TABLE OF CONTENTS
Part I HYDRUS and The Basic Theory of Soil Physics
1 Overview of HYDRUS....................................................................................................................... 3
1.1

Brief Introduction of HYDRUS ................................................................................................... 3

1.2 HYDRUS-1D Software Interface ................................................................................................ 4
1.3

HYDRUS-(2D/3D) Software Interface........................................................................................ 5

1.3.1 HYDRUS-(2D/3D) Menu Bar .............................................................................................. 5
1.3.2 HYDRUS-(2D/3D) Toolbar, View Window And Status Bar .............................................. 13
1.3.3 HYDRUS-(2D/3D) Navigator Bar ...................................................................................... 14
1.3.4 HYDRUS-(2D/3D) Edit Bar ............................................................................................... 16
2

Soil Physical Properties .................................................................................................................... 19
2.1

Soil Texture ................................................................................................................................ 19

2.2

Soil as A Three-Phase System and Its Properties ....................................................................... 19

2.3

Soil Water Content and Its Representation Method ................................................................... 21

3 Soil Water Flow ................................................................................................................................ 23
3.1

Soil Water Potential ................................................................................................................... 23

3.2Soil Water Characteristic ........................................................................................................... 25

3.2.1 Definition of Soil Retention Curve ..................................................................................... 25
3.2.2

Mathematic Models of Soil Retention Curve...................................................................... 25

3.2.3 Applications of Soil Retention Curve ................................................................................. 27
3.3Saturated Steady Flow ............................................................................................................... 28

3.3.1

Soil Water Flow Status ........................................................................................................ 28

3.3.2 Darcy’s Law ........................................................................................................................ 28
3.4 Unsaturated Flow ....................................................................................................................... 30
3.4.1 Buckingham-Darcy’s Law .................................................................................................. 30
3.4.2 Unsaturated Hydraulic Conductivity................................................................................... 31
3.4.3

Mathematic Models of Unsaturated Hydraulic Conductivity ............................................. 31

3.5 Governing Equations of Soil Water Flow .................................................................................. 33
3.5.1

Continuity Equation ............................................................................................................ 33

3.5.2

Richards Equation ............................................................................................................... 34

3.5.3 Extension of Richards Equation .......................................................................................... 35
3.6

Scaling of Soil Hydraulic Properties.......................................................................................... 35

3.7 Hysteresis................................................................................................................................... 36
3.8

Root Water Uptake..................................................................................................................... 37

3.8.1Root Distribution Density Functions .................................................................................. 37

3.8.2

Potential Transpiration and Evaporation ............................................................................. 38

3.8.3

Stresses by Soil Water And Solute ...................................................................................... 40

3.8.4 Compensation of Root Water Uptake .................................................................................. 42
3.8.5

Root Growth ....................................................................................................................... 42

3.9

Initial Conditions of Soil Water Flow ........................................................................................ 43

3.10

Boundary Conditions of Soil Water Flow ................................................................................ 43

3.10.1 Pressure Head Boundary Conditions ................................................................................ 43
3.10.2 Flux Boundary Conditions ................................................................................................ 44
3.10.3 Gradient Boundary Conditions ......................................................................................... 44
3.10.4 Atmospheric Boundary Conditions ................................................................................... 44
3.10.5 Deep Drainage .................................................................................................................. 46
3.10.6 Seepage Face..................................................................................................................... 47
3.10.7 Tile Drains ........................................................................................................................ 47
3.10.8 Snow Boundary Condition ................................................................................................ 47
3.11 Dual-Porosity Model................................................................................................................ 48
3.12

Dual-Permeability Model ........................................................................................................ 49

3.13

Vapor Flow .............................................................................................................................. 50

3.14

Temperature Dependence of The Soil Hydraulic Parameters .................................................. 51

4 Soil Solute Transport ........................................................................................................................ 53
4.1

Soil Solutes and Their Migration and Transformation ............................................................... 53

4.1.1

Existences of Solute in Soil ................................................................................................ 53

4.1.2 Governing Equations of Soil Solute Transport ................................................................... 53
4.1.3

Reactions of Solute in Soil .................................................................................................. 57

4.1.4

Root Solute Uptake ............................................................................................................. 58

4.2

Convection-Dispersion Equation ............................................................................................... 61

4.3

Transport of Adsorbing Solute ................................................................................................... 61

4.3.1

Equilibrium Adsorption ...................................................................................................... 61

4.3.2

Transport of Non-volatile, Non-reactive, Linear Adsorbed Solute ..................................... 62

4.3.3

Two-sites Chemical Nonequilibrium Sorption Model ........................................................ 63

4.3.4

Colloids Transport............................................................................................................... 65

4.3.5 Dual-Porosity Physical Nonequilibrium Model .................................................................. 69
4.3.6 Dual-Porosity with One-site Sorption Model...................................................................... 69
4.3.7 Dual-Permeability Physical Nonequilibrium Model ........................................................... 70
4.3.8 Dual-Permeability Model with Mobile and Immobile Water in the Matrix ........................ 71
4.3.9 Dual-Permeability with Two-sites Sorption Model............................................................. 72
4.4

Initial Conditions of Soil Solute Transport ................................................................................ 73

4.4.1

Solution Concentrations ...................................................................................................... 73

4.4.2 Adsorbed Concentrations .................................................................................................... 74
4.5

Boundary Conditions of Soil Solute Transport .......................................................................... 74

4.5.1 Ordinary Boundary Conditions ........................................................................................... 74
4.5.2
4.65

Boundary Conditions for Volatile Solutes ........................................................................... 75

Temperature and Water Content Dependence of Transport and Reaction Parameters ............... 76

4.6.1

Temperature Dependence of Transport and Reaction Parameters ....................................... 764.6.2

Water Content Dependence of Transport and Reaction Parameters .................................... 76

Soil Heat Transport ........................................................................................................................... 77
5.1

Soil Thermal Properties ............................................................................................................. 77

5.1.1

Soil Heat Capacities ............................................................................................................ 77

5.1.2

Soil Thermal Conductivity .................................................................................................. 77

5.2

Soil Heat Flux ............................................................................................................................ 78

5.3

Governing Equation of Soil Heat Transport .............................................................................. 79

5.4

Initial Conditions of Soil Heat Transport ................................................................................... 80

5.5

Boundary Conditions of Soil Heat Transport............................................................................. 80

5.6

Diurnal Variation of Soil Temperature ....................................................................................... 81

Part II HYDRUS-1D Models
6 Water Flow Models .......................................................................................................................... 85
6.1

Ponded Infiltration Through a Single Layer Soil ....................................................................... 85

6.1.1

Problem Definition.............................................................................................................. 85

6.1.2

Model Building ................................................................................................................... 85

6.1.3 Graphical Edit of Soil Profile.............................................................................................. 94
6.1.4

Execution Model ................................................................................................................. 97

6.1.5

Results................................................................................................................................. 98

6.2

Steady Flow Through a Single Layer Soil ............................................................................... 104

6.2.1

Problem Definition............................................................................................................ 104

6.2.2

Model Building ................................................................................................................. 104

6.2.3 Graphical Edit of Soil Profile............................................................................................ 104
6.2.4
6.3

Results............................................................................................................................... 105

Transient Water Flow and Root Water Uptake Through Multi-layered Soil ............................ 105

6.3.1

Problem Definition............................................................................................................ 105

6.3.2

Model Building ................................................................................................................. 106

6.3.3 Graphical Edit of Soil Profile............................................................................................ 111
6.3.4
6.4

Results............................................................................................................................... 113

Inverse Solution – One-step Outflow Experiment ................................................................... 115

6.4.1

Problem Definition............................................................................................................ 115

6.4.2

Model Building ................................................................................................................. 116

6.4.3

Types of Inversion Data .................................................................................................... 118

6.4.4 Graphical Edit of Soil Profile............................................................................................ 121
6.4.5
6.5

7Results............................................................................................................................... 122

Inverse Solution – Root Water Uptake in A Tomato Field ....................................................... 123

6.5.1

Problem Definition............................................................................................................ 123

6.5.2

Model Building ................................................................................................................. 125

6.5.3

Results without Hysteresis and Root Growth ................................................................... 126

6.5.4

Results with Hysteresis of Soil Retention Curve .............................................................. 127

6.5.5

Results with Root Growth ................................................................................................. 128

Solute Transport Models................................................................................................................. 131
7.1

Solute Transport Through A Single Layer Soil with A Constant Pressure Head...................... 131

7.1.1

Problem Definition............................................................................................................ 131

7.1.2

Model Building ................................................................................................................. 131

7.1.3

Results............................................................................................................................... 135

7.1.4

Results with Reduced Dispersivity ................................................................................... 137

7.1.5

Results with Increased Sorption Coefficient ..................................................................... 138

7.1.6

Results with Reactions ...................................................................................................... 138

7.2

Solute Transport Through A Single Layer Soil with A Constant Flux ..................................... 140

7.2.1

Problem Definition............................................................................................................ 140

7.2.2

Model Building ................................................................................................................. 140

7.2.3

Results............................................................................................................................... 140

7.2.4 Results with Chain Reactions ........................................................................................... 140
7.3

Problem Definition............................................................................................................ 143

7.3.2

Model Building ................................................................................................................. 143

7.3.3

Results............................................................................................................................... 144

7.4

Inverse Solution – Breakthrough Curve of Tracer ................................................................... 145

7.4.1

Problem Definition............................................................................................................ 145

7.4.2

Model Building ................................................................................................................. 145

7.4.3

Results............................................................................................................................... 147

7.5

Inverse Solution – Breakthrough Curve of Organic Pollutant ................................................. 148

7.5.1

Problem Definition............................................................................................................ 148

7.5.2

Model Building ................................................................................................................. 148

7.5.3

Results of Two-sites Chemical Nonequilibrium Sorption Model ..................................... 149

7.5.4

Results of One-site Chemical Nonequilibrium Sorption Model ....................................... 150

7.6

8

Solute Transport and Root Uptake Through Multi-layered Soil with Transient Flow ............. 143

7.3.1

Inverse Solution – Breakthrough Curve of Colloids ................................................................ 151

7.6.1

Problem Definition............................................................................................................ 151

7.6.2

Model Building ................................................................................................................. 151

7.6.3

Results of TKSM3 ............................................................................................................ 153

7.6.4

Results of OKSM3 ............................................................................................................ 154

7.6.5

Results of OKSM2 ............................................................................................................ 155

Coupled Model of Vapor-Heat-Solute Transports .......................................................................... 156
8.1

Problem Definition .................................................................................................................. 156

8.2

Model Building ........................................................................................................................ 156

8.3

Results ..................................................................................................................................... 158

Part III HYDRUS-(2D/3D) Models
9Colloid Facilitated Pollutant Transport (C-Ride)............................................................................ 161
9.1

Problem Definition .................................................................................................................. 161

9.2

Theory Basis ............................................................................................................................ 161

9.2.1 Colloid Transport Equation ............................................................................................... 161
9.2.2 Pollutant Transport Equation ............................................................................................ 163
9.3

Model Building ........................................................................................................................ 164

9.4

Graphic Design of Soil Profile................................................................................................. 172

9.4.1 Geometry .......................................................................................................................... 172
9.4.2 FE-Mesh............................................................................................................................ 175
9.4.3 Domain Properties ............................................................................................................ 176
9.4.4 Initial Conditions .............................................................................................................. 178
9.4.5
9.5
10

Boundary Conditions ........................................................................................................ 181

Results ..................................................................................................................................... 183

Pollution Source Leakage ............................................................................................................. 186

10.1

Problem Definition ................................................................................................................ 186

10.2

Model Building ...................................................................................................................... 186

10.3

Graphic Design of Soil Profile............................................................................................... 188

10.3.1 Geometry ........................................................................................................................ 188
10.3.2 FE-Mesh.......................................................................................................................... 189
10.3.3 Initial Conditions ............................................................................................................ 190
10.3.4 Boundary Conditions ...................................................................................................... 191
10.4 Results with A Variable Flux Boundary ................................................................................. 191
10.5
11

Results with A Constant Pressure Head Boundary ................................................................ 193

Furrow Irrigation and Root Water Uptake .................................................................................... 196

11.1

Problem Definition ................................................................................................................ 196

11.2

Model Building ...................................................................................................................... 196

11.3 Graphic Design of Soil Profile ............................................................................................... 198
11.3.1 Geometry......................................................................................................................... 198
11.3.2 Domain Properties........................................................................................................... 199
11.3.3

Initial Conditions............................................................................................................. 201

11.3.4

Boundary Conditions ...................................................................................................... 202

11.4
12Results.................................................................................................................................... 202

3D Simple Model for Pollutant leakage ....................................................................................... 204

12.1

Problem Definition ................................................................................................................ 204

12.2

Model Building ...................................................................................................................... 204

12.2.1 Domain Properties .......................................................................................................... 207
12.2.2 Initial Conditions ............................................................................................................ 208
12.2.3 Boundary Conditions ...................................................................................................... 210
12.3
13Results ................................................................................................................................... 211

3D Layered Model for Soil Washing ............................................................................................ 213

13.1

Problem Definition ................................................................................................................ 213

13.2

Model Building ...................................................................................................................... 213

13.3

Graphic Design of Soil Profile............................................................................................... 214

13.3.1 Geometry ........................................................................................................................ 214
13.3.2 FE-Mesh.......................................................................................................................... 215
13.3.3 Initial Conditions ............................................................................................................ 216
13.3.4 Boundary Conditions ...................................................................................................... 216
13.4

Results ................................................................................................................................... 218

References ............................................................................................................................................ 219
Appendix

Objective Functions for Inverse Solution in HYDRUS-1D .............................................. 221