Scientific Investigations Report 2005–5215
U.S. GEOLOGICAL SURVEY
Scientific Investigations Report 2005–5215
VS2DI (Hsieh and others, 2000) is a graphical software package for modeling flow and transport in a variably saturated porous media. VS2DI contains a preprocessor that enables easy input of data into the software, a postprocessor (VS2POST) that enables viewing of previous simulation runs, and the numerical model VS2DH (Healy and Ronan, 1996). VS2DH is a two-dimensional, variably saturated, ground‑water flow model that has been modified to simulate heat transport by advection and conduction; it uses the advective-dispersion equation to model energy transport (Healy, 1990).
Setting up the two-dimensional VS2DI model involves defining model options, textural classes, initial conditions, and boundary conditions for each recharge period. VS2DI defines a recharge period as a period of time during which model conditions and stresses do not change. Once the model is set up, it can be run either by using the VS2DI postprocessor for a graphical display of the model run, or by running the VS2DH model directly from the command line. A thorough explanation of VS2DI model setup and usage is available in Hsieh and others (2000) and Stonestrom and Constantz (2003).
VS2DI model options include settings to specify the flow and transport processes, computational algorithm, and model output. All models were set up with the same options; for example, the use of metric units, hydraulic characteristic functions defined by the van Genuchten model, and numerical model solver options.
Textural classes must be defined for the entire area of the VS2DI models. Textural classes define the hydraulic and transport properties of the medium such as, porosity, saturated hydraulic conductivity, and the vertical to horizontal ratio of saturated hydraulic conductivity (hence referred to as the anisotropy ratio). A textural class was defined for the region around the piezometers at which slug tests were performed (piezometers B, C, E, and F). Saturated hydraulic conductivity values were then assigned to the textural class according to the slug-test results. For adjacent piezometers with similar saturated hydraulic conductivity values, one textural class was defined for that region instead of two. The textural classes encompassed an area approximately 6 ft below the piezometers, and the upper area of the model was divided between the slug-test defined textural classes. The lower and outer areas of the VS2DI model were assigned a general, predefined textural class (representative of medium sand) that was provided with the VS2DI modeling software.
Boundary conditions are required for each recharge period of the model. All models used a recharge period of 1 hour. Surface boundaries representing the stream-subsurface interface were assigned a specified total head flow boundary condition of the measured head value from the stream-stage measurement. Other surface boundaries were assigned a no-flow boundary condition. The vertical or side‑flow boundary conditions were set to the head measurement from the nearest piezometer, and the lower boundary was set to the difference between the two side boundary conditions. VS2DI also allows for flux or seepage‑face flow boundary conditions, but these conditions were not applicable to this modeling study. Surface-transport boundary conditions were set using the upper or external temperature from the nearest measured piezometer, while the vertical or side-transport boundary conditions were interpolated from the deepest temperature measurements in the piezometers. The transport boundary condition for the lower boundary was set at a temperature of 14.5°C, which represents the average ground-water temperature in the study area at a depth of 50 ft.
A linear trend for ground-water head and stage values was used to interpolate the actual measurements because continuous measurements were not available. A linear regression comparing the stage measurements at each of the four transects and stage data for the USGS gaging station on the Boise River near Parma (13213000) resulted in good correlations for two of the transects. Stage values derived from the regression analysis were tested in modeling transect three, which had the best R2 value. However, modeling results were not substantially improved; therefore, the linear interpolated values were used for all models to maintain consistency between the models.
The VS2DH grids have a 1.5-meter horizontal spacing and a 0.5-meter vertical spacing. Each model represents a two-dimensional cross section of the stream oriented vertically. The vertical grid spacing was decreased to 0.25 m for the 3-meter model area below the stream bottom. The total grid depth was 15 m and the total width was 150 m.
The VS2DH models require initial conditions for the hydraulic condition and temperature of the model area. The initial hydraulic condition was set to the model option of ‘initial equilibrium profile’, which is defined as the pressure head equaling the negative elevation head above the water table. This value was determined by taking the mean water level of the seven piezometers at a transect. The total difference in head between the seven piezometers was typically about 3–4 in.
The initial temperature for the model is input by drawing temperature contours. The contours were interpolated from the temperature measurements. The first model of each transect was simulated for an extra initial 10 days (240 recharge periods) to allow the models to stabilize with the boundary conditions. After the first model of each transect was completed, the ending temperature data were then entered into the following month’s model run as the initial temperature.
Slug tests estimate the saturated hydraulic conductivity for a small volumetric area around the perforated section of a piezometer. However, the slug-test area represents a very small portion of the textural classes in VS2DI models. The slug tests provide a starting point for estimating saturated hydraulic conductivities, but additional estimation is necessary to represent the full area of each textural class in the VS2DI models.
The Parameter ESTimation code, or PEST (Doherty, 2004), was used to refine the slug-test estimate for the saturated hydraulic conductivity and to estimate the anisotropy ratio for the textural classes in the VS2DI models. PEST exists independently of the VS2DI software and adjusts the two parameters using the Gauss-Marquardt-Levenberg optimization algorithm (Doherty, 2004). PEST automatically reruns the VS2DH models until the objective function is minimized in a weighted least-squares sense using the measured and simulated temperatures. The initial value of the anisotropy ratio was set to 0.5, and the saturated hydraulic conductivity initial value came from the slug-test estimates. PEST allows the user to set the range within which the parameters can be altered. The saturated horizontal hydraulic conductivity was allowed to adjust within the range of 1×10-6 to 1×10-2 m/s and the saturated vertical to horizontal anisotropy ratio had a range of 0.1 to 1.
For more information about USGS activities in Idaho, visit the USGS Idaho Water Science Center home page .
U.S. Department of the Interior |
U.S. Geological Survey
Persistent URL: https://pubs.water.usgs.gov/sir
Page Contact Information: Publications Team
Page Last Modified:
