HYDRUS
User Manual
Version 3

Software Package for Simulating
the Two- and Three-Dimensional Movementof Water, Heat and Multiple Solutes
in Variably-Saturated MediaJanuary 2018, PC-Progress, Prague, Czech Republic© 2018 J.šimůnek and M. Šejna. All rights reserved

The HYDRUS Software Package for Simulating
the Two- and Three-Dimensional Movementof Water, Heat, and Multiple Solutes
in Variably-Saturated Porous Media

User Manual
Version 3.03

M. Šejna1, J. Šimůnek2, and M. Th. van Genuchten3,4

December 2020

1

PC-Progress, Prague, Czech Republic
University of California Riverside, Riverside, CA
3
Department of Nuclear Engineering, Federal University of Rio de Janeiro, Brazil
4
Department of Earth Sciences, Utrecht University, Netherlands
2© 2020 J. Šimůnek and M. Šejna. All rights reserved.

2

Table of Contents
Table of Contents................................................................................................................................. 3
List of Figures ...................................................................................................................................... 9
List of Tables ...................................................................................................................................... 19
Abstract .............................................................................................................................................. 21
History of the HYDRUS (2D/3D) Development ............................................................................. 23
Introduction to the HYDRUS Graphical User Interface .............................................................. 27
1. Project Manager and Data Management ................................................................................. 31
2. Projects Geometry Information ............................................................................................37
3. Flow and Transport Parameters ..........................................................................................43
3.1.

3.2.

3.3.

3.4.

General Information ....................................................................................................43
3.1.1.

Main Processes .............................................................................................43

3.1.2.

Inverse Solution ............................................................................................46

3.1.3.

Time Information ..........................................................................................49

3.1.4.

Output Information .......................................................................................51

Water Flow Parameters ...............................................................................................53
3.2.5.

Iteration Criteria...........................................................................................53

3.2.2.

Soil Hydraulic Model ....................................................................................56

3.2.3.

Water Flow Parameters ................................................................................57

3.2.4.

Neural Network Predictions .........................................................................62

3.2.5.

Anisotropy in the Hydraulic Conductivity ....................................................63

3.2.6.

Constraints on Hysteretic Model ..................................................................64

Solute Transport Parameters .......................................................................................65
3.3.1.

Solute Transport - General ...........................................................................65

3.3.2.

Solute Transport Parameters ........................................................................70

3.3.3.

Solute Reaction Parameters ..........................................................................71

3.3.4.

Temperature Dependence of Solute Transport Parameters ...........................75

3.3.5.

Water Content Dependence of Solute Transport Parameters ........................76

3.3.6.

Solution Compositions for the UNSATCHEM Module ...................................77

3.3.7.

Chemical Parameters for the UNSATCHEM Module ....................................78

3.3.8.

Additional Fumigant Application ...................................................................79

Heat Transport Parameters .........................................................................................80

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3.5.

Root Uptake and Growth .............................................................................................82
3.5.1.

Root Water Uptake Model ............................................................................82

3.5.2.

Root Water Uptake Parameters ....................................................................84

3.5.3.

Root Distribution Parameters .......................................................................87

3.5.4.

Root Growth Parameters ..............................................................................88

3.6.

Time Variable Boundary Conditions ...........................................................................90

3.7.

Constructed Wetlands ..................................................................................................93

3.8.

The Slope Stability Modules.......................................................................................103
3.8.1.

The Slope Classic Module...........................................................................103

3.8.2.

The Slope Cube Module ..............................................................................107

4. Geometry of the Transport Domain...................................................................................109
4.1.

Boundary Objects.......................................................................................................109
4.1.1. Points .............................................................................................................112
4.1.2. Lines and Polylines ........................................................................................115
4.1.3. Arcs and Circles .............................................................................................116
4.1.4. Curves and Splines .........................................................................................119
4.1.5. Common Information for a Graphical Input of Objects ................................121
4.1.6. Translate, Copy, Rotate, Mirror, Stretch, and Skew Operations...................122
4.1.7. Additional Operations....................................................................................125

4.2.

Surfaces .....................................................................................................................126
4.2.1. General Definitions. .......................................................................................126
4.2.1.1. Planar Surfaces ...............................................................................128
4.2.1.2. Curved Surfaces ..............................................................................129
4.2.1.3. Partial Surfaces ..............................................................................131
4.2.2. Steps to Define a Two-Dimensional Domain. ................................................131
4.2.3. Several notes on rules for correct definition of the Geometry. ......................132
4.2.4. Internal Objects. ............................................................................................133
4.2.5. Check and Repair Geometry. .........................................................................135

4.3.

Openings ....................................................................................................................129

4.4.

Solids .........................................................................................................................138
4.4.1. 3D-Simple (Hexahedral) Solids. ....................................................................138
4.4.2. 3D-Layered Solids. ........................................................................................139
4.4.2.1. Division of a Solid into Columns. ...................................................1434

4.4.2.2. Division of a Solid into Geo-Layers................................................143
4.4.2.3. Individual specification of different Thicknesses of Geo-Layers
at different Thickness Vectors. ........................................................143
4.4.2.4. Steps to Define a 3D-Layered Domain. ..........................................144
4.4.3. 3D-General Solids. ........................................................................................144
4.5.

Thickness Vectors.......................................................................................................147

4.6.

Intersections of Surface and Solids ............................................................................151

4.7.

Auxiliary Objects .......................................................................................................151
4.7.1. Dimensions .....................................................................................................153
4.7.2. Labels .............................................................................................................154
4.7.3. Bitmaps (Textures) .........................................................................................155
4.7.4. Cross-Sections................................................................................................156
4.7.5. Mesh-Lines .....................................................................................................157
4.7.6. Points Probes .................................................................................................159
4.7.7. Lines Probes...................................................................................................161
4.7.8. Background Layers ........................................................................................164

4.8.

Other Notes on Objects .............................................................................................166
4.8.1. Object Numbering ..........................................................................................166
4.8.2. Relations among Objects ...............................................................................166
4.8.3. References among Objects and Convention for Writing a List of Indices .....166

4.9.

Import Geometry from a Text File .............................................................................166

4.10.

Import Geometry from a DXF File ............................................................................169

4.11.

Import Geometry from a TIN File..............................................................................169

5. Finite Element Mesh ............................................................................................................171
5.1.

Finite Element Mesh Generator.................................................................................171

5.2.

Structured Finite Element Mesh Generator ...............................................................171

5.3.

Unstructured Finite Element Mesh Parameters ........................................................174

5.4.

Finite Element Mesh Refinement ...............................................................................182
5.4.1. Finite Element Mesh Refinement for MeshGen2D ........................................182
5.4.2. Finite Element Mesh Refinement for Genex/T3D ..........................................185

5.5.

Unstructured Finite Element Mesh Generator MeshGen2D .....................................187

5.6.

Finite Element Mesh Statistics ...................................................................................191

5.7.

Finite Element Mesh Sections......................................................................................... 192

56. Domain Properties, Initial and Boundary Conditions......................................................195
6.1.

Default Domain Properties ........................................................................................195

6.2.

Initial Conditions .......................................................................................................196

6.3.

Boundary Conditions .................................................................................................198
6.3.1. Time-Variable Head/Flux 1 BCs ...................................................................199
6.3.2. Special Boundary Conditions ........................................................................201
6.3.3. Triggered Irrigation .......................................................................................2036.3.4. Reservoir Boundary Condition ......................................................................204

6.4.

Domain Properties .....................................................................................................2086.4.1. Stochastic Distribution of Scaling Factors ....................................................209

6.5.

Defining Properties on Geometric Objects................................................................2116.5.1. Materials on Geometric Objects ....................................................................213
6.5.2. Observation Nodes on Geometric Objects .....................................................216
6.5.3. Initial Conditions on Geometric Objects .......................................................217
6.5.4. Boundary Conditions on Geometric Objects .................................................218
6.5.5. Additional Notes on Properties at Geometric Objects ..................................219

6.6.

Import of Domain Properties and/or Initial and Boundary Conditions ....................220
6.6.1. Import Initial Condition from HYDRUS Projects ..........................................220
6.6.2. Import Data from HYDRUS Projects ............................................................2216.6.3. Import Data from a Text File .........................................................................222

7. Graphical Output .................................................................................................................227
7.1.

Results – Graphical Display ......................................................................................227
7.1.1. Displayed Variables .......................................................................................228
7.1.2. Display Options .............................................................................................232
7.1.3. Edit Isoband Value and Color Spectra ..........................................................233
7.1.4. Export Isolines ...............................................................................................239
7.1.5. Streamlines .....................................................................................................240
7.1.6. Clipper and Slicer ..........................................................................................242
7.1.7. Velocity Vectors .............................................................................................245
7.1.8. Export to ParaView........................................................................................247

7.2.

Convert to ASCII ........................................................................................................248

7.3.

Results – Other Information.......................................................................................249

8. Graphical User Interface Components ..............................................................................253
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8.1.

View Window ............................................................................................................ 253
8.1.1

Scene and Viewing Commands ......................................................................253

8.1.2

Grid and Work Plane .....................................................................................254

8.1.3

Stretching Factors ..........................................................................................255

8.1.4. Rendering Model ...........................................................................................255
8.1.5. Selection and Edit Commands .......................................................................256
8.1.6. Pop-up Menus ...............................................................................................257
8.1.7. Drag and Drop ...............................................................................................258
8.1.8. Sections ..........................................................................................................258
8.2.

Navigator Bars ...........................................................................................................261

8.3.

Edit Bars ....................................................................................................................262

8.4.

Toolbars .....................................................................................................................266

8.5.

HYDRUS Menus.........................................................................................................271

8.6.

Input Tables in HYDRUS ...........................................................................................296

8.7.

New Features in Version 3.0 of GUI .........................................................................296

9. Miscellaneous Information..................................................................................................297
9.1.

Program Options .......................................................................................................297

9.2.

HYDRUS License and Activation...............................................................................301
9.2.1. Brief Description of HYDRUS Activation Using a Software Lock ................301
9.2.2. Detailed Description of HYDRUS Activation Using a Software Lock ..........301
9.2.2.1.

On-Line Activation ........................................................................304

9.2.2.2.

Activation by E-mail ......................................................................306

9.2.3. Reinstallation, Moving to another Computer ................................................312
9.2.3.1.

On-Line Deactivation ....................................................................312

9.2.3.2.

Deactivation by E-mail ..................................................................313

9.2.4. Extending Activation ......................................................................................315
9.2.5. Hardware Key ................................................................................................315
9.3.

Print Options..............................................................................................................317

9.4.

Print Preview and Copy to the Clipboard Commands ..............................................318

9.5.

Coordinate Systems ....................................................................................................319

9.6.

DOS Window During Calculations............................................................................320

9.7.

Running Computational Modules Outside of GUI or in a Batch...............................321

9.8.

The HyPar Module, a parallelized version ................................................................322
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9.9.

Video Files .................................................................................................................323

9.10.

About HYDRUS ..........................................................................................................325

References ...................................................................................................................................327

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List of Figures
Figure 1. The HYDRUS Graphical User Interface (the main window). .....................................28
Figure 2. The project Manager with the Project Groups tab. ......................................................31
Figure 3. The Project Manager with the Projects tab. .................................................................32
Figure 4. The Project Information dialog window. .....................................................................34
Figure 5. General description of the HYDRUS Project Groups. .................................................34
Figure 6. The Domain Type and Units dialog window (with 3D preview). ................................37
Figure 7. Domain Type and Units dialog window (with 2D axisymmetrical preview). .............38
Figure 8. Examples of rectangular (top) and general (bottom) two-dimensional geometries. .....39
Figure 9. Example of a hexahedral three-dimensional geometry. ...............................................40
Figure 10. The Rectangular Domain Definition dialog window. ..................................................40
Figure 11. The Hexahedral Domain Definition dialog window. ..................................................41
Figure 12. The Main Processes dialog window. ..........................................................................45
Figure 13. The Inverse Solution dialog window. .........................................................................46
Figure 14. The Data for Inverse Solution dialog window. ...........................................................47
Figure 15. The Time Information dialog window. ............................................................................ 49
Figure 16. The Output Information dialog window. ......................................................................... 51
Figure 17. The Iteration Criteria dialog window...........................................................................53
Figure 18. The Soil Hydraulic Model dialog window...................................................................56
Figure 19. The Water Flow Parameters dialog window for direct (top) and inverse (bottom)
problems.......................................................................................................................58
Figure 20. The Rosetta Lite (Neural Network Predictions) dialog window. ................................62
Figure 21. The Edit Local Anisotropy dialog window for two-dimensional applications. ...........63
Figure 22. The Tensors of the Anisotropy dialog window............................................................63
Figure 23. The Constraints on Hysteresis Model dialog window. ................................................64
Figure 24. The Solute Transport dialog window...........................................................................65
Figure 25. The Solute Transport dialog window for the UNSATCHEM module. .......................69
Figure 26. The Solute Transport Parameters dialog window. .......................................................70
Figure 27. The Solute Reaction Parameters dialog window. ........................................................71
Figure 28. The Solute Reaction Parameters dialog window for the UNSATCHEM module. ......74
Figure 29. The Temperature-Dependent Solute Transport and Reaction Parameters dialog
window. ........................................................................................................................759

Figure 30. The Water Content Dependent Solute Reaction Parameters dialog window. .............76
Figure 31. The Solution Compositions dialog window for the UNSATCHEM module. .............77
Figure 32. The Chemical Parameters dialog window for the UNSATCHEM module. ................78
Figure 33. The Add Fumigant dialog window for the Fumigant module. ....................................79
Figure 34. The Heat Transport Parameters dialog window...........................................................80
Figure 35. The Root Water Uptake Model dialog window. ..........................................................82
Figure 36. The Root Water Uptake Parameters dialog window for the stress response
function of Feddes et al. [1978] (left) and van Genuchten [1985] (right). ..................84
Figure 37. The Root Water Uptake Parameters dialog window for the solute stress response
function based on the threshold model (left) and S-shape model of van
Genuchten [1985] (right). ............................................................................................85
Figure 38. The Root Distribution Parameters dialog window.......................................................87
Figure 39. The Root Growth Parameters specified either using the logistic growth function(top) or a table (bottom). ..............................................................................................89
Figure 40. The Time Variable Boundary Conditions dialog window. ..........................................90
Figure 41. The Constructed Wetland Model (CW2D) Parameter I dialog window......................95
Figure 42. The Constructed Wetland Model (CWM1) Parameter I dialog window. ....................98
Figure 43. The Constructed Wetland Model (CW2D) Parameter II dialog window. ...................99
Figure 44. The Constructed Wetland Model (CWM1) Parameter II dialog window..................101
Figure 45. The main window of the Slope Stability Module. .....................................................103
Figure 46. The Slope Stability Parameters dialog window. ........................................................104
Figure 47. The Default Parameters for Slope Stability Module dialog window. ........................105
Figure 48. An example of the Print and Export document generated by the Slope Stability
module........................................................................................................................106
Figure 49. Illustration of the physical processes in the SLOPE Cube module. ..........................107
Figure 50. The Slope Cube Parameters dialog window. .............................................................108
Figure 51. Examples of selected outputs (maximum and minimum effective stresses,
suction stress, and local factor of safety) from the Slope Cube module. ...................108
Figure 52. A base surface showing several basic geometric objects...........................................112
Figure 53. The Edit Bar during the process of defining a new point (left) and a new line
(right) graphically. .....................................................................................................113
Figure 54. The Edit Point dialog window. ..................................................................................114
Figure 55. Different ways of adding Parametric Points on a curve. ...........................................115
Figure 56. The Edit Curve dialog window. .................................................................................116

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Figure 57. The Edit Bar during the process of defining a radius for a new arc (left) or a newcircle (right) graphically.............................................................................................117
Figure 58. The New Line (Arc) dialog window. .........................................................................118
Figure 59. The New Line (Circle) dialog window. .....................................................................119
Figure 60. Edit Bar during the process of defining a spline graphically. ....................................120
Figure 61. Snap to a point (left) and snap to a curve (right). ......................................................121
Figure 62. The Translate - Copy dialog windows. ......................................................................122
Figure 63. The Rotate (left) and Mirror (right) dialog windows. ................................................123
Figure 64. The Stretch (left) and Skew (right) dialog windows. .................................................123
Figure 65. The Manipulation Options dialog window. The bitmaps indicate connecting lines
between points, surfaces between lines, and solids between surfaces. ...............................124
Figure 66. The Insert Point on Curve dialog window. ......................................................................125
Figure 67. The warning issued when Surfaces cannot be created automatically and must be
defined manually.................................................................................................................127
Figure 68. Edit Bar during defining a surface graphically (left) and the General tab of theEdit Surface dialog window (right). ...........................................................................127
Figure 69. A solid showing the base surface. ..............................................................................128
Figure 70. Solid showing separate vertical columns. ..................................................................128
Figure 71. A solid with its base surface in the XZ plane and thickness vectors in the Y
direction. ..................................................................................................................129
Figure 72. FE-Mesh for a solid with its base surface in the XZ plane and thickness vectors
in the Y direction........................................................................................................129
Figure 73. Examples of Curved Surfaces (Rotary, Pipe, B-Spline, and Quadrangle
Surfaces). ...................................................................................................................130
Figure 74. The Integrated Tab of the Edit Surface dialog window. ............................................134
Figure 75. An example of internal objects. .................................................................................134
Figure 76. An example of an Upper Surface definition using Internal Curves and Thickness
Vectors. ......................................................................................................................135
Figure 77. The Repair Domain Definition dialog window. ........................................................136
Figure 78. The New Opening dialog window. ............................................................................137
Figure 79. The Edit Bar during the process of graphically defining a Hexahedral Solid.
Definition of a Base Surface on the left and a Thickness on the right.......................138
Figure 80. The Edit Bar during the process of graphically defining a Solid by extruding a
Base Surface. Selection of a Surface (left) and definition of a Thickness Vector(right). ........................................................................................................................139
Figure 81. The 3D-Layered Solid dialog window: the General and Geo-Layers Tabs. ..............14111

Figure 82. The 3D-Layered Solid dialog window; the FE-Mesh Tab for single and multiple
layers. .........................................................................................................................142
Figure 83. Examples of 3D-General Solids. Top - formed by Planar Surfaces, bottom –formed by curved surfaces. ........................................................................................145
Figure 84. Edit Bar during the process of graphically defining a Thickness Vector. .................148
Figure 85. The New Thickness dialog window. ..........................................................................148
Figure 86. A solid with several thickness vectors. ......................................................................149
Figure 87. FE-Mesh for the solid in Figure 86. ...........................................................................149
Figure 88. Missing internal curves in the base surface. ..............................................................150
Figure 89. Consequence of missing an internal curve in the base surface on the FE-Mesh of
the top surface. ...........................................................................................................150
Figure 90. The Edit Intersection dialog window (for two Surfaces (left) and two Solids(right). ........................................................................................................................151
Figure 91. An example of an Intersection of two Surfaces and a resulting Partial Surface
and Intersection Curve. ..............................................................................................152
Figure 92. Edit Bar during the process of graphically defining a Dimension. Selection of
two definition points, the distance of which is to be labeled (left) and thedimension type (right). ...............................................................................................153
Figure 93. The Edit Comment dialog window. ...........................................................................154
Figure 94. The Edit Bar during the process of graphically defining a Comment. Selectionof the Comment Position, Comment Text, Font, and Color (left), and Offset(right). ........................................................................................................................155
Figure 95. The Edit Bitmap dialog window. ...............................................................................155
Figure 96. The Cross-Section dialog window. ............................................................................156
Figure 97. The Mesh-Line dialog window. .................................................................................157
Figure 98. The Fluxes across Mesh-Line dialog window. ..........................................................158
Figure 99. The New Point Probe dialog window. .......................................................................159
Figure 100. The display of Point Probes with their values. .......................................................160
Figure 101. The Tools and Options section of the Results Edit Bar with Point Probes
commands. ..............................................................................................................160
Figure 102. The Probe Points section of the Results Edit Bar when Point Probes aredefined.....................................................................................................................161
Figure 103. The New/Edit Line Probe dialog window. .............................................................162
Figure 104. The Line Points section of the Results Edit Bar when Line Probes are defined.....163
Figure 105. The Line Points section of the Results Edit Bar when Line Probes are defined.....163
Figure 106. An example of the Background Layer. ...................................................................164

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Figure 107. The New Background Layer dialog window. .........................................................165
Figure 108. The Import Geometry from a DXF File dialog window. ........................................169
Figure 109. The Rectangular Domain Discretization dialog window. .......................................172
Figure 110. The Hexahedral Domain Discretization dialog window. ........................................173
Figure 111. The FE-Mesh Parameters dialog window (the Main Tab for 3D-Layered (left)and 3D-General (right) geometries). .......................................................................174
Figure 112. The FE-Mesh Parameters dialog window (Tab Stretching). ..................................175
Figure 113. The Mesh Stretching dialog window for a Local FE-Mesh Stretching. .................176
Figure 114. Listing of FE-Mesh Stretchings on the Navigator Bar. ..........................................177
Figure 115. An example of the FE-Mesh with three FE-Mesh Stretchings assigned to areas
below the domain surface. ......................................................................................177
Figure 116. The FE-Mesh Parameters dialog window (Tab MG Options). ...............................178
Figure 117. The FE-Mesh Parameters dialog window (Tab Options). ......................................180
Figure 118. The FE-Mesh Parameters dialog window (Mesh Section Tab). .............................181
Figure 119. The New FE-Mesh Refinement dialog window for the MeshGen2D modulewith four different types of refinements (applied to a Point, a Line with agiven FE-size or the number of Points, and to a Surface). .....................................183
Figure 120. Example of FE-Mesh Refinements (top) and FE-Mesh (bottom). .........................184
Figure 121. Circular (left) and rectangular (right) refinements around a node. .........................185
Figure 122. Refinement on a line (by defining either the size or the number of finite
elements along a line). ............................................................................................186
Figure 123. Refinements on a surface (left) or solid (right). ......................................................186
Figure 124. The FE-Mesh Refinement dialog window for the Genex/T3D module with six
different types of refinements (applied to a Point, a Line with a given FE-sizeor a number of points, to a Surface, and to a Solid)................................................187
Figure 125. Example of mesh stretching using a stretching factor of 3 in the x-direction. ..........190
Figure 126. The FE-Mesh Information dialog window for a two-dimensional problem(top) and a three-dimensional problem (bottom). ...................................................191
Figure 127. The FE-Mesh Sections dialog window. ..................................................................193
Figure 128. The Default Domain Properties dialog window. ....................................................196
Figure 129. The Water Flow Initial Condition dialog window. .................................................197
Figure 130. The Temperature distribution dialog window.........................................................198
Figure 131. The Time-Variable Head/Flux 1 BCs tab of the Boundary Condition Options
dialog window.........................................................................................................201
Figure 132. The Special Boundary Conditions tab of the Boundary Condition Options
dialog window.........................................................................................................203
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Figure 133. The Triggered Irrigation tab of the Boundary Condition Options dialog
window. ...................................................................................................................204
Figure 134. Three different types of the reservoir boundary condition: a well, a furrow,and a wetland. .........................................................................................................205
Figure 135. The Reservoir Boundary Condition tab for the Well (top), Furrow (middle),
and Wetland (bottom) reservoir of the Boundary Conditions Options window. ....207
Figure 136. The Stochastic Distribution of Scaling Factors dialog window..............................210
Figure 137. An example of the transport domain defined using three components S1, S2,
and S3.....................................................................................................................211
Figure 138. The upper part of the Edit Bar displaying defined materials and commands forvarious actions with materials. ................................................................................213
Figure 139. The Set Materials dialog window. ..........................................................................214
Figure 140. The transport domain with materials specified on geometric objects. ....................214
Figure 141. The Sort Property Objects dialog window. .............................................................215
Figure 142. The Edit Materials dialog window. .........................................................................216
Figure 143. The Observation Node dialog window. ..................................................................217
Figure 144. The Edit Pressure Head (left) and Concentration (right) Initial Conditions
dialog window. ........................................................................................................218
Figure 145. The Edit Water Flow Boundary Condition dialog window. ...................................219
Figure 146. The Import Initial Condition dialog window. .........................................................220
Figure 147. The Import Selected Quantities dialog window......................................................221
Figure 148. The Import of Values from Scattered Points dialog window. ................................224
Figure 149. The "Results - Graphical Display" part of Data Tab of the Navigator Bar forthe standard (left), Unsatchem (center), and Wetland (right) modules. ..................231
Figure 150. The "Results" part of the View Tab of the Navigator Bar displaying various
alternative variables. ...............................................................................................231
Figure 151. The Display Options dialog window. .....................................................................232
Figure 152. The Edit Isoband Value and Color Spectra dialog window. ...................................233
Figure 153. The use of intermediate isolines. ............................................................................234
Figure 154. The Color dialog window. ......................................................................................235
Figure 155. Adjusting scale in the Edit Isoband Value and Color Spectra dialog window. ......236
Figure 156. The use of the Custom Scale. ..................................................................................237
Figure 157. The color smoothing. ..............................................................................................238
Figure 158. An example of the Project_Property_Isolines.txt text file (e.g.,
Furrow_Pressure_Head_Isolines.txt; an excerpt) for the Furrow project(displayed in the top of the figure). .........................................................................239
14

Figure 159. Example showing 3D Streamlines. Streamlines can be calculated for a given
time layer (i.e., steady-state flow) from a set of seed points. Seed point
sources of several types can be set graphically .......................................................240
Figure 160. Example of Particle Animation. The movement of particles can be animatedas flowing-lines or flowing-particles. .....................................................................240
Figure 161. The Streamlines Options dialog window. ...............................................................241
Figure 162. Example showing 3D Clipping. When working with 3D models, the visible
mesh (or geometric objects) can be clipped to view values inside the domain.
The clipper is controlled by a graphical tool (a manipulator; see Fig. 162). ..........242
Figure 163. Example showing 3D Slicing. The slicer is another tool for better
visualization of 3D objects. The number of slices, their position, and rotation
can be set either in a dialog or graphically (see Figs. 162 and 165). ......................242
Figure 164. The Clipper Tab on the Edit bar (left) and the Clipper/Slicer setting dialog
window activated from the toolbar. ........................................................................243
Figure 165. Slicer Options dialog window. ................................................................................243
Figure 166. An example of the Slicer tool with 6 vertical and one horizontal crosssectinal planes. ........................................................................................................244
Figure 167. An example of the Clipper Plane tool with a displayed manipulator (defining
the position and rotation of a display plane). ..........................................................244
Figure 168. An example of the Clipper Box tool with a displayed manipulator (defining
the position and rotation of the box). ......................................................................245
Figure 169. Rasters for Vector Fields. Vector fields can be displayed in meshindependent rasters, i.e., regular 2D/3D grids with an arbitrary density ofpoints. Rasters can also be used with the Clipper and Slicer. .................................246
Figure 170. The Vector Field Options dialog window. ..............................................................246
Figure 171. Example showing Export to ParaView. ParaView is an open-source, multiplatform data analysis and visualization application. New visualization
options include custom post-processing based on scripting or plugin modules.
Details are at www.paraview.org. .............................................................................247
Figure 172. x-y graph dialog window displaying pressure heads in observation nodes. ...........249
Figure 173. The Convert to ASCII dialog window. ...................................................................248
Figure 174. The Grid and Work Plane dialog window. .............................................................254
Figure 175. The View Stretching Factors dialog window..........................................................255
Figure 176. The Rendering part of the View Tab of the Navigator Bar. ...................................256
Figure 177. Example of the Transparent mode of the HYDRUS GUI. The Transparent
mode is available for all types of graphical displays of scalar and vector fields.
Isolines are automatically numbered, and min/max values of a particularvariable in the transport domain are automatically identified. ...............................256

15

Figure 178. The Pop-up Menu from the View window. ............................................................258
Figure 179. Options for Generation of Geo-Sections and FE-Mesh Sections dialog
window. ...................................................................................................................259
Figure 180. Selected Navigator Bars (Data Tab on the left, View Tabs in the middle, andClipper Tab on the right).........................................................................................261
Figure 181. Selected Edit Bars (from left to right) for Material Distribution in Domain
Properties, Water Flow Boundary Conditions, Pressure Head Initial
Conditions, and Water Content Results. .................................................................262
Figure 182. The Color Scale Display Options menu..................................................................265
Figure 183. Selected Edit Bars (for Domain Geometry and FE-Mesh). ....................................265
Figure 184. The Customize Toolbars dialog window (the Toolbars tab -top, theCommands tab - bottom left, and the Options tab - bottom right). .........................266
Figure 185. The HYDRUS Menus I (File, Edit, and View). ......................................................271
Figure 186. The HYDRUS Menus II (Insert, Calculations, and Results). .................................271
Figure 187. The HYDRUS Menus II (Tools, Options, Windows, and Help). ...........................272
Figure 188. The Program Options dialog window (the Graphics Tab). .....................................297
Figure 189. The Program Options dialog window (the Program Tab).......................................298
Figure 190. The Program Options dialog window (the FE-Mesh Tab). ....................................299
Figure 191. The Program Options dialog window (the Files and Directories Tab). ..................300
Figure 192. The HYDRUS Authorization Status dialog window (Tab Status). ........................302
Figure 193. Warning issued when attempting to make changes to the Authorization Status
while not running HYDRUS with administrator privileges....................................303
Figure 194. The HYDRUS Authorization Status dialog window (Tab Add-on Modules). .......303
Figure 195. The HYDRUS License and Activation dialog window (Tab History of
Activation). ...........................................................................................................304
Figure 196. The Online Activation dialog window. ...................................................................305
Figure 197. Window requesting confirmation of entered parameters. .......................................306
Figure 198. The Activation by E-mail dialog window (Tab Step 1).. ........................................318
Figure 199. The Activation by E-mail dialog window (Tab Step 2). .........................................308
Figure 200. An email with the HYDRUS Activation Request in Outlook. ...............................309
Figure 201. Window inquiring if the user wants to enter the Activation Code..........................310
Figure 202. The Activation by E-mail dialog window (Tab Step 3). .........................................310
Figure 203. Window confirming successful HYDRUS authorization. ......................................311
Figure 204. Window reporting a failure of HYDRUS authorization. ........................................312
Figure 205. The Online Deactivation dialog window. ...............................................................313
16

Figure 206. Window confirming successful online deactivation of HYDRUS. ........................313
Figure 207. The HYDRUS Deactivation dialog window...........................................................314
Figure 208. Window confirming the successful deactivation of HYDRUS by email. ..............314
Figure 209. The HYDRUS 2.xx Setup window with a choice to install the hardware-key
driver. ......................................................................................................................316
Figure 210. The General, Picture, and Legend tabs of the Print Options dialog window..........317
Figure 211. The Coordinate Systems dialog windows. ..............................................................319
Figure 212. The Create Video File dialog window. ...................................................................323
Figure 213. Result of commands Print Preview or Copy to the Clipboard. ...............................318
Figure 214. The About HYDRUS dialog window (the Program tab (top) and the Authorstab (bottom). ............................................................................................................325

17

18

List of Tables
Table 1.

Commands in the Project Manager. .............................................................................33

Table 2.

Data types for the objective function (Inverse Problem). ............................................48

Table 3.

Definition of column X in Fig. 14 based on Data Type (Inverse Problem). ..................48

Table 4.

Definition of column Y in Fig. 14 based on Data Type (Inverse Problem). ..................49

Table 5.

Time Information variables. .........................................................................................51

Table 6.

Time Step Control variables. ........................................................................................55

Table 7.

Soil hydraulic parameters for the analytical functions of van Genuchten [1980]
for twelve textural classes of the USDA soil textural triangle, according toCarsel and Parrish [1988]. ..........................................................................................60

Table 8.

Soil hydraulic parameters for the analytical functions of van Genuchten [1980]
for twelve textural classes of the USDA textural triangle as obtained with the
Rosetta Lite program [Schaap et al., 2001]. ................................................................60

Table 9.

Soil hydraulic parameters for the analytical functions of Brooks and Corey[1964] for twelve textural classes of the USDA soil textural triangle, according
to Carsel and Parrish [1988]. ......................................................................................61

Table 10. Soil hydraulic parameters for the analytical functions of Kosugi [1996] fortwelve textural classes of the USDA soil textural triangle. .........................................61
Table 11. Comparison of CW2D and CWM1 components. ........................................................93
Table 12. Comparison of CW2D and CWM1 processes. ............................................................94
Table 13. Kinetic parameters in the CW2D biokinetic model [Langergraber and Šimunek,
2005]. ...........................................................................................................................96
Table 14. Kinetic parameters in the CWM1 biokinetic model [Langergraber et al., 2009]. ......97
Table 15. Temperature dependencies, stoichiometric parameters, composition parameters,
and parameters describing oxygen transfer in the CW2D biokinetic model[Langergraber and Šimunek, 2005]. ..........................................................................100
Table 16. Temperature dependencies, stoichiometric parameters, composition parameters,
and parameters describing oxygen transfer in the CWM1 biokinetic model[Langergraber et al., 2009]. ......................................................................................102
Table 17. Definition of terms related to geometry design. ..........................................................110
Table 18. Definition of terms related to boundary discretization. ...............................................188
Table 19. Finite element mesh sections generated in different HYDRUS versions. ...................192
Table 20. Domain properties. .....................................................................................................208
Table 21. Definition of commands used to manipulate Property Objects. ................................212
Table 22. Standard variables displayed in the View Window of the Results tab (Results Graphical Display). ....................................................................................................228

19

Table 23. Alternative variables that can be displayed in the View Window of the Resultstab...............................................................................................................................229
Table 24. Definition of various concentration modes (for linear sorption model). ...................230
Table 25. Graph options in the HYDRUS interface. .................................................................250
Table 26. HYDRUS menu commands. ......................................................................................273
Table 27. Brief description of HYDRUS menu commands.......................................................282
Table 28. A comparison of the HyPar module to standard computational modules. ...................322

20

AbstractŠejna, M., J. Šimůnek, and M. Th. van Genuchten, The HYDRUS Software Package for Simulating
Two- and Three-Dimensional Movement of Water, Heat, and Multiple Solutes in VariablySaturated Porous Media, User Manual, Version 3.03, PC Progress, Prague, Czech Republic, 332 pp.,
2020.
This report documents version 3.0 of the Graphical User Interface of HYDRUS, a software
package for simulating water, heat, and solute movement in two- and three-dimensional variably
saturated porous media. The software package consists of the computational computer program andthe interactive graphics-based user interface. The HYDRUS program numerically solves theRichards equation for variably saturated water flow and advection-dispersion equations for bothheat and solute transport. The flow equation incorporates a sink term to account for water uptake byplant roots. The heat transport equation considers transport due to conduction and convection withflowing water. The solute transport equations consider advective-dispersive transport in the liquid
phase, as well as diffusion in the gaseous phase. The transport equations also include provisions fornonlinear nonequilibrium reactions between the solid and liquid phases, linear equilibrium reactions
between the liquid and gaseous phases, zero-order production, and two first-order degradation
reactions. In addition, physical nonequilibrium solute transport can be accounted for by assuming a
two-region, dual-porosity type formulation which partitions the liquid phase into mobile andimmobile regions. Attachment/detachment theory, including filtration theory, is additionally
included to enable simulations of the transport of viruses, colloids, and/or bacteria.
HYDRUS may analyze water and solute movement in unsaturated, partially saturated, or fully
saturated porous media. The program can handle flow regions delineated by irregular boundaries.
The flow region itself may be composed of nonuniform soils having an arbitrary degree of local
anisotropy. Flow and transport can occur in the two-dimensional vertical or horizontal plane, athree-dimensional region exhibiting radial symmetry about the vertical axis, or a fully threedimensional domain. The program also includes a Marquardt-Levenberg type parameter
optimization algorithm for inverse estimation of soil hydraulic and/or solute transport and reaction
parameters from measured transient or steady-state data for two-dimensional problems. Details of
the various processes and features included in HYDRUS are provided in the Technical Manual[Šimůnek et al., 2018].
The main program unit of the HYDRUS Graphical User Interface (GUI) defines the overall
computational environment of the system. This main module controls the execution of the programand determines which other optional modules are necessary for a particular application. The module
contains a project manager and both the pre-processing and post-processing units. The preprocessing unit includes specification of all necessary parameters to run the HYDRUS FORTRAN
codes successfully, grid generators for relatively simple rectangular and hexahedral transportdomains, a grid generator for unstructured finite element meshes for complex two-dimensional
domains, a small catalog of soil hydraulic properties, and a Rosetta Lite program for generating soil
hydraulic properties from soil textural data. The post-processing unit consists of simple x-y graphics
for graphical presentation of soil hydraulic properties, as well as such output as distributions versus
time of a particular variable at selected observation points, and actual or cumulative water andsolute fluxes across boundaries of a particular type. The post-processing unit also includes options

21

to present results of a particular simulation by means of contour maps, isolines, spectral maps, andvelocity vectors, and/or by animation using both contour and spectral maps.
This report serves as a User Manual and reference document of the Graphical User Interface ofthe HYDRUS software package. Technical aspects such as governing equations and details about
the invoked numerical techniques are documented in a separate Technical Manual.
Other Useful Information Online:
1. Outside reviews of the HYDRUS software packages:
http://www.pc-progress.com/en/Default.aspx?h3d-reviews
2. HYDRUS 2D/3D Selected References:
http://www.pc-progress.com/en/Default.aspx?h3d-references
3. HYDRUS Quick Tour and Tutorials:
4. http://www.pc-progress.com/en/Default.aspx?h3d-tutorials
5. HYDRUS Applications and Public Library of HYDRUS Projects:
http://www.pc-progress.com/en/Default.aspx?h3d-applications
6. HYDRUS Book: Soil Physics with HYDRUS: Modeling and Applications:
http://www.pc-progress.com/en/Default.aspx?h3d-book
7. HYDRUS FAQ:
http://www.pc-progress.com/en/Default.aspx?hydrus-faq
8. HYDRUS (2D/3D) Troubleshooting:
http://www.pc-progress.com/en/Default.aspx?h3d-troubleshooting

22

History of the HYDRUS (2D/3D) Development
Version 1 of HYDRUS (2D/3D) software package [Šimůnek et al., 2008] was an extension andreplacement of HYDRUS-2D (version 2.0) and SWMS_3D. This software package was acomplete rewrite of HYDRUS-2D and its extensions for two- and three-dimensional geometries.
In addition to features and processes available in HYDRUS-2D and SWMS_3D, the newcomputational modules of HYDRUS (2D/3D) considered (a) water flow and solute transport in adual-porosity system, thus allowing for preferential flow in fractures or macropores while storingwater in the matrix [Šimůnek et al., 2003], (b) the spatial root distribution functions of Vrugt et al.
[2001], (c) the soil hydraulic property models of Kosugi [1996] and Durner [1994], (d) thetransport of viruses, colloids, and/or bacteria using an attachment/detachment model, filtration
theory, and blocking functions (e.g., Bradford et al., 2002), (e) a constructed wetland module(only in 2D) [Langergraber and Šimůnek, 2005, 2006], (f) the hysteresis model of Lenhard et al.
[1991] to eliminate pumping by keeping track of historical reversal points, (g) new print
management options, (h) dynamic, system-dependent boundary conditions, (i) flowing particles
in two-dimensional applications, and (j) calculations of actual and cumulative fluxes acrossinternal meshlines.
New features of the Graphical User Interface of HYDRUS (2D/3D) included, among other things,(a) a completely new GUI based on Hi-End 3D graphics libraries, (b) the MDI architecture withmultiple projects and multiple views, (c) a new organization of geometric objects, (d) a navigator
window with an object explorer, (e) many new functions improving the user-friendliness, such as
drag-and-drop and context-sensitive pop-up menus, (f) improved interactive tools for graphicalinput, (g) options to save cross-sections and mesh-lines for charts within a given project, (h) a
new display options dialog where all colors, line styles, fonts and other parameters of graphicalobjects can be customized, (i) extended print options, and (j) extended information in the ProjectManager (including project previews).
Version 2.0, which included the 3D-Professional Level of HYDRUS, included many new features
as compared to version 1.0. New features and changes in the HYDRUS GUI:
1) Supports for complex general three-dimensional geometries (Professional Level).
2) Domain Properties, Initial Conditions, and Boundary Conditions can be specified onGeometric Objects (defining the transport domain) rather than on the finite element mesh.
3) Import of initial conditions from existing HYDRUS projects even with (slightly) different
geometry or FE mesh.
4) Import of various quantities (e.g., domain properties, initial and boundary conditions)from another HYDRUS project even with (slightly) different geometry or FE mesh.
5) Support of ParSWMS (a parallelized version of SWMS_3D) [Hardelauf et al., 2007].
6) Support of UNSATCHEM (a module simulating the transport of and reactions between
major ions) [Šimůnek et al., 2012c].
7) The Mass Balance (Inverse) Information dialog window enables to display texts larger
than the capacity of the Edit window.
8) Root distribution can be specified using GUI parallel with the slope for hillslopes.
9) Display of results using Isosurfaces.
10) Support of a new CWM1 constructed wetland module [Langergraber et al., 2009].

23

New features and changes in the HYDRUS in the computational modules:
1) New initializations conditions for solute transport (initial conditions can be specified in the
total solute mass and nonequilibrium phases can be initially equilibrated).
2) Various new boundary conditions (e.g., gradient, surface drip, subsurface drip, and seepage
face with a specified pressure head boundary conditions).
3) Triggered Irrigation - irrigation is triggered by the program when the pressure head at aparticular observation node drops below a specified value (only in 2D).
4) HYDRUS calculates and reports surface runoff, evaporation, and infiltration fluxes for theatmospheric boundary.
5) Water content dependence of solute reaction parameters using Walker’s [1974] formula was
implemented.
6) A new option to consider root solute uptake, including both passive and active uptake(only in 2D) [Šimůnek and Hopmans, 2009].
7) The Per Moldrup’s tortuosity models [Moldrup et al., 1997, 2000] were implemented as
an alternative to the Millington and Quirk [1961] model.
8) An option to use a set of Boundary Condition records multiple times.
9) Executable programs are about 1.5 - 3 times faster than in the standard version due to theloop vectorization.
10) Options related to the fumigant transport (e.g., removal of tarp, temperature dependent
tarp properties, additional injection of fumigant).
11) A new CWM1 constructed wetland module [Langergraber et al., 2009].
Version 2.02 additionally supported several add-on modules that have their own user manuals:
1) The DualPerm module [Šimůnek et al., 2012e],2) The UNSATCHEM module [Šimůnek et al., 2012c],3) The Wetland module [Langergraber and Šimůnek, 2011],
4) The C-Ride module [Šimůnek et al., 2012b], and
5) The HP2 module [Šimůnek et al., 2012a].
Version 2.03:
1) Offers some new functionality with respect to the import of various properties from either
existing HYDRUS projects or from text files (see Section 6.6),
2) Allows users to import the definition of isolines (only in 3D-Professional). and
3) Resolved problems with fonts for the Chinese, Japanese, and other similar Windows
systems.
Version 2.04 additionally supported two add-on modules:
1) the HyPar module (see Section 9.1) is a parallelized version of the standard twodimensional and three-dimensional HYDRUS computational modules (h2d_calc.exe andh3d_calc.exe), and2) the Slope Classic module is intended to be used mainly for stability checks ofembankments, dams, earth cuts, and anchored sheeting structures.
Version 2.05 additionally supported the new add-on module Slope Cube. While the Slope Classic
module (added in version 2.04) is based on classical engineering soil mechanics theories anduses the effective stress approach only for saturated conditions, the new add-on module "Slope24

Cube" (Slope Stress and Stability) was developed to provide a unified effective stress approachfor both saturated and unsaturated conditions [Lu et al., 2010].
New features in Version 3.01, among many others, include:
1) 64bit version, which can now use all physical memory available on modern PCs.
2) 3D streamlines (see Section 7.1.5).
3) Particle animation (see Section 7.1.5).
4) 3D mesh clipping (see Section 7.1.6).
5) 3D mesh slicing (see Section 7.1.6).
6) Rasters for 3D Vector Fields (see Section 7.1.7).
7) The new "Reservoir" boundary condition (see the Technical Manual and Section 6.3.4).
8) A dynamic rooting system (root growth) (see the Technical Manual and Section 3.5.4).
9) Export data to ParaView (see Section 7.1.8).
10) Numbering of isolines.
New features in Version 3.02, among many others, include:
1. The Furrow module [Brunetti et al., 2018, 2019].
2. The Slope Cube module in 3D.
New features in Version 3.03, among many others, include:
1. A dynamic rooting system (root growth) was included also into the UnsatChem andWetland modules.
2. Point Probes (see Section 4.7.6).
3. Line Probes (see Section 4.7.7).
4. Inverse Solution for 3D projects.
5. Clipping of the 3D model and the FE-mesh has been extended with a new option, the"Clipper-Box" tool (see Section 7.1.6).
A detailed description of the development of various HYDRUS versions and a review of theirapplications can be found in:Šimůnek, J., M. Th. van Genuchten, and M. Šejna, Development and applications of the
HYDRUS and STANMOD software packages and related codes, Vadose Zone Journal,
Special Issue “Vadose Zone Modeling”, 7(2), 587-600, doi: 10.2136/VZJ2007.0077, 2008.
Šimůnek, J., M. Th. van Genuchten, and M. Šejna, Recent developments and applications of the
HYDRUS computer software packages, Vadose Zone Journal, 15(7), pp. 25, doi:
10.2136/vzj2016.04.0033, 2016.
Šimůnek, J., M. Šejna, and M. Th. van Genuchten, New features of version 3 of the HYDRUS(2D/3D) computer software package, Journal of Hydrology and Hydromechanics, 66(2), 133142, doi: 10.1515/johh-2017-0050, 2018.

25

26

Introduction to the HYDRUS Graphical User Interface
The past several decades have seen an explosion of increasingly sophisticated numerical models for
simulating water flow and contaminant transport in the subsurface, including models dealing with
one- and multi-dimensional flow and transport processes in the unsaturated or vadose zone between
the soil surface and the groundwater table. Even with an abundance of well-documented models
now available, one major problem often preventing their optimal use is the extensive work requiredfor data preparation, numerical grid design, and graphical presentation of the output results. Hence,
the more widespread use of multi-dimensional models requires ways that make it easier to create,
manipulate and display large data files, facilitating interactive data management. Introducing suchtechniques will free users from cumbersome manual data processing and should enhance theefficiency in which programs are being implemented for a particular example. To avoid or simplify
the preparation and management of relatively complex input data files for two- and threedimensional applications, and to graphically display the final simulation results, we developed aninteractive graphics-based user-friendly interface HYDRUS for the MS Windows 95, 98, NT, ME,
XP, Vista, 7, and 10 environments. The interface is connected directly to the computational codes.
The current version 3 of the HYDRUS graphical user interface represents a major upgrade ofprevious versions 1 and 2. Version 1 itself was a complete rewrite of version 2.0 of HYDRUS-2D
that expanded the capabilities of HYDRUS-2D to three-dimensional problems. Version 2, which
includes the 3D-Professional Level of HYDRUS, included many new features compared to version
1. In particular, it included support for complex general three-dimensional geometries and an
option to specify various domain properties and initial and boundary conditions on geometricobjects, rather than directly on the finite element mesh. Version 3 of HYDRUS (2D/3D) includes aflexible reservoir boundary condition, expanded root growth features, and the GUI's newgraphical capabilities.
In addition to information given in this user manual, extensive context-sensitive on-line help ismade part of the graphical user interface (GUI). By holding the F1 button or clicking on the Help
button while working in any window, the user obtains information about the window content. In
addition, context-sensitive help is available in every module using the "SHIFT+F1" help button. In
this mode, the mouse cursor changes to a help cursor (a combination arrow + question mark), which
a user can use to select a particular object for which help is needed (e.g., a menu item, toolbar button,
or other features). A help file will be displayed, giving information about the item on which the user
clicked. Except for the computational modules that are written in FORTRAN, the entire GUI is
written in C++.
The HYDRUS Graphical User Interface (Fig. 1) is the main program unit defining the overall
computational environment of the system. This main module controls the execution of the programand determines which other optional modules are necessary for a particular application. The module
contains a project manager and both the pre-processing and post-processing units. The preprocessing unit includes specification of all the parameters required to successfully run the
HYDRUS FORTRAN codes (modules H2D_CALC, H2D_CLCI, H2D_WETL, H2D_UNSC,
and/or H3D_CALC), grid generators for relatively simple rectangular and hexahedral transportdomains, a grid generator for unstructured finite element meshes appropriate for more complex twodimensional domains, a small catalog of soil hydraulic properties, and a Rosetta Lite program forgenerating soil hydraulic properties from textural information. The post-processing unit consists of27

simple x-y graphs for graphical presentation of the soil hydraulic properties, distributions versus
time of a particular variable at selected observation points, as well as actual or cumulative water andsolute fluxes across boundaries of a particular type. The post-processing unit also includes options
to present results of a simulation by means of contour maps, isolines, isosurfaces, spectral maps, andvelocity vectors, and/or by animation using both contour and spectral maps.

Figure 1. The HYDRUS Graphical User Interface (the main window).
Figure 1 shows the main window of the HYDRUS graphical user interface, including its main
components, such as the Menu, Toolbars, the View Window, the Navigator Bar, Tabs, and theEdit Bar. These terms will be used throughout this user manual. The text below provides adetailed description of all major components of the graphical user interface. At the end of thisuser manual, a list is given of all commands accessible through the menu (Table 26), as well as abrief discussion of the action taken with particular commands (Table 27). More detailed
descriptions are available through the on-line help.

28

Work for a new project should begin by opening the Project Manager (see Chapter 1) and giving a
name and a brief description of the new project. Next, the Domain Type and Units dialog Window(Figs. 6 and 7) appears (this window can also be selected from the Pre-processing Menu). From thispoint on, the program will navigate users through the entire process of entering input files. Users
may either choose particular commands from a menu or allow the interface to lead them through theprocess of entering input data by selecting the Next button. Alternatively, clicking the Previous
button will return users to the previous window. Pre- and post-processing commands and processes
are also sequentially listed on the Data Tab of the Navigator Bar. Green arrows on the Edit Bar
always direct users to subsequent or previous input processes for a particular command. Many
commands and processes can be alternatively accessed using either the Toolbars and Menus, or the
Navigator and Edit Bars.

29

30

1. Project Manager and Data Management
A Project Manager (called by the command File->Project Manager, Figs. 2 and 3) is used to
manage the data of existing projects and helps to locate, open, copy, delete and/or rename desired
projects or their input or output data. A Project represents any particular problem to be solved by
HYDRUS. The project name, as well as a brief description of the project (Fig. 4), helps to locate aparticular problem. Projects are represented by a file project_name.h3d3 (the final digit 2 (or 3)
refers to version 2 (or 3) of HYDRUS; extension h3d was used with version 1.0) that contains all
input and output data when the Temporary Working Directory option (Fig. 4) is used. It contains
only the input data when the Permanent Working Directory option is selected. HYDRUS input files(used by the computational modules) are extracted from the project_name.h3d3 file into a working
subdirectory; output data created by the calculation module are sent into the same folder. Whensaving a project, output files (created by the computational modules) are also included in the
project_name.h3d3 file (when the Temporary Working Directory option is used). The input andoutput files can be either permanently kept in the external working directory or are stored in thisfolder only during calculations (Fig. 4, the radio buttons Temporary – is deleted after closing the
project and Permanent – result files are kept in this directory). The location of the external working
directory is specified in the Project Description (Fig. 4) and the Program Options dialog
window (Fig. 189).

Figure 2. The project Manager with the Project Groups tab.

31

Figure 3. The Project Manager with the Projects tab.
The Project Manager gives users considerable freedom to organize their projects. The projects aregrouped into Project Groups (Fig. 2), which can be placed anywhere in accessible memory (i.e., on
local and/or network hard drives). Project Groups serve to organize projects into logical groups
defined by a user. Each Project Group has its own name, description, and pathway (Figs. 2 and 5).
A Project Group can be any existing accessible subdirectory (folder). HYDRUS is installed
together with two default Project Groups, 2D_Tests and 3D_Tests, located in the HYDRUS3D
folder. The 2D_Tests and 3D_Tests Project Groups contain test examples for two- and threedimensional problems, respectively. We suggest that users create their own Project Groups (e.g., the
My_2D_Direct, My_2D_Inverse, and My_3D_Direct Project Groups) and keep the provided
examples intact for future reference. Projects can be copied with the Project Manager only withina particular Project Group. Users can copy projects between Project Groups (or share theirHYDRUS projects with colleagues and clients) using standard file managing software, such as
Windows Explorer. In that case, one must copy only the project_name.h3d3 file (when the radio
buttons Temporary – is deleted after closing the project is used, Fig. 4). When temporary data are
kept permanently in the working directory (i.e., the radio button Permanent – results files are kept
in this directory is selected, Fig. 4), the working directory must be copied together with the
project_name.h3d3 file.

32

In addition to a Name and a brief Description of a Project, the Project Manager also displays
dimensions for a particular problem (Type: the dimensions are either 2D or 3D, and the geometry iseither Simple (S), Layered (L), or General (G), see Section 2), what Processes are involved (W –water flow, S – solute transport, T – heat transport, R – root water uptake, Inv – Inverse problem),the size of the project (MB), when the project was created (Date) and whether or not the Results
exist (Fig. 3). The Project Manager can also display a preview of the Project’s geometry (seethe check box Show Project Preview in Fig. 3). Commands of the Project Manager are listed inTable 1.
Table 1. Commands in the Project Manager.
Group

Command

Description

Project Group New
Edit

Registers a new Project Group in the Project Manager.
Renames the selected Project Group and changes its description
and/or location.
RemoveRemoves registration of a selected Project Group from the ProjectManager.
Set As Current Sets a selected Project Group as the active Project Group.
Close
Closes the Project Manager.

Project

New
Copy
RenameDeleteOpen
Close
ConvertCalculate

Creates a new project in the current Project Group.
Copies a selected project within the current Project Group.
Renames a selected project.
Deletes a selected project.
Opens a selected project.
Closes the Project Manager.
Converts projects created by earlier HYDRUS versions (i.e., either
HYDRUS-2D or version 1.0 of HYDRUS (2D/3D)).
Calculates selected HYDRUS projects. This command allows
users to calculate multiple selected projects simultaneously.

Options

Description

Show Project Preview

Provides a preview of the geometry of a particular project in thebottom left corner of the Project Manager.
Shows projects created using earlier HYDRUS versions, i.e.,either HYDRUS-2D or version 1.0 of HYDRUS (2D/3D).
Opens the Project Manager at the Project Groups Tab.

Show Old Projects
Start on Project Groups Page

The commands New and Rename from the Project Tab of the Project Manager dialog window(Fig. 3) call the Project Information dialog window (Fig. 4), which contains the Name and
Description of the project, as well as information about the Project Group (name, description, andpathway) to which the project belongs. It also contains information on whether or not the input

33and output data are kept permanently in an external directory (the radio buttons Temporary – isdeleted after closing the project and Permanent – result files are kept in this directory, Fig. 4).

Figure 4. The Project Information dialog window.

Figure 5. General description of the HYDRUS Project Group.
Projects created by the previous versions of HYDRUS (e.g., HYDRUS-2D) can be imported into
the current version of HYDRUS using two ways:
A. Individual projects can be converted using the command File->Import and Export->Import
HYDRUS-2D Project. This is done by first creating a new Project, and then selecting theabove command and browsing for the location of a project created with a previous version of
HYDRUS-2D. The input data of the older project are then converted into the new HYDRUS
format. Results of the older project can then be viewed using the new version of HYDRUS,
while projects can be modified or recalculated as needed.
B. Multiple HYDRUS-2D projects (or HYDRUS projects created by earlier versions of
HYDRUS) can be converted simultaneously using the Convert command of the ProjectManager. One first creates a HYDRUS Project Group for a folder in which the HYDRUS-2D
projects are located and selects the Show Old Projects option at the Project Tab of the34

Project Manager. One then selects projects to be converted and clicks the Convert command.
HYDRUS, in this way, creates HYDRUS projects and stores all input and output files in the
project_name.h3d3 files.
Input data can be edited either using the HYDRUS graphical user interface (this modifies directly
the project_name.h3d3 file) or the input data can be modified manually. In such case, HYDRUS
input files need to be stored in the working external directory (sent there by the command File>Import and Export->Export Data for HYDRUS Solver), and then can be imported back into the
HYDRUS project_name.h3d3 file using the command File->Import and Export->Import Input
Data from *.In Files.
The Working Directory is a folder into which the program stores temporary data. Each open
project has its own Working Directory, where the program stores, for example, input files forcomputational modules, and where computational modules write the output files. When saving a
project, data from the Working Directory are copied into the main project file project_name.h3d3.
When the project is closed, the Working Directory is deleted. Only when a user selects the option“Permanent – result files are kept in this directory” (Fig. 4) is the Working Directory not deleted
after closing the project, in which case the temporary data are not copied into the main project file.
The Working Directory includes additional folders (e.g., Furrow, Genex, Genex_tmp,
H_Compounds, H_Grids, H_VTK, Slope, and Textures) that contain auxiliary data that are notrelated to calculated results.

35

36

2. Projects Geometry Information
In the first dialog window that a user encounters after creating a new project, he/she needs tospecify whether the flow and transport problem occurs in two- or three-dimensional transportdomains. Geometry type is selected in the Domain Type and Units dialog Window (Fig. 6 and
7). In this dialog window, users specify the Type of Geometry, the 2D Domain Options, theLength Units, and the size of the Initial Project Group (the approximate size of the transportdomain).
Type of Geometry: This section allows a user to choose between simple geometries having a
structured finite element mesh (i.e., 2D-Simple (Parametric) and 3D-Simple (Parametric)), or
more general geometries having an unstructured finite element mesh (i.e., 2D-General (BoundaryRep.), 3D-Layered, and 3D-General (Boundary Rep.)). Available options depend on the level ofauthorization (purchased License). Only simple geometries 2D-Simple (Parametric) and 3DSimple (Parametric) are available for HYDRUS Levels 2D-Lite and 3D-Lite, respectively. 2DGeneral (Boundary Rep.) is available for the 2D-Standard Level, 3D-Layered for the 3DStandard Level, and 3D-General (Boundary Rep.) for the 3D-Professional Level.

Figure 6. The Domain Type and Units dialog window (with 3D preview).

37

Figure 7. The Domain Type and Units dialog window (with 2D axisymmetrical preview).
There are two types of two-dimensional transport domains (Surfaces, see also Section 4.2)
depending upon the selection made in the Domain Type and Units dialog window (Fig. 6 and 7):•

2D-Simple (Parametric): This type of solid has a Rectangular Shape and is defined byits basic dimensions. Rectangular domains are defined by three straight lines, one at thebottom of the domain and two at the sides, whereas the upper boundary may or may not be
straight. Nodes along the upper boundary line may, in that case, have variable x- and zcoordinates. However, the lower boundary line must always be horizontal (or have a
specified slope), while the left and right boundary lines must be vertical. The flow region isthen discretized into a structured triangular mesh. Examples of simple rectangular
geometries are shown in Figure 8 (top).

•

2D-General (Boundary Rep.): This type of Surface is defined by a set of Boundary
Curves see Section 4.2). Examples of general two-dimensional geometries are shown in
Figure 8 (bottom) and Figure 52.

There are three types of three-dimensional transport domains (Solids, see also Section 4.4)
depending upon the selection made in the Domain Type and Units dialog window (Fig. 6 and 7):38

•

3D-Simple (Parametric): This type of solid has a Hexahedral Shape and is defined byits basic dimensions. The base can have a certain slope in the X and Y dimensions (Fig.
9). Hexahedral domains must have similar properties as rectangular domains, i.e., verticalplanes at the sides, a horizontal (or with a specified slope) plane at the bottom boundary, andwith only the upper boundary not needing to be a plane. An example of a simple hexahedral
three-dimensional geometry (i.e., 3D-Simple) is given in Figure 9.

•

3D-Layered: This type of solid is defined by the Base Surface (see Section 4.2) and one
or more Thickness Vectors (see Section 4.5).

•

3D-General (Boundary Rep.): This type of solid is defined using a set of surfaces thatfully form its boundaries. This type of geometries is available only in the 3DProfessional version. 3D-General Geometries can be formed from three-dimensional
objects (Solids) of general shapes. Three-dimensional objects are formed by boundary
surfaces, which can be either Planar surfaces or Curved surfaces (Quadrangle, Rotary,
Pipe, or B-Spline).

Figure 8. Examples of rectangular (top) and general (bottom) two-dimensional geometries.

39

Figure 9. Example of a hexahedral three-dimensional geometry.
2D-Domain Options: Two-dimensional flow and transport can occur in a horizontal or verticalplane, or in an axisymmetrical quasi-three-dimensional transport domain. When a threedimensional axisymmetrical system is selected, the z-coordinate must coincide with the verticalaxis of symmetry. A typical example of the selected 2D or 3D geometry is shown in the preview
part of the dialog window.
The simple geometries are defined in the Rectangular (Fig. 10) or Hexahedral Domain Definition(Fig. 11) dialog windows for two-dimensional and three-dimensional problems, respectively. In
each of these windows, users need to specify the vertical and horizontal dimensions of the transportdomain, as well as a possible slope of the base of the domain in different directions (if applicable;
α is in the x-direction and β is in the y-direction). The preview in the middle of the dialog
window of a simple example showing all geometry parameters should help users in specifying
their desired transport domain (Dimensions and Slope).

Figure 10. The Rectangular Domain Definition dialog window.

40

Figure 11. The Hexahedral Domain Definition dialog window.
In the Domain Type and Units dialog Window (Figs. 6 and 7) users also select the geometry
Units to be used throughout the application (mm, cm, m) and the size of the Initial ProjectGroup. When units are changed during specification or after reading the input data, then all
input variables are automatically converted into the new units.
Initial Project Group: This part of the dialog allows users to define the initial dimensions of thegraphical view window.
Model Precision and Resolution: Epsilon is a minimum resolution recognized when defining
geometric objects. Epsilon is by default defined as R/100,000, where R is a domain radius, i.e., aradius of a circle/sphere circumscribing the domain. Epsilon is used, for example, for evaluationof positions of two points. If their distance is less than Epsilon, then the two points are replaced
by a single point. A user-defined epsilon may lead to unstable behavior of the program, and it isintended only for advanced users who may need it for special purposes. The correct functionalityof geometrical calculations and generation of FE-meshes is not guaranteed for user-defined
epsilons.
Edit Properties on Geometric Objects: When the check box "Edit domain properties, initialand boundary conditions on geometric objects" is checked, users can specify various properties
and conditions on the Geometric Objects (See Section 6.5 "Defining Properties on GeometricObjects" for details), rather than only on FE-Mesh, as available in Version 1.0 of HYDRUS. This
option will be by default "On" for new projects, and it is "Off" for projects converted from
Version 1.0. Users can turn this option "Off" and continue defining various properties on FEMesh, as they have been used to. Users can turn this option "On" for projects converted from
Version 1.0 of HYDRUS. However, they will lose their original definitions and have to specify
them again on Geometric Objects.

41

42

3. Flow and Transport Parameters
Flow and transport parameters are entered in a series of dialog windows that are divided into
multiple groups: a) General Information, b) Water Flow Parameters, c) Solute TransportParameters, d) Heat Transport Parameters, and e) Root Water Uptake and Growth Parameters.

3.1. General Information
3.1.1. Main Processes
In the Main Processes dialog window (Fig. 12), users specify the processes to be simulated, i.e.,
Water Flow, Solute Transport, Heat Transport, and/or Root Water Uptake. When Solute
Transport is selected, users can choose from multiple modules of different complexity. The
Standard Solute Transport module is described in detail in the HYDRUS Technical Manual[Šimůnek et al., 2012d]. This module allows consideration of individual solutes (one or several)that are either independent or subject to sequential (or consecutive) first-order decay reactions.
Other solute transport modules (briefly described below) can consider multiple solute componentsthat can mutually interact.
Wetland Module

Check this box if the Wetland module is to be used. The Wetland Module(for two-dimensional problems only) was developed to model biochemicaltransformation and degradation processes in subsurface flow constructedwetlands. In the wetland module, two biokinetic model formulations canbe chosen: (1) the biokinetic model as described in CW2D [Langergraberand Šimunek, 2005, 2006, 2011] and (2) the CWM1 (ConstructedWetland Model #1) biokinetic model [Langergraber et al., 2009]. In
CW2D aerobic and anoxic transformation and degradation processes fororganic matter, nitrogen and phosphorus are described, whereas in CWM1
aerobic, anoxic, and anaerobic processes for organic matter, nitrogen, andsulfur.

Unsatchem Module The Major Ion Chemistry Module [UNSATCHEM; Šimůnek andSuarez, 1994] can be used instead of the standard solute transport module.
A detailed description of the UNSATCHEM Module is given in the
UNSATCHEM user manual [Šimůnek et al., 2012c]. A more detailed
description of the concepts used in the UNSATCHEM module is provided
in the HYDRUS-1D manual [Šimůnek et al., 2008], which provides all
relevant information about the one-dimensional version of this module.
C-Ride Module

The C-Ride module simulates two-dimensional variably-saturated water
flow, colloid transport, and colloid-facilitated solute transport in porous
media. The module accounts for transient variably-saturated water flow
and both colloid and solute movement due to advection, diffusion, anddispersion, as well as for solute movement facilitated by colloid transport.

43

A detailed description of the C-Ride Module is given in the C-Ride user
manual [Šimůnek et al., 2012b].
HP2 Module

The HP2 module is the result of coupling Hydrus (its two-dimensionalpart) with the PHREEQC geochemical code [Parkhurst and Appelo,1999], and corresponds to a similar one-dimensional module HP1[Jacques and Šimůnek, 2005, 2010; Jacques et al., 2006, 2008]. HP2 has,apart from the dimensionality (2D), the same capabilities as HP1. HP2
contains modules simulating (1) transient water flow, (2) the transport ofmultiple components, (3) mixed equilibrium/kinetic biogeochemical
reactions, and (4) heat transport in two-dimensional variably-saturated
porous media (soils). A detailed description of the HP2 Module is givenin the HP2 user manual [Šimůnek et al., 2012a].

Slope Classic Module The Slope Classic add-on module uses results obtained by HYDRUS (i.e.,
relative saturations and water fluxes) for subsequent slope-stability
analyses. The module is intended mainly for stability tests ofembankments, dams, earth cuts, and anchored sheeting structures. The
influence of water is modeled using the distribution of pore pressure,which is imported automatically from HYDRUS runs into the SLOPE
module at specified times, each of which can be analyzed separately. The
slip surface in the SLOPE module is considered to be circular and isevaluated using the Bishop, Fellenius/Petterson, Morgenstern-Price or
Spencer method [Lu and Godt, 2013]. More details can be found in theuser manual of this module. See Section 3.23.
Slope Cube Module While the Slope Classic module (added in version 2.04) is based onclassical engineering soil mechanics theories and uses the effective stressapproach only for saturated conditions, the new add-on module "Slope
Cube" (Slope Stress and Stability) was developed to provide a unified
effective stress approach for both saturated and unsaturated conditions [Luet al., 2010]. The module is intended to predict spatially and temporally
infiltration-induced landslide initiation and to carry out slope stability
analyses under variably-saturated soil conditions. Transient moisture andpressure head fields are directly obtained from the HYDRUS-2D modeland subsequently used to compute the effective stress field of hillslopes[Lu and Godt, 2013]. Furthermore, instead of the methodology of oneslope for one-factor safety in the classical slope stability analysis, the
SLOPE Cube module computes fields of the factor of safety in the entire
domain within hillslopes [Lu et al., 2012], thus allowing identification of
the development of potential failure surface zones or surfaces.
The program automatically considers transient water flow when the “Water Flow” option is
selected. Otherwise, the code tries to calculate steady-state flow from the specified initial andboundary conditions. The success of such calculations depends on the complexity and/or
nonlinearity of the problem. If unsuccessful, then a model run with constant boundary conditions
and long simulation time may be required. The Dual-Permeability Model can be selected as analternative description of water flow.

44

If the solute transport, heat transport, or root water uptake options originally considered in anexisting project are switched off by the user, the program issues a warning that all data related tothese processes will be lost. If this loss is undesirable, we recommend that users first copy the
input data of the current project to a new project before switching off the solute transport, heattransport and/or root water uptake options.

Figure 12. The Main Processes dialog window.
For two-dimensional problems, a user can also select if a Direct or Inverse Problem (Inverse
Solution?) is to be solved. Inverse problems involve the estimation of selected parameters fromavailable experimental data.
A new add-on module Slope Classic was included in Version 2.04. The Slope Classic module isintended to be used mainly for stability checks of embankments, dams, earth cuts, and anchoredsheeting structures (see Section 3.23).
A new add-on module Slope Cube was included in Version 2.05. Details about the Slope Cube
module are given in its own manual.

45

3.1.2. Inverse Solution
HYDRUS implement a Marquardt-Levenberg type parameter estimation technique [Šimůnek andHopmans, 2002] for inverse estimation of soil hydraulic (Hopmans et al., 2002) and/or solutetransport and reaction [Šimůnek et al., 2002] parameters from measured transient or steady-stateflow and/or transport data. The Inverse Solution dialog window (Fig. 13) appears only when the
Inverse Problem in the Main processes dialog window (Fig. 12) is selected. Users select whichparameters (the soil hydraulic, solute transport and reaction, and/or heat transport parameters) areto be optimized (Estimate …) from the specified experimental data.
One also selects the method of Weighting of Inversion Data in the objective function. Users
can choose between no weighting, weighting by mean ratios, or weighting by standard deviations.
When no weighting is selected, one needs to supply weights for particular data points in the Datafor Inverse Solution dialog window (Fig. 14). When weighting by mean ratio or weighting bystandard deviation is selected, then the code calculates either the means or the standard
deviations of the different data sets (e.g., water contents, pressure heads, concentrations, …) andadjusts the weights proportionally. These internal weights can still be multiplied by weights fromthe Data for Inverse Solution dialog window (Fig. 14).

Figure 13. The Inverse Solution dialog window.
The objective function for the inverse estimation of solute transport parameters can be definedusing different types of concentrations. Available Concentration Types are: a) the resident
concentration in the liquid phase, b) a log-transformation of the resident concentration in theliquid phase, c) the outflow (flux) concentration, d) the solute concentration flux, e) the46

cumulative concentration (solute) flux, and f) the total resident concentration. The total resident
concentration includes concentrations in the sorbed and nonequilibrium phases.
The maximum number of iterations for the inverse solution is also specified in this dialog
window. If one selects a zero number of iterations, then only the direct simulation is carried out.
However, users can still enter measured data, in which case the code compares the results of thedirect simulation with the measured data.

Figure 14. The Data for Inverse Solution dialog window.
In the table Data for Inverse Solution (Fig. 14), one specifies the measured data analyzed during
the parameter optimization process. Many different types of data can be used to define theobjective function that will be minimized for this purpose. How the values in the X and Y
columns are interpreted depends on the Type and Position values. Weight is the weightassociated with a particular data point. The following information can be included in theobjective function:

47

Table 2. Data Types for the objective function (Inverse Problem).
Type
0
1
2
3
4
5
6
7
8
9
10
11

Data Point
Cumulative boundary fluxes across a specified boundary
Pressure head measurements at selected observation point(s)Water content measurements at selected observation point(s)Boundary flux across a specified boundary
Concentration or temperature measurements at observation point(s)h(θ) measurements; soil water retention data
K(h) measurements; hydraulic conductivity data point
Prior knowledge of parameter αPrior knowledge of parameter nPrior knowledge of parameter θr
Prior knowledge of parameter θs
Prior knowledge of parameter Ks

Depending upon the value of parameter Type, the first column (X) contains the following
information:

Table 3. Definition of column X in Fig. 14 based on Data Type (Inverse Problem).
X
Time
Pressure head
Dummy variableType0, 1, 2, 3, 4
5, 6
7, 8, 9, 10, 11

Depending upon the value of parameter Type, the second (Y) and fourth (Position) columns
contain the following information:48

Table 4. Definition of column Y in Fig. 14 based on Data Type (Inverse Problem).
Y
Cumulative boundary flux across a specified
boundary
Pressure head
Water content
Averaged water content of the entire flow domain
Averaged water content of the subregion
Concentrations/temperatures
Concentrations for the second soluteType0Position
Code for the specified boundary*

1
2
2
2
4
4

The total amount of solute in the entire flow
domainBoundary flux across a specified boundary
Water content
Hydraulic conductivity
Particular parameter

4

Observation node number
Observation node number0
Negative subregion number
Observation node number
Negative observation node
number
0

3
5
6
7-11

Code for the specified boundary*Material number
Material number
Material number*

1 – constant pressure head or flux boundary; 2 – seepage face; 3 – variable pressure head or flux boundary 1; 4 –atmospheric boundary; 5 – drains; 6 – free or deep drainage boundary; 7, 8, and 9 – variable pressure head or flux
boundaries 2, 3, or 4, respectively.

3.1.3. Time Information
The Time Information dialog window (Fig. 15) contains information associated with the Time
Discretization, the Time Units, and the implementation of Boundary Conditions.

Figure 15. The Time Information dialog window.

49

Table 5. Time Information variables.
Time Units

Time units [T] to be used throughout the application (years, days,
hours, min, sec). When units are changed during or after data entry,
then all input variables are converted automatically into the newunits.

Initial Time

Starting time [T] of the calculation.

Final Time

Final time [T] of the calculation.

Initial Time Step

Initial time increment, ∆t [T]. The recommended value for the initialtime step depends on the type of simulation and boundary conditions
used. When simulating a process that starts with a large initialpressure head or concentration gradient at the boundary (e.g.,ponded infiltration or a sudden change of the boundary
concentration), use a small value of the initial time step (e.g., 1 s).
When simulating a long-term process with variable boundary
conditions (e.g., seasonal or multiyear simulation), start with a larger
time step (e.g., 15 min). This is because this initial time step is usedwhenever time-variable boundary conditions significantly change(e.g., the water flux changes by 25% or more). If needed (if there isno convergence for ∆tinit), the program will still use a smaller time
step than ∆tinit, but starting with a larger ∆tinit leads to more efficient
calculations. In general, smaller initial time steps must be used forsoils with more nonlinear soil hydraulic properties (e.g., coarse
textured soils), and larger initial time steps can be used for soils withless nonlinear soil hydraulic properties (e.g., loam).

Minimum Time Step

Minimum permitted value of the time increment, ∆tmin [T]. The
minimum time step must be smaller than a) the initial time step, b)interval between print times, and c) interval between time-variableboundary condition records. Always specify a small minimum
allowed time step, on the order of 1 s. This value may never be used,
but it provides the code with the flexibility when needed, e.g., when
there is a sudden change in boundary fluxes, and HYDRUS may notconverge with larger time steps.

Maximum
Step

Time The maximum permitted value of the time increment, ∆tmax [T]. Thisis a relatively unimportant parameter, and a large value may be
specified. Since HYDRUS automatically selects its optimal time
step, there is usually no need to constraint that. The only time when
there is a need to constrain the time step is likely for cases when
HYDRUS is asked to generate intra-daily variations in temperatureinternally, or in evaporation and transpiration fluxes. Then there is aneed to have time steps smaller (e.g., 1 h) so that these daily
variations can be properly modeled.

50

Boundary Conditions
Time-Variable Boundary Condition - The Number of Time-Variable Boundary Records andtime-dependent boundary conditions must be specified when this box is checked. The boundary
conditions otherwise are assumed to be constant in time.
The same set of boundary records can be repeated a number of times (Number of times torepeat the same set of BC records) (periodically) with a time period tPeriod=tAtmLast-tInit,
where tInit is the Initial Time and tAtmLast is the time of the last specified time boundary
record. Note that tMax< tInit +n*tPeriod.
3.1.4. Output Information
The Output Information dialog window (Fig. 16) contains information governing output fromthe computational module of HYDRUS.

Figure 16. The Output Information dialog window.

In the Print Options part of the dialog window, one decides whether certain information
concerning mean pressure heads and concentrations, mean water and solute fluxes, cumulative
water and solute fluxes, and time and iteration information is printed at each time step (T-Level
Information), after n time steps (Every n time steps), at a certain defined time interval (Interval
Output), or if the information is sent to the screen during the calculations (Screen Output). Whenthe simulation ends, users are, by default, asked to hit the Enter key of the keyboard to return to
the GUI from the computational window. This action can be disabled by unchecking the Hit
Enter at the End check box.
T-Level Information This check box decides whether certain information concerning meanpressure heads and concentrations, mean water and solute fluxes,
cumulative water and solute fluxes, and time and iteration information, areto be printed at each time step, after n time steps, or only at preselected
times (Print Times) or Time Intervals.

51

Interval Output

Users can specify whether or not information concerning mean pressure
heads and concentrations, mean water and solute fluxes, cumulative waterand solute fluxes, and time and iteration information is to be printed at aregular Time Interval.

Screen Output

Check box to decide whether or not information about the simulation run
is to be printed to the screen during the execution of the HYDRUS
computational code. We recommend to check this box for direct problems,
but not for inverse problems.

In the Print Times part of the dialog window, one specifies the number of Print Times (Count)
at which detailed information about the pressure heads, water contents, concentrations,temperatures, fluxes, and the soil water and solute balances will be printed. Clicking on the
Default command button will cause the print times to be distributed evenly between the initial andfinal time. Clicking on the Default (log) command button will cause the print times to be
distributed evenly between the initial and final time on the log scale. This option is enabled only
for larger times.
Finally, in the Subregions part, one selects the number of regions for which a mass balance will
be evaluated and printed to the Balance.out output file.

523.2. Water Flow Parameters3.2.1. Iteration Criteria
The Iteration Criteria dialog window (Fig. 17) contains information related to the iterative
process that is used to solve the Richards equation. Because of the nonlinear nature of the
Richards equation, an iterative process must be used to obtain solutions of the global matrix
equation at each new time step. For each iteration, a system of linearized algebraic equations is first
derived and then solved using either Gaussian elimination or the conjugate gradient method. After
solving the matrix equation, the coefficients are re-evaluated using this solution, and the new
equations are again solved. The iterative process continues until a satisfactory degree of
convergence is obtained, i.e., until for all nodes in the saturated (unsaturated) region, the absolutechange in pressure head (water content) between two successive iterations becomes less than somesmall value determined by the imposed absolute Pressure Head (or Water Content) Tolerance.
The first estimate (at zero iteration) of the unknown pressure heads at each time step is obtained byextrapolation from the pressure head values at the previous two-time levels.

Figure 17. The Iteration Criteria dialog window.

In the Iteration Criteria part of the dialog window, one specifies the maximum number of
iterations during one time step, and the water content and pressure head precision tolerances.
Max. Number of Iterations Maximum number of iterations allowed during any time step while solving
the nonlinear Richards equation using a modified Picard method. The

53

recommended and default value is 10. It is usually not helpful to use alarger value than 10. If HYDRUS does not converge in 10 iterations,then there is a relatively small probability that it will do so during moreiteration. Even if it does, it is much more efficient to reduce the time stepand attempt to find the solution with a smaller time step, which is done
automatically by the program when Itcrit is reached.

Water Content Tolerance

Absolute water content tolerance for nodes in the unsaturated part of theflow region [-]. When the water contents between two successive iterations
during a particular time step change less than this parameter, the iterative
process stops, and the numerical solution proceeds to the new time step. Its
recommended and default value is 0.001.

Pressure Head Tolerance

Absolute pressure head tolerance for nodes in the saturated part of the flow
region [L]. When the pressure heads between two successive iterations
during a particular time step change less than this parameter, the iterative
process stops, and the numerical solution proceeds to the new time step. Its
recommended and default value is 1 cm.

Information specified in the Time Step Control part of the dialog window is related to theautomatic adjustment of the time step during calculations. Four different time discretizations are
introduced in HYDRUS: (1) time discretizations associated with the numerical solution, (2) time
discretizations associated with the implementation of boundary conditions, (3) time discretizations
associated with data points used in the inverse problem, and (4) time discretizations which provide
printed output of the simulation results (e.g., nodal values of dependent variables, water and solute
mass balance components, and other information about the flow regime).
Discretizations 2, 3, and 4 are mutually independent; they generally involve variable time steps as
described in the input data file (Time-Variable Boundary Conditions, Fig. 40 and Output
Information, Fig. 16). Discretization 1 starts with a prescribed initial time increment, ∆t. This timeincrement is automatically adjusted at each time level according to the following rules:
a. Discretization 1 must coincide with time values resulting from time discretizations 2, 3,
and 4.
b. Time increments cannot become less than a preselected minimum time step, ∆tmin, nor
exceed a maximum time step, ∆tmax (i.e., ∆tmin ≤ ∆t ≤ ∆tmax).
c. If, during a particular time step, the number of iterations necessary to reach convergenceis ≤3, the time increment for the next time step is increased by multiplying ∆t with apredetermined constant >1 (usually between 1.1 and 1.5). If the number of iterations is≥7, ∆t for the next time level is multiplied by a constant <1 (usually between 0.3 and0.9).
d. If, during a particular time step, the number of iterations at any time level becomes
greater than a prescribed maximum (usually between 10 and 50), the iterative process
for that time level is terminated. The time step is subsequently reset to ∆t/3, and theiterative process restarted.
We note that the selection of optimal time steps, ∆t, during execution is also influenced by the
adopted solution scheme for solute transport.

54

Table 6. Time Step Control variables.
Lower Optimal Iteration
Range

Upper Optimal Iteration
Range

Lower Time Step
Multiplication Factor

Upper Time Step
Multiplication Factor

When the number of iterations necessary to reach convergencefor water flow is less than this number, the time step ismultiplied by the lower time step multiplication factor (thetime step is increased). The recommended and default value is3.
When the number of iterations necessary to reach convergencefor water flow is higher than this number, the time step ismultiplied by the upper time step multiplication factor (thetime step is decreased). The recommended and default value is7.
If the number of iterations necessary to reach convergence forwater flow is less than the lower optimal iteration range, thetime step is multiplied by this number (time step is increased).
The recommended and default value is 1.3.
If the number of iterations necessary to reach convergence forwater flow is higher than the upper optimal iteration range, thetime step is multiplied by this number (time step is decreased).
The recommended and default value is 0.7.

Internal Interpolation Tables. At the beginning of a numerical simulation, HYDRUS generates
for each soil type in the flow domain a table of water contents, hydraulic conductivities, andspecific water capacities from the specified set of hydraulic parameters. The values of thehydraulic properties are then computed during the iterative solution process using linear
interpolation between entries in the table. If the pressure head h at some node falls outside theprescribed interval (ha, hb), the hydraulic characteristics at that node are evaluated directly fromthe hydraulic functions (i.e., without interpolation). The above interpolation technique was foundto be much faster computationally than direct evaluation of the hydraulic functions over theentire range of pressure heads. Interpolation using tables can be avoided by setting ha and hb bothto zero. Then the soil hydraulic properties are always evaluated directly from the hydraulicfunctions (i.e., without interpolation). Output graphs of the soil hydraulic properties will also begiven for the interval (ha, hb).
The lower limit of
the tension interval
The upper limit of
the tension interval

The absolute value of the lower limit [L] of the pressure head interval
for which a table of hydraulic properties will be generated internally foreach material.
The absolute value of the upper limit [L] of the pressure head interval
for which a table of hydraulic properties will be generated internally foreach material.

Finally, in the Initial Conditions part of the dialog window, a user specifies whether the initialconditions for the water flow calculations are to be specified in terms of pressure heads or watercontents.

55

3.2.2. Soil Hydraulic ModelIn the Soil Hydraulic Model dialog window (Fig. 18), users select the Hydraulic Model todescribe the soil hydraulic properties and specify whether or not Hysteresis is to be consideredduring the calculations.

Figure 18. The Soil Hydraulic Model dialog window.

Hydraulic Model: The code allows users to select six types of models for the soil hydraulicproperties: a) the van Genuchten-Mualem model [van Genuchten, 1980], b) the van GenuchtenMualem model with an air-entry value of -2 cm, c) the modified van Genuchten type equations[Vogel and Cislerova, 1988], d) the equations of Brooks and Corey [1964], e) the lognormal
distribution model of Kosugi [1996], and f) a dual-porosity model [Durner, 1994]. Additionally,users can select two dual-porosity nonequilibrium flow models with mass transfer between themobile and immobile zones assumed to be proportional to either g) the water content or h) thepressure head [Šimůnek et al., 2003]. For a detailed description of these models, see the technicalmanual of HYDRUS. Two other approaches (a dual-permeability model and look-up tables) are
not available in the current version of HYDRUS.
Hysteresis: When the van Genuchten model is used, either a) a non-hysteretic description (NoHysteresis), b) a hysteretic description only in the retention curve (Hysteresis in Retention

56

Curve), or c) hysteretic descriptions in both the retention curve and the hydraulic conductivity
curve (Hysteresis in Retention Curve and Conductivity) can be used. When hysteresis in the soil
hydraulic properties is assumed, users must specify whether the initial condition is associatedwith the main wetting (Initially Wetting Curve) or main drying (Initially Drying Curve)
retention curve. The HYDRUS code incorporates hysteresis by using the empirical model
introduced by Scott et al. [1983]. This model was also employed by Kool and Parker [1987],
who modified the formulation to account for air entrapment. While relatively simple toimplement, the above model has sometimes suffered from a so-called pumping effect, when thehysteresis loops can move to physically unrealistic parts of the retention function. As analternative, we also incorporated in HYDRUS the hysteresis model of Lenhard et al. [1991] andLenhard and Parker [1992] that eliminates pumping by keeping track of historical reversal
points (Hysteresis in Retention Curve, no pumping, Bob Lenhard).
3.2.3. Water Flow Parameters
Parameters for the soil hydraulic models are specified in the Water Flow Parameters dialog
window (Fig. 19).
In all models (i.e., Brooks and Corey, 1964; van Genuchten, 1980; Vogel and Cislerova, 1988;
Kosugi, 1996, and Durner, 1994), θr (Qr) and θs (Qs) denote the residual and saturated watercontents, respectively; Ks (Ks) [LT-1] is the saturated hydraulic conductivity, and l is a poreconnectivity parameter. The parameters α (Alpha) [L-1] and n [-] are empirical coefficientsaffecting the shape of the hydraulic functions.
The modified van Genuchten model has four additional parameters: θa (Qa) – a water content
smaller or equal to θr, θm (Qm) – a water content larger or equal to θs, Kk (Kk) [LT-1] – theunsaturated hydraulic conductivity at water content θk, and θk (Qk) – the water content associatedwith Kk.

57

Figure 19. The Water Flow Parameters dialog window for direct (top) and inverse (bottom)
problems.
Durner’s [1994] model has three additional parameters: w2 (w2), α2 (Alpha2) [L-1], and n2 (n2),where w2 is the weighting factor for the second overlapping region, and α2 and n2 are empiricalparameters for the second region.
The hysteretic model also has three additional parameters: θsw (QsW) – the saturated watercontent of the main wetting branch, αw (AlphaW) [L-1] – the shape parameter of the main wetting
branch, and Ksw (KsW) [LT-1] - the saturated hydraulic conductivity associated with the main
wetting branch (in case hysteresis also occurs in the conductivity function).
Temperature Dependence: Check this box if the hydraulic properties are considered to betemperature-dependent. Using capillary theory, the influence of temperature on the soil waterpressure head is then quantitatively predicted from the influence of temperature on the surface
tension. The influence of temperature on the hydraulic conductivity is predicted from theinfluence of temperature on viscosity and the density of water.
Soil Catalog: The hydraulic parameters of selected soils were included in a catalog from whichusers can select. The van Genuchten parameters were taken from Carsel and Parrish [1988](Table 7), the Brooks and Corey parameters are from Rawls et al. [1982]. Rawls et al. (1982)
used multiple linear regression to estimate the Brooks and Corey parameters from a large
database of some 2540 soil horizons. Their regression equations were subsequently used by
Carsel and Parrish [1988], but the results were further manipulated statistically to get van
Genuchten parameters probability density functions (superficially, the van Genuchten parameters
are the same or closely related to the BC parameters, such as n=lambda+1). Hence the Carsel
and Parrish ([1988] parameters were statistically derived from the Rawls et al. [1982] estimates;
they were not fitted independently to the Rawls database. Some caution is needed when using
these parameter values since they only represent very approximate averages for different texturalclasses. The soil hydraulic parameters in the catalog for the Kosugi’s model were obtained byfitting retention curves generated using the Carsel and Parrish [1988] parameters for the van
Genuchten’s [1980] model using RETC.

58

The following soil textural classes are represented in the soil hydraulic catalog:
Sand
Loamy Sand
Sandy Loam
Loam
Silt Loam
Sandy Clay Loam
Clay Loam
Silty Clay Loam
Sandy Clay
Silty Clay
Clay
Neural Network Prediction: The program uses pedotransfer functions (PTFs) based on neuralnetworks [Schaap et al., 2001] to predict van Genuchten’s [1980] water retention parameters andthe saturated hydraulic conductivity (Ks) based on textural information (see Section 3.8 below).
When the parameter estimation option is selected, then users have to provide initial estimates of the
optimized soil hydraulic parameters, specify which parameters are to be optimized (checkappropriate checkboxes), and provide parameter constraints for the optimization. Entering zeros(the default values) for the minimum and maximum values signify that the parameters areunconstrained.

59

Table 7. Soil hydraulic parameters for the analytical functions of van Genuchten [1980] fortwelve textural classes of the USDA soil textural triangle, according to Carsel and Parrish[1988].
Textural class

Sand
Loamy Sand
Sandy Loam
Loam
Silt
Silty Loam
Sandy Clay Loam
Clay Loam
Silty Clay Loam
Sandy Clay
Silty Clay
Clay

θr

θs

α

[L3L-3][L3L-3][cm-1]n[-]Ks[cm d-1]

0.045
0.057
0.065
0.078
0.034
0.067
0.100
0.095
0.089
0.100
0.070
0.068

0.430
0.410
0.410
0.430
0.460
0.450
0.390
0.410
0.430
0.380
0.360
0.380

0.145
0.124
0.075
0.036
0.016
0.020
0.059
0.019
0.010
0.027
0.005
0.008

2.68
2.28
1.89
1.56
1.37
1.41
1.48
1.31
1.23
1.23
1.09
1.09

712.8
350.2
106.1
24.96
6.00
10.80
31.44
6.24
1.68
2.88
0.48
4.80

Table 8. Soil hydraulic parameters for the analytical functions of van Genuchten [1980] fortwelve textural classes of the USDA textural triangle as obtained with the Rosetta Lite program[Schaap et al., 2001].
Textural class

Sand
Loamy Sand
Sandy Loam
Loam
Silt
Silty Loam
Sandy Clay Loam
Clay Loam
Silty Clay Loam
Sandy Clay
Silty Clay
Clay

θr

θs

α

[L3L-3][L3L-3][cm-1]n[-]Ks[cm d-1]

0.053
0.049
0.039
0.061
0.050
0.065
0.063
0.079
0.090
0.117
0.111
0.098

0.375
0.390
0.387
0.399
0.489
0.439
0.384
0.442
0.482
0.385
0.481
0.459

0.035
0.035
0.027
0.011
0.007
0.005
0.021
0.016
0.008
0.033
0.016
0.015

3.18
1.75
1.45
1.47
1.68
1.66
1.33
1.41
1.52
1.21
1.32
1.25

643.
105.
38.2
12.0
43.7
18.3
13.2
8.18
11.1
11.4
9.61
14.8

60

Table 9. Soil hydraulic parameters for the analytical functions of Brooks and Corey [1964] fortwelve textural classes of the USDA soil textural triangle, according to Rawls et al. [1982].
Textural class

Sand
Loamy Sand
Sandy Loam
Loam
Silt
Silty Loam
Sandy Clay Loam
Clay Loam
Silty Clay Loam
Sandy Clay
Silty Clay
Clay

θr
3 -3

[L L ]θs
3 -3[L L ]

0.020
0.035
0.041
0.027
0.015
0.015
0.068
0.075
0.040
0.109
0.056
0.090

0.417
0.401
0.412
0.434
0.486
0.486
0.330
0.390
0.432
0.321
0.423
0.385

α
[cm ]

n
[-]

Ks
[cm d-1]

0.13800.11500.06820.08970.04820.04820.0356
0.03860.03070.03430.02920.0268

0.592
0.474
0.322
0.220
0.211
0.211
0.250
0.194
0.151
0.168
0.127
0.131

504.0
146.6
62.2
31.7
16.3
16.3
10.3
5.52
3.60
2.88
2.16
1.44

-1

Table 10. Soil hydraulic parameters for the analytical functions of Kosugi [1996] for twelve
textural classes of the USDA soil textural triangle.
Textural class

Sand
Loamy Sand
Sandy Loam
Loam
Silt
Silty Loam
Sandy Clay Loam
Clay Loam
Silty Clay Loam
Sandy Clay
Silty Clay
Clay

θr

θs

α

[L3L-3][L3L-3][cm-1]n[-]Ks[cm d-1]

0.045
0.057
0.065
0.078
0.034
0.067
0.100
0.095
0.089
0.100
0.070
0.068

0.430
0.410
0.410
0.430
0.460
0.450
0.390
0.410
0.430
0.380
0.360
0.380

303.7
12.47
27.42
101.8
510.6
325.9
80.89
666.3
2853.
1129.
140538.
103815.

0.383
0.950
1.26
1.80
2.48
2.30
2.04
2.81
3.26
3.41
4.49
4.67

712.8
350.2
106.1
24.96
6.00
10.80
31.44
6.24
1.68
2.88
0.48
4.80

Note that in Version 2, each material can have a name (e.g., Material 1, Sand, Clay). When soil
hydraulic parameters are assigned using the Soil Catalog, the names of textural classes willappear in the Name column. These names will then appear throughout the HYDRUS GUI, e.g.,
at the Edit Bar or in the Sort Property Object window.

61

3.2.4. Neural Network Predictions
The HYDRUS code was coupled with the Rosetta Lite DLL (Dynamically Linked Library) (Fig.
20), which was independently developed by Marcel Schaap at the U.S. Salinity Laboratory[Schaap et al., 2001]. Rosetta implements pedotransfer functions (PTFs), which predict van
Genuchten’s [1980] water retention parameters and the saturated hydraulic conductivity (Ks) in ahierarchical manner from soil textural class, the soil textural distribution, bulk density, and one
or two water retention points as input. Rosetta has its own help features containing all relevant
information and references. Rosetta provides soil hydraulic parameters for the analytical
functions of van Genuchten [1980] for twelve textural classes of the USDA textural triangle(Table 8).

Figure 20. The Rosetta Lite (Neural Network Predictions) dialog window.

62

3.2.5. Anisotropy in the Hydraulic Conductivity
For two-dimensional problems, users may need to specify the principal components of theanisotropy tensor, K1A and K2A, together with the angle ωa between the principal direction of K1A andthe x-axis of the global coordinate system for each element (Fig. 21).

Figure 21. The Edit Local Anisotropy dialog window for two-dimensional applications.
This has been simplified for three-dimensional problems where users can specify one or more
Tensors of Anisotropy (Fig. 22), which may be assigned to different parts of the transport domain.
The anisotropy tensor is defined by three principal components, K1A (ConAX), K2A (ConAY), andK3A (ConAZ), and six coefficients aij that represent the cosine of angles between the ith principal
direction of the tensor KA and the j-axis of the global coordinate system (i.e., Cos(X-x), Cos(Y-y),Cos(Z-y), Cos(X-y), Cos(X-z), Cos(Y-z)).

Figure 22. The Tensors of the Anisotropy dialog window.

63

3.2.6. Constraints on Hysteretic ModelIn this dialog window, users can constrain optimized parameters (in the inverse mode) for
problems involving hysteresis in the soil hydraulic properties. This dialog window is available
only when an Inverse Problem is solved and when hysteresis is considered.

Figure 23. The Constraints on Hysteresis Model dialog window.

643.3. Solute Transport Parameters3.3.1. Solute Transport - General
The basic information needed for defining the solute transport problem is entered in the Solute
Transport dialog window (Fig. 24). In this window, users specify the Space and Time
Weighting Schemes, the Iteration Criteria (for nonlinear problems), and additional Solute
Information such as mass units, pulse duration (if applicable), and a number of solutes.

Figure 24. The Solute Transport dialog window.
a) Time Weighting Scheme
The Time Weighting Scheme defines the temporal weighting coefficient, ε, used in the
numerical solution of the transport equation. The temporal weighting coefficient is equal to 0.0 foran explicit scheme, 0.5 for a Crank-Nicholson time-centered implicit scheme, and 1.0 for a fully
implicit scheme. The structure of the final set of linear equations [G] {c} = {g}, obtained after the
spatial and temporal discretization of the governing advection-dispersion equation, depends upon
the value of the temporal weighing factor, ε. The explicit (ε=0) and fully implicit (ε=1) schemes
require that the global matrix [G] and the vector {g} be evaluated at only one-time level (theprevious or current time level). The other two schemes require evaluation at both time levels. Also,65

the Crank-Nicholson and implicit schemes lead to an asymmetric banded matrix [G]. By contrast,
the explicit scheme (ε=0) leads to a diagonal matrix [G], which is much easier to solve (butgenerally requires much smaller time steps).
The Crank-Nicholson centered scheme is recommended in view of solution precision. The fully
implicit scheme also leads to numerical dispersion, but is better in avoiding numerical instabilities.
The explicit scheme is most prone to numerical instabilities with undesired oscillations (and iscurrently disabled).
b) Space Weighting Scheme
HYDRUS provides three options for the Space Weighting Scheme, i.e., the regular Galerkin
Finite Elements formulation, the Upstream Weighting Finite Elements formulation, and theGalerkin Finite Elements formulation with Artificial Dispersion.
While the Galerkin Finite Elements formulation is recommended in view of solution precision,
Upstream Weighting is provided as an option in HYDRUS to minimize some of the problems withnumerical oscillations when relatively steep concentration fronts are being simulated. For thispurpose, the second (flux) term of advective-dispersive equation is not weighted by regular linear
basis functions, but instead using nonlinear functions [Yeh and Tripathi, 1990]. The weighing
functions ensure that relatively more weight is placed on flow velocities of nodes located at the
upstream side of an element.
Additional Artificial Dispersion may also be added to stabilize the numerical solution and tolimit or avoid undesired oscillations in the Galerkin finite element results. Artificial dispersion isadded so that a Stability Criterion involving Pe.Cr (the product of the Peclet number and the
Courant number) [Perrochet and Berod, 1993] is satisfied. The recommended value for Pe.Cr is
2.0.
c) Solute Information
Number of Solutes

Number of solutes to be simulated simultaneously or involved in a
decay chain reaction.

Pulse Duration

Time duration of the concentration pulse. Concentrations (flux orresident) along all boundaries, for which no time-variableboundary conditions are specified, are then set equal to zero fortimes larger the "Pulse Duration". When the Fumigant option is
active, this variable is used instead to define Time of Tarp
Removal.

Mass Units

Units to be printed to the output files or displayed in various
graphs. Mass units have no effect on the calculations.
Concentration units, in general, should be given in [ML-3], where
M is Mass Units specified in the Solute Transport dialog window(Fig. 22), and L is Length Units specified in the Domain Typeand Units dialog window (Fig. 6). However, since theconcentration variable appears in each term of the governing solute66transport equations (Eq. 3.1 and 3.2 of the Technical Manual), it ispossible to use different length units than those used to definegeometry and fluxes (e.g., geometry may be specified in meters
while concentrations are given in mg/cm3). In such cases the solute
fluxes (cq) will then be in units of MLc-3LgT-1 where Lc is thelength unit (e.g., cm) used to define concentrations and Lg thelength unit defining geometry and fluxes (e.g., m). Similarly, thesolute mass (cθV) obtained by integrating solute over the transportdomain will be in units of MLc-3Lg2. Similar adjustments of units
need to be done for other variables that involve both concentrationand length units.
Stability Criterion

Product of the dimensionless Peclet and Courant numbers (Pe.Cr).
This criterion is used either to add artificial dispersion in theGalerkin Finite Elements with Artificial Dispersion scheme or tolimit the time step (leading to lower Courant numbers for a given
Peclet number) for the Galerkin Finite Elements scheme.

Use Tortuosity Factor

Check this box when molecular diffusion coefficients in the waterand gas phases are to be multiplied by a tortuosity factor according
to the formulation of either Millington and Quirk [1961] or
Moldrup et al. [1997, 2000].

Temperature Dependence Check this box if the solute transport and reaction parameters are
assumed to be temperature-dependent.
Water Content Dependence Check this box if the solute reaction parameters are assumed to bewater content dependent [Walker, 1974].
Attachment/Detachment

Check this box if the solute is assumed to be subject toattachment/detachment to/from the solid phase. This process isoften used in simulations of the transport of viruses, colloids, orbacteria.

Filtration Theory

Check this box if the attachment coefficient is to be calculated
from filtration theory.

Fumigant Module

Additional options related to fumigant transport (e.g., tarp removal,temperature-dependent tarp properties, an additional injection of
fumigants) can be used with this module.

d) Iteration Criteria
The advection-dispersion solute transport equation becomes nonlinear when nonlinear adsorption isconsidered. Similarly, as for the Richards equation, an iterative process must then be used to obtainsolutions of the global matrix equation at each new time step. During each iteration, a system of
linearized algebraic equations is derived and solved using either Gaussian elimination or the
conjugate gradient method. After inversion, the coefficients are re-evaluated using the initialsolution, and the new equations are again solved. This iterative process continues until a satisfactory
degree of convergence is obtained, i.e., until at all nodes the absolute change in concentration67

between two successive iterations becomes less than some concentration tolerance (defined in
HYDRUS as the sum of an Absolute Concentration Tolerance and the product of theconcentration and a Relative Concentration Tolerance (the recommended and default value is0.001)). The Maximum Number of Iterations allowed during a certain time step needs to be
specified (recommended value is 10). When the Maximum Number of Iterations is reachedthen the numerical solution is either (a) terminated for problems involving transient water flowor (b) restarted with a reduced time step for steady-state flow problems.
e) Initial Conditions
Initial Conditions can be specified either using liquid-phase concentrations in units of mass ofsolute [Mc] per volume of water [McLw-3] or using total concentrations in units of mass of soluteper volume of soil [McLs-3]. In the latter case, the liquid phase concentration is calculated fromthe total concentration depending on the distribution coefficients (e.g., Kd, or Henry’s constant)between different phases.
Rather than specifying directly the initial values of the nonequilibrium phase concentrations (e.g.,concentrations in the immobile water for the dual-porosity models or concentrations kineticallysorbed to the solid phase for the two-site sorption models, or for concentrations associated withthe solid phase for the attachment/detachment models), users can specify that the nonequilibriumphase concentrations are initially at equilibrium with the equilibrium phase concentrations. Initialconditions need to be then specified only for the liquid phase concentrations, and thenonequilibrium phase concentrations are calculated by HYDRUS.
The UNSATCHEM Module
When the UNSATCHEM module is used, basic information needed for defining solute transport
problem is entered in the Solute Transport dialog window displayed in Figure 25 (instead of
Figure 24, which is used for the standard solute transport module). In this window, users specify
again the Space and Time Weighting Schemes and additional Solute Information such as massunits. Note that all concentrations in the UNSATCHEM module are either in meq/L (in the liquid
phase) or meq/kg (in the solid phase) (meq=mmolc). The pulse duration is not used in
UNSATCHEM, and the number of solutes is fixed to 8 (i.e., the number of considered major
ions: Ca2+, Mg2+, Na+, K+, Alkalinity, SO42-, Cl-, and an independent tracer). The number ofsolution, adsorbed, and precipitated concentration combinations is specified when simulating thetransport of major ions in the UNSATCHEM module. This value represents the maximum
number of (solution, adsorbed, and precipitated) concentration combinations, which can be used
to specify the initial and boundary conditions.
Since there is currently no technical manual describing the two-dimensional version of the
UNSATCHEM module, users are referred to the HYDRUS-1D manual [Šimůnek et al., 2008],
which provides all relevant information about this module.

68Figure 25. The Solute Transport dialog window for the UNSATCHEM module.

693.3.2. Solute Transport Parameters
Soil and Solute Specific Transport Parameters are specified in the Solute TransportParameters dialog window (Fig. 26).

Figure 26. The Solute Transport Parameters dialog window.
The following Soil Specific Parameters (left part of the dialog window) are specified for eachsoil material:
Bulk.d.
Disp.L.
Disp.T.
Frac

ThImob

Bulk density, ρ [ML-3]
Longitudinal dispersivity, DL [L]Transverse dispersivity, DT [L]Dimensionless fraction of adsorption sites classified as type-1 sites, i.e., sites withinstantaneous sorption when the chemical nonequilibrium option is considered [-].
Set this parameter equal to 1 when equilibrium transport is considered. Frac
becomes the dimensionless fraction of adsorption sites in contact with mobile water
when the physical nonequilibrium option is considered [-]. In that case, Fracshould be set equal to 1 when all sorption sites are in contact with mobile water.
The immobile water content. Set equal to 0 when the physical nonequilibrium
option is not considered.

The following Solute Specific Parameters (right part of the dialog window) are specified foreach solute:
Diffus.W
Diffus.G

Molecular diffusion coefficient in free water, Dw [L2T-1]
Molecular diffusion coefficient in soil air, Da [L2T-1]

703.3.3. Solute Reaction Parameters
The Solute Reaction Parameters and concentrations for Boundary Conditions are specified in the
Solute Reaction Parameters dialog window (Fig. 27). Each solute has its own Solute Reaction
Parameters dialog window.

Figure 27. The Solute Reaction Parameters dialog window.
The following Solute Reaction Parameters are specified for each soil material:
Kd
Nu
Beta
Henry
SinkL1
SinkS1
SinkG1
SinkL1'
SinkS1'
SinkG1'
SinkW0
SinkS0SinkG0Alpha

Adsorption isotherm coefficient, ks [M-1L3]
Adsorption isotherm coefficient, η [M-1L3]
Adsorption isotherm exponent, β [-]Equilibrium distribution constant between liquid and gaseous phases, kg [-]First-order rate constant for dissolved phase, µw [T-1]
First-order rate constant for the solid phase, µs [T-1]
First-order rate constant for the gas phase, µg [T-1]
First-order rate constant for the dissolved phase, µw‘ [T-1], as part of a solutedecay chain
First-order rate constant for the solid phase, µs‘ [T-1], as part of a solute decay
chainFirst-order rate constant for the gas phase, µg‘ [T-1], as part of a solute decay
chain
Zero-order rate constant for the dissolved phase, γw [ML-3T-1]
Zero-order rate constant for the solid phase, γw [T-1]
Zero-order rate constant for the gas phase, γs [ML-3T-1]
First-order rate coefficient for one-site or two-site nonequilibrium adsorption,
mass transfer coefficient for solute exchange between mobile and immobile liquid
regions, ω [T-1]71When the Attachment/Detachment Model (Fig. 24) is used, then some parameters listed above
are replaced with different parameters needed for the attachment/detachment model:
D_Soil

iPsi2

iPsi1
SMax2
AttachSolid2
DetachSolid2
SMax1
AttachSolid1
DetachSolid1

Diameter of the sand grains, dc [L]. Note that HYDRUS allows only one value(for all materials) and that this value is used only in the Depth-dependent
blocking function (iPsi=4) developed by Bradford et al. [2002], which wasdeveloped for homogeneous laboratory column. It is less clear what value
should be used in multi-layered systems (for other than the first layer). Also,
note that this blocking function depends on a vertical spatial coordinate. Thismeans that one needs to specify the origin of the function, i.e., the inflow andinter-material interfaces. HYDRUS allows doing this for up to 2 materials using
the cBnd vector, as described in the help.
Type of blocking on the second sorption sites:= 0: No blocking.
= 1: Langmuirian dynamics.
= 2: Ripening.
= 3: random sequential adsorption model.
= 4: depth-dependent blocking coefficient.
Same for the first sorption sites.
Parameter in the blocking function for the second sorption sites (smax forblocking options (1), (2) and (3), and b for (4)).
First-order deposition (attachment) coefficient, ka [T-1], for the second sorption
sites.
First-order entrainment (detachment) coefficient, kd [T-1], for the second
sorption sites.
Parameter in the blocking function for the first sorption sites.
First-order deposition (attachment) coefficient, ka [T-1], for the first sorption
sites.
First-order entrainment (detachment) coefficient, kd [T-1], for the first sorption
sites.

When Filtration Theory (Fig. 24) is used to calculate the attachment coefficient, then thefollowing parameters must be entered instead:
D_SoilD_Virus
SMax2
Stick. Eff2
DetachSolid2
SMax1
Stick. Eff1
DetachSolid1

Diameter of the sand grains, dc [L].
Diameter of the particle, dp (e.g., virus, bacteria) (e.g., = 0.95 µm or 0.95e-6 m)[L].
Parameter in the blocking function for the second sorption sites (smax for model(1)).
Sticking efficiency, a [-], for the second sorption sites.
First-order entrainment (detachment) coefficient, kd [T-1], for the second
sorption sites.
Parameter in the blocking function for the first sorption sites.
Sticking efficiency, a [-], for the first sorption sites.
First-order entrainment (detachment) coefficient, kd [T-1], for the first sorption
sites.

72

Boundary Conditions:Concentrations for time-independent Boundary Conditions are also specified in this dialog
window.
cBnd1

Value of the concentration for the first time-independent boundary condition [ML-3].
Set equal to zero if no time-independent boundary condition is specified. The samefor cBnd2 through cBnd4

cRoot

Value of the concentration for the fifth time-independent boundary condition [ML3]. If water uptake is considered, then cRoot is automatically used for the maximum
concentration of water removed from the flow region by root water uptake. Whenzero is specified, then all solute is left behind in the soil, and only a solute-freesolution is being taken up. When the concentration is lower than cRoot, all soluteis taken up. When the concentration is higher than cRoot, the excess solute stays
behind. Set equal to zero if no fifth time-independent boundary condition and nosolute uptake by roots is considered.

cWell

Value of the concentration for the sixth time-independent boundary condition [ML3]. If internal sources are specified, then cWell is automatically used for theconcentration of water injected into the flow region through internal sources. Set
equal to zero if no sixth time-independent boundary condition and no internalsources are specified.

cBnd7

Concentration of the incoming fluid for a volatile type boundary condition at thesoil surface [ML-3]. Set equal to zero if no volatile boundary condition is specified.

cAtm

Concentration above the stagnant boundary layer, gatm [ML-3], for a volatile typeboundary condition. Set equal to zero if no volatile boundary condition is being
specified.

dThickness of the stagnant boundary layer, d [L], for a volatile type boundary
condition. Set equal to zero if no volatile boundary condition is being specified.

When the parameter estimation option is selected, users have to provide initial estimates of the
optimized solute transport parameters, specify which parameters are to be optimized (selectappropriate checkboxes), and provide parameter constraints for the optimization. Zero values forminimum and maximum values signify that the parameters are unconstrained. The Solute
Transport and Reaction Parameters dialog window for the inverse problem is not further shown
here.

73

Figure 28. The Solute Reaction Parameters dialog window for the UNSATCHEM module.

The UNSATCHEM Module
When the UNSATCHEM module is used, the Solute Reaction (and transport) Parameters are
specified in the Solute Reaction Parameters dialog window displayed in Figure 28 (instead of
Figure 27, used for the standard solute transport module). The following Soil SpecificParameters are specified for each soil material:
Bulk.d.
Dw
Disper.L.
Disper.T.
CEC
Calc.SA
Dol.SA
DOC
K[Ca/Mg]
K[Ca/Na]K[Ca/K]

Bulk density, ρ [ML-3]
Molecular diffusion coefficient in free water, Dw [L2T-1]
Longitudinal dispersivity, DL [L]Transverse dispersivity, DT [L]
Cation exchange capacity, CEC [meq/kg]
Calcite surface area [m2/dm3]
Dolomite surface area [m2/dm3]
Dissolved organic carbon [mmol/dm3]
Gapon constant for exchange of calcium and magnesium
Gapon constant for exchange of calcium and sodium
Gapon constant for exchange of calcium and potassium

74

3.3.4. Temperature Dependence of Solute Reaction Parameters
Several of the diffusion (Dw, Dg), zero-order production (γw, γs, γg), first-order degradation (µw’,µs’, µg’, µw, µs, and µg), and adsorption (ks, kg, β, η, ω) coefficients may be strongly dependent
upon temperature. HYDRUS assumes that this dependency can be expressed by the Arrhenius
equation [Stumm and Morgan, 1981]. This equation can be expressed in the general form
 E (T A - T A) 
aT = ar exp  a A Ar 
 R uT T r 
where ar and aT are values of the coefficient being considered at a reference absolute temperature
TrA and absolute temperature TA, respectively; Ru is the universal gas constant, and Ea [ML2T-2M-1]
is the activation energy of the particular reaction or process being modeled.
The activation energy characterizing the temperature dependence of the solute transport, andreaction parameters is entered in the dialog window shown in Figure 29.
When the Fumigant option is active, the fifth variable (normally reserved for the Frendlich
exponent) is used to enter the activation energy for the resistance of surface tarp.

Figure 29. The Temperature-Dependent Solute Transport and Reaction Parameters dialog
window.

75

3.3.5. Water Content Dependence of Solute Reaction Parameters
The water content dependence of degradation coefficients is implemented using a modified
equation of Walker [1974]:  θ B µ (θ ) = µr (θ r ) min 1,     θ r  
where µr is the values of a particular coefficient (rate constant) at the reference water content θr,µ is the value of this coefficient at the actual water content θ, and B is a solute dependent
parameter (usually 0.7). The reference water content, θr, which may be different for different soil
layers, is calculated from the reference pressure head, hr, which is considered to be constant for aparticular compound. The solute dependent exponent, B, and the reference pressure head, hr, areentered in the Water Content Dependent Solute Reaction Parameters dialog window shownin Figure 30.

Figure 30. The Water Content Dependent Solute Reaction Parameters dialog window.

76

3.3.6. Solution Compositions for the UNSATCHEM Module
The set of solution, adsorbed, and precipitated concentration combinations for the
UNSATCHEM module is specified in the Solution Compositions dialog window (Fig. 31).
These (solution, adsorbed, and precipitated) concentration combinations can be used to specify
the initial and boundary conditions. The number of solution, adsorbed, and precipitatedconcentration combinations is specified in the General Solute Transport Information window(Fig. 25). Solution Concentrations need to be specified for all major ions: Ca2+, Mg2+, Na+, K+,
Alkalinity, SO42-, Cl-, and an independent tracer; Adsorbed Concentrations for all cations: Ca2+,
Mg2+, Na+, and K+; and Precipitated Concentrations for all solids that UNSATCHEM canconsider: calcite, dolomite, gypsum, nesquohonite, hydromagnesite, and sepiolite. Solution
Concentrations need to be specified in meq/L (L = liter), and Adsorbed Concentrations andPrecipitated Concentrations in meq/kg (meq=mmolc).

Figure 31. The Solution Compositions dialog window for the UNSATCHEM module.

773.3.7. Chemical Parameters for the UNSATCHEM module.
The following chemical parameters and selections for the UNSATCHEM module are specified
in the Chemical Parameters dialog window (Fig. 32):
- Whether the kinetic or equilibrium model for the precipitation and dissolution of calcite
and dissolution of dolomite is to be used (the Kinetic Precipitation/Dissolution checkbox).
- Whether the silica content in the solution is to be calculated based on the solution pH, orwhether the effect of pH is to be neglected (the Silica in Solution (pH Dependency) checkbox).
- The Critical Ionic Strength, i.e., the ionic strength, below which the extended DebyeHückel equation is used to calculate ion activity coefficients. Pitzer virial-type equations
are used above this value.
- The Maximum Number of Iterations allowed during any time step between the solutetransport and chemical modules. When the maximum number of iterations is reached, thenthe code proceeds to the new time level. The recommended value (if the iterative approachis to be used; from our experience) is 5. Set equal to one if no iteration (we recommend thisnon-iterative approach) is required (this, in general, leads to significantly lower
computational time without significantly altering the results in most cases).
- Whether the hydraulic conductivity is to be modified depending on the solution chemistry
using the McNeal [1968] semi-empirical approach (the Conductivity Reduction due toChemistry check box).

Figure 32. The Chemical Parameters dialog window for the UNSATCHEM module.

783.3.8. Additional Fumigant Application
When the Fumigant Module is used and an option Additional Fumigant Application at aGiven Time is selected (Fig. 24), users can specify an additional application of a specified mass
(Mass of Applied Fumigant) of a chemical into a specified location of the transport domain(defined by x, y, and z coordinates; the y-coordinate is disabled for 2D applications) at a
specified time (Time of Additional Fumigant Application).

Figure 33. The Add Fumigant dialog window for the Fumigant module.

793.4. Heat Transport Parameters
The information needed for defining the heat transport problem is entered in the Heat Transportdialog window (Fig. 34). In this window, users specify Heat Transport Parameters andtemperatures for the Boundary Conditions.

Figure 34. The Heat Transport Parameters dialog window.

The following Heat Transport Parameters (bottom part of the dialog window) are specified foreach soil material:
Solid
Org.M.
Disp.L.
Disp.T.
b1
b2
b3
Cn
Co
Cw

Volume fraction of solid phase, θn [-]Volume fraction of organic matter, θo [-]Longitudinal thermal dispersivity, λL [L]Longitudinal thermal dispersivity, λT [L]
Coefficient b1 in the expression for the thermal conductivity function [W/L/K]
Coefficient b2 in the expression for the thermal conductivity function [W/L/K]
Coefficient b3 in the expression for the thermal conductivity function [W/L/K]
Volumetric heat capacity of the solid phase, Cn [J/L3/K]
Volumetric heat capacity of organic matter, Co [J/L3/K]
Volumetric heat capacity of the liquid phase, Cw [J/L3/K]

Boundary Conditions:80Temperatures for Boundary Conditions with time-independent boundary conditions are also
specified in this dialog window.
TBound1

Value of the temperature for the first time-independent boundary condition [K]. Set
equal to zero if no time-independent boundary condition is specified. The same for
TBound2 through TBound4

TWell

Value of the temperature for the sixth time-independent boundary condition [K]. If
internal sources are specified, then TWell is automatically used for the temperatureof water injected into the flow region from sources in the transport domain. Set
equal to zero if no sixth time-independent boundary condition and no internalsources are specified.

The boundary condition at the soil surface may be approximated using a sinus wave with the
maximum one hour after noon and the minimum one hour after midnight as follows:  t − 13  
T= T0 + A cos  2π   24  
where T0 is the average temperature at the soil surface [K], A is the Temperature Amplitude at
the soil surface [K], and p is the Time Interval for completion of one sine wave temperature(usually 1 day, the default value). The second part of the sine term is included to set the
maximum temperature at 1 p.m.
Default values for the parameters in the Thermal Conductivities of three textural classes (sand,loam, and clay) are provided by HYDRUS [Chung and Horton, 1987]. Default volumetric heat
capacities for the solid phase (1.92 MJ m-3K-1), organic matter (2.51 MJ m-3K-1), and liquid phase(4.18 MJ m-3K-1) are also given (Set Default Volumetric Heat Capacities).
When the parameter estimation option is selected, then users must provide initial estimates of the
optimized heat transport parameters, specify which parameters are to be optimized (checkappropriate checkboxes), and provide parameter constraints for the optimization. Zero values forthe minimum and maximum values signify that parameters are unconstrained. The Heat
Transport Parameters dialog window for the inverse problem is not further shown here.
Notice that thermal conductivity and volumetric heat capacity parameters have units of [Wm-1K1] and [Jm-3K-1], respectively. These units, when converted to basic SI units, are [ML-1T-2K-1] and[MLT-3K-1], respectively, and thus contain time to the negative second or third power, which needs
to be taken into account during any time conversion.

81

3.5. Root Uptake and Growth
3.5.1. Root Water Uptake Model
Users may select a particular Water Uptake Reduction Model and a Solute Stress Model in
the Root Water Uptake Model dialog window (Fig. 35).

Figure 35. The Root Water Uptake Model dialog window.

a) Water Uptake Reduction Model
Either a water stress response function suggested by Feddes et al. [1978] or an S-shaped function
suggested by van Genuchten [1985] can be used to reduce the potential root water uptake to theactual water uptake rate (Fig. 36). Root water uptake with compensation can be simulated when
the Critical Stress Index is smaller than one (see the Technical Manual; Šimůnek et al. [2010]).
b) Solute Stress Model
The effect of salinity stress on the root water uptake can be either neglected (No Solute Stress) or
considered using the Additive or Multiplicative models, i.e., salinity stress is either added towater stress, or uptake reduction due to water stress and salinity stress are multiplied. When themultiplicative model is used for salinity stress, one can use either the Threshold Model [Maas,
1990] or an S-Shaped Model [van Genuchten, 1985] (Fig. 37).
82c) Active Solute Uptake Model
Total root nutrient uptake is determined from the total of active (only in 2D) and passive
nutrient uptake. The partitioning between passive and active uptake is controlled by the a priori
defined concentration value cRoot (Fig. 27). Passive nutrient uptake is simulated by multiplying
root water uptake with the dissolved nutrient concentration, for soil solution concentration values
below cRoot. Passive nutrient uptake is thus zero when cRoot is equal to zero. One must
therefore specify the maximum allowed concentration, cRoot, in the passive root solute uptake
term. When zero is specified, all solute is left behind in the soil (there is no passive root solute
uptake), and only solute free solution is taken up. When the concentration is lower than cRoot,
all solute is taken up (unlimited passive root solute uptake). When the concentration is higher
than cRoot, additional solute stays behind.
As the Active Nutrient Uptake is obtained from the difference between plant nutrient demand(the Potential Solute Uptake Rate [ML-2T-1] needs to be specified) and Passive Nutrient
Uptake, the presented model thus implies that reduced passive nutrient uptake is compensatedfor by active nutrient uptake. Active nutrient uptake is simulated using Michaelis-Menten
kinetics (the Michaelis-Menten constant and a Minimum Concentration for Uptake need to
be specified). In addition, the proposed root uptake model includes compensation for active
nutrient uptake, in a similar way as used for root water uptake (using the Critical Stress Index).
Reduction in root water uptake will decrease passive nutrient uptake, thereby increasing active
nutrient uptake proportionally. In other words, total nutrient uptake is not affected by soil water
stress, as computed by the proportion of actual to potential root water uptake. This is not realistic
since one would expect that plant nutrient requirements will be reduced for water-stressed plants.
For that reason, the uptake model includes additional flexibility, by reducing the potential
nutrient demand (Potential Solute Uptake Rate), in proportion to the reduction of root water
uptake (see the last check box Reduce Potential Solute Uptake due to Reduced Water
Uptake).
Active solute uptake is implemented only for a single solute (not for multiple solutes). Details
about the root water and solute uptake can be found in the Technical Manual or Šimůnek andHopmans [2009].

83

3.5.2. Root Water Uptake Parameters
Parameters for the water and salinity stress response functions are specified in the Root Water
Uptake Parameters dialog window (Fig. 36 and Fig. 37, respectively).

Figure 36. The Root Water Uptake Parameters dialog window for the water stress response
function of Feddes et al. [1978] (left) and van Genuchten [1985] (right).
The Root Water Uptake Parameters for the water stress response function suggested by
Feddes et al. [1978] (Fig. 36, left) are described in detail in the HYDRUS technical manual.
Water uptake in this model is assumed to be zero close to saturation (i.e., wetter than somearbitrary “anaerobiosis point” P0). Root water uptake is also zero for pressure heads less (morenegative) than the wilting point (P3). Water uptake is considered optimal between pressure heads
Popt and P2, whereas for pressure heads between P2 and P3 (or P0 and Popt), water uptake
decreases (or increases) linearly with the pressure head. Root water uptake occurs at its optimalvalue even at full saturation, when both P0 and POpt are set equal to zero.
P0

Value of the pressure head [L] below which roots start to extract water from the soil.

POpt

Value of the pressure head [L] below which roots extract water at the maximum
possible rate.

P2H

Value of the limiting pressure head [L] below which roots cannot longer extract waterat the maximum rate (assuming a potential transpiration rate of r2H).

P2L

As P2H, but for a potential transpiration rate of r2L.

P3

Value of the pressure head [L] below which root water uptake ceases (usually taken at
the wilting point). P3 (to avoid numerical instabilities, similarly as for hCritA below)
should be selected so that the corresponding water content is at least 0.005 higher
than the residual water content.

r2H

Potential transpiration rate [LT-1] (currently set at 0.5 cm/day).

84

r2L

Potential transpiration rate [LT-1] (currently set at 0.1 cm/day).

The above input parameters permit one to make the variable P2 a function of the potential
transpiration rate, Tp (P2 presumably decreases at higher transpiration rates). HYDRUS currently
implements the same linear interpolation scheme as used in several versions of the SWATRE code(e.g., Wesseling and Brandyk, 1985). The interpolation scheme is defined in the manual.
A database of suggested values for different plants for the Feddes et al. [1978] model is provided
in HYDRUS based on studies by Wesseling [1991] and Taylor and Ashcroft [1972].
The Root Water Uptake Parameters for the S-shaped water stress response function, as
suggested by van Genuchten [1985] (Fig. 36, right) are as follows:
P50

The coefficient, h50, in the root water uptake response function associated with water
stress [L]. Root water uptake at this pressure head is reduced by 50%.

P3

The exponent, p3, in the root water uptake response function associated with water
stress [-]; its recommended and default value is 3.

We have additionally included a parameter PW, i.e., pressure head at the wilting point [L], below
which transpiration stops.

Figure 37. The Root Water Uptake Parameters dialog window for the solute stress response
function based on the threshold model (left) and S-shaped model of van Genuchten [1985] (right).
The Root Water Uptake Parameters for the Threshold Model [Maas, 1990] of the salinity
stress response function (multiplicative) (Fig. 37, left) are as follows:
Threshold Value of the minimum osmotic head [L] (the salinity threshold) above which root
water uptake occurs without a reduction.

85

SlopeSlope of the curve determining the fractional root water uptake decline per unit
increase in salinity below the threshold.

The Root Water Uptake Parameters for the S-Shaped Model [van Genuchten, 1985] of thesalinity stress response function (multiplicative) (Fig. 37, right) are as follows:P3

The exponent, p, in the root water uptake response function associated with salinity
stress [-]. The recommended value is 3.

c50

The coefficient, h50, in the root water uptake response function associated withsalinity stress [L]. Root water uptake at this osmotic head is reduced by 50%.

Both salinity stress response functions require a coefficient (Osmotic Coefficient) that transforms
concentrations into equivalent osmotic pressure heads (Fig. 37). The osmotic coefficients shouldbe negative for the additive model (to be added to negative pressure heads) and positive for themultiplicative model. Note that this conversion needs to be made mainly when one uses the
Additive Model. That is because then one needs to add pressure heads (i.e., units of m or cm)
and osmotic heads (calculated from concentrations, which likely have units of dS/m). If one uses
the Multiplicative Model, then one does not need to use this conversion and can keep Osm.
Coeff equal to one, since a) both water stress and salinity stress response functions can have theirown units, and b) both the Threshold Model parameters (specified above) and selectedconcentrations units are likely already the same (e.g., units of EC (dS/m)).
A database of suggested values for different plants for the threshold-slope salinity stress modelis provided based on the work by Maas [1990]. The database for the threshold model provides
suggested values based on the electric conductivity of the saturation extract ECe in dS/m. These
values are converted internally in the GUI into the electric conductivity of soil water (at the field
capacity) as follows: ECw ≈ ke * ECe, where ke is approximately 2 [Skaggs et al., 2006].
Consequently, the threshold value of Maas [1990] is multiplied by 2 (ke) and the slope is divided
by 2. A user is responsible for converting these values in the regular HYDRUS further to theosmotic pressure in the head units [L] or concentration units used in your project. For guidance,
see Eqs. 13.3 and 13.4 in Maas [1990].
The threshold-slope salinity stress model is implemented in the standard HYDRUS solutetransport model as R=1-0.01(c-cT)s, while in the UNSATCHEM module as R=1-0.01(hφ- hφT)s*,
where cT is the concentration threshold, hφT is the osmotic head threshold, s is the slope in
HYDRUS and s* is the slope in UNSATCHEM.

86

3.5.3. Root Distribution Parameters
The spatial distribution of the roots can be specified using the Root Distribution Parameters
dialog window (Fig. 38). The following two- and three-dimensional root distribution functions
are implemented in HYDRUS [Vrugt et al., 2001, 2002]:
 p

p



z
r

z 
x  − Zm z − z + X m x − x b ( x, z ) =
1 −
1 −
e
 Z m  X m 
*

 p

*

py

p



x
z

x 
y 
z  − X m x − x + Ym y − y + Z m z − z b ( x, y , z ) =1 −1 − 1 −e
 X m  Ym  Z m ***

Figure 38. The Root Distribution Parameters dialog window.
where Xm, Ym, and Zm are the maximum rooting lengths in the x-, y-, and z- directions [L],respectively; x, y, and z are distances from the origin of the plant (tree) in the x-, y-, and zdirections [L], respectively; px [-], py [-], pz [-], x* [L], y* [L], and z* [L] are empirical parameters(x*, y*, and z* are in Fig. 38 indicated as Depth of Maximum Intensity or Radius of Maximum
Intensity; parameters px, py, and pz are assumed to be equal to one for x> x*, y> y*, z> z*,
respectively [Vrugt et al., 2002]), and b(x,z) and b(x,y,z) denote two- and three-dimensional
spatial distribution of the potential root water uptake [-]. See Vrugt et al. [2001, 2002] fordifferent configurations of the normalized spatial distribution of potential root water uptake rate.

87

The equations above are given and used in absolute coordinates, i.e., they are independent of any
actual selection in GUI. The x and y coordinates are identical to x and y coordinates for thegeometry of the transport domain. The only exception is that the beginning of the z coordinate
for the root distribution starts at the highest located node of the entire transport domain (again
independent of any actual selection).
3.5.4. Root Growth Parameters
A simple root growth model with similar capabilities as in HYDRUS-1D was implemented into
Version 3 of HYDRUS (2D/3D) (its 2D version). The rooting depth, LR, can now be either
constant (the standard approach) or variable in time. Time-variable rooting depth values can beeither calculated using the classical Verhulst-Pearl logistic Growth Function (Fig 39, top) or
provided using a Table (Fig. 39, bottom). The user can select between three different root
distribution functions, which can be either described using the Vrugt et al. (2001, 2002) or
Hoffman and van Genuchten (1983) functions, or can be constant with depth (Shape of the Root
Zone). The roots can be distributed uniformly in the horizontal direction or can vary horizontallyas well (Horizontal Distribution). When Horizontal Distribution of roots is considered, users
have an option to specify multiple plants (Number of Plants), their location (Plant Position), andalso specify the lateral extent of roots (Half Width), which can again be either constant orvariable in time. When the Vrugt et al. (2001, 2002) function is used to describe vertical roots
distribution, it can be used to describe the horizontal distribution of roots as well. When Hoffman
and van Genuchten (1983) or constant functions are used, then the horizontal distribution isconstant as well.

88

Figure 39. The Root Growth Parameters specified either using the logistic growth function (top)or a table (bottom).
The Verhulst-Pearl logistic growth function, which may be used to describe the time-variablerooting depth, requires a parameter that characterizes the growth rate. The growth rate can becalculated either from the assumption that 50% of the rooting depth will be reached after 50% of
the growing season has elapsed (50% after 50% Growing Season) or from a given data point of
the rooting depth at a specified time (From Given Data). In the latter case, one data point on theroot growth curve (Time Root Data - Depth Root Data) has to be provided. The same growth
pattern can be repeated at a certain time period (Time Period) and for multiple plants.
When the Root Depth is Specified Using a Table, users have to provide a table with entries ofTime, the Depth of the rooting zone, and the Width of the rooting zone. The same pattern is used
for all plants (if multiple plant locations are specified). Rooting depths and widths are linearlyinterpolated between individual time entries.

893.6. Time Variable Boundary Conditions
The Time Variable Boundary Conditions dialog window is shown in Figure 40.

Figure 40. The Time Variable Boundary Conditions dialog window.
The following variables are specified in the Time Variable Boundary Conditions dialog
window:
Time

Time for which a data record is provided [T]. Boundary condition values are
specified for the time interval preceding time given at the same line. Thus, the BC
values specified in the first row are for the time interval between the initial time
and time specified on the same line.

PrecipPrecipitation rate [LT-1] (in absolute value) (applied to the atmospheric boundary).

Evap

Potential evaporation rate [LT-1] (in absolute value) (applied to the atmosphericboundary).

Trans

Potential transpiration rate [LT-1] (in absolute value).

hCritA

Absolute value of the minimum allowed pressure head at the soil surface [L](applied to the atmospheric boundary). hCritA (should be selected so that thecorresponding water content is at least 0.005 higher than the residual watercontent (to avoid numerical instabilities, especially for coarse-textured soils).

90

Var.Fl1

Drainage flux [LT-1] across the bottom boundary, or another time-dependentprescribed flux boundary condition (positive when the water leaves the flow
region); set to zero when no time-dependent flux boundary condition is specified.
Same for Var.Fl2, Var.Fl3, or Var.Fl4. The Var.Fl4 value is used for internal timevariable nodal flux sinks or sources (if they exist) (in such case, the units are [L2T-1]
or [L3T-1] for 2D or 3D applications, respectively).

Var.H-1

Groundwater level [L] (usually negative), or other time-dependent prescribed headboundary condition; set equal to zero when no time-dependent head boundary
condition is specified. Same for Var.H-2, Var.H-3, or Var.H-4. The Var. H-4 value
is used for internal time-variable nodal pressure head sinks or sources (if they exist).

TVal1

The first time-dependent temperature [K] that can be used for nodes with timevariable boundary conditions (atmospheric BC, variable head/flux BC) (is not
specified when heat transport or time-variable boundary conditions are notconsidered).

TVal2

The second time-dependent temperature [K] that can be used for nodes with timevariable boundary conditions (is not specified when heat transport or time-variableboundary conditions are not considered).

CVal1

The first time-dependent solute concentration [ML-3] that can be used for nodes
with prescribed time-variable boundary conditions (atmospheric BC, variable
head/flux BC) (not specified when solute transport is not considered). This column
should preferably be used only for the atmospheric boundary because theconcentration value is adjusted based on values of precipitation and evaporation
as follows: cVal1=Precip/(Precip-Evap)*cVal1. The cVal1 is adjusted to be zero
when Evap > Precip. Similar adjustments are not done for cVal2, and otherconcentration values.

CVal2

The second time-dependent solute concentration [ML-3] that can be used for nodes
with prescribed time-variable boundary conditions (atmospheric BC, variable
head/flux BC) (not specified when solute transport is not considered).

CVal3

The third time-dependent solute concentration [ML-3] that can be used for nodes
with prescribed time-variable boundary conditions (atmospheric BC, variable
head/flux BC) (not specified when solute transport is not considered).

The last three entries are entered for each solute.
The table in Figure 40 can be edited by manually adding or deleting lines. The table has a capacity
for about 32,000 records (depends on the number of columns). When a longer time record is to be
simulated, then one needs to directly edit the Atmosph.in input file in the working directory using
any standard software, such as MS Excel. The manually modified Atmosph.in file then needs tobe imported back into the HYDRUS project_name.h32d file using the command File->Import andExport->Import Input Data from *.In Files. Data for the Time Variable Boundary Conditions
can be prepared in any spreadsheet software and then copied into the table using Windows paste
hotkeys (i.e., Ctrl+V).
The total number of atmospheric data records is given in the Main Time Information dialog
window (Fig. 15).

91

Surface Area Associated with Transpiration: The total transpiration flux from a simulatedtransport domain is equal to the potential transpiration Tp (L/T) multiplied by the Surface
boundary Area (length in 2D) Associated with Transpiration (see Figure 2.2. of the Technical
Manual). It is usually the entire soil surface (usually the boundary area/length with anatmospheric boundary condition). By dissociating this value (i.e., the surface area associatedwith transpiration) from the surface boundary area/length of the transport domain, we provide
HYDRUS users with more flexibility in how to specify transpiration (e.g., for sparsely vegetatedsoil surface, or for row crops or trees). In any case, the definition of the Surface Area
Associated with Transpiration depends on how the potential transpiration, Tp, is calculated,which is usually done for the entire soil surface.
Linear Interpolation of Time Between the Initial and Final Time: When this option is
selected, the values in the first column will be linearly interpolated between the initial and final
times. For example, when the initial and final times are zero and 75 days, respectively, and there
are 75 records, the first column values will be increasing by 1 d (i.e., 1, 2, 3,…, 74, 75).

92

3.7. Constructed Wetlands
Two biokinetic model formulations can be chosen: (1) the biokinetic model as described in
CW2D [Langergraber and Šimůnek, 2005, 2006] and (2) the CWM1 (Constructed Wetland
Model #1) biokinetic model [Langergraber et al., 2009]. In CW2D aerobic and anoxictransformation and degradation processes for organic matter, nitrogen and phosphorus aredescribed, whereas in CWM1 aerobic, anoxic, and anaerobic processes for organic matter,
nitrogen, and sulfur. Comparisons between CW2D and CWM1 components and processes are
given in Tables 11 and 12, respectively. Details about both modules can be found in the abovereferenced literature.
Parameters for constructed wetlands are entered in the Constructed Wetland Model
Parameters I and II dialog windows for the CW2D (Fig. 41 and 43, respectively) and CWM1
(Fig. 42 and 44, respectively) modules.

Table 11. Comparison of CW2D and CWM1 components.
CW2D[Langergraber and Šimunek, 2005]
Components
1. SO: Dissolved oxygen, O2.
2. CR: Readily biodegradable soluble
COD.
3. CS: Slowly biodegradable soluble
COD.
4. CI: Inert soluble COD.
5. XH: Heterotrophic bacteria
6. XANs: Autotrophic ammonia-oxidizing
bacteria (Nitrosomonas spp.)
7. XANb: Autotrophic nitrite-oxidizing
bacteria (Nitrobacter spp.)
8. NH4N: Ammonium and ammonia
nitrogen.
9. NO2N: Nitrite nitrogen.
10. NO3N: Nitrate nitrogen.
11. N2: Elemental nitrogen.
12. PO4P: Phosphate phosphorus

CWM1[Langergraber et al., 2009]
Soluble components, S?
1. SO: Dissolved oxygen, O2.
2. SF: Fermentable, readily biodegradable soluble
COD.
3. SA: Fermentation products as acetate.
4. SI: Inert soluble COD.
5. SNH: Ammonium and ammonia nitrogen.
6. SNO: Nitrate and nitrite nitrogen.
7. SSO4: Sulphate sulfur.
8. SH2S: Dihydrogensulphide sulfur.
Particulate components, X?
9. XS: Slowly biodegradable particulate COD.
10. XI: Inert particulate COD.
11. XH: Heterotrophic bacteria.
12. XA: Autotrophic nitrifying bacteria.
13. XFB: Fermenting bacteria.
14. XAMB: Acetotrophic methanogenic bacteria.
15. XASRB: Acetotrophic sulfate-reducing bacteria.
16. XSOB: Sulphide oxidizing bacteria.

Organic nitrogen and organic phosphorus are
Organic nitrogen and organic phosphorus are modeled
modeled as part of the COD.
Nitrification is modeled as two-step process. as part of the COD.
Bacteria are assumed to be immobile.

93

Table 12. Comparison of CW2D and CWM1 processes.
CW2D[Langergraber and Šimunek, 2005]
Heterotrophic bacteria:
3. Hydrolysis: conversion
of CS into CR.
4. Aerobic growth of XH
on CR (mineralizationof organic matter).
5. Anoxic growth of XH
on CR (denitrification
on NO2N).
6. Anoxic growth of XH
on CR (denitrification
on NO3N).
7. Lysis of XH.
Autotrophic bacteria:
8. Aerobic growth of
XANs
on
SNH
(ammonium oxidation).
9. Lysis of XANs.
10. Aerobic growth of
XANb on SNH (nitriteoxidation).
11. Lysis of XANb.

CWM1[Langergraber et al., 2009]
Heterotrophic bacteria:
1. Hydrolysis: conversion of XS into SF.
2. Aerobic growth of XH on SF (mineralization oforganic matter).
3. Aerobic growth of XH on SA (mineralization oforganic matter).
4. Anoxic growth of XH on SF (denitrification).
5. Anoxic growth of XH on SA (denitrification).
6. Lysis of XH.
Autotrophic bacteria:
7. Aerobic growth of XA on SNH (nitrification).
8. Lysis of XA.
Fermenting bacteria:
9. Growth of XFB (fermentation).
10. Lysis of XFB.
Acetotrophic methanogenic bacteria:
11. Growth of XAMB: Anaerobic growth of acetotrophic,
methanogenic bacteria XAMB on acetate SA.
12. Lysis of XAMB.
Acetotrophic sulphate reducing bacteria:
13. Growth of XASRB: Anaerobic growth of acetotrophic,sulphate reducing bacteria.
14. Lysis of XASRB.
Sulphide oxidizing bacteria:
15. Aerobic growth of XSOB on SH2S: The opposite
process to process 13, the oxidation of SH2S to SSO4.
16. Anoxic growth of XSOB on SH2S: Similar to process
15 but under anoxic conditions.
17. Lysis of XSOB.

94

Figure 41. The Constructed Wetland Model (CW2D) Parameter I dialog window.

95

Table 13. Kinetic parameters in the CW2D biokinetic model [Langergraber and Šimůnek, 2005].
Description [unit]

Value
Hydrolysis
for 20°C (10°C)
Kh
hydrolysis rate constant [1/d]3 (2)KXsaturation/inhibition coefficient for hydrolysis [g CODCS/g CODBM] 0.1 (0.22)
Heterotrophic bacteria (aerobic growth)
the maximum aerobic growth rate on CR [1/d]
6 (3)
µH
bH
rate constant for lysis [1/d]0.4 (0.2)
Khet,O2
saturation/inhibition coefficient for SO [mg O2/L]
0.2
Khet,CR
saturation/inhibition coefficient for substrate [mg CODCR/L]
2
Khet,NH4N
saturation/inhibition coefficient for NH4 (nutrient) [mg N/L]
0.05
Khet,IPsaturation/inhibition coefficient for P [mg N/L]
0.01
Heterotrophic bacteria (denitrification)
the maximum aerobic growth rate on CR [1/d]4.8 (2.4)µDN
Khet,O2
saturation/inhibition coefficient for SO [mg O2/L]
0.2
Khet,NO3N
saturation/inhibition coefficient for NO3 [mg N/L]
0.5
Khet,NO2N
saturation/inhibition coefficient for NO2 [mg N/L]
0.5
Khet,CR
saturation/inhibition coefficient for substrate [mg CODCR/L]
4
Khet,NH4N
saturation/inhibition coefficient for NH4 (nutrient) [mg N/L]
0.05
Khet,IPsaturation/inhibition coefficient for P [mg N/L]
0.01
Ammonia oxidizing bacteria (Nitrosomonas spp.)
the maximum aerobic growth rate on SNH [1/d]0.9 (0.3)µANs
bANs
rate constant for lysis [1/d]0.15 (0.05)
KANs,O2
saturation/inhibition coefficient for SO [mg O2/L]
1
KANs,NH4N
saturation/inhibition coefficient for NH4 [mg N/L]
0.5
KANs,IPsaturation/inhibition coefficient for P [mg N/L]
0.01
Nitrite oxidizing bacteria (Nitrobacter spp.)
the maximum aerobic growth rate on SNH [1/d]1 (0.35)µANb
bANb
rate constant for lysis [1/d]0.15 (0.05)
KANb,O2
saturation/inhibition coefficient for SO [mg O2/L]
0.1
KANb,NO2N
saturation/inhibition coefficient for NO2 [mg N/L]
0.1
KANb,NH4N
saturation/inhibition coefficient for NH4 (nutrient) [mg N/L]
0.05
KANb,IPsaturation/inhibition coefficient for P [mg N/L]
0.01

96

Table 14. Kinetic parameters in the CWM1 biokinetic model [Langergraber et al., 2009].
Parameter
Hydrolysis
Kh
KX

Description [unit]

Value
for 20°C (10°C)
hydrolysis rate constant [1/d]3 (2)saturation/inhibition coefficient for hydrolysis [g CODSF/g CODBM] 0.1 (0.22)
correction factor for hydrolysis by fermenting bacteria [-]0.1
ηH
Heterotrophic bacteria (aerobic growth and denitrification)
the maximum aerobic growth rate on SF and SA [1/d]6 (3)µH
correction factor for denitrification by XH [-]
0.8
ηg
bH
rate constant for lysis [1/d]0.4 (0.2)
KOH
saturation/inhibition coefficient for SO [mg O2/L]
0.2
KSF
saturation/inhibition coefficient for SF [mg CODSF/L]
2
KSA
saturation/inhibition coefficient for SA [mg CODSA/L]
4
KNOH
saturation/inhibition coefficient for SNO [mg N/L]
0.5
KNHH
saturation/inhibition coefficient for SNH (nutrient) [mg N/L]
0.05
KH2SH
saturation/inhibition coefficient for SH2S [mg S/L]
140
Autotrophic bacteria
the maximum aerobic growth rate on SNH [1/d]1 (0.35)µA
bA
rate constant for lysis [1/d]0.15 (0.05)
KOA
saturation/inhibition coefficient for SO [mg O2/L]
1
KNHA
saturation/inhibition coefficient for SNH [mg N/L]
0.5 (5)
KH2SA
saturation/inhibition coefficient for SH2S [mg S/L]
140
Fermenting bacteria
the maximum aerobic growth rate for XFB [1/d]3 (1.5)µFB
bFB
rate constant for lysis [1/d]
0.02
KOFB
saturation/inhibition coefficient for SO [mg O2/L]
0.2
KSFB
saturation/inhibition coefficient for SF [mg CODSF/L]
28
KNOFB
saturation/inhibition coefficient for SNO [mg N/L]
0.5
KNHFB
saturation/inhibition coefficient for SNH (nutrient) [mg N/L]
0.01
KH2SFBsaturation/inhibition coefficient for SH2S [mg S/L]
140
Acetotrophic methanogenic bacteria
the maximum aerobic growth rate on for XAMB [1/d]
0.085
µAMB
bAMB
rate constant for lysis [1/d]
0.008
KOAMB
saturation/inhibition coefficient for SO [mg O2/L]
0.0002
KSAMB
saturation/inhibition coefficient for SA [mg CODSA/L]
56
KNOAMBsaturation/inhibition coefficient for SNO [mg N/L]
0.0005KNHAMBsaturation/inhibition coefficient for SNH (nutrient) [mg N/L]
0.01
KH2SAMBsaturation/inhibition coefficient for SH2S [mg S/L]
140
Acetotrophic sulfate-reducing bacteria
the maximum aerobic growth rate for XASRB [1/d]
0.18
µASRB
bASRB
rate constant for lysis [1/d]0.012
KOASRBsaturation/inhibition coefficient for SO [mg O2/L]
0.0002
KSASRBsaturation/inhibition coefficient for SA [mg CODSA/L]
24
KNOASRB
saturation/inhibition coefficient for SNO [mg N/L]
0.0005KNHASRB
saturation/inhibition coefficient for SNH (nutrient) [mg N/L]
0.01
KSOASRB
saturation/inhibition coefficient for SSO4 [mg S/L]
19
KH2SASRB
saturation/inhibition coefficient for SH2S [mg S/L]
140

97

Sulfide oxidizing bacteria
the maximum aerobic growth rate for XSOB [1/d]µSOB
correction factor for anoxic growth of XSOB [-]
ηSOB
bSOB
rate constant for lysis [1/d]
KOSOB
saturation/inhibition coefficient for SO [mg O2/L]
KNOSOBsaturation/inhibition coefficient for SNO [mg N/L]
KNHSOBsaturation/inhibition coefficient for SNH (nutrient) [mg N/L]
KSSOB
saturation/inhibition coefficient for SH2S [mg S/L]

5.28
0.8
0.15
0.2
0.5
0.05
0.24

Figure 42. The Constructed Wetland Model (CWM1) Parameter I dialog window.

98Figure 43. The Constructed Wetland Model (CW2D) Parameter II dialog window.

99

Table 15. Temperature dependencies, stoichiometric parameters, composition parameters, andparameters describing oxygen transfer in the CW2D biokinetic model [Langergraber andŠimunek, 2005].
Parameter
Description [unit]
Temperature dependences (activation energy [J/mol] for Arrhenius equation)
Tdep_het
activation energy for processes caused by XH [J/mol]
Tdep_aut
activation energy for processes caused by XA [J/mol]
Tdep_Kh
activation energy Hydrolyses [J/mol]
Tdep_KX
activation energy factor KX for hydrolyses [J/mol]
Tdep_KNHA
activation energy for factor KNHA for nitrification [J/mol]Stoichiometric parameters
fHyd,CI
production of CI in hydrolysis
fBM,CRa fraction of CR generated in biomass lysis
fBM,CIa fraction of CI generated in biomass lysis
YHetyield coefficient for XH
YANs
yield coefficient for XANs
YANb
yield coefficient for XANb
Composition parameters
iN,CR
N content of CR [g N/g CODCR]
iN,CS
N content of CS [g N/g CODCS]
iN,CIN content of CI [g N/g CODCI]iN,BMN content of biomass [g N/g CODBM]
iP,CRP content of CR [g P/g CODCR]
iP,CS
P content of CS [g P/g CODCS]
iP,CIP content of CI [g P/g CODCI]iP,BMP content of biomass [g P/g CODBM]OxygencO2_sat_20
saturation concentration of oxygen [g/m³]
Tdep_cO2_sat
activation energy for saturation concentration of oxygen [J/mol]
rate_O2
re-aeration rate [1/d]

100

Value
47800
69000
28000
-53000-160000
0.0
0.1
0.02
0.63
0.24
0.24
0.03
0.04
0.01
0.07
0.01
0.01
0.01
0.02
9.18
-15000240

Figure 44. The Constructed Wetland Model (CWM1) Parameter II dialog window.

101

Table 16. Temperature dependencies, stoichiometric parameters, composition parameters, andparameters describing oxygen transfer in the CWM1 biokinetic model [Langergraber et al.,2009].
Parameter
Description [unit]
Temperature dependences (activation energy [J/mol] for Arrhenius equation)
Tdep_HyKh
activation energy Hydrolyses [J/mol]
Tdep_HyKX
activation energy factor KX for hydrolyses [J/mol]
Tdep_H
activation energy for processes caused by XH [J/mol]
Tdep_A
activation energy for processes caused by XA [J/mol]
Tdep_KNHA
activation energy for factor KNHA for nitrification [J/mol]
Tdep_mueFB
activation energy for XFB growth [J/mol]
Tdep_bFB
activation energy for XFB lysis [J/mol]
Tdep_AMB
activation energy for processes caused by XAMB [J/mol]
Tdep_ASRB
activation energy for processes caused by XASRB [J/mol]
Tdep_SOB
activation energy for processes caused by XSOB [J/mol]Stoichiometric parameters
fHyd,SI
production of SI in the hydrolysis
fBM,SFa fraction of SF generated in biomass lysis
fBM,XIa fraction of XI generated in biomass lysis
YH
yield coefficient for XH
YA
yield coefficient for XA
YFB
yield coefficient for XFB
YAMB
yield coefficient for XAMBYASRByield coefficient for XASRBYSOByield coefficient for XSOBComposition parameters
iN,SF
N content of SF [g N/g CODSF]
iN,SI
N content of SI [g N/g CODSI]iN,XSN content of XS [g N/g CODXS]iN,XIN content of XI [g N/g CODXI]iN,BMN content of biomass [g N/g CODBM]OxygencO2_sat_20
saturation concentration of oxygen [g/m³]
Tdep_cO2_sat
activation energy for saturation concentration of oxygen [J/mol]
rate_O2
re-aeration rate [1/d]

102

Value
28000
-5440047800
75800-160000
47800
0
0
0
0
0.0
0.05
0.1
0.63
0.24
0.053
0.032
0.05
0.12
0.03
0.01
0.04
0.03
0.07
9.18
-15000240

3.8. The Slope Stability Modules
3.8.1. The Slope Classic Module
The add-on Slope Stability module (Fig. 45) can be activated in the Main Processes window(Fig. 12) and is available only for projects with the domain type "2D-General" (see Section 2).
Once the module is active, related commands can be found in the main menu (Modules -> Slope
Stability) or in the Navigator data tree (item Slope Stability). A detailed description of themodule is available in the separate help and/or User's manual of the Slope Stability module.
The Slope Stability module (Fig. 45) is intended to be used mainly for stability checks ofembankments, dams, earth cuts, and anchored sheeting structures. The influence of water ismodeled using the distribution of pore pressure, which is imported automatically from the
HYDRUS results for specified times. Each time step of water distribution can be analyzed
separately. The slip surface is considered as circular (and evaluated using the Bishop,
Fellenius/Petterson, Morgenstern-Price, or the Spencer method). Hydrus installation program
contains several examples for calculating slope stability, which are located in the Slope Stability
Project Group (see Project Manager).

Figure 45. The main window of the Slope Stability Module.

103

The main features of the Slope Stability module include:
•
•
•
•
•
•
•
•

Presence of water modeled by pore pressure imported from HYDRUS results
An arbitrary number of surcharges (strip, trapezoidal, concentrated loading)An arbitrary number of anchors
Simple modeling of rigid bodies
Earthquake effects
Geo-reinforcement may be included
Analysis according to the safety factor
Analyses methods - Bishop, Fellenius/Petterson, Spencer, Morgenstern-Price

The basic input parameters of the Slope Stability module, such as basic Soil Characteristics,
Water Influence, and the Factor of Safety, are specified in the Slope Stability Parameters
window (Fig. 46). All additional parameters (such as for Earthquake, Anchors, Reinforcements,
Surcharge, and Analysis options) are specified directly in the Slope Stability module.

Figure 46. The Slope Stability Parameters dialog window.

Additional parameters (Soil Characteristics) needed for the calculations of slope stability slope
are specified here for all materials used in HYDRUS. Parameters for each particular material canbe selected from the catalog using the "Select from Catalogue" button or can be defined
individually. Also, a Safety Factor, for which slope stability is considered satisfactory, is given
here. The value of the Safety Factor must be in the interval of (1; 5).

104

The global parameters for the Slope Stability module are set in the Default Parameters for
Slope Stability Module dialog window (Fig. 47). These parameters are not specific for one
particular project, but are the default parameters that are used in new projects dealing with slope
stability. In addition to the default values for the Safety Factor and the Influence of Water, it isalso possible to edit here the Catalog of Soil Characteristics. The initial soil catalog is based on
the Hydrus soil catalog (using the classification based on the USDA textural triangle). Users canchange the names of materials and their parameters and can also extend (or reduce) this catalog
using New (or Delete) commands. They can also reorganize soil textures in the catalog using thecommands Up and Down. Soil Characteristics, as defined in this catalog, can then be
automatically assigned in new projects to materials taken from HYDRUS on the basis ofmatching their material names (see the check box Assign soil characteristics ...).

Figure 47. The Default Parameters for Slope Stability Module dialog window.

The command Printout Report and Results (Fig. 48) produces a standard Report thatsummarizes results obtained by the Slope Stability module. Users can then edit and modify thisreport.

105

Figure 48. An example of the Print and Export document generated by the Slope Stability
module.

1063.8.2. The Slope Cube Module
The Slope Cube (Slope Stress and Stability) module (added in version 2.04) was developed by
the Soil Water Retention, LLC as a supplemental module of the HYDRUS (2D) software
package to simulate two-dimensional transient fields of soil moisture, soil suction, suction stress,
total and effective stresses, and local factor of safety. While the SLOPE Stability module isbased on classical and engineering soil mechanics theories and uses the effective stress approach
only for saturated conditions, a new add-on module "SLOPE Cube" (Slope Stress and Stability),
recently developed in cooperation with Dr. Ning Lu from the Colorado School of Mines, uses aunified, effective stress approach for both saturated and unsaturated conditions [Lu et al., 2010].
The module is intended to predict spatially and temporally infiltration-induced landslide
initiation and to carry out the slope stability analysis under variably-saturated soil conditions.
Transient moisture and suction fields are directly obtained using the HYDRUS-2D model andare used to compute the effective stress field in hillslopes [Lu and Godt, 2013]. Furthermore,
instead of the methodology of one-factor safety for the entire slope in the classical slope stability
analysis, the SLOPE Cube module computes the field of the factor of safety in the entire
domain within hillslopes [Lu et al., 2012], allowing identification of the development of potential
failure surface zone or surface.

Figure 49. Illustration of the physical processes in the SLOPE Cube module.
Slope Cube is a physically-based hydro-mechanical framework focusing on assessment andprediction of the initiation and locations of landslide occurrences under rainfall conditions. Slope
Cube couples variably-saturated flow and stress fields to simulate transient hillslope hydrologic
and mechanical responses to rainfall events (Fig. 49). Two recent advancements are implemented
in Slope Cube that are beyond the traditional, physically based landslide models. The first is theutilization of the suction stress-based effective stress to unify the description of effective stress
distribution in hillslopes under variably-saturated conditions. The second is to employ a recently
established concept of the local factor of safety to capture the evolution of stress paths toward thefailure state in hillslopes.
107Figure 50. The Slope Cube Parameters dialog window.
The inputs for the Slope Cube module are entered in the Slope Cube Parameter dialog window (Fig.
50). Here is the link to the Slope Cube Manual [Lu et al., 2016]. Examples of selected outputs(maximum and minimum effective stresses, suction stress, and local factor of safety; otherparameters not shown here are maximum and minimum total stresses) from the Slope Cube
module are given in Figure 51.

Figure 51. Examples of selected outputs (maximum and minimum effective stresses, suction
stress, and local factor of safety) from the Slope Cube module.

1084. Geometry of the Transport Domain
The transport domain may be defined using relatively simple two-dimensional rectangular (Fig.
10) or three-dimensional hexahedral (Fig. 11) objects. In that case, the dimensions and otherparameters of the transport domain are specified numerically using either the Rectangular (Fig.
10) or Hexahedral Domain Definition (Fig. 11) dialog windows. In both of these cases, thetransport domain is discretized into a structured finite element mesh. Alternatively, a more general
two-dimensional geometry can be defined from basic boundary objects, such as points, lines,
splines, polylines, arcs and/or circles. Boundary curves can consist of any combination of polylines,
arcs, circles, or cubical splines. The program permits one to specify internal boundaries (e.g., drains,
wells, impermeable objects), as well as internal curves. A user can define from these boundary
objects either a two-dimensional transport domain, the base plane (base surface) of the threedimensional layered domain, or multiple surfaces that can then define the three-dimensional
general domain. In the former two cases, the two-dimensional transport domain or the base planeof the three-dimensional domain is discretized into an unstructured finite element mesh.

4.1. Boundary Objects
The computational domain (the two-dimensional transport domain or the base surface of thethree-dimensional domain) is formed by an arbitrary number of mutually nonintersecting curves.
Each curve can be formed by connecting an arbitrary number of objects. Objects are defined bynodes, the positions of which can be specified either graphically with the mouse withpossibilities to use grid alignment (Fig. 174) or by numerically defining their coordinates X, Y,
and Z. It is also possible to read in the objects with a large number of nodes (spline, polyline)from a file containing the x-(, y-,) and z-coordinates for each node using the command Insert>Domain Geometry->Points->Read from File …. The order of inputting particular objects isarbitrary; the code automatically forms the desired curves. In order to have a physically realistic
domain, only one closed outer curve can exist (for multicomponent domains, such a curve must
exist for each component of the domain). The domain can have an arbitrary number of holes orinternal curves. The consistency of the geometry can be verified at any time using the command
Check Data Consistency (Tools Menu). Any change in geometry can be undone using theundo command (up to ten levels backward in time) or redone using the redo command (again up
to 10 levels).
An object type (e.g., polyline, spline, arc, or circle) must be selected first when designing a new
object from the Edit Bar on the right side of the view window or from the menu (e.g., Insert>Domain Geometry->Nodes). Then points defining a particular object should be entered. The
manner in which nodes are entered depends on the selected input style. When entering datagraphically, an appropriate Work Plane (x-y y-z, x-z) and a grid with appropriately set
parameters (Fig. 174 and Section 8.1.2) can be used to facilitate the input, while the coordinates
X, Y, and Z of the cursor are continuously displayed in the bottom right corner of the window.
It is possible to edit existing objects by double-clicking on a particular object. The current
selection, displayed in yellow, may be modified (edited) using the following operations: delete,copy (Fig. 62), move (Fig. 62), rotate (Fig. 63, left), and mirror (Fig. 63, right). Note that, in109

addition to objects, particular nodes of an object can belong to a selected set as well, in whichcase the edit operations are carried out also for these points. Editing of selected objects (e.g.,
moving objects) also depends on the currently selected input style. The objects are moved withthe cursor when the graphical mode is selected, while in numerical mode, a vector of translation(X, Y, and Z) must be specified. It is possible to directly edit nodes of objects with the commands
insert point (Fig. 54), delete point, and/or move point.
Before saving the data, an option is always displayed whether or not to verify the consistency of
the geometry. We strongly recommend to regularly perform this test in order to prevent errors in
subsequent calculations, e.g., during mesh generation.

Table 17. Definition of terms related to geometry design.
Objects
Objects are basic elements for building a geometric model of the computational domain and for
defining other properties of the computational problem. Objects are divided into several
categories (e.g., Geometry, FE-mesh, or Auxiliary), with each category containing several fields
of objects of the same type. The shape (boundary) of the computational domain is defined using
Geometric objects. Basic types of geometric objects are:- points- curves (polylines, arcs, circles, splines)- surfaces- openings- thickness vectors- solids
Points
A point is a basic geometric object which is used to define Curves and other objects. A point
location is defined using two or three coordinates depending on the dimensions of a particular
problem.
Curves
A curve is a set consisting of a finite number of objects connected by boundary nodes. Except at
point nodes, objects cannot intersect with each other or themselves. A curve can be open or
closed.
Outer Boundary Curves
An outer boundary curve is a boundary curve with the following properties: the curve is closed,
positively oriented (i.e., in a counter-clockwise direction), does not intersect any other curve or
itself, and has the computational domain (surface) located on its left side (in the sense of positiveorientation), while the right side is not part of a computational domain.
Internal Curves110

An internal curve must be located entirely within the computational domain. It can touch (but notintersect) the outside boundary of the computational domain at its definition points. An internal
curve can be open or closed, and can intersect itself, provided the intersect occurs at a definition
point of the internal curve.
Openings
An opening is defined by one or more boundary curves that form a closed boundary.
Lines
Lines and polylines are the most commonly used objects for describing boundaries of a domain
or internal curves. Lines are defined by two points specifying their beginning and end. Several
lines can be connected to form “polylines” by connecting the beginning and end of twoneighboring lines. Nodes cannot coincide, while lines cannot intersect with each other.
Arcs
An arc can be defined either by a) three points on its circumference, b) a center, a radius, twoangles (starting and final angle) and its orientation, and c) two points, a center, and a radius.
CirclesA circle can be defined either by a center and a radius, or by three different points.
SurfaceA surface (the computational domain of two-dimensional applications) is defined by a finite
number of continuous disjunctive bounded two-dimensional subdomains (Fig. 52). This meansthat the domain can be multicomponent, but that each of its components must have only one
outer boundary curve. The domain can contain any finite number of internal holes or internal
curves. Surfaces can be either planar surfaces (defined in a single plane) or curved surfaces(e.g., Quadrangle, Rotary, Pipe, or B-Spline). The base surface is a two-dimensional planar
surface that can be extended into a three-dimensional solid (the computational domain of
three-dimensional applications) using thickness vectors.
Thickness Vectors
The term thickness vector is used for a vector perpendicular to the base surface that extends theBase Surface to form a solid (three-dimensional computational domain).
Solids
The term solid represents a three-dimensional computational domain that is formed either by
the base surface and thickness vectors (3D-Layered Solids), or boundary surfaces (3DGeneral Solids), which can be either planar or curved (e.g., Quadrangle, Rotary, Pipe, or BSpline).
Computational Domain
A Computational Domain is a continuous part of a two- or three-dimensional space for whichwater flow or solute transport is simulated. The Domain Geometry term relates to the shape of
this space. The Domain Geometry can be defined for simple cases using parameters (using a
Generalized Rectangle in 2D projects or a Generalized Hexahedral in 3D projects) and for111

general cases using boundaries (boundary curves for two-dimensional domains and boundary
surfaces for three-dimensional domains).
In the 3D-Standard version, the Geometry is defined using the Base Surface, which is a 2D
domain of an arbitrary shape, and a set of Thickness Vectors that define the variable thicknessof the 3D domain or thicknesses of an arbitrary number of Geo-Layers (the term Sublayers wasused in version 1, and is used alternatively in the text below). Such a domain is then called the
3D-Layered domain. Although such domains cannot be fully general, they allow the definitionof a majority of realistic 3D problems. In the 3D-Professional version, the Geometry is definedusing three-dimensional objects (Solids, bodies) of general shapes, which are formed byboundary surfaces, which can be either planar or curved.
A Computation domain can be formed using several surfaces that can touch each other, butcannot overlap (Fig. 52). It is possible to create an opening in the base surface and then enter
another surface into it. The division of the transport domain into individual surfaces enables
easier work with it. The program creates for each surface its own section, and users can thenspecify different domain properties and initial and boundary conditions on these sections.

Figure 52. A base surface showing several basic geometric objects.

4.1.1. Points
Points can be either used to define Boundary Objects or can be located inside of the Surface(computational domain) and not be associated with any boundary object (Single Points). Points
can be entered either graphically using a cursor (most common) or using the New Point dialog
window (identical to the General Tab of the New Point dialog, Fig. 54). To enter a new pointgraphically, select the command Insert->Domain Geometry->Point->Graphically from the112menu, or Points from the Insert Object part of the Domain Geometry version of the Tool Bar
at the right side of the View Window, and then enter the points using a cursor.
Once a command for defining a new point graphically is selected, a cursor in the View window
will become a cross with a small empty circle in the middle. The coordinates of the location of
the cursor will be displayed next to the cursor and on the Edit Bar, which will automaticallychange to the one displayed in Figure 53 (left). The Edit Bar will also show, which point (itsnumber) is being defined and what reference coordinate system (the current coordinate system or
the grid origin) is used. The process of defining new points is ended by pressing the Esc
keyboard button, the right mouse button (see the Help part of the Edit Bar), or clicking the Stop
button on the Edit Bar.

Figure 53. The Edit Bar during the process of defining a new point (left) and a new line (right)
graphically.
Double-clicking on an existing point will recall the Edit Point dialog window (Fig. 54). In
addition to the General Tab (Fig. 54, left) in the New Point dialog window, the Edit Point
dialog window also has the FE-Mesh Tab (Fig. 54, right). Coordinates of a point and its number
are entered in the General Tab, while the FE-Mesh Refinement at a given point can be definedin the FE-Mesh Tab.

113

Figure 54. The Edit Point dialog window.

Although Cartesian Coordinates are usually used, it is possible to use also other coordinate
systems:
Coordinate Systems in 3D Projects

Coordinate Systems in 2D Projects

•
•
•
•
•

•
•

Cartesian
X-cylindricalY-cylindrical
Z-cylindrical
Spherical

Cartesian
Polar

Reference Point: Point coordinates are usually related to the defined origin of the coordinate
system. They can nevertheless be also related to another existing point, whose index is specified
in the box Reference Point No. Locations of all related points are automatically adjusted when
the location of the reference point is changed. The dependence of points on the Reference Pointis, however, canceled during more complex operations, such as Copy, Rotate, or Drag and Drop.
The coordinates of such points are then recalculated using the absolute Cartesian coordinate
system.
Point Type: Current version of HYDRUS recognizes two types of points:•

Standard – These are regular points defined using two or three coordinates.

•

Parametric – These points are located on a curve. Their location is calculated using a
specified parameter from the interval (0.1), where 0 and 1 represent the beginning andend of the curve, respectively. For example, a point with a parametric coordinate t=0.5
is located exactly in the middle of the curve. A parametric point is not a defining pointof a curve; i.e., it does not define its shape. On the contrary, the shape of a curve
defines the location of a parametric point. A Parametric Point can be redefined as a114

Standard Point in the Edit Point dialog window (Fig. 54). Parametric Points canbe added on a curve using the command Insert Points on Line on the Edit Bar, using
the menu command Tools ->Insert Points On Line->Graphically, or by clicking on a
curve with the right mouse button and selecting the Insert Points On Line>Graphically from the popup menu (Fig. 55). Either the parametric coordinate of apoint or its distance from boundary points (L) of a curve is displayed on the Edit Bar
when specifying a Parametric Point.

Figure 55. Different ways of adding Parametric Points on a curve.

4.1.2. Lines and Polylines
Lines and Polylines are the most commonly used objects for describing the boundaries of a twodimensional domain and its internal curves. Similarly, as above for Points, Lines and Polylines
can be entered either graphically using a cursor (most common) or using the New Line dialog
window (identical to the General Tab of the Edit Line dialog, Fig. 56). When entering a new115

line graphically, users can select the command Insert->Domain Geometry->Line(Polyline)>Graphically from the menu, or Line - Abscissa or Line - Polyline from the Insert Object partof the Domain Geometry version of the Tool Bar at the right side of the View Window andthen enter the lines using a cursor.
Once a command for defining a New Line (a single abscissa) or a New Polyline is selected, acursor in the View window will become a cross with a small empty circle in the middle. The
coordinates of the location of the cursor will be displayed next to the cursor and on the Edit Bar,
which will automatically change to the one displayed in Figure 53 (right). The Edit Bar will also
show which point and curve (their numbers) are being defined and what reference coordinate
system (the current coordinate system, the grid origin, or the last inserted point) is used. Once asingle Line is specified (for a new line), one can immediately continue in specifying the second
one, while the last point of the first line will be the beginning point of the second line. Eachabscissa is considered to be a single curve. When a New Polyline is being created, the entire
polyline is considered to be a single curve. The process of defining new lines is ended bypressing the Esc keyboard button, the right mouse button (see the Help part of the Edit Bar), or
clicking the Stop button on the Edit Bar.
Double-clicking on an existing line will recall the Edit Line dialog window (Fig. 56). Before
using the New Line dialog window, a user needs to first define points that are then used to define
the line. In addition to the General Tab (Fig. 56, left) in the New Line dialog window, the Edit
Curve dialog window also has the FE-Mesh Tab (Fig. 56, right). Points defining the line areentered in the General Tab, while the FE-Mesh Refinement along a given line can be definedin the FE-Mesh Tab.

Figure 56. The Edit Curve dialog window.

4.1.3. Arcs and Circles
An arc is part of a circle. An object arc is always internally defined using three definition points.
However, to simplify its specification, it is possible to define an arc graphically in multiple ways
using: a) three points on its circumference, b) a center, a radius, two angles (starting and final
angle) and its orientation, or c) by two points, a center, and a radius. Again, arcs can be entered116

either graphically using a cursor (most common) or using the New Line dialog window (Fig. 58).
When entering a new arc or circle graphically, a user must select the command Insert->Domain
Geometry->Arc->Graphically from the menu, or one of the following commands (a) Arc by 3
Points, b) Arc by 2 Points and R, or c) Arc by Center, R, and Angle) from the Insert Object
part of the Domain Geometry version of the Tool Bar at the right side of the View Window
and then enters arc using a cursor.
The graphical definition of Arcs and Circles is rather similar to the definition of Points andLines. Differences occur when Radii or Angles are used to define these objects. For example,
when a user defines Arc by 2 Points and Radius, he/she first needs to define the two points,
after which both the cursor and the Edit Bar change (Fig. 57, left) for the definition of the third
type of information defining the arc. This can be a radius, an internal angle, or a height. The
selection can be made on the Edit Bar that also displays the magnitude of this variable (R, A)
and a step (dR, dA) in which it can be increased.

Figure 57. The Edit Bar during the process of defining a radius for a new arc (left) or a newcircle (right) graphically.

In addition to the General Tab (Fig. 58, left) in the New Line dialog window, the Edit Linedialog window also has the Arc Tab (Fig. 58, right). A list of points defining the arc is given in
the General Tab, while coordinates of points defining the arc, its center, and other parameters
are entered in the Arc Tab. Double-clicking on an existing line will recall the Edit Curve dialog
window (Fig. 58). The Edit Curve dialog window (Fig. 58) has an additional FE-Mesh Tab(similarly as for a line in Fig. 56; not shown here) where a user can refine the FE-Mesh along agiven arc.

117

Figure 58. The New Line (Arc) dialog window.

An object circle is always defined internally using three definition points. However, to simplify
its specification, it is possible to define a circle also using a center and a radius. Threedefinition points are then created automatically. Again, circles can be entered either graphicallyusing the cursor (most common) or using the New Line dialog window (Fig. 58). A new circle
can be entered graphically by selecting the command Insert->Domain Geometry->Arc(Circle)>Graphically from the menu, or by using one of the following commands (a) Circle by 3 Points,or b) Circle by Center and Radius) from the Insert Object part of the Domain Geometry
version of the Tool Bar at the right side of the View Window, and then entering lines using the
cursor. The list of points defining the circle must be entered in the General Tab (Fig. 59, left),while coordinates of points defining the circle, its center, and radius are entered in the Circle
Tab (Fig. 59, right). When a Circle is defined by Center and Radius graphically, then the first
definition point is created at the mouse click, while the other two are at the circle circumference
at -90 and -180 degrees.
Adjustable Point: When a radius or the center of an arc is modified, it is usually also necessary tomodify the location of one of the arc definition points. An adjustable point enables one to choosea point whose coordinates are to be changed.

118

Figure 59. The New Line (Circle) dialog window.

4.1.4. Curves and Splines
The term “Curve” is used in the program and its documentation in two ways, while the meaning
depends on where it is used.
1/ The term Curve is a general term for objects Line, Polyline, Arc, Circle, Spline.
2/ The term Curve can also refer to multiple objects (ad 1/) connected in their boundary points.
This meaning of the term Curve is mainly used in connection with “Boundary Curve”,“Internal Curve”, and so on.
There are several rules that need to be followed during the definition of a Curve.
•

Curves cannot intersect with each other or themselves except at their definition nodes.

•

No point that is not either its definition or Parametric Point can lie on a Curve.

Curves are always defined using their definition points (their indexes). The list of indexes can bechecked or changed using the Edit Curve dialog (the first Tab “General”).
A Spline is a set of more than 2 points connected smoothly by cubic arcs. Splines are generalsmoothed curves defined using points in the 2D or 3D space. Three-dimensional splines do not
generally have to lie in the same plane. However, if a spline is used to define a boundary of asurface, then all its definition points need to lie on this surface. A spline can be defined either
graphically using a command on the Edit Bar or in the dialog where we select a particular typeof spline. HYDRUS allows three types of splines:119- cubic spline, i.e., a curve defined by multiple polynomials of the third order. It passes smoothly
through all points.
- Bezier’s curve – a smooth curve that passes through boundary points, but does not have to passthrough internal points .
- B-spline – a general Bezier’s curve.
More information can be found at
http://mathworld.wolfram.com/BezierCurve.html
http://mathworld.wolfram.com/B-Spline.html
Once a command for defining a new spline graphically is selected, a cursor in the View window
will become a cross with a small empty circle in the middle. The coordinates of the location of
the cursor will be displayed next to the cursor and on the Edit Bar, which will automaticallychange to the one displayed in Figure 60. The Edit Bar will also show which point and curve(their numbers) are being defined and what reference coordinate system (the current coordinate
system, the grid origin, or the last inserted point) is used. One node is specified after the other. A
user can also select on the Edit Bar the type of the spline (standard spline, B-spline, or Bezier
curve). The process of defining a new spline is ended by pressing the Esc keyboard button, theright mouse button (see the Help part of the Edit Bar), or clicking the Stop button on the Edit
Bar.

Figure 60. The Edit Bar during the process of defining a spline graphically.

120

4.1.5. Common Information for a Graphical Input of Objects
A/ A Numerical Input of Values. Edit controls displayed on the Edit Bar can be used to enter
some values that are difficult to enter graphically as follows. Using a mouse, one defines theapproximate shape of an object. Then using a keyboard, one enters selected values numerically.
While entering values using a keyboard one cannot move a mouse, or entered values will be lost.
One needs to use the „Tab“ key or „Shift + Tab“ keys at the keyboard to move forward of
backward from one edit controls to another one, respectively. A control of Combo Boxes andRadio buttons is done using a standard way as in dialog windows, i.e., using keys Arrow Up or
Arrow Down, etc. After all values are entered, one pushes the Enter key to finish the actual stepof the running tool.
B/ Adjusting View. When graphically entering objects, one often needs to move or turn thescene, or to enlarge or reduce a selected detail. This can be done without interrupting the input ofa particular object. The fastest way is to press the center mouse button (a wheel) and then a)
dragging the scene with the mouse move, b) moving forward or backward an object by scrollingthe wheel, or c) rotating the scene by simultaneously also pushing the right mouse button. Afterreleasing the center mouse button, one can continue in the graphical input of an object. Similar
operations can also be performed using the button on the View Toolbar:

A majority of buttons on the View Toolbar do not interrupt the graphical input of an object, i.e.,
after the adjustment of the View Window on can continue in the graphical input of an object.
C/ Snapping. When entering Points graphically (points created when entering curves orsurfaces), a process called Snapping is taking place. This means that a cursor snaps to points ofa Grid (Fig. 61, left) or to existing points. Snapping can be disabled using a button Snap to
Grid on the Tools Toolbar. Snapping on existing points or curves cannot be disabled.
Snapping occurs when a center of a cursor comes close to an existing point and when this pointis redrawn with a yellow color (or any pre-select color assuming that redrawing of preselected
points is not switched off). One can simultaneously observe on the Edit Bar that an index of apreselected point and its coordinates are displayed in edit controls. These controls are disabled
since displayed values cannot be changed. Snapping on curves (Fig. 61, right) occurs in addition
to Snapping on existing points. An automatic calculation of coordinates of a point on a curveand snapping to this point occurs when a center of a cursor comes close to an existing curve. A
location of this point is marked using a yellow cross, which indicates that after this point isentered, it becomes a definition point of a curve. This is important since entering a point on a
curve that is not its definition point leads to the wrongful definition of a domain. A Check of aGeometry discovers such errors, and the Repair Geometry function will automatically correctit.

Figure 61. Snap to a point (left) and snap to a curve (right).

121

4.1.6. Translate, Copy, Rotate, Mirror, Stretch, and Skew Operations
All boundary objects can be manipulated using the Translate, Copy, Rotate, Mirror, Stretch,or Skew operations in the Translate – Copy (Fig. 62), Rotate (Fig. 63, left), Mirror (Fig. 63,
right), Stretch (Fig. 64, left), and Skew (Fig. 64, right) dialog windows. These commands can beaccessed either from the Tools Menu or from the Transform Object part of the Domain
Geometry version of the Tool Bar at the right side of the View Window. Users first select anobject to be manipulated, then click on the command, and specify the Vector of Translation for
the Translate or Copy operations, or the Angle of Rotation for a Rotation, or define theMirroring Plane/Axis for a Mirroring operation.

Figure 62. The Translate - Copy dialog window.

Rather than simply Translating or Rotating a given object, one can choose to use this operation(e.g., Translate/Move or Rotate) to create one or multiple copies of a given object by specifying
the Number of Copies (see Figs. 62 and 63, left). Once one or more copies of a given object are
to be created, one can also choose to Generate Connecting Objects Between Copies (e.g., Fig.
62). What types of connecting objects are to be created is selected in the Manipulation Options
window (Figs. 65). HYDRUS can generate a) lines between selected nodes and their copies, b)
surfaces between selected lines and their copies, and c) solids between selected surfaces and theircopies). Lines can be either straight or curved when a copy is created using the Rotate operation.

122

Figure 63. The Rotate (left) and Mirror (right) dialog windows.

Figure 64. The Stretch (left) and Skew (right) dialog windows.

123

Figure 65. The Manipulation Options dialog window. The bitmaps indicate connecting lines between
points, surfaces between lines, and solids between surfaces.

1244.1.7. Additional Operations

Additional operations that can be used to manipulate boundary objects are Intersect Lines, Insert
Points on Line, and Split Line. All three commands again can be accessed either from the Tools
menu or from the Transform Object part of the Domain Geometry version of the Tool Bar on
the right side of the View Window. The first command (Intersect Lines) finds the Intersect of
two lines, whereas the second command Inserts Points on a Line. This can be done either
graphically or numerically by specifying the number of nodes to be inserted on the line or distanceof the point from the beginning of the line (Fig. 66). The third (Split Line) command can be used
to split a line into two or more parts.

Figure 66. The Insert Point on Curve dialog window.

1254.2. Surfaces
4.2.1. General Definitions
An object Surface refers to, depending on the problem type and the selection made in the
Domain Type and Units dialog window:•

2D-General: For two-dimensional problems, a Surface serves to define the shape ofthe computational domain or its parts. See also Geometry Information.

•

3D-Layered: In this case, the term Surface is used to define the Base Surface for
Solid - 3D-Layered domains. This type of Solids is available in the 3D-Standard
version.

•

3D-General: The term Surface serves to define boundary surfaces of a general 3D
solid. This type of Solids is available only in the 3D-Professional version. Moredetailed information can be found in the section about Solid – General (Section 4.4).

In the 3D-Standard version, the only available type of a Surface is a Planar Surface. This typeof Surface is defined by its boundary curves that must all lie in the same plane and cannot crosseach other. In the 3D-Professional version, also the Curved Surfaces (Quadrangle, Rotary,
Pipe, or B-Spline) are available.
A surface is a closed two-dimensional domain that is either the computational domain for twodimensional applications or the base surface that can be extended into a solid for threedimensional applications. A surface is defined by the List of Boundary Curves. It can becreated using either the Insert->Domain Geometry->Surfaces->Graphically or Insert->Domain
Geometry->Surfaces->Graphically Rectangle commands. Alternative commands on the Insert
Object part of the Domain Geometry version of the Tool Bar are Planar Surface via
Rectangle and Planar Surface via Boundaries. In the first case, a cursor appears, and users cancreate a rectangular surface using the mouse. The Edit Bar displayed during this operation issimilar to the one displayed in Figure 53 (right). The Edit Bar will also show which point, curve,
and surface (their number) are being defined. In the second case, users can create a surface byclicking on a closed curve (one or more boundary objects forming a close curve). The Edit Bar
displayed during the operation will list Boundary Curves defining the Surface (Fig. 68, left). A
surface can be edited using the Edit Surface dialog window (Fig. 68, right), which specifies thesurface type, the number of boundary curves defining the surface, its number, and had a box forpossible comments or a description. A surface must be created before one can do finite element
discretization.
A Surface can also be created automatically by using the menu command Tools->Generate
Domain Surfaces or the Edit Bar command Planar Surfaces - Generate. After this command isclicked on, the program analyses existing boundary curves and attempts to generate planar
surfaces automatically, i.e., without the user being required to define its boundaries. This
operation is usually successful when there is a single uninterrupted boundary curve. The
operation may fail when there are some ambiguities, such as when there are multiple curves orwhen boundary curves are not closed. If this operation fails, the following warning is displayed(Fig. 67) and the user needs to define Surfaces manually.
126

Figure 67. The warning issued when Surfaces cannot be created automatically and must be
defined manually.

Figure 68. The Edit Bar during defining a surface graphically (left) and the General tab of theEdit Surface dialog window (right).

1274.2.1.1. Planar Surfaces
A base surface is formed by a planar surface of arbitrary shape. The base surface can containopenings, internal curves, and internal points (Fig. 69). In the current version of HYDRUS, abase surface can be formed by a single surface. Future versions will permit multiple surfaces toform one single base surface.

Figure 69. A solid showing the base surface.

If the solid needs to be divided into vertical columns, then these columns must be defined using
internal curves in the base surface. The FE-mesh then follows exactly the specified shape ofthese internal curves (Fig. 70):

Figure 70. Solid showing separate vertical columns.

128

A base surface can be defined by a plane other than the horizontal plane, while thickness vectors
can be defined in other than the vertical direction. Figures 71 and 72 show an example of a solidthat has a base surface in the XZ plane and thickness vectors in the Y direction.

Figure 71. A solid with its base surface in the XZ plane and thickness vectors in the Y direction.

Figure 72. FE-Mesh for a solid with its base surface in the XZ plane and thickness vectors in the
Y direction.
4.2.1.2. Curved Surfaces
There are currently four types of Curved Surfaces (Fig. 73) available in the 3D-Professionalversion: Quadrangle, Rotary, Pipe, and B-Spline. While the boundary of a Planar Surface
must be formed by multiple different Curves, the boundary of a Curved Surface can containone curve two times. An example is a Pipe Surface (Fig. 73), in which the curve along a pipe
occurs twice, each time with a different orientation. Note that the list of curves defining Pipe andRotary Surfaces is generated automatically and cannot be edited, contrary to the list of curves
defining Quadrangle or B-Spline, for which curves are selected by a user.
A Quadrangle is a Surface defined by its boundary curves of an arbitrary type (except a circle).
Curves do not have to be placed in a single plane, that is, in general, a Quadrangle can be a
curved surface. This type of surface corresponds to a general surface with four corners, i.e., it is129

typically defined by four boundary curves (although this is not a necessary condition). If there isanother number of boundary curves than four, it is necessary to define corner nodes of a
Quadrangle.
A B-Spline Surface is a Surface defined using Boundary Curves (similarly as a Quadrangle).
However, for this type of Surface, one needs to also define an additional matrix of N*N internal
nodes, which allows one to curve the inside of a Surface. One needs to define a number ofinternal nodes N and an order of the Surface Spline. Internal nodes are created automaticallywhen a B-Spline Surface is defined. Their coordinates can be subsequently edited. An order of
the Surface Spline is an order of the polynomial, which is used for modeling the surface (either
quadratic or cubic).
A Rotary Surface is defined by an Axis of Rotation (defined using two nodes), a Rotated
Curve (of arbitrary type, as long as the created surface makes sense), and an Angle of Rotation(from 0 to 360 degrees).
A Pipe Surface is defined by an Axis Curve (a smooth curve of an arbitrary type – only apolyline does not have to be smooth) and a radius.
Rotary Curved Surface:

Pipe

B-Spline

Quadrangles

Figure 73. Examples of Curved Surfaces (Rotary, Pipe, B-Spline, and Quadrangle Surfaces).

1304.2.1.3. Partial Surfaces
A Partial (or Component) Surface (Fig. 91) is created by an Intersection of Surfaces or
Solids (see Section 4.6), which divides an original Surface into smaller Sub-Surfaces, or theso-called Component Surfaces. Although this Surface has its own number and can be used todefine, for example, a Solid, its shape and boundaries are defined (generated) by the shape of
its original Surface and a given Intersection. A list of Components resulting from the divisionof the original Surface by an Intersection can be found on the Tab Components of the Edit
Surface dialog window. Since Partial Surfaces are generated objects, they cannot be deleted,or their shape cannot be edited (only the parental Surfaces can be edited). When a parental
Surface is divided into Components, it still exists (is listed in the Navigator), but is not
displayed in the View anymore; only its Components can be displayed.
One can define for each Component its activity (using commands Activate Partial Surface
and Deactivate Partial Surface), i.e., whether it should be a part of the domain and whether an
FE-Mesh should be generated on it or not. In this way, one can cut from the original Surface
unneeded parts. When an option „Display components as independent surfaces“ is selected,
Components are displayed in the Navigator Data Tree as independent Surfaces, and it ispossible to select them graphically and use them for a definition of Solids. A selected
Component is displayed in a view, in order to facilitate visual identification of Components.

4.2.2. Steps to Define a Two-Dimensional Domain
1/ Definition of Boundary Curves of Particular Surfaces
Boundary Curves are formed using basic geometric objects, such as Points and Curves. These
objects can be specified in three different ways:
1. Graphically. One selects on the Edit Bar an appropriate tool and specifies new objects
graphically in the View Window. This is usually done by specifying coordinates ofpoints while using the Grid Alignment or snapping to already existing objects (points).
2. Numerically. Objects can be entered numerically by defining their X, Y, and Z
coordinates and indexes in a dialog window. The dialog is obtained by using the Menu
command Insert –> Domain Geometry or the Navigator Bar command Data Tab –>Domain Geometry and selecting the desired object type with a click of the right mousebutton and the New command …
3. Import from a File. Particular objects (with a large number of nodes (spline, polyline)or the entire Geometry can be read from the text file using several formats. Moredetailed information is at Read points from a text file and Import Geometry from a
Text File.
The order of inputting particular objects is arbitrary.
2/ Definition a Surfaces131Boundary Curves do not yet form the Computational Domain. The Computational Domain
is formed using one or more Surfaces that need to be defined. A Surface is defined using a listof Curves that form a closed external boundary. A Surface can be defined Graphically by
sequentially clicking on particular Boundary Curves or Numerically in a dialog where one candefine a list of indexes of Boundary Curves.
3/ Internal Objects
Any surface can have an arbitrary number of Openings (Holes), Internal Curves, or Internal
Points. Additional information can be found at Internal Objects.
4/ Openings
Each surface can have an arbitrary number of Openings (Holes). An Opening is defined by aclosed internal boundary (one or more Internal Curves), which entirely lies inside of a Surface.
An Opening can be formed by clicking with the right mouse button in the View Window on theclosed internal boundary and selecting from the popup menu the "Create Opening" command.
Additional information can be found at Openings.
5/ Geometry Check
The consistency of the geometry can be verified at any time using the command Check Data
Consistency (Tools Menu).
6/ Remarks•

Any change in geometry can be undone using the undo command or redone using theredo command. The number of undo or redo steps is limited by the buffer memory,which can be set in the Program Options dialog window (Tab Options andDirectories).

•

When the Computation Domain is formed by several subdomains with different
properties (e.g., different materials, and so on), one can form this domain frommultiple Surfaces corresponding to these subdomains. An advantage is that after the
FE-Mesh is generated, it is possible to automatically form Mesh Sections forparticular Surfaces and use them to easily define materials and other properties or
initial and boundary conditions. Additional information can be found at FE-Mesh
Sections (Section 5.7).

4.2.3. Several Notes on Rules for Correct Definition of Surfaces
1. Contrary to the old HYDRUS-2D program, internal curves can touch or cross other internal
curves and can touch boundary curves. A point where two curves intersect (or touch) must bea definition point of both curves (must be a part of the Geometry). This point can be foundautomatically using commands Intersect Lines (Tools->Intersect Lines or Intersect Linesfrom the Edit Bar) or Repair Geometry (Tools->Repair Geometry).
2. Curves cannot lie upon each other.
3. Multiple points cannot be defined at the same location. A frequent error is when the initialand final points of a curve are defined at the same location. The curve is then not closed, and132

a surface cannot be defined using this curve. The initial and final points of a closed curve
must be defined using the same point.
4. A point cannot lie on a curve without being its definition point.
5. All the above-mentioned errors in the definition of the Geometry can be automatically solved
using the command Repair Geometry (Tools->Repair Geometry).
6. Contrary to the old HYDRUS-2D program, the number of Surfaces is virtually unlimited (upto 30,000). Surfaces can touch each other (in a point or on a boundary line), or one Surface
can lie inside of the other Surface. In this case, one needs to first create an internal Hole in
the first Surface and then insert the second Surface into this hole. This process can berecursive, i.e., it is possible to create a Hole in the internal Surface and insert an additional
Surface there). When defining a new Surface graphically (e.g., using a rectangle), HYDRUS
recognizes when the new Surface is located inside the existing Surface and automaticallyoffers its integration.
7. Surfaces cannot partially cover each other (see also 6).
8. Points located outside of Surfaces are ignored when generating FE-Mesh.

4.2.4. Internal Objects
Internal Objects are objects of the type Point, Curve, or Opening, integrated in the Surface
object. Objects are by default integrated into the Surface automatically (see Option “Autodetect”
in Figure 1). It is possible to edit objects manually when the “Autodetect” option is turned off.
{bmct Internal_Object_Dlg.bmp}

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Figure 74. The Integrated Tab of the Edit Surface dialog window.

Main reasons for integrating objects into a Surface:•

Objects integrated into a Surface are respected when the FE Mesh is generated. On theother hand, objects that lie on a Surface but are not integrated into it are ignored during
the FE Mesh generation.

•

Internal Points allow users to precisely define the location of Observation Points
and other objects.

•

Internal Curves allow users to precisely define geometric boundaries inside of thetransport domain. They can be used for many different purposes (e.g., Mesh Lines,
Material Boundaries, etc.).

•

Curves integrated into a Surface that is used as a Base Surface for the 3D-Layered
Solid are also projected at the Upper Surface and enable thus more precise modeling of
its shape (see Figs. 75 and 76).

Figure 75. An example of internal objects.

134Figure 76. An example of an Upper Surface definition using Internal Curves and Thickness
Vectors.
There are several rules that must be followed when defining Internal Objects:•

An Internal Curve must be entirely within a Computational Domain.

•

An Internal Curve can touch (but cannot intersect) the outside boundary of a parent
Surface at its definition points (definition points of its boundary curves).

•

An Internal Curve can be open or closed, and can intersect itself, provided that theintersect occurs at a definition point of an Internal Curve.

An Internal Curve or an Opening must lie entirely inside of the parent Surface. Common
reasons why a Curve or an Opening are not automatically integrated into a Surface is that there
exist small deviations between them and a Surface that are not visible, but are larger thanallowed tolerance (usually 0.1 mm).

4.2.5. Check and Repair Geometry
The Check Data Consistency command performs a consistency test of the domain boundaries.
It checks especially whether each domain component is bounded by an outer boundary curve andwhether or not the curves are intersecting each other. When the geometry is not correct, the code
sends a warning and select those curves which do not fulfill the rules for a correct definition ofboundaries. The command Repair Geometry may then be used to fix existing problems.

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The Repair Geometry command attempts to fix errors in the ill-defined Geometry that were
found using the command Check Data Consistency. This command calls the Repair Domain
Definition dialog window (Fig. 77). The List of Corrections section of this dialog lists various
operations that can be used automatically by the program when attempting to correct the illdefined Geometry. Some of these corrections depend on the model precisions, which are definedin the Model Precision and Precision of Corrections section. Users can define these precision
criteria or use those suggested by HYDRUS.

Figure 77. The Repair Domain Definition dialog window.
HYDRUS automatically analyzes defined Geometry, and if it is not consistently defined, it
displays a warning at the Edit Bar in its Help section: Errors in Domain Definition. After
double-clicking on this warning, HYDRUS displays a message informing what is wrong(incorrect), similarly as when using the Check Data Consistency command.

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4.3. Opening
An opening is an internal hole defined by a boundary curve having the following properties:
the curve is closed, positively oriented (in a counter-clockwise direction), does not intersect anyother curve or itself, and has the computational domain located on its right-hand side (in thesense of positive orientation), while the left side is not part of a computational domain. An
opening is not part of the computational domain or surface. An opening is created graphically as
follows: One first defines boundary objects that create a closed boundary curve. One then uses
the command Insert->Domain Geometry->Opening->Graphically from the menu, oralternatively, the command Opening via Boundaries on the Insert Object part of the Domain
Geometry version of the Tool Bar. A user creates an opening by clicking on the closed curve(one or more boundary objects forming a closed curve). The Edit Bar displayed during theoperation will list Boundary Curves defining the Opening (similar to Fig. 68, left).
Alternatively, an opening can be created using the New Opening dialog window (Fig. 78) byclicking on the command Insert->Domain Geometry->Opening->Dialog from the menu. An
opening can be edited using the Edit Curve dialog window (Fig. 56), which specifies thenumber of boundary curves defining the opening, its number, and has a box for possiblecomments or a description.

Figure 78. The New Opening dialog window.

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4.4. Solids
Solids are three-dimensional objects defined by the base surface and one or more thickness
vectors (See also Section 2 - Projects Geometry Information). There are three types of Solids
depending upon the selection made in the Domain Type and Units dialog window (Figs. 6 and
7):•3D-Simple (Hexahedral): This type of solid has a Hexahedral Shape and is definedby its basic dimensions (Figs. 6 and 9). The base can have a certain slope in the X andY dimensions.

•

3D-Layered: This type of solid is defined by the Base Surface and one or more
Thickness Vectors.

•

3D-General: This type of solid is defined using a set of surfaces (either Planar or
Curved Surfaces) that form its boundaries. This selection is available only in the 3DProfessional version of HYDRUS.

4.4.1. 3D-Simple (Hexahedral) Solids

Figure 79. The Edit Bar during the process of graphically defining a Hexahedral Solid.
Definition of a Base Surface on the left and a Thickness on the right.
A simple Hexahedral Solid can be created graphically using the menu command Insert>Domain Geometry->Solid->Graphically or alternatively the command Solid - Extruded on theInsert Object part of the Domain Geometry version of the Tool Bar. Once a command for138defining a new Hexahedral Solid is selected, a cursor in the View window will become a crosswith a small empty circle in the middle. The coordinates of the location of the cursor will be
displayed next to the cursor and on the Edit Bar, which will automatically change to the one
displayed in Figure 79 left. The Edit Bar will also show which point, curve, and surface (their
numbers) are being defined and what reference coordinate system (the current coordinate system,
the grid origin, or the last inserted point) is used. After two points defining a surface are
specified, both the cursor and the Edit Bar change (Fig. 79 right) for the definition of theThickness Vector. The selection can be made on the Edit Bar that also displays the height of theThickness Vector (L) and a step (dL) in which it can be increased. The Thickness Vector can becreated (a) Perpendicular to the Base Surface, b) in X-direction, c) in Y-direction, or d) in Zdirection). The process of defining a new Hexahedral solid is ended after the Thickness Vector isdefined.
4.4.2. 3D-Layered Solids

Figure 80. The Edit Bar during the process of graphically defining a Solid by extruding a Base
Surface. Selection of a Surface (left) and definition of a Thickness Vector (right).
A Solid can be created graphically (Insert->Domain Geometry->Solid->Graphically from themenu or alternatively the command Solid - Extruded on the Insert Object part of the Domain
Geometry version of the Tool Bar) by clicking on one point defining the Base Surface andextruding the base to form a three-dimensional solid. During the first part of the operation, theEdit bar (Fig. 80 left) displays numbers for a Solid, a Thickness Vector, a Point, and a Surface,
while during the second part, it (Fig. 80, right) displays the Thickness Vector length (andincrement) and in which direction it is created (a) Perpendicular to the Base Surface, b) in Xdirection, c) in Y-direction, or d) in Z-direction). A user should, during the first step, select (click139on) the Base Surface that is to be used to define the Solid. It is also possible to click on any
Point that defines the Base Surface. The second step depends on whether Thickness Vectors
are already defined in Points of the Base Surface. If they are, they are used to define the Solid,
and the second step is not done. If they are not, the thickness of the solid needs to be defined
during the second step. The length and direction of the Thickness Vector are defined using amouse in the Point on the Base Surface closest to the mouse click, which selected it.
How to create a Solid once the Base Surface and multiple Thickness Vectors are defined?
1. Graphically: Use the “Solid Extruded” tool and click on the Base Surface. A Solid iscreated using existing Thickness Vectors.
2. Numerically: By using a command from the Insert menu or by clicking with the rightmouse button on Solids in the Data tree of the Navigator Bar. From the popup menu,
select the New Solid command. In the New 3D-Layered Solid dialog, select the Base
Surface and Thickness Vectors. Since the Autodetect function is automatically on, theBase Surface and Thickness Vectors will likely be detected automatically.
Thickness vectors do not have to be perpendicular to the base surface. A Solid, i.e., its basesurface and thickness vectors, is defined and can be edited in the Edit Solid dialog window(Fig. 81) that has four tabs: General, Sub-Layers, Thickness Profiles, and FE-Mesh. The
General Tab provides information on which base surface and which thickness vectors define
the solid. The Sub-Layers Tab informs whether the solid is divided into one or more Layers.
Layers are other objects that can be used to subdivide a single solid. These layers can be used,
for example, to keep constant thicknesses of selected horizons or constant discretization close to
the soil surface (to get good estimates of evaporation) across the entire transport domain (solid).
Layers can have different Thickness Profiles (the Thickness Profiles Tab). One profile iscreated by the code automatically. Users can then define one or more Thickness Profiles that areassociated with different Thickness Vectors. These profiles can then be subdivided into multiple
layers that can have either constant or variable thickness (T) across the transport domain.
Thicknesses and the mode (constant or variable) of particular layers are specified in a table.
Thickness Sum (TS) is then calculated by adding thicknesses of particular layers. At least one
layer thickness must be variable. The finite element discretization then follows these layers.
Finally, the FE-Mesh Tab (Fig. 82) specifies how many horizontal FE-Layers are used todiscretize the solid. When only one layer exists then users can specify relative finite element
spacing (spacing of vertical discretization layers) on the vertical side (FE-Mesh Layer Spacing)using the RS1 (relative size at the top) and RS2 (relative size at the bottom) factors below
Generate Mesh Layer Spacing. The element sizes are then proportionally distributed. The
preview part of the dialog window shows the main terms used on each Tab. When multiple
layers exist, then users can specify relative sizes of elements for each layer (FE-Mesh Density in
Layers).

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Figure 81. The Edit Solid dialog window: the General and Geo-Layers Tabs.

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Figure 82. The Edit Solid dialog window; the FE-Mesh Tab for a single and multiple layers.

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4.4.2.1. Division of a Solid into Columns
Notice that the Base Surface must be defined using several Surfaces (see Fig. 69). Parts of the
Solid above each Surface are called Columns and serve to geometrically divide the Solid in thevertical direction. All Surfaces defining the Base Surface must lie in a single plane. A list ofthese Surfaces can be defined manually using indexes or can be Autodetected by the program(the “Autodetect” option). A division of a Solid into Columns leads to automatic creation ofMesh Sections that correspond with Columns after the generation of the FE-Mesh. These Mesh
Sections can be used to define various properties (e.g., materials distribution) or initial andboundary conditions.
4.4.2.2. Division of a Solid into Geo-Layers
Geo-Layers (alternative term Sublayers, which was used in Version 1 is used alternatively
below) are used to divide a Solid in the horizontal direction (Fig. 81).
It is possible in the Edit Solid dialog to define the number of Layers and their Thicknesses. A
Solid always has one Master Thickness Vector, which is one of the Thickness Vectors of a
Solid, that has a special meaning as described below.
A thickness of a Layer is calculated as follows:•

Thicknesses of Layers given in the Table are calculated on the Master Thickness
Vector•

The sum of the Thicknesses of all Layers should be equal to the length of the Master
Thickness Vector. If it is not so, a program will issue a warning and recalculate theThicknesses of Layers automatically.

A Solid can have more Thickness Vectors of different lengths so that specified Thicknesses ofLayers cannot be maintained. The program then does the following: For Geo-Layers with theConstant Thickness Type, the specified thickness is maintained at all Thickness Vectors, i.e.,over the entire computational domain. For Geo-Layers with the Variable Thickness Type, their
thicknesses are linearly increased or decreased so that the sum of the Thicknesses of all Layers
corresponds with the length of a particular Thickness Vector.
4.4.2.3. Individual specification of different Thicknesses of Geo-Layers at different Thickness
Vectors.
In the preceding paragraph, we have described how to define Thicknesses of Layers on the
Master Thickness Vector using a table (Fig. 81). This table represents the so-called Profile, i.e.,a particular distribution of thicknesses. If one wants to define precisely the division of
thicknesses also on other vectors than the Master Thickness Vector, then it is necessary tocreate additional Special Profiles and use then on corresponding Thickness Vectors. There isalways a Default Profile, which corresponds to the table described in 4.4.2 above. One cancreate new profiles, change their thicknesses, or delete them. One can simultaneously also see alist of Thickness Vectors where the selected Profile is used.

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The desired Profile can be associated with a particular Thickness Vector after opening a dialog
with its properties (e.g., by double-clicking on a vector) and selecting a Profile from a Combo
Box “Thickness Profile No.” (see Fig. 85). This operation can even be carried out globally by
first selecting desired Thickness Vectors, then opening a dialog with their properties (Alt +Enter), and finally repeating the above-described process. Note that one Profile can beassociated with many Thickness Vectors, which enables one to change Thicknesses of Layers
easily on all Thickness Vectors by changing a single Profile.

4.4.2.4. Steps to Define a 3D-Layered Domain
1/ Definition of the Base Surface
The Base Surface is a 2D domain of an arbitrary shape. How to specify the Base Surface is
described in Building a Two-Dimensional Domain.
2/ Definition of Thickness Vectors
One inserts one or more Thickness Vectors in points that lie in the Base Surface, so that theshape of a Solid is defined as needed.
3/ Definition of a Solid
On the Edit Bar (or the Menu command Insert –> Domain Geometry), one clicks on the Solid –> Extruded command and selects (clicks on) one of the Surfaces defining the Base Surface.
This operation creates the 3D-Layered Solid. One can do this even when no Thickness Vectors
are defined. In such a case, after clicking on the Base Surface, a graphical tool is started, using
which one can extrude the Solid into space. A Thickness Vector is simultaneously created in the
Point on the Base Surface that is closest to the location of the click.
4/ Formation of a Solid
A Solid can be further formed using additional Thickness Vectors and Internal Lines.
5/ Definition of Geo-Layers
A Solid can be vertically divided into Layers.

4.4.3. 3D-General Solids
Solids in the 3D-Professional version are defined using boundary Surfaces (either Planar (seeSection 4.2.1.1) or Curved (see Section 4.2.1.2)) and identified as 3D-General Solids. In one
project, one cannot use at the same time 3D-General Solids and 3D-Layered Solids (created inthe 3D-Standard Version) or the parametric blocks (created in the 3D-Lite Version). It is,144however, possible to convert 3D-Layered Solids into 3D-General Solids by changing the
project type from 3D-Layered to 3D-General.
Boundary Surfaces of a Solid must enclose a closed space and cannot intersect with each other.
Interior of a Solid must form a three-dimensional “simply continuous space”, i.e., it must be
possible to connect any two internal points using a polyline that is entirely located inside of a
Solid. Boundaries of a Solid thus can be formed by any number of either Planar or Curved
Surfaces. Figure 83 shows two examples of 3D-General solids. While the Solid at the top is
formed using 8 Planar Surfaces and 4 Quadrangles, the Solid at the bottom is formed bymultiple Curved Surfaces.

Figure 83. Examples of 3D-General Solids. Top - formed by Planar Surfaces, bottom – formed
by Curved Surfaces.

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General Solids can be created in the following ways:
1. Using a standard dialog, from which Boundary Surfaces can be picked graphically(individually, or using a Quadrilateral or Rhomboid Selection Tool).
2. Creating a Simple Block (Brick).
3. Extruding a Solid from a Surface (one or multiple simultaneously).
Process of Extruding:Approach 1: Start a tool and click on a given Surface, which is to be extruded. It is important
where a click occurs. The program finds the closest Node on a Surface
Boundary, and the extruding distance (height) is measured in this node. The
extruding height is measured on a line passing through this node.
Approach 2: When you want to extrude multiple surfaces at the same time, you need to press
the Left Shift keyboard button before selecting the desired Surfaces (you can add
or remove Surfaces). After a selection is made, release the Left Shift button andstart extruding selected surfaces.
Approach 3: First select desired Surfaces and then click the Edit Bar command “Solid –Extruded”. This will start the extruding process for all selected surfaces.
One can extrude Surface in the direction of X, Y, and Z axis, or in the direction perpendicular toan extruded Surface. When a Surface is not in a plane (e.g., is curved) and perpendicular
extruding is selected, extruding is done in directions of local perpendicular lines to an extruded
Surface.
During extruding, one can select on the Edit Bar the length step (dL) or enter the numericallydesired length of extruding (L).
Note that the command Extrude can be used only for Planar, Quad, and B-Spline Surfaces,
and it cannot be used for Partial Surfaces and for Surfaces containing a zero Curve (i.e., acurve with a zero length from point P to point P).

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4.5. Thickness Vectors
The term Thickness Vector is used for a vector (usually but not always perpendicular to theBase Surface) that extends the Base Surface to form a solid (the three-dimensional
computational domain). A new Thickness Vector can be defined either graphically or
numerically (Fig. 85).
There are several ways in which a Thickness Vector can be specified graphically and these aredisplayed at the Edit Bar (Fig. 84), which appears once a command for defining a Thickness
Vector is selected.
a) Point and Length: A user specifies the length of the Thickness Vector on the Edit Bar(Vector Length) and with the mouse selects the point to which the Thickness vector is
assigned.
b) Point and Coordinate: A user specifies the End Coordinate of the Thickness Vector on
the Edit Bar (End Coordinate) and with the mouse selects the point to which theThickness vector is assigned. This method is suitable, especially in the case, when points
located at the upper surface of the domain already exist (see Tutorial 2.07). In this case, weneed to specify Thickness Vectors whose upper points were read in from a GIS file, andwe need to create the lower (beginning) points that would be located in the plane of theBase Surface. Note (in the Tutorial) that the Reverse Points option was automaticallychecked on the Edit Bar. This is because the thickness Vectors have to originate from theBase Surface and not from the upper surface. If the Reverse Points option was notchecked, Thickness Vectors would originate from the upper surface and end at the Base
Surface.
c) Two Points: A user selects graphically two existing Points to form the Thickness Vector.
In this case, an Anchoring (beginning) Point of a Thickness Vector is the first selected
point. Therefore, it is important to select points defining a Thickness Vector in the rightorder, i.e., to first select a point at the Base Surface and only then a point at the uppersurface of the domain.
d) Three Points: A Thickness Vector is, in general, defined by three points: an Anchoring
Point, a Beginning Point, and an End Point (Fig. 85). The Anchoring Point must be
located on the Base Surface. The Anchoring Point is usually the same as the Beginning
Point (i.e., both Point indices are the same), and one does not have to pay attention to it.
However, in general, the Anchoring Point can be different than the Beginning Point,
which leads to the so-called “offset”. This option allows defining Domains that have both
upper and lower surfaces deformed, i.e., not a plane.
Vector Direction can be specified to be a) Perpendicular to the Base Surface, b) in X-direction,c) in Y-direction, or d) in Z-direction.
Thickness Vectors can be defined by:- clicking on individual Points- selecting points with a rectangle (rhomboid, circle, polygon)- clicking on a curve – Thickness Vectors will be added to all points of a curve.

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Figure 84. The Edit Bar during the process of graphically defining a Thickness Vector.
A definition of the Thickness Vector (i.e., its Boundary Points) is given and can be edited in
the Thickness dialog window (Fig. 85).

Figure 85. The New Thickness dialog window.

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The height of a solid is defined using one or more Thickness vectors. Each thickness vector isdefined by an Anchor Point P and two Boundary Points N1 and N2. The anchor point P mustbe part of the base surface, i.e., it must be either a defining point of the external boundary or theinternal curve, or an internal point in the base surface. Boundary points N1 and N2 are arbitrary
points in 3D space. Coordinates of these points can be edited, thus allowing one to specify the
thickness vector in an arbitrary direction (i.e., not necessarily perpendicular to the base surface).
Usually, the anchor point P is the same as boundary point N1 so that one can use the same index
for both P and N1. If, for whatever reason, we do not want to have the base surface on thebottom of the transport domain (Solid) (e.g., when the bottom of the transport domain is not in
the same plane), users can make the N1 node different from P (the red part in Fig. 86).

Figure 86. A solid with several thickness vectors.

Figure 87. FE-Mesh for the solid in Figure 86.
The height of a solid is constant when less than three thickness vectors are used. Three thickness
vectors define a linear plane (with generally an inclined surface). More than three thickness149vectors with different lengths then define the top surface that is formed by triangles, whose
coordinates are calculated from the thickness vectors using linear interpolation or extrapolation.
When breaks in the slope of the top surface are to be defined exactly, then it is necessary todefine internal curves in the base surface. Figures 88 and 89 show the importance of having
internal curves (or not having them) in the Y direction for a proper definition of the solid(compare Figures 86 and 88 Figures 87 and 89).

Figure 88. Missing internal curves in the base surface.

Figure 89. A consequence of missing an internal curve in the base surface on the FE-Mesh of the
top surface.
Note: Three Thickness Vectors need to be specified to define a Domain with a linearlychanging thickness. As long as only two Thickness Vectors are specified, the thickness of theDomain is constant and defined using the first Thickness Vector (with lower index) (since threepoints are needed to define a plane).

1504.6. Intersections of Surface and Solids
Intersections of Surfaces and Solids (Fig. 90) can be created using the following approaches:
A. Intersection of Surfaces: Select two or more Surfaces, click with the right mouse buttonon these selected Surfaces, and select the command “Create Intersection”. When moretypes of different objects are selected (e.g., nodes, lines, or surfaces), which can, forexample, occur when selection is made by a Rectangle (or a Rhomboid), then thecommand is located in the submenu “Surfaces”.
B. Intersection of Solids (this option not yet available): Select two or more Solids, clickwith the right mouse button on these selected Solids, and select the command “Create
Intersection”. When more types of different objects are selected (e.g., nodes, lines, or
surfaces), which can, for example, occur when selection is made by a Rectangle (or aRhomboid), then the command is located in the submenu “Solids”. For the Intersection„Solids A-B” (Fig. 90), Solid A will remain in its original shape, and Solid B will be cut
off. For the Intersection „Solids B-A”, Solid B will remain in its original shape, andSolid A will be cut off.
C. Intersection of Surfaces and Solids (this option not yet available): It is possible tocreate this intersection using the menu command Insert->Domain Geometry>Intersection or by clicking with the right mouse button on the item “Intersections” inthe data tree of the Navigator bar and selecting “Insert Intersections” from thedisplayed popup menu. In the dialog, select s desired type of Intersection (e.g., surfaces
or solids).

Figure 90. The Edit Intersection dialog window (for two Surfaces (left) and two Solids (right).

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A Partial (or Component) Surface (Fig. 91) is created by an Intersection of Surfaces or Solids,
which divides an original Surface into smaller Sub-Surfaces, or the so-called Component
Surfaces. Although this Surface has its own number and can be used to define, for example, a
Solid, its shape and boundaries are defined (generated) by the shape of its original Surface and agiven Intersection. A list of Components resulting from the division of the original Surface byan Intersection can be found on the Tab Components.

Figure 91. An example of an Intersection of two Surfaces and a resulting Partial Surface andIntersection Curve.

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4.7. Auxiliary Objects
In addition to objects that define the computational domain, the HYDRUS GUI allows users to
employ several Auxiliary Objects that can be used to, for example, add Dimensions to thecomputational domain, include various Labels, or define permanent Cross Sections or MeshLines.

4.7.1. Dimensions
Dimensions can be added to describe spatial properties of the computational domain in the View
window using the Insert->Auxiliary Objects->Dimensions command or the Dimensions
command from the Insert Object part of the Domain Geometry version of the Edit Bar. Then
one needs to click on two points defining the computational domain and drag Dimensions to therequired position. Figure 120 shows an example of how Dimensions can be used.
After a command for defining a Dimension is selected, a user needs to first select by a cursor
two existing points, the distance between which is to be labeled. The Edit Bar lists during thisoperation two definition points and the Dimension number (Fig. 92 left). After the second pointis selected, a cursor in the View window and the Edit Bar (Fig. 92 right) change and allow auser to define where a Dimension is to be displayed. In which plane a Dimension is to be
displayed can be done on the Edit Bar (Fig. 92 right).

Figure 92. The Edit Bar during the process of graphically defining a Dimension. Selection of two
definition points, the distance of which is to be labeled (left) and the dimension type (right).

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4.7.2. Labels
Labels can add any desired text to the computational domain in the View window using theInsert->Auxiliary Objects->Dimensions command or the Comments command from the Insert
Object part of the Domain Geometry version of the Edit Bar. One then clicks simply anywherein the View window and write the desired text. The text itself, its color, frame, and its offset canbe specified in the Edit Comment dialog window (Fig. 93). Figure 120 shows an example of
how the “Furrow” Label is used.

Figure 93. The Edit Comment dialog window.
After a command for defining a Comment is selected, a user needs first to select a location towhich the comment will point using a cursor. The Edit Bar lists during this operation thecoordinates of a cursor (Position), the color to be used for a comment, and the comment text
(Text) (Fig. 94 left). A user can also select the Font to be used for the comment text. After the
position is selected, a user defines an Offset of the Comment text. The comment text, thecomment font and color, and offset are displayed at the Edit Bar (Fig. 94 right).

4.7.3. Bitmaps (Textures)
Bitmaps (Textures) serve to use scanned figures (maps) as a means to define the computational
domain in the View window. Bitmaps can be added using the Insert->Auxiliary Objects>Textures command. Corners of the Bitmap must be anchored at 4 points, coordinates of whichmust be selected such that the scale of the Bitmap corresponds with the scale of the View
window. Anchor points can be selected one at a time using either a Listbox (containing a list of
all defined nodes) or using a command Pick and selecting nodes using a cursor. All anchor
points can also be selected simultaneously using the command Pick ABCD. The Edit Bitmap
dialog window then provides information about the selected Bitmap, such as its Size in pixels
and kB. One can then simply trace the bitmap to specify the computational domain.

154

Figure 94. The Edit Bar during the process of graphically defining a Comment. Selection of theComment Position, Comment Text, Font, and Color (left), and Offset (right).

Figure 95. The Edit Bitmap dialog window.

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4.7.4. Cross-Sections
In the HYDRUS-2D software package, one could click at any two points of the transport domain
to display the results of selected variables between those two points, i.e., along a specified crosssection. The exact location of these cross-sections was not saved, and they had to be redefinedwhenever a new graph was required. In HYDRUS, one can define the cross-sections and savetheir locations so that graphs along the cross-sections can be recalled at any time by simply
clicking at them. Graphs along pre-defined cross-sections can be displayed for both the initialconditions and the output results. For example, if a plot of the pressure head along a predefinedcross-section at a particular time is needed, one needs to display the pressure head outputs, find aparticular time, and then click on the predefined cross-section. The graph is displayed
instantaneously. Specifying the cross-section within a two-dimensional domain isstraightforward.
In 3D problems, a Cross-Section is a plane that is defined using two points, which are defined(either graphically or numerically (in the Cross-Section dialog window (Fig. 96))) in a currently
active Workplane, and is perpendicular to this Workplane. When a 2D Mesh-Section is displayedin the View Window, the Cross-Section Chart displays a particular variable at the cross-sectionof this 2D Mesh-Section with the Cross-Section Plane. When a 3D Mesh-Section is displayed,
the Cross-Section Chart displays a particular variable at the cross-section of this 3D MeshSection with the Cross-Section Plane.

Figure 96. The Cross-Section dialog window.
The ability of charts displaying the distribution of various quantities along boundary-lines andcross-section lines has been extended in Version 3. The GUI now allows the display of results at
multiple time-layers simultaneously in one chart. This feature allows one to compare the valuesof a given quantity very easily at different times. Note that cross-section lines and charts can also
be applied to mesh slices created by the Clipper tool as described below and shown in Figure 162.

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4.7.5. Mesh-Lines
Mesh-Lines are very similar to Cross-Sections, except that Mesh-Lines follow edges of thefinite elements and do not have to be straight. They are used, similarly to Cross-Sections, todisplay selected variables along defined Mesh-Lines. Similarly to Cross-Sections, the locationsof Mesh-Lines are saved and can be recalled at any time.

Figure 97. The Mesh-Line dialog window.
A description of the Mesh-Line is given in the Mesh-Line dialog window (Fig. 97), whichcontains the Mesh-Line number, its description, a list of nodes defining the Mesh-Line, andwhether or not the computational module should calculate (actual and cumulative) water andsolute fluxes across this Mesh-Line. The fluxes across the Mesh-Line are then displayed using
the Fluxes across Mesh-Lines dialog window (Fig. 98) after using the Results->Fluxes across
Mesh-Lines command. This dialog displays actual and cumulative, water and solute (onlyconvective) fluxes across individual Mesh-Lines.

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Figure 98. The Fluxes across Mesh-Line dialog window.
Information for this graph is read from the CrossSect.out file that contains data organized into
the following columns:
VariableTime
Flux(i)CumFlux(i)SolFlux(i)Description
Time
Water flux across the ith cross-section
Cumulative water flux across the ith cross-section
Convective solute flux across the i-th cross-section

Units
[T]
[L2/T] or [L3/T]†[L2] or [L3]†[M/L3*L2/T = M/L/T] or[M/L3*L3/T = M/T]†
CumSFlx(i) Cumulative convective solute flux across the i-th [M/L3*L2 = M/L] orcross-section[M/L3*L3 = M]††
for 2D and three-dimensional axisymmetrical problems, respectively.
Water Fluxes across internal lines (mesh-lines) are calculated in HYDRUS similarly as fluxes
through the boundary nodes with prescribed Dirichlet boundary conditions (see the Technical
Manual). Nodal fluxes are calculated from the finite element matrix equation that is obtained by
the discretization of the Richards equation and assembled for all elements on one side of theselected internal line. The finite element matrix equation for internal fluxes is calculated at thelast iteration after convergence for a given time level had been achieved. Fluxes calculated
directly from the Richards equation are much more accurate than fluxes calculated using Darcy’s
law and have the same accuracy as the overall solution. Convective Solute Fluxes are thencalculated simply by multiplying water flux values with nodal concentrations. Note that thereported solute fluxes across mesh-lines do not include dispersive/diffusive solute flux. Note thatmesh-lines are oriented (from the first selected node to the last one), and reported fluxes are
positive or negative depending on this orientation.

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4.7.6. Points Probes
As an alternative to “Observation Nodes,” which need to be defined on FE nodes and before
calculations are carried out, Hydrus also provides an option to specify “Point Probes,” which
can be defined anywhere in the transport domain (independent of FE nodes) and after
calculations are done.
When presenting simulation results, HYDRUS displays these “Point Probes” and values of aparticular displayed quantity (e.g., water contents or concentrations) (Fig. 100). Since “Point
Probes” are specified after the simulation is finished, HYDRUS cannot display continuous timeseries as for Observation Nodes, but only values at pre-specified Print Times. When the Point
Probe is not located directly on a FE node, the quantity value is linearly interpolated from thecorner values of a particular finite element.
A Point Probe can be inserted using the Point Probe command, available on the Insert Menu.
One can create a set of Point Probes either a) numerically using a table in the New Point Probe
dialog window (Fig. 99) or b) graphically after clicking on the button “Set Graphically.” Whendefining Point Probes numerically, one must predefine their number (Number of Points) andclick on the Update button to update the table before entering Point Probe coordinates.

Figure 99. The New Point Probe dialog window.
When defining Point Probes graphically (after clicking the button Set graphically), one defines
Points in the View window directly on the Transport Domain using the mouse (clicking the left
mouse bottom at selected locations):

159

Figure 100. The display of Point Probes with their values.
Point Probes (and associated quantity values) can be displayed or hidden using the Show Point
Probes check box on the “Edit bar – Results” tab (in the section “Tools and Options”).
The Point Probes can be Deleted, Inserted, Saved, and Edited using the command in the“Current Point Probe” section of the “Edit bar – Results” tab (Fig. 101).

Figure 101. The Tools and Options section of the Results Edit Bar with Point Probes commands.

The Point Probes can be grouped into multiple named groups. The initial set of Point Probes isdenominated 0 - Temporary. To save it permanently, use the Save Probe Copy button on the160

Edit Bar below the list of point probes. A new dialog box is opened where you can define theName of the Group of Probe Points and check the coordinates of each point.
There are several Snap modes (Points Probes can be defined on different geometrical objects)
that can be used when inserting Probe Points graphically (Fig. 102).

Figure 102. The Probe Points section of the Results Edit Bar when Point Probes are defined.
All saved Point Probes are shown on the Navigator Bar under the Auxiliary Objects, where
one can select various Edit Commands using the right mouse button click, for example, Edit andDelete.
4.7.7. Lines Probes
As an alternative to “Mesh-lines,” which need to be defined along edges of finite elements (andthus are broken lines) before calculations are carried out, and “Cross-Sections,” which arestraight lines through the transport domain (independent of finite elements) that can be defined
after calculations are done, Hydrus also provides an option to specify c) “Line Probes,” which
are broken lines defined anywhere in the transport domain (also possibly independent of finite
elements) and which can be specified after calculations are done.
When presenting simulation results, HYDRUS displays these “Line Probes” and values of aparticular displayed quantity (e.g., water contents or concentrations) along these lines. HYDRUS
can display graphs of a particular quantity along a Line Probe for a particular Print Time or for
all Print Times. When Points defining a Line Probe are not located directly on FE nodes, thequantity values are linearly interpolated from the values in FE nodes.
A Line Probe can also be inserted using the Line Probe command, available on the Insert
Menu. One can create a set of definition points for the new Line Probe either a) numericallyusing a table in the New Line Probe dialog window (Fig. 103), or b) graphically after clicking
on the button “Set Graphically.” When defining a Line Probe numerically, one must predefine
the number of definition points (Number of Points) and click on the Update button to update
the table before entering definition points coordinates

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Figure 103. The New/Edit Line Probe dialog window.
The Graph Polyline Probe function (on the “Edit bar – Results” tab, in the section “Tools andOptions”) enables you to define a line in the transport domain or in the slicer plane and, thus,
create a sectional diagram of the results along the line (Fig. 104).
To display a line chart, use a) the Graphs -> Polyline Probe command which is available on the
Results menu, or b) double-clicking on a Line Probe. When the line is activated, you can selectthe relevant points of the line (or polyline) by mouse-clicks. The coordinates of the points are
displayed in the panel, which has a specific layout for this purpose. Here, you can also modify
the Snap object, if necessary (Fig. 104).
The Line Probes can be grouped into multiple named groups. The initial set of Line Probes isdenominated 0 - Temporary. To save it permanently, use the Save Probe Copy button on the
Edit Bar below the list of point probes. A new dialog box is opened where you can define theName of the Group of Probe Points and check the coordinates of each point.
All saved Line Probes are shown on the Navigator Bar under the Auxiliary Objects, where
can select various Edit commands, such as Delete All Line Probes.

162

Figure 104. The Line Points section of the Results Edit Bar when Line Probes are defined.

Figure 105. An example of the Line Probes graph.

163

4.7.8. Background Layers
Background Layers are geometric objects that can serve as a template for defining the transportdomain. A Background Layer consists of nodes and curves that are not part of the transportdomain, but its components can be used to define the transport domain. A Background Layer isusually read from the DXF file (AutoCAD) (Figure 108), but may also be read from another
HYDRUS project (h3d, h3d2, or h3d3), or from STL (stereolithography), TIN (Triangular
Irregular Network), or BMT (bitmap) formats (Figure 107). An example of a very complex
Background Layer (unrelated to hydrology) read from the DXF file is given in Figure 106.
In the New Background Layer dialog window (Figure 107), one selects a) the format of theimported file (i.e., either HYDRUS formats h3d, h3d2, and h3d3, or DXF, STL, TIN, or BMT
formats), b) units of the imported file, c) whether or not to place the Background Layer so that its
bottom-left corner is located in the origin of the coordinate system, d) whether or not to make the
Background Layer visible in the View window, and e) whether or not the Grid and Workspacesettings should be adjusted according to the Background Layer dimensions.

Figure 106. An example of the Background Layer.

164

Figure 107. The New Background Layer dialog window.

STL is a file format native to the stereolithography CAD software created by 3D Systems. This
file format is supported by many other software packages; it is widely used for rapid prototyping
and computer-aided manufacturing. STL files describe only the surface geometry of a threedimensional object without any representation of color, texture or other common CAD model
attributes. The STL format specifies both ASCII and binary representations. Binary files are
more common since they are more compact. An STL file describes a raw unstructured
triangulated surface by the unit normal and vertices of the triangles using a three-dimensional
Cartesiancoordinate
system.
The
STL
file
specificationsareat:
http://en.wikipedia.org/wiki/STL_(file_format).
TIN files are used for storing triangulated irregular networks using a simple set of xyz
coordinates. The TIN file specifications are at:
http://www.ems-i.com/wmshelp/Files/File_Formats/TIN_Files.htm.
The project may have at the same time multiple Background Layers (virtually any number) andtheir visibility can be turned on and off using the View Tab at the Navigator Bar (Auxiliary
Objects->Background Layers). Background Layers are displayed in the View window using
suppressed (less intense) colors so that they do not visually disturb when objects of the geometry
are being defined. The intensity of display and other parameters can be set (intensity of theirdisplay can be set between 0 and 1) in the Display Options dialog window (the Menu command
Options->Display Options->Edit) (Fig. 151). If the location of the template (background layer)
is not satisfactory, it can be Moved (Fig. 62), Rotated (Fig. 63, left), Mirrored (Fig. 63, right),
Stretched (Fig. 64, left), and/or Skewed (Fig. 64, right) as needed.

165

4.8. Other Notes on Objects
Objects Mesh Refinement define a local density of the FE-Mesh in the vicinity of a particular
object. Possible types of Mesh Refinement are:•Mesh Refinement at Point•

Mesh Refinement on Curve given by a number of points•

Mesh Refinement on Curve given by FE size•

Mesh Refinement on Surface

4.8.1. Object Numbering
Each object has its own number (index) that serves for the unique identification of an object for
operations such as Edit, Delete, or Find. Object numbering is fully controlled by the user (a user
specifies the object index) and does not have to be continuous (indexes do not have tosequentially increase).
4.8.2. Relations among Objects
More complex objects are defined using simpler objects. For example, a surface is defined byindices of its boundary curves, and a boundary curve is defined by indices of its points. The
curve, however, does not own its points since these points can also be used to define other curves.
This is especially true for points at the beginning and end of a curve, since these points areusually used also by neighboring curves. A relation „Parent – Descendent“ exists among objects.
In the case of a curve, points are „Parent“ objects, and a Surface is its „Descendent“.
4.8.3. References among Objects and Convention for Writing a List of Indices
Objects are referenced using a list of indices. A list of indices is written using a text format,
where individual indices are separated by a comma and dash (-) between two indices indicates arange “from-to” (e.g., 1,5-10,35-30,8,11). After inserting new indices, the list is always
reformatted to minimize the length of the text. Depending on circumstances, the list of indicesrespects/does not respect the sequence, in which objects were defined.

4.9. Import Geometry from a Text File
It is possible to Import the definition of objects defining the Geometry of the transport domainfrom a text file using the command “Import Geometry from a Text File”. It is possible to import(export) points, curves (polylines, circles, arcs, and splines), surfaces, openings, and thickness
vectors.
a) The definition of each object starts with the word OBJECT=KEY_WORD, followed bycoordinates of points defining the given object. Two or three coordinates (for two- andthree-dimensional problems; units must always be in meters) of a single point are given ona single line. Numbers can be delimited using a space, a semicolon, or a tabulator.
166b) Points associated with higher objects, i.e., lines, openings, or surfaces, are listed as part ofthis object. Similarly, lines associated with higher objects, i.e., openings or surfaces, arelisted as part of this object. Only points that are not part of any higher object should thus
be listed under the object POINTS, and only lines that are not part of any higher object(e.g., that do not form boundaries of surfaces) should thus be listed under the object
LINES.
c) Lines with a semicolon at the beginning are ignored as „Comments". Note that comment
lines can appear only between blocks, but not inside of any particular block.
d) It is possible that exported Geometry once imported back into HYDRUS can havedifferent numbering, i.e., the project may not be identical.
e) Below is a list (KEY_WORD) of all possible objects. "POLYLINE" is a single line
defined by multiple nodes, while "LINES" is a series of lines (multiple objects). Surfaces
or Openings must be defined by a single closed curve, the type of which is given in thename of the object (e.g., SURFACE_CIRCLE). When this rule is not fulfilled (e.g., for asurface with complex boundary), this complex boundary will be saved as a series of lines,
i.e., SURFACE_LINES.
f) The THICKNESS_ARR3Z_NLAYERS command allows importing multiple Thickness
Vectors to define the variable thickness of a Solid. On each Thickness Vector, one candefine multiple z-coordinates that are used to divide a Solid automatically into Layers withvariable thicknesses. The number of Layers is arbitrary (min=1, max=100), and their
number is given by the number of columns in the file.
KEY_WORD for Import/Export:
POINTSLINESPOLYLINE
SPLINECIRCLEARC
SURFACE_LINESSURFACE_POLYLINESURFACE_SPLINE
SURFACE_CIRCLEOPENING_LINESOPENING_POLYLINEOPENING_SPLINEOPENING_CIRCLE
THICKNESS
THICKNESS_ARR3Z
THICKNESS_ARR3Z_NLAYERS

Notes on the THICKNESS_ARR3Z_NLAYERS command (the THICKNESS_ARR3Z commandhas only the first five columns):
Particular columns in the input file have the following meaning:167

1. X coordinate (m).
2. Y coordinate (m).
3. Z coordinate (m) of the Definition Point of the Thickness Vector (Anchor Point, see
Figure 85 of the User Manual with the Edit Thickness Vector dialog and the point
denoted "P"). The Definition (Anchor) Point must lie in the plane of the Base surface.
The Z-coordinate in the third column will thus likely be constant for all Thickness
Vectors unless the Base Surface is inclined.
4. Z coordinate (m) of the lower point of the first layer of the Thickness Vector (a point
denoted "N1" in Figure 85 of the User Manual). When P=N1, this coordinate is the sameas the 3rd coordinate.
5. Z coordinate (m) of the upper point of the first layer of the Thickness Vector.
6. Z coordinate (m) of the upper point of the second layer of the Thickness Vector.
7. …
8. Z coordinate (m) of the upper point of the last layer of the Thickness Vector, i.e., thecoordinate of the surface of the solid.
Here is an example of the file for the import of a Solid divided into three Geo-Layers:
OBJECT=THICKNESS_ARR3Z_NLAYERS
4.500000e+000
4.000000e+000
5.500000e+000
2.500000e+000
7.000000e+000
4.500000e+000
7.000000e+000
2.500000e+000
6.500000e+000
9.999999e-001
5.000000e+000
2.000000e+000
4.500000e+000
2.000000e+000
5.000000e+000
9.999999e-001
5.500000e+000
9.999999e-001;

0.000000e+000
0.000000e+000
0.000000e+000
0.000000e+000
0.000000e+000
0.000000e+000
0.000000e+000
0.000000e+000
0.000000e+000

0.000000e+000
0.000000e+000
0.000000e+000
0.000000e+000
0.000000e+000
0.000000e+000
0.000000e+000
0.000000e+000
0.000000e+000

1.300000e+000
1.300000e+000
1.400000e+000
1.200000e+000
1.600000e+000
1.200000e+000
1.400000e+000
1.500000e+000
1.100000e+000

2.100000e+000
2.200000e+000
2.300000e+000
2.600000e+000
2.400000e+000
2.500000e+000
2.400000e+000
2.500000e+000
2.100000e+000

3.300000e+000
3.400000e+000
3.000000e+000
3.500000e+000
3.600000e+000
3.700000e+000
3.400000e+000
3.300000e+000
3.200000e+000

Other notes:
9. The minimum number of columns is 5 (this corresponds to a single layer).
10. Z coordinates must be entered in the correct sequence, i.e., from the bottom (BaseSurface) up towards the end of the Thickness Vector.
11. If layers are to be defined in a different direction than Z (e.g., when the Base Surface lie
in the XZ plane), one needs to first carry out the standard import in the Z direction andthen to rotate the entire domain using the Rotate function.
12. When the “THICKNESS_ARR3Z_NLAYERS” is used, i.e., the input file includes dataof thickness vectors with multiple geo-layers, this keyword can be processed fully only if
the domain already contains a 3D-Layered Solid. If there is no Solid defined yet, thenHYDRUS is not able to create a Solid automatically from imported points because its
Base Surface can have a very complex shape. There are two ways how to proceed:a) Press “OK” to continue. HYDRUS will import first only thickness vectors without
geo-layers. Then define a 3D-Layered Solid using imported points and import thesame file again. Geo-layers will be added to the Solid during this second import.
b) Press “Cancel” to cancel this import. First, define a 3D-Layered Solid and thenimport this file again. Thickness vectors with layers will be added to the Solid.

1684.10. Import Geometry from a DXF File
It is possible to Import the definition of objects defining the Geometry of the transport domainfrom a file in the DXF format. AutoCAD DXF (Drawing Interchange Format, or Drawing
Exchange Format) is a CAD data file format developed by Autodesk for enabling datainteroperability between AutoCAD and other programs. Autodesk now publishes the DXF
specifications on its website for versions of DXF dating from AutoCAD Release 13 to AutoCAD
2010. The menu command Import Geometry from a DXF File calls the dialog window (Fig.
108) of the same name that allows users to select (or browse for) the DXF file with thedescription of the transport domain and to specify units that are used in this file.

Figure 108. The Import Geometry from a DXF File dialog window.

Since local coordinates defining the transport domain in the coordinate system used in the DXF
files may include very large numbers, users can ask the HYDRUS GUI to convert thesecoordinates so that the bottom-left corner of the transport domain is located in the origin of thecomputational coordinate system. This will likely lead to much smaller values of local
coordinates. Finally, users can ask the HYDRUS GUI to automatically adjust the Grid andWorkspace variables to accommodate the imported geometry.
4.11. Import Geometry from a TIN File
It is possible to also Import the definition of objects defining the Geometry of the transportdomain from a file in the TIN format. TIN files are used for storing triangulated irregular
networks using a simple set of xyz coordinates. The TIN file specifications are at:
http://www.ems-i.com/wmshelp/Files/File_Formats/TIN_Files.htm.

169

170

5. Finite Element Mesh
5.1. Finite Element Mesh Generator
The Finite Element Mesh Generator dialog window was used in earlier versions to select astructured finite element mesh for a relatively simple rectangular or hexahedral domain, or amore general unstructured finite element mesh. The dialog provided a brief description of eachmesh generator and a simple bitmap with an explanation of the main terms involved. In later
versions (after 1.03), a decision on which generator to use is made in the Domain Type and Units
Window (Fig. 6 and 7). While the structured finite element generator can be used only for simple
rectangular (i.e., the Geometry Type "2D-Simple (Parametric)" - see the Projects Geometry
Information Section 2) or hexahedral domains (3D-Simple (Parametric)), the unstructured finite
element generator is used for more complicated geometries (i.e., 2D-General (Boundary Rep.),
3D-Layered, and 3D-General (Boundary Rep.)). While the unstructured mesh generator
MeshGen2D is used to generate FE meshes for two-dimensional domains (2D-General(Boundary Rep.)) and for the Base Surface of three-dimensional layered domains (3D-Layered),the mesh generator Genex/T3D is used to generate three-dimensional FE meshes for the 3DGeneral (Boundary Rep.) geometry.
5.2. Structured Finite Element Mesh Generator
As discussed in Section 2, two-dimensional transport domains can be defined using modified
rectangles. Simple rectangular domains are defined by three straight lines, one at the bottom of thedomain and two at the sides, while the upper boundary may or may not be straight (see examples inFig. 8). Nodes along the upper boundary may, in that case, have variable x- and z-coordinates, but
the lower boundary line must be straight (horizontal or with a specified slope), whereas the left andright boundary lines must be vertical. The flow region can then be discretized into either astructured or an unstructured triangular finite element mesh.
When the structured mesh is used, one then needs to specify in the Rectangular Domain
Discretization dialog window the number of nodes (Count) on the horizontal (Horizontal
Discretization in X-Direction) and vertical (Vertical Discretization in Z-Direction) sides of therectangular region, including their nodal coordinates (Fig. 109). The relative size of finite
elements on the vertical side can be modified using the RS1 (relative size at the top) and RS2(relative size at the bottom) factors below General Vertical Coordinates. The element sizes arethen proportionally distributed. Smaller RS factor leads to smaller elements.
The upper boundary is by default parallel with the bottom boundary. Any possible verticaldeviations from this parallel line can be defined using dz values (in the Horizontal Discretizationin X-Direction part of the window). Relatively general domains can still be defined by properly
adjusting the dz values (see Fig. 8).

171

Figure 109. The Rectangular Domain Discretization dialog window.
A similar approach can be used to discretize simple hexahedral domains in three dimensions.
Hexahedral domains must have similar properties as rectangular domains in that they are defined byvertical planes at the sides, a horizontal plane (possibly with a certain slope) at the bottom boundary,
and with only the upper boundary not having to be a plane. The discretization of the hexahedral
domain is then defined in the Hexahedral Domain Discretization dialog window. Again, one
needs to specify the number of nodes (Count) on the horizontal (Horizontal Discretization in X,
Horizontal Discretization in Y) and vertical (Vertical Discretization in Z-Direction) sides of thehexahedral region and their nodal coordinates (Fig. 110). The relative size of finite elements on
the vertical side can again be modified using RS1 (relative size at the top) and RS2 (relative sizeat the bottom) factors (General Vertical Coordinates). The vertical final element sizes are thenproportionally distributed.
Any possible vertical deviations from the plane parallel with the bottom of the domain can be
defined using the dz values (in the Horizontal Discretization in X and Horizontal Discretization
in Y parts of the window). This feature still allows relatively general domains to be created (seeFig. 9).

172

Figure 110. The Hexahedral Domain Discretization dialog window.

1735.3. Unstructured Finite Element Mesh Parameters
Parameters for generating the Unstructured Finite Element Mesh are specified in the FE-MeshParameters dialog window (Figs. 111 through 117). This dialog window has six and four Tabs
for the MeshGen2D and T3D generators, respectively, in which various parameters of the
unstructured finite element mesh can be specified.
The Main Tab
The Targeted FE size (i.e., the average size of the triangular elements in the generated finite
element mesh) is specified on the Main Tab (Figs. 111). The program selects by default a
Targeted FE Size. Users can change this value by deselecting the Automatic check box. The
finite element mesh with this Targeted FE size can be further modified using various tools, suchas Stretching in different directions (on the Stretching Tab, Fig. 112) to make the meshanisotropic, specifying the Maximum Number of Nodes on Boundary Curve (on the MG-Options
Tab, Fig. 116) and Minimum Number of Nodes on Boundary Curve (on the Options Tab, Fig.
117), and using Finite Element Mesh Refinement (Fig. 119). While the Default command sets
default values on a particular tab of the FE-Mesh Parameters, the All Default command sets
default values on all four tabs. For three-dimensional applications (only for 3D-Layered
geometries), a user can specify on the Main Tab the No. of Horizontal Layers, which are layers
parallel with the Base Surface to add the third dimension to the problem and if the finite
elements used to discretize the three-dimensional domain are to be Tetrahedrals or Triangular
Prisms for 3D-Layered geometries, or Tetrahedrals or Mixed Elements (multiple types of
elements) for 3D-General geometries. It is recommended to use Triangular Prisms or Mixed
Elements rather than Tetrahedrals since then the number of finite elements is three or more times
smaller, and thus, the calculations are faster.

Figure 111. The FE-Mesh Parameters dialog window (the Main Tab for 3D-Layered (left) and
3D-General (right) geometries).

174

For 3D-General geometries, users also need to specify the Maximum Number of Nodes in the
FE mesh. This is the maximum number of finite element nodes in the entire three-dimensional
domain. Similarly, as below for MeshGen, when this is specified for a two-dimensional domain(Fig. 116) when this maximum number is reached a warning will appear Achieved the maximum
number of nodes! This means that the maximum allowed number of nodes was reached during
the mesh generation process and the user needs to decide whether or not so many nodes areneeded for the envisioned FE mesh and either increase this number or adjust other parameters sothat fewer nodes (and FE elements) are generated.
For 3D-General geometries, there is in the Mesh Consistency Check section an additional checkbox Detect Collisions. This check box is important only for complex 3D-General geometries
consisting of multiple solids. When this check box is on, the program checks "collisions" ofdifferent objects. The solids cannot intersect each other without having the intersections properly
defined using boundary curves. The program also detects if one Solid is entirely inside ofanother Solid (i.e., its boundaries do not intersect). The former Solid has to be in such casedefined as an Opening (Hole, Cavity). The check box "Detect Collisions" enables users to turnoff this check in cases, when they are absolutely sure that there are no such collisions, and they
still receive a warning about a collision of solids.
The Stretching Tab
Stretching of the finite element mesh (i.e., the degree of mesh anisotropy in a certain direction)
is defined using the Stretching Factor and Stretching Direction (Fig. 112). The finite elements
are made larger in the particular Stretching Direction if the Stretching Number is larger than
one and smaller if smaller than one. The result of this transformation is a mesh deformed in thegiven direction, which can be desirable for problems that, for example, require different spatial
steps (mesh sizes) in the X and Y directions.

Figure 112. The FE-Mesh Parameters dialog window (Tab Stretching).
175

The Stretching Direction is defined either by the direction of main X, Y, and Z coordinates (inboth 2D and 3D projects) or by a general vector V with two coordinates (Vx and Vz for vertical
two-dimensional domains and Vx and Vy for horizontal two-dimensional domains). An example
of a mesh stretched using a Stretching Factor of 3 in the x-direction is shown in Figure 125.
One can define a Global FE-Mesh Stretching using the Stretching Tab (Fig. 112) of the FEMesh Parameters window or a Local FE-Mesh Stretching, using the Insert->FE-Mesh->Mesh
Stretching command. While a Global FE-Mesh Stretching is applied to the entire transportdomain, a Local FE-Mesh Stretching can be assigned to individual Surfaces (On Surface No.). A
local FE-Mesh Stretching can be defined in the direction of main coordinates or parallel (VParallel) or perpendicular (V - Perpendicular) to a general vector V, which is defined by two (orthree) coordinates (Vx and Vz or Vx and Vy (or Vx, Vy, and Vz)) or by selecting two points in thetransport domain (Pick Two Points). Note that Local FE-Mesh Stretchings are ignored when a
Global FE-Mesh Stretching is defined (i.e., a Global FE-Mesh Stretching has to be equal to 1 if
one wants to consider Local FE-Mesh Stretchings). FE-Mesh Stretching is available only for 2DGeneral and 3D-Layered domains.

Figure 113. The Mesh Stretching dialog window for a Local FE-Mesh Stretching.
In the example below (a listing from the Navigator Bar), the first FE-Mesh Stretching has a
Stretching Factor of 0.03 in the direction of the Z coordinates assigned to Surface 3, the second
FE-Mesh Stretching has a Stretching Factor of 0.01 in the direction of the general V2 vector
assigned to Surface 2, etc.

176

Figure 114. Listing of FE-Mesh Stretchings on the Navigator Bar.
Local FE-Mesh Stretchings can be edited by clicking at them at the Navigator Bar. Figure 115
below shows an example of the finite element mesh with three FE-Mesh Stretchings assigned toareas below the domain surface. These Stretchings were defined either using the Menu
Command "Insert->FE-Mesh->Mesh Stretching - Dialog" or the Edit Bar Command "Insert
Mesh Stretching". All Local FE-Mesh Stretchings can be deleted using the Edit Bar Command"Delete All Stretching".

Figure 115. An example of the FE-Mesh with three FE-Mesh Stretchings assigned to areas below
the domain surface.

177

The MG-Options Tab
Parameters for the unstructured triangular finite element generator are given in the MG-Options(Meshgen) Tab of the FE-Mesh Parameters dialog window (Fig. 116). The parameters are
divided into FE-Mesh Limits (which limits the number of elements) and FE-Mesh Quality(which affects the smoothness of the FE mesh) groups.
The following parameters are specified in the FE-Mesh Limits group:
Maximum Number of Nodes on Boundary Curves: This is the maximum total number ofnodes on all boundary curves for two-dimensional applications, or on all boundary curves
defining the bottom plane (base surface) for three-dimensional applications.
Maximum Number of FE-Mesh Nodes (2D Mesh): This is the maximum total number of finite
element nodes in two-dimensional domains, or on the bottom plane (base surface) of threedimensional domains.
Both parameters are mainly informative and may lead to an interruption of the FE-meshgeneration process. The mesh generation is interrupted by the message: Achieved the maximum
number of nodes! This means that the maximum allowed number of nodes (either on theboundary curves or in the two-dimensional domain) was reached during the mesh generation
process. This is usually a consequence of having too many nodes along the boundaries (thenumber of mesh nodes inside a domain increases approximately with the square of the number ofboundary nodes). It is then necessary to decide whether or not so many nodes are needed for theenvisioned triangular mesh. If the answer is ‘yes’ then the maximum number of nodes must be
increased in this dialog window. If the answer is ‘no’, then it is necessary to decrease theTargeted FE Size (Figs. 111) or to increase the Smoothing Factor (in the FE-Mesh Quality
group discussed below).

Figure 116. The FE-Mesh Parameters dialog window (Tab MG-Options).

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The following parameters are specified in the FE-Mesh Quality group:
Maximum Number of Overall Remeshing Iterations:This number defines the maximum number of iterations during finite element mesh remeshing.
In most cases, the resulting mesh is obtained within fewer iterations than the default value of 10.
In some cases, the repeated adding and removing of nodes can cause an infinite loop. In that case(or when the mesh generation process converges very slowly) the code terminates after reaching
the maximum number of iterations as defined by this value.
The number of Intensive Smoothing Steps:
Intensive smoothing repeats the operations of Delaunay remeshing and smoothing until there are
no more changes during the Delaunay remeshing step. This parameter specifies the number ofintensive smoothing cycles at the beginning of the mesh generation process, which cansignificantly influence the mesh smoothness. However, too many smoothing cycles cansignificantly slow down the mesh generation process. The recommended value is between 1 (lesssmoothing) and 3 (more smoothing).
The number of Internal Iterations for Intensive Smoothing:This number defines the maximum number of iterations during one intensive smoothing step.
This number guarantees that intensive smoothing will stop after a specified number of iterations,even when the prescribed criterion is not reached (i.e., some changes would still occur during
Delaunay remeshing).
The number of Internal Iterations for Standard Smoothing:This number defines the maximum number of iterations while solving the elliptic equations, a
process needed during mesh smoothing; it significantly influences the final smoothness of themesh. A higher number of iterations improves mesh smoothness. It serves little purpose toincrease the number above 20 since the mesh is then virtually constant anyway, while the wholeprocess of mesh generation would be slowed down significantly.
Smoothing Factor:
The smoothing factor is the ratio of the maximum and minimum height of a finite element
triangle. For a triangle with equal sizes, this factor is equal to 1 (which is theoretically notachievable for finite element meshes). The smoothing factor can be decreased to a value of about
1.1 when a highly smooth finite element mesh is required and, vice-versa, can be increased whena course mesh can be tolerated. The smoothing factor significantly affects the final number of
elements.
In general, the default values in the FE-Mesh Parameters dialog window should be preserved;
only experienced users should modify the various parameters needed for the mesh generation
process.
When the option at the bottom of Figure 116 is checked, HYDRUS compares distances between
the neighboring nodes on the domain boundaries. When the ratio of distances between two
neighboring nodes is larger than F, the FE mesh is automatically refined.

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The Options Tab
Minimum Number of Points Boundary Curves is set by default equal to 15. This number canbe changed in the FE-Mesh Parameters dialog window of the Options Tab (Fig. 117). Thisparameter is important when such objects as openings representing wells or drains are includedin the transport domain. These objects may be very small compared to the global finite element
mesh (i.e., smaller than the targeted finite element size). Having a minimum number of nodes onboundary curves will then lead to local refinement of the finite element mesh around theseobjects, thereby ensuring that relatively small objects are accurately represented in the numericalsolution.

Figure 117. The FE-Mesh Parameters dialog window (Tab Options).
The Export Tab
In the Export Tab (not shown), users can select options for export of the FE-Mesh to a text file.
One can, for example, choose, which points to export (including or excluding the intermediate
points on boundary curves) and whether or not to include in the export also internal curves.

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The Mesh Section Tab
The program can generate default FE-Mesh Sections (the Mesh Section Tab of the FE-MeshParameters dialog window, Fig. 118) or FE-Mesh Sections (for detailed description, see Section
5.7) can be created by a user. Default FE-Mesh Sections depend on the geometry of the transportdomain. For example, the default section includes a) Entire FE Mesh, b) Vertical (horizontal)
shell, and c) Each horizontal (vertical) layer. Mesh Sections can also be generated for each GeoSection (see Section 8.1.8). The Mesh Sections are generated automatically when the FE-Meshis generated or anytime using the menu command Edit->Sections->Generate Sections (note thatthe dialog window to Options for Generation of Geo-Sections and FE-Mesh Sections (Fig.
179) is similar to the Sections Tab of the FE-Mesh Parameters window (Fig. 118)).

Figure 118. The FE-Mesh Parameters dialog window (Mesh Section Tab).

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5.4. Finite Element Mesh Refinement.
The Finite Element Mesh Refinement is carried out in two steps:
1. One must first define the desired type of FE Mesh Refinement using the dialog window
shown in Figure 119. Mesh refinement can be defined around Points, Lines, Number ofPoints on the Line, Surfaces, or Solids.
2. Next, users must assign the refinement to particular Points, Lines, or Surfaces, so theprogram knows where the refinement should take place. After double-clicking on a particularpoint, line, arc, circle, or spline, the corresponding dialog window will appear (the Edit
Point dialog window, Fig. 54; or the Edit Curve dialog window, Fig. 56), where users
should select FE-Mesh Refinement in the FE-Mesh Tab. The code will then create a list ofnodes (or lines or surfaces) for a particular refinement that can be further edited by a user. FE
Mesh Refinement is graphically displayed using red dots in green circles for nodes, green
nodes for lines, and a small square in the corner of a surface. By clicking on these coloreditems, the FE Refinement can be deleted or edited. Editing of the FE mesh refinement willaffect all objects to which a particular refinement was assigned.
5.4.1. Finite Element Mesh Refinement for MeshGen2D
Figure 119 below shows the New FE-Mesh Refinement dialog windows that are used with the
MeshGen module for four different types of refinements. FE-Mesh Refinements can be applied
to a Point, a Line, and a Surface.
When the FE-Mesh Refinement is assigned to a Point (Figure 119 top left), users only need todefine the finite element size that is to be used at a given point. This FE-size will be used arounda given point, while the sizes of neighboring FE will be gradually increased until the Targeted
FE Size is reached further away in the computational domain. Notice that the dialog window
also displays the Global Targeted FE Size. The same FE-Mesh Refinement, i.e., the samerefined FE size, can be assigned to multiple Points in the transport domain.
There are two ways how the FE-Mesh Refinement can be assigned to a Line (Figure 119 top
right and bottom left). Users can either specify the FE-Size (Line – FE-Size; Figure 119 top
right) or the Number of Points (Line – Number of Points; Figure 119 bottom left) to be usedon the entire line. Similarly, as for points, the FE-Size (either given directly or calculated fromthe number of points) will be used on the Line, while the sizes of FE away from the Line will
gradually increase until the Targeted FE Size is reached further away in the computational
domain. Again, the same FE-Mesh Line Refinement, i.e., the same refined FE size, can be
assigned to multiple Lines in the computational domain. The size of FEs specified by the
Number of Points (on the Line) does not affect the sizes of FEs on neighboring lines.
The FE-Mesh Refinement can also be assigned to a selected Surface (Figure 119 bottom right).
In this case, users need to define FE-Size for a selected Surface. Note that this option is useful
only when multiple Surfaces are used in the computational domain. The refined FE-Size is thenused on the entire surface, including boundaries with other Surfaces, and the Targeted FE Sizeis reached only further away in the other Surfaces of the computational domain.

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The Point or Surface with an assigned FE-Mesh Refinement are indicated using the following
marks:
and, respectively. FE-Mesh Refinement is marked on curves using green points,
visible in the edit mode. Contrary to other green points on the curves, they can be selected.

Figure 119. The FE-Mesh Refinement dialog window for the MeshGen2D module with four
different types of refinements (applied to a Point, a Line with a given FE-size or the number ofPoints, and to a Surface).

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As an example, Figure 120 shows the transport domain (700 * 650 cm) and the finite element
mesh of a problem with a furrow and a drain. The mesh was generated with a Targeted FE Sizeof 50 cm and three FE-Mesh Refinements (Fig. 120, top). Refinement 1 (with a finite element
size of 10 cm) was assigned to nodes 1, 2, 4, and 5, refinement 2 (5 cm) to node 3, andrefinement 3 (15 cm) to nodes 8 and 9. There were 15 nodes on the drain boundary (due to thecommand Minimum Number of Points on Each Closed Boundary Curve). The resulting
finite element mesh is shown in Figure 120 (bottom).

Figure 120. Example of FE-Mesh Refinements (top) and FE-Mesh (bottom).

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5.4.2. Finite Element Mesh Refinement for Genex/T3D
While the MeshGen2D module discretizes the computational domain into unstructured FE-meshusing triangles (in 2D) and tetrahedrals (in 3D), the Genex/T3D module uses primarily
quadrilateral (in 2D) and hexahedral (in 3D) finite elements. Genex/T3D uses triangles only inparts of the domain where needed, e.g., when it refines the grid. Although quadrilateral orhexahedral elements may be generated by Genex/T3D, the computational module subdivides
these elements into triangles or tetrahedrals, respectively. While the transition between domains
with refined FE-mesh and domains with global mesh size in MeshGen2D is relatively smoothand gradual (see Figure 120), in Genex/T3D the extent of this transition zone is defined exactly
by users (see Figures below). Similarly, as MeshGen2D, the same FE-Mesh Line Refinements
can be assigned to multiple Points, Lines, Surfaces, and Solids in the computational domain.
There are two ways how the FE-Mesh Refinement can be assigned to a Point (Figure 121).
Users can use either Circular or Rectangular refinement. For a Circular Refinement around apoint, a radial refinement area is defined around a node in all directions. Users need to specify
the Radius of the refinement area, the Inner Targeted FE-Size (i.e., an FE-size immediatelyaround a point), and the Outer Targeted FE-Size (i.e., an FE-size at the outer end of the radialrefinement area) (Fig. 124). The Outer Targeted FE-Size should be equal or slightly smaller
than the Global Targeted FE-Size. When generating the FE mesh, the mesh refinement iscarried out gradually towards the center because the FE length at the periphery of the refinement
area is usually identical to the global mesh width. For larger differences between the inner andouter FE length, it is recommended to set the radius not too small to avoid acute-angled
triangular finite elements in the refinement area. For a Rectangular Refinement, a rectangularrefinement area is defined around a node in all directions. Users need to specify the Side Lengthof the refinement area and the Inner Targeted FE-Size (i.e., an FE-size immediately around apoint) (Fig. 124).

Figure 121. Circular (left) and rectangular (right) refinements around a node.
FE-Mesh Refinements assigned to a Line are handled in Genex/T3D similarly as in
MeshGen2D. One can again define either the size (spacing; Line through FE-Length) or thenumber (a specific number of equidistant sub-divisions; Line through Division) of finite

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elements along a line. In the former case, one needs to define the Target FE Length, in the latter
case, the Number of Division FE Nodes. However, while in MeshGen2D there was a gradualincrease in sizes of finite elements away from the Line, in Genex/T3D the refinement affects
only one row of finite elements (Figure 122).

Figure 122. Refinement on a line (by defining either the size or the number of finite elements
along a line).
It is also possible to define Fe-Mesh Refinements for Surfaces or Solids (Figure 123). In bothcases, users need to specify the Targeted FE-Size, which will be set as the target size of thefinite elements for the entire surface or solid.

Figure 123. Refinements on a surface (left) or solid (right).

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Figure 124. The FE-Mesh Refinement dialog window for the Genex/T3D module with six
different types of refinements (applied to a Point, a Line with a given FE-size or a number ofpoints, to a Surface, and to a Solid).

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5.5. Unstructured Finite Element Mesh Generator MeshGen2D
The MeshGen2D module may be used to discretize a two-dimensional flow region (or a base planeof the three-dimensional domain) into an unstructured triangular mesh. The algorithm used for thispurpose is general and can be applied to virtually any two-dimensional computational domain. The
first step of the mesh generation process discretizes the boundary curves, while the second step
generates the unstructured triangular mesh.
Generation of Boundary Points
The first step of the mesh generation process involves discretization of the boundary curves. During
this step, boundary nodes are generated on all boundaries and internal curves by dividing them inabscissas (i.e., short boundary edges). If no previous boundary nodes existed, the programautomatically generates a default equidistant point distribution. Boundary nodes can be edited byusers to optimize the lengths of the boundary edges using the FE-Mesh Parameters dialog
window (Figs. 111 through 117). The local density of the mesh can thereby be determined in any
part of the domain (also taking into account the use of internal curves). There are two ways to obtainappropriate distributions of the boundary nodes, i.e., by (1) specifying the Targeted FE size (Figs.
111, the Main Tab), and (2) refining the FE-Mesh (the FE Mesh refinement dialog window, Fig.
119).
1) A global Targeted FE Size (Fig. 111) is the main variable of the FE-Mesh process.
Although a default Targeted FE-Size is specified by the program, this value should be
adjusted by users in most applications. The default value is used to generate at least areasonable initial mesh, even for inexperienced users.
2) The finite element mesh can be adjusted locally in the domain by using FE-Mesh
Stretching (Fig. 112 and 125) or FE-Mesh Refinement (Figs. 54, 35, and 119). FE-Mesh
Refinement can be implemented for various geometric objects, including Points, Lines, orSurfaces (Fig. 119). When several FE-Mesh Refinements overlap in one location (such as
when the FE-Mesh Refinement is defined for both a point and a line), then the FE-Mesh
Refinement specified for the lower-level objects (i.e., a point rather than a line) is used.
The boundary nodal distribution determines in a very substantial manner the ultimate quality andsize of the unstructured finite element mesh. Optimally distributing nodes along the boundaries ofrelatively complicated domains (e.g., a very irregular anisotropic domain) can be a very difficult
problem and may require some experience.
Table 18. Definition of terms related to the boundary discretization.
Boundary Nodes

Boundary nodes are points marked by green squares, which discretizeboundary curves. These nodes are generated along every boundary curveand are ordered in a counter-clockwise direction (on closed curves).
Boundary nodes determine the local densities of the triangular meshgenerated for a given boundary nodal distribution and are part of thetriangular mesh.

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Boundary Edges

Boundary edges are abscissas discretizing boundary curves. They connect
generated boundary nodes, are oriented in a counter-clockwise direction,
and are located on the edge of the mesh.

Fixed Points

Fixed points are points on boundary curves marked by red squares. These
points may be used to adjust the local density of boundary nodes (using FE
Mesh refinement). By default, fixed points are placed on all nodes ofpolylines and on all object boundary points describing the boundary, butthey can also be inserted or deleted at any other point on boundary curves.

Generation of the Unstructured Triangular Mesh
The unstructured triangular mesh is generated by means of five operations:(1) discretization of the flow domain into triangles with vertices at given boundary nodes(Fundamental Triangulation),(2) inserting new points in all triangles which do not fulfill a certain smoothness criterion(Mesh Refinement),(3) implementation of Delaunay's retriangulation for the purpose of eliminating all nodes
surrounded by more than six triangles, as well as to avoid extreme angles (Remeshing),(4) smoothing of the mesh by solving a set of coupled elliptic equations in a recursive manner(Smoothing), and(5) correction of possible errors that may appear during the smoothing of the finite element
mesh (Convexity Check).
Operations 2 through 5 are repeated until a prescribed smoothness of the mesh has been achieved.
An unstructured triangular mesh for a given boundary nodal distribution can be generated in two
different ways: a step-by-step approach (Calculation->Advanced FE-Mesh Generation>Fundamental Triangulation and subsequent commands, or by clicking on the Fundamental
Triangulation command of the FE-Mesh Advanced part of the FE-Mesh version of the Tool
Sidebar), or by using automatic mesh generation (Calculation->Generate FE-Mesh or the
Generate FE-Mesh command on the Edit FE-Mesh part of the FE-Mesh version of the Tool
Sidebar). The step-by-step approach should be used only for special cases and then only by
experienced users. Automatic generation (recommended) is a much faster and easier approach. The
mesh generation parameters must be specified before the mesh generation process is started. By
modifying the mesh generation parameters, users can influence the smoothness of the mesh
(Smoothing Factor, Fig. 116), its anisotropy (Figs. 112 and 125), computational time, and thepossible display of intermediate results, among other features. The most important mesh generation
parameter is the "smoothing factor", which can significantly affect the final number of elements.
The smoothing factor is defined as the ratio of the minimum and maximum dimensions of a triangle.
When a very smooth finite element mesh is required, the smoothing factor should be decreased toabout 1.1; when a coarser mesh is possible, the smoothing factor can be increased.
The code saves mesh data, by default, in a binary format (the file MESHTRIA.000). However, users
have the option to also save mesh data into a file (MESHTRIA.TXT) in ASCII format (the Program
Options dialog window, Fig. 189), and then use possibly the data later for other calculations.
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When users do not have the authorization to use the MeshGen2D module, they can employ theinternal mesh generator for relatively simple rectangular or hexahedral transport domains.

Figure 125. Example of mesh stretching using a stretching factor of 3 in the x-direction.

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5.6. Finite Element Mesh Statistics

Figure 126. The FE-Mesh Information dialog window for a two-dimensional problem (top) and athree-dimensional problem (bottom).
Figure 126 shows dialog windows that provide information about the finite element mesh for
two- and three-dimensional applications. For two-dimensional grids, the window shows thenumber of finite element Nodes, the number of boundary 1D-Elements (boundary edges between
boundary nodes), and the number of 2D-Elements (triangles). For three-dimensional grids, thewindow shows again the number of finite element Nodes (in the entire 3D domain), the numberof boundary 1D-Elements (boundary edges between boundary nodes on the bottom plane, i.e.,the 2D base surface of the transport domain), the number of 2D-Elements (the number oftriangles on the bottom plane of the domain), and the number of 3D-Elements (tetrahedrals) inthe entire transport domain.

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5.7. Finite Element Mesh Sections
FE-Mesh Sections allow users to split the computational (transport) area into arbitrarily
complicated shapes that are defined by external 3D points. These FE-Mesh Sections can then be
used, for example, to define the material distribution or other properties. FE-Mesh Sections areparts of the FE-Mesh used to specify input variables and to display results of calculations. By
default, two-dimensional problems have only one section consisting of the entire transport domain.
For three-dimensional problems, one section by default is formed by the Whole FE-Mesh (Section
D0_000 in Fig. 127), whereas each horizontal (vertical for some applications) layer forms one
additional section (Sections ML_001 through ML_010 – Mesh Layer in Fig. 127), while the lastsection is made up by the vertical surface (Section ML_000 Shell Fig. 127). For example, thebottom Mesh Layer can be displayed when the bottom boundary conditions are specified, while the
top Mesh Layer (Section) can be displayed when the surface boundary conditions are provided.
One can similarly display results at different depths using different horizontal sections (Mesh
Layers). The Mesh Sections are generated automatically when the FE-Mesh is generated oranytime using the menu command Edit->Sections->Generate FE-Mesh Sections. Automaticallygenerated FE-Mesh Sections in different HYDRUS versions are listed in Table 19. Mesh Sections
can also be generated for each Geo-Section (see Section 8.1.8).
Additional sections can be created using commands from the FE-Mesh Sections part of the FEMesh version of the Edit Bar. One can display any existing section (or set of sections) and modify
them using the Cut with Rectangle command, and then create a new section using the New Section
from View command. This new section will then appear in the list of sections in the Section Tab of
the Navigator Bar and can be recalled at any time. Existing sections can be manipulated (Display,
Hide, Select, Unselect, Rename, Delete, Move Up, and Move Down) using the Edit Sectioncommand from the Edit Bar, or using Edit->Sections->Edit Sections.

Table 19. Finite element mesh sections generated in different HYDRUS versions.
HYDRUS Version

Generated FE-Mesh Sections

2D-LiteNothing

2D-Standard

For each Surface (of more than one) and each Geo-Section(see Section 8.1.8) defined by user.

3D-LiteFor each layer of the FE-Mesh

3D-Standard

For each FE layer, each geometric layer, and for each
Column3D-Professional

For each Geo-Section as defined in Section 8.1.8.

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Figure 127. The FE-Mesh Sections dialog window.
The function "Import FE-Mesh Section" allows importing FE-Mesh Sections by reading theirdefinition from a text file. The text file has the following format: The first three columns are thecoordinates of the point, and the fourth is an index of the FE-Mesh Section (this Section will becreated after the text file is read), into which the point belongs. An example of the text file
(http://www.pc-progress.com/Images/Pgm_Hydrus3D/Test3_Sections.txt) can be downloaded
from Tutorial 2.12 (http://www.pc-progress.com/en/Default.aspx?h3d-tutorials), which
demonstrates the use of FE-Mesh Sections.
OBJECT=INDEXES_AT_POINTS-1.200000e+000 -1.200000e+000-1.000000e+000 -1.200000e+000-8.500000e-001 -1.200000e+000-7.500000e-001 -1.200000e+000-6.700000e-001 -1.200000e+000-6.000000e-001 -1.200000e+000-7.450580e-009 2-7.450580e-009 3-7.450580e-009 3-7.450580e-009 3-7.450580e-009 3-7.450580e-009 3

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194

6. Domain Properties, Initial and Boundary Conditions
Initial and boundary conditions for both water flow and solute (heat) transport, and the spatial
distribution of other parameters characterizing the flow domain (e.g., the spatial distribution of soilmaterials, hydraulic scaling factors, root-water uptake parameters, and possible hydraulicanisotropy) and/or observation nodes are specified in a graphical environment with the help of amouse. The program automatically controls the logical correspondence between the water flow andsolute transport boundary conditions.
Various spatially variable properties (e.g., material distribution, initial and boundary conditions)can be specified in Version 2.0 of HYDRUS (Standard and Professional, not Lite) eithera) directly on the finite element mesh (as done in Version 1.0), orb) on geometric objects (e.g., boundary curves, rectangles, circles, surfaces, volumes).
The main advantage of the latter approach is that when the FEM is changed, these properties are
not automatically lost, but can be recalculated to the new FEM from their definition on
Geometric Objects. Which option is used depends on the menu command Edit->Properties andConditions on FE-Mesh. A similar button switch is also available at the end of the toolbar ( ),next to the Results button, and at the Edit Bar. The latter approach (i.e., on Geometric Objects) is
described in detail below in Section 6.5.
6.1. Default Domain Properties
For rectangular two-dimensional domains and for layered three-dimensional domains,immediately after the finite element mesh is generated, one can specify the initial Default
Domain Properties in the dialog window shown in Figure 128. Values listed in this window are
initially assigned to each horizontal layer of the transport domain, but can later be modified
graphically. The following variables are involved:
Code

h

Q
Mater
Roots
Axz
Bxz
Dxz
Temp
Conc
Sorb

Code of the boundary condition (0 for no flow, -1 for constant flux, +1 for constanthead, -2 for unsaturated seepage face, +2 for saturated seepage face, -3 (-7, -8, -9) for
variable flux, +3 (+7, +8, +9) for variable head, -4 for atmospheric, - 5 for tile drain, 6 for free drainage)
Initial value of the pressure head [L]. The initial pressure head changes linearly
between the first and last layer if one clicks on the command at the bottom of the
dialog (Linear interpolation of the pressure heads between the first and last layer).
Recharge flux, [L2T-1] and [L3T-1] for 2D and 3D applications, respectively. Since
this variable is usually specified in individual nodes, it is uncommon to specify it here.
Material number
Root distribution
Scaling factor for the pressure head
Scaling factor for the hydraulic conductivity
Scaling factor for the water content
Initial temperature [K]Initial concentration (of the equilibrium phase) [ML-3]
Initial concentration of the nonequilibrium phase (kinetically sorbed [MM-1] or of theimmobile region [ML-3])
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Values from each line are assigned to the entire layer within the FE-Mesh with the exception of
Code (the boundary condition code), which is assigned only to boundary nodes. When multiple
values are encountered within the single layer when initiating the table, the cell is left empty
instead of displaying any particular value. Unless changed, this variable will not be assigned in aparticular layer (after closing the dialog with OK), and original values will remain unchanged.
The three commands (Copy Sel., Copy All, and Paste, MS Excel Import/Export) facilitate thetransfer of data from this HYDRUS dialog window to the Excel (or other) spreadsheet. The
command “Set Boundary Conditions for Solute Transport and Heat Transport for changed
Codes:” leads to assigning Cauchy boundary conditions for solute and heat transport to nodes
where the Code was changed.

Figure 128. The Default Domain Properties dialog window.

6.2. Initial Conditions
After selecting nodes (using either the mouse in the View Window, selecting geometrical objects
on the Data Tab of the Navigator Bar, selecting Sections on the Section Tab of the Navigator Bar,or selecting objects by the mouse in the View Window and using the Ctrl keyboard button) for
which the initial condition is to be specified, and clicking on the command Set Values at the
Edit Bar (on the right side of the view window), the Water Flow Initial Condition dialog
window (Fig. 129) appears. Using this command, one can specify the initial conditions for waterflow by defining the initial spatial distribution of the pressure head or water content over theflow domain. The decision whether to use the pressure head or the water content initial196

distribution is made in the main module of the Iteration Criteria dialog window (Fig. 17). One
can specify:a) the same value to all selected nodes (Same value for all nodes),b) a distribution versus depth that is in hydrostatic equilibrium with the pressure head of thelowest point in the selected region (Hydrostatic Equilibrium from the lowest located nodal
point),c) a distribution versus depth that is in hydrostatic equilibrium with the pressure head at thesoil surface (Hydrostatic Equilibrium from the domain top surface),d) a Linear distribution with depth, ande) equal to the field capacity (see below).
When options a), b) or c) are selected, only one value of the pressure head needs to be specified.
For option d), one needs to provide values of the pressure head (or water content) for the top andbottom of the selected domain. Option c) is currently available only for 2D-Simple, 3D-Simple,
and 3D-Layered Geometries, and the vertical lines connecting different layers of FE nodes haveto be vertical.

Figure 129. The Water Flow Initial Condition dialog window.
To simplify definition of the initial condition for problems that involve slopes, an option isprovided to have pressure heads decrease in the x- and y- (the latter only for three-dimensional
problems) directions (Slope in X- direction and Slope in Y- direction).
The right top part of the dialog window (Values in selected nodes) in Figure 129 provides
information about the selected nodes, i.e., the number of selected nodes and the minimum andmaximum values of the pressure head or water content.
If a certain node is selected that is not located on the boundary, this node can be declared an
Internal Pressure Head Sink/Source. The pressure head at that node can then be kept constant or
be time-variable during the simulation.

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When the option "Set to Field Capacity" is selected, the initial pressure heads or water contents(depending on the selection made in the Iteration Criteria window, Fig. 17) is assigned to
selected nodes as follows [Twarakavi et al., 2009]:
S fc =

θ fc − θ r= n −0.60(2+ log ( K ))θs −θr10swhere θfc and Sfc are the water content and saturation at field capacity, and θr, θs, n, and Ks are
the soil hydraulic parameters for the van Genuchten [1980] model. Note that the water content at
field capacity corresponds to the hydraulic conductivity of about 0.01 cm/d [Twarakavi et al.,2009]. The initial pressure head at field capacity is calculated from the water content at field
capacity using the van Genuchten [1980] retention curve model.
Similar, but simpler, dialog windows are used to specify initial values of the temperature and theliquid and adsorbed concentrations (e.g., Temperature Distribution dialog window, Fig. 130).
The dialog window will then again provide information about the selected nodes (Values inselected nodes), i.e., the number of selected nodes and their minimum and maximum
temperatures (concentrations). One can specify either constant value for all selected nodes or
have the values change linearly with depth. When the box Use top value for the entire selected
region is checked, the value in the Top box is assigned to all selected nodes.

Figure 130. The Temperature distribution dialog window.
The initial conditions for the UNSATCHEM module are defined in terms of the Solution
Composition numbers (integer), Exchange Species numbers, Solid Species numbers and CO2
Concentrations (real). The composition numbers refer to different Solution Compositions,Exchange Species, and Solid Species defined in Figure 31.

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6.3. Boundary Conditions
The specification of the boundary conditions is relatively straightforward. Users must first selectfrom the Navigator Bar particular Boundary Conditions (i.e., water flow, solute transport, or heattransport) and then click on the Edit Bar on the particular boundary condition (e.g., constant head).
They subsequently need to move the mouse to the selected position and click the left mouse button.
Implementation of the boundary condition terminates with a repeated click of the left mouse button.
The boundary nodes will acquire the same color as the corresponding type of the boundary
condition. See the rules for specifying boundary conditions, as described in Chapter 8 of theTechnical Manual [Šimůnek et al., 2010]. Alternatively, users can first select boundary nodes andthen assign desired boundary conditions by clicking at a particular boundary condition at the
Edit Bar. Note that the Free Drainage and Deep Drainage boundary conditions cannot be
specified simultaneously in one project. Similarly, when the Gradient Boundary Conditions is
specified (see description below), the Time-Variable Flux 4 Boundary Condition is disabled.
In addition to system-dependent boundary conditions available in version 2.x of HYDRUS-2D,
several new options are available in HYDRUS. These new options are specified in the
Boundary Condition Options dialog window (Fig. 131) that is called using the menu command
Edit->Boundary Conditions->Boundary Conditions Options or from the Edit Bar for Water
Flow Boundary Conditions version using the BDRC Options command. This dialog window
has three tabs: a) Time-Variable Head/Flux 1 BCs, b) Special Boundary Conditions, and c)
Triggered Irrigation.
6.3.1. Time-Variable Head/Flux 1 BCs
The options that are available on the first tab (Time-Variable Head/Flux 1 BCs, Fig. 131) apply
to the first Time-Variable Head/Flux boundary condition. The following new options areavailable here:a) Interpolate Time-Variable Pressure Head and Flux (1) boundary conditions in time:
While in version 2.0 of HYDRUS-2D, all boundary conditions (i.e., fluxes or pressure
heads) changed in abrupt steps, the new version allows boundary pressure heads tochange smoothly with time. Abrupt changes in the pressure heads lead to sudden changes
in fluxes, while smoothly changing pressure heads provide smoothly changing fluxes. An
example of such a boundary condition is the water level in a stream or furrow.
b) Switch the boundary condition from Time-Variable Pressure Head to "No Flux BC when
Var-H.1.>99999": While version 2.0 of HYDRUS-2D only allowed either time-variable
pressure heads or time-variable fluxes on a particular part of the boundary, the newversion allows boundary conditions to change from variable pressure heads to a zero flux
and vice-versa. This boundary condition can be used, for example, for a discpermeameter where the specified head changes to a zero flux during time periods when
the permeameter is re-supplied with water. The zero flux is initiated by specifying a value
larger than 999999.

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c) Switch the boundary condition from Time-Variable Pressure Head to "No Flux BC when
the specified nodal pressure head is negative": When a time-variable pressure headboundary condition is specified along a boundary, then the specified value is assigned to
the lowest nodal point of a particular boundary, while pressure heads at other nodes areadjusted based on the z-coordinate. When this option is selected, then nodes withcalculated negative pressure heads are not associated with a Dirichlet boundary condition,
but rather with a zero flux. A fluctuating water level in a stream or furrow is an exampleof this type of boundary condition. While positive pressure head values are below thewater table, negative values occur above the water table.
d) Switch the boundary condition from Time-Variable Pressure Head to "Atmosperic BC
when the specified nodal pressure head is negative": This is similar to c) except that an
atmospheric boundary condition is assigned to nodes with negative calculated pressure
heads.
e) Switch the boundary condition from Time-Variable Pressure Head to "Seepage Face BC
when the specified nodal pressure head is negative": This is similar to c) except that a
seepage face boundary condition is assigned to nodes with negative calculated pressure
heads. Note that a Seepage Face boundary condition needs to be assigned to all boundary
nodes, for which this option is to be used.
f) Treat the Time-Variable Flux boundary condition as the Atmospheric BC: When this typeof system-dependent boundary condition is selected, then HYDRUS treats the timevariable flux boundary conditions similarly as atmospheric fluxes. This means thatpressure heads have two limiting values, with the maximum pressure head equal to
hCritS and the minimum pressure head equal to hCritA. This is true also for TimeVariable Flux 2, 3, and 4 BCs.
g) Apply Atmospheric boundary condition to nonactive Seepage Face: While in version 2.xof the code, the flux across the nonactive part of the seepage face was always equal tozero, the new version can apply atmospheric boundary conditions on a nonactive seepageface.
h) Consider snow accumulation at the soil surface when temperatures are negative: Whenheat transport is simulated simultaneously with water flow and atmospheric boundary
conditions, then snow accumulation on top of the soil surface can be simulated. The code
then assumes that when the air temperature is below -2 C all precipitation is in the formof snow. When the air temperature is above +2 C all precipitation is in the form of liquid,
while a linear transition is used between the two limiting temperatures (-2,2). The code
further assumes that when the air temperature is above zero, the existing snow layer (if itexists) melts proportionally to the air temperature.
Boundary condition options a) through e) and g) can be used only with the first time-variable
head condition.

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Figure 131. The Time-Variable Head/Flux 1 BCs tab of the Boundary Condition Options dialog
window.
6.3.2. Special Boundary Conditions
The following Special Boundary Conditions (Fig. 132) can be selected from the second tab of
the Boundary Condition Options dialog window:
1. Gradient Boundary Conditions
2. Subsurface Drip Characteristic Function
3. Surface Drip Irrigation with a Dynamic Evaluation of the Wetted Area
4. Seepage Face with a Specified Pressure Head
Gradient Type Boundary Condition
Version 1 of HYDRUS implements the Gradient Type Boundary Condition only as the Free
Drainage boundary condition, or the unit gradient boundary condition. However, in many
situations, one needs a non-unit gradient BC. For example, it is difficult to select appropriate
boundary conditions for vertical boundaries for flow in a hill slope where the side-gradient ismore or less parallel with the direction of the slope. In version 2 of HYDRUS, users can specify
a gradient other than one (unit gradient). This option, i.e., non-unit gradient boundary condition,needs to be selected from the Special Boundary Conditions tab of the Boundary Conditions
Options dialog window. Gradients are positive for flow against a particular axis, i.e., from rightto left (in the x-direction) and from back to front (in the y-direction), and should be used only (ormainly) on sides of the transport domain. In 3D, the gradient BC can be specified only in one
direction (i.e., either in x- or y-direction).
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Subsurface Drip Characteristic Function
The infiltration rate of water from a subsurface cavity (dripper) is affected by many factors,
including the pressure in the cavity, its size and geometry, and the hydraulic properties of thesurrounding soil [Lazarovitch et al., 2005]. When a predetermined discharge of a subsurface
source (e.g., a subsurface emitter) is larger than the soil infiltration capacity, the pressure head in
the source outlet increases and becomes positive. The built up pressure may significantly reduce
the source discharge rate. A special system-dependent boundary condition for flow fromsubsurface sources that uses the drip characteristic function was implemented in HYDRUS (seethe Technical Manual). This function has two variables, i.e., the nominal discharge (Optimal
Flux in Fig. 132) of the source for the reference inlet pressure hin (usually being 10 m) and theback pressure equal to zero, and an empirical constant (Exponent in Fig. 132) that reflects theflow characteristics of the emitter. Normally, c = 0.5 corresponds to a turbulent flow emitter andc = 1 to a laminar one. This option is currently available only for two-dimensional andaxisymmetrical geometries.
Implementation: The user needs to specify the “Time-Variable Flux 1” boundary condition
along the dripper boundary and hin in the “Var.H-1” column of the “Time Variable Boundary
Conditions” dialog window. A positive pressure indicates an irrigation period, and a negative
pressure indicates a non-irrigation period.
Surface Drip Irrigation – Dynamic Evaluation of the Wetted Area
The radius of the wetted area for drip irrigation for transient conditions can be calculated in
Hydrus as follows. The irrigation flux Q is applied to the single boundary node that represents
the dripper with the Neumann (flux) boundary condition. If the pressure head required toaccommodate the specified flux Q is larger than zero, the boundary condition in this particular
node is changed into the Dirichlet (head) boundary condition with zero pressure head value andthe actual infiltration flux Qa through this node is calculated. The excess flux (Q - Qa) is thenapplied to the neighboring node, again with the specified Neumann boundary condition. This
procedure is iteratively repeated until the entire irrigation flux Q is accounted for and the radiusof the wetted area is obtained. Since the infiltration flux into the dry soil is larger for early times,
the wetted area continuously increases as irrigation proceeds. This option is currently available
only for two-dimensional and axisymmetrical geometries.
Implementation: The user needs to specify the “Time-Variable Flux 1” boundary condition at
the surface boundary. The length of this boundary needs to be sufficient to accommodate theentire wetting zone. The drip discharge flux, Q, needs to be entered in the “Var.Fl-1” column of
the “Time Variable Boundary Conditions” dialog window. The user also needs to specify fromwhich node of the Time-Variable Flux 1 boundary irrigation starts. Irrigation can start in the left
node of the boundary, and then the wetting zone will be spreading to the right (From left toright); it can also start in the right node of the boundary, and then the wetting zone will be
spreading to the left (From right to left), or it can start in the arbitrary middle node of theboundary (Center Node) and spread in both direction (From the center).

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Seepage Face with a Specified Pressure HeadThis type of boundary condition is often applied to laboratory soil columns when the bottom of
the soil column is exposed to the atmosphere (gravity drainage of a finite soil column). The
condition assumes that the boundary flux will remain zero as long as the pressure head is
negative. However, when the lower end of the soil profile becomes saturated, a zero pressure
head is imposed at the lower boundary, and the outflow is calculated accordingly. This type ofboundary condition is often used for lysimeters.
Users can specify a pressure head value other than zero (Pressure Head) for triggering flux
across the seepage face (in several experimental settings, negative pressure can be applied at thebottom of laboratory columns or lysimeters).

Figure 132. The Special Boundary Conditions tab of the Boundary Condition Options dialog
window.

6.3.3. Triggered Irrigation
Triggered Irrigation can be specified on the third tab of the Boundary Condition Options
dialog window (Fig. 133). Irrigation can be triggered by a user-specified “Pressure Head
Triggering Irrigation” (input) reached in the selected “Observation Node Triggering
Irrigation”. The irrigation starts after a user-specified Lag Time (input) at a user-specified
Irrigation Rate or Pressure Head (input). The Duration of Irrigation has to be also specified.
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This option is currently available only for two-dimensional and axisymmetrical geometries. An
output file IRRIG.OUT is created when the triggered irrigation option is used containing
information about irrigation scheduling and all triggered irrigation events (see Table 11.11 of theTechnical Manual).

Figure 133. The Triggered Irrigation tab of the Boundary Condition Options dialog window.

6.3.4. Reservoir Boundary Condition
Version 3 of the two-dimensional module of HYDRUS (2D/3D) offers a new system-dependent
boundary condition, further referred to as the Reservoir Boundary Condition. This option
allows users to consider a reservoir that is external to the HYDRUS transport domain, whilewater can be added (injected) to or removed (pumped) from the reservoir. Flow into or out of thereservoir through its interface with the subsurface transport domain depends on the prevailingconditions in the transport domain (e.g., the position of the groundwater table) and external
fluxes. Since mass balances of water and solute in the external reservoir are constantly being
updated (based on all incoming and outgoing fluxes), the boundary conditions along the transportdomain are dynamically adjusted depending upon the water level in the reservoir.
The Reservoir BC is implemented in HYDRUS (2D/3D) for three different geometries (Figure1): a well, a furrow, and a wetland. While the furrow BC is implemented only for twodimensional transport domains, the well and wetland BCs are implemented for both twodimensional planar and axisymmetric transport domains.

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Figure 134. Three different types of the reservoir boundary condition: a well, a furrow, and awetland. In the figure hw is the water level in the reservoir [L], S is the volume of water in thereservoir ([L2] or [L3] for two-dimensional and axisymmetric systems, respectively), Qp is thepumping rate (positive for removal of water, negative for adding water) ([L2T-1] or [L3T-1] for twodimensional and axisymmetric systems, respectively), c is the solute concentration in reservoir water[ML-3], cp is the solute concentration in injected water [ML-3], P and E refer to the precipitation andevaporation rates [LT-1], rw is the radius of the well [L], a is the half-width of the furrow [L], α is theslope of the furrow side [-], rmax is the maximum width (radius) of the wetland [L], zmax is the
maximum depth of the wetland [L], and b represents the width of the water table ([L] or [L2] for twodimensional and axisymmetric systems, respectively).

The parameters for the Reservoir Boundary Condition are specified using the Reservoir
Boundary Condition Tab of the Boundary Conditions Options dialog window. Users have tofirst check the Reservoir BC check box and select the Reservoir Type, which can be either Well
(rectangular, cylindrical), Furrow, or Wetland (Figure 134). Users have then to provide
information about the reservoir geometry (i.e., the z-coordinate of the well (furrow, wetland)bottom, Well (Wetland) Radius or Half-Width of the Furrow Bottom, the initial position of thewater table in the reservoir (Z-coordinate of the initial water level), and Pumping or Injection
Rate. When solute transport is considered, then the Solute concentration initially in the reservoir
water needs to be specified as well. The Pumping or Injection Rate specified in this window is
considered to be constant in time. When time-variable pumping or injection of water from/into
the reservoir is to be simulated, this rate needs to be provided using the "Var.Fl.-1" column in theTime-Variable Boundary Conditions dialog window. Note that this rate is in units of [L2T-1] or[L3T-1] for two-dimensional or axisymmetrical applications. An output file WELL.OUT iscreated when the reservoir boundary condition is used containing information about fluxes intoand from a reservoir (see Table 11.10 of the Technical Manual).

205

206

Figure 135. The Reservoir Boundary Condition tab for the Well (top), Furrow (middle), andWetland (bottom) reservoir of the Boundary Conditions Options window.

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6.4. Domain Properties
Domain Properties are variables or parameters that may vary in space and are therefore definedeither on Geometrical Objects or Finite Element Mesh. The table below lists Domain Properties
recognized by HYDRUS.
Table 20. Domain properties.
Materials

Roots

Nodal
Recharge

Scaling
Factors

Anisotropy

Subregions

Observation
Nodes

Subsurface is usually composed of various material layers (horizons) that
may have similar or dramatically different properties. Users must first
define the Number of Materials needed to fully describe the subsurface intheir project, then provide various parameters characterizing this material(e.g., Soil Hydraulic Properties and Solute Transport and Reaction
Parameters), and finally describe the Spatial Distribution of Materials.
Roots, and correspondingly the root water uptake, are spatially distributed.
There are usually more roots closer to the soil surface, and their number
then decreases with depth. There are more roots closer to the trunk of thetree or a shrub and less further away. Users can either manually specify
Spatial Distribution of Root Water Uptake or use predefined RoodDistribution Analytical Functions.
Nodes in the finite element mesh can be assigned either positive or negative
Nodal Recharge, which may represent either sink or source of water in aparticular node, respectively. These nodes can represent, for example,
pumping or injecting wells.
The spatial distribution of soil hydraulic properties can also be describedusing the so-called Scaling Factors. These Scaling Factors, which can be
specified for Pressure Head, Hydraulic Conductivity, and Water Content,
then linearly transform the basic soil hydraulic functions. The spatial
distribution of scaling factors can be defined either manually or they can begenerated Stochastically.
Hydraulic conductivity can have different values in different directions. For
example, hydraulic conductivity may be significantly larger in thehorizontal direction than in the vertical direction (likely due to theorganization of soil particles). The Anisotropy is fully described by the
Tensor of Anisotropy (angles between directions of anisotropy and spatial
coordinates; and individual components of anisotropy).
Subregions are parts of the transport domain, for which mass balances (forwater, solutes, etc.) are evaluated and printed to the Balance.out output file.
Their spatial distribution can correspond with the spatial distribution ofMaterial Layers, but can also be different. One can, for example, request
separate mass balances for the root zone and the rest of the transportdomain (even when the domain is homogeneous or there are multiple soil
horizons in the root zone).
Observation Nodes are selected finite elements nodes for which various
output variables, such as pressure heads, water contents, temperatures, and208

Drains
Particles

concentrations, are reported at specified time intervals. Such information
can then be used, for example, to compare HYDRUS predictions withmeasured data (e.g., pressure heads measured by tensiometers, watercontents measured by TDR, etc.) or to calibrate the model against measured
data.
A simplified way of representing Tile Drain.
Users can specify the initial positions of a set of hypothetical Particles(currently available only in two-dimensional applications), and the program
then calculates trajectories and positions of these particles with time.

Parameters characterizing the flow domain (e.g., material distribution) are defined in a similar way
as initial conditions (Section 6.2). Users must first select that part of the transport domain to which
he/she wants to assign a particular value of the selected variable. It is possible to select the entire
transport domain, part of it, or only individual nodes or elements. A particular part of the transportdomain can be selected as follows: first, move the mouse to a selected position. The beginning andend of the selection operation are framed by clicking the left mouse button. The selected area is therectangle defined by the two mouse positions when the left mouse button was clicked. Selection canalternatively (instead of using the rectangular selection) be made using a rhomboid (with the
Edit->Select->Select by Rhomboid command), circle (Edit->Select->Select by Circle), or
polygon (Edit->Select->Select by Polygon). When the selection is completed, users must click the
Set values button and specify the value of a particular variable. The given value will then be
assigned to the selected area. When material numbers are to be specified, users can do this directly
by clicking on the color representing a particular material (at the Edit Bar). All variables are
assigned to nodal points, except for those defining anisotropy angles, the first and second
components of anisotropy, and subregion numbers, which are all assigned to elements.

6.4.1. Stochastic Distribution of Scaling Factors
Scaling Factors can be generated for two-dimensional applications using a random generator byclicking on the command Edit->Domain Properties->Stochastic Distribution of S.F. that calls the
Stochastic Distribution of Scaling Factors dialog window (Fig. 136). Each scaling factor can begenerated either independently of the other scaling factors or by assuming Miller-Miller
similitude. In that case, the program generates hydraulic conductivity scaling factors andautomatically calculates from their values the pressure head scaling factors.
Parameters for random generation of the scaling factors are specified in the Stochastic
Distribution of Scaling Factors dialog window (Fig. 136). In this dialog, users need to specify
whether the scaling factors are normally or log-normally distributed using the check box LogNormal Distribution), and provide values for the standard deviation of a particular scaling factor,
and correlation lengths in the x- and z-directions (if the scaling factors are spatially correlated).

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Figure 136. The Stochastic Distribution of Scaling Factors dialog window.

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6.5. Defining Properties on Geometric Objects
As described above, various spatially variable properties (e.g., material distribution, initialconditions, etc.) can be specified in Version 2.0 of HYDRUS (Standard and Professional, notLite) either:a) directly on the Finite Element Mesh (FEM) (as done in Version 1.0), orb) on Geometric Objects (e.g., boundary curves, rectangles, circles, surfaces, solids) or
Geo Sections (only in Version 2.0 and the Professional Version).
To be able to define properties on Geometric Objects, one needs to first enable this option (Editdomain properties, initial and boundary conditions on Geometric Objects) in the Domain Typeand Units dialog window (see Figs. 6 or 7).
Which option is used depends on the menu command Edit->Properties and Conditions on FEMesh (disabled when the FE-Mesh does not exist). A similar button switch is also available atthe end of the toolbar ( ), next to the Results button, and at the Edit Bar.
However, to be able to use this option (to specify properties on Geo Sections), the Transport
Domain must be defined using (or divided into) a set of Geometric Objects, on which various
properties can then be specified. An example of the transport domain divided into threecomponents (or Surfaces) S2, S2, or S3 is shown in Figure 137.

Figure 137. An example of the transport domain defined using three components S1, S2, and S3.
While for two-dimensional problems, the Geo Sections (displayed at the Navigator Bar at theSection Tab) need to be defined manually, for three-dimensional problems, they can also be
generated automatically (see Section 8.1.8 what and how are these Sections generated). At thesame time, when HYDRUS generates 3D objects, it also generates Surfaces belonging to each of211

these objects. Some of these Surfaces are Horizontal, and some are Vertical (although theseterms are only approximate). Surfaces can then be used to specify Boundary Conditions.
Vertical Surfaces are always created over the entire curve, which forms the boundary of the Base
Surface. When the boundary of the Base Surface consists of several curves, then an independent
Vertical Surface is created above each curve. Since the curves of the Base Surface can bearbitrarily divided, Vertical Surfaces can be created relatively freely.
While the text above in Section 6 refers to the first approach (specifying properties at FE-Mesh),
the second approach (on Geo Objects) is briefly described below. While this latter approach canbe used for all Domain Properties, and Initial and Boundary Conditions, we will demonstrate its
use below on Material Distribution, for which it seems to be the most relevant. There are
multiple commands that are common for most properties when defining Domain Properties,
Boundary Conditions, and Initial Conditions on Geometric Objects. These commands are listed
in the Commands part of the Edit Bar and are listed in Table 21.

Table 21. Definition of commands used to manipulate Property Objects.
--------------------------------------------------------------------------------------------------------------------Command
Description--------------------------------------------------------------------------------------------------------------------Creates a new Property Object. For some Properties, there is a list of
New Property*
available options, and the user needs to select from this list (e.g., waterflow boundary conditions) or can extend this list (e.g., Materials). For
others, the user needs to define values (e.g., scaling factors) or functional
forms (e.g., initial conditions) of new Property Objects.
Set Property

Selects one particular Property from a list or Property Objects and assigns
it to a selected Geo Object(s).

Clear Property

Clears a particular Property from selected Geometric Points. This
command is used only for Properties that do not have a default Property(e.g., Nodal Recharge, Observation Nodes).

Clear All Properties

Clears all assigned Properties from geometric objects and assigns default
properties where required (e.g., Materials) to the entire transport domain.
Note that this command does not delete definitions of Properties (as doneby the Delete All Properties command), which thus remain available in thedata tree of the Navigator Bar.

Delete Property

Deletes a Property Object selected in the data tree of the Navigator Bar.
This command is not used for Materials or Subregions, the number ofwhich is specified elsewhere.

Delete All Properties Deletes all Property Objects defined for a particular Property, except for a
default Property (which is defined for those Properties where a default
Property is needed). Similarly, as for the Delete Property commands, thiscommand does not exist for Materials and Subregions.

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Sort Properties

Calls a dialog window "Sort Property Objects", which displays all
available Property Objects. Here, (the sequence of) the Property Objects
can be arbitrarily rearranged.

Transfer to FE-Mesh Transfers information about a particular Property defined on Geo Objects
to the FE-Mesh. Note that this command is available only when
information about a particular Property on Geo Objects and FE-Mesh does
not correspond. This can occur, for example, when Property is defined (orrefined) on FE-Mesh.
Edit Property

Recalls a dialog window with parameters of a particular Property to edit.

--------------------------------------------------------------------------------------------------------------------*

Note that the word Property is used in place of a particular Property Object, such as Domain Property (e.g.,
Material, Observation Node), Boundary Condition, or Initial Condition.

6.5.1. Materials on Geometric Objects
Let's assign three different materials to three Surfaces in Figure 137. When only one material isdefined (which is a default option in each new project), one needs to first define multiple
materials (and/or their soil hydraulic properties). This can be done as usual using the Menu
command Edit->Flow and Transport Parameters->Water Flow Parameters->Soil HydraulicParameters. The same dialog window (Fig. 19) can also be displayed by clicking on the New
Material or Edit Materials commands on the Edit Bar (Fig. 138). Note that in Version 2.0 of
HYDRUS, one can name materials.

Figure 138. The upper part of the Edit Bar displaying defined materials and commands forvarious actions with materials.
There are three different ways of assigning materials to particular geometric objects (Surfaces):a) Click on a particular Surface (Geo Object) (to select it) and then on a Material (1, 2, or
3) in the Materials section of the Edit Bar to assign it.

213b) Click on a Material (1, 2, or 3) in the Materials section (to select it) of the Edit Bar andthen on a particular Surface (to assign it).
c) Click on the command Set Material in the Commands section of the Edit Bar, from thelist box of the Set Materials window (Fig. 139) Select Material to set, click Assign toclose the window, and click on a particular Surface to assign the selected material.

Figure 139. The Set Materials dialog window.
Note that nodes that are at the curve shared by two surfaces will be assigned material with ahigher number. Color squares at nodes defining the Geometry (Fig. 140) indicate which material
will be assigned to curves shared by two Surfaces.

Figure 140. The transport domain with materials specified on geometric objects.
The sequence of materials (as well as other objects, such as Initial Conditions) can be reorderedor sorted using the Sort Materials command on the Edit Bar and the Sort Property Objects
dialog window (Fig. 141). In this dialog, the order of materials can be sorted using the Top, Up,
Down, and Bottom command. While the sequence of materials can be sorted, colors
representing the first, second, and other materials will remain the same.

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Sorting can be done in two modes. When the Auto-apply check box is checked, any change
done in the Sort Property Object window is immediately transferred to the transport domain
and to the rest of the program. When this checkbox is unchecked, changes made in this dialog
are transferred to the rest of the program only when the Apply command is clicked or after thewindow is closed using the OK button.
The command Renumber All can be used to renumber the Property Objects. This is usefulwhen some previously defined Properties were deleted, and the numbering is no longer
sequential.

Figure 141. The Sort Property Objects dialog window.
A single click on any Surface will select this surface. A double click on any Surface will open a
dialog for a Property assigned to a particular surface that is currently displayed, e.g., the Edit
Materials dialog window (Fig. 142). In this dialog, one can change the Name of the material, its
Color (the Default check box indicates whether the Color has been changed), Assign it todifferent Surfaces (indicated by their numbers), and register brief Remarks characterizing aparticular material.

215

Figure 142. The Edit Materials dialog window.
Once the FE-Mesh exists, assigned properties (e.g., Materials) can be transferred on the FE
Nodes (if it exists) using the Edit Properties on FE-Mesh (when FEM exists and a particular)
Property has not been yet edited on FEM) or the Transfer to FE-Mesh ((when a particular Property has already been edited on FEM) commands located on the Edit Bar(Fig. 138). Here the assignment of materials can be further edited, refined, and finalized.
However, these changes cannot be transferred back to Geometric Objects. After changes havebeen made on FEM and thus Properties assigned on FEM and Geo Objects no longer correspond,
the command Transfer to FE-Mesh can be used to synchronize the information in the twomodes (from Geometric Objects to FEM) again.
The Edit Bar commands Edit Properties on FE-Mesh and Edit Properties on Geo Objects
switches from one way of assigning properties (on Geo Objects) to another (on FEM).
A similar approach and similar commands can be used to assign other Domain Properties, andInitial and Boundary Conditions.

6.5.2. Observation Nodes on Geometric Objects
Observation Nodes are entered on Geometric Objects using either the Menu command Insert>Domain Properties->Observation Nodes or the New Observation Node command on the Edit
Bar. The New Observation Node command can be used in the Edit Properties on Geo Objects
mode to define observation nodes only on Points defining the Geometry (i.e., Points defining
boundary curves). Observation nodes for any other location have to be specified on the FE-Meshdirectly. The same is true also for Drains and Flowing Particles.
The Edit Observation Node window (Fig. 143) is displayed when double-clicking on an
observation node in the View window (when working in the Properties on Geometric Objectsmode) or an Observation Node item in the Navigator Bar. This window displays
216a) the Name of the observation node (note that the observation node can be renamed using abrief text, such as drain, tensiometer, TDR, etc.),b) indication whether it is Defined at Geometric Node or FE-Mesh Node, andc) a brief Remark (note).

Figure 143. The Observation Node dialog window.

6.5.3. Initial Conditions at Geometric Objects
Property Objects for Initial Conditions are defined or edited using the New or Edit Pressure
Head (Concentration) Initial Condition dialog windows shown in Figure 144. Note that theparameters and values that are entered in these dialogs are the same as those entered in Figure
129 when defining Initial Conditions directly at the FE-Mesh. Here, one can additionally define
the Name of the Initial Condition, the Color which represents it (either Default or selected),register a brief Remark, and select to which surfaces it is assigned to (Assigned to Surfaces
No:).

217

Figure 144. The Edit Pressure Head (left) and Concentration (right) Initial Conditions dialog
window.

6.5.4. Boundary Conditions at Geometric Objects
New Property Objects for Boundary Conditions must be selected from existing boundary
conditions used in HYDRUS. For example, for Water Flow Boundary Conditions, new Objects
are selected from the list box Boundary Condition Type displayed in Figure 145. Similarly, as
for other Properties, in this dialog, one can define Name, Color, register a Remark, assigned
Boundary Condition at selected Boundary Curves, and, if needed, specify required parameters(e.g., for Deep Drainage BC).
Notes:
1. When the same pressure head initial (or boundary) condition involving either"Equilibrium from the lowest located point" or "A linear distribution" is chosen for
multiple surfaces (or curves), then this condition is applied globally to all selectedsurfaces (e.g., a single point with the lowest z-coordinate is found for all selectedsurfaces).
2. The default solute and heat transport boundary conditions are the Third-Type BCs,
which are listed right after the No Flux BC. This BC is by default assigned to allboundaries, to which the water flow BCs have been defined. Note that if you redefine thisBC (e.g., change the Third-Type BC into the First-Type BC), the newly defined BC will
be used as a default BC for solute and or heat transport.

218

Figure 145. The Edit Water Flow Boundary Condition dialog window.

6.5.5. Additional Notes on Properties at Geometric Objectsa) When the same pressure head initial (or boundary) condition involving either"Equilibrium from the lowest located point" or "A linear distribution" is chosen for
multiple surfaces (or curves), then this condition is applied globally to all selectedsurfaces (e.g., a single point with the lowest z-coordinate is found for all selectedsurfaces).
b) Nodes that are at the boundary line shared by two surfaces (or at the surface shared by
two volumes) are assigned the property value with a higher number. The sequence in thelist of properties can be adjusted using the command Sort Property (where Property iseither Material, Scaling Factor, etc.) at the Edit Bar (Fig. 141).
c) The option to assign Properties at Geometric Objects is not available for simple
parametric (i.e., Rectangular or Hexahedral) Geometries available in the Lite Versionof HYDRUS.
d) Name: One can provide a Name for each newly defined Property Object. When the user
does not define a Name for a Property Object, the GUI will automatically generate ageneric name that is then used throughout the project (e.g., on the Navigator and Edit
Bars).
e) When different values are specified on Geometric Objects and FE-mesh, the warning
Different Values on FE-Mesh is displayed in the Help section of the Edit Bar. A similar
warning is also issued in such a case before calculations are started.
f) All properties can be transferred from Geometric Objects to FE-Mesh using the menu
command Edit->Transfer all Properties to FE-Mesh.

219

6.6. Import of Domain Properties and/or Initial and Boundary Conditions
Various domain properties and initial and boundary conditions can be imported either fromexisting HYDRUS projects and from data text files with values defined at specified locations.
6.6.1. Import Initial Condition from HYDRUS Projects
The initial condition can be imported from the results of previous calculations (from an existing
HYDRUS project) using the Import command (Edit->Initial Condition->Import, or Insert>Initial Condition->Import). After clicking on any of these two commands, an Open dialog
window appears with Files of type preselected for HYDRUS applications (i.e.,*.h3d3). One thenneeds to browse for the HYDRUS project from which the initial condition is to be imported.
After selecting a particular project, the Import Initial Conditions dialog window appears (Fig.
146). This window provides information from which project the initial conditions will be
imported (Import data from Hydrus project) and offers quantities that can be imported as initialconditions (Select quantities to import). Users must then also decide in the Select Time Layerpart of the dialog if values for The Last (Final) Time Layer or for any intermediate time layer(using Time Layer No.: from the lower list box) are to be imported. Time Layers correspond with
Print Times (Fig. 16) for which the output in the existing project was calculated.

Figure 146. The Import Initial Condition dialog window.
220

Note: While in the previous HYDRUS versions, the import of results from previous calculations
as initial conditions for the new simulation could be done only from a project that had an
identical geometry and FE-Mesh discretization as the actual project, in newer HYDRUS versions(version 2.02 and later), the geometry may be slightly different (should not differ too much) andthe FE-Mesh discretization can be different as well. Whether the FE-Meshes of the two projects
are identical can be identified by the user (a check box Identical FE-Meshes) so that the code cansimply transfer nodal values without the need to interpolate.
6.6.2. Import Data from HYDRUS Projects
Various other properties, such as Domain Properties, Initial Conditions, and Boundary
Conditions, can be imported from an existing HYDRUS project using the Import command(File->Import->Import Input Data from Another HYDRUS Project). After clicking on thiscommand, an Open dialog window appears with Files of type preselected for HYDRUS
applications (i.e.,*.h3d3). One then needs to browse for the HYDRUS project from which theinitial condition is to be imported. After selecting a particular project, the Import Selected
Quantities dialog window appears (Fig. 147). This window provides information from which
project the initial conditions will be imported (Import data from Hydrus project) and offers
quantities that can be imported as initial conditions (Select quantities to import). Select All or
Unselect all commands can be used to make a selection.

Figure 147. The Import Selected Quantities dialog window.
221

Warning: The import of selected quantities from another HYDRUS project can be done only
from a project that has a similar geometry and FE-Mesh discretization as the actual project!
Geometry cannot be significantly different! Users need to carefully check the results of theimport if Geometries or FE mesh are different.
6.6.3. Import Data from a Text FileHYDRUS users often encounter a problem of defining a certain property, for which they have
only limited information from multiple locations (such as the initial location of a contamination
plume). A new function (File->Import->Import Quantity defined by values at Scattered Points...)was implemented in version 2.03 (and later) that allows users to import such information from atext file of a specified format. This function reads values defined in generally spaced points (forboth 2D and 3D problems) and transfers them to the current FE-mesh using a linear interpolationof these values.
a. Only input variables defined using real numbers (scalars) can be imported this way.
Integer values specified in points (e.g., material numbers) can be imported differently –using FE-mesh Sections – see Tutorial 2.12 at http://www.pcprogress.com/en/Default.aspx?h3d-tutorials. It is not also possible to import output
variables (results).
b. The variable to be imported has to be displayed in the active View before the importprocess can be started.
c. The values are transferred onto the current FE-mesh, which implies additional restrictions
on quantities that can be imported this way. If the entire domain is displayed in the View,
the values are transferred to all FE nodes of the domain. If only a certain part of thedomain (FE-mesh Section) is displayed in the View, the values are transferred only to FE
nodes of this Section.
Format of a text file (with spatial coordinates and property values):
a. The input text file must have the following format (depending on the type of the transportdomain of a project, to which data are imported):
For 3D Domains:
Column1 = x-coordinate [m]Column2 = y-coordinate [m]Column3 = z-coordinate [m]Column4 = value [unit of the quantity displayed in the active view]
Example:0.000000e+000
0.000000e+000
3.000000e+000...

0.000000e+000 8.000000e-001 -3.000000e+001
0.000000e+000 0.000000e+000 5.000000e+001
0.000000e+000 0.000000e+000 5.000000e+001

For 2D-XY Domains:
Column1 = x-coordinate [m]222Column2 = y-coordinate [m]Column3 = value [unit of the quantity displayed in the active view]
Example:0.000000e+000
0.000000e+000
3.000000e+000...

8.000000e-001 -3.000000e+001
0.000000e+000 5.000000e+001
0.000000e+000 5.000000e+001

For 2D-XZ Domains:
Expected format:
Column1 = x-coordinate [m]Column2 = z-coordinate [m]Column3 = value [unit of the quantity displayed in the active view]
Example:0.000000e+000
0.000000e+000
3.000000e+000...

8.000000e-001 -3.000000e+001
0.000000e+000 5.000000e+001
0.000000e+000 5.000000e+001

Other Formats:
In addition to the formats described above, one can also import values from a file
generated using the function File->Export->Export Current Quantity…. Although thisfile has a somewhat different format, HYDRUS will automatically detect that and loads
the correct values from the block „TABLE_01: NODAL INFORMATION“.
b. Data in columns can be entered in free format (a column width is not fixed); spaces, tabs,
and semicolons can be used as column separators.
c. Points in which values are defined should not overlap, nor should be very close to eachother. The best way is to use points in a regular grid (2D or 3D), covering the entire
computational domain.
The minimum number of points is 3 for 2D domains and 4 for 3D domains. The points must be
linearly independent, i.e., they cannot lie in a straight line (2D) or in a plane (3D). The maximum
number of points is not limited, but an excessive number of points (>10,000) may lead to
extremely long calculation (linear interpolation of values for generally located nodes requires
relatively complex geometric calculations) or to other problems.
Once the text file is read by the GUI, a dialog window "Import of Values from Scattered Points"
shows up.
a. This window first summarizes imported information in the top section "Imported Values"(i.e., the number of imported points, minimum and maximum values, and minimum andmaximum x, y, and z coordinates, for points with given values).
b. Users can then select whether or not- a Linear interpolation of values or- a Linear interpolation/extrapolation of values should be done when transferring values
from Scattered Points to the FE-Mesh Nodes. Alternatively to linear interpolation, values
can be- Transferred to FE-Mesh nodes from the nearest points without
interpolation/extrapolation.

223

Note that when the Linear interpolation of values option is selected, linear interpolation
is done only between locations with imported values, and a Transfer of values form
nearest points is done in the rest of the domain (outside of the area/space with imported
values, but within the transport domain).
c. Users can also select the Minimum and Maximum Values that cannot be exceeded byinterpolation (Value Limited).
d. Finally, users can define the so-called Clipping Box. This is a part of the transport domain,
defined by the minimum and maximum x, y, and z coordinates (X min, X max, Y min, Y
max, Z min, Z max), for which a transfer of values from Scattered Points to FE-Mesh
Nodes is done. There is no transfer of values outside of this box.
The actual transfer of values from Scattered Points to the FE-Mesh Nodes is done only after the
button OK is clicked.

Figure 148. The Import of Values from Scattered Points dialog window.
When imported values (possibly available only in some part of the transport domain) are"linearly interpolated/extrapolated" to the rest of the transport domain, the calculated nodal
values can be lower or higher (when extrapolated) than those measured (imported). If users wantto prevent that, they have several options on how to proceed:f) They may specify additional import values for selected nodes in the transport domain orat the domain boundaries so that "interpolation" (rather than "extrapolation") is used in
the entire transport domain. Extrapolation is used in the part of the domain where noimported values are located.

224g) They may constrain "interpolation/extrapolation" to only a certain part of the transportdomain ("clipping box").
h) They may specify what the minimum and maximum value could be ("Value Limits").
It is up to the users to select optimal import and interpolation options suitable for their purpose(also depending on an imported variable).
Note: For the maximum accuracy in the transfer of measured values to the finite element nodes,
it is recommended to create FE nodes exactly in the points with measured values. This task
depends on the type of the domain:
1. 3D-Layered Domain:
Here we recommend that you first import the projection of the points' locations to theBase Surface. Points obtained in this way will then become Internal Points of the Base
Surface, and FE nodes generated in other layers above these base points will then be very
close to locations with imported values, thereby increasing the accuracy of interpolated
values. In practice, this can be done as follows (assuming that the Base Surface lies in thex-y plane and its z = 0):
A. Make a copy of the file with coordinates of points with imported values and values
themselves, prepared for the import of values, and delete the last column (values).
B. In HYDRUS, use the command "File -> Import -> Import Points from Text File" andread points coordinates from this file.
C. You will need to move imported points to the Base Surface. Select all imported points,press Alt + Enter, and, in the dialog for editing points, set z=0.
2. 3D-General Domain:
Here, it is possible to make the points with imported values to be directly part of the FEmesh as follows:
A. Import the 3D points as described in item 1 above, but omit the projection to the Base
Surface (item 1C above).
B. Include the imported points into the Solids that form the Computational Domain as
Integrated Points. Click on the Solid (either in View or Navigator), open the tab"Integrated Objects", and in the edit box "Points" insert a list of integrated points (it ispossible to make a graphical selection).
Generated 3D FE-Mesh will then have some of its nodes located exactly in points with
imported values, thereby achieving a higher accuracy when interpolating values to therest of the FE-Mesh nodes.
3. 2D-General domain:
The procedure is the same as in item 2 above, except instead of 3D points, we have 2D
points, which will be integrated into Surfaces.
4. 2D-Simple a 3D-Simple:
Here the situation is quite difficult because the locations of FE-Mesh nodes can be
defined only using coordinates in the tables for generating structured FE-Mesh.

225

226

7. Graphical Output
Graphical output is divided into two main parts. In the first part, variables that change spatiallythroughout the transport domain are displayed by means of contour maps, isolines, isosurfaces,
or isobands (Results – Graphical Display on the Data Tab of the Navigator Bar, or Options>Graph Type). Additional information such as boundary fluxes and/or soil hydraulic propertiesare displayed using x-y graphs (Results – Other Information on the Data Tab of the Navigator
Bar, or using the Results Menu).

7.1. Results – Graphical Display
Results of a simulation can be displayed by means of contour maps, isolines, isobands, isosurfaces,
color points, color edges, spectral maps, and/or velocity vectors (Graph Type at the View Tab of theNavigator Bar or Options->Graph Type->Isolines), and/or by animation using both contour andspectral maps. The number of colors in the color spectrum, as well as the numerical increment
between isolines, can be selected using the Edit Isoband Value and Color Spectra dialog
window (Fig. 152). Contour and spectral maps may be drawn for the pressure head, water content,
temperature, solute concentration (in the equilibrium or nonequilibrium phase), and/or velocity.
Animation of these four variables is also possible (Flow Animation on the Results version of theEdit Bar, or using Results->Time Layer->Animation).
Graphs of all variables along the boundaries (Boundary-Line Chart on the Results version of theEdit Bar, or using Results->Charts->Boundary Line), as well as those along any selected crosssection (Cross-Section Chart on the Results version of the Edit Bar or Results->Charts->CrossSection) can be readily obtained. The ability of charts displaying the distribution of various
quantities along boundary-lines and cross-section lines has also been extended in Version 3. The
GUI now allows the display of results at multiple time-layers simultaneously in one chart. Thisfeature allows one to compare the values of a given quantity at different times very easily. Notethat cross-section lines and charts now can also be applied to mesh slices created by the Clipper
tool as described earlier and shown in Figure 162.
The entire finite element mesh, the boundary nodes, and the numbering of nodes, elements and/or
edges can also be displayed (using the Display Options dialog window (Fig. 151), or Options>Display Options->Edit), together with isolines and spectral graphs. Users may zoom into a certain
part of the transport domain and can enlarge or reduce the transport domain, among other features.
Flow animation is an alternative to displaying results at one particular time. Distributions during
flow animation are displayed continuously at consecutive times, thereby visualizing the flow andtransport process. Note, however, that display times are defined by the print time intervals specified
in the input data file. This means that the print times must be at constant intervals so that the timescale of the flow animation will not be distorted. In other words, undistorted flow animation
requires that the print time intervals be constant. The speed of the flow animation depends on the
hardware being used, i.e., the speed of the microprocessor and graphical card.

227

7.1.1. Displayed VariablesMultiple variables can be displayed in the View window. A comprehensive list of standard andalternative variables that can be displayed in the View window are summarized in Tables 22 and23, respectively.

Table 22. Standard variables displayed in the View Window of the Results tab (Results Graphical Display).
--------------------------------------------------------------------------------------------------------------------Variable
Description--------------------------------------------------------------------------------------------------------------------Pressure Head
Pressure head h [L]; displayed always
Water Content
Water content θ [-] (or θm when the dual-porosity model is used);
displayed always
Velocity
Values of Darcy's flux q [LT-1]; displayed always
Velocity Vectors
Darcy's flux vectors q [LT-1]; displayed always
Root Water Uptake
Root water uptake S [T-1]; displayed when root water uptake isconsidered
Concentration i
Liquid phase concentration c [McLw-3]; displayed when solute transport
in the standard module is simulated.
Sorbed Noneq. Conc. i Concentration of kinetically sorbed solute sk [McMs-1]+; displayed whensolute transport in the standard module is simulated and when the twosite sorption model is considered.
Immobile Conc. i
Concentration in the immobile water cim [McLw-3]; displayed when solutetransport in the standard module is simulated and mobile-immobile
water or dual-porosity models are considered.
Temperature
Temperature T [oC]; displayed when heat transport is simulated.
Unsatchem Variables Major ions: Ca, Mg, Na, K, HCO3, SO4, Cl, tracer, sorbed Ca, sorbed
Mg, sorbed Na, sorbed K, calcite, gypsum, dolomite, nesquohonite,hydromagnesite, sepiolite; displayed when the Unsatchem module isused.
Wetland Variables
Various variables used in the two constructed wetlands modules CW2D
and CWM1 (see the Wetlands module manual for details).
--------------------------------------------------------------------------------------------------------------------+
Subscripts c, s, and w refer to the contaminant, soil, and water.

228

Table 23. Alternative variables that can be displayed in the View Window of the Results tab.
--------------------------------------------------------------------------------------------------------------------Variable
Description--------------------------------------------------------------------------------------------------------------------Pressure Head
Standard display
Total Pressure Head
Total Pressure Head H (=h+z) [L]; alternative display
Water Content
Mobile Water Content
Immobile Water Content
Total Water Content

Standard display
Water content in the mobile phase θ or θm [-]; default display
Water content in the immobile phase q im [-]; displayed when the
dual-porosity model is used.
Total water content θ (=θm+θim); displayed when the dual-porosity
model is used.

Velocity
Total Value
x-component
y-component
z-component

Standard display
Darcy's flux [LT-1]; default display
x-component of the Darcy's flux q [LT-1]
y-component of the Darcy's flux q [LT-1]
z-component of the Darcy's flux q [LT-1]

Concentration Options
Liquid Equil. Phase Conc.
Sorbed Equilibrium Conc.
Sorbed Total Concentration
Gas Phase Concentration
Total Concentration

Liquid phase concentration c [McLw-3]+; default display.
The concentration of instantaneously sorbed solute se [McMs-1].
Sorbed concentration s= se + sk [McMs-1].
Gas phase concentration g (=KHc) [McLa-3]
Total concentration mass S [McLs-3]

Sorbed Concentration Options
Sorption Sites 1
Sorbed concentration on first kinetic sorption sites s1k [McMs-1]
Sorption Sites 2
Sorbed concentration on second kinetic sorption sites s2k [McMs-1]
Total Sorbed Conc.
Total sorbed concentration sk = s1k + s2k [McMs-1]--------------------------------------------------------------------------------------------------------------------+
Subscripts c, s, a, and w refer to the contaminant, soil, air, and water.

229

Table 24. Definition of various concentration modes (for linear sorption model).

Sorbed Equilibrium
Concentration[M c M s-1 ]Sorbed Nonequil.
Concentration[M c M s-1 ]Sorbed Total
Concentration[M c M s-1 ]Gas-phase
concentration[M c L-3a ]Solute mass in theliquid phase,Sl [M c L-3s ]Solute mass in the solid
phase, Ss [M c L-3s ]Solute mass in the gas
phase, Sg [M c L-3s ]Total Concentration, S[M c L-3s ]
a
c
cm
cim

θ
θm
θim
KD
KH
Sl
Ss
Sg
S
s
sk
s1 k

Equilibrium
model
K Dc

Mobile-immobilemodel
K D fcm

Two-site
sorption modelfe K Dc

Two-kinetic
sites model
K Dc-

K D (1 − f )cimsk

s1k + s2k

K Dc

K D [ fcm + (1 − f )cim ]fe K Dc + s k

K D c + s1k + s2k

KH c

KH c

KH c

KH c

cθ

cmθ m + cimθimcθcθ

ρ K Dcρ K D [ fcm + (1 − f )cim ] ρ ( f e K D c + s k )ρ ( s1k + s2k )K H caK H caK H caK H caSl+Ss+Sg

Sl+Ss+Sg

Sl+Ss+Sg

Sl+Ss+Sg

air content [La3Ls-3]
liquid phase concentration [McLw-3]
liquid phase concentration in the mobile phase [McLw-3]
liquid phase concentration in the immobile phase [McLw-3]
water content [Lw3Ls-3]
water content in the mobile phase [Lw3Ls-3]
water content in the immobile phase [Lw3Ls-3]
distribution (sorption) coefficient [Lw3Ms-1]
Henry's law constant [-]solute mass in the liquid phase [McLs-3]
solute mass in the solid phase [McLs-3]
solute mass in the gas phase [McLs-3]
total concentration (solute mass), S=Sl+Ss+Sg [McLs-3]
solid phase concentration [McMs-1]
solid phase concentration on kinetic sorption sites [McMs-1]
solid phase concentration on first kinetic sorption sites [McMs-1]

230

Figure 149. The "Results - Graphical Display" part of Data Tab of the Navigator Bar for the
standard (left), Unsatchem (center), and Wetland (right) modules.

Figure 150. The "Results" part of the View Tab of the Navigator Bar displaying various
alternative variables.

231

7.1.2. Display Options
The Display Options dialog window (Fig. 151) allows users to selecta) how different objects from the Category list are to be displayed,b) what colors are to be used (colors can be redefined by clicking on the Edit Color
command button),c) whether lines are displayed as solid, dotted, dashed, or dash-dotted (Line Type), and what
Thickness should be used, andd) the position of numbers for various types of numberings, fonts for the numbers, andwhether or not numbers are Transparent.

Figure 151. The Display Options dialog window.

2327.1.3. Edit Isoband Value and Color Spectra
The Edit Isoband Value and Color Spectra dialog window (Fig. 152) (called by left-clicking
the color scale display options of the Results version of the Edit Bar) allows users to definecolors for the display of isobands isosurfaces, and color spectra, and values of particular isolines.
The default scale always has 11 values, which corresponds to 11 colors for color contours and 12
colors for isolines. Values at the scale are calculated by evenly dividing the interval between theminimum and maximum of a particular variable. Numbers are formatted depending on units used
to display a particular variable. When the number of displayed digits is insufficient, it is possible
to use a scientific format (E-format). The E-format is then used also on the Edit Bar and forprinting (only for a particular variable).
Note that switching from a regular format to the E-format represents also switching from theStandard Scale to the Custom Scale (see below), which is then kept for the display of the same
variable at other times. Returning to the Standard Scale may be required to adjust the scale asneeded to display a given variable at the new time.

Figure 152. The Edit Isoband Value and Color Spectra dialog window.

Users can also define the Isoline scales. This can be done by simply changing numbers in theedit boxes next to the colors. If the numbers are not in an increasing or decreasing order, awarning will be issued. Newly created Isoline scales can be saved (again locally or globally) andused later. Users need to specify only the maximum and minimum values (the top and bottom

233edit boxes); after clicking the Fill command, the program will calculate and fill (complete) theintermediate numbers by interpolation. A specified Number of Intermediate Isolines can be
drawn between the main isolines using When drawing Isolines or When drawing Color Contours.
This number is by default equal to zero. Five intermediate isolines are used in Figure 153.
Version 3 also offers a new option for automatic numbering of isolines and displaying positionsof minimum/maximum values of a current quantity.

Figure 153. The use of intermediate isolines.
The minimum and maximum numbers of the scale are automatically adjusted to a particular
problem and for a particular variable. By default, HYDRUS searches all output time levels of aparticular project for the minimum and maximum values of a particular variable and then leaves
the scale invariant in time between these two values. The scale, however, can also be
automatically adjusted for each time level by specifying the minimum and maximum values for aparticular variable and a particular print time when the option Min/Max glob. in time from theColor Scale View Options of the View Tab of the Navigator Bar is deselected. Similarly, thescale can be automatically adjusted for a particular layer of the FE-mesh (a section) (theminimum and maximum values for a particular variable and a particular section) when the option
Min/Max glob. in space from the Color Scale View Options of the View Tab of the Navigator
Bar is unselected.
234

After clicking on the color panel with the left mouse button, the Color dialog window (Fig. 154)
appears, in which one can redefine colors to be used in displays. By default, a Standard Palette
is used. If a Custom Scale exists for a displayed variable, colors for this scale will be displayedeven when the Standard Scale was currently used (since the Standard Scale cannot be edited).
Palettes with newly defined colors can be saved (Save Palette) under a new name and used for
different purposes. The new palette can be saved locally and used with the given application or
globally and used for all HYDRUS applications. Users hence can, in this way, define different
palettes for displaying water contents, pressure heads, concentrations, or temperatures. Since theStandard Palette cannot be changed, once any color is changed, the program will request to savea new scale under a new name. The changed colors will be used for all displayed variables (notonly the actual one).

Figure 154. The Color dialog window.

Custom Scale
A user can define his/her own scale that is then remembered by the software and used for aparticular variable in a given project. When one wants to use a certain scale also in other projects,
he/she needs to save it using the Save command.
Other commands:••

Default – Sets the number of intervals to 11 and automatically fills values for the default
scale
Empty – Deletes all values (used with commands Fill and Fill Max/Min)

235

•
•
•
•

Fill – Fills empty spaces between specified upper and lower values using linear
interpolation
Fill Max-Min – Similar to Default, except that this command does not set the number ofvalues to 11 (it uses the number of values selected by a user)
Save – Saves the Scale for use with other projects
Delete – Deletes a selected Custom Scale

The number of values at the Scale cannot be increased; it can only be lowered (from 11) using a“slider“. By drawing a slider, one can also generate values at a Scale (see Figure 155):

Figure 155. Adjusting scale in the Edit Isoband Value and Color Spectra dialog window.

When using a Custom Scale, the actual minimum or maximum of a displayed variable can beoutside of the interval of the scale. Values outside of the interval of the scale are not displayed inthe View window, resulting in empty spaces, as shown in the upper part of see Figure 156.

236

Figure 156. The use of the Custom Scale.

A right mouse button click on the Color Scale at the Edit Bar displays the menu for a fastchange of various options related to scale.
•
•
•
•
•
•

Color Smoothing – colors will change smoothly between particular iso-spectra
corresponding to changes of the displayed variable (upper View at Figure 157).
Min/Max global in Time - the scale of a certain variable is defined by the minimum andmaximum of all values from all time levels
Min/Max global in Space - the scale of a certain variable is defined by the minimum andmaximum of all values over the entire transport domainStandard Scale – uses the Standard Scale, while the Custom Scale for a given variable(if it exists) is remembered
Custom Scale – uses the Custom Scale if it exists. If it does not exist (default), thisbutton is disabled. If one wants to use the Custom Scale, he/she needs to first create it in
the Edit Scale and Colors dialog.
Edit Scale and Colors

237Figure 157. The color smoothing.
The values associated with individual isolines can be displayed using the checkbox on the
Navigator Bar: Scalar Fields->Isolines->Display Values (see Figure 177). If one wants to add
manually values to a particular point in the display, one can do that using the tool called Point
Probes (see Section “4.7.6. Points Probes” and Fig. 100).
The Separation Lines between different Contours can be displayed (or hidden) using thecheckbox on the Navigator Bar: Scalar Fields->Colormaps->Separation Lines.

238

7.1.4. Export Isolines
The Export Isolines command (File->Export->Export Isolines) saves coordinates of all
currently displayed isolines (the Isolines Graph Type has to be selected) into a
Project_Property_Isolines.txt text file (e.g., Furrow_Pressure_Head_Isolines.txt). Figure 158
displays an example of this file for the Furrow project. In the text file, a definition of eachisoline is given first (e.g., Isoline 1, Value=-60.000, Segment 1), followed by the x and z
coordinates of sequential points, in which the isoline crosses edges of finite elements. The
Export Isolines command can be used, for example, to export coordinates of the groundwatertable. In such a case, a custom scale with one single value (h=0) could be prepared and exported.

; Program: HYDRUS 2.03
; File Version : 1;------------------------------------; Isoline 1, Value=-60.000, Segment 1;------------------------------------; Description:; C1 = x-coordinate [m]; C2 = z-coordinate [m];------C1------|------C2------|
2.761816e+000 8.381839e-001
2.670929e+000 8.391035e-001
2.577883e+000 8.403773e-001
2.559808e+000 8.406094e-001
2.542170e+000 8.409753e-001….
1.537666e+000 9.790872e-001
1.477832e+000 1.000000e+000

Figure 158. An example of the Project_Property_Isolines.txt text file (e.g., Furrow_Pressure
Head_Isolines.txt; an excerpt) for the Furrow project (displayed in the top of the figure).

239

7.1.5. Streamlines
Previous Version 2 of HYDRUS (2D/3D) allowed one to show flowing particles, but only in two
dimensions. Flowing particles are hypothetical objects that can be defined at any location of thetransport domain by users, with the program then calculating trajectories and positions of theseparticles with time considering unretarded convective transport. The “flowing particles” feature
is now available for both 2D and 3D projects.
A new feature of Version 3 is the calculation and display of streamlines for a given steady-stateflow velocity field. Streamlines are one of the most commonly used graphical representations of
CFD (computational flow dynamics) results in that they can display very clearly the flow
direction, such as shown in Figure 159. The software now also has an option to run flow
animations, i.e., the movement of particles along streamlines (Fig. 160). Users can save thisanimation as a video file and use in presentations of HYDRUS results.

Figure 159. Example showing 3D Streamlines. Streamlines can be calculated for a given timelayer (i.e., steady-state flow) from a set of seed points. Seed point sources of several types can be
set graphically.

Figure 160. Example of Particle Animation. The movement of particles can be animated as
flowing-lines or flowing-particles.

240

Figure 161. The Streamlines Options dialog window.
The Streamline Options are selected in the Streamlines Options dialog window (Fig. 161). In thiswindow, users can select whether streamlines are displayed when the movement of particles isanimated (Display streamlines when animating the movement of particles), the Line thickness of
streamlines, whether the streamlines are calculated from the seep points "Downstream"or ”Upstream", and the parameters for the Animation of particles and flowlines".

2417.1.6. Clipper and Slicer
New graphical tools called “Clipper” and "Slicer" that can be used to cut or slice a 3D mesh isavailable in Version 3.0. Figures 162 and 163 show examples of these two applications. The
Clipper and Slicer are controlled by a graphical tool called a Manipulator (see Figs. 162 and
165). Using this tool, the position and rotation of the plane can be defined. The Clipper has toomodes, i.e, a Plane mode (Figs. 162 and 167) and a Box mode (Fig. 168).

Figure 162. Example showing 3D Clipping. When working with 3D models, the visible mesh(or geometric objects) can be clipped to view values inside the domain. The clipper is controlled
by a graphical tool (a manipulator; see Fig. 162).

Figure 163. Example showing 3D Slicing. The slicer is another tool for better visualization of 3D
objects. The number of slices, their position, and rotation can be set either in a dialog orgraphically (see Figs. 162 and 165).

242

Figure 164. The Clipper Tab on the Edit bar (left) and the Clipper/Slicer setting dialog window
activated from the toolbar.

Figure 165. Slicer Options dialog window.

243

Figure 166. An example of the Slicer tool with 6 vertical and one horizontal cross-sectinal
planes.

Figure 167. An example of the Clipper Plane tool with a displayed manipulator (defining theposition and rotation of a display plane).

244Figure 168. An example of the Clipper Box tool with a displayed manipulator (defining theposition and rotation of the box).
7.1.7. Velocity Vectors
One of the variables that can be displayed spatially are Velocity Vectors (Darcian fluid flux
densities). By default, velocity vectors are shown in all finite element nodes. All velocity vectors
can be enlarged or reduced by using constant Arrow Size on the Edit Bar. The sizes of vectors
can be either variable indicating the magnitude of fluxes by both the color and the size of thevectors, or uniform (Uniform Size of Vectors) when the magnitude of velocity vectors isindicated only by color.
However, the graphical display of velocity vectors for millions of mesh nodes is not only slow
but usually also too complex for viewing. Version 3.0 of the GUI allows displaying velocity
vectors either at mesh nodes or raster points, while the raster parameters (such as the density ofpoints) are fully adjustable (Fig. 170). While Raster is a grid of points defining positions ofvelocity vectors, a Raster Step is a multiple of Unit Distance" between raster points. Figure 169
shows an example of velocity vectors displayed at a Raster and Figure 170 shows how raster isdefined.

245

Figure 169. Rasters for Vector Fields. Vector fields can be displayed in mesh-independent
rasters, i.e., regular 2D/3D grids with an arbitrary density of points. Rasters can also be used with
the Clipper and Slicer.

Figure 170. The Vector Field Options dialog window.

2467.1.8. Export to ParaView
Although we believe that HYDRUS post-processing has all of the most important featuresneeded for project execution, some users may require additional functions specific to their own
needs. The new version of HYDRUS offers a robust solution by exporting all results to VTK
files. VTK is a well-known open-source library intended for the visualization of scientific data.
Exported HYDRUS results can then be opened in ParaView, such as illustrated in Figure 171,which is a free program based on VTK. Since both software products (VTK and ParaView) areopen source, users have full control over the exported data and can implement any special postprocessing as judged optimal for their application.

Figure 171. Example showing Export to ParaView. ParaView is an open-source, multi-platform
data analysis and visualization application. New visualization options include custom postprocessing based on scripting or plugin modules. Details are at www.paraview.org.

247

7.2. Convert to ASCIIThe output files H.OUT, TH.OUT, CONCx.OUT, SORBx.OUT, TEMP.OUT, and V.OUT provide
a binary output of specific variables. The user interface can convert these binary files into the ASCII
files H.TXT, TH.TXT, CONCx.TXT, SORBx.TXT, TEMP.TXT, and V.TXT using the Convert to
ASCII dialog window (Fig. 172) (Results – Other Information on the Data Tab of theNavigator Bar, or Results->Convert Output to ASCI). The ASCII (text) files (e.g., h.txt, th.txt,
v.txt) simply provide Print Time followed by a sequential list of values of a particular variable.
These values are listed in the same order as Finite Element nodes. Coordinates for each FE node
can be found in the MeshTria.txt file.

Figure 172. The Convert to ASCII dialog window.

248

7.3. Results – Other Information
Additional information, such as boundary fluxes and/or soil hydraulic properties, can bedisplayed using x-y graphs (Results – Other Information on the Data Tab of the Navigator
Bar, or Results Menu, Fig. 173). Figure 173 shows the x-y graph dialog window that displays
pressure heads in observation nodes.). Table 25 gives an overview of the different graph options
that are possible. Two list boxes at the top of the x-y graph dialog window provide various
combinations of graphs that are possible to display (Table 25). Browsing through various graphs
is additionally also enabled using the Previous and Next command. Double-clicking at various
objects of the x-y graph (e.g., axis, title, captions, legend) will allow users to redefine them, i.e.,
to change their text, colors, or fonts. When the right mouse button is clicked above the graph, a
pop-up menu will appear that will also allow users to redefine various objects of the x-y graph.
One can, for example, change the text of both vertical and horizontal axis (Axis->Title) captions
and titles (Title), their fonts, and colors; one can copy the content of the graph to the clipboard(Copy) for later paste in various other windows applications (e.g., MS Word, PowerPoint, or
Excel), or one can change the thickness and colors of displayed lines. Many other modificationsof the displayed x-y graph are possible. Data shown in the x-y graph can be exported into an
ASCII file using the Export command. The x-y graph settings can be saved using the Savecommand. A selected variable can be displayed either for all or selected observation nodes.

Figure 173. The x-y graph dialog window displaying pressure heads in observation nodes.

249

Table 25. Graph options in the HYDRUS interface.
Command

Horizontal Axis

Vertical Axis

Observation Points

Time

Pressure Head
Water Content
Temperature
Concentration – x+
Sorbed Concentration - x+

Pressure Heads

Time

Atmospheric Boundary HeadRoot Zone Head
Variable Boundary Head 1
Constant Boundary Head
Seepage Face Head
Drainage Boundary HeadFree and Deep Drainage Boundary Head
Variable Boundary Head 2
Variable Boundary Head 3
Variable Boundary Head 4
All Boundaries

Water Boundary Fluxes

Time

Potential Atmospheric Flux
Potential Root Water Uptake Rate
Actual Atmospheric Flux
Actual Root Water Uptake Rate
Variable Boundary Flux 1
Constant Boundary Flux
Seepage Face Flux
Drainage Boundary Flux
Free and Deep Drainage Boundary Flux
Variable Boundary Flux 2
Variable Boundary Flux 3
Variable Boundary Flux 4
All Atmospheric Fluxes
All non-Atmospheric Fluxes
Surface Runoff
Infiltration
Evaporation

Cumulative Water Boundary Fluxes

Time

Potential Atmospheric Flux
Potential Root Water Uptake Rate
Actual Atmospheric Flux
Actual Root Water Uptake Rate
Variable Boundary Flux 1
Constant Boundary Flux
Seepage Face Flux
Drainage Boundary Flux
Free and Deep Drainage Boundary Flux
Variable Boundary Flux 2
Variable Boundary Flux 3
Variable Boundary Flux 4
All Boundaries Fluxes
Surface Runoff
Infiltration
Evaporation

250

+

Solute Fluxes+

Time

Cumulative Zero-Order Reaction
Cumulative First-Order Reaction
Cumulative Root Solute Uptake
Cumulative Non-Equil. Mass Transfer
Cumulative Constant Boundary Solute Flux
Cumulative Seepage Face Solute Flux
Cumulative Variable Boundary 1 Solute Flux
Cumulative Atmospheric Solute Flux
Cumulative Drain Boundary Solute Flux
Cum. Free/Deep Drainage Bound. Solute Flux
Cumulative Variable Boundary 2 Solute Flux
Cumulative Variable Boundary 3 Solute Flux
Cumulative Variable Boundary 4 Solute Flux
Constant Boundary Flux
Seepage Face Flux
Variable Boundary Flux 1
Actual Atmospheric Flux
Drain Boundary Flux
Free and Deep Drainage Boundary Flux
Variable Boundary Flux 2
Variable Boundary Flux 3
Variable Boundary Flux 4
All Solute Cumulative Fluxes
All Solute Fluxes

Soil Hydraulic Properties

Pressure Head
Log Pressure Head
Water Content

Water Content
Soil Water Capacity
Hydraulic Conductivity
Log Hydraulic Conductivity
Effective Water Content
Pressure Head
Log Pressure Head

Run-Time Information

Time Level
Time

Time Step
Number of Iterations
Cumulative Number of Iterations
Peclet Number
Courant Number
Number of Solute Iterations

This graph is given for each solute

The x-y graphs have only a limited capacity and can display at most 6,000 data points and 20
lines. If a dataset to be displayed has more data points than allowed, then the automatic selection
is made by the program (only each n data point is displayed), and a warning (File is too big to be
displayed entirely! Automatic selection has been made.) is issued. If the number of observation
nodes is larger than 20, only the first 20 observation nodes are displayed.
Additional text output is provided under the command Mass Balance Information on the Data Tabof the Navigator Bar (also at the Results Menu). This output gives the total amount of water,
heat, and solute inside each specified subregion, and the inflow/outflow rates to/from that
subregion, together with the mean pressure head (hMean), mean temperature (TMean) and themean concentration (cMean) over each subregion (see Table 11.6 of the Technical Manual).

251

Absolute and relative errors in the water and solute mass balances are also printed to this file.
Output related to the inverse problem is provided under the command Inverse Solution Results on
the Data Tab of the Navigator Bar. The Chemical Mass Balance information (on the Data Tab of
the Navigator Bar or at the Results Menu) is provided for the Unsatchem module. This file gives
mass balances in different phases (liquid, sorbed, solid) for all major ions (i.e., Ca, Mg, Na, K,
HCO3, SO4, and Cl).
The text dialog displaying Mass Balance Information or Inverse Solution Results had only alimited capacity in Version 1.x of HYDRUS. If the file to be displayed was larger than thiscapacity (when there are too many print times or a large number of data points in the inverse
problem), a warning “File is too big to be displayed entirely! Open it in any text editor.” wasgiven. Users, in such cases, needed to display the Balance.out or Fit.out files, respectively,
directly using any text editor, such as Notepad or WordPad. Both files are located in the
Temporary Working Directory (see Section 1). This capacity problem was overcome in Version
2, and the dialog window now displays the button Next (or Previous), which allows browsing
through larger text files.

252

8. Graphical User Interface Components
8.1. View Window
8.1.1. Scene and Viewing Commands
We will use here the term ‘Scene” for the content of the View window. Four types of commands
are available to change the display of the Scene in the View window.
a) Commands to define a required Display of the Scene.
Detailed information about particular commands is given in Section 8.4. In addition to thosecommands, it is always possible to adjust the Display of the Scene using the “mouse scroll
wheel“ as follows:
•
•
•
•
•

Simultaneously holding the mouse scroll wheel and moving the mouse will move theScene in the same direction as the mouse, i.e., to the left, right, up, or down.
Simultaneously holding the Ctrl keyboard button and the mouse scroll wheel whilemoving the mouse rotates the Scene around the center of the displayed object (available
only for three-dimensional objects).
Simultaneously holding the Shift keyboard button and the mouse scroll wheel whilemoving the mouse leads to zooming in or out of the Scene from the center of the View
window.
Rotating the scroll wheel (up or down) while pointing the mouse to a particular point in
the View window results in zooming (in or out) the Scene from this point.
Simultaneously holding the right mouse button and the mouse scroll wheel while moving
the mouse rotates the Scene around the center of the displayed object (available only forthree-dimensional projects).

The above-described operations are available not only during selection (on existing transportdomain), but also when defining basic geometric objects. This allows users to adjust the View
window as needed without interrupting the process of graphically defining objects of thetransport domain.
b) Commands to define the Content of the Scene.
In every view, one can independently specify what is to be displayed, e.g., a variable, the type ofgraph, or the numbering of objects. All possible options related to the Content of the Scene arelocated on the Navigator Bar of the View Tab (Section 8.2).
c) Displaying and/or hiding parts of complicated objects.
One often needs to display only some part of a complicated object while hiding the rest. For thispurpose, one can use commands related to Sections (i.e., parts of the computational domain or
FE-Mesh). Detailed information is given in Chapter 8.1.8 on Sections.
d) Colors, fonts, and types of lines.

253

One can define colors, the style, and thickness of lines, fonts for numbering, and other displaying
options for almost all displayed/used objects. Separate default sets exist for the display for thescreen and the printer. Users can create and save additional combinations of display options.
Detailed information is provided in Chapter 7.1.1 on Display Options.
8.1.2. Grid and Work Plane
The Grid and Work Plane dialog window (Fig. 174) allows users toa) select a Work Plane (i.e., a plane in which users can specify various boundary objects,
initial and boundary conditions, or other information),b) define the Origin of the coordinate system, andc) define the Alignment Grid. The Grid is defined by its Origin, the type (Grid Type) of thecoordinate system involved (either Cartesian or Polar), and the Grid Spacing. The Grid
can also be rotated to facilitate work, for example, when defining the domain for a hillslope problem.

Figure 174. The Grid and Work Plane dialog window.

254

8.1.3. Stretching Factors
In many applications, one direction of the transport domain dominates the other direction (or theother two directions). To facilitate work in the graphical environment, HYDRUS allows stretchingof the domain in one (or two) direction(s) using Stretching Factors. This is done using the View
Stretching Factors dialog window (Fig. 175) that is called with the command View->View
Stretching.

Figure 175. The View Stretching Factors dialog window.
Two options of View Stretching are available:a) Strict Stretching when all transport domain dimensions will be displayed as being thesame. For example, a hexahedral of any dimensions will be displayed as a cube.
b) Mild Stretching, which adjust view stretching only when large differences in dimensions
in different directions exist. By default, there will be no view stretching when the larges
dimension is five times larger than the smallest dimension.
A user should first select the Method for Calculation of Stretching Factors (either Strict orMild), then click the command Calculate Factors (which will calculate stretching factors basedon the method of stretching selected), and finally click the Apply command to update the View
Window.

8.1.4. Rendering Model
Rendering serves to rapidly switch between displays of surfaces and solids. One can select the
Wire and Full Rendering options. An advantage of Wire Rendering is mainly the speed of thedisplay, while Full Rendering provides a more realistic display of three-dimensional objects.

255

Figure 176. The Rendering part of the View Tab of the Navigator Bar.
The 3D graphics of Version 3 of HYDRUS was further improved by allowing the rendering to besmoother and faster. A transparent mode (object translucency) is now (in Version 3.0) available
also for the graphical display of results. An example of this is shown in Figure 177.

Figure 177. Example of the Transparent mode of the HYDRUS GUI. The Transparent mode isavailable for all types of graphical displays of scalar and vector fields. Isolines are automatically
numbered, and min/max values of a particular variable in the transport domain are automatically
identified.

8.1.5. Selection and Edit Commands
The selection of graphical objects is based on standards used in MS Office. An object is selectedby clicking the left mouse button; a multiple selection is made by simultaneously holding theShift button. A selection can be made using a rectangle (by clicking with the left mouse button
outside of objects and holding the left mouse button while moving the mouse), rhomboid (see256

Chapter 8.4. on Toolbars and Tools, with the Edit->Select->Select by Rhomboid command),circle (Edit->Select->Select by Circle) or polygon (Edit->Select->Select by Polygon).
In the Standard Selection Mode (Edit->Select->Standard Selection Mode), the status of theselected object is changed (selected or unselected) after its selection, i.e., the selection is toggled.
If we want to only add or remove objects to or from existing selection (i.e., we want to prevent
switching the status of selected objects (toggling)), respectively, it is possible to choose two
special selection modes: “Add to Selection” (Edit->Select->Add to Selection) or “Remove from
Selection”. (Edit->Select-> Remove from Selection). Both commands are accessible from thesubmenu Edit->Select or from the toolbar under the button “Tools for Selection”. Two special
Selection Modes can also be activated by holding the “Left Ctrl” (Add to Selection) or “Right
Ctrl” (Remove from Selection) keyboard buttons.
When the cursor (mouse) is moved above an object, information about that object appears on thestatus bar, and the object is temporarily highlighted; this process is referred to as pre-selection.
Apart from selecting objects graphically, they can also be selected using their Indices or bymeans of Sections.
Double-clicking on selected objects or simultaneous holding the Alt+Enter buttons recalls
dialogs for editing properties of particular objects. Most dialogs support multiple editing, i.e., ifedit boxes with different values remain empty, the original values will not change. This featureallows, for example, Z-coordinates of multiple selected points to be changed while leaving the Xand Y-coordinates unchanged.
When different objects are selected simultaneously (e.g., points and curves), double-clicking
causes a dialog window to appear from which objects can be selected for editing.
8.1.6. Pop-up Menus
Context-sensitive menus with useful commands for a particular object can be called from theView window when clicking the right mouse button. While the commands are also accessible
from the main menu, right-clicking the mouse is much faster. Menus for multiple selections that
may contain different types of objects operate in the same way. When the right mouse button isclicked, a default menu will appear when no object is close to the cursor.
When one clicks the right mouse button on the view window, the pop-up menu of Figure 178
will appear. This menu will allow users toa) select different views (View), i.e., Isometric, in X-direction, in Y-direction, in Z-direction,Reverse X-direction, Reverse Y-direction, Reverse Z-direction, or a perspective view.
b) select Numbering (turns on and off the display of numbering for objects selected underNumbering Options on the Navigator Bar).
c) go quickly to various Numbering Options (this command will bring the Navigator Bar tothe View Tab on Numbering).
d) switch Full Rendering/Wire Rendering (see 8.1.4).
e) start the Autorotate function that will rotate the transport domain in the View windowf) call the Show Work Plane, i.e., to show the axis, and the origin of the Work Plane257g) call the Set Grid and Work Plane dialog window (Fig. 174) (Set Grid and Work Plane)h) select the Coordinate System (call the List of Available Coordinate Systems dialog
window), andi) call the Display Options dialog window (Fig. 151).

Figure 178. The Pop-up Menu from the View window.

8.1.7. Drag and Drop
By clicking and holding the left mouse button on selected objects in the View window, the Dragand Drop operation is started. This operation allows selected objects to be moved to a newlocation. Simultaneous holding the Ctrl keyboard button leads to the creation of a copy of theselected object. The copy can be moved into a different view or in a different open project. The
operation terminates by holding the Esc button or by clicking the right mouse button. Drag andDrop can be used for most geometric objects, but also for auxiliary objects such as comments,
labels, and bitmaps.
Holding the Shift button during the Drag and Drop operation leads to the movement of selected
objects in a direction perpendicular to the current Working Plane (available only for threedimensional objects).

8.1.8. Sections
Sections serve to divide complex objects (models) into simpler parts. Only the simpler parts arethen displayed in the View window while the remaining parts are hidden. Two types of sections
exist: those for geometric objects (Geo Sections) and those for the FE-Mesh (FE-Mesh
Sections) (see also Section 5.7 and Table 19). New sections for both types can be created andnamed, a list of which is displayed on the Section Tab of the Navigator Bar. Clicking on the258Section of the Navigator Bar causes the Section to be displayed in the View window. Multiple
Sections can be displayed simultaneously by holding the “Shift” button during the selection.
Undesired (to be displayed) parts can be cut off and hidden from the View window using the Cutwith Rectangle command. This leads to a temporary section that is remembered by the program
and renewed after the project is closed and reopened. New sections can be named and listed in
the Navigator Bar by using commands to create new sections. The simplest menu command is
the New Section from the View command (alternatively, one can use the Create New Section
from Current View command from the Edit Menu of the Sections Tab of the Navigator Bar),
which creates a newly named section from currently displayed objects in the View window. The
New Section from Selection menu command (alternatively, one can use the Create New
Section from Selected Objects command from the Edit Menu of the Sections Tab of theNavigator Bar) creates a newly named section from currently selected objects or the FE-Mesh.
The Display Whole Domain (View All) and Display Whole FE-mesh commands cause theentire computational domain or FE-Mesh to be displayed.
Geometric Sections can be created manually (as described above) or automatically. The
automatically generated Geo Sections are generated as follows. An object above each part of theBase Surface (in the 3D-Layered Domain) forms a Column, which is divided into Layers,
depending on how many vertical layers the domain is divided into. Each such Layer of eachsuch Column then forms one Object (a Domain Section). When we have N Columns (that is, N
parts in the Base Surface) and the domain is divided into M horizontal Layers, then the numberof generated objects is N*M. At the same time, Surfaces belonging to each of these objects arealso generated. Some of these Surfaces are Horizontal, and some are Vertical (although theseterms are only approximate). Surfaces can then be used to specify Boundary Conditions.

Figure 179. Options for Generation of Geo-Sections and FE-Mesh Sections dialog window.
Selected Geo-Sections and/or FE-Mesh Sections can be generated using the command
Generate Sections in this dialog window (Fig. 179) obtained using the menu command Edit259

>Sections->Generate Sections. Geo-Sections can be generated either only for Solids or also for(Boundary and/or internal) Surfaces. Since working with Geo-Sections can be rather tediouswhen the number of Surfaces exceeds a certain limit, users can select this limit. The default
setting (Program Default) is to generate Geo-Sections for up to 50 Surfaces. Note that the
number of Surfaces can be prohibitively large for certain 3D-Layered Domains with multiple
internal lines and/or layers. Users can therefore choose to generate FE-Mesh Section only for
Boundary Surfaces, which are useful when specifying the boundary conditions, and not forinternal Surfaces. Users can change the default setting (Program Default), save it using the
button Save as Default, and then recall it using the button Set Default. Note that different
default settings can be saved for different types of domains.
Different FE-Mesh Sections are generated depending on the type of Domain. For the 3DLayered Domains, FE-Mesh Sections can be generated for the Boundary Shell, for each Mesh
Layer, and for both automatically Generated and User-Defined Geo-Sections. For the 3DGeneral Domains, FE-Mesh Sections can be generated for the Boundary Shell, and, again, forboth automatically Generated and User-Defined Geo-Sections.
The Section View is the status of the display (in the View window) when only part of thetransport domain is displayed (i.e., only one or few, but not all, Sections are displayed). The parts
that are not displayed are still visible in the background (thin gray lines and/or surfaces), but areinactive and cannot be selected for various operations. The Section View can be canceled (andthe entire domain displayed) using the menu command Cancel Section View or the popup menu
command Display Whole Domain.

260

8.2. Navigator Bars
The Navigator Bar (Fig. 180) is, by default, located on the left side of the HYDRUS main
window. A user can, however, move the Navigator bar to other positions. The Navigator Bar
has three Tabs:a) A Data Tab to allow quick access to all input and output data. Input data include Domain
Geometry, Flow Parameters, FE-Mesh, Domain Properties, Initial and Boundary
Conditions, and Auxiliary Objects. Output data include various Results. Data areorganized in a tree-like structure. Figure 180 shows Data with expanded Domain
Properties on the left and Results in the middle.
b) A View Tab (on the right of Figure 180) to specify what and how the information will be
displayed in the View window, andc) A Sections Tab to show various Sections (not shown here and defined elsewhere).
View Options on the View Tab of the Navigator Bar mirror more or less the Project Data, i.e.,
View Options exists for Domain Geometry, FE-Mesh, Domain Properties, Initial and Boundary
Conditions, and Results. Users can then select which objects (Domain Geometry objects, Domain
Properties objects, FE-Mesh objects, such as nodes, edges, triangles, and tetrahedrals) are to benumbered (Numbering), display Auxiliary Objects, and initiate Rendering (Outline, transparent,
filled). Users can also select the Graph Type (Isolines, Isosurfaces, Contours with or without
Separation Lines, and Color Edges, Color Points, and Velocity Vectors) and Color Scale (eitherwith or without Min/Max glob. in time or Min/Max glob. in space). Finally, Lighting can beturned on or off; the location of light sources can be shown (Show Light Sources), and thelocation of lights can be selected (Light Switches).

Figure 180. Selected Navigator Bars (Data Tab on the left, View Tabs in the middle, and Clipper
Tab on the right).

261

8.3. Edit Bars
The Edit Bar is by default located on the right side of the HYDRUS main window. A user can,however, move the Edit Bar to other positions. The Edit Bar is very dynamic since it changes
depending upon the process being carried out. Figure 181 shows the Edit Bars for different
processes, i.e., for the Material Distribution in the Domain Properties, the Water Flow Boundary
Conditions, the Pressure Head Initial Conditions, and the Water Content Results.

Figure 181. Selected Edit Bars (from left to right) for Material Distribution in Domain Properties,
Water Flow Boundary Conditions, Pressure Head Initial Conditions, and Water Content Results.
As an example, the Edit Bar for Domain Properties and Material Distribution displays
materials that can be assigned to selected nodes (in this case Materials 1, 2, and 3), the Command
Edit Materials (which calls the Water Flow Parameters dialog window, Fig. 19), thecommand Values by Pointer (which displays the material number for a node closest to thecursor), and Help. The Help part of the Edit Bar usually contains help on a particular process(How to …), and the direction of the data inputting process (next or backward).
The Edit Bar for Boundary Conditions and Water Flow displays the various boundary
conditions that can be specified along boundaries of the transport domain, as well the command
Display Codes (which displays boundary codes for all boundary nodes in the View window), thecommand Codes by Pointer (which displays boundary codes only for the node closest to thecursor), Numbering Options (which changes the Navigator Bar to the View Tab andNumbering option), Boundary Conditions Options (which allows additional system-dependent262

boundary conditions for water flow, see the Technical manual and Fig. 131), and Help (which issimilar as discussed above).
The Edit Bar for Initial Conditions and Pressure Head - h displays a color spectrum that isused to draw the initial conditions, and lists the minimum and maximum values that are used in
the entire domain. This Edit Bar also includes:a) Edit Commands: Set Values and Values by Pointer. When nodes for which the initialconditions are to be specified are already selected, then the Set Values command calls
the Water Flow Initial Condition dialog window (Fig. 129). When no nodes are
selected, then clicking on the Set Values command causes a square cursor to appear,
which may be used to select particular nodes, after which the Water Flow Initial
Condition dialog window appears. The command Values by Pointer again displays theinitial pressure head of the node closest to the cursor.
b) Two Chart Tools commands: The Cross-Section Chart and the Boundary-Line Chart.
The Cross-Section Chart command allows users to display a particular variable between
any two points of the transport domain. The Boundary-Line Chart command allows
users to display a particular variable between any two points on the boundary of thetransport domain or along any line that is drawn along edges of finite elements within thetransport domain. This line hence does not have to be straight, but can turn in any
direction along finite element edges.
c) The Help commands as before.
The Edit Bar for Results and Water Content displays, similarly as for the initial conditions, aspectrum that is used to draw results, and the minimum and maximum values for the entire
domain. This bar further includes:a) A Time Layer command to specify which time layers (corresponding to print times
specified in the Output Information dialog window, Fig. 16) are to be displayed. Timelayers can be chosen either from the list box or from a scroll bar. It is also possible toperform the animation of results by clicking on the Flow Animation check box.
b) Two Chart Tools commands (Cross-Section Chart and Boundary-Line Chart), whichhave the same purpose as above for the initial condition. The last command (i.e., Display
Values at Nodes) again causes the value of a particular variable (e.g., water content) of
the node closest to the cursor to be displayed.
c) The Help command. One useful feature of the Help command here is the Right click on
the Color Scale displays options (a right-click displays the Edit Isoband Value andColor Spectra dialog window, Fig. 152). Right-clicking results in the display of the popup menu (Fig. 182) that allows users to choose different display options, such as Color
Smoothing, Isolines, and Isobands. These options are defined in more detail below.

263

Figure 182. The Color Scale Display Options menu.
Color Smoothing

Min/Max Global in Time

Min/Max Global in SpaceStandard Scale
Custom Scale
Edit Scale and Colors
Isolines
Colormap
Isosurfaces
Color Points
Color Edges
Velocity Vectors

Colors are by default constant between isolines, but change
abruptly at the isoline. Colors change gradually when this option ischecked.
The minimum and maximum values for the color spectrum are
selected based on the minimum and maximum values of a certain
variable during the entire simulation.
The minimum and maximum values for the color spectrum are
selected based on the minimum and maximum values of a certain
variable in the entire transport domain (even when only part of thedomain is displayed, e.g., one horizontal layer).
Users can select between a standard or user-defined scale.
Users can select between a standard or user-defined scale.
Calls the Edit Isoband Value and Color Spectra dialog window(Fig. 152).
Displays a selected variable using isolines.
Displays a selected variable using isobands (color spectrum).
Displays a selected variable using isosurfaces.
Displays a selected variable using color points.
Displays a selected variable using color edges.
Displays velocities using velocity vectors.

Figure 183 shows two more Edit Bars, i.e., those for Domain Geometry and FE-Mesh. The
Insert Object of the Domain Geometry Edit Bar allows users to Insert Objects with which atransport domain is defined (i.e., points, lines, arcs, circles, splines, surfaces), as well as auxiliary
objects such as dimensions and comments. The Edit Objects part allows objects to be editedusing various actions, such as Move, Copy, Rotate, and Mirror. This Edit Bar also provides
Help on how to Edit Domain Geometry and to Check Domain Definition.

264

The FE-Mesh Edit Bar allows quick access to various commands needed for editing andgenerating the finite element mesh (Edit FE-Mesh), such as the FE-Mesh Generator (Fig. 111),
FE-Mesh Parameters (Figs. 111 through 117), Insert Mesh Refinement (Fig. 119), Delete All
Refinements, Generate FE-Mesh, Delete FE-Mesh, and FE-Mesh Information (Fig. 126). The
FE-Mesh Edit Bar also allows users to generate the finite element mesh step by step (FE-Mesh
Advanced), i.e., using individual steps such as Fundamental Triangulation, Mesh Refinement,
Delaunay Retriangulation, Convex Retriangulation, and Mesh Smoothing. This Edit Bar
additionally provides tools to work with FE-Mesh Sections, allows users to select how to makeselections (FE-Mesh Sections) and Help.

Figure 183. Selected Edit Bars (for Domain Geometry and FE-Mesh).

265

8.4. Toolbars
Users can use various toolbars that allow easy access to the most frequently used commands.
These commands are grouped into two toolbars that can be displayed using the command View>Customize Toolbars (Fig. 184). Users can also create their own toolbars and customize them invarious ways using the Customize dialog window (Fig. 184).

Figure 184. The Customize Toolbars dialog window (the Toolbars tab -top, the Commands tab bottom left, and the Options tab - bottom right).

266

The default toolbars (i.e., Standard Toolbar, Tools Toolbar, View Toolbar, GUI Toolbar, andTime Layer Toolbar) are briefly summarized below (definitions in each case are from left toright).
a) Standard Toolbar:

New ProjectOpen a Project
Save Project

Project Data Manager

Print (Ctrl+P)
Navigator Window
Edit Bar

Creates a new project.
Opens an existing project (represented by the project_name.h3d3
file)
Saves the input data of the current project specified in the main
program module if the data were either newly created or changed
during an application run.
Calls the project manager to manage data of existing projects; helps
to locate, open, copy, delete, or rename the desired projects and theirdata (Figs. 2 and 3).
Prints the content of the View window.
Displays or hides the Navigator Window.
Displays or hides the Edit Bar.

b) Tools Toolbar:

Undo
Redo
Tools for Selection

Reverses the last edit actions.
Repeats the last edit actions.
Select by Rhomboid Selects objects using rhomboid.
Select by Circle
Selects objects using a circle.
Select by Polygon
Selects objects using a polygon.
Add to Selection
Add additional objects to the existing
selection.
Remove from Selection Remove objects from an existing selection.
Standard Selection Mode
Grid and Work Plane Settings Calls the Grid and Work Plane dialog window (Fig 174).
Show Grid
Shows a Work Plane (axis and origin of the grid) in the View
window.
Set Grid Origin
Redefines the origin of the grid.
Snap to Grid
Mouse moves in steps given by the grid.
Set XY-Work Plane
Sets Work Plane to the XY plane.
Set YZ-Work Plane
Sets Work Plane to the YZ plane.
Set XZ-Work Plane
Sets Work Plane to the XZ plane.
c) View Toolbar:

267

Rotate View
Scroll View
Zoom View

Allows objects in the View windows to be rotated using the mouse
while holding the left mouse button.
Allows moving (scrolling) of objects in the View window using
the mouse while holding the left mouse button.
Allows zooming of objects in the View window using the mouse
while holding the left mouse button.

Similar functions can be achieved by pressing various buttons on the keyboard. Rotating isachieved by holding simultaneously the Ctrl button on the keyboard and the left mouse button.
Scrolling occurs by holding simultaneously the Shift button on the keyboard and the left mousebutton. And finally, zooming is achieved by holding simultaneously the Alt button on the
keyboard and the left mouse button.
Zoom by Rectangle
View All
Previous view
In Reverse Z-direction
View Commands

Isometric View
Perspective View
View Stretching Factors
Rendering Commands

Zooms in on a certain part of the View window using a rectangle.
Shows the default view of the View window.
Shows the previous view of a certain part of the View window.
Sets the view of the transport domain in the reverse Z-direction.
Shows a pop-up menu with the following commands:
Isometric
In X-direction
In Y-direction
In Z-direction
In Reverse X-direction
In Reverse Y-direction
In Reverse Z-direction
Perspective
Default View
Specifies the isometric view.
Specifies the perspective view.
Calls the View Stretching Factors dialog window (Fig 175).
Displays a menu with three commands on how to display thetransport domain (see 8.1.4):
Displays the transport domain as a full object.
Displays the transport domain as a transparent object.
Displays the transport domain as a wired object.
Displays a menu with nine commands for editing sections:

Full Model
Transparent Model
Wire Model
Sections Commands
Cut with Rectangle
Cut with Indexes
Create New Section from Selection
Create New Section from Current View
Display All
Display Previous
Hide Selection
Display only Selection
Display Reverse

268

Edit Section
Graph Type Commands
Isolines
Colormap
Isosurfaces
Color Points
Color Edges

Displays a menu with five commands.
Displays the spatial distribution of a certain variable by means ofisolines.
Displays the spatial distribution of a certain variable by means ofcolor contours.
Displays the spatial distribution of a certain variable by means ofisosurfaces.
Displays the spatial distribution of a certain variable by means ofcolor points.
Displays the spatial distribution of a certain variable by means ofcolor edges.
Displays Darcy velocity vectors.
Displays the menu with seven commands:

Velocity Vectors
Color Scale Options
Color Smoothing
Surface Lighting
Min/Max Values Global in Time
Min/Max Values Global in SpaceStandard Scale
Custom Scale
Edit Scale and Colorsd) GUI Toolbar:

View/Edit Domain Geometry
View/Edit FE-Mesh
View/Edit Domain Properties

Sets the View window to View/Edit Domain Geometry mode.
Sets the View window to View/Edit FE-Mesh mode.
Sets the View window to View/Edit Domain Properties mode,
to edit materials.
View/Edit Initial Conditions
Sets the View window to View/Edit Initial Conditions mode, toedit pressure head initial conditions.
View/Edit Boundary Conditions Sets the View window to View/Edit Boundary Conditions
mode to edit water flow boundary conditions.
Execute Calculation
Executes a HYDRUS version 3.0 FORTRAN application.
View Results
Sets the View window to View Results mode to view thepressure head distribution.
e) Time Layer Toolbar:

List box of Time Layers
First Time Layer
Previous Time Layer
Next Time Layer
Last Time Layer

Displays a list box with Time Layers with available results.
Displays the first time layer.
Displays the previous time layer.
Displays the next time layer.
Displays the last time layer.

269

Flow Animation

Displays time layers of a particular variable consecutively andcontinuously.

2708.5. HYDRUS Menus
The main window of HYDRUS contains a menu that has ten submenus, i.e., File, Edit, View
(Fig. 185), Insert, Calculations, Results (Fig. 186), Tools, Options, Windows, and Help (Fig.
187). Table 26 lists the main groups, the main menu items, as well as the main submenu and subsubmenu commands. Table 27 then provides brief descriptions of all menu commands.

Figure 185. The HYDRUS Menus I (File, Edit, and View).

Figure 186. The HYDRUS Menus II (Insert, Calculations, and Results).

271

Figure 187. The HYDRUS Menus III (Tools, Options, Windows, and Help).

272

Table 26. HYDRUS menu commands.
Group

Menu

A File

New
Open
Close

Submenu

Sub-Submenu

Save
Save As
Save All
Project Information
Project Manager
ImportImport Hydrus-2D Project
Import Input Data from another HYDRUS Project
Import Input Data from *.IN Files
Import Quantity defined by values at Scattered Points
Import Points from Text File
Import Geometry from Text File
Import Geometry from DXF File
Import Geometry from ESRI File
Import Background Layer
Import Data to ParSWMS

ExportExport Data for Hydrus Solver in Text Format
Export Geometry to Text File
Export Selected Geometrical Objects
Export FE-Mesh
Export Current Quantity
Export Isolines
Export Data to ParView
Export Data from ParSWMS

Print
Print Preview
Print to the Clipboard
Print Options
Print Setup
Recent FilesExit

B Edit

Undo
Redo
Copy
Paste
SelectSelect by Rhomboid
Select by Circle
Select by Polygon
Add to Selection
Remove from Selection
Standard Selection Mode

Properties
Find

273

DeleteDelete All
Domain Geometry

Domain Type and Units
Simple Domain
3D-Layered Domain
Delete 3D-Layered Domain
Points
Lines
Surfaces
Openings
Thickness Vectors
SolidsFlow and Transport Parameters

Main Processes
Inverse Solution
Time Information
Output Information
HP2 Print Information
Water Flow Parameters

Solute Transport Parameters

Heat Transport Parameters
Root Water Uptake

Iteration Criteria
Hydraulic Properties Model
Soil Hydraulic Parameters
Anisotropy Tensors
General Information
HP2 Components
HP2 Definitions
Solute Transport Parameters
Solution Composition
Solute Reaction Parameters
Wetlands Parameters I
Wetlands Parameters II
Temperature Dependence
Water Content Dependence
Chemical Parameters
Fumigant Application
Root Water Uptake Models
Pressure Head Reduction
Osmotic Head Reduction
Root Growth

Variable Boundary Condition
Data for Inverse Solution
Stability Analysis

Slope Cube - Soil Stress Parameters

FE-Mesh

FE-Mesh Parameters
Generate FE-Mesh
FE-Mesh Statistics
Delete FE-MeshInsert Mesh Refinement
Insert Mesh Stretching
Delete All Mesh Refinements
Delete All Mesh Stretchings
Remove Selected FE-Elements
Select Mesh Nodes
Select Mesh Elements
Material Distribution
Root Distribution

Domain Properties274

Nodal Recharge
Scaling Factor

Local Anisotropy

Subregions
Observation Nodes

DrainsFlowing Particles

Hydraulic Conductivity
Pressure Head
Water Content
Angle
First Component
Second Component
Index
Table of Anisotropy Tensors
Edit in View
DeleteClear All
Edit in View
DeleteClear All
Drain Parameters
Edit in View
DeleteClear All

Stochastic Distribution of S.F.
Subregions = Material Distribution
Nonequilibrium Conc. = a * Equil. Conc.
Parameters for Root Distribution
Delete All Domain Properties
Default Domain Parameters
Initial Conditions

Pressure Head/Water Content
Concentration
Nonequilibrium Concentration
Temperature
ImportDelete All Initial Conditions

Boundary Conditions

Water Flow
Solute Transport
Heat Transport
Boundary Conditions Options
Delete All Boundary Conditions

Edit Properties and Conditions on FE-Mesh
Edit Properties and Conditions on Geometric Objects
Transfer all Properties to FE-Mesh
Mesh Sections and Geo Sections Edit Sections
Generate Sections
New Section from Selection
New Section from View
Display Whole Domain
Display Previous Section View
Display only Selection
Hide Selection
Toggle Visibility
Cut with Rectangle
Cut with Indexes
Import FE-Mesh Sections
Dimensions

Delete Selected275Delete All
Comments

Edit
Delete Selected
Delete All

BitmapsEdit
Delete Selected
Delete All

Cross-Sections

Edit
Delete Selected
Delete All
Adjust Work Plane

Point Probes

Current Probe Editor

Edit Point Probes
Delete Selected Point Probes
Delete All Point Probes
Show All Probes
Show only Current Probe
Export Probe Values

C ViewLine Probes

Edit
Delete Selected Line Probes
Delete All Line Probes

Background Layers

Edit
Move
RotateMirrorStretch
Skew
Delete All

Geometry
FE MeshDomain Properties
Initial Conditions
Boundary Conditions
Results
Navigator

Data Tree
View Tree
Sections
Edit Bar
Clipper Pane

Status Bar
Reset Toolbars
Customize Toolbars
Default View
Zoom by Rectangle
View All
Previous View
Dynamic View (Scroll, Zoom, Rotate)
View Stretching276

Insert Points
Clear Points
Save Current Copy

Perspective
Auto-Rotate
Center of Rotation

Pick
Reset
Show/Hide

Cancel Section View Mode
View in Direction

Isometric
In X-direction
In Y-direction
In Z-direction
Reverse X-direction
Reverse Y-direction
Reverse Z-direction

Save Current View
Edit Named Views
Import/Export View Settings

Export View Transformation
Import View Transformation

List Boxes for Inverse Data

D Insert

Domain Geometry

PointsCurves

Surfaces

Openings
Thickness Vectors
SolidsFE-MeshDomain Properties

GraphicallyDialogImport Points from Text FileLine
Polyline
Arc
CircleSplineRectangle Graphically
PlanarQuadrangle
RotaryPipe
B-Spline
GraphicallyDialogGraphicallyDialog
3D-Block Graphically
3D-Layered Domain
General Solid

Mesh Refinement - GraphicallyInsert Mesh Refinement - Dialog
Insert Mesh Stretching
Material Distribution
Root Distribution
Nodal Recharge
Scaling Factor
Hydraulic Conductivity
Pressure Head
Water Content
Local Anisotropy
Angle
First Component
Second Component
Index
Subregions

277

Initial Conditions

Boundary Conditions

Dimension
Comment
BitmapCross-Sections
Mesh Line

Observation Nodes
DrainsFlowing Particles
Pressure Head/Water Content
Concentration
Nonequilibrium Concentration
Temperature
ImportWater FlowNo Flux
Constant Head
Constant Water Content
Constant Flux
Seepage Face
Variable Head 1-4
Variable Flux 1-4
Gradient BoundaryFree Drainage
Deep Drainage
Atmospheric Boundary
Solute Transport
First-Type
Third-Type
Volatile TypeHeat Transport
First-Type
Third-Type
Slope Cube
Free Displacement
X-displacement
Z-displacement
XZ-displacement
X-forceZ-force
XZ-force

GraphicallyDialogGraphicallyDialogPoint ProbeLine Probe
Background Layer

E Calculation

FE-Mesh Parameters
Generate FE-Mesh
Delete FE-Mesh
FE-Mesh Statistics
Advanced FE-Mesh Generation

Fundamental Triangulation
Mesh Refinement
Homogeneous Triangulation
Check of Convexity
Mesh Smoothing

Calculate Current ProjectCalculate All Open Projects
Select Projects to Calculate278

F Results

Display Quantity

Pressure Heads
Water Content
Concentration
Nonequilibrium Concentration
Temperature
Velocity
Root Water Uptake
Water Mass Transfer
Solute Mass Transfer
Dual-permeability Matrix
Dual-permeability Fractures

Boundary Information

Pressure Heads
Boundary Fluxes
Cumulative Fluxes
Solute Fluxes

Observation Points
Soil Hydraulic Properties
Run Time Information
Mass Balance Information
Chemical Mass Balance Information
Convert Output to ASCII
Inverse Solution Results
Fluxes across Mesh Lines
HP2 Text Output
Furrow Module
Stations
RunoffAdvance and Recession times
Time Layer
First
Last
Previous
Next
Animation
Graphs
Cross-Section Line
MeshLine
Boundary Meshline
Line Probe
Flowing Particles
Draw Particles Positions
Draw Particles Trajectories
Streamlines
Show Manipulator or Seed Points
Apply Changes Immediately
Apply Changes
Edit Seed Points Sources
Streamlines animation
Delete Results

G Tools

Show Grid
Snap to Grid
Grid and Work Plane
Define Work Plane

Set Origin
Define XY
Define YZ
Define XZ

Coordinate System
Graphical Manipulator
Translate279

RotateMirrorStretch
Skew
Intersect Lines
Intersect Surfaces
Split Lines

Insert Points on Line

Graphicallyn Points
Distance
Graphicallyn Points
Distance

Extend Lines
Extend Thickness Vectors
Generate Boundary Lines from Points
Generate Surfaces from Curves
Check Data Consistency
Repair Geometry
Create Video File

H Options

Display Options

Program Options
Model Display

Scalar Field Display

Color Scale

Edit
Default
ImportExportSolid Model
Transparent Model
Wire Frame Model
Use Material Colors for Geo-Objects
Isolines
Colormaps
Isosurfaces
Color Points
Color Edges
Show Min/Max Values
Color Smoothing
Min/Max Values Global in Time
Min/Max Values Global in SpaceStandard Scale
Custom Scale
Edit Scale and Colors

Streamline Options
Vector Field Options
Slicer Options
Transparency Options

I

Modules

Slope Stability - Classic

Input Parameters
Open Slope Stability Module
Printout Report and Results
Delete Results
Settings
Slope Stability Help
Slope Stability User's Manual

Slope Stability - Cube

Slope Cube Stress Parameters
Slope Cube Users Manual280

Slope Cube Tutorial

J

Windows

K Help

New Window
Tile Horizontally
Tile VerticallyCascadeMain and Secondary
Close All
Arrange Icons
Context Sensitive Help
Help – Contents and Index
Hydrus User Manual
Hydrus Technical Manual
Hydrus Online
Check for Updates
Hydrus License and Authorization
About Hydrus

281

Table 27. Brief description of HYDRUS menu commands.

Group Command

A

Brief description of the command

File
New

Open

Close
Save

Save As
Save All
Project Information
Project Manager

Creates a new project after the user provides required information(name and description) in the New Project dialog window (Fig. 4).
The project will be located in the current Project Group.
Opens an existing project (represented by the project_name.h3d3file) using the Open dialog window, which a user uses to browse for
the HYDRUS project.
Closes an open project.
Saves the input data of an actual project specified in the main
program module if the data were either newly created or changed
during an application run.
Saves data of a particular project under a new project name using theSave As dialog window.
Saves data of all projects.
Displays information about the current project (in the General Datadialog window (Fig. 4)).
Calls the Project Manager (Figs. 2 and 3) to manage data ofexisting projects; helps to locate, open, copy, delete or rename thedesired projects and their data.

ImportImport Hydrus-2D Project
Imports Hydrus-2D projects from Version 2.0.
Import Input Data from another HYDRUS Project Imports data from another project and interpolates
properties when FE-Mesh grids are different.
Import Input Data from *.IN Files
Imports input data from *.in files that may have been modified
manually outside of the HYDRUS GUI.
Import Quantity defined by values at Scattered Points Imports various quantities (such as initial conditions)from a text file with values given for a series of locations.
Import Points from Text File
Reads single point coordinates from a text file.
Import Geometry from Text File
Reads definition of the entire geometry from a text file.
Import Geometry from DXF File
Reads definition of the entire geometry from a DXF file.
Import Geometry from ESRI File
Reads definition of the entire geometry from an ESRI file.
Export Isolines
Exports spatial coordinates of isolines.
Import Background Layer
Imports background layer as a template for defining the transportdomain.
Imports Data from ParSWMS
Imports output data created by ParSWMS on a supercomputer orcluster of computers and display them in HYDRUS GUI.

ExportExport Data for Hydrus Solver in Text Format
Exports data for the HYDRUS solver into the working
directory from which the computational module reads inputs andinto which it writes outputs.
Export Geometry to Text File
Writes a definition of the entire geometry to a text file.
Export Selected Geometrical Objects
Writes a definition of the selected objects to a text file.
Export FE-Mesh
Exports information about the FE-Mesh to a text file.
Export Current Quantity
Exports information about the currently displayed quantity (e.g.,water content) into a text file.
Export Isolines
Exports spatial coordinates of isolines.

282

Export Data To ParView
Export Data to ParSWMS

Print
Print Preview
Print to the Clipboard

Print Setup

Prints the content of the View window.
Previews the content of the View window before printing.
Copies the content of the View window to the clipboard for
subsequent pasting into other software packages.
Select various print options, such as print quality, text size, frame,
and text content (Fig. 210).
Selects a printer and printer connection.

Recent Files

Displays recently opened projects.

Exit

Closes open projects and leaves the program. This command
informs users before exiting the application whether or not the input
data of open projects were changed during the application run. Ifchanges did occur, users are given an option to save data before
exiting the application.

Print Options

B

Exports HYDRUS results to an external graphical package
ParView.
ParSWMS is a parallelized version of SWMS-3D, which can be run
on clusters or supercomputers. This command creates input files for
ParSWMS from the HYDRUS project.

Edit
Undo
Redo

Reverses the last edit action.
Repeats the last edit action.

Copy
Paste

Copies a selected object.
Pastes a selected object.

SelectSelect by Rhomboid
Select by Circle
Select by Polygon
Add to Selection
Remove from Selection
Standard Selection Mode

Selects objects by means of a rhomboid.
Selects objects by means of a circle.
Selects objects by means of a polygon.
Add a new object to the existing selection
Remove objects from the existing selection
Selects objects by means of a quadrilateral.

Properties
Find

Displays properties of a selected object.
Finds an object.

DeleteDelete All

Deletes a selected object.
Deletes all objects.

Domain Geometry
Domain Type and Units

Simple Domain

3D-Layered Domain
Delete 3D-Layered Domain
Points
Lines
Surfaces
Openings

Specifies whether the flow and transport problem occurs in a twoor three-dimensional transport domain and whether the domain is
simple or complex using the Domain Type and Units dialog
window (Fig. 6).
Specifies parameters (dimensions and slopes) for simple rectangularor hexahedral transport domains using the Rectangular (Fig. 10) or
Hexahedral Domain Definition (Fig. 11) dialog windows.
Calls Edit 3D-Layered Domain dialog window for editing the object.
Deletes 3D-Layered Domain.
Edits selected points.
Edits selected lines using the Edit Curve dialog window (Fig. 56).
Edits selected surfaces.
Edits selected openings.

283

Thickness Vectors
SolidsEdits selected thickness vectors.
Edits solids.

Flow and Transport Parameters
Main Processes

Inverse Solution

Time Information
Output Information
HP2 Print Information
Water Flow Parameters
Iteration Criteria

Hydraulic Properties Model

Soil Hydraulic Parameters
Anisotropy Tensors
Solute Transport Parameters
General Information

HP2 Components
HP2 Definitions
Solute Transport Parameters
Solution Composition

Solute Reaction Parameters
Constructed Wetlands Parameters I
Constructed Wetlands Parameters II
Temperature Dependence

Water Content Dependence

Selects the processes to be simulated, i.e., water flow, multiple
solute transport, heat transport, and/or root water uptake (the Main
Processes dialog window (Fig. 12)).
Selects the type of weighting of measured data, and whether soil
hydraulic parameters, solute transport parameters, and/or heattransport parameters, are to be fitted (the Inverse Solution dialog
window (Fig. 13)).
Selects time units and gives the time discretization information (theTime Information dialog window (Fig. 15)).
Specifies print options (The Output Information dialog window(Fig. 16)).
Specifies print options for the HP2 modules.
Specifies iteration criteria for the solution precision and parameters
for the time step control (The Iteration Criteria dialog window(Fig. 17)).
Selects the type of model used for the soil hydraulic properties anddecides whether hysteresis is considered (the Soil Hydraulic Modeldialog window (Fig. 18)).
Specifies parameters in the soil hydraulic model (the Water Flow
Parameters dialog window (Fig. 19)).
Defines anisotropy tensors for three-dimensional applications (theTensors of Anisotropy dialog window (Fig. 22)).
Selects the time and spatial weighting schemes for the numericalsolution of the solute transport equation; specifies the number ofsolutes to be considered (the Solute Transport dialog window (Fig.
24)).
Specifies the path to the thermodynamic database and components tobe considered in PHREEQC calculations.
Text editors for defining input for PHREEQC.
Specifies solute transport parameters (the Solute TransportParameters dialog window (Fig. 26)).
Specifies solution, adsorbed, and precipitated concentration
combinations for the UNSATCHEM module (the Solution
Compositions dialog window (Fig. 31)).
Specifies solute reaction parameters (the Solute Reaction
Parameters dialog window (Fig. 27)).
Specifies parameters for constructed wetlands (the ConstructedWetland Model Parameters I dialog windows (Fig. 41)).
Specifies parameters for constructed wetlands (the ConstructedWetland Model Parameters II dialog windows (Fig. 43)).
Specifies parameters defining the temperature dependence ofreaction and transport parameters (the Temperature-Dependent
Solute Transport and Reaction Parameters dialog window shown in
Figure 29).
Specifies parameters defining the water content dependence ofreaction parameters (the Water Content Dependent Solute Reaction
Parameters dialog window shown in Figure 30).

284

Chemical Parameters

Fumigant Application
Heat Transport Parameters
Root Water Uptake
Root Water Uptake Models

Pressure Head Reduction

Osmotic Head Reduction

Root Growth
Variable Boundary Condition

Data for Inverse Solution

Specifies various chemical parameters and selections for the
UNSATCHEM module (the Chemical Parameters dialog window(Fig. 32)).
Allows additional application of a specified mass of a chemical
into the transport domain (a specified location) at a specified time.
Specifies heat transport parameters (the Heat Transport dialog
window; Fig. 34).
Selects the root water uptake stress response models for both salinity
and water stress (the Root Water Uptake Model dialog window,
Fig. 35).
Specifies parameters in the root water uptake water stress responsemodel (the Root Water Uptake Parameters dialog window; Fig.
36).
Specifies parameters in the root water uptake salinity stress responsemodel (the Root Water Uptake Parameters dialog window; Fig.
37).
Specifies parameters for root growth.
Specifies time-dependent boundary conditions for all transport
processes (the Time Variable Boundary Conditions dialog
window; Fig. 40).
Specifies data for the inverse solution, their type, location, andassociated weight (the Data for Inverse Solution dialog window;
Fig. 14).

Stability Analysis
Soil Cube - Soil Stress Parameters

Specifies soil stress parameters.

FE-Mesh
FE-Mesh Generator
FE-Mesh Parameters

Generate FE-Mesh
FE-Mesh Statistics
Delete FE-MeshInsert Mesh Refinement
Insert Mesh Stretching
Delete All Mesh Refinements
Delete All Mesh Stretchings
Remove Selected FE-Elements

Select Mesh Nodes

Select Mesh Elements

Selects the structured or unstructured finite element mesh generator(the Finite Element Mesh Generator dialog window.
Specifies either parameters of the Unstructured Finite Element
Mesh Generator (the FE-Mesh Parameters dialog window; Figs.
111 through 117) or parameters of the structured mesh (theRectangular Domain Discretization dialog window (Fig. 109) or
the Hexahedral Domain Discretization dialog window (Fig. 110)).
Generates unstructured finite element mesh.
Provides information about finite element mesh (the FE-Mesh
Information dialog window (Fig. 126).
Deletes unstructured finite element mesh.
Inserts new FE-mesh refinement using the FE-Mesh Refinement
dialog window; Fig. 119).
Inserts new FE-mesh stretching using the FE-Mesh Stretching
dialog window; Fig. 113).
Deletes All Mesh Refinements
Deletes All Mesh Stretchings
Removes selected finite elements from the finite element mesh. Notethat this operation should not be performed when properties are
specified on Geometric Objects.
Selects FE-Mesh nodes. This command is usually used to selectnodes that are then either used to define the new FE-Mesh Section or
removed from the FE-Mesh.
Selects FE-Mesh elements (to perform similar operations as forselected mesh nodes).

285

Advanced FE-Mesh Generation
Fundamental Triangulation
Mesh Refinement
Homogeneous Retriangulation
Check of Convexity
Mesh Smoothing

Performs triangulation of boundary nodes based on the Delaunay
criterion.
Inserts a new point in the center of all triangles that do not fulfill thesmoothness criterion.
Retriangulates mesh according to the Delaunay criterion.
Corrects possible errors that may appear during smoothing andretriangulating.
Smoothes the mesh by solving a set of coupled elliptic equations
using a recursive algorithm.

Domain Properties
Material Distribution
Root Distribution
Nodal Recharge
Scaling Factor
Hydraulic Conductivity
Pressure Head
Water Content
Local Anisotropy
Angle
First Component
Second Component
Index
Table of Anisotropy Tensors
Subregions
Observation Nodes
Edit

Specifies the spatial distribution of soil materials.
Specifies the spatial distribution of root water uptake.
Specifies the spatial distribution of nodal recharge.
Specifies the spatial distribution of hydraulic conductivity scaling
factors.
Specifies the spatial distribution of pressure head scaling factors.
Specifies the spatial distribution of water content scaling factors.
Specifies the spatial distribution of the angle of local anisotropy.
Specifies the spatial distribution of the first component of local
anisotropy.
Specifies the spatial distribution of the second component of local
anisotropy.
Specifies the spatial distribution of the index that represents the local
anisotropy tensor.
Displays the Anisotropy dialog window (Fig. 22).
Specifies the spatial distribution of subregions for the mass balancecalculations.

DeleteClear All

Specifies observation nodes for output of the pressure head, watercontent, temperature, and concentration at each time step.
Deletes selected observation nodes.
Deletes all observation nodes.

Drains
Edit
DeleteClear All
Drain Parameters

Specifies nodal points representing tile drains.
Deletes selected tile drains.
Deletes all tile drains.
Specifies drain parameters.

Flowing Particles
Edit
DeleteClear All

Specifies nodal points representing flowing particles.
Deletes selected flowing particles.
Deletes all flowing particles.

Stochastic Distribution of S.F.
Subregions = Material Distribution

Generates a stochastic distribution of scaling factors.
Makes the subregions for mass balance calculations similar to thosefor the soil materials.
Nonequilibrium Conc. = a * Equil. Conc. Specifies that nonequilibrium concentrations (i.e., kinetically sorbed
concentrations or concentrations in the immobile water) are a
multiple of the liquid phase concentrations.
Parameters for Root Distribution
Specifies parameters for the spatial distribution of root water uptake.

286Delete All Domain Properties
Default Domain Parameters

Command used when defining properties on Geometric Objects.
Deletes all defined domain properties and assigns default values.
Specifies default domain properties that are constant for the same
depths (the Default Domain Properties dialog window; Fig. 128).

Initial Conditions
Pressure Head/Water Content
Concentration
Nonequilibrium Concentration
Temperature
ImportDelete All Initial Conditions

Specifies the initial condition for water flow.
Specifies the initial condition for solute transport (equilibrium
concentrations).
Specifies the initial condition for solute transport (nonequilibrium
concentrations).
Specifies the initial condition for heat transport.
Imports the initial condition from previous simulations for waterflow and solute and heat transport.
Command used when defining Initial Conditions on GeometricObjects. Deletes all defined Initial Conditions and assigns default
values.

Boundary Conditions
Water Flow
Solute Transport
Heat Transport
Boundary Conditions Options
Deletes All Boundary Conditions

Specifies boundary conditions for water flow.
Specifies boundary conditions for solute transport.
Specifies boundary conditions for heat transport.
Specified additional system-dependent water flow boundary
conditions.
Clears all boundary conditions and assigns a No Flow boundary
condition on all boundaries

Edit Properties and Conditions on FE-Mesh Selects that spatially variable properties (e.g., materials, initialconditions) are assigned directly to the FE-Mesh rather than toGeometric Objects
Edit Properties and Conditions on Geometric Objects Selects that spatially variable properties (e.g., materials,
initial conditions) are assigned to Geometric Objects
Transfer all Properties to FE-Mesh
Transfer all properties (e.g., materials, initial conditions) from
Geometric Objects to FE-Mesh
Mesh Sections and Geo Sections
Edit Sections

Generate Sections
New Section from Selection
New Section from View
Display Whole Domain
Display Previous Section View
Hide Selection
Display only Selection
Toggle Visibility
Cut with Rectangle
Cut with Indexes
Import FE-Mesh Sections

Calls the FE-Mesh Section dialog (Fig. 127). HYDRUS recognizes
two different definitions of Sections – one for geometric objects andone for the FE-mesh. A different dialog appears when called fromthe “Domain Geometry” part of the program. In all other cases, theFE-mesh Section dialog appears.
Generates Geo-Sections and FE-Mesh Sections.
Creates a new section from currently selected objects/FE-Mesh
Creates a new section from currently displayed objects/FE-Mesh
Displays all objects or entire FE-Mesh
Displays a previously displayed view (sections)
Hides selected elements.
Displays only currently selected objects/FE-Mesh
Hides currently displayed objects/FE-Mesh and displays currently
hidden objects/FE-Mesh
Displays objects/FE-mesh nodes within a certain rectangle orrhomboid and hides all the others
Displays objects with given indexes and hides all the others
Import FE-Mesh Sections

Dimensions
Delete Selected
Delete All

Deletes selected dimensions
Deletes all dimensions

287

Comments
Edit
Delete Selected
Delete All

Edits a comment
Deletes selected comments
Deletes all comments

Cross-Sections
Edit
Delete Selected
Delete All
Auto-Adjust Work Plane

Edits a cross-section
Deletes selected cross-sections
Deletes all cross-sections
Adjusts Work Plane

Point Probes
Insert Points
Clear Points
Save Current Copy
Edit Point Probes
Delete All Point Probes
Show All Probes
Show Only Current Probe
Export Probe Values

Inserts coordinates of Point Probes
Deletes Point Probes
Saves current Point Probes under a group name
Edits coordinates of Point Probes
Deletes all Point Probes
Displays all Point Probes in the View window
Displays selected Point Probes in the View window
Exports values at Point Probes

Line Probes
Edit
Delete Selected Line Probes
Delete All Line Probes

Edits coordinates of Line Probes
Deletes Selected Line Probes
Deletes all Line Probes

Background Layers

Geometric objects that are imported to HYDRUS and are used as
templates for defining HYDRUS geometries
Edits a selected Background Layer
Moves a selected Background Layer
Rotates a selected Background Layer
Mirrors a selected Background Layer
Stretches a selected Background Layer
Skews a selected Background Layer
Deletes all Background Layers

Edit
Move
RotateMirrorStretch
Skew
Delete All

C

View
Geometry
FE MeshDomain Properties
Initial Conditions
Boundary Conditions
Results

Sets the View window to View/Edit Domain Geometry mode.
Sets the View window to View/Edit FE-Mesh mode.
Sets the View window to View/Edit Domain Properties mode toedit materials.
Sets the View window to View/Edit Initial Conditions mode to edit
pressure head initial conditions.
Sets the View window to View/Edit Boundary Conditions mode toedit water flow boundary conditions.
Sets the View window to View Results mode to view pressure
head distribution.

Navigator
Status Bar

Displays or hides the Navigator window.
Displays or hides the Status Bar.

Reset Toolbars
Customize Toolbars

Reset toolbars.
Customizes toolbars (the Customize Toolbars dialog window, Fig.
Fig. 184).

Standard View

Sets a default viewing direction (in 3D) and performs the “View
All” command
Zooms in on a certain part of the View window using a rectangle.

Zoom by Rectangle

288

View All

Previous View
Dynamic View (Scroll, Zoom, Rotate)

View Stretching
Perspective
Auto-Rotate
Display Whole Domain

Changes a scroll position and a zoom factor so that all currently
displayed objects are visible in the View Window. This command
does not change the viewing direction.
Shows the previous view on a certain part of the View window.
Sets the View windows so that dynamic actions can be carried out
with a cursor. Moving the cursor while holding the left mousebutton allows the object to be displayed in a different part of theView window. Pressing the Shift button on the keyboard allow
zooming actions around the cursor.
Calls the View Stretching Factors dialog window (Fig. 175) andadjust stretching factors.
Sets perspective view.
Starts Autorotate function that will rotate the transport domain in
the View window.
Cancels the Section View and displays the entire transport domain.

Center of Rotation
Pick
Reset
Show/Hide

Selects graphically (using a mouse) the Center of Rotation.
Resets the Center of Rotation previously manually selected to thedefault Center of Rotation (center of the domain).
Shows or hides the Center of Rotation from the View window.

Cancel Section View Mode

Cancel the current display mode and displayes the entire domain.

View in Direction
Isometric
In X-direction
In Y-direction
In Z-direction
Reverse X-direction
Reverse Y-direction
Reverse Z-direction

Sets isometric view.
Sets the view of the transport domain in the X-direction.
Sets the view of the transport domain in the Y-direction.
Sets the view of the transport domain in the Z-direction.
Sets the view of the transport domain in the reverse X-direction.
Sets the view of the transport domain in the reverse Y-direction.
Sets the view of the transport domain in the reverse Z-direction.

Save Current View
Edit Named Views

Saves the definition of the current view
Edits Named Views

Import/Export View Settings
Export View Transformation
Import View Transformation
List Boxes for Inverse Data

D

Export information describing camera settings (andle of view andzoom).
Export information describing camera settings.
Shows text information in the inverse data list (the Data for Inverse
Solution dialog window; Fig. 14).

InsertDomain Geometry
PointsGraphicallyDialogLines
Line
Polyline
Arc
CircleInserts single points graphically.
Inserts single points numerically (the Edit Point dialog window
without the FE-Mesh tab; Fig. 54).
Inserts a line either graphically or numerically (the Edit Curve
dialog window without the FE-Mesh tab; Fig. 56).
Inserts a polyline either graphically or numerically (the Edit Curve
dialog window without the FE-Mesh tab; Fig. 56).
Inserts an arc either graphically or numerically.
Inserts a circle either graphically or numerically.

289

SplineInserts a spline either graphically or numerically (the Edit Curve
dialog window without the FE-Mesh tab; Fig. 56).

Surfaces
Planar Surface
Quadrangle Surface
Rotary Surface
Pipe Surface
B-Spline Surface
Openings
Thicknesses
Solids3D-Layered Domain
General Solid

Inserts a surface either graphically or numerically.
Inserts a planar surface either graphically or numerically.
Inserts a Quadrangle surface either graphically or numerically.
Inserts a Rotary surface either graphically or numerically.
Inserts a Pipe surface either graphically or numerically.
Inserts a B-Spline surface either graphically or numerically.
Inserts an opening either graphically or numerically.
Inserts thicknesses either graphically or numerically.
Inserts solids either graphically or numerically.
Inserts Layered solids either graphically or numerically.
Inserts General solids either graphically or numerically.

FE-Mesh Refinement
Insert Mesh Refinement - GraphicallyInsert Mesh Refinement - Dialog

Inserts new FE-mesh refinement graphically (the FE-Meshrefinement dialog window; Fig. 119).
Defines new FE-mesh refinement graphically (the FE-Meshrefinement dialog window; Fig. 119).

Domain Properties
Material Distribution
Root Distribution
Nodal Recharge
Scaling Factor
Hydraulic Conductivity
Pressure Head
Water Content
Local Anisotropy
Angle
First Component
Second Component
Index
Subregions
Observation Nodes
DrainsFlowing Particles

Specifies the spatial distribution of soil materials.
Specifies the spatial distribution of root water uptake.
Specifies the spatial distribution of nodal recharge.
Specifies the spatial distribution of the hydraulic conductivity
scaling factors.
Specifies the spatial distribution of the pressure head scaling factors.
Specifies the spatial distribution of the water content scaling factors.
Specifies the spatial distribution of the angle of local anisotropy (fortwo-dimensional applications).
Specifies the spatial distribution of the first component of local
anisotropy (for two-dimensional applications).
Specifies the spatial distribution of the second component of local
anisotropy (for two-dimensional applications).
Specifies the spatial distribution of anisotropy tensors (for threedimensional applications).
Specifies the spatial distribution of subregions for mass balancecalculations.
Specifies observation nodes for the output of the pressure head,water content, temperature, and concentration at each time step.
Specifies nodal points representing tile drains.
Specifies nodal points representing flowing particles.

Initial Conditions
Pressure Head/Water Content
Concentration
Nonequilibrium Concentration
Temperature
ImportSpecifies the initial condition for water flow.
Specifies the initial condition for solute transport.
Specifies the initial condition for nonequilibrium solute transport.
Specifies the initial condition for heat transport.
Imports initial conditions for water flow, solute transport, and/or
heat transport.

Boundary Conditions
Water Flow290

No Flux
Constant Head
Constant Flux
Seepage Face
Variable Head 1-4
Variable Flux 1-4
Free Drainage
Deep Drainage
Atmospheric Boundary
Solute Transport
First-Type
Third-Type
Volatile TypeHeat Transport
First-Type
Third-Type
Slope Cube
Free Displacement
X-displacement
Z-displacement
XZ-displacement
X-forceZ-force
XZ-force

Specifies a no-flux boundary condition along a selected part of theboundary.
Specifies a constant pressure head boundary condition along aselected part of the boundary.
Specifies a constant flux boundary condition along a selected part ofthe boundary. Flux is positive for inflow.
Specifies a seepage face boundary condition along a selected part ofthe boundary.
Specifies a variable pressure head boundary condition along aselected part of the boundary.
Specifies a variable flux boundary condition along a selected part ofthe boundary. Flux values are negative for inflow.
Specifies a free drainage boundary condition along a selected part ofthe boundary.
Specifies a deep drainage boundary condition along a selected partof the boundary.
Specifies an atmospheric boundary condition along a selected part ofthe boundary.
Specifies a first-type boundary condition for solute transport along aselected part of the boundary.
Specifies a third-type boundary condition for solute transport along aselected part of the boundary.
Specifies a volatile-type boundary condition for solute transport
along a selected part of the boundary.
Specifies a first-type boundary condition for heat transport along aselected part of the boundary.
Specifies a third-type boundary condition for heat transport along aselected part of the boundary.
Specified Free Displacement boundary condition for the Slope Cube
soil stability module
Specified X-displacement boundary condition for the Slope Cube
soil stability module
Specified Z-displacement boundary condition for the Slope Cube
soil stability module
Specified XZ-displacement boundary condition for the Slope Cube
soil stability module
Specified X-force boundary condition for the Slope Cube soil
stability module
Specified Z-force boundary condition for the Slope Cube soil
stability module
Specified XZ-force boundary condition for the Slope Cube soil
stability module

Cross-Sections
GraphicallyDialogInserts a cross-section graphically.
Inserts a cross-section using the dialog window.

Mesh Line
GraphicallyDialogInserts a mesh line graphically.
Inserts a mesh line using the dialog window.

Auxiliary Objects291

Dimension
Comment
BitmapBackground LayerE

Calculation
FE-Mesh Parameters

Generate FE-Mesh
Delete FE-Mesh
FE-Mesh Statistics
Advanced FE-Mesh Generation
Fundamental Triangulation
Mesh Refinement
Retriangulation
Check of Convexity
Mesh Smoothing
Calculate Current ProjectCalculate Current Project
Select Projects to Calculate

F

Inserts auxiliary object (dimensions).
Inserts auxiliary object (comment).
Inserts auxiliary object (bitmap).
Inserts auxiliary object (background layer).

Specifies either parameters of the Unstructured Finite Element
Mesh Generator (the FE-Mesh Parameters dialog window; Figs.
111 through 117) or parameters of the structured mesh (theRectangular Domain Discretization dialog window (Fig. 109) or
the Hexahedral Domain Discretization dialog window (Fig. 110)).
Generates the unstructured finite element mesh.
Deletes the unstructured finite element mesh.
Provides information about the finite element mesh (the FE-Mesh
Information dialog window (Fig. 126).
Performs triangulation of boundary nodes based on the Delaunay
criterion.
Inserts a new point in the center of all triangles that do not fulfill thesmoothness criterion.
Retriangulates mesh according to Delaunay criterion.
Corrects possible errors which may appear during smoothing andretriangulating.
Smoothes the mesh by solving a set of coupled elliptic equations
using a recursive algorithm.
Carries out calculations for the currently active project.
Carries out calculations for all currently open projects.
Opens the Project Manager to select projects to be calculated.

Results
Display Quantity
Pressure Head
Water Content
Velocity
Concentration
Nonequilibrium Concentration
Temperature

Displays results in terms of pressure heads.
Displays results in terms of water contents.
Displays results in terms of velocities.
Displays results in terms of concentrations
Displays results in terms of nonequilibrium concentrations(kinetically sorbed or in the immobile water)
Displays results in terms of temperatures

Boundary Information
Pressure Heads
Boundary Fluxes
Cumulative Fluxes
Solute Fluxes
Observation Points

Soil Hydraulic Properties

Graphical presentation of pressure heads at different boundaries andin the root zone.
Graphical presentation of potential and actual boundary water fluxes
at different boundaries.
Graphical presentation of potential and actual cumulative boundarywater fluxes.
Graphical presentation of actual and cumulative boundary solute
fluxes.
Graphical presentation of changes in water content, pressure head,temperature, and/or solute and sorbed concentration at specified
observation nodes.
Graphical presentation of the soil hydraulic properties.

292

Run Time Information
Mass Balance Information
Chemical Mass Balance Information
Convert Output to ASCII
Inverse Solution Results
Fluxes across Mesh Lines
HP2 Text Output
Furrow Module
Stations

RunoffAdvance and Recession times

Graphical presentation of information about the number of iterations,time step, and Peclet and Courant numbers.
Displays mass balance information and mean profile properties.
Displays chemical mass balance information.
Convert binary input and output files into ASCII files.
Displays information about the inverse solution.
Displays actual and cumulative, water and solute fluxes across
selected mesh lines.
Displays the PHREEQC.out text output file.
Displays furrow water depths,
infiltration rates, cumulative
infiltration rates, concentrations, and solute infiltration rates atindividual furrow stations.
Displays actual and cumulative, water and solute fluxes at theoutflow from the furrow.
Displays advance and recession times.

Time Layer
First
Last
Previous
Next
Animation

Displays a particular variable at the first time layer.
Displays a particular variable at the last time layer.
Displays a particular variable at the previous time layer.
Displays a particular variable at the next time layer.
Displays time layers of a particular variable consecutively andcontinuously.

Graphs
Cross-Section Line
Mesh Line
Boundary Line
Line Probe

Displays the values of a particular variable along an arbitrary crosssection.
Displays the values of a particular variable along a selected mesh
line.
Displays the values of a particular variable along a certain part of aboundary.
Displays the values of a particular variable along a line probe.

Flowing Particles

G

Draw Particles Positions
Draw Particles Trajectories

Draws positions of flowing particles.
Draws trajectories of flowing particles.

Streamlines
Show Manipulator or Seed Points
Apply Changes Immediately
Apply Changes
Edit Seed Point Sources

Display the Manipulator tool and Seed Points.
???
???
Edits locations of Seed Points.

Delete Results

Deletes all output results.

Tools
Show Grid
Snap to Grid
Grid and Work Plane

Shows or hides the grid.
Specifies whether or not the mouse should move in steps definedby the grid.
Calls the Grid and Work Plane dialog window (Fig 174).

Define Work Plane
Set Origin
Define XY
Define YZ
Define XZ

Redefines origin of the grid.
Sets Work Plane to the XY plane.
Sets Work Plane to the YZ plane.
Sets Work Plane to the XZ plane.

293

H

Coordinate System

Selects coordinate system

Graphical Manipulator???

Translate
RotateMirrorStretchSkew

Moves or copies a selected object.
Rotates a selected object.
Mirrors a selected object.
Stretches a selected object.
Skews a selected object.

Intersect Lines
Intersect Surfaces
Split Lines
Insert Points on LineFinds the intercept of two lines and insert an interception point on
the lines.
Finds the curve that is created by the intercept of two surfaces.
Splits lines.
Inserts points on a line.

Extend Lines
Extend Thickness Vectors

Extends selected lines.
Extends selected thickness vectors.

Check Geometry
Repair Geometry
Generate Domain Surfaces

Checks geometry for consistency.
Repairs geometry if inconsistentAttempts to generate Domain Surface if they were not specified.

Create Video File

Allows users to save flow animation in a video file.

Options
Display Options
Edit
Default
ImportExportProgram Options

Edits display options in the Display Options dialog window (Fig
151).
Sets display options to their default values.
Reads display options from a file.
Saves display options to a file.
Displays program options information (the Program Options
dialog window has two tabs, one related to Graphics (Fig. 188)
and one to Program itself (Fig. 189)).

Model Display
Solid Model
Transparent Model
Wire Frame Model
Use Material Colors for Geo-Objects

Displays the transport domain as a solid object.
Displays the transport domain as a transparent object.
Displays the transport domain as a wired object???.

Scalar Field Display
Isolines
Colormaps
IsoSurfaces
Color Points
Color Edges
Show Mix/Max Values

Displays the spatial distribution of a particular variable by means ofisolines.
Displays the spatial distribution of a particular variable by means ofisobands.
Displays the spatial distribution of a particular variable by means ofisosurfaces.
Color Points Displays the spatial distribution of a particular variable
by means of color points.
Displays the spatial distribution of a particular variable by means ofcolor edges.
Display values of property minimum and maximum

Color Scale
Color Smoothing
Min/Max Values Global in Time

Changes color from abrupt to gradual at isolines.
Selects minimal and maximal values for the color scale either for theentire time duration or only for a selected time layer.

294

Min/Max Values Global in SpaceStandard Scale
Custom Scale
Edit ScaleI

Selects minimal and maximal values for the color scale either for theentire transport domain or only for the displayed part of the domain.
Selects a standard color scale for the display of a particular variable.
Selects a custom color scale for the display of a particular variable.
Calls the Edit Isoband Value and Color Spectra dialog window(Fig. 152).

Streamline Options

Selects options for displaying streamlines (Fig. 161)

Vectors Field Options

Selects options for displaying Darcy velocity vectors.

Slicer Options

Selects options for the Slicer display.

Modules
Slope Stability
Input Parameters
Open Slope Stability Module
Printout Report and Results
Delete Results
Settings
Slope Stability Help
Slope Stability User's Manual

Contains basic input parameters of the Slope Stability module.
Opens the add-on Slope Stability module, which carries out
required slope stability calculations.
Produces a standard Report that summarizes results obtained by
the Slope Stability module.
Deletes results calculated by the Slope Stability module.
Sets the global parameters for the Slope Stability module
Displays help information for the Slope Stability module
Displays a PDF version of the Slope Stability module User Manual.

Slope Cube
Slope Cube Stress Parameters
Slope Cube Users Manual
Slope Cube Tutorial

J

Windows
New Window
Main and Secondary
Tile Horizontally
Tile VerticallyCascadeClose All
Arrange Icons

K

Specifies stress parameters for the Slope Cube module.
Opens Slope Cube Users Manual.
Opens Slope Cube Tutorial.

Open a new View window.
Displays open View windows as main and secondary windows.
Tiles open View windows horizontally.
Tiles open View windows vertically.
Cascades open View windows.
Closes all open View windows.
Arranges minimized windows as icons at the bottom of the View
window.

Help
Context Sensitive Help
Help – Contents and Index
Hydrus User Manual
Hydrus Technical Manual
Hydrus Online
Check for Updates

Hydrus License and Activation
About Hydrus

Help for various objects of GUI.
Displays help information.
Displays a PDF version of the HYDRUS User Manual.
Displays a PDF version of the HYDRUS Technical Manual.
Launches Internet Explorer Browser and opens the HYDRUS web
page.
Displays a window that informs the user about the latest version of
the program and, and if available, recommends an update. If
prompted, it launches an Internet Explorer Browser and opens the"Program Updates and Upgrades" page of the HYDRUS web page,from which an upgrade can be downloaded.
Displays the Hydrus license and activation information (theHYDRUS License and Activation dialog window; Fig. 192).
Displays the version and authors of the HYDRUS application.

295

8.6. Input Tables in HYDRUS
Tables (e.g., in the "Water Flow Parameters" (Fig. 19) or the "Time-Variable Boundary
Conditions" (Fig. 40) windows) are compatible with various standard spreadsheet software (e.g.,
MS Excel). Input data can be prepared in such software (e.g., MS Excel) and then copied into
various input tables of HYDRUS. One can use keyboard keys Ctrl+C to Copy a content selected
cells (in Excel) into the clipboard and Ctrl+V to Paste it into the HYDRUS table.
8.7. New Features in Version 3.0 of GUI
The GUI of Version 3 of HYDRUS (2D/3D) now includes a significant number of major new
features (Šimůnek et al., 2018), as well as a large number of smaller corrections andimprovements. Although the external look has been preserved and is similar to Version 2,
Version 3 internally uses the latest software development tools and libraries, which is critical toensure compatibility with new Windows operating systems and the development of more
efficient software in the future. This section provides a brief overview of the most important
improvements and extensions.
One important objective of the new version was to increase the performance and capacity of theGUI. The limit of Version 2 of HYDRUS (about 1 million finite elements) was extended byalmost an order to 10 million finite elements. The extension was achieved by overall
optimization of the code and developing a 64-bit version of HYDRUS, which can now use allphysical memory available on modern PCs. This feature permitted a considerable increase in thesize of HYDRUS simulations, with the main limiting factor now being the speed of thecalculation module(s).
We further replaced many old HYDRUS (2D/3D) software components for charts and tables in
Version 3 with new components, which also included fixing some known errors. Now all dialogs
containing charts or tables are resizable, thus making entering and viewing data more
comfortable. The GUI also supports Unicode and can now correctly display special characterssuch as Greek symbols. Although manipulating graphical objects in HYDRUS, in general, wasrelatively easy thanks to drag-and-drop features, some operations (such as rotations) had to be
defined numerically in a dialog box. Version 3 offers a new graphical tool called “Manipulator”
for more user-friendly transformations of selected objects in two or three dimensions.
We also improved several features related to Mesh-sections, 3D mesh clipping and slicing. The
optimization of a GUI for work with relatively large FE meshes required certain changes in usingmesh-sections. While mesh-sections are still fully supported, the program by default does not
generate as many mesh-sections as in Version 2.

296

9. Miscellaneous Information
9.1. Program Options
The Program Options dialog window has four tabs, one related to Graphics (Fig. 188), one to
Program Options (Fig. 189), one to FE-Mesh (Fig. 190), and one to Files and Directories (Fig.
191).

Figure 188. The Program Options dialog window (the Graphics Tab).
In the top part of the Graphics Tab (Fig. 188) (OpenGL) one can turn on or off the OpenGL
Hardware Acceleration (OpenGL is a library of functions developed by Silicon Graphics Inc. forhandling graphical objects), and select the speed for OpenGL optimization.
In the bottom part of the Graphics Tab (Options) one can selecta) Simplified display in Move modusb) whether to Invert direction of mouse scroll wheel when zoomingc) whether or not an object is selected when the cursor hovers above it (Pre-selection (Markobject while hovering above it with cursor)),d) whether or not values and properties are displayed numerically when the cursor is close
to a selected object (Display values/properties at pre-selected objects),e) a different background (Gradient Background) (visually more effective background isdisplayed, which may be useful for presentations), and297f) minimum time for one frame during flow animation.
Simplified Display Mode: When the graphics (View Window update) is too slow, this option
accelerates it during dynamic rotating, moving, or zooming. When rotating the model, only its
simplified version is drawn, which results in a faster display of the model. When rotating isfinished, the full model is displayed again. This option is initiated only when the number of“refreshments” per second falls below the specified number.
When the checkbox "Synchronize selection in the Navigator and Views" is checked, clicking
on any object on the Navigator Bar leads to its automatic selection in Views. When thischeckbox is not checked, one can select an object by clicking on it with the right mouse button at
the Navigator Bar and using the Select command from the popup menu.

Figure 189. The Program Options dialog window (the Program Options Tab).
In the Undo and Autosave part of the Program Options Tab (Fig. 189) one cana) select a time interval for Auto-saveb) specify Memory size for the Undo buffer, andIn the General Options part of the Program Options Tab one cana) specify whether or not the program Reloads last opened projects at startupb) specify whether or not the program should Save automatically windows settings on close
project

298c) select whether Domain properties, and boundary and initial conditions are edited bydefault on Geometrical objects or finite element mesh.
d) select how often (every nn days) the program should "Check for available updates atHydrus startup" at the Hydrus website. This check can be disabled by entering zero (0).
Note that customers who own a HYDRUS license are entitled to free updates of thepurchased version within the next two years.
In the Calculation and Results part of the Program Options Tab one cana) specify whether the results are to be kept in an external directory (By default keep results
in an external directory),b) select whether the FE-Mesh is to be saved in text format (Save FE-Mesh in text format),c) select whether or not Domain Properties are to be saved in text format (Save Domain
Properties in text format).
d) Select whether the parallelized version, i.e., the HyPar module (see Section 9.8), of thestandard computational module (h2d_calc.exe and h3d_calc.exe) is to be used (UseParallel Calculation Module).

Figure 190. The Program Options dialog window (the FE-Mesh Tab).
In the Mesh Limits part of the FE-Mesh Tab (Fig. 190) one cana) specify the Recommended maximum number of finite elements for 2D projects,b) specify the Recommended maximum number of finite elements for 3D projects.

299

In the Export Options part of the FE-Mesh Tab one can select various export options, such asa) whether to Export intermediate points on boundary curves,b) whether to Include internal curves in Boundary Information Table, andc) whether to Write Description Tables.
Finally, in the Preferred Generator for 2D Meshes part of the FE-Mesh Tab, one can selectwhether to use the MESHGEN (default) or Genex program.
In the Files and Directories Tab (Fig. 191) (Options) one can specify locations of various
HYDRUS files and the file having information about display options:• Directory for HYDRUS Settings and Authorization Files• Working Directory for Temporary Files• Default Directory for HYDRUS Projects• Configuration file for display options• Directory for Thermodynamic Databases (for the HP2 program)

Figure 191. The Program Options dialog window (the Files and Directories Tab).

300

9.2. HYDRUS License and Activation
HYDRUS is protected either by a Software Lock that is based on information about the
hardware on which it is run or, starting with version 2.02, using a Hardware Key (HASP).
Starting with version 2.02, the software key can be used to authorize only separate computers,
while a Hardware Key is required for the network or server installations designated for remote
access (see Section 9.2.5). Without activation, HYDRUS works as a demo version - you can run
it but you will not be able to run calculations and save your data. A customer using a Software
Lock can choose to Activate HYDRUS by E-mail with the help of the HYDRUS support or
directly On-line (an internet connection is required). Using the Online activation system,
customers can themselves manage their HYDRUS license, i.e., installation, de-installation,
and/or reinstallation of HYDRUS. The HYDRUS software package is activated (using theSoftware Lock) using the HYDRUS Authorization Status dialog window (Fig. 192) that iscalled using the command Help->Hydrus License and Activation.
9.2.1. Brief Description of HYDRUS Activation Using a Software Lock
A. On-Line Activation (recommended)- To activate online you need to know your License Number (four digits) and the Activation
Key (hexadecimal, 32 characters). You should receive both numbers from the HYDRUS
distributor from whom you purchased the license for HYDRUS or from HYDRUS customer
support support@pc-progress.cz.
- Enter both numbers into the Online Activation dialogue window (Fig. 196).
- After clicking the Activate Now command, HYDRUS establishes a connection over theInternet with the license server and performs its activation.
B. Activation by E-Mail (when encountering problems with on-line activation)
The activation process by email consists of generating two request codes that need to be sent to
the HYDRUS distributor together with information about the license, customer, and workplace.
Based on this information, the HYDRUS distributor will generate a corresponding activation
code and send it back to the HYDRUS user. Different HYDRUS functions will be activated after
inserting the activation code depending upon the type of purchased license.
- In the dialog window Activation by E-mail (Fig. 211), generate Request Codes.
- Send the Request Codes by email to support@pc-progress.cz or to the HYDRUS distributor,
from whom you purchased the license for HYDRUS.
- After that, you will receive by email the Activation Code, which you enter into the dialog
window Activation by E-mail (Step 3 Tab, Fig. 202), and activate HYDRUS.
9.2.2. Detailed Description of HYDRUS Activation Using a Software Lock
The HYDRUS Authorization Status dialog window (Fig. 192) displays information about
Authorization Status, Last Activation, and License Information, such as License Number,
Computer ID, Workplace, and License Owner. Authorization Status information includes
information abouta) Status, which can be either Not Authorized or Authorization OK,

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b) Level of authorization, which can be either 2D-Lite, 2D-Standard, 3D-Lite, 3D-Standard,
or 3D-Professional,c) whether or not the Authorization is Time-Limited (if yes, then the Expiration Time isgiven), andd) whether or not the Network Installation is active (if yes, then the Number of Clients isgiven)All this information is displayed as read-only text that is filled in during the first activation of thesoftware. The button “Send Authorization Report” is used when resolving problems with
software activation.

Figure 192. The HYDRUS Authorization Status dialog window (Tab Status).
For the commands in this dialog window to be active (e.g., Activate by E-mail or Activate online), HYDRUS needs to be run with administrator privileges. That means that you need to belogged as an Administrator (or as a user belonging to the "Administrators" group) when making
changes to the authorization. To run HYDRUS as administrator under Windows Vista or Windows
7 operating systems, click on the HYDRUS icon on your desktop using the right mouse button and302

select "Run as Administrator" from the popup menu. Warning displayed in Figure 193 is issued
when attempting to make changes to the Authorization Status while not running HYDRUS
with administrator privileges.

Figure 193. Warning issued when attempting to make changes to the Authorization Status while
not running HYDRUS with administrator privileges.

Figure 194. The HYDRUS Authorization Status dialog window (Tab Add-on Modules).
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The second Tab of the HYDRUS Authorization Status window, i.e., the Add-in Modules Tablist additional HYDRUS modules (e.g., Unsatchem, Wetland, DualPerm, C-Ride, or HP2) thatare currently available and activated. At the top of the Tab, there is an indication, which
Authorization Method (either of Software Key or a Hardware Key) is used.
The third Tab of the HYDRUS Authorization Status window, i.e., the History of Activation
Tab reports recent actions related to HYDRUS activation.

Figure 195. The HYDRUS Authorization Status dialog window (Tab History of Activation).

9.2.2.1. On-Line Activation
Online activation is the fastest and most convenient way to activate HYDRUS. The Online
Activation window (Fig. 196) appears after clicking on the Activate on-line button on the
HYDRUS Activation Status window. Here you need to enter information about the License
Number and the appropriate Activation Key that you received, together with an invoice from304

the HYDRUS Customer Support. This Activation Key is used for all Workplaces of a particularlicense. For special purposes, different Activation Keys can be generated for individual
Workplaces (e.g., when a particular Workplace has authorization for a different HYDRUS Levelor a specific HYDRUS module).
In the section Specify the required authorization level, select the required HYDRUS Level to
Activate (i.e., 2D-Lite, 2D-Standard, 3D-Lite, 3D-Standard, or 3D-Professional; please note that
this Level has to correspond with the purchased Level) and the Type of License to activate (e.g.,
Time-Limited Authorization with the Expiration Date, or the Network Installation with the
Number of Clients). If no checkbox is selected, a Time-Unlimited Single User License isauthorized. With regard to a possible loss of authorization due to failure of hardware, it isrecommended to choose a shorter period of validity (default is 0.5 years). An item Computer
Description serves for the future identification of a particular computer in the electronic
licensing system and is usually characterized by a user or its location (e.g., John - Laptop, Harry- Lab 001).

Figure 196. The Online Activation dialog window.
After clicking on the Activate Now button, you will be asked to confirm all specified parameters(Fig. 197) (note that you may be prompted by your firewall to allow communication between
your computer and the license server of PC Progress). At this point, all specified information will
be verified against the data of our electronic licensing system, and if confirmed, the actual
activation of HYDRUS will occur. This communication applies only to data entered in theOnline Activation window, and no other information stored on your PC is transferred. In case of
unsuccessful activation, an error message is displayed explaining the problem. After correcting
the problem, you can use the Activate Now command again.

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Figure 197. Window requesting confirmation of entered parameters.
Prior to the expiration (Expiry Day) of the Time-Limited Authorization, the user will bealerted about it, and the license can be easily repeatedly extended using the Extend Activation
function.
9.2.2.2. Activation by E-mailFor this option, the user is guided through a three-step form (three Tabs of the Activation by Email dialog window, Fig. 211). During the first two steps, he/she prepares information needed toobtain HYDRUS Authorization and emails it to the HYDRUS distributor. In the third step, theuser enters the Activation Code that he receives by e-mail on the third Tab (Step 3) of the
Activation by E-mail and activates HYDRUS.
The first step is to fill in information about the license (License Number), the name of thelicense owner (Customer), and a description of the Workspace (WP Description). This last item
(i.e., WP Description) serves for future identification of a particular computer in the electronic
licensing system and is usually characterized by a user or its location (e.g., John - Laptop, Harry- Lab 001).
In the section Required Authorization select the required HYDRUS Level to Activate (i.e.,
2D-Lite, 2D-Standard, 3D-Lite, 3D-Standard, or 3D-Professional; please note that this Level has
to correspond with the purchased Level) and the Type of License to activate (e.g., Time-Limited
Authorization with the Expiration Date, or the Network Installation with the Number ofClients). If no checkbox is selected, a Time-Unlimited Single User License is authorized. With
regard to a possible loss of authorization due to failure of hardware, it is recommended to choosea shorter period of validity (default is 0.5 years).

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Figure 198. The Activation by E-mail dialog window (Tab Step 1).
After clicking on the Generate Request Codes button on the Step 1 Tab of the Activation by
E-mail window (Fig. 211), the user is prompted to confirm all entered information (Fig. 197),
and then the Step 2 Tab (Fig. 199) appears.

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Figure 199. The Activation by E-mail dialog window (Tab Step 2).
Information entered during Step 1 (on Tab Step 1) is summarized in the Authorization Request
Codes section of the Step 2 Tab. This information can be copied to the clipboard using the Copy
to Clipboard button and then sent by email to the HYDRUS support or other HYDRUS
distributors. The command Send Request Codes by E-mail will attempt to start the emailingprogram (e.g., Microsoft Outlook) directly and copy there automatically an email address of the
HYDRUS support (support@pc-progress.cz) and all required information (see an example ofsuch email displayed in Outlook in Fig. 200).

308

Figure 200. An email with the HYDRUS Activation Request in Outlook.
On the basis of this information, the HYDRUS support or other resellers will promptly emailback the Activation Code.
Notes on Request Codes
1. Request Code 1 is a randomly generated number that can be used for a single activation.
After the activation (either successful or unsuccessful), this number is changed, and therefore,
the same number cannot be used repeatedly even for the same computer.
2. Request Code 2 (Computer ID) is a number that uniquely characterizes the hardware of acomputer or a computer network (for the network license). This number should be constantfor a particular computer unless there is a change of hardware. If this number changes, theauthorization system will evaluate the license as invalid. It is thus necessary before thechange of hardware (e.g., a change of the motherboard) or reinstallation of the operating
system (Windows) to deactivate HYDRUS since HYDRUS will need to be reactivated after
hardware changes are completed.
3. There are only three attempts available to activate HYDRUS with a particular request andactivation codes. If wrong activation codes are inserted during the first three attempts,
HYDRUS issues a warning. After the third attempt with wrong activation codes, the Request
Code 1 is changed, and new activation codes need to be requested.
4. We recommend using standard functions Copy & Paste when inserting activation codes tominimize the risk of inserting wrong numbers.

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When starting unauthorized HYDRUS again, the user is informed that request codes haverecently been generated and if he/she wants to enter the Activation Code and activate HYDRUS(Fig. 201). It is important not to regenerate request codes at this time as the Activation Codewould then not be active any more since one of the request codes would be changed.

Figure 201. Window inquiring if the user wants to enter the Activation Code.
After receiving the Activation Code, enter this code on the Step 3 Tab of the Activation by Email dialog window (Fig. 202) and click on the Activate Now button. You should receive a
confirmation that the authorization process was successful (Fig. 203).

Figure 202. The Activation by E-mail dialog window (Tab Step 3).

310

Figure 203. Window confirming successful HYDRUS authorization.
Note that the Request Code and a Computer ID are displayed in the upper part of the Step 3
Tab. Remember that your Request Code and Computer ID are hardware-dependent. After
upgrading your hardware (e.g., BIOS, hard drives), you will very likely have to request a new
Activation Code. You are eligible to obtain those codes for free (although subject to some
limitations - ask for details).
When the activation fails three times (likely due to incorrectly entered information), the request
keys will change, and windows shown in Figure 204 will be displayed, providing instructions on
how to proceed further. The user will be requested to send a report to the HYDRUS support sothat the cause of the problem can be analyzed.

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Figure 204. Window reporting a failure of HYDRUS authorization.

9.2.3. Reinstallation, Moving to another Computer
With a "single-user" license, you are eligible to install and use HYDRUS on two computers (forexample, a computer in your office and your notebook). If you reinstall HYDRUS on an
activated computer or if you install a newer HYDRUS version, then your previous authorization
will remain active.
Deactivation of HYDRUS and/or Reinstallation to another computer
Users should deactivate HYDRUS before a) any hardware change (motherboard, hard-drives,graphic card, BIOS, etc.), b) reinstallation of the Windows OS, c) reformatting the hard-drivewith HYDRUS, d) changing the network path to HYDRUS (applies to the network installation),and e) moving HYDRUS license to another computer. The HYDRUS software package isdeactivated using the HYDRUS Authorization Status dialog window (Fig. 192), which is calledusing the command Help->Hydrus License and Activation. Similarly, as for HYDRUS activation,
you can deactivate HYDRUS either by email (the command Deactivate by E-mail) or online (thecommand Deactivate on-line).
9.2.3.1. On-Line Deactivation
After clicking on the command Deactivate on-line in the HYDRUS Authorization Status
dialog window (Fig. 192), in the Online Deactivation window (Fig. 205), enter the Activation
Key and press the button Deactivate Now. You should receive a warning that this action willdeactivate HYDRUS, and after clicking Yes, the confirmation that HYDRUS has beensuccessfully deactivated on your computer (Fig. 206).

312

Figure 205. The Online Deactivation dialog window.

Figure 206. Window confirming successful online deactivation of HYDRUS.

9.2.3.2. Deactivation by Email
After clicking on the command Deactivate by E-mail in the HYDRUS Authorization Status
dialog window (Fig. 192), in the HYDRUS Deactivation window (Fig. 207), press the button
Deactivate HYDRUS Now. You should receive a series of warnings that this action willdeactivate HYDRUS, and after clicking Yes, the confirmation that HYDRUS has beensuccessfully deactivated on your computer (Fig. 208). The Deactivation Code will then appear
in the HYDRUS Deactivation window (Fig. 207). This code can be copied to the clipboard
using the Copy to Clipboard button and then sent by email to the HYDRUS support or other
HYDRUS distributors. The command Send Deactivation Code by E-mail will attempt to startan emailing program (e.g., Microsoft Outlook) directly and copy there automatically an email
address of the HYDRUS support (support@pc-progress.cz) and all required information (see an
example of such email displayed in Outlook in Fig. 200).

313

Figure 207. The HYDRUS Deactivation dialog window.

Figure 208. Window confirming the successful deactivation of HYDRUS by email.

314

9.2.4. Extending Activation
Prior to the expiration (Expiry Day) of the Time-Limited Authorization, the user will bealerted about it, and the license can be easily repeatedly extended using the Extend Activation
On-Line button. This button will appear instead of the Activate on-line button on the Status
Tab of the HYDRUS Authorization Status window (Fig. 192). To extend the activation, youwill need again the Activation Key (either for the entire license or for a particular Workspace).

9.2.5. Hardware Key
Starting with Version 2.02, the network authorization of the HYDRUS program can be done
either as in previous versions using the software key (activation) or newly using a Hardware
Key (HASP). The software key can be used to authorize only separate computers, while a
Hardware Key is required for the network or server installations designated for remote access.
A Hardware Key (HASP), also called a "dongle", is a software copy protection device thatplugs into the USB port of the computer. Upon startup, the application looks for the key and will
run only if the key contains the appropriate code. Hardware keys are very effective copyprotection devices, because they cannot be duplicated by the user.
1. The HASP for HYDRUS is sent (by PC Progress) by mail, and its use is very simple.
You just connect it to the computer via the USB port, and HYDRUS is then immediately
authorized. The HYDRUS software then does not require any further activation.
2. Although the drivers for the HASP should normally be installed automatically when it isconnected to the USB (Windows operating system and Plug-and-play should take care ofthat), we still recommend installing the drivers at the same time when the Hydrus
software is installed (during the HYDRUS installation). In one of the dialog windows thatappears during installation, there is a special check-box "Install the hardware-key
driver" (Fig. 209), which needs to be checked - see the picture below:

315

Figure 209. The HYDRUS 2.xx Setup window with a choice to install the hardware-key driver.
Advantages of HASP:•

Proven solutions by SafeNet, verified by hundreds of installations and users.

•

No activation of the software (e.g., HYDRUS) is needed. Activation of the program
brings some disadvantages, such as that the program can be activated only on the allowed
number of computers, and the activation is always time-limited (up to 1 year) and needs
to be repeatedly renewed. Under certain circumstances, the activation code may not be
immediately available, and users have to wait till they get it (e.g., activation by e-mail).
The hardware key (dongle) gives users assurance that the program can be easily installed
and used, for example, on a new computer.

•

The program (e.g., HYDRUS) can be used on multiple computers (e.g., desktop andlaptop) only by transferring a small USB key.

•

Easier and safer installation of a network version. The network installation using asoftware key (activation) is somewhat more complicated, and some network
administrators have complained about its lack of flexibility. The use of HASP eliminates
these problems.

316

9.3. Print Options Dialog Window
The Print Options dialog window contains four tabs (Fig. 210). In the General Tab a user
selects whether the content of the View window (Picture) is to be printed with or without a
Legend, Page Orientation (Portrait or Landscape), and Page Margins. In the Picture Tab,
users further select Print Quality (the Standard print quality, which can be changed by users, is
5,000*5,000 pixels), whether the Frame is to be printed in black or color (Colors and Frame),and Text Size. In the Color Scale Tab, users select Orientation of the Color Scale, its Position,
Alignment, and Size. Finally, in the Legend Tab, users select what texts (Legend Rows) are to
be printed, with what Font, and how far from the picture. Users can use a predefined text or canwrite their own.

Figure 210. The General, Picture, and Legend tabs of the Print Options dialog window.

317

9.4. Print Preview and Copy to the Clipboard Commands
The result of commands Print Preview and Copy to the Clipboard is shown in Figure 211. The
Print Preview command displays the content of the View Window on the screen as it would
appear in printed form, while the Copy to the Clipboard command copies the same content to ametafile (enhanced metafile, EMF, http://en.wikipedia.org/wiki/Windows_Metafile) in the
Clipboard for subsequent pasting into other software packages, such as Word, PowerPoint, etc.
Additional content of the metafile (in addition to the content in the View Window, such as the
text of the legend) is defined using the Print Options window. The metafile contains the bitmap(the resolution of this bitmap (max 6000x6000 pixels) can be specified in the Print Options
window) with the graphics displayed in the View Window and additional vector objects (e.g.,texts and/or numbering).

0.000 0.004 0.008 0.012 0.016 0.020 0.024 0.028 0.033 0.037 0.041 0.045

Concentration - c[mmol/cm^3], Min=0.000, Max=0.045

Project 3DFumig6 - 3D, Finite res., Heat Tr., Tarp, Tarp removal, part untarped
Results, Concentration, Time 6 - 1.50 days

Figure 211. Result of commands Print Preview or Copy to the Clipboard.

318

9.5. Coordinate systems
The Coordinate System used for the transport domain definition can be selected from the Listof Available Coordinate Systems dialog window (Fig. 212, top) called by the Tools>Coordinate System command. Cartesian, Cylindrical, and Spherical systems are available. The
Cartesian coordinate system is selected by default. A New Coordinate System can be definedusing the dialog window of the same name (Fig. 212, bottom).

Figure 212. The Coordinate Systems dialog windows.

319

9.6. DOS Window During Calculations
During the calculations, a different type of information can be written to the screen. The
following information may be written to the screen depending upon the problem:
Time
T-Level
ItW
ItC
ItCum
CumAtmBC
CumConst
CumDrain
CumRootUp
CumCh0
CumCh1
CumChS
hAtm
hConsthDrainhRoothSeep
vConstBC
vSeep

Time
Time level
Number of iterations to solve the water flow problem at a certain time
step
Number of iterations to solve the solute transport problem at a certain
time step
Cumulative number of iterations
Cumulative flux across the atmospheric boundary
Cumulative flux across the boundary having a constant flux or pressure
head
Cumulative flux across the boundary having a time-variable flux orpressure head
Cumulative actual root water uptake
Cumulative zero-order production in the domain (solute transport)
Cumulative first-order degradation in the domain (solute transport)
Cumulative solute flux across the boundary having a time-variable flux
or pressure head
The average pressure head at the atmospheric boundary
The average pressure head at the boundary having a constant flux orpressure head
The average pressure head at the boundary having a time-variable flux
or pressure head
The average pressure head in the root zone
The average pressure head at the boundary with the seepage face
Flux across the boundary having a constant flux or pressure head
Flux across the boundary having a seepage face320

9.7. Running Computational Modules Outside of GUI or in a Batch
Computational modules (e.g., h2d_calc.exe, h2d_clci.exe, h3d_calc.exe) can be run either
directly from GUI or by clicking on any of them in the folder in which HYDRUS is installed.
When these modules are run from GUI, GUI will send them as a parameter the path to the folder
in which the input and output files are located (the working folder, the path to which is displayedin the project manager (h1d) or in the project information dialog (h3d)). When the program does
not receive a path as a parameter, it will look for the text file called Level_01.dir that needs to belocated in the same folder as the computational module. This file can be written using any text
editor, such as Notepad. This file must have one line, which provides the path to the folder inwhich the input and output files are located.
Example of the “Level_01.dir” file:
c:\program files\pc-progress\hydrus3d\mydirect\run1
For the input files to be available in the Working Folder, the Working Folder needs to be either'Permanent' (see the Project Information dialog) or the HYDRUS GUI needs to be opened when
the Working Folder is 'Temporary'. In each case, the text input files need to be created using themenu command File->Import and Export->Export Data for HYDRUS Solver in Text Format.
HYDRUS (2D/3D) allows users to select multiple projects and run them simultaneously using
the “Calculate All Open Projects” or “Select Projects to Calculate”. To run several projects
sequentially is more complex. One needs to prepare a batch file (e.g., run.bat) and files
describing paths (e.g., path1, path2, etc) to project folders (to be run) in advance. One needs tocopy these files into the program folder (e.g., c:\program files\ussl\hydrus3d). Additionally, thecheck box "Hit Enter at the End?" in the Output Information window has to be unchecked for all
projects to be run sequentially.
Example of the “run.bat” file:
copy path1 level_01.dir
h2d_calc
copy path2 level_01.dir
h2d_calc
Example of the “Path1” file:
c:\program files\ussl\hydrus3d\mydirect\run1
Example of the “Path2” file:
c:\program files\ussl\hydrus3d\mydirect\run23219.8. The HyPar Module, a parallelized version
HyPar is a parallelized version of the standard two-dimensional and three-dimensional
HYDRUS computational modules (h2d_calc.exe and h3d_calc.exe). HyPar uses parallel
programming tools and techniques to take advantage of multiple cores and to acceleratecalculations on multi-core processor computers. HyPar currently supports only calculations in
the direct mode (does not support the inverse mode), and it does not support any add-on modules(e.g., HP2, UnsatChem, Wetland, and/or C-Ride). The HyPar module is initialized on the
Program Tab of the Program Options dialog window (Fig. 189).
The name HYPAR (HyPar) is an acronym for "Hydrus Parallelized". The term, which has beensuggested by Rien, is also intended to indicate a "Hyper" action when multiple cores of a PC
processor work in unison like 'a bunch of bees'. The results of the speedup of the HyPar module
compared to the standard modules are presented in (Table 28).
Table 28. A comparison of the HyPar module to standard computational modules.
SystemInfo

Computer

HP Elite 7300 Series MT

Operating System

W7/64

Processor

Intel(R) Core(TM) i7-2600 CPU @ 3.40 GHz

Number of cores

8

2D Tests:
Project Name

Processes

Number of Elements

Standard Module

HyPar Module

Ratio

2DWater1

2D WF

20 k

8.36 s6.12 s0.73

2DWater1s

2D WF, ST

20 k

13.83 s8.08 s

0.58

2DWater2

2D WF

200 k

310.24 s

169.45 s

0.55

2DWater2s

2D WF, ST

200 k

508.79 s

262.87 s

0.52

2DWater3

2D WF

1,000 k3134.9 s

1666.2 s

0.53

2DWater3s

2D WF, ST

1,000 k7296.0 s

3549.2 s

0.49

WF - Water Flow; ST - Solute Transport

3D Tests:
Project Name

Processes

Number of Elements

Standard Module

HyPar Module

Ratio

3DWater1

3D WF

20 k

15.88 s5.78 s0.36

3DWater1s

3D WF, ST

20 k

32.24 s12.19 s0.38

3DWater2

3D WF

200 k

211.41 s

87.07 s0.41

3DWater2s

3D WF, ST

200 k

502.0 s194.33 s

0.39

3DWater3

3D WF

1,000 k1554.3 s

689.71 s

0.44

3DWater3s

3D WF, ST

1,000 k7078.0 s

2427.4 s

0.34

322

9.9. Video Files
Users can save the flow animation using the Create Video File command (Tools->Create Video
File). This command calls the Create Video File dialog window (Fig. 213), in which a userneeds to specify where the Video File should be saved and under what name, type of the video
file [a) Cinepac Codec by Radius, b) Microsoft Video 1, c) Intel Indeo Video 4.5, d) Intel Indeo
Video 5.10, e) Microsoft MPEG-4 Video Codec V1, and f) Microsoft MPEG-4 Video Codec V2]
and its Quality, and finally whether the recording is carried out at Real Time (i.e., the video will
run at the same speed as HYDRUS animation) or only when frames in the View Window change(only changes in View Window are recorded). Additional options (such as Smoothness, Data
Rate (i.e., kilobits per second)) are available for each particular video format. OpenGL
acceleration should be disabled when problems occur when creating a Video File.

Figure 213. The Create Video File dialog window.

Animation files (*.avi) created by the HYDRUS command Create Video File can be displayedusing standard video software, such as the Windows Media Player. Animation files can also be
inserted directly into PowerPoint presentations using the menu command "Insert->Movie>Movie from File …" and selecting whether animation starts Automatically or When Clicked.
Animation can then be stopped and restarted using additional mouse clicks.
Notes on Video Editing:
1. Video records only change in View. Thus, if nothing changes in the View window, only
the first picture is recorded. When one records animation of flow or transport, then while
the View window is redrawn, each change is recorded. Similarly, one could record video
for any other manipulation of the View, which requires its redrawing (e.g., rotation of themodel).

323

2. If the option "Real-Time" is on, each recorded View has an assigned time, which elapsed
between redrawing of the View window. This means that the video is then played at
approximately the same rate as redrawing of the View window.
3. If the option "Changed Frames Only" is on, then changes in the View window are stored
regardless of the actual time elapsed in redrawing the View. For example, if somechanges in redrawing of view take place quickly, followed by a pause, and again fastchanges, in the resulting video, all changes will be played back with a constant time delay.
The current version of HYDRUS does not have an option of allowing to set a timeinterval between recorded frames. It is entirely possible that one can edit Video
recordings created by HYDRUS using some public domain programs for editing videos.
We currently do not have any experience with that and cannot make any
recommendations.

324

9.10. About HYDRUS
This window displays the program version (the Program Tab), authors of the HYDRUS
application (the Authors Tab), and the License agreement (the License Agreement Tab). The
Program Tab additionally displays other software products (such as mesh generators) that areused in HYDRUS.

Figure 214. The About HYDRUS dialog window (the Program tab (top) and the Authors tab(bottom).

325

326

References
Bradford, S. A., S. R. Yates, M. Bettehar, and J. Šimůnek, Physical factors affecting the transportand fate of colloids in saturated porous media, Water Resour. Res., 38(12), 1327,
doi:10.1029/2002WR001340, 63.1-63.12, 2002.
Brooks, R. H., and A. T. Corey, Properties of porous media affecting fluid flow. J. Irrig. Drainage
Div., ASCE Proc. 72(IR2), 61-88, 1966.
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