Computer Session 4

Subsurface Line Source The example in this computer session considers a subsurface line source (e.g. drip irrigation) of water (first without and then with a solute) in a vertical cross-section. The (x, z) transport domain is 75 x 100 cm2, with the source located 20 cm below the soil surface on the left boundary of the transport domain. Infiltration is initiated with a variable flux boundary condition and is maintained for 1 day, with the duration of the solute pulse being 0.1 days; with 2 cycles per week. An unstructured finite element mesh is generated using the Meshgen program. The example is again divided into two parts: first only water flow is considered, after which solute transport is added. This example will familiarize users with the basic concepts of transport domain design in the graphical environment of HYDRUS, with boundaries and domain discretization, and with the graphical display of results using contour and spectral maps.

(0, 100) (75, 100)

(75, 0) (0, 0)

(0, 80)

Computer Session 4

A. Infiltration of Water From a Subsurface Source Project Manager (File->Project Manager)

Button "New" New Project (or File->New)

Name: Source1 Description: Infiltration of Water from a Subsurface Source Working Directory: Temporary – exists only when the project is open Button "Next"

Domain Type and Units (Edit->Domain Geometry->Domain Type and Units)

Type of Geometry: 2D - General 2D-Domain Options: 2D - Vertical Plane XZ Units: cm Check "Edit domain properties, initial and boundary conditions on geometric objects" Initial Workspace: X-Min=-25, X-Max=100, Z-Min=-25, Z-Max=125 cm (to accommodate the transport domain) Button "Next"

Main Processes (Edit->Flow and Transport Parameters->Main Processes)

Check Box: Water Flow Button "Next"

Time Information (Edit->Flow and Transport Parameters->Time Information)

Time Units: days Final Time: 7 Initial Time Step: 0.0001 Minimum Time Step: 0.000001 Maximum Time Step: 5

Time Variable Boundary Conditions : Check Number of Time-Variable Boundary Records: 4 Number of times to repeat the same set of BC records: 1 Button "Next"

Output Information (Edit->Flow and Transport Parameters->Output Information)

Print Options: Check T-Level Information Check Screen Output Check Press Enter at the End Print Times: Count: 14 Update Print Times: 0.1, 0.25, 0.5, 0.75, 1, 1.5, 2, 3.5, 3.6, 3.75, 4, 4.5, 5.5, 7 d Button "Next"

Computer Session 4

Water Flow - Iteration Criteria (Edit->Flow and Transport Parameters->Water Flow Parameters->Iteration Criteria)

Leave default values as follows: Maximum Number of Iterations: 10 Water Content Tolerance: 0.001 Pressure Head Tolerance: 1 Lower Optimal Iteration Range: 3 Upper Optimal Iteration Range: 7 Lower Time Step Multiplication Factor: 1.3 Upper Time Step Multiplication Factor: 0.7 Lower Limit of the Tension Interval: 0.0001 Upper Limit of the Tension Interval: 10000 Initial Condition: In Pressure Heads Button "Next"

Water Flow - Soil Hydraulic Model (Edit->Flow and Transport Parameters->Water Flow Parameters->Hydraulic Properties Model)

Leave default values as follows: Radio button - van Genuchten-Mualem Radio button - No hysteresis Button "Next"

Water Flow - Soil Hydraulic Parameters (Edit->Flow and Transport Parameters->Water Flow Parameters->Soil Hydraulic Parameters)

Leave default values for loam Button "Next"

Variable Boundary Conditions (Edit->Flow and Transport Parameters->Variable Boundary Conditions) Time Transp Var.Fl1 (variable flux)

1.0 0 -60 (drip discharge distributed over the circumference of the drip)

3.5 0 0 4.5 0 -60 7 0 0 Button "Next"

FE-Mesh - FE-Mesh Parameters (Edit->FE-Mesh->FE-Mesh Parameters) Targeted FE Size – Unselect Automatic and specify TS = 5 cm

Button "OK" Definition of the Transport Geometry

Click on Grid and Work Plane Setting ( ) at the toolbar (or Tools->Grid and Work Plane) Grid Point Spacing – Distance w = 1 cm, Distance h = 1 cm

Computer Session 4

Make sure that Snap to Grid is checked a) Outer Boundary Select the Line->Connected Abscissae command ( )from the Edit Bar (or Insert->Domain Geometry->Curves->Line->Graphically) Nodes coordinates: (0,79), (0,0), (75,0), (75,100), (0,100),(0,81) b) Drip

Click on Zoom by Rectangle ( ) at the Toolbar (or View-> Zoom by Rectangle) and zoom at the source. Select the Arc via Three Points command ( ) from the Edit Bar (or Insert->Domain Geometry->Curves->Arc->Graphically via->Three Points) and specify coordinates of three points: (0,81), (1,80), (0,79).

Click on View All ( ) at the Toolbar (or View->View All). Define the Planar Surface

Select the Planar Surface via Boundaries command ( ) from the Edit Bar (or Insert->Domain Geometry->Surfaces->Planar->Graphically) and click at the outer boundary. Alternatively, you can use the Planar Surfaces - Generate command

( ) from the Edit Bar to generate the Planar Surface automatically. Define FE-Mesh Click on the FE-Mesh Tab under the View Window. Select the Insert Mesh Refinement command ( ) from the Edit Bar (or Insert->FE-Mesh Refinement->Graphically): a dialog "New FE Mesh Refinement" appears, in which specify Finite Element Size S=0.5 cm. After clicking OK, select three nodes defining the drip (arc) at the left side of the domain. Small green circles should appear around these nodes indicating the size of finite elements. Click again on the Insert Mesh Refinement at the Edit Bar, then click New, and in the dialog specify Finite Element Size = 2 cm. Assign this refinement to the node at the top left corner. A larger green circle should appear there.

Click Generate FE-Mesh ( ) from the Edit Bar (or Edit->FE-Mesh->Generate FE-Mesh) Initial Condition Click on the Initial Conditions Tab under the View Window. On the Edit Bar click on New Initial Condition ( ) and in the window "New Pressure Head Initial Condition" specify Pressure Head IC = -400.

Click on the newly defined initial condition at the Edit Bar ( ) and then click at the transport domain to assign it.

Computer Session 4

Water Flow Boundary Conditions Click on the Boundary Conditions Tab under the View Window.

a) On the Edit Bar click on New Boundary Condition and in the window "New Water Flow Boundary Condition" check Variable Flux 1 and type Dripper for Name.

Click on Zoom by Rectangle ( ) at the Toolbar (or View-> Zoom by Rectangle) and zoom on source: (0,80). Click on the newly defined boundary condition at the Edit Bar ( ) and then assign it by clicking on the arc representing the dripper.

b) Click on View All ( ) at the Toolbar (or View->View All) On the Edit Bar click on New Boundary Condition and in the window "New Water Flow Boundary Condition" check Free Drainage (No need to change the name here). Click on the newly defined Free Drainage boundary condition at the Edit Bar ( ) and then assign it by clicking on the bottom line of the transport domain.

Observation Nodes Click on the Domain Properties Tab under the View Window. On the Navigator Bar click on Domain Properties – Observation Nodes (or Insert->Domain Properties->Observation Nodes). Since we do not have any Points inside of the transport domain, which we could define as Observation Nodes, we will define Observation Nodes directly using FE-Mesh Nodes. To do that, click on the Edit Properties on FE-Mesh command ( ) on the Edit Bar, then on the Insert Observation Node command ( ), and specify 5 points arbitrarily in the transport domain between the dripper and the bottom of the domain. Save

Save the project using the Save command ( ) on the Toolbar (or File->Save). Run Calculations

Click the Calculate Current Project command ( ) on the Toolbar (or Calculation->Calculate Current Project) (Execution time on 3 GHz PC – 18 s) OUTPUT: Click on the Results Tab under the View Window. Results – Other Information: Observation Points (from the Navigator Bar, or Results->Observation Points from menu)

Pressure Heads Water Contents

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Results – Other Information: Boundary Fluxes (from the Navigator Bar, or Results->Boundary Information->Boundary Fluxes from menu)

Variable Boundary Flux Free Drainage Boundary Flux

Results – Other Information: Cumulative Fluxes (from the Navigator Bar, or Results->Boundary Information->Cumulative Fluxes from menu)

Variable Boundary Flux

Results – Other Information: Mass Balance Information (from the Navigator Bar, or Results->Mass Balance Information from menu) Results – Graphical Display: Pressure Heads (from the Navigator Bar, or Results->Display Quantity->Pressure Heads from menu)

Use Listbox Time Layer or Slidebar on the Edit Bar to view results for different print times Check Flow Animation Select Boundary Line Chart from the Edit Bar and draw pressure heads for one vertical column Select Cross Section Chart and draw pressure heads through the middle of the column

Select different display modes using the Graph Type Commands ( ) at the Toolbar or Options->Graph Type

Results – Graphical Display: Water Contents (from the Navigator Bar, or Results->Display Quantity->Water Contents from menu) Results – Graphical Display: Velocity Vectors (from the Navigator Bar, or Results->Display Quantity->Velocity Vectors from menu)

Computer Session 4

B. Infiltration of Water and Solute From a Subsurface Source

Close the Source1 Project (click Save Project ( ) at the Toolbar or File->Save)

Project Manager (Menu: File->Project Manager, Toolbar: ) Select the Source1 project Button "Copy" Name: Source2 Description: Infiltration of Water and Solute from a Subsurface Source Button "OK"

Main Processes (Menu: Edit->Flow and Transport Parameters->Main Processes or Navigator Bar: Source2->Flow and Transport Parameters->Main Processes)

Check Box: Solute Transport You will be warned that this action will lead to deleting results. Click Yes. Button "OK"

Solute Transport – General Info (Edit->Flow and Transport Parameters->Solute Transport Parameters->General Information)

Leave default values Button "Next"

Solute Transport - Solute Transport Parameters (Edit->Flow and Transport Parameters->Solute Transport Parameters->Solute Transport Parameters)

Leave default values Bulk Density = 1.5 cm3/g Longitudinal Dispersivity, Disp.L = 2 cm Transverse Dispersivity, Disp.T = 0.2 cm Molecular Diffusion Coefficient for Liquid Phase, Diffus.W.=0 Button "Next"

Solute Transport - Transport Parameters (Edit->Flow and Transport Parameters->Solute Transport Parameters->Solute Reaction Parameters)

Leave default values for tracer (all values are zero except for the Freundlich exponent Beta) Button "Next"

Variable Boundary Conditions (Edit->Flow and Transport Parameters->Variable Boundary Conditions)

Click on Time 1 and click the Add Line command Click on Time 4.5 and click the Add Line command Edit the table as follows:

Computer Session 4

Time Transp Var.Fl.1 cValue1 0.1 0 -60 1 (this is to the right of the table) 1.0 0 -60 0 3.5 0 0 0 3.6 0 -60 1 4.5 0 -60 0 7 0 0 0 Button "Next"

Initial Conditions: Import the final pressure head profile from the Source1 Project as the initial condition for Source2 (Edit->Initial Conditions->Import) Find the project Source1 Select Pressure Head and click OK If you do not see imported values, click on the Navigator Bar Initial Condition->Pressure

Head and the Edit Conditions on FE-mesh command ( ) on the Edit Bar. Run Calculations

Click the Calculate Current Project command ( ) on the Toolbar (or Calculation->Calculate Current Project) You will get a warning that the Pressure Head Initial Conditions on Geo Objects are different than those on FE-Mesh. That is correct since the imported pressure head initial conditions are defined only on FE-Mesh. Click Yes to start calculations. (Execution time on 3 GHz PC – 50 s) OUTPUT: Click on the Results Tab under the View Window. Results – Other Information: Solute Fluxes (from the Navigator Bar, or Results->Boundary Information->Solute Fluxes from menu)

Variable Boundary Flux Free Drainage Boundary Flux

Results – Graphical Display: Concentrations (from the Navigator Bar, or Results->Display Quantity->Concentrations from menu) Click with the right mouse button on the color scale and from the pop-up menu click on Min/Max Global in Time. See how the display changed.

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Time [days]

Observation Nodes: Concentration

Computer Session 4

C. Infiltration of Water and Solute From a Subsurface Source - Additional Root Water Uptake

Close the Source2 Project (click Save Project ( ) at the Toolbar or File->Save)

Project Manager (Menu: File->Project Manager, Toolbar: ) Select the Source2 project Button "Copy" Name: Source3 Description: Infiltration of Water and Solute from a Subsurface Source, Root Water Uptake Button "OK"

Main Processes (Menu: Edit->Flow and Transport Parameters->Main Processes or Navigator Bar: Source3->Flow and Transport Parameters->Main Processes)

Check Box: Root Water Uptake You will be warned that this action will lead to deleting results. Click Yes. Button "OK"

Root Water and Solute Uptake – Models (Edit->Flow and Transport Parameters->Root Water and Solute Uptake->Root Water/Solute Uptake Models)

Leave default values Button "Next"

Root Water and Solute Uptake – Pressure Head Reduction (Edit->Flow and Transport Parameters->Root Water and Solute Uptake->Pressure Head Reduction)

Leave default values Button "Next"

Variable Boundary Conditions (Edit->Flow and Transport Parameters->Variable Boundary Conditions)

Add Transpiration in the table as follows: Time Transp Var.Fl.1 cValue1

0.1 1 -60 1 (this is to the right of the table) 1.0 1 -60 0 3.5 1 0 0 3.6 1 -60 1 4.5 1 -60 0 7 1 0 0

Surface area associated with transpiration: 75 cm (length of the soil surface) Button "OK"

Initial Conditions: Import the final pressure head and concentration profiles from the Source2 Project as the initial condition for Source3 (Edit->Initial Conditions->Import)

Computer Session 4

Find the project Source2 Select Pressure Head and Concentration and click OK If you do not see imported values, click on the Navigator Bar Initial Condition->Pressure

Head and the Edit Conditions on FE-mesh command ( ) on the Edit Bar. Spatial Root Distribution Menu: Edit->Domain Properties->Parameters for Root Distribution

Maximum Rooting Depth: 60 Depth of Maximum Intensity: 15 Parameter Pz: 1 Check "Specify Parameters for Horizontal Distribution" Maximum Rooting Radius: 60 Depth of Maximum Intensity: 0 Parameter Py: 1

Run Calculations

Click the Calculate Current Project command ( ) on the Toolbar (or Calculation->Calculate Current Project) You will get a warning that the Pressure Head and Concentration Initial Conditions on Geo Objects are different than those on FE-Mesh. That is correct since the imported pressure head and concentration initial conditions are defined only on FE-Mesh. The same warning is issued also for root water uptake, which was also defined on FE-Mesh. Click Yes to start calculations.