1 Introduction 1
1.1 The approach followed in this book 1
1.1.1 Statics and kinetics 1
1.1.2 Dynamic approach 2
1.1.3 Balance approach 3
1.1.4 The system in thermodynamics 4
1.1.5 Fundamentals of the theory of potential 6
1.1.6 The macroscopic approach 8
1.1.7 Aggregation and buffering 9
1.1.8 The term "model" 10
1.2 Classifying the processes in the soil 10
1.3 The organization of this book 11
1.4 Literature 12
2 Heat conduction in soils 14
2.1 Significance of heat dispersion in soils 14
2.2 Phenomena of heat dispersion 14
2.2.1 Examples of daily temperature courses in soils 14
2.2.2 Example of an annual course of the temperature16
2.3 Heat conductivity and capacity in relation to soil composition
and structure 17
2.4 Deriving the transport equation using local balance and
principle of causality 20
2.4.1 Local balance for matter and energy without transformation 20
2.4.2 One-dimensional transport equation of matter and energy
in a rigid system with continuous pores 21
2.4.3 The equation for heat transport 22
2.5 Analytical solutions of the heat transport equation with
constant α_T 24
2.5.1 The stationary case 24
2.5.2 Sudden change in temperature as boundary condition 24
2.5.3 Oscillating temperature as boundary condition 25
2.6 Numerical solution of the heat transport equation with
constant α_T 26
2.7 Heat balance of the soil and heat conversion 29
2.7.1 Estimating the soil-absorbed energy 29
2.7.2 Heat to evaporate 1 mm water 30
2.8 Literature 31
3 Gas regime of soils 32
3.1 The significance of the gas regime in the soil 32
3.2 Phenomena in soil gas regime 33
3.2.1 Profiles of CO₂ and O₂ concentrations in the soil 34
3.2.2 Cycles and depth profiles ofCO₂ production 36
3.3 Parameters of the gas regime in soils 39
3.3.1 The apparent diffusion coefficient D_s 39
3.3.2 The storage of gases in the soil 41
3.4 Quantitative description of the gas regime in soils 42
3.4.1 Extending the transport equation 42
3.4.2 Partial pressure and diffusive gas transport 44
3.5 Solving the equation of gas regime 47
3.5.1 An analytical solution for the stationary case 47
3.5.2 Numerical solution for a stationary example 49
3.6 Applications of the gas transport and gas regime equation 50
3.6.1 The measurement of the diffusion coefficient D_s 50
3.6.2 The "tortuous" macropore as a structure model52
3.6.3 Vapour flow in the soil 55
3 6 4 Micro-anoxia as a problem of aeration, and the redox
potential ΔE_H 56
3.7 Literature 59
4 Soil water regime 61
4.1 The significance of soil water; annual balances 61
4.2 Phenomena of soil water flow 63
4.2.1 Water tension and water content profiles in the soil 63
4.2.2 Flows at the boundary area and in the soil 66
4.3 Hydraulic conductivity and the moisture retention curve 68
4.3.1 The hydraulic conductivity K(Ψ_m) 68
4.3.2 The moisture retention curve Ψ_m (Φ) 70
4.4 The water regime equation 73
4.4.1 The local water balance 74
4.4.2 The equation for the water flow q_w 74
4.4.3 The hydraulic potential Ψ_h 74
4.4.4 Different formulations of the water transport equation 76
4.5 Characteristic flow conditions of water in the bare soil 77
4.5.1 Equilibrium and quasi-equilibrium 78
4.5.2 Stationary and quasi-stationary conditions 79
4.5.3 Non-stationary flow 80
4.6 Applications and numerical solutions for the water regime
equation 80
4.6.1 Moisture equilibrium in the soil 80
4.6.2 Stationary flow in the soil during drying in summer 81
4.6.3 Solution methods for non-stationary flow 84
4.6.4 Simple water regime models for the flat, homogeneous
cropped soil; the root uptake function P(z,t) 89
4.6.5 Calculating the evapotranspiration E 90
4.6.6 The water regime of a wheat field on a loess-Parabraunerde 94
4.7 Literature 97
5 Regime of matter in soils 99
5.1 Introduction 99
5.1.1 Significance of "matter" in the soil 99
5.1.2 Extension of the transport models 99
5.2 Phenomena of ion flows 99
5.2.1 Movement of non-interacting ions during winter 100
5.2.2 Movement of interacting ions during winter 100
5.3 Parameters of solute transport 102
5.3.1 Transport parameter: effective dispersion coefficient DB 102
5.3.2 Quantity/intensity relation for components that do interact with the soil matrix; the specific storage capacity B 103
5.3.3 Specific storage capacity C (and the diffusion coefficient D) 108
5.4 Coupled transport flows of components that do not interact
with the soil matrix 109
5.4.1 General description of coupled transport 109
5.4.2 Transport of dissolved non-interacting components in the soil. 111
5.4.3 Particle charge 113
5.5 Introduction to reaction dynamics 114
5.5.1 Fundamentals of the course of reactions 114
5.5.2 Order of elementary reactions in homogeneous systems 115
5.5.3 A special case: second-order reactions of sigmoidal shape 118
5.5.4 Complex reactions in homogeneous systems 121
5.5.5 Heterogeneous reactions (interactions with the surfaces of
solids) 124
5.6 Models for reactive components and ions in the soil 128
5.6.1 Dynamic description of interactions of substances with
the solid phase 129
5.6.2 Description of interactions of ions with charged surfaces
of the solid phase (ion-exchange) 131
5.7 Simple regime models of substances in the soil 134
5.7.1 Models for nitrification and simultaneous movement of
nitrogen 135
5.7.2 Simulating the nitrogen regime of loess field soils during
winter 138
5.7.3 A site model for the displacement of physically interacting
ions for the example potassium 140
5.7.4 Simulating the degradation of herbicides in soils 142
5.7.5 Simulating the behaviour of heavy metals in the soil 145
5.7.6 "Complete" models of material components regime 148
5.8 Literature 149
6 Looking ahead 152
6.1 Beyond the assumptions 152
6.2 The soil as a non-rigid solid 153
6.2.1 Mechanical deformations and changes of the state of stress 154
6.2.2 Mechanical cause-and-effect relations 157
6.2.3 Changes of the parameters with mechanical deformations 162
6.3 The explicit modelling of nutrient uptake by plants 163
6.4 Field and regional models 167
6.4.1 Simulating solute transport in heterogeneous pore systems 167
6.4.2 Geostatistical formulation of spatial variability 168
6.4.3 Combining deterministic and stochastic approaches:
Monte-Carlo simulation of salt transport 169
6.4.4 Alternative approaches: plate and compartment models 171
6.5 Modelling soil development 177
6.6 Literature 177
7 Appendix 180
7.1 Numerical solutions for non-stationary water transport and for
solute transport under stationary flow conditions 180
7.1.1 Vertical solute movement under stationary flow conditions 180
7.1.2 Vertical water transport 184
7.1.3 Difference formulationwith the help of the Taylor equation 185
7.1.4 Literature 185
7.2 Gas solubilities in water 186
7.3 Conversion of units 187
7.4 List of symbols and indices 189
Register 190