 1) and elevated EC (14,350–64,099 μS cm− 1). A large-scale sugar cane field application is taking place in Valle del Cauca (Colombia), where monitoring of soil, unsaturated zone and the aquifer underneath has been made since 2006 to evaluate possible impacts on three experimental plots. For this assessment, monitoring wells and piezometers were installed to determine groundwater flow and water samples were collected for chemical analysis. In the unsaturated zone, tensiometers were installed at different depths to determine flow patterns, while suction lysimeters were used for water sample chemical determinations. The findings show that in the sandy loam plot (Hacienda Real), the unsaturated zone is characterised by low water retention, showing a high transport capacity, while the other two plots of silty composition presented temporal saturation due to La Niña event (2010–2011). The strong La Niña effect on aquifer recharge which would dilute the infiltrated water during the monitoring period and, on the other hand dissolution of possible precipitated salts bringing them back into solution may occur. A slight increase in the concentration of major ions was observed in groundwater (~ 5% of TDS), which can be attributed to a combination of factors: vinasse dilution produced by water input and hydrochemical processes along with nutrient removal produced by sugar cane uptake. This fact may make the aquifer vulnerable to contamination.