Simulating One-Dimensional Unsaturated Flow in Heterogeneous Soils with Water Content-Based Richards Equation

The horizontal variability of soil hydraulic parameters, water content and suction measured within two research fields in Denmark is analyzed and discussed. A numerical analysis of the flow in the two spatially heterogeneous fields is carried out by assuming that the fields are composed of ensembles of one-dimensional non-interacting soil columns, each column representing a possible soil profile in statistical terms. Flow predictions based on the classical Richards' equation are carried out for all columns, and the mean and standard deviation of water content and suction in planes perpendicular to the flow direction is derived and compared to measurements. The analysis shows that the model to a reasonable degree is able to describe most of the variation in flow variables within the two fields. The concept of equivalent soil properties is also investigated and applied to the two fields. Based on the average retention properties it is possible to predict the horizontal averages of flow variables within the fields.

Download Full-text

Reply [to “Comment onRusso[1991],Serrano[1990, 1998], and Other applications of the water-content-based form of Richards' Equation to heterogeneous soils”]

Water Resources Research ◽

10.1029/1998wr900036 ◽

1999 ◽

Vol 35 (2) ◽

pp. 609-610

Author(s):

David Russo

Keyword(s):

Water Content ◽

Richards Equation ◽

Heterogeneous Soils

Download Full-text

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.

Download Full-text

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

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.

Download Full-text