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Models for Processes in the Soil

Programs and Exercises

Ed.: R. Anlauf; K. Ch. Kersebaum; Liu Ya Ping; A. Nuske-Schüler; J. Richter; G. Spingob; K. M. Syring; J. Utermann

1990. 227 pages, 47 figures, 14 tables, Catena ISBN 978-3-923381-24-1, US-ISBN 978-59326-254-9, 14x20cm, 370 g
Language: English

(Catena paperback)

ISBN 978-3-510-65397-3, paperback, price: 19.50 €

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Keywords

soilwatermovementsoil heattransformationmodelling

Contents

Synopsis top ↑

This volume is to stimulate the interest in soil processes on an applied basis. The programs and exercises were written K in BASIC and are as simple as possible. They are explained in detail and can be used as the basis for the development of new models by the individual user. The programs contained in the book are also available on diskette.

Table of Contents top ↑

1 Introduction (Richter, Anlauf) 1
1.1 Principal structure of a BASIC program 1
1.2 The BASIC-dialect used 3
1.3 To solve a differential equation using BASIC 4
1.4 Exercises with the transport equation 7
2 Simulation of simple one-dimensional transport processes (Anlauf, Liu) 9
2.1 Introduction: A remark about analytical and numerical solutions 9
2.2 Heat conduction in the dry homogeneous soil 9
2.2.1 Analytical solutions 9
2.2.2 Numerical solution 11
2.2.3 Programs and examples 11
2.2.4 Exercises 13
2.3 Explicit and implicit solutions for solute transport problems 14
2.3.1 Compartimentation and boundary conditions 14
2.3.2 Explicit solution 17
2.3.3 Implicit solution 19
2.3.4 Implict-explicit solution according to Crank-Nicolson 20
2.3.5 Techniques to solve a system of linear equations 22
2.3.5.1 Gaussian elimination method 22
2.3.5.2 Gauss-Seidel-Iteration method 24
2.3.6 Programs and program structure 24
2.4 Example simulations of solute transport 25
2.4.1 Numerical dispersion 25
2.4.2 Stability problems 27
2.4.3 Duration of calculation 28
2.4.4 Exercises 29
3 Simulation of the one-dimensional water transport (Syring, Kersebaum) 30
3.1 Soil water movement as an example for the solution of a non-linear differential equation 30
3.2 The Newton-Raphson method to solve the water transport equation 31
3.2.1 Development of the algorithm 31
3.2.2 A simple demonstration of the Newton-Raphson algorithm 33
3.2.3 The Newton-Raphson algorithm to solve systems of equations 34
3.2.4 Program description for the Newton-Raphson algorithm 34
3.3 The Wind-van Doome method to solve the water transport equation 36
3.4 Infiltration into homogeneous soils 37
3.4.1 Exercises 39
3.5 Infiltration into a two-layer soil 41
3.5.1 Exercises 42
3.6 Capillary rise in homogeneous and multi-layered soils 43
3.6.1 Theory 43
3.6.2 Description of the program CAPRISE 43
3.6.3 Example 46
3.6.4 Exercises 46
4 Transformation processes (Richter) 47
4.1 Simple reactions in homogeneous soils 47
4.1.1 Exercises 48
4.2 Complex reactions in homogeneous soils 50
4.2.1 Exponential and logistic growth 50
4.2.2 Chain reactions 51
4.2.3 Exercises 52
4.3 Reactions in heterogeneous soils: kinetic adsorption and desorption processes 53
4.3.1 Exercises 54
4.4 Other source and sink terms; uptake by roots 54
4.4.1 Exercise 55
5 Simple soil heat, water and matter regime models 56
5.1 A simple soil heat regime model (Richter) 56
5.1.1 Exercises 57
5.2 A simple model of the soil gas regime (C02; Springob) 58
5.2.1 Introduction 58
5.2.2 Simulation program for the soil gas regime (C02 regime) 59
5.2.2.1 Program C02 59 . 5.2.2.2 Program C02TB 61
5.2.3 Exercises 65
5.3 A simple water regime model (Syring) 65
5.3.1 Introduction 65
5.3.2 Program flow of NEW.BAS used as water regime model 67
5.3.3 Exercises 71
5.4 A model to simulate nitrogen regime during the winter half year (Kersebaum) 71
5.4.1 Theory 71
5.4.2 Description of the program XN03 74
5.4.3 Example 76
5.4.4 Exercises 78
5.5 Movement of solutes in soils (Utermann) 79
5.5.1 Fundamentals 79
5.5.2 Numerical solution 81
5.5.3 Program description 83
5.5.3.1 Water model 84
5.5.3.2 Nutrient model 85
5.5.4 Examples and exercises 90
5.5.4.1 Displacement of inert solutes 90
5.5.4.2 Displacement of physically interacting ions 91
5.5.4.3 Exercises 92
6 Regional models (Anlauf, Liu) 93
6.1 Modelling water and solute transport according to Burns 93
6.1.1 Theory 93
6.1.2 Description of the sample program 94
6.1.3 Exercises 96
6.2 Geostatistical representation of spatial heterogeneity 97
6.2.1 The variogram 97
6.2.2 Kriging interpolation 101
6.2.3 The programs 108
6.2.4 Examples 111
6.2.5 Exercises 117
6.3 Monte-Carlo simulations of steady state solute transport 117
6.3.1 Theory 117
6.3.2 The program MCSIM 120
6.3.3 Examples 120
6.3.4 Exercises 124
7 Literature 125
8 Appendix: Programs 128
SMITH.BAS 129
TRANSAN .BAS 130
HEATSUDBAS 131
HEATPERBAS 134
EXPLICITBAS 137
IMPGASEI.BAS 139
CRNG ASEI.BAS 142
CRNELIM.BAS 145
NEW.BAS 148
WIND.BAS 155
CAPRISE.BAS 160
KINETIC1.BAS 164
KINETIC9.BAS 172
KINET10.BAS 173
HEATREG.BAS 174
C02.BAS 176
C02TB.BAS 179
XN03.BAS 183
IOVER.BAS 193
BURNS.BAS 204
DATINP.BAS 208
VGRAM.BAS 210
KRIGING.BAS 216
PLOTMAP.BAS 221
MCSIM.BAS 224