Theory and Applications of Transport in PorousMedia

Volume 32

Series editor

S. Majid Hassanizadeh, Department of Earth Sciences, Utrecht University, Utrecht,The Netherlands

Founding series editor

Jacob Bear

More information about this series at http://www.springer.com/series/6612

Viliam Novák • Hana Hlaváčiková

Applied Soil Hydrology

123

Viliam NovákInstitute of HydrologySlovak Academy of SciencesBratislava, Slovakia

Hana HlaváčikováInstitute of HydrologySlovak Academy of SciencesBratislava, Slovakia

ISSN 0924-6118 ISSN 2213-6940 (electronic)Theory and Applications of Transport in Porous MediaISBN 978-3-030-01805-4 ISBN 978-3-030-01806-1 (eBook)https://doi.org/10.1007/978-3-030-01806-1

Library of Congress Control Number: 2018957062

© Springer Nature Switzerland AG 2019This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or partof the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations,recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmissionor information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilarmethodology now known or hereafter developed.The use of general descriptive names, registered names, trademarks, service marks, etc. in thispublication does not imply, even in the absence of a specific statement, that such names are exempt fromthe relevant protective laws and regulations and therefore free for general use.The publisher, the authors and the editors are safe to assume that the advice and information in thisbook are believed to be true and accurate at the date of publication. Neither the publisher nor theauthors or the editors give a warranty, express or implied, with respect to the material contained herein orfor any errors or omissions that may have been made. The publisher remains neutral with regard tojurisdictional claims in published maps and institutional affiliations.

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Preface

The water that we are drinking nowadays is the very same as was drunk bydinosaurs millions of years ago. Even the quantity of water on Earth is approxi-mately the same; it is continuously recycled and cleaned by evaporation as a partof the so-called hydrologic cycle powered by the energy of the Sun. The number ofinhabitants on Earth has increased about 40 times since the Roman era; the demandfor freshwater has grown even more than proportionally since then to cover man-kind’s material and hygienic needs.

Precipitation is the basic source of freshwater. Rainwater is transformed by theEarth’s ‘skin’, represented by a relatively thin (up to 2 m) layer of soil whichdivides into the surface and subsurface bodies of water; these are the sources ofwater for communal and industrial use. The majority of freshwater is consumedsimultaneously by plant-canopy transpiration and biomass production. Therefore,soil can be denoted as the basic hydrological interface, transforming rainwater tosoil and groundwater, as well as to surface run-off, and thus creating the structureof the land’s water balance.

Soil hydrology is the science focused on understanding the role of soil in theEarth’s water cycle and expressing its function in the water cycle in quantitative andqualitative terms.

The aim of this book is to present and quantify the role of soil in the hydrologiccycle. It is our intention to do this as simply as possible with minimum mathe-matics, but without neglecting the complexity of the processes. The book is focusedon the physical interpretation of soil-water transport processes, as a part of the soil–plant–atmosphere continuum (SPAC). The basic phenomena and characteristics ofsoil hydrology as soil-water potential, soil-water retention, soil hydraulic conduc-tivity, and methods for their measurement and calculation are described in detail, tobe used as input data for simulation models of soil-water movement.

This book describes the basic topics of soil hydrology. However, in addition wepresented also results of actual research such as water movement in water-repellentsoils, water transport and retention of stony soils, evapotranspiration, and basicprinciples of soil-water-flow modelling. Illustrations are mostly derived from theresults of our original research.

v

This book is intended to serve as a source of information not only for hydrol-ogists, but also for agronomists, foresters, environmental protectionists, meteorol-ogists, and for anybody who is interested in the applications of soil hydrology towater-resource formation and management to preserve water resources in adequatequantitative and qualitative conditions for future generations.

Bratislava, Slovakia Viliam NovákHana Hlaváčiková

vi Preface

Acknowledgements

The authors would like to acknowledge the Slovak National Grant Agencies VEGAProject No. 2/0055/15 and APVV Project No. 15-0497, as well as the Project ITMS26240120004 ‘Centre of excellence for integrated flood protection of land’ sup-ported by the Research and Development Operational Program funded by theEuropean Regional Development Fund (ERDF) for supporting their scientific work.Some equipment that provided data for this book was obtained within the frame-work of the Project ITMS 26220120062 ‘Centre of excellence for the IntegratedRiver Basin Management in the Changing Environmental Conditions (CEIMP)’supported by the Research and Development Operational Program funded byERDF.

vii

Contents

1 Soil as a Part of the Soil–Plant–Atmosphere Continuum(SPAC) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.1 Soil Hydrology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.1.1 Conceptual Approaches in Soil Hydrology . . . . . . . . 31.2 Soil and Its Role in SPAC . . . . . . . . . . . . . . . . . . . . . . . . . . . 61.3 Atmosphere . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

1.3.1 Water Vapour . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81.3.2 Oxygen . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101.3.3 Carbon Dioxide . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

1.4 Plant Canopy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

2 Basic Physical Characteristics of Soils . . . . . . . . . . . . . . . . . . . . . . 152.1 Porous Media, Capillary-Porous Media and Soil.

Are There Differences? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152.2 Soil as a Three-Phase System . . . . . . . . . . . . . . . . . . . . . . . . 172.3 Pedogenesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192.4 Soil Texture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

2.4.1 Soil-Texture Analysis . . . . . . . . . . . . . . . . . . . . . . . 212.5 Soil Type . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 232.6 Rock Fragments in Soil . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 242.7 Clay Minerals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 242.8 Soil Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 262.9 Chemical and Mineralogical Properties of Soil . . . . . . . . . . . . 27References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

3 Physical Properties of Water . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 293.1 Soil Water and Soil Solution . . . . . . . . . . . . . . . . . . . . . . . . . 293.2 Air in Water and Its Solubility . . . . . . . . . . . . . . . . . . . . . . . . 323.3 Water Density, Compressibility and Expansion . . . . . . . . . . . . 33

ix

3.4 Water-Surface Tension . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 333.5 Viscosity of Water . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

4 Soil-Water Interface Phenomena . . . . . . . . . . . . . . . . . . . . . . . . . . . 374.1 Wetting of the Solid-Phase by Liquids . . . . . . . . . . . . . . . . . . 374.2 Capillarity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

4.2.1 Soil as a Bundle of Capillary Tubes . . . . . . . . . . . . . 394.2.2 Height of Capillary Rise . . . . . . . . . . . . . . . . . . . . . 424.2.3 Decrease of Water-Vapour Pressure in Capillary

Tubes Above the Menisci . . . . . . . . . . . . . . . . . . . . 434.2.4 Capillary Phenomena and Their Influence

on Soil-Water Retention . . . . . . . . . . . . . . . . . . . . . 444.3 Adsorption and Desorption of Water on Soil Surfaces . . . . . . . 45References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47

5 Soil-Water Content and Its Measurement . . . . . . . . . . . . . . . . . . . . 495.1 Quantitative Expression of Soil-Water Content . . . . . . . . . . . . 495.2 Measurement of Soil-Water Content . . . . . . . . . . . . . . . . . . . . 51

5.2.1 Gravimetric Method for Measurementof Soil-Water Content . . . . . . . . . . . . . . . . . . . . . . . 51

5.2.2 Soil-Moisture Probes . . . . . . . . . . . . . . . . . . . . . . . . 545.2.3 Neutron Method . . . . . . . . . . . . . . . . . . . . . . . . . . . 545.2.4 Capacitance Method . . . . . . . . . . . . . . . . . . . . . . . . 555.2.5 Electrical Resistance Method . . . . . . . . . . . . . . . . . . 565.2.6 Time-Domain Reflectometry (TDR) Method . . . . . . . 575.2.7 Frequency-Domain Reflectometry (FDR) Method . . . 595.2.8 Geophysical Methods . . . . . . . . . . . . . . . . . . . . . . . 605.2.9 Remote-Sensing Methods . . . . . . . . . . . . . . . . . . . . 60

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61

6 Soil-Water Potential and Its Measurement . . . . . . . . . . . . . . . . . . . 636.1 Energy of Soil Water . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 636.2 Soil Water Potential of a Capillary Porous Medium (Soil) . . . . 656.3 Quantitative Expression of Soil-Water Potential . . . . . . . . . . . 676.4 Components of the Total Soil-Water Potential . . . . . . . . . . . . 68

6.4.1 Gravitational Component of the Total Soil-WaterPotential . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68

6.4.2 Matric (Moisture) Potential of Soil Water . . . . . . . . . 696.4.3 Pneumatic (Pressure) Soil-Water Potential . . . . . . . . 70

6.5 Total Soil-Water Potential . . . . . . . . . . . . . . . . . . . . . . . . . . . 716.6 Measurement of Soil-Water Potential Components . . . . . . . . . 72

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6.6.1 Piezometer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 726.6.2 Tensiometer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76

7 Soil-Water Retention Curve . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 777.1 Definition of the Soil-Water Retention Curve . . . . . . . . . . . . . 777.2 Hysteresis of Soil-Water Retention Curves . . . . . . . . . . . . . . . 78

7.2.1 Main Branches of Soil-Water Retention Curves . . . . 807.3 Soil-Water Retention Curves and Their Analytical

Expression . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 837.4 Hydrolimits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 847.5 Measurement of Soil-Water Retention Curves . . . . . . . . . . . . . 87

7.5.1 Tension Methods . . . . . . . . . . . . . . . . . . . . . . . . . . 887.5.2 Pressure Methods . . . . . . . . . . . . . . . . . . . . . . . . . . 907.5.3 Combined Method for SWRC Estimation . . . . . . . . . 927.5.4 Psychrometric Method . . . . . . . . . . . . . . . . . . . . . . 927.5.5 Adsorption and Desorption Methods . . . . . . . . . . . . 94

7.6 Estimation of Soil-Water Retention Curves fromPressure-Chamber Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96

8 Soil-Water Movement in Water-Saturated Capillary PorousMedia . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 978.1 Two Concepts of the Quantification of Soil-Water

Movement in Saturated Capillary Porous Media (Soils) . . . . . . 978.1.1 Darcian (Macroscopic) Approach . . . . . . . . . . . . . . . 988.1.2 Model Porous Medium . . . . . . . . . . . . . . . . . . . . . . 99

8.2 Darcy Equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1008.3 Macroscopic (Darcian) and Porous (Real) Water-Flow

Rate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1028.4 Distribution of Pressure During Water Flow Through

Various Measuring Devices . . . . . . . . . . . . . . . . . . . . . . . . . . 1038.4.1 Horizontal Soil Sample . . . . . . . . . . . . . . . . . . . . . . 1038.4.2 Vertically Positioned Soil Sample, Downward

Water Flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1048.4.3 Vertically Positioned Soil Sample, Water Flows

Bottom-Up . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1048.5 Hydraulic Conductivity of Soil Saturated with Water

Measured in the Laboratory . . . . . . . . . . . . . . . . . . . . . . . . . . 1058.5.1 Simple Laboratory Method for Measurement

of Saturated-Soil Hydraulic Conductivity . . . . . . . . . 1078.6 Hydraulic Conductivity and Properties of Soil . . . . . . . . . . . . 110

8.6.1 Darcian and Non-Darcian Flow . . . . . . . . . . . . . . . . 1118.6.2 Air Entrapped in Soil Pores . . . . . . . . . . . . . . . . . . . 111

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8.6.3 Temperature and Saturated-Soil HydraulicConductivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112

8.6.4 Flow of Water in Layered Saturated PorousMedium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112

8.7 Field Measurement of Saturated-Soil HydraulicConductivity Above Groundwater Table in the Field . . . . . . . . 1148.7.1 Measurement of Saturated-Soil Hydraulic

Conductivity in the Field Above GroundwaterTable at Variable Hydraulic Gradient . . . . . . . . . . . . 114

8.7.2 Measurement of Saturated-Soil HydraulicConductivity in the Field Above GroundwaterTable at Constant Hydraulic Gradient . . . . . . . . . . . 115

8.8 Pedotransfer Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116

9 Water in Unsaturated Soil . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1199.1 The Differences Between Water Movements in Saturated

and Unsaturated Soils . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1199.2 Basic Equations of Water Movement in Unsaturated Soil . . . . 120

9.2.1 Darcy–Buckingham Equation . . . . . . . . . . . . . . . . . 1209.2.2 Equation Describing Water Movement in

Unsaturated Soil: The Richards Equation . . . . . . . . . 1219.3 Basic Characteristics of Water Flow in an Unsaturated

Soil . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1239.4 Measurement and Calculation of the Unsaturated-Soil

Hydraulic Conductivity Function k(hw) . . . . . . . . . . . . . . . . . . 1279.4.1 Measurement of Unsaturated Hydraulic

Conductivity of Soils . . . . . . . . . . . . . . . . . . . . . . . 1289.4.2 Unsaturated Hydraulic Conductivity of Soil,

Calculated by Analysis of Soil-Water Contentand Soil-Water Matric Potential Profiles . . . . . . . . . . 129

9.4.3 Calculation of the Function k = f(hw) UsingSoil-Water Retention Curve and Saturated-SoilHydraulic Conductivity . . . . . . . . . . . . . . . . . . . . . . 131

9.5 Water Movement at Low Soil-Water Content and Diffusivityof Soil . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132

9.6 Diffusion of Water Vapour in Soil . . . . . . . . . . . . . . . . . . . . . 133References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135

10 Infiltration of Water into Soil . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13710.1 Infiltration into Homogeneous Soil . . . . . . . . . . . . . . . . . . . . . 137

10.1.1 The Basic Characteristics of Infiltration . . . . . . . . . . 13810.2 Infiltration into Soil from Rain or Sprinkling Irrigation . . . . . . 13910.3 Ponding Infiltration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141

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10.4 The Influence of Initial Soil-Water Content and RainRate on Infiltration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143

10.5 Infiltration and Entrapped Air . . . . . . . . . . . . . . . . . . . . . . . . 14410.6 Soil-Water Content Profiles During Infiltration . . . . . . . . . . . . 14610.7 Infiltration Calculation According to Green and Ampt . . . . . . . 149

10.7.1 Horizontal Infiltration . . . . . . . . . . . . . . . . . . . . . . . 15110.7.2 Vertical Ponding Infiltration . . . . . . . . . . . . . . . . . . 15310.7.3 Pressure Head at the Infiltration Front . . . . . . . . . . . 15410.7.4 Ponding-Time Calculation by the Green–Ampt

Approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15510.8 Infiltration Curves Expressed by Empirical Equations . . . . . . . 15610.9 Analytical Expression of Unsteady Infiltration into

Homogeneous Soil . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15810.10 Infiltration into Nonhomogeneous Soil . . . . . . . . . . . . . . . . . . 161

10.10.1 Infiltration into Layered-Soil Profiles . . . . . . . . . . . . 162References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 164

11 Redistribution of Water in Homogeneous Soil . . . . . . . . . . . . . . . . 16511.1 Basic Characteristics of Water Redistribution in Soil . . . . . . . . 16511.2 Water Movement in Soil During Redistribution . . . . . . . . . . . 16611.3 Quantitative Analysis of the Redistribution Process . . . . . . . . . 168References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 170

12 Interaction of Groundwater and Soil Water . . . . . . . . . . . . . . . . . . 17112.1 Types of Groundwater and Soil-Water Interactions . . . . . . . . . 17112.2 Water-Flow Direction Between Groundwater

and an Unsaturated Zone of Soil . . . . . . . . . . . . . . . . . . . . . . 17212.3 Uptake of Water to the Soil from Groundwater . . . . . . . . . . . . 17512.4 Empirical Equations to Calculate Flow of Water

from Groundwater to the Soil . . . . . . . . . . . . . . . . . . . . . . . . 17812.5 Flow of Soil Water to Groundwater—Internal Drainage

of Soil . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17912.6 Groundwater Drainage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181

12.6.1 Drainage-Design Equation Describing SteadyGroundwater Flow to Drains . . . . . . . . . . . . . . . . . . 182

12.6.2 Drainage-Design Equation of Unsteady WaterFlow to Drains . . . . . . . . . . . . . . . . . . . . . . . . . . . . 184

12.7 Drainable and Wettable Porosity . . . . . . . . . . . . . . . . . . . . . . 18412.8 Risk of Soil Salinization by Groundwater and Surface

Irrigation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 186References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 187

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13 Evaporation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18913.1 Transport of Water in the Soil–Plant–Atmosphere

Continuum (SPAC) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18913.2 Evaporation as a Physical Process . . . . . . . . . . . . . . . . . . . . . 191

13.2.1 Water Evaporation . . . . . . . . . . . . . . . . . . . . . . . . . 19213.2.2 The Basic Characteristics of Water Evaporation . . . . 19213.2.3 Evaporation from the Water Table and Bare Soil . . . 194

13.3 Water Transport in Bare Soil During Evaporation . . . . . . . . . . 19713.3.1 Calculation of Water Movement in Bare Soil

During Evaporation . . . . . . . . . . . . . . . . . . . . . . . . . 19813.4 Transpiration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 199

13.4.1 Soil-Water Movement During Transpiration . . . . . . . 20013.4.2 Soil-Water Uptake Patterns by Plant Roots . . . . . . . . 20113.4.3 Distribution of Root-Extraction Patterns Evaluated

from Field Measurements . . . . . . . . . . . . . . . . . . . . 20313.5 Methods for Evapotranspiration Estimation . . . . . . . . . . . . . . . 205

13.5.1 Method of Evapotranspiration Estimation fromthe Energy-Balance Equation of the EvaporatingSurface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 206

13.5.2 Evaporation Calculation from a Wet Surface:The Penman Equation . . . . . . . . . . . . . . . . . . . . . . . 208

13.6 Calculation of Plant-Canopy Potential Evapotranspiration . . . . 21213.6.1 Evapotranspiration Calculation: The

Penman–Monteith Equation . . . . . . . . . . . . . . . . . . . 21313.7 Reference Evapotranspiration and Plant-Canopy

Evapotranspiration (FAO Method) . . . . . . . . . . . . . . . . . . . . . 21513.7.1 Reference Evapotranspiration . . . . . . . . . . . . . . . . . . 21513.7.2 Plant-Canopy Evapotranspiration . . . . . . . . . . . . . . . 216

13.8 Calculation of Actual Evapotranspiration from PotentialEvapotranspiration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 217

13.9 Structure of Potential Evapotranspiration . . . . . . . . . . . . . . . . 21813.10 Daily and Annual Courses of Evapotranspiration

and Its Components . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21913.11 Evapotranspiration Estimation by the Eddy-Correlation

Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22113.12 Calculation of Potential Evapotranspiration by Empirical

Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22213.12.1 Linacre Equation . . . . . . . . . . . . . . . . . . . . . . . . . . 22213.12.2 Ivanov Equation . . . . . . . . . . . . . . . . . . . . . . . . . . . 22313.12.3 Tichomirov Equation . . . . . . . . . . . . . . . . . . . . . . . 223

13.13 Evaporation from Various Evaporating Surfaces . . . . . . . . . . . 22313.13.1 Evaporation in Slovak Territory . . . . . . . . . . . . . . . . 225

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 226

xiv Contents

14 Transport of Solutes in Soils . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22914.1 Basic Processes of Solute Transport in Soils . . . . . . . . . . . . . . 22914.2 Concentration of Dissolved Compounds in Solution . . . . . . . . 23014.3 Transport of Dissolved Compounds in Soils . . . . . . . . . . . . . . 231

14.3.1 Convection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23214.3.2 Diffusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23214.3.3 Hydrodynamic Dispersion . . . . . . . . . . . . . . . . . . . . 233

14.4 Equation of Soil-Solution Transport . . . . . . . . . . . . . . . . . . . . 23514.5 Péclet Number and Identification of Transport Mechanisms

of Dissolved Compounds . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23614.6 Outflow and Breakthrough Curves . . . . . . . . . . . . . . . . . . . . . 238

14.6.1 Outflow Curves . . . . . . . . . . . . . . . . . . . . . . . . . . . 23814.6.2 Breakthrough Curves . . . . . . . . . . . . . . . . . . . . . . . 239

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 242

15 Water and Energy Balance in the Field and Soil-WaterRegimen . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24315.1 Soil-Water Balance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24315.2 Water and Energy Balance of the Land . . . . . . . . . . . . . . . . . 24515.3 Soil-Water Regimen . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24615.4 Soil-Water Regimen and Its Diagnostics . . . . . . . . . . . . . . . . . 247

15.4.1 Soil-Water Regimen Classification . . . . . . . . . . . . . . 24715.4.2 Hydrological Classification of the Soil-Water

Regimen . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24815.5 Soil-Water Regimen Diagnostics and Biomass Production . . . . 249References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 251

16 Swelling and Shrinking Soils . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25316.1 Cracks Porosity and Soil-Water Content . . . . . . . . . . . . . . . . . 25316.2 Specific Volume and Specific Surface of Soil Cracks . . . . . . . 25516.3 Formation and Kinetics of Soil Cracks . . . . . . . . . . . . . . . . . . 25716.4 Soil Characteristics Influenced by Soil Swelling and

Shrinking . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25916.5 Infiltration of Water into Soils with Cracks . . . . . . . . . . . . . . . 259References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 261

17 Stony Soils . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26317.1 Specific Features of Stony Soils . . . . . . . . . . . . . . . . . . . . . . . 26317.2 Stony Soils Classification . . . . . . . . . . . . . . . . . . . . . . . . . . . 26417.3 Stony Soils Occurrence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26517.4 Representative Elementary Volume of Stony Soils . . . . . . . . . 26617.5 Sampling of Undisturbed Stony Soils . . . . . . . . . . . . . . . . . . . 26617.6 Physical Characteristics of Stony Soils . . . . . . . . . . . . . . . . . . 267

Contents xv

17.6.1 Stoniness of Stony Soils . . . . . . . . . . . . . . . . . . . . . 26717.6.2 Stony Soils’ Bulk Density . . . . . . . . . . . . . . . . . . . . 26917.6.3 Stony Soils’ Porosity . . . . . . . . . . . . . . . . . . . . . . . 269

17.7 Hydrophysical Characteristics of Stony Soils . . . . . . . . . . . . . 27017.7.1 Stony Soils’ Volumetric Water Content . . . . . . . . . . 27017.7.2 Stony Soils’ Water Retention. . . . . . . . . . . . . . . . . . 27017.7.3 Hydraulic Conductivity of Stony Soils . . . . . . . . . . . 27217.7.4 Effective Hydrophysical Characteristics of Stony

Soils . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27317.7.5 Soil-Water Content of Stony Soils Measurement . . . 275

17.8 Water Flow in Stony Soils . . . . . . . . . . . . . . . . . . . . . . . . . . . 27517.8.1 Modelling of Water Flow in Stony Soils . . . . . . . . . 27617.8.2 More Complex Modelling Approach to Water

Flow in Stony Soils . . . . . . . . . . . . . . . . . . . . . . . . 27717.8.3 An Example of Measured Characteristics

of the Stony Soil and Estimation of Input Datafor a Deterministic Simulation Model(a Case Study) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 277

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 280

18 Water Repellent Soils . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28318.1 Water Repellency of Soils and Its Identification . . . . . . . . . . . 28318.2 Characteristics of Soil-Water Repellency . . . . . . . . . . . . . . . . 284

18.2.1 Severity of Soil-Water Repellency . . . . . . . . . . . . . . 28418.2.2 Persistence of Soil-Water Repellency . . . . . . . . . . . . 28518.2.3 The Repellency Index . . . . . . . . . . . . . . . . . . . . . . . 287

18.3 Water Repellent Compounds in Soils . . . . . . . . . . . . . . . . . . . 28718.4 Water Repellency and Soil-Water Characteristics . . . . . . . . . . 28818.5 The Effects of Soil-Water Repellency on Soil-Water

Movement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 288References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 290

19 Soil Air and Its Dynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29319.1 Soil Aeration and Plant Respiration . . . . . . . . . . . . . . . . . . . . 29319.2 Composition of Soil Air . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29519.3 Transport of Soil Air . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 295

19.3.1 Convective Flow of Soil Air . . . . . . . . . . . . . . . . . . 29619.3.2 Diffusion of Soil Air . . . . . . . . . . . . . . . . . . . . . . . . 297

19.4 Movement of Oxygen from Soil to Plant Roots . . . . . . . . . . . 298References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 301

xvi Contents

20 Soil Temperature and Heat Transport in Soils . . . . . . . . . . . . . . . . 30320.1 Soil Temperature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 303

20.1.1 Soil-Temperature Regimen . . . . . . . . . . . . . . . . . . . 30420.2 Soil-Heat Transport . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 305

20.2.1 Transport of Heat in Soil by Conduction . . . . . . . . . 30620.3 Soil-Heat Capacity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30820.4 Thermal Diffusivity of Soil . . . . . . . . . . . . . . . . . . . . . . . . . . 31020.5 Soil-Water Transport Under Non-isothermal Conditions . . . . . 31120.6 Temperature and Water Properties . . . . . . . . . . . . . . . . . . . . . 313

20.6.1 Water Density and Temperature . . . . . . . . . . . . . . . . 31320.6.2 Water Viscosity and Temperature . . . . . . . . . . . . . . 31320.6.3 Surface Tension of Water and Temperature . . . . . . . 313

20.7 Hydrophysical Characteristics of Soil and Temperature . . . . . . 31420.7.1 Hydraulic Conductivity of Saturated Soil

and Temperature . . . . . . . . . . . . . . . . . . . . . . . . . . . 31420.7.2 Soil-Water Retention Curves and Temperature . . . . . 315

20.8 Soil-Water Movement Under Non-isothermal Conditions . . . . . 316References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 317

21 Modelling of Water Flow and Solute Transport in Soil . . . . . . . . . 31921.1 Modelling in Soil Hydrology . . . . . . . . . . . . . . . . . . . . . . . . . 31921.2 Governing Equations of Water and Solute Transport

in Soil . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32121.3 Characteristics of the Soil-Plant-Atmosphere Continuum:

Model Inputs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32221.4 Main Model Outputs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32221.5 Governing Equations and Their Solutions . . . . . . . . . . . . . . . . 323

21.5.1 Initial and Boundary Conditions . . . . . . . . . . . . . . . 32421.6 Water Flow Modelling in Heterogeneous Soils . . . . . . . . . . . . 325

21.6.1 Dual-Porosity Model . . . . . . . . . . . . . . . . . . . . . . . . 32621.6.2 Dual-Permeability Model . . . . . . . . . . . . . . . . . . . . . 327

21.7 Calibration, Verification and Validation of Soil-WaterFlow Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 328

21.8 Overview of Some Soil-Water Flow Models . . . . . . . . . . . . . . 32921.9 Current Trends and Future Challenges Concerning

Water-Flow Modelling in the Unsaturated Soil Zone . . . . . . . . 334References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 335

Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 339

Contents xvii

Symbols

Variables are presented in metric (SI) units. In the text, variables’ dimensions aregiven even in generalised units: (L length, M mass, T time, and K temperature).

a Relative volume of air in soil (aeration) (−)c Solute concentration (kg m−3); specific heat capacity of soil (J kg−1 K−1)c(hw) Specific soil-water capacity (m−1)ci Specific heat capacity of ice (J kg−1 K−1); concentration of ith component

of solute in a unit volume of soil solution (kg m−3)cpa Specific heat capacity of air at constant pressure (J kg−1 K−1)cw Specific heat capacity of water (J kg−1 K−1)d Saturation deficit of air (Pa); particle diameter (m)de Effective height of a plant canopy (m)e Water-vapour pressure (Pa)eo Saturated water-vapour pressure (Pa, N m−2)g Acceleration of gravity (m s−2)h Pressure head (m)ha Pressure head corresponding to the anaerobiosis point of soil-water

content (m)hb Pressure head corresponding to the entrance pressure of air into soil pores

(bubbling pressure) (m)hg Pressure head of the gravitational component of the total potential of soil

water (m)hk Height of water-capillary rise (m)ho Thickness of the water layer above the soil surface (m)hw Matric (moisture) potential of soil water (head with a negative sign) (m)i Cumulative (total) infiltration (m)k Hydraulic conductivity of soil unsaturated with water, unsaturated

conductivity (m s−1)l Empirical parameter of van Genuchten’s equation expressing tortuosity and

connectivity of pores (−)

xix

lr Specific length of roots (m m−3)m Shape parameter of van Genuchten’s equation (−)md Mass of a dry-soil sample (kg)mdb Mass of dry solid phase of stony soil together with rock fragments (kg)

mdrf Mass of dry-rock fragments (kg)

mw Mass of water in a soil sample (kg)n Shape parameter of van Genuchten’s equation (−)pa Air pressure (Pa, N m−2)pk Capillary pressure (Pa, N m−2)q Darcian water-flux rate (m s−1), specific humidity of air (kg kg−1)qa Absolute humidity of air (kg m−3)qc Rate of soil airflow (kg m−2 s−1)qd Rate of air diffusion in soil (kg m−2 s−1)qh Rate of heat flow in soil (W m−2)qr Rate of oxygen consumption by plant roots (kg m−2 s−1)qs Specific humidity of air just above the evaporating surface (kg kg−1)qso Specific humidity of air saturated with water vapour (kg kg−1)r Relative humidity of fair (−); radius (m)ra Aerodynamic resistance of air layer above the evaporating surface (m−1 s)rc Canopy resistance to water-vapour flow (m−1 s)rs Stomata resistance to water-vapour flow (m−1 s)s Specific soil surface (m2 kg−1)sp Soil covering; relative covering of soil by a plant canopy (m2 m−2)srs Specific surface of roots (m2 m−3)t Time (s)tp Ponding time (s)u Rate of airflow, wind velocity (m s−1)u* Friction velocity of air (m s−1)v Rate of liquid flow (m s−1)vc Steady rate of infiltration (m s−1)vi Infiltration rate (m s−1)vp Average rate of water flow in soil pores (m s−1)vz Rain rate (intensity) (m s−1)w Soil-water content in mass units (mass soil-water content) (kg kg−1)z (vertical) Coordinate (m)zk Critical depth below soil surface at which water-flow rate to soil from

groundwater can be neglected (m)zo Roughness of surface (m)zr Root system depth (m)A Area (m2)Aco Specific crack area of soil; soil crack area per unit area of soil surface

(m2 m−2)C Specific volumetric heat capacity of soil (J m−3 K−1)Ci Concentration of ith component of solute in mass units in a unit soil volume

(kg m−3)

xx Symbols

D Turbulent transport coefficient of air (m s−1)D(h) Soil-water diffusivity (m2 s−1)Da Coefficient of molecular diffusion of an air component in air (m2 s−1)Das Coefficient of molecular diffusion of air in soil (m2 s−1)De Effective coefficient of hydrodynamic dispersion of a particular ion in soil

(m2 s−1)Dv Water-vapour diffusivity in soil (m2 s−1)Dl Water-vapour diffusivity of liquid water in soil (m2 s−1)Dlh Coefficient of hydrodynamic dispersion (m2 s−1)Dls Effective diffusion coefficient of particular ions in soil (m2 s−1)

Dlw Coefficient of molecular diffusion of particular ions in water (m2 s−1)

Doa Coefficient of molecular diffusion of oxygen in air (m2 s−1)Dos Coefficient of molecular diffusion of oxygen in soil (m2 s−1)Dow Coefficient of molecular diffusion of oxygen in water (m2 s−1)Dva Coefficient of molecular diffusion of water vapour in air (m2 s−1)Dvs Coefficient of molecular diffusion of water vapour in soil (m2 s−1)E Evapotranspiration (mm); evapotranspiration rate (m3m−2 s−1)Ee Evaporation rate (m3 m−2 s−1)Eep Potential evaporation rate (m3 m−2 s−1)Ep Potential evapotranspiration rate (m3 m−2 s−1)Et Transpiration rate (m3 m−2 s−1)Etp Potential transpiration rate (m3 m−2 s−1)ETc Potential evapotranspiration rate of a particular plant canopy (not reference

evapotranspiration) (m3 m−2 s−1)ETo Reference (canopy) evapotranspiration rate (m3 m−2 s−1)F Force (capillary, gravity) (N)G Heat-flux rate to the soil through a soil surface (W m−2)H Turbulent (sensible) heat flux (heat-flux rate from an evaporating surface

into the atmosphere) (W m−2; J m−3 s−1); hydraulic head (m)Hf Effective pressure head at the infiltration front (m)I Plant-canopy interception (mm; m3 m−2 s−1)Jw Steady rate of water flow (m s−1)K Hydraulic conductivity of saturated soil (saturated-soil hydraulic conduc-

tivity) (m s−1)Kb Effective hydraulic conductivity of saturated stony soil (m s−1)Kc Crop coefficient (−)Kef Effective hydraulic conductivity of saturated layered soil (m s−1)Kf Hydraulic conductivity of saturated fine earth of stony soil (m s−1)Kp Soil permeability (m2)Krs Relative hydraulic conductivity of saturated stony soil (Kb/Kf) (−)L Latent heat of evaporation (liquid water–water vapour) (J kg−1); length (m)Lco Length of cracks per unit soil-surface area (m m−2)Lf Infiltration front depth below soil surface (m)Ls Latent heat of ice sublimation (J kg−1)

Symbols xxi

Lt Latent heat of ice melting (J kg−1)LAI Leaf-area index (m2 m−2)O Surface run-off, surface-run-off rate (mm; m3 m−2 s−1)P Soil porosity (m3 m−3)Pb Effective porosity of stony soil (m3 m−3)Pc Soil crack porosity (m3 m−3)Pd Drainable porosity, specific yield (m3 m−3)Pf Porosity of fine-earth fraction of stony soil (m3 m−3)Pn Wettable porosity (m3 m−3)Prf Rock fragments’ porosity of stony soil (m3 m−3)Q Discharge or inflow of water (m3 s−1)Rl Long-wave radiation rate (W m−2)Rm Relative mass of rock fragments (stoniness) (kg kg−1)Rn Net radiation (W m−2)Rs Short-wave radiation rate (W m−2)Rv Relative volume of rock fragments (stoniness) (m3 m−3)S Sorptivity (m s−½); soil saturation (−)S(z) Inflow (outflow) of water into (from) a unit volume of soil per unit time

(m3 m−3 s−1)Scs Specific surface of soil cracks (m2 m−3)Se Effective soil saturation (−)Sp Potential (maximum) rate of water uptake by roots (m3 m−3 s−1)T Temperature (°C, K)V Volume; soil volume (m3)Va Volume of air in soil (m3)Vb Total (bulk) volume of stony soil (m3)Vc Volume of cracks in soil (m3)Vcv Specific volume of soil cracks (m3 m−3)Vf Volume of fine-earth fraction of stony soil (m3)Vrf Rock fragments’ volume in stony soil (m3)Vs Volume of dry solid phase of a soil sample (m3)Vw Volume of water in a soil sample (m3)Vwb Volume of water in stony soil (m3)

Vwf Volume of water in a fine-earth fraction of stony soil (m3)

Vwrf Volume of water in rock fragments of stony soil (m3)

Y Biomass production, yield (t ha−1)Z Precipitation total; precipitation rate (mm; m3 m−2 s−1)Zz Irrigation-water total; irrigation rate (mm; m3 m−2 s−1)a Albedo of surface (reflection coefficient) (−); parameter of van Genuchten’s

equation expressing SWRC (s−1)e Permittivity (m−3 kg−1 s4 A2)c Psychrometric constant (m−1 kg s−2 K−1)gw Dynamic viscosity of water (m−1 kg s−1)u Contact angle, wetting angle (-)kðhÞ Thermal conductivity of soil (W m−1 K−1)

xxii Symbols

ka Thermal conductivity of air (W K−1)ki Thermal conductivity of ice (W K−1)kw Thermal conductivity of water (W K−1)h Volumetric soil-water content (m3 m−3)hawc Plant available water capacity (m3 m−3)hb Effective (total) volumetric soil-water content of stony soil (m3 m−3)

h f Volumetric soil-water content of stony-soil fine earth (m3 m−3)hfc Volumetric soil-water content corresponding to the field capacity of soil

(m3 m−3)hh Hygroscopicity coefficient (adsorption water capacity) (m3 m−3)hla Volumetric soil-water content corresponding to the point of limited

availability of water to plants (m3 m−3)hmac Monomolecular soil-water capacity (m3 m−3)hr Residual volumetric soil-water content (m3 m−3)hbr Effective residual volumetric soil-water content of stony soil (m3 m−3)

hrf Volumetric soil-water content of stony-soil rock fragments (m3 m−3L3 L−3)hs Saturated volumetric soil-water content (m3 m−3)hbs Effective volumetric soil-water content of saturated stony soil (m3 m−3)

h fs

Volumetric soil-water content of a saturated stony-soil fine-earth fraction(m3 m−3)

hwp Volumetric soil-water content corresponding to wilting point (m3 m−3)qa Density of (moist) air (kg m−3)qad Density of dry air (kg m−3)qb Density of dry soil (bulk density) (kg m−3)qbb Effective density of dry stony soil (kg m−3)

q fb

Density of dry fine-earth fraction of stony soil (kg m−3)

qrfb Density of dry-rock fragments of stony soil (kg m−3)

ql Density of liquid (water) (kg m−3)qp Density of plant canopy (number of plants per unit of soil-surface area)

(m−2)qr Density of dry roots in soil (kg m−3)qs Specific density of soil (particle density) (kg m−3)qv Density (bulk density) of water vapour (kg m−3)qw Density (bulk density) of liquid water (kg m−3)rw Surface tension of water (N m−1)s Tangential tension (N m−2); tortuosity of pores (−)t Kinematic viscosity of water (m2 s−1)Cw Parameter characterising water transport between two domains in

dual-porosity model (s−1)wt Energy of soil water (total soil-water potential) (J kg−1)

Symbols xxiii