Cover Modeling with SVFlux


A Typical hydrological cycle SVFlux is the world's premier software package for analyzing near-surface climatic/soil interactions. It simulates the transport of water between the climatic interface, plants/vegetation, and the upper unsaturated vadose zone. It also implements rigorous evaporative flux boundaries and is therefore the ideal software to use for applications involving interaction between the atmosphere and the soil. SVFlux can represent the conductive and convective movement of heat as well as the thermally insulating impact of snow on the ground surface when coupled with the SVHeat software. The diffusive/adsorptive behavior of salts in the water phase or the diffusive flow of oxygen through the water or the air phase can be simulated with the coupling of the ChemFlux software. The domain which is typically modeled extends from just above the plant canopy to below the groundwater table. The extraction of water in the vadose zone due to plant roots is handled in the unsaturated flow equation. The software implements an easy-to-use interface which significantly shortens the numerical modeling experience start-to-finish. The software accuracy has been benchmarked based on published examples which have been re-created in the software and are in the list of publicly distributed example models.

Many of the processes near the ground surface are 1D and therefore can be modelled in the 1D version of SVFlux. All formulations in the software have been extended to 2D and 3D and can be modeled as such in the software.

Typical applications involve the design and long-term performance evaluation of earth covers for mine or municipal waste facilities. Similar applications involve the influence of climate on slope stability, agricultural or irrigation applications. Influences on the ground surface such as precipitation, evaporation, and transpiration are becoming increasingly noted the application of unsaturated soils technologies. As noted by Dr. D.G. Fredlund in 2001 “unsaturated soil mechanics may have more to do with the ground surface moisture flux conditions than it has to do with the thickness of the unsaturated soil zone” (D.G. Fredlund, Geotechnical News, Dec. 2001).

Even though finite element software for cover design has been available for several years, the majority of software is i) complicated to use, ii) extremely slow to analyze problems, and iii) convergence problems are common. When performing a long-term analysis of a cover design, interpretation of daily data input can cause small solution errors, which result in overall solution errors from 5 to 70%. SVFlux 5 was designed to alleviate the common problems experienced with other software and offer the most technically advanced software for cover analysis currently available.

The modeling of near-surface conditions may be thought of as consisting of three components; the atmosphere, the unsaturated (vadose) zone, and the saturated groundwater zone. SVFlux now provides the tools for analyzing water movement between all three zones.

Understanding Evaporation The Modified Penman method has been implemented for the calculation of potential evaporation (PE) after Wilson (1990) and Gitirana (2005). Transpiration has been implemented based on the methodology proposed by Dave Tratch (1995). Actual evaporation (AE) calculation has been implemented as proposed in the Ph.D. thesis of Dr. Ward Wilson. SVFlux therefore implements soil-atmospheric flow theory that links the subsurface water seepage with the current atmospheric conditions. The software can therefore predict the flow of water between the soil and the atmosphere.

Proven Technology - New Features
Why use SVFlux in your application? SVFlux makes use of an advanced finite element solver that has been developed over the course of the past 20 years by one highly qualified mathematician. Due to it’s intensive development it implements the most advanced mesh refinement and time stepping refinement algorithms currently available. The effectiveness of these algorithms has been benchmarked in the solution of infiltration problems (Mansell, 2002), the computation of runoff (Gitirana, 2005), and against soil-atmosphere interaction for unsaturated surfaces problems (Gitirana, 2006). The implementation of these technologies make SVFlux the most accurate software available for the calculation of infiltration and runoff. Other features that set SVFlux apart include:

What are the features that bring SVFlux to the forefront?

1.   Automatic mesh refinement

2.      Speed: 1D solutions

3.      Advanced automatic time refinement

4.      Flexible precipitation intensity applications

5.      Simplicity

6.      Reliability

1. Automatic Mesh Refinement: SVFlux is the only commercial seepage software package to offer
automatic mesh refinement. The use of automatic mesh refinement is critical for evaluation of infiltration
into dry soils as described by Mansell:

"Critical cases of water flow such as evaporation near the soil surface and infiltration into initially dry soil profiles typically create local mobile regions with large gradients of water head. Highly nonlinear relationships between hydraulic conductivity and pressure head contribute to very steep wetting fronts during infiltration into initially dry soil. In the vicinity of the wetting front for the initially dry soil, small values of hydraulic conductivity require very large gradients to move even a small amount of water (Pan and Wierenga, 1995). A short distance behind the wetting front, water content increases providing a much higher conductivity and much smaller head gradients. Insufficient local resolution for such cases of water flow can result in numerical oscillation and numerical smearing." (Mansell et al., 2002)

Further documentation regarding the benefits of automatic mesh refinement may be found here.

2. Speed - 1D solutions: SVFlux now implements true 1D FE analysis. This feature results in speed improvements of between 5x and up to 200x over 2D “column” pseudo-1D analysis. Accuracy is improved and there is also a general reduction in convergence problems as calculations involving lateral flow are eliminated. For advanced analysis SVFlux still supports the ability of analyzing solutions in 2D or 3D.

3. Automatic time-step refinement: Proper calculation of infiltration, potential and actual evaporation as well as runoff requires advanced time-step adjustment. The SVFlux solver implements the most advanced time-stepping adjustment algorithms to improve the accuracy of your results. Inaccuracy in the time-stepping for a problem can result in the following errors:

a) “Missing” of precipitation applications for entire days

b) Incorrect calculation of true infiltration

c) Incorrect calculation of runoff

Correct SVFlux calculation of daily values for difficult runoff cases is illustrated in the following figure.

4. Flexible precipitation intensity applications: Long-term cover performance is often evaluated based on daily precipitation values. An assumed storm intensity is selected in the software (often 8 hours) and the analysis is performed. Many long term cover evaluations are highly sensitive to the assumed storm intensity and the results of such analysis can be varied by over 70% in some cases. SVFlux is one of the
only software packages which allows complete freedom in the selection of applied storm intensity. Variational studies can be performed using SVFlux and the the true picture presented by the model presented to the client.

5. Simplicity: Most evaporative seepage modeling is not performed due to the complexity of currently available software. The current SVFlux user interface is designed to be simple, intuitive, and easy to use. Climate data such as temperature data, relative humidity, and net radiation is often collected at varying timestep intervals. SVFlux allows tables of climate data to be passed in separately and with individual timesteps. This feature alone greatly reduces the amount of data reduction needed prior to analysis.

6. Reliability: Hundreds of man hours have been invested in benchmarking the performance of the SVFlux software. SVFlux is already used by the majority of large consulting firms and seminars for regulators have been conducted.

The separate aspects of infiltration, evaporation, transpiration, and runoff calculations have been individually tested. The results of these tests are available in the verification manual as well as in requested supplementary documentation. SVFlux currently represents the most reliable software available for long-term soil cover performance evaluation.

Computing Surface Infiltration/Evaporation/Runoff
SVFlux extends the Modified Penman method (Wilson, 1990) first implemented in the SoilCover software into 2D and 3D. More recent improvements have resulted in the improved Fredlund-Wilson-Penman calculation of actual evaporation. The improved Fredlund-Wilson-Penman climatic boundary condition is the most technically rigorous boundary condition currently available. This allows the calculation of actual evaporation (AE) based on stress state rather than empirical formulations. The effectiveness of this approach is well documented (Gitirana, 2005). The extensive ability of SVFlux to model evaporative flux is apparent in the benchmark to the laboratory measurements presented below (Wilson, 1990).

Actual and Potential Evaporation

The Modified Penman - Wilson method has been implemented for the calculation of actual evaporation (AE) as proposed in the Ph.D. thesis of Dr. Ward Wilson with modifications proposed in the Ph.D. thesis of Dr. Gilson Gitirana. SVFlux therefore implements soil-atmospheric flow theory that links the subsurface water seepage with the current atmospheric conditions. The software can therefore predict the flow of water between the soil and the atmosphere. SVFlux has been benchmarked against the evaporative laboratory measurements as well as the predictions of SoilCover as presented in the thesis. SVFlux implements portions of the theory of the 1D SoilCover software (MEND, 1991) and improves upon the original calculations of infiltration and runoff as well as extending the formulation to 2D and 3D. SVFlux therefore implements the primary portions of the original SoilCover software as well as applying advanced numerical concepts such that the calculation accuracy is improved. A comparison of the features between SoilCover and SVFlux are presented below. The SoilCover software is currently not maintained.

Gitirana Jr., G.F.N. (2005). “Weather-Related Geo-Hazard Assessment for Railway Embankment Stability”. Ph.D. Thesis. University of Saskatchewan, Saskatoon, SK, Canada, 411p.
Wilson, G. W., 1990. Soil Evaporative Fluxes for Geotechnical Engineering Problems. Ph.D. Thesis, University of Saskatchewan, Saskatoon, Saskatchewan, Canada.
Wilson, G. W., Fredlund, D. G. & Barbour, S. L. 1994. Coupled soil-atmosphere modelling for soil evaporation. Canadian Geotechnical Journal, 31(2): 151-161.


Evapotranspiration consists of the combined processes of evaporation and transpiration. Transpiration has been implemented in SVFlux based on the methodology proposed by Tratch (1995). The transpiration process is applied as a sink term below a specified evaporation boundary condition in SVFlux.

Vegetation plays a significant and dynamic role in the overall evapotranspiration process (Saxton 1982). There are a number of factors that control the amount of water that can be transpired by the vegetation including the bare soil potential evaporation, leaf-area index (LAI), plant limiting function (PLF) as it relates to soil suction, and the root zone profile. Lack of available plant water and/or high evaporative demands will cause most plants to biologically react by closing stoma, reducing transpiration, and reducing metabolic reactions (Saxton 1982). Under continued and increasing stress the plant will reach its wilting point. The wilting point results in leaf drop and tissue death (Saxton, 1982).

Tratch (1995) suggested a 4 – step methodology for the prediction of moisture uptake from transpiration of a plant population:

1. The determination of the potential evaporation. This is a measure of the maximum evapotranspiration rate possible in the specified atmospheric conditions.

2. Determination of the potential transpiration rate based upon the potential evaporation and the plant population characteristics at the site. This is a measure of the maximum transpiration rate possible in the specified atmospheric conditions.

3. Distribution of the potential transpiration, which is a surface flux, into a potential root uptake profile throughout the active root zone.

4. Modification of the potential root uptake based upon the moisture availability to deliver the actual root uptake profile.

SVFlux has been benchmarked against the labratory results and 1D SoilCover software (MEND, 1991) analysis presented by Tratch (1995):

"I believe the transpiration formulation implemented in the SVFlux software is consistent with that suggested during the course of my M.Sc. thesis work on the SoilCover 1D software at the University of Saskatchewan. We have had ongoing discussions regarding the appropriate incorporation of the transpiration equations and I believe the SVFlux simulation of vegetation transpiration to be rigorous."

David J. Tratch, M.Sc., P.Eng.
Sr. Engineer
WaterMark Consulting Ltd.
Regina, Saskatchewan

Tratch, D.J. (1995). “A Geotechnical Engineering Approach to Plant Transpiration and Root Water Uptake,” University of Saskatchewan, Saskatoon, Saskatchewan.Tratch, D.J. (1995). “A Geotechnical Engineering Approach to Plant Transpiration and Root Water Uptake,” University of Saskatchewan, Saskatoon, Saskatchewan.

Feature Summary



The SVFlux solver (FlexPDE) represents an “open” approach to finite element calculations in that every variable used in the formulation can be contoured, or reported over a point, region, or over time. As such the software moves away from the typical “black box” approach and allows the user full access to all variables in the computation.

In evaporative analysis SVFlux extends this concept to allow the user access to plotting any or all of the following variables. Variables may be combined on the same plot or plotted individually.

Variable Description
Ta Air Temperature
Rhair Air Relative Humidity
uvsat Saturation pore-air vapor pressure
uvsata Saturation air vapor pressure
uva Air partial vapor pressure
Dvap Diffusion Coefficient of vapour through air
PE Potential Evaporation
AE Actual Evaporation
FBC Precipitation
Evaporation Ratio
Wind Speed
Net Radiation (Heat Budget)
Shortwave radiation
Boundary Flux
Leaf Area Index
Potential Evapotranspiration
Root Depth

Data Requirements

The data requirements for an evaporative analysis using SVFlux include air temperature, precipitation, net radiation, wind speed and air relative humidity. All data can be cut and pasted into the software in tables that do not necessarily contain the same resolution of readings. This allows for a significant amount of flexibility in the analysis. These parameters are in addition to the standard parameters needed for an unsaturated seepage analysis.

Related Research

Gitrana, G. Jr., M.D. Fredlund & D.G. Fredlund - 2005
"Inflitration-Runoff Boundary Conditions in Seepage Analysis "
58th Canadian Geotechnical Conference and 6th Joint IAH-CGS Conference, September 19-21, 2005, Saskatoon, SK, Canada

G.W. Wilson, D. Williams & M.D. Fredlund - 2002
"The Application of Knowledge-Based Surface Flux Boundary Modeling"
Unsat 2002, Recief, Brazil