Modelling non-equillibrium unsaturated flow in soils during sudden pressure head changes by solving Richards' equation with a Method of lines approach

Mapping Intimacies ◽

10.5194/egusphere-egu21-15546 ◽

2021 ◽

Author(s):

Robert Mietrach ◽

Thomas Wöhling ◽

Niels Schütze

Keyword(s):

Water Content ◽

Preferential Flow ◽

Unsaturated Flow ◽

Full Range ◽

Method Of Lines ◽

Pressure Head ◽

Richards Equation ◽

Extended Model ◽

Solution Methods ◽

Numerical Robustness

The classical formulation of Richards' equation is relying on a unique functional relationship between water content, conductivity and pressure head. Some phenomena like hystersis effects in the water content during wetting and drying cycles and hydraulic non-equillibrium cannot be accounted for with this formulation. Therefor it has been extended in different ways in the past to be able to include these effects in the simulation. Each modification comes with its own challenges regarding implementation and numerical stability. The Method Of Lines approach to solving the Richards' equation has already be shown to be an efficient and stable alternative to established solution methods, such as low-order finite difference and finite element methods applied to the mixed form of Richards' equation. In this work a slightly modified Method Of Lines approach is used to solve the pressure based 1D Richards' equation. A finite differencing scheme is applied to the spatial derivative and the resulting system of ordinary differential equations is reformulated as differential-algebraic system of equations. The open-source code IDAS from the Sundials suite is used to solve the DAE system. Different extensions to Richards' equation have been incorporated into the model to address the shortcomings mentioned above. These extensions are a model able to simulate preferential flow using a coupled two domain approach, a simple hysteretic model to account for hysteresis in the water retention curve and also two models to either fully or partially calculate hydraulic non-equillibrium effects. To verify the numerical robustness of the extended model, stochastic parameterizations were generated that represent the full range of all soil types. Simulations were carried out using these parameter sets and real-world meteorological boundary conditions at 10 minutes time intervals, that exhibit drastic flux changes and poses numerical challenges for classical solution methods.The results show that not only does the extended model converge for all parameterizations, but that numerical robustness and performance is maintained. Where applicable the results have been verified against solutions from the software Hydrus and show good agreement with those.

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MEASUREMENT OF PREFERENTIAL FLOW DURING INFILTRATION AND EVAPORATION IN POROUS MEDIA

Bulletin of the Geological Society of Greece ◽

10.12681/bgsg.11374 ◽

2017 ◽

Vol 43 (4) ◽

pp. 1831

Author(s):

A. Papafotiou ◽

C. Schütz ◽

P. Lehmann ◽

P. Vontobel ◽

D. Or ◽

...

Keyword(s):

Porous Media ◽

Water Distribution ◽

Preferential Flow ◽

Unsaturated Flow ◽

Coupling Effect ◽

Heterogeneous Systems ◽

Heterogeneous Porous Media ◽

Richards Equation ◽

Hydraulic Coupling ◽

Experimental Findings

Infiltration and evaporation are governing processes for water exchange between soil and atmosphere. In addition to atmospheric supply or demand, infiltration and evaporation rates are controlled by the material properties of the subsurface and the interplay between capillary, viscous and gravitational forces. This is commonly modeled with semi-empirical approaches using continuum models, such as the Richards equation for unsaturated flow. However, preferential flow phenomena often occur, limiting or even entirely suspending the applicability of continuum-based models. During infiltration, unstable fingers may form in homogeneous or heterogeneous porous media. On the other hand, the evaporation process may be driven by the hydraulic coupling of materials with different hydraulic functions found in heterogeneous systems. To analyze such preferential flow processes, water distribution was monitored in infiltration and evaporation lab experiments using neutron transmission techniques. Measurements were performed in 2D and 3D, using homogeneous and heterogeneous setups. The experimental findings demonstrate the fingering effect in infiltration and how it is influenced by the presence of fine inclusions in coarse background material. During evaporation processes, the hydraulic coupling effect is found to control the evaporation rate, limiting the modeling of water balances between soil and surface based on surface information alone.

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Laboratory Experiments of Drainage, Imbibition and Infiltration under Artificial Rainfall Characterized by Image Analysis Method and Numerical Simulations

Water ◽

10.3390/w11112232 ◽

2019 ◽

Vol 11 (11) ◽

pp. 2232 ◽

Cited By ~ 2

Author(s):

Belfort ◽

Weill ◽

Fahs ◽

Lehmann

Keyword(s):

Image Analysis ◽

Numerical Simulations ◽

Water Content ◽

Laboratory Experiments ◽

Pressure Head ◽

Richards Equation ◽

Analysis Method ◽

Image Analysis Method ◽

Artificial Rainfall ◽

Classical Image

Two laboratory experiments consisting of drainage/imbibition and rainfall were carried out to study flow in variably saturated porous media and to test the ability of a new measurement method. 2D maps of water content are obtained through a non-invasive image analysis method based on photographs. This method requires classical image analysis steps, i.e., normalization, filtering, background subtraction, scaling and calibration. The procedure was applied and validated for a large experimental tank of internal dimensions 180 cm long, 120 cm wide and 4 cm deep that had been homogenously packed with monodisperse quartz sand. The calibration curve relating water content and reflected light intensities was established during the main monitoring phase of each experiment, making this procedure very advantageous. Direct measurements carried out during the water flow experiments correspond to water content, pressure head, temperature, and cumulative outflow. Additionally, a great advantage of the proposed method is that it does not require any tracer or dye to be injected into the flow tank. The accuracy and other benefits of our approach were also assessed using numerical simulations with state-of-the-art computational code that solves Richards’ equation.

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Handling the water content discontinuity at the interface between layered soils within a numerical scheme

Soil Research ◽

10.1071/sr05069 ◽

2005 ◽

Vol 43 (8) ◽

pp. 945 ◽

Cited By ~ 8

Author(s):

C. J. Matthews ◽

F. J. Cook ◽

J. H. Knight ◽

R. D. Braddock

Keyword(s):

Numerical Solution ◽

Water Content ◽

Numerical Scheme ◽

Iterative Scheme ◽

Method Of Lines ◽

Soil Layer ◽

Iterative Solution ◽

Richards Equation ◽

Layered Soils ◽

Fine Soil

In general, the water content (θ) form of Richards’ equation is not used when modeling water flow through layered soil since θ is discontinuous across soil layers. Within the literature, there have been some examples of models developed for layered soils using the θ-form of Richards’ equation. However, these models usually rely on an approximation of the discontinuity at the soil layer interface. For the first time, we will develop an iterative scheme based on Newton’s method, to explicitly solve for θ at the interface between 2 soils within a numerical scheme. The numerical scheme used here is the Method of Lines (MoL); however, the principles of the iterative solution could be used in other numerical techniques. It will be shown that the iterative scheme is highly effective, converging within 1 to 2 iterations. To ensure the convergence behaviour holds, the numerical scheme will be tested on a fine-over-coarse and a coarse-over-fine soil with highly contrasting soil properties. For each case, the contrast between the soil types will be controlled artificially to extend and decrease the extent of the θ discontinuity. In addition, the numerical solution will be compared against a steady-state analytical solution and a numerical solution from the literature.

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The importance of preferential flow in controlling groundwater recharge in tropical Africa and implications for modelling the impact of climate change on groundwater resources

Journal of Water and Climate Change ◽

10.2166/wcc.2010.040 ◽

2010 ◽

Vol 1 (4) ◽

pp. 234-245 ◽

Cited By ~ 24

Author(s):

M. O. Cuthbert ◽

C. Tindimugaya

Keyword(s):

Soil Moisture ◽

Preferential Flow ◽

Unsaturated Flow ◽

Uniform Flow ◽

Richards Equation ◽

Tropical Africa ◽

Lateritic Soils ◽

Flow Models ◽

Spatial Coverage ◽

The Impact

An improved water table fluctuation technique for estimating recharge is applied to a sustained (10-year) groundwater level monitoring record in Uganda, a rare dataset for tropical Africa, and compared against results from soil moisture balance models (SMBMs) and unsaturated flow models. The results show that recharge is directly proportional to rainfall (long-term average rainfall is around 1200 mm/a), even during times when high soil moisture deficits are anticipated. This indicates that preferential and/or localized flow mechanisms dominate the recharge behaviour. SMBMs and unsaturated flow models, based on uniform flow governed by the Richards equation, are shown to be inappropriate for estimating recharge in this location underlain by lateritic soils. Given the large spatial coverage of lateritic soils both globally and in tropical Africa, and despite the convenience of physically based uniform flow models and, in particular, SMBMs, concern is raised over the use of such models for recharge estimation, and thus for exploring future trends due to climate or land use change, unless backed up by sufficient hydraulic data to enable the recharge processes to be confirmed. More research is needed to assess how widespread preferential flow may be within other major soil groups and climate zones.

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Examples of numerical simulations of two-dimensional unsaturated flow with VS2DI code using different interblock conductivity averaging schemes

Geologos ◽

10.1515/logos-2015-0015 ◽

2015 ◽

Vol 21 (3) ◽

pp. 161-167 ◽

Cited By ~ 4

Author(s):

Adam Szymkiewicz ◽

Witold Tisler ◽

Kazimierz Burzyński

Keyword(s):

Hydraulic Conductivity ◽

Unsaturated Flow ◽

Water Pressure ◽

Geometric Mean ◽

Pressure Head ◽

Richards Equation ◽

Test Problems ◽

Simulation Code ◽

Arithmetic Average ◽

The Difference

AbstractFlow in unsaturated porous media is commonly described by the Richards equation. This equation is strongly nonlinear due to interrelationships between water pressure head (negative in unsaturated conditions), water content and hydraulic conductivity. The accuracy of numerical solution of the Richards equation often depends on the method used to estimate average hydraulic conductivity between neighbouring nodes or cells of the numerical grid. The present paper discusses application of the computer simulation code VS2DI to three test problems concerning infiltration into an initially dry medium, using various methods for inter-cell conductivity calculation (arithmetic mean, geometric mean and upstream weighting). It is shown that the influence of the averaging method can be very large for coarse grid, but that it diminishes as cell size decreases. Overall, the arithmetic average produced the most reliable results for coarse grids. Moreover, the difference between results obtained with various methods is a convenient indicator of the adequacy of grid refinement.

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Solute movement through undisturbed soil columns under pasture during unsaturated flow

Soil Research ◽

10.1071/s96113 ◽

1997 ◽

Vol 35 (5) ◽

pp. 1153 ◽

Cited By ~ 11

Author(s):

I. Vogeler ◽

D. R. Scotter ◽

S. R. Green ◽

B. E. Clothier

Keyword(s):

Water Content ◽

Unsaturated Flow ◽

Sandy Loam ◽

Richards Equation ◽

Initial Water Content ◽

Soil Columns ◽

Initial Water ◽

Undisturbed Soil ◽

Significant Difference ◽

Solute Movement

Previous studies of solute movement concerning the influence of initial soil water content have led to apparently contradictory results. Here we describe some experiments which aimed to determine the effect of both pasture and initial water content on solute movement. Solid SrCl2, CaCl2, and Ca(NO3)2 were surface-applied to undisturbed columns of a fine sandy loam under short pasture. The soil columns were 300 mm in both diameter and length. A rotating rainfall simulator delivered steady-state rainfall at about 10 mm/h. The leachate at the base was collected under suction and analysed, and one column was analysed for resident concentrations of strontium. Solute transport could be accurately described by coupling Richards’ equation with the convection dispersion equation, when ion exclusion or exchange were taken into account. The dispersivity was about 70 mm, only slightly higher than found previously for the same soil without vegetation. There was no significant difference in intrinsic behaviour when solute was applied to either an initially wet or a dry topsoil. The contrasting results from earlier published studies were probably due to incipient ponding and macropore flow. This will not usually occur in New Zealand pasture soils under typical rainfall intensities, but might under irrigation or when the soil structure is degraded. It is suggested that soil cores need to have dimensions at least as large as the dispersivity if they are to encompass most of the local variation in solute concentration.

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Heterogeneity of unsaturated flow measured in the dry summer of 2018 in Germany recorded by the combination of ERT and soil data

10.5194/egusphere-egu2020-16417 ◽

2020 ◽

Author(s):

Stadler Susanne ◽

Fishkis Olga ◽

Noell Ursula

Keyword(s):

Electrical Resistivity ◽

Water Content ◽

Soil Water ◽

Preferential Flow ◽

Unsaturated Flow ◽

Small Scale ◽

Seepage Water ◽

Water Conductivity ◽

Rainfall Events ◽

Water Contents

In 2018 the weather in Germany was extreme: The highest temperatures since 1881 (= start of regular weather recording) were observed during the months of April &#8211; August (temperature anomaly of +3.6 K) and the second lowest precipitation amounts (anomaly of -150 mm). In that year, we measured the soil conditions (soil water tension, water content, electrical resistivity, temperature, seepage water at suction plates) in a maize field in Northern Germany continuously down to a depth of about 1.5 m using a combined geophysical and soil scientific small-scale instrumentation array.This unique dataset revealed the heterogeneity of the subsurface water content, changes in soil water conductivity, heterogeneity of the water retention function, indications for preferential flow after the onset of precipitation (and locally increased nitrate concentrations) in seepage water. The electrical resistivity (ERT) data clearly detected the infiltration of local rainfall events by the change of near surface resistivity. The resistivity changes differ spatially reflecting dm-scale variations most probably caused by the dense maize plants. Soil water contents measured by TDR detected the summer rainfall events in some locations, in others, very small-scale preferential flow paths were found overlooked by ERT. The detected changes in pore water conductivity need to be taken into account when recalculating water contents from ERT data. Our data allow for a description of different scale effects on the derivation of flux processes and total flux estimations under extreme weather conditions but also show that cross-scale methods are needed for an adequate assessment of unsaturated flow.

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Modelling gravity-driven fingering in soils having an intrinsic non-zero contact angle (water repellent soils) using the innovative moving-boundary approach

10.5194/egusphere-egu2020-2647 ◽

2020 ◽

Author(s):

Rony Wallach ◽

Naaran Brindt

Keyword(s):

Contact Angle ◽

Water Content ◽

Preferential Flow ◽

Moving Boundary ◽

Richards Equation ◽

Water Repellent ◽

Wetting Front ◽

Unstable Flow ◽

Pressure Distributions ◽

Gravity Driven

Quantitative and Qualitative description of infiltration into soils in general and initially dry soils in particular those in which the hydraulic properties vary spatial and temporal have been challenging soil physicists and hydrologists. Water repellent soils, whose contact angle is higher than 40&#176; and can even reach values that are greater than 90&#176; (noted as hydrophobic soils) are an example of such challenge cases. Infiltration in these soils takes usually place along preferential flow pathways (noted as gravity-induced fingering), rather than in a laterally uniform moving wetting front. The water content and capillary pressure distributions along these fingers are non-monotonic with water accumulation behind the moving wetting front (noted as saturation overshoot) and a decreasing water content toward the soil surface. Being a parabolic-type partial differential equation, the Richards equation that is commonly used to model flow in soils can't handle such water content/pressure distributions. Many attempts have been made to modify the Richards equation to enable it to model the non-monotonic water content profiles. These attempts that are not based on the measurable soil properties that can highlight the physics that induces the formation of such non-monotonic distribution. &#160;A new conceptual modelling approach, noted as the moving-boundary approach, will be presented. This approach overcomes the existing theoretical gaps in the quantitative descriptions that have been suggested for the non-monotonic water content distribution in the gravity-induced fingers. The moving-boundary approach is based on the presumption that non-monotonicity in water content is formed by an intrinsic higher-than-zero contact angle. Note that non-zero contact angle have been rarely incorporated in models used for quantifying infiltration into field soils, in spite of the findings that most soils feature some degree of repellency. The verified moving-boundary solution will be used to demonstrate the synergistic effect of contact angle and incoming flux on the stability of 2D flow and its associated plume shapes. The physically-based moving-boundary approach fulfils several criteria raised by researchers to adequately describe gravity-driven unstable flow.&#160;

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