Soil, Plant and Atmosphere978-3-030-19322-5/1.pdfwhich agronomists and soil physicists collaborate to improve productivity and further develop Brazil’s agriculture and ag-related

Soil, Plant and Atmosphere

Klaus Reichardt • Luís Carlos Timm

Soil, Plant andAtmosphereConcepts, Processesand Applications

Klaus ReichardtCentro de Energia Nuclear na Agriculturaand Escola Superior de agricultura“Luiz de Queiróz”University of Sao PauloPiracicaba, São Paulo, Brazil

Luís Carlos TimmRural Engineering DepartmentFaculty of AgronomyFederal University of PelotasCapão do Leão, Rio Grande do SulBrazil

Translation from the Portuguese language edition: “Solo, planta e atmosfera” by KlausReichardt and Luís Carlos Timm, 2nd Edition © Editora Manole 2012. All rightsreserved.

ISBN 978-3-030-19321-8 ISBN 978-3-030-19322-5 (eBook)https://doi.org/10.1007/978-3-030-19322-5

© Springer Nature Switzerland AG 2020This work is subject to copyright. All rights are reserved by the Publisher, whether the whole orpart of the material is concerned, specifically the rights of translation, reprinting, reuse ofillustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way,and transmission or information storage and retrieval, electronic adaptation, computer software, orby similar or dissimilar methodology 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 areexempt from the 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 inthis book are believed to be true and accurate at the date of publication. Neither the publisher northe authors or the editors give a warranty, express or implied, with respect to the materialcontained herein or for any errors or omissions that may have been made. The publisherremains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

This Springer imprint is published by the registered company Springer Nature Switzerland AGThe registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland

To my wife, Ceres; my sons, Roberto (in memoriam)and Gustavo; and my daughter, Fernanda.

Klaus Reichardt

To my parents, Ely and Edemar Timm (in memorium).To my wife, Cristiane; my daughter, Ana Clara;and my two sons, Luís Augusto and José Henrique.

Luís Carlos Timm

Foreword

It is a Thursday morning in Davis, California, on September 7, 1995, and I ampretty nervous because in about 2 h, I will have to give an oral presentation onbehalf of the Vadose Zone Hydrology Conference, which is held to honor thecareer achievements of Donald R. Nielsen and James W. Biggar. Whilewaiting in the foyer of the conference hall, a person with a very friendlyappearance greets me and introduces himself with “I am Klaus!” So, this isKlaus Reichardt, I think to myself. Finally, I have the pleasure to meet him inperson. As a graduate student more than 20 years ago, he was already apioneer in introducing scaling concepts into soil physics. And returning toBrazil, his unprecedented creative sampling of fields to learn more aboutsymbiotic nitrogen fixation greatly affected my entire career. As he is talkingto me with a radiating smile and positive attitude, my nervousness immedi-ately subsides. Later during the conference, I learn about the great artisticability of Klaus when I admire his hand-painted picture of the main buildingof the campus of the University of São Paulo, Piracicaba, attractivelysurrounded by the names of Don’s students and scholars.

Looking back over the years as I became more thoroughly acquainted withKlaus and Ceres, his wife, I have learned more and more about his tremendousachievements in his scientific career. One day, one of my colleagues said: “Itseems that soil physics is one of the strongest agricultural disciplines in Brazil.Do you know why?”—“I do. Because of Klaus Reichardt.”Klaus is one of themost influential scientists worldwide. The many awards he has received do notdo justice to celebrate his outstanding capacity, creativity, and personality.One of his greatest achievements was the foundation of the National Center ofResearch and Development of Agricultural Instrumentation (CNPDIA) inwhich agronomists and soil physicists collaborate to improve productivityand further develop Brazil’s agriculture and ag-related science. But there isalso one award that deserves to be mentioned here as an expression of Klaus’special personality and citizenship: in 2013, he became elected citizen of hishometown, Piracicaba.

No more than 5 years after our first meeting, I had the unique pleasure tointeract with Klaus’ graduate student, Luís Carlos Timm, who worked withme for half a year at ZALF in Germany. During this time, he workedintensively on the analysis of internal drainage experiments and on manyspatial data sets that he had collected in Brazil. Today, Timm, who carriesdegrees in Agricultural Engineering and Agronomy and teaches soil physics

vii

and hydrology, is a professor at the Federal University of Pelotas, is one of theleading experts in state-space analysis, and has applied this stochasticmodeling approach to a variety of data sets that he and his students havebeen accumulating over the years. For many years, Professors Reichardt andTimm have taught soil physics and spatial and temporal statistics to studentsand young scientists from around the world at the International Centre forTheoretical Physics in Trieste, Italy, causing everlasting inspirations for theseyoung scientists to enhance education, research, and practical agriculture ineach of their countries. The memories of my first visit in Piracicaba on theoccasion of the “First Brazilian Soil Physics Conference” in September of2011, which is organized by Professor Quirijn de Jong van Lier, when Klaus,Ceres, and I met again, are still fresh in my mind. The experiences of thisconference and the following one in Rio de Janeiro, which is organized byMarcos Ceddia and Marta Vasconcelos Ottoni in 2013, were inspirational forme in many ways: the strong link between applied and basic sciences as aresult of the high level of education and, among individuals, the respect foreach other. These visits were a wonderful initiation of continuing our existingand the foundation of new friendships and interaction.

With this translation of their newest book O SOLO, A ÁGUA, A PLANTA EA ATMOSFERA (Soil, Water, Plant and Atmosphere), Professors Reichardtand Timm reach out to a broader audience. Especially for those readerswithout a strong background in agronomy and earth sciences, this book is agreat “primer” and provides insights and understanding of the role of humanbeings in managing soils, water, crops, and atmosphere in sustainable ways.While introducing many complex topics and presenting state-of-the-artknowledge of many agro-ecosystem processes, this book is written in a waythat can easily be understood by laymen, i.e., without many equations andwith very explanatory illustrations.

Reichardt and Timm walk the readers through 19 chapters in which theyemphasize the importance of knowledge about natural systems and about howfood and fiber can be produced efficiently while sustaining the resources andimportant ecosystem-regulating functions. With their first chapter, the authorsintroduce and illustrate the major challenge of a growing population on earthand the increasing scarcity of resources. In Chap. 2, the fundamentalproperties of water and its role in the environment, its national abundance,and its relevance for agricultural management are explained. In Chap. 3, theauthors present the fundamentals of soils, beginning with a profile description,exploring the details of clay mineral structure, and then transitioning to anoverview of soil types in Brazil. Crop vegetative growth, different phenologi-cal stages, and aspects of the plant life cycle are elucidated in Chap. 4. Anoverview of gas composition of the atmosphere and fundamentals of pressurelaws, temperature, and radiation is given in Chap. 5. In the next chapter, thereader is able to grasp some principles of thermodynamics and is introduced tothe capillarity of the soil pore system. A nice overview on the instruments forthe measurement of fundamental soil state variables related to soil moisture isprovided in Chap. 6. The logical next step is the introduction to principles ofwater transport in soils. Of course, when we consider water transport in soils,we have to account for solutes that are transported with water, while their

viii Foreword

electrical charges determine the interaction with the solid phase and betweensolutes. A thorough insight in the thermal regime of soils is given in Chap. 10,and the reader has the opportunity to learn about theoretical aspects andpractical implications of soil water infiltration in Chaps. 11 and 12, beforethe attention is directed toward evaporation, evapotranspiration, and cropcoefficient. Chapter 14 is focused on the soil-plant-atmosphere continuum.The aspects of the soil water balance are illustrated in Chap. 15, which endswith the impact of agricultural production on the water balance. Plant nutrientuptake is the topic of Chap. 16, and Chaps. 17 and 18 are devoted to the studyof the variability of measurements within the Soil-Plant-Atmosphere System,an important subject involving statistics and space and time data series. Theyclose the book with Chap. 19, on dimensional analysis. This book is animportant resource for those who want to make themselves familiar with thebasic mass and energy transfer processes in agricultural ecosystems. It is agreat stimulation for those who decide to study the relevant processes of thewater cycle, the crop production, and the processes that govern the cyclicalterations of climate in further detail.

Klaus Reichardt and Luís Carlos Timm deserve a great appreciation for thisextremely well-written book and for their successful attempt to present com-plex matters in a digestible way to the readers who do not yet have a hugescientific background or those at the entrance to agricultural and geosciencesin Brazil as one of the strongest nations in terms of agricultural production andother countries. This book is truly inspirational, and with its great educativevalue, it will help to replace emotion-driven beliefs and assumptions withqualified knowledge, leading to rationale solutions for food supply for oursociety and clean, sustainable management of resources.

University of KentuckyLexington, KY, USA

SSSAMadison, WI, USA

Ole Wendroth

Foreword ix

Preface

One of the goals of this book is to give a broad and detailed view of soilphysics applied to the Soil-Plant-Atmosphere System (SPAS). Because of therelative depth in physics, the text involves a great number of mathematicalconcepts, which chase away agronomists and environmentalists, who rejectreading texts full of mathematical expressions. Therefore, we chose to writethe chapters in a very comprehensive way, progressing slowly with the use ofmath. Only in Chap. 3 we start introducing derivatives and integrals. Thereaf-ter, math becomes more and more present, culminating with the solution ofdifferential equations needed for the discussion of most processes that occur inthe SPAS. So, if the reader goes directly to Chap. 11 because he is interestedin infiltration, he probably will soon give up. In this Preface, the authorsintend to illustrate the thoughts made above, placing a parallel between theexact sciences, used to describe here the Soil-Plant-Atmosphere System,which are predictable and Cartesian, and the human sciences that involve allof us, like art, love, smell, nostalgia, and envy, all considered inexact, difficultto quantify, and almost always unpredictable.

For this parallel, we begin with the academic career of a starting individual,which, for sure, involves exact aspects intertwined with human aspects, andeach one, whether student, researcher, or teacher, evolves according to hisunique path, with successes and stumblings, to conquer his place in thescientific world. The pathway is long, in which each one develops his ownresources for a self-assertion and arrival to a destiny that never comes. DanielHillel (1987) was able to formulate an interesting model to describe what hecalls the flow of scientific development through the interaction of processesaddressed by the exact sciences, interconnected by those who addressed thehuman sciences. The following figure, adapted from this author, illustrates thisflow, imagining a researcher (you, the reader) who, at the beginning of hisacademic career, takes his sailboat and, departing from a point A, navigates inthe River of Science, against the water current and the wind, in thedirections B, C, D, etc., taking part of the scientific development of human-kind. On the right hand, the bank of the River of Science is the Margin of theTheory, where theoretical aspects are mainly dealt with, and on the left handside, the Data Margin or that of Practice where scientific experimentationprevails. For the reader not versed in the art of sailing, it has to be said that theonly alternative to sail against the wind is the zigzag path, which, in ourscenery, is from one margin to the other. The journey starts from point A,

xi

passing through B, C, etc., toward Z (placed in infinity that is never reached).We might consider that Einstein, Freud, Newton, and so many more haveattained Z, but in fact, each of them has made his own journey. In this travel,the researcher is going through obstacles, with voluntary deviations of route ornot, entering in the rivers, tributaries, and lakes or beating on the rocks. Thenavigation from the Data Margin to the Theory Margin symbolizes theinductive processes that, based on some experimental and particular data,lead to the establishment of generalizations and general conclusions ortheories. From the Theory Margin to the Data Margin, the sailor implementsthe deductive processes, which take a theory to its verification, validation, orproof by means of experimental observations.

The ideal trajectory is indicated by the solid zigzag line with arrows,without hitting obstacles (1, 2, 3, etc.) and without route deviations into therivers or lakes. Few are able to follow this clean route; each one is at the mercyof his destiny and makes his own trajectory. Some get lost in the River of theDevil on the margin of the theory, where they believe that only the theorybrings us to the truth, using models without validation and concluding withoutexperimental evidence. Others hit on the rock, using unstable formulations,non-converging models, and equations without solution and becoming lost insingularities. Still others, on the margin of data and practice, get lost in the

III. THE ROCKUnstable mathematicalformulationsNon convergent modelsEquations withoutSolutionSingularities

Theoretical modelswithout validationPremature

theoreticalspeculation

only theoryleads to the truth

Theoreticalconclusionswithoutexperimental support

I. RIVER OF THE DEVIL MARGIN OF THE THEORY

1 2

3

4

5A B C D E F X Y Z

Predominantwind

Direction of increasing knowledge

Waterflow

MARGIN OF DATA AND EXPERIMENTATIONS

Dive into a sea of dataDrawers full of dataData collected withoutscientific basisDeviation from theoretical aspects

Experiments of too long durationMeasurements that always failExcessive replications by insecurityDeviation from theoretical aspectsExperimental designs out of reality

II. BLUE AND DEEP OCEAN IV. FORCED LABOR CAMP

The flow of scientific development along the River of Science, going from A to Z. I, II, II, and IV, indicates the deviationsfrom the main route; 1, 2, 3, 4, and 5 indicate trajectory obstacles hit during travel. Source: Adapted from Hillel, 1987

xii Preface

Blue and Deep Ocean, submerging in a sea of data, storing enormous volumesof data sometimes collected without scientific basis, and deviating abruptlyfrom the theory, or do not abandon the Forced Labor Field, conductingexperiments of unlimited duration, employing methods that do not work,and making a great number of unnecessary replicates only because of insecu-rity, with experimental designs out of reality.

During his travel along the River of Science, the sailor might also hitobstacles: (1) delay by conventional wisdoms; (2) institutional administration;(3) financing agencies; (4) publication policies and peer reviews; and (5) judg-ment committees, concurrence, family barriers, retirement, etc. What is impor-tant is that, when making its own way, by dribbling the most varied obstacles,the sailor ends up contributing with its share to the scientific development.During the sailing, it is important to be open to changes of course, toinnovations, to partnerships, and to collaborations. The worst obstacle onecan find is the resistance to change. You never know if what seems bad todayis definitely evil forever.

Time is a fundamental coordinate during the navigation on the River ofScience, for both the exact and the human sciences. Albert Einstein certainlyrepresents the scientists in the field of exact sciences, who contributed most tothe definition of time t, recognizing it as the fourth dimension, next to thespatial coordinates x, y, and z, and showing that their interconnection is sointense as to make time “shrink” or “swell” with the relative velocity betweenobject and observer. All demonstrated by well-founded theories and equationsbut difficult to understand for a simple mundane.

In the human sciences, which also involve emotion, we can cite theBrazilian composer Chico Buarque de Holanda as the representative of thelovely and poetic interpretation of time. In most of his verses, time stands out,if not directly, at least as a backdrop; he shows how time passes through ourlives while everything happens and showing the ephemeral character of time,which often leads us to miss the “trains” of life.

To close this Preface, we will state that we intend with this book to take inhands each student or scientist along the arduous path of the scientificdevelopment to advance little by little, chapter by chapter, through the Soil-Plant-Atmosphere System. At the end of this journey, hoping to becomemature, ready to lead the frontier of knowledge, with the whish that oldercareer colleagues will have their accomplishments recognized and that sad,insecure, timid colleagues turn around, react, and have strength to enter theacademic dance and, finally, recognize that great colleagues, those who haveachieved affirmation and recognition, learn to be young again, smile, behumble and tolerant, and aware that there is always something more to belearned and that the end never comes to an end.

São Paulo, Brazil Klaus ReichardtRio Grande do Sul, Brazil Luís Carlos Timm

Preface xiii

Contents

1 Man and the Soil–Plant–Atmosphere System . . . . . . . . . . . . . 11.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

2 Water, the Universal Solvent for Life . . . . . . . . . . . . . . . . . . . 72.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72.2 Molecular Structure and Phase Change of Water . . . . . . 72.3 Surface Tension . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102.4 Viscosity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112.5 The Importance of Water for Agricultural

Production . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122.6 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132.7 Answers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

3 The Soil as a Water Reservoir for Plants . . . . . . . . . . . . . . . . 153.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153.2 The Solid Fraction of the Soil . . . . . . . . . . . . . . . . . . . . 163.3 Liquid Fraction of the Soil . . . . . . . . . . . . . . . . . . . . . . 283.4 Gaseous Fraction of the Soil . . . . . . . . . . . . . . . . . . . . . 403.5 Thermal Properties of the Soil . . . . . . . . . . . . . . . . . . . . 433.6 Soil Mechanics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 443.7 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 443.8 Answers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47

4 Plant: The Solar Energy Collector . . . . . . . . . . . . . . . . . . . . . 494.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 494.2 Plant Anatomy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 574.3 Water in the Plant . . . . . . . . . . . . . . . . . . . . . . . . . . . . 584.4 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 604.5 Answers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60

xv

5 Atmosphere: The Fluid Envelope That Coversthe Planet Earth . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 635.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 635.2 Thermodynamic Characteristics of the Air Close

to Soil Surface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 655.3 Solar Radiation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 695.4 Wind . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 795.5 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 795.6 Answers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80

6 The Equilibrium State of Water in the Systems . . . . . . . . . . . 816.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 816.2 Thermodynamic Basis of the Soil Water

Potential Concept . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 836.3 Total Potential of Water in the Soil . . . . . . . . . . . . . . . . 876.4 Pressure Component . . . . . . . . . . . . . . . . . . . . . . . . . . . 906.5 Gravitational Component . . . . . . . . . . . . . . . . . . . . . . . 916.6 Osmotic Component . . . . . . . . . . . . . . . . . . . . . . . . . . . 936.7 Matric Component . . . . . . . . . . . . . . . . . . . . . . . . . . . . 946.8 Total Water Potential of the Plant . . . . . . . . . . . . . . . . . 1006.9 Equilibrium of the Water . . . . . . . . . . . . . . . . . . . . . . . 1026.10 Instruments for Soil Water Measurements . . . . . . . . . . . 110

6.10.1 Porous Plate Funnel . . . . . . . . . . . . . . . . . . . . 1106.10.2 The Water Tensiometer with Mercury

Manometer . . . . . . . . . . . . . . . . . . . . . . . . . . 1116.10.3 The Polymer Tensiometer . . . . . . . . . . . . . . . 1136.10.4 Electric Resistance Sensors . . . . . . . . . . . . . . 1146.10.5 Richard’s Pressure Membrane . . . . . . . . . . . . 1146.10.6 Psychrometer for Air Water Potential . . . . . . . 1166.10.7 Psychrometer for Soil Matric Potential . . . . . . 1166.10.8 Measurement of Soil Bulk Density

and Water Content . . . . . . . . . . . . . . . . . . . . . 1176.10.9 Soil Bulk Density ds . . . . . . . . . . . . . . . . . . . 1176.10.10 Soil Water Content (u and θ) . . . . . . . . . . . . . 121

6.11 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1276.12 Answers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129

7 The Movement of Water in the Systems . . . . . . . . . . . . . . . . . 1337.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1337.2 Water Movement in the Soil . . . . . . . . . . . . . . . . . . . . . 134

7.2.1 The Darcy Equation . . . . . . . . . . . . . . . . . . . . 1347.3 Equation of Continuity . . . . . . . . . . . . . . . . . . . . . . . . . 1497.4 Saturated Soil Water Flux . . . . . . . . . . . . . . . . . . . . . . . 1537.5 Non-saturated Soil Water Flux . . . . . . . . . . . . . . . . . . . 1587.6 Water Movement from the Plant to the Atmosphere . . . . 1687.7 Water Movement in Open Channels and Pipes . . . . . . . . 169

xvi Contents

7.8 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1717.9 Answers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 175References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177

8 Soil Water as a Nutrient Solution . . . . . . . . . . . . . . . . . . . . . . 1798.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1798.2 Soil Solution Thermodynamics . . . . . . . . . . . . . . . . . . . 1798.3 Activity of an Electrolytic Solution . . . . . . . . . . . . . . . . 1828.4 The Theory of Donnan . . . . . . . . . . . . . . . . . . . . . . . . . 1848.5 The Ionic Double Layer . . . . . . . . . . . . . . . . . . . . . . . . 1868.6 Ionic Exchange Capacity . . . . . . . . . . . . . . . . . . . . . . . 1888.7 Ion Flux in the Soil . . . . . . . . . . . . . . . . . . . . . . . . . . . 1918.8 Solute Diffusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1928.9 Solute Mass Transfer . . . . . . . . . . . . . . . . . . . . . . . . . . 1958.10 Solute Sources and Sinks . . . . . . . . . . . . . . . . . . . . . . . 1968.11 Miscible Displacement . . . . . . . . . . . . . . . . . . . . . . . . . 1978.12 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2008.13 Answers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 201References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 201

9 Aspects of the Soil Atmosphere . . . . . . . . . . . . . . . . . . . . . . . 2039.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2039.2 Flow of Gases in the Soil . . . . . . . . . . . . . . . . . . . . . . . 203

9.2.1 Gas Diffusion . . . . . . . . . . . . . . . . . . . . . . . . 2039.3 Sources and Sinks of Gases . . . . . . . . . . . . . . . . . . . . . 2069.4 Gas Mass Transfer . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2079.5 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2079.6 Answers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 208References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 208

10 How Heat Is Propagated in the Soil . . . . . . . . . . . . . . . . . . . . 20910.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20910.2 Heat Conduction in Soils . . . . . . . . . . . . . . . . . . . . . . . 20910.3 Model for the Description of Temperature

Changes in the Soil . . . . . . . . . . . . . . . . . . . . . . . . . . . 21110.4 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21410.5 Answers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 215References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 215

11 Water Infiltration into the Soil . . . . . . . . . . . . . . . . . . . . . . . . 21711.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21711.2 Horizontal Infiltration into Homogeneous Soils . . . . . . . 21811.3 Vertical Infiltration into Homogeneous Soil . . . . . . . . . . 22711.4 Infiltration Direction . . . . . . . . . . . . . . . . . . . . . . . . . . . 23311.5 Infiltration into Heterogeneous Soils . . . . . . . . . . . . . . . 23411.6 Some Practical Agronomic Implications . . . . . . . . . . . . 23811.7 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23811.8 Answers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 239References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 239

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12 Water Redistribution After Infiltration into the Soil . . . . . . . 24112.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24112.2 Analysis of the Redistribution Process . . . . . . . . . . . . . . 24112.3 Field Capacity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25012.4 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25212.5 Answers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 253References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 256

13 Evaporation and Evapotranspiration: The VaporLosses to the Atmosphere . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25913.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25913.2 Evaporation Under Steady State . . . . . . . . . . . . . . . . . . 26013.3 Evaporation in the Absence of a Water Table . . . . . . . . . 26213.4 Potential and Real Evaporation . . . . . . . . . . . . . . . . . . . 26413.5 Potential and Real Evapotranspiration . . . . . . . . . . . . . . 26513.6 Measurement of the Evapotranspiration . . . . . . . . . . . . . 267

13.6.1 The Thornthwaite Method . . . . . . . . . . . . . . . 26813.6.2 Penman Method . . . . . . . . . . . . . . . . . . . . . . 26913.6.3 Penman–Monteith Method . . . . . . . . . . . . . . . 270

13.7 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27113.8 Answers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 272References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 272

14 How Do Plants Absorb Soil Water? . . . . . . . . . . . . . . . . . . . . 27514.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27514.2 Water Availability for Plants . . . . . . . . . . . . . . . . . . . . . 27514.3 The Soil-Plant-Atmosphere System Considered

as a Whole . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27714.4 Water Flux from Soil to Root . . . . . . . . . . . . . . . . . . . . 27914.5 Available Water and Evapotranspiration . . . . . . . . . . . . 28214.6 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28714.7 Answers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 287References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 287

15 The Water Balance in Agricultural and Natural Systems . . . . 28915.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28915.2 The Balance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28915.3 Thornthwaite and Mather Water Balance . . . . . . . . . . . . 30115.4 Water-Depleted Productivity . . . . . . . . . . . . . . . . . . . . . 30515.5 A Holistic View of the Agricultural Production

System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30615.6 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30815.7 Answers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 309References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 310

16 How Plants Absorb Nutrients from the Soil . . . . . . . . . . . . . . 31316.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31316.2 Movement of Nutrients from the Soil

to the Surface of Roots . . . . . . . . . . . . . . . . . . . . . . . . . 313

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16.3 Diffusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31416.4 Mass Flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31416.5 Relative Importance of Root Extension

in Relation of Nutrient Absorbtion . . . . . . . . . . . . . . . . 31416.6 Influence of Soil Physical Condition

on the Transport of Nutrients . . . . . . . . . . . . . . . . . . . . 31516.6.1 Soil Water Content . . . . . . . . . . . . . . . . . . . . 31516.6.2 Soil Air . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31616.6.3 Soil Texture . . . . . . . . . . . . . . . . . . . . . . . . . 31716.6.4 Soil Temperature . . . . . . . . . . . . . . . . . . . . . . 31716.6.5 Root System . . . . . . . . . . . . . . . . . . . . . . . . . 317

16.7 Examples of Nutrient Movement in the Soil . . . . . . . . . . 31816.8 Nutrient Root Absorbtion . . . . . . . . . . . . . . . . . . . . . . . 32016.9 Nutrient Balance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32216.10 Use of Isotopes in Agricultural Experimentation . . . . . . . 32416.11 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32916.12 Answers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 329References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 329

17 How Soil, Plant, and Atmosphere Properties Varyin Space and Time in the SPAS: An Approachto Geostatistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33117.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33117.2 Mean (Average), Variance, Standard Deviation,

and Coefficient of Variation . . . . . . . . . . . . . . . . . . . . . 33217.3 Quartiles and Moments . . . . . . . . . . . . . . . . . . . . . . . . . 33417.4 Total Amplitude and Interquartile Range . . . . . . . . . . . . 33517.5 Skewness and Kurtosis Coefficients . . . . . . . . . . . . . . . . 33517.6 Identification of Outliers (Discrepant Values) . . . . . . . . . 33617.7 Box Plot (Box-and-Whisker Plot) . . . . . . . . . . . . . . . . . 33717.8 Normal Frequency Distribution . . . . . . . . . . . . . . . . . . . 33717.9 Covariance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34017.10 Autocorrelogram . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34217.11 Semivariogram . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 343

17.11.1 Models with Defined Sill(Bounded Models) . . . . . . . . . . . . . . . . . . . . . 346

17.11.2 Models Without Defined Sill(Unbounded Models) . . . . . . . . . . . . . . . . . . . 346

17.12 Ordinary Kriging: A Geostatistical Methodof Interpolation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 352

17.13 Pedotransfer Functions . . . . . . . . . . . . . . . . . . . . . . . . . 35717.14 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36017.15 Answers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 362References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 363

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18 Spatial and Temporal Variability of SPAS Attributes:Analysis of Spatial and Temporal Series . . . . . . . . . . . . . . . . 36718.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36718.2 Cross-Correlogram . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36818.3 Temporal and Spatial Series: Definition

and Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36818.4 Spectral Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37218.5 Wavelet Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37518.6 Multivariate Empirical Mode Decomposition

(MEMD) Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37818.7 The State-Space Approach . . . . . . . . . . . . . . . . . . . . . . 37918.8 Shumway’s Approach to State-Space . . . . . . . . . . . . . . . 382

18.8.1 Analysis of the Behavior of Soil WaterContent and Temperature . . . . . . . . . . . . . . . . 382

18.8.2 Relation Between Physical and ChemicalSoil Properties . . . . . . . . . . . . . . . . . . . . . . . . 385

18.8.3 Soil-Plant System Evaluation . . . . . . . . . . . . . 39318.9 State-Space Approach as Described by West

and Harrison . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40518.9.1 West and Harrison’s State-Space Approach:

An Application Using Space Data Series . . . . . 40818.9.2 Application of Both State-Space Approaches

to Forecast Space Data Series . . . . . . . . . . . . . 41418.10 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41818.11 Answers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 420References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 420

19 Dimensional Analysis, Scaling, and Fractals . . . . . . . . . . . . . . 42319.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42319.2 Physical Quantities and Dimensional Analysis . . . . . . . . 42619.3 Physical Similarity . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42819.4 Nondimensional Quantities . . . . . . . . . . . . . . . . . . . . . . 42819.5 Main Variables Used to Quantify the SPAS . . . . . . . . . . 42919.6 Coordinate Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . 43219.7 Scales and Scaling . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43219.8 Fractal Geometry and Dimension . . . . . . . . . . . . . . . . . 43819.9 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44319.10 Answers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 443References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 443

Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 445

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About the Authors

Klaus Reichardt holds a degree and a PhD in Agronomy (1963 and 1965,respectively), a “Frei Docent” degree in Physics and Meteorology (1968), anda full professor in Physics and Meteorology (1981) all from the University ofSão Paulo and a PhD in Soil Science from the University of California (UC,Davis) (1971). He is currently retired senior professor of the Center forNuclear Energy in Agriculture (USP) and crop science advisor at the graduateprogram in Crop Production of the Agricultural College, ESALQ, USP, bothin Piracicaba, SP, Brazil. Furthermore, he has experience in physics applied toagronomy, acting mainly on the following subjects: soil water, neutron probe,soil hydraulic conductivity, soil tomography, agricultural balance of water andnitrogen in agricultural crops, spatial variability of soil parameters withemphasis in geostatistics and regionalized variables, and the use of isotopesas markers in agricultural experiments, agrometeorology, soil physics, andcrops like corn, soybean, sugarcane, and coffee. In 2019, he has eight graduatestudents for PhD and MS.

Luís Carlos Timm holds a degree in Agricultural Engineering from theFederal University of Pelotas (1991), a master in Irrigation and Drainagefrom Federal University of Viçosa (1994), and a PhD in Agronomy fromthe University of São Paulo (2002). He is currently associate professor of theDepartment of Rural Engineering, Faculty of Agronomy, Federal Universityof Pelotas. In addition, he has experience in soil physics and statistics, actingmainly on the following subjects: soil water, neutron and capacitance probes,soil hydraulic conductivity, balance of agricultural crops, spatial and temporalvariability of soil and crop parameters with emphasis in time series analysis,and geostatistics.

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