PROGRAMA DE DOCTORADO EN TECNOLOGÍAS INDUSTRIALES
TESIS DOCTORAL
MODELADO DE LAS PROPIEDADES DIELÉCTRICAS DEL SUELO. APLICACIÓN EN EL DISEÑO DE SENSORES PARA SISTEMAS DE CONTROL EN AGRICULTURA DE
PRECISIÓN
Presentada por Juan Domingo González Teruel para optar al grado de Doctor
por la Universidad Politécnica de Cartagena
Dirigida por:
Dr. Roque Torres Sánchez Codirigida por:
Dra. Ana Belén Toledo Moreo
Cartagena, 2022
DOCTORAL PROGRAMME IN INDUSTRIAL TECHNOLOGIES
PhD THESIS
MODELING OF SOIL DIELECTRIC PROPERTIES. APPLICATION IN SENSOR DESIGN FOR PRECISION AGRICULTURE CONTROL SYSTEMS
Presented by Juan Domingo González Teruel to the Technical University of Cartagena in fulfilment of
the thesis requirement for the award of PhD
Supervisor:
Dr. Roque Torres Sánchez Co-supervisors:
Dra. Ana Belén Toledo Moreo
Cartagena, 2022
PROPERTIES. APPLICATION IN SENSOR DESIGN FOR PRECISION AGRICULTURE
CONTROL SYSTEMS
Juan D. González-Teruel
To those who always believed
A constant knock will break the stone Dyfal donc a dyrr y garreg
with the terms of article 20 of the Regulations for Official Doctoral Studies of the Technical University of Cartagena of 24th March 2021. The works have been published with the express authorisation of the director and co-director of this thesis. These papers were prepared and published after the start of the doctoral studies and their references are listed below:
- Article I. González-Teruel, J.D., Torres-Sánchez, R., Blaya-Ros, P.J., Toledo-Moreo, A.B., Jiménez-Buendía, M., Soto-Valles, F., 2019. Design and Calibration of a Low-Cost SDI-12 Soil Moisture Sensor. Sensors, 19, 491.
DOI: 10.3390/s19030491 Impact Factor (2019): 3.275
Quartile: Q1; 15/64 Instruments and Instrumentation.
- Article II. González-Teruel, J.D., Jones, S.B., Soto-Valles, F., Torres-Sánchez, R., Lebron, I., Friedman, S.P., Robinson, D.A., 2020. Dielectric Spectroscopy and Application of Mixing Models Describing Dielectric Dispersion in Clay Minerals and Clayey Soils. Sensors, 20, 6678.
DOI: 10.3390/s20226678 Impact Factor (2020): 3.576
Quartile: Q1; 14/64 Instruments and Instrumentation.
- Article III. González-Teruel, J.D., Jones, S.B., Robinson, D.A., Giménez-Gallego, J., Zornoza, R., Torres-Sánchez, R., 2022. Measurement of the broadband complex permittivity of soils in the frequency domain with a low-cost Vector Network Analyzer and an Open-Ended coaxial probe. Computers and Electronics in Agriculture, 195, 106847.
DOI: 10.1016/J.COMPAG.2022.106847 Impact Factor (2021): 6.757
Quartile: Q1; 4/59 Agriculture, Multidisciplinary.
- Article IV. González-Teruel, J.D., Ruiz-Abellon, M.C., Blanco, V., Blaya-Ros, P.J., Domingo, R., Torres-Sánchez, R., 2022. Prediction of Water Stress Episodes in Fruit Trees Based on Soil and Weather Time Series Data. Agronomy, 12, 1422.
DOI: 10.3390/agronomy12061422 Impact Factor (2021): 3.949 Quartile: Q1; 18/90 Agronomy.
Acknowledgements
“The more I learn, the less I know”. This has been quoted by many along history in its different nuances; Albert Einstein himself, as a famous representative; and it is something likely inherent to the human being mind, or at least for those who have a realistic notion of knowing. This describes my feeling after almost five years of deep exploration of a realm that was totally alien and strange to me and that I never imagined digging into. One gradually discovers that the processes of the universe are branching out in such a way that the smartest answer to any question one can ask ends up being: “it depends”. However, this learning process is probably the most intense source of happiness, and accordingly, I would like to thank those who have made this stage of my life the happiest.
All my gratitude to my PhD supervisor, Roque Torres Sánchez, who gave me the opportunity to live these wonderful past five years of personal fulfilment; always encouraged me to go abroad;
supported both morally and economically this learning joy; and brought me back to reality when required. Thanks for investing in future and science and thanks for your altruism, you are one of the most powerful engines of this University. I cannot promise anything but hard work in return to make it worth it.
Thanks to my co-supervisor, Ana B. Toledo Moreo, for her support, willingness and always good vibes. Your joy is always inspiring to me. Some of my fondest memories of these past five years are in our chats as we strolled along the canals of Edam and Volendam, and the bike rides through Amsterdam to celebrate the end of a conference.
Thanks to Pencho Soto, probably the best human definition of altruism. He was the one who introduced me into this and gave me as much as he could without ever asking something in return.
Thanks for making me part of your projects and taking me under your wing. I will never forget our time in Bangor with Ana and Miriam, our trips along the North Wales coast and the hiking to the Snowdon Summit. I am glad we had the opportunity to share the enjoyment of such wonderful places. Thanks for your generosity.
Thanks to David A. Robinson and Inma Lebron for opening their “home” to me in Bangor despite the fact that I was a complete stranger from whom they had no reference at all. Thanks for trusting and believing in science and people’s kindness. You cannot imagine how important this experience was for me, how happy I felt in that place and how long I have been telling everyone
about North Wales, where I belong now and recognize myself as an official ambassador. Thanks David for building the bridges to my connection with the international scientific community.
Thanks to Scott B. Jones for also opening his “home” to me in Logan and for continuously insisting in my visit to Utah State University. I still find it hard to understand how deep an interest you could have in welcoming an almost stranger like me to take care of for 3 months, but all I have to say is: thank you for doing it. Thank you for your trust and for allowing me to live again a wonderful experience away from home; for discovering me Panda Express, Costa Vida and Annie Chun’s noodles; for our long chats about soil dielectrics and associated history; for your extreme hospitality; and for treating me like as if I was part of your family. Extended thanks to Teresa for letting us stay in the lab until late and on Saturdays.
Special mention to my friends and family in Bangor, who made my experience there so unforgettable. To the Latin Crew: Thales, Gabi, Josi, Andre, Bruna, Jessica and Antonio. For our Friday evenings hanging out at Wetherspoon and Tap & Spile; our always longed-for lunch time at the CEH hall; the “meriendas” eating Oreo cake, beijinhos and brigadeiros and playing Wizard; the barbecues at the beach and for introducing me into picanha. To Josi and Andre, for inviting me to their home and showing me Llandudno and TK Maxx. To my housemates at 49th Caernarfon Road:
Marco, Khaled and Hani, for making my first weeks abroad easier, loving football as much as I do, driving me around, and letting me improve my English with their constant willingness to discuss anything. To the rest of the people I met in Bangor and at the CEH, who contributed to this wonderful adventure: Michelle, Manuel, Fiona, Lydia, Kike, Jeevi, Rachel, Jenny, Bob, Adam, Jamie, Milo, Nathan and Julia. To Rodrigo and Antonio for coming to visit me to the red dragon kingdom.
And when I thought I had been very lucky in Wales, I arrived in Utah without any hope of similar experience, but they were waiting for me: Chihiro, Sam, Chieh-Yun (a.k.a Carolin), Ji-Jhong (a.k.a JJ), Shannon, Greg, Phearen, Miles, Mila and Kerem. Thank you for making a temporary place for me in your lives, for the board games meetings, the discovery of Camel Up, the visits to the Antelope Island, Arches and Canyonlands National Parks, for the hiking of Fiery Furnace and the unforgettable sight of the milky way from the Double Arch, for your kindness, dinner invitations and the farewell you gave me. You made me feel truly loved and proud to be a True Aggie. To Chris and Shayla, for being wonderful hosts, for always showing willingness to help me and for lending me their telephoto lens, without which I would not have enjoyed half of Utah's scenery. To Hsin and Yurika, for opening their home to me and making me enjoy playing board games. To Bill, who from the workshop was of critical help for my experiments and to the rest of people I met at the
Dylan, Grace, Riley and Tina.
Thanks to the co-authors of the articles presented in this thesis and other publications along this period who I have not mentioned yet. To Manuel Jiménez, for his hard work and constant willingness to create new devices; to Jaime, for being my PhD fellow, the one I can discuss with about important things and the only one I have a full understanding with; to Pedro and Víctor, for their kindness and invaluable work in the field; to Rafael Domingo, for his wise advice and experience in agronomy; to Raúl Zornoza, for his warmth, cordial attention and collaboration; to Antonio Lozano Guerrero, for letting me use his equipment and trying to help me when I was lost at the beginning of this adventure; to Martin Oates, for bringing me experience, cutting-edge technology and constant ideas; to Mari Carmen Ruiz, for being of great support from the mathematical side and for our great understanding; and to Shmulik, a famous scientist that was present in many papers of my bibliography and that I ended up meeting while eating burritos in San Antonio, Texas. He brought me invaluable knowledge and friendship, and always took me seriously despite being a newbie.
To my mentors on my debut as a university lecturer: Roque, José Luis and Julio. Thanks for your patience, humbleness, trust, generosity and good deeds. To the rest of the people from the UPCT I have shared moments with or have tried to help me. To José Alfonso, Villa, Esther and Antonio Mateo; my lab mates: Sergio Tárraga, John Paul, Fran Calatrava, Alejandro Castro, Isa, Arantxa, Sandra, Fran (a.k.a KFC) and Blanca; to the laboratory technicians Andrés, Pablo, Juan and José Juan; to Ana Belén Viudes for her joy and help with the paperwork; to my student Javier Garrido for his valuable work; to Marisa Rubio, Trini Galera and Yolanda Méndez for their thorough management; to Ana G. Garre and Antonio M. Lozano for our mutual support in this process; to Antonio S. Kaiser, for introducing me in research and teaching me the great truth that “research is 29 days of sorrow and one day of joy, but on that day of joy you are the happiest person in the world”.
To Rodrigo, Elena, Antonio and Fran for encouraging me to embark on this adventure. To my very friends Juan, Andrea, Juan G.T., Pedro, Lola, Mae, Yogui, Julia, Eli, Ángel, Quini, Cris, Rafa, Mario, Pepe and Rubén.
To my family and my brother.
To my parents, for investing not money, but effort, their own discomfort, time and discipline in my education. Here is the proof that you did better than anyone could advice.
To Miriam and my buddy Skye, for supporting this with so much love, pain and patience.
This thesis has been supported by the different funding sources listed below:
- Ministerio de Educación y Formación Profesional, grant number: FPU17/05155;
- Agencia Estatal de Investigación (AEI), project numbers: AGL2016-77282-C3-3-R, PID2019-106226-C22, AEI/https://doi.org/10.13039/501100011033;
- Ministerio de Economía y Competitividad (MINECO), project number: AGL2013-49047- C2-1-R;
- Polish National Agency for Academic Exchange, grant number: PPI/APM/2018/1/
- 00048/U/001;
- Roque Torres Sánchez personal funds from Universidad Politécnica de Cartagena;
- Scott B. Jones personal funds from Utah State University.
This thesis is framed in a period of my life in which my artistic facet has been centred on photography. Thus, my learning about the interaction of electromagnetic fields with the soil, Precision Agriculture and photography started at the same time and went hand in hand. Therefore, inspired by the format chosen by my friend Antonio M. Lozano in his PhD dissertation, each chapter cover and the main cover of this thesis is accompanied by a photograph taken in my different adventures during this time, either related with water, soil or landscape. Please, use them with proper citation and explicit permission.
Contents
Resumen ... i
Abstract ... iii
CHAPTER 1. MOTIVATION AND OBJECTIVES ... 1
CHAPTER 2. STATE OF THE ART ... 6
1. Crop water stress estimations ... 7
2. Available methods for determination of soil moisture ... 9
3. Dielectric soil moisture sensors challenges ... 10
3.1. Soil spatial variability ... 11
3.2. Parameters affecting the soil dielectric response ... 13
4. The interest of the frequency domain ... 16
5. Dielectric modelling ... 18
CHAPTER 3. ORIGINAL SCIENTIFIC ARTICLES ... 20
Article I. Design and Calibration of a Low-Cost SDI-12 Soil Moisture Sensor ... 23
Article II. Dielectric Spectroscopy and Application of Mixing Models Describing Dielectric Dispersion in Clay Minerals and Clayey Soils ... 43
Article III. Measurement of the broadband complex permittivity of soils in the frequency domain with a low-cost Vector Network Analyzer and an Open-Ended coaxial probe ... 77
Article IV. Prediction of Water Stress Episodes in Fruit Trees Based on Soil and Weather Time Series Data ... 92
CHAPTER 4. CONCLUSIONS ... 115
CHAPTER 5. REFERENCES... 118
CHAPTER 6. OTHER PUBLICATIONS AND MERITS ... 134
APPENDIX. IMPACT FACTOR ... 140
Abbreviations
Abbreviation Description
2D Two dimensions
3D Three dimensions
ANN Artificial neural network CWSI Crop water stress index
DC Direct current
DL Double layer
DNA Deoxyribonucleic acid
DOY Day of the year
DPHP Dual probe heat pulse
EM Electromagnetic
ETo Reference evapotranspiration
FD Frequency domain
FDR Frequency domain reflectometry GDR Generalized dielectric response GPR Ground penetrating radar
MDS Maximum daily shrinkage
ML Machine Learning
MW Maxwell-Wagner
NMR Nuclear Magnetic Resonance
OWL Open-Water-Liquid
PCB Printed circuit board
PVS Polder van Santen
RDI Regulated deficit irrigation
RF Random forest
RH Relative Humidity
RMSE Root mean square error
SF Sap flow
SVM Support vector machine
TD Time domain
TDR Time domain reflectometry
TDT Time domain transmission TDV Trunk diameter variation
TGR Trunk growth rate
VNA Vector network analyser VPD Vapour pressure deficit
Symbols
Symbol Description
Ka Apparent permittivity R2 Coefficient of determination 𝑆𝑆11∗ Complex S11 reflection parameter VT Total volume of soil
VW Volume of soil water
α Heuristic parameter in the Sihvola-Kong mixing model ε Absolute dielectric permittivity
ε' Real part of the absolute dielectric permittivity ε'' Imaginary part of the absolute dielectric permittivity ε0 Dielectric permittivity of the vacuum
εbw Dielectric permittivity of bound water εeff Dielectric effective permittivity
εr* Complex relative dielectric permittivity εr' Real part of the relative dielectric permittivity εr'' Imaginary part of the relative dielectric permittivity
εr,rel'' Imaginary part of the relative dielectric permittivity due to relaxation εr,s Relative dielectric static permittivity
θv Soil water volumetric water content ρb Soil dry bulk density
σa Apparent electrical conductivity σDC Direct current electrical conductivity ΨL Leaf water potential
Ψm Soil matric water potential Ψstem Midday stem water potential
ω Angular frequency
i
Resumen
El agua es una sustancia clave para el desarrollo de la vida en La Tierra. Es por ello que la búsqueda de oportunidad de vida en otros planetas y satélites se basa en la presencia de agua en los mismos. La gestión ecológica del agua es necesaria para la sostenibilidad de los ecosistemas. Uno de los ecosistemas más amplios y donde el agua juega un papel más importante es el suelo, que alberga multitud de variedades de microorganismos cuya actividad, en parte resultante en la generación de nutrientes para el desarrollo de las especies vegetales, es totalmente dependiente del contenido de agua en el suelo.
En zonas áridas y semiáridas, como es el caso de la cuenca Mediterránea, la escasez de agua supone un grave problema a la hora de gestionar los pocos recursos hídricos disponibles. En este caso, donde las condiciones geográficas son idóneas para el desarrollo de la agricultura, las soluciones pasan por una optimización de las técnicas de riego y un mayor control sobre los recursos hídricos. En este sentido, las técnicas de riego deficitario controlado se han mostrado exitosas en la reducción de la dotación hídrica a los cultivos en fases no críticas. Sin embargo, para realizar una aplicación prudente y eficiente de las mismas, resulta necesario monitorizar el estado hídrico de los cultivos, con el objetivo de que éstos no alcancen situaciones de estrés irreversible en términos de producción o estado vegetativo. Los indicadores que mayor información aportan sobre el estado hídrico de la planta suelen estar relacionados con variables medibles a partir de la propia planta, pero que son difícilmente automatizables debido a las operaciones de manejo asociadas. Este es el caso del potencial hídrico de tallo a mediodía medido con cámara de presión, considerado hasta la fecha como el indicador más fiable del estado hídrico de los cultivos en general. Es por ello que, para lograr una monitorización continua de esta variable, se busquen otras variables del continuo suelo-planta-atmósfera que puedan estar relacionadas y a partir de las cuales obtener una estimación indirecta.
El suelo es la matriz de donde la planta adquiere la mayor parte del agua y los nutrientes que necesita para realizar la fotosíntesis. La relación entre el estado hídrico del suelo y el estado hídrico de los cultivos está más que demostrada. Sin embargo, la precisión alcanzada en los modelos de correlación entre ambos estados requiere de una mejora considerable para hacer un uso realmente fiable de los mismos, y esta mejora no solo pasa por encontrar mejores métodos de correlación, sino también por mejorar la precisión de las medidas obtenidas del suelo.
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Para monitorizar el estado hídrico del suelo, existen diversas metodologías que ofrecen parámetros medibles como el contenido de agua. El método de medida más extendido para monitorizar el contenido de agua en el suelo es a través del uso de sensores dieléctricos. Sin embargo, la precisión de los mismos está sujeta a diversos factores, entre ellos las características propias del suelo donde se instalan y su coste, relativamente alto para el pequeño y mediano agricultor, condicionando una implantación extensiva de la Agricultura de Precisión y limitando a veces la aplicación de algunos desarrollos únicamente a trabajos de investigación.
Esta tesis, elaborada bajo la modalidad de compendio de publicaciones, aborda a través de cuatro artículos científicos la propuesta de soluciones accesibles para la medida del estado hídrico del suelo, con especial enfoque en el contenido de agua; explora las limitaciones y retos asociados con la calibración de los sensores dieléctricos de suelo; participa en la generación de nuevos conocimientos y propuestas para un mejor entendimiento del comportamiento del agua en el suelo y de su interacción con las ondas electromagnéticas; y establece nuevos enfoques y modelos que mejoran la predicción del estado hídrico de los cultivos a partir de medidas indirectas y automatizables en suelo y atmósfera.
Juan Domingo González Teruel, 4 de julio de 2022
iii
Abstract
Water is a fundamental substance for the development of life on Earth. That is why the search for life on other planets and satellites is based on the presence of water on them. Ecological water management is necessary for the sustainability of ecosystems. One of the most extensive ecosystems where water plays a major role is soil, which hosts a large variety of micro-organisms whose activity, partly resulting in the generation of nutrients for the development of plant species, is totally dependent on the water content of the soil.
In arid and semi-arid regions, as it is the case in the Mediterranean basin, water scarcity is a serious problem when it comes to managing the few water resources available. In this case, where the geographical conditions are ideal for the development of agriculture, the solutions involve optimization of irrigation techniques and greater control over water resources. In this sense, regulated deficit irrigation strategies have proven to be successful in reducing the water supply to crops in non-critical periods. However, in order to apply them prudently and efficiently, it is necessary to monitor the water status of the crops, so that they do not reach irreversible stress situations in terms of yield or vegetative state. The indicators that provide the highest amount of information on the water status of the plant are usually related to variables that can be measured from the plant itself, but which are difficult to automate due to the labor and time-consuming associated operations. This is the case of the midday stem water potential measured with a pressure chamber, considered to date to be the most reliable indicator of the crop's water status in general.
In order to achieve a continuous monitoring of this variable, it is necessary to look for other variables of the soil-plant-atmosphere continuum that may be related and from which to obtain an indirect estimate.
Soil is the matrix from which the plant acquires most of the water and nutrients it needs for photosynthesis. The relationship between soil water status and crop water status is well established.
However, the accuracy achieved in the correlation models between the two requires considerable improvement to make a truly reliable use of them, and this improvement is not only to find better correlation methods, but also to improve the accuracy of the measurements obtained from the soil.
To monitor soil water status, there are several methodologies that provide measurable parameters such as water content. The most widespread measurement method for monitoring soil water content is through the use of dielectric sensors. However, the accuracy of these sensors is subject to various factors, including the characteristics of the soil where they are installed, and their
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relatively high cost for small and medium-sized farmers, conditioning the extensive implementation of precision agriculture and sometimes limiting the application of some developments only to research work.
This thesis, elaborated under the modality of a compendium of publications, addresses through four scientific articles the proposal of affordable solutions for the measurement of soil water status, with special focus on water content; it explores the limitations and challenges associated with the calibration of soil dielectric sensors; participates in the generation of new insights and proposals for a better understanding of the behavior of water in soil and its interaction with electromagnetic waves; and establishes new approaches and models that improve the prediction of crop water status from indirect and automatable measurements in soil and atmosphere.
Juan Domingo González Teruel, July 4th 2022
CHAPTER 1 MOTIVATION AND OBJECTIVES
La Contraparada, Javalí Nuevo, Murcia, Spain.
Chapter I Motivation and objectives
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Water is the substance that supports all living organisms on Earth. Its molecular structure confers a polar nature that makes it a unique resource for the development of the processes and structures necessary for life. Water contributes to 45−70% of the human being body weight (Schloerb et al., 1950; Schoeller, 1989; Van Loan et al., 1993) and whereas a person could survive up to 30 days without food, it would not be possible for more than 3 days without water. Due to its polar characteristics, water is considered to be a “universal solvent”, and acting like that it helps biological cells on transport and use of other substances like oxygen and nutrients. Additionally, water plays a critical role as a structural component in biological and physical systems, as cells turgor, supported by water forces, is essential for biochemical processes, whereas cellular membranes arrangement, proteins structure or DNA shape would not be possible without the lead of water molecules (Sargen and Utter, 2019).
Water is an important participant in soil processes, from substrates transport to soil microbial activity. Soil microorganisms contribute to organic carbon sequestration in soil, reducing the enrichment of atmospheric CO2 (Lal, 2004), and participate in chemical processes which make nutrients available for plants from organic matter content decomposition. The lack of water hinders microbial activity and growth (Bottner, 1985; Kieft et al., 1987), disrupts microbial community structure (Hueso et al., 2012; Sorensen et al., 2013) and reduces nitrogen and carbon mineralization (Paul et al., 2003; Pulleman and Tietema, 1999; Sleutel et al., 2008; Yan et al., 2015). Likewise, abundance of water in soil complicates oxygen diffusion, reducing the activity of aerobic microorganisms (Kozlowski, 1984; Skopp et al., 1990) and creating an environment more susceptible to the growth of anaerobes (Yan et al., 2015). The interaction of soil water with soil living organisms is unavoidably related to soil salinity. High concentration of soluble salts in soil water leads to a more negative osmotic potential, making it more difficult for roots and microbes to draw water from soil. Also, biological membranes are permeable to water (Oren, 1999), so that when exposed to hypertonic conditions, i.e., the extracellular brine salt concentration is higher than the intracellular, cells lose their volume and structure through plasmolysis as the water moves out of the cells to balance the salt concentration (Yan et al., 2015).
Water is also involved in many chemical reactions of living organisms, being photosynthesis one of the most relevant for all life forms as the main energy provider. The sun is the ultimate source of all metabolic energy on Earth. Through photosynthesis, plants synthetize carbohydrates from atmospheric CO2 and soil water, also producing O2 to counterbalance the CO2 emitted to the atmosphere in cellular respiration (Hall and Rao, 1999).
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The role of water in soil for life development is evident and crucial. The presence of water in Earth biosphere is abundant, being about 71% of Earth’s surface covered by water (U.S. Geological Survey, 2019). However, not all of this water is initially available for plants and soil microorganisms, since about 96.5% of water global reserves are held in the oceans as saline water, whereas only 2.53% corresponds to fresh water, approximately, with a large fraction of it (68.7%) in the form of ice and permanent snow in the Arctic and Antarctic regions (Shiklomanov, 1993). The global fresh water potentially available for plants, coming from ground water, mountain regions, lakes, swamps, river flows and the atmosphere, together with soil moisture, is estimated to be approximately 10,704,600 km3, which corresponds to 30% of the fresh water in the hydrosphere and 0.77% of total water. Not so much the amount of fresh water available, but how it is globally allocated is a major concern, especially in arid and semi-arid populated regions, where water availability has to supply human consumption, agricultural and livestock demand, industrial uses and energy generation, mainly. Climate change is undoubtedly affecting global water resources and future projections suggest the increasing drought risk in this kind of regions (Gerten et al., 2007).
As the main fresh water consuming activity, agriculture needs to adapt to this challenging scenario of limited water resources and it is globally assumed that solutions must be associated to increasing the efficiency of water use. Consequently, deficit irrigation strategies (Blanco et al., 2020, 2019b; Ruiz-Sanchez et al., 2010) and precision irrigation based on monitoring the soil-plant- atmosphere continuum with sensors have proven successful in this regard (Vera et al., 2017). When applying deficit irrigation, both soil and crops are subjected to a water stress that has to be kept at control thresholds if irreversible damage to the plant is not desired. Thus, monitoring soil and crop water status is essential for effective and safe management of water resources without compromising soil and crop integrities.
Soil moisture can be measured in many ways, from the reference thermo-gravimetric method to the use of sophisticated radioactive devices, such as the neutron scattering probe. However, among them, the dielectric techniques stand out as they allow for easy in-situ measurements and installation with almost no training required for operation; the devices can be automated, thus allowing for continuous monitoring; and superior accuracy to within 1 – 2% of volumetric water content (θv) can be obtained.
The reference method to estimate crops water status is through the measurement of the midday stem water potential (Ψstem) with a pressure chamber (Shackel et al., 1997). However, this method is destructive and time and labor-consuming, as well as non-automatable. Therefore, in order to have a continuous monitoring of crop water status, models that relate Ψstem with other automatable
Chapter I Motivation and objectives
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measurements from the soil-plant-atmosphere continuum, such as those provided by the soil dielectric sensors, are required.
Soil dielectric sensors are commonly used to measure soil water content, bulk or apparent electrical conductivity (σa) and soil matric potential (Ψm), making use of a calibrated porous ceramic matrix for the latter. Four major topics and concerns surrounding dielectric soil sensors can be summarized from the literature: (i) cost, (ii) calibration, (iii) principle of operation and (iv) installation procedure.
On the one hand, soils are well-known to be heterogeneous media and soil dielectric sensors do not have a large volume of influence as do have Ground Penetrating Radar (GPR) or the neutron scattering probe. For field scale purposes, this makes the spatial information obtained strongly dependent on the number and distribution of sensors installed in the soil. The cost of commercial sensors limits their massive deployment and also constitutes an economic barrier to the implementation of Precision Agriculture for small and medium farmers. Therefore, alternative low- cost solutions are demanded.
On the other hand, several challenges and questions associated to the soil water content to dielectric permittivity calibration, in terms of calibration procedures and physical variables influencing the soil dielectric response are yet to be solved and open to discussion. D.H. Lawrence (1929), in his book Pansies, wrote: “Water is H2O, hydrogen two parts, oxygen one, but there is also a third thing that makes it water and nobody knows what it is.” Interactions of water with other substances and under certain conditions are still unsolved and their contribution to soil dielectric behaviour is of major interest, not only to solve the calibration challenges and enhance the accuracy of soil moisture dielectric sensors, but also to get new physico-chemical information from the soil and estimate other physical parameters. Within the dielectric techniques, it is assumed that Time Domain Reflectometry (TDR) is the most robust and accurate option. Nonetheless, the under- explored frequency domain offers a different point of view, from which the influence of some of these physical parameters seems more evident and promises to be a source of new information worth investigating further.
This doctoral thesis aims to contribute to addressing and providing alternative perspectives to the challenges and discussions described above, by setting the following objectives:
- To develop affordable solutions for soil water content measurement in order to make Precision Agriculture more economically accessible.
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- To provide new insight in soil and porous media dielectric properties for a better understanding of soil dielectric sensors behavior, limitations and challenges, as well as to highlight their calibration needs.
- To explore and evaluate new information provided by frequency domain dielectric spectroscopy to tackle soil moisture dielectric sensors challenges and to dig into new sensing opportunities of other soil physical properties.
- To demonstrate that crops water status can be effectively, indirectly and continuously estimated from easy, automatable and low-maintenance measurements, making exclusive use of soil dielectric sensors and weather stations.
CHAPTER 2 STATE OF THE ART
Upper Bangor, Bangor, Gwynedd, Wales, UK.
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1. Crop water stress estimations
The water held by plants in their tissues is critical to ensure enough cell turgor for structural purposes and evapotranspiration, and osmotic potential for water transport to the leaves for photosynthesis accomplishment (Shackel et al., 1997; Steudle, 1997). A dehydration of plant tissues would lead to a loss of cell turgor and consequently to a reduction of plant growth motivated by a lower stomatal opening and expansive growth (Shackel et al., 1997). Despite this risk, over the last 40 years several authors have studied the effect of this water deficit on plant physiology with the aim of making more efficient use of water and controlling vegetative growth, obtaining satisfactory results (Antunez-Barria, 2006; Bacelar et al., 2012; Blanco et al., 2020, 2019a, 2019b; Blaya-Ros et al., 2021; Chalmers D.J. et al., 1981; Chen et al., 2022; Conesa et al., 2021, 2016; Domingo, 1994;
Naor, 2006; Ruiz-Sanchez et al., 2010). However, these studies have revealed certain plant water deficit limits that should not be trespassed in determined moments if the integrity of the crop is not to be endangered by permanently limiting its growth or affecting the quantity and quality of the yield. Therefore, a physical indicator that provides relevant information about this crop water stress is required.
The proposal of Shackel et al. (1997) to measure Ψstem with a pressure chamber as an index of plant water status is still considered as the reference method. However, this practice is time and labor consuming as well as non-automatable, which prevents from a constant monitoring of plant water status, required for practical application of Regulated Deficit Irrigation (RDI) strategies and the proper control of crops integrity in water-scarce conditions. The proposed solutions in the literature involve the identification of other physiological crop water indicators of the soil-plant- atmosphere continuum, whose monitoring does allow for automatic measurement and which also offer information as relevant as that provided by Ψstem. Leaf water potential (ΨL), Sap Flow (SF) and leaf turgor pressure are other indicators, directly measured in the plant, that have been used to estimate crop water status. However, ΨL was reported to have high degree of variability under field conditions (Shackel et al., 1997; Smart and Barrs, 1973) and opposite response to the one expected according to the applied irrigation treatments (Jones et al., 1983), as it was the case reported by Garnier and Berger (1985) in peach trees, where Ψstem indicated differences between the wet and dry treatment trees, whereas ΨL did not. Ortuño et al. (2010) reported a higher mean noise for SF than for ΨL and trunk Maximum Daily Shrinkage (MDS), measured in peach trees during an irrigation withholding of nine days. Additionally, SF sensor probes are nailed to the trunk, which heals after several months, making the sampling area not representative anymore. When trying to remove the probe from the trunk in order to install it at another point, it often breaks, so that the sensors are
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not very durable and require frequent relocation. Leaf turgor pressure sensors, which measure the leaf cells hydrostatic pressure (Zimmermann et al., 2008, 1969) are not capable of measuring excessively negative potentials, thus limiting their use to detect severe crop water stress conditions.
Padilla-Díaz et al. (2016) performed irrigation scheduling in olive trees based on leaf turgor pressure measurements made with the ZIM probe and compared these measurements with those obtained for Ψstem with a pressure chamber, suggesting that crop water stress monitoring should not rely on absolute turgor pressure values, at least for the case of study. Additionally, the leaf turgor pressure has not been numerically correlated with Ψstem yet, but the curve shape in a timeline is related with Ψstem thresholds in a subjective visual process (Fernández et al., 2011). Despite potentially accurate estimators of crop water status, the devices used to get these alternative indicators are neither feasible to implement nor robust enough to manage deficit irrigation strategies on commercial farms. Therefore, several studies have looked for relationships between other physical variables and stem water potential and tried to obtain models that allow the latter to be estimated accurately.
Intrigliolo and Castel (2004) made use of soil matric potential (Ψm) and short-period Trunk Diameter Variation (TDV), based on MDS and Trunk Growth Rate (TGR), to estimate Ψstem, obtaining reasonable but limited correlation between Ψm and Ψstem along the season (R2 = 0.62); and a better correlation with TDV, with R2 = 0.89 for MDS during most of the fruit growth period, although it was considerable worsened in the period after harvest (R2 = 0.73 – 0.52), as the value of MDS reduced. Looking for SF, MDS and Ψstem baselines for irrigation scheduling, Ortuño et al.
(2006), also studied the correlation of Ψstem with other soil-plant-atmosphere continuum variables in lemon trees. Thus, determination coefficients of 0.66, 0.43, 0.39, 0.60, 0.55, 0.78, 0.65 were obtained with solar radiation, daily mean air Vapour Pressure Deficit (VPD), midday VPD, daily mean air temperature, midday air temperature, MDS and daily SF, respectively. Abrisqueta et al.
(2015) estimated Ψstem from the soil water content measured with a neutron scattering probe (Gardner and Kirkham, 1952) at eight different soil depths and considering the specific irrigation treatment and Day of the Year (DOY) in the model, obtaining an R2 = 0.74. Correlations were also stablished with agro-meteorological variables, such as mean air temperature and relative humidity, solar radiation, mean VPD, crop reference evapotranspiration (ETo) and growing degree hours accumulated, obtaining an R2 = 0.56. An intermediate performance was obtained when combining VPD, growing degree hours accumulated and soil moisture average throughout the eight soil depths (R2 = 0.72). Carrasco-Benavides et al. (2020) studied the relationship between cherry tree leaves temperature, measured with thermal infrared cameras, and Ψstem, observing a linear correspondence between them, but showing a very low coefficient of determination (R2 = 0.35 in the best case).
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Ben-Gal et al. (2009) also resorted to thermal imagery to estimate Ψstem in olive trees, correlating it with the canopy temperature and analytical and empirical Crop Water Stress Indexes (CWSI), obtaining an R2 = 0.52 in the best case.
All the studies mentioned above made use of simple and multiple linear regression analysis, yet recent works employed more sophisticated modelling approaches. For instance, Valdés-Vela et al.
(2015) applied soft-computing techniques on agro-meteorological and soil water content data to estimate Ψstem. A fuzzy modelling fed with soil water content at 0.3 m depth, DOY and the mean daily air temperature resulted in an estimation of Ψstemwith RMSE = 0.16. Martí et al. (2013), also using agro-meteorological and soil moisture data, applied Artificial Neural Networks (ANN) modelling to compute Ψstem, improving the estimation performance found in the literature for similar input variables.
As reported in the literature described above, the single use of agro-climatic variables and soil water information leads to models capable of efficiently predicting Ψstem, although there is still room for improvement, especially if we take into account the current potential of Machine Learning (ML) techniques, which are on the rise thanks to up-to-date computational capabilities. Moreover, the estimation of Ψstem has always been approached as a problem based on one-time single measurements, whilst the variables related to the soil-plant-atmosphere continuum show in most cases time-delayed transitions. Thus, it is of particular interest to assess the ability to estimate Ψstem
using simplified measurement systems, based only on soil sensors and weather stations, making use of artificial intelligence algorithms and novel modelling approaches.
2. Available methods for determination of soil moisture
As described in the previous section, the water available in soil is strongly related with the crop water status, being a relevant source of information about the plant soil water intake behavior, so the accurate measurement of soil moisture is critical for a precise estimation of Ψstem. From the soil physics perspective, soil is defined as a three-phase particulate and porous system with a solid phase that constitutes the soil matrix, a liquid phase that consists of soil water or soil solution (soil water + dissolved substances) and a gaseous phase that is considered as the soil air (Or et al., 2022).
The state of water in soil is characterized by the amount of water and the energy it is held in the soil with. Soil water content or soil moisture, which refers to the amount of water held in the soil, can be defined in a gravimetric or volumetric basis. For irrigation purposes and soil agricultural management, the volumetric basis is generally preferred, since the water amounts processed are
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normally expressed in volume. The soil volumetric water content, θv, defined as the volume of water filling the soil pores (VW) divided by the total volume of the soil (VT), can be obtained in many ways. However, all of them rely on the reference gravimetric or thermo-gravimetric method, which consists of oven-drying the soil sample at 110 ± 5 ºC until a constant weight is achieved (ASTM, 1998), although it is generally assumed that after 24 h it is sufficient (S.U. et al., 2014). The drawback of this method is that it is laboratory-based and it cannot be used for field constant monitoring applications.
Among the alternative methods for soil moisture measurement, radioactive techniques, such as neutron scattering and gamma attenuation (Gardner and Kirkham, 1952), thermal methods, like the Dual Probe Heat Pulse (DPHP) (Campbell et al., 1991; He et al., 2018; Naruke et al., 2021; Ochsner et al., 2003; Tarara and Ham, 1997), optical methods (polarized light technique, fibre optic sensors and near-infrared sensors (Kaleita et al., 2005; Robinson et al., 2008; S.U. et al., 2014; Zazueta and Xin, 1994)), Nuclear Magnetic Resonance (NMR) (Bird et al., 2005; Bloch, 1952; Hinedi et al., 1999, 1993; Legchenko et al., 2004, 2002; Purcell, 1952) or Electromagnetic (EM) techniques can be found in the literature and are commercially available. However, for constant monitoring purposes, only DPHP, optical methods and EM sensors are feasible. Among the optical methods, the polarized technique and near-infrared sensors, due to their principle of operation, are limited to provide only surface measurements (Robinson et al., 2008), so they present difficulties to be used for subsurface measurements, where most of the soil-plant interaction takes place. Fibre optics sensors can indeed be buried into the soil, but their measurement volume is extremely reduced (Robinson et al., 2008).
DPHP is a very flexible method with many potential applications that has been widely developed in the last 30 years and that allows to obtain several soil physical properties, such as heat and water flux (Cobos and Baker, 2003; Ochsner et al., 2003; Yang et al., 2013), subsurface evaporation rate (Heitman et al., 2008) and thermal properties (Ochsner et al., 2007; Yang et al., 2013), apart from soil moisture. However, the resolution offered for the latter is lower than that of EM technologies, which makes them be the preferable method for subsurface soil moisture monitoring.
3. Dielectric soil moisture sensors challenges
EM soil moisture sensors can be divided into two main sensing principles: the measurement of the soil electrical resistivity/conductivity (Wenner method (Wenner, 1915)) and the measurement of the soil dielectric permittivity. The resistivity method is highly affected by soil salinity and it is, in fact, the preferable method to measure it (Mualem and Friedman, 1991), so it is rarely used to measure soil moisture anymore. The dielectric sensors base their sensing principle on the great difference between the dielectric permittivity (ε) of water and that of air. The relative static
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permittivity (𝜀𝜀𝑟𝑟,𝑠𝑠) of water at 25 ºC is around 78 (Kaatze, 1989), whereas the one of air is assumed to be 1, as well as that of a vacuum. Since the soil is a porous matrix whose pores can be filled with water and air, the bulk permittivity of a soil is highly dependent on the proportion of pores filled by water, that is, the soil water content.
In comparison to all other methods for soil water content measurement, dielectric sensors combine most of the conditions which are suitable for use in soil monitoring applications. Their electrical nature makes them easily automatable; they require no external operation or maintenance beyond installation, except for GPR, which requires high degree user knowledge (Robinson et al., 2008); they are generally highly accurate (up to ±0.01 m3 m-3 with soil specific calibration)(10 HS Soil Moisture Sensor Manual, 2016, 5TE Water Content, EC and Temperature Sensor Manual, 2016, GS1 Soil Moisture Sensor Manual, 2015; Baumhardt et al., 2000); and they provide great flexibility in adapting the probe geometry to very specific conditions, such as measurements at different soil profile depths (Chavanne and Jean-Pierre, 2014; Kafarski et al., 2018; Kojima et al., 2016) or larger or smaller volumes of influence.
However, two main challenges can be addressed to soil dielectric sensors, which are their limited volume of influence and the impact of other EM and soil physical properties, different from water content, in the soil dielectric response.
3.1. Soil spatial variability
Among the dielectric techniques, one can find time domain and frequency domain methods as well as GPR. Time Domain (TD) is well represented by TDR, largely considered the reference dielectric method (Robinson et al., 2003), and Time Domain Transmission (TDT) (Blonquist et al., 2005); whereas in the Frequency Domain (FD), capacitive (Bogena et al., 2007; Eller and Denoth, 1996; Kargas and Soulis, 2011; Oates et al., 2014) impedance-based sensors (Chavanne and Jean- Pierre, 2014) and Frequency Domain Reflectometry (FDR) (Campbell, 1990; Lewandowski et al., 2019; Seyfried et al., 2005; Skierucha and Wilczek, 2010; Szypłowska et al., 2013; Woszczyk et al., 2019) are the main categories found in the literature. TDR and the different implementations of the FD method are the most usual commercially available sensors for Precision Agriculture and soil surveys because of their relatively low cost and easy operation. Their cost (several hundred euro for capacitive, impedance-based and new generations of electronics-embedded TDR sensors, and several thousand euro for classic TDR devices) is low in comparison with the majority of alternative soil moisture measurement technologies (e.g. a GPR unit typically costs over 10,000 euro).
However, they are still non-affordable for Precision Agriculture implementation by small and medium farmers. Moreover, despite the fact that the design of the probe geometry can provide with
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larger or smaller sampling volumes, the volume of influence of TDR and FD sensors is generally in the range of 0.01 – 1 dm3 (Huisman et al., 2001), resulting in point measurements, although soil profile sensors typically include several single sensors allocated at different depths (Campbell Scientific Ltd., 2021; Sentek Technologies, 2020), thus enlarging the volume of influence of the sensor as a whole.
Soil is well-known to be a heterogeneous medium with great spatial variability (Schulz et al., 2006). Therefore, point measurements are very likely to be dependent on the specific characteristics of the installation point and, depending on the soil structure, not fully representative. Bogena et al.
(2006) raised the need for terrestrial observatories implementation for studying the impact of land use changes and climate change, describing processes controlling matter fluxes in the soil-plant- atmosphere continuum or promoting and supporting the development of early warning systems (flooding, fresh water quality, etc.). To that end, they emphasized the need of including plot scale soil moisture sensor networks based on TDR and FD sensors and multi-depth soil moisture monitoring. Galagedara et al. (2012) performed a soil subsurface mapping experiment by combining TDR and borehole GPR measurements in a sandy loam soil, finding a soil moisture change variability of up to 5% at 1 m depth along an horizontal line during a wetting process, and a soil volumetric water content variation of up to 0.2 m3 m-3 over a 12 m3 volume, according to GPR tomographs. Bogena et al. (2010) installed an extensive soil moisture sensors network with a total of 900 capacitive sensors distributed at three different soil depths (5, 20, and 50 cm), with two sensors per depth at a separation of 5 cm and ensuring a minimum of 300 sensor units in a 60 x 60 m raster, considering all soil depths and duplicates. They showed that the soil water content spatial variability was relatively high and the variability at the 50 cm depth was significantly lower than that at 5 cm, suggesting that factors controlling the longer travel time reduce the spatial variability of the soil water content.
GPR allows a support for larger volumes (0.5 – 30 m3) (Chanzy et al., 1996; Du and Rummel, 1994; Van Overmeeren et al., 1997; Weiler et al., 1998), yet its cost is prohibitive for irrigation management purposes and soil constant monitoring. Besides, as the rest of dielectric methods, it requires of soil specific calibration for enhanced accuracy. This large sampling volume has itself an associated calibration challenge, since other forms of measurement with a smaller volume of influence are needed to calibrate it due to the impossibility of controlling θV over large volumes.
Hence, the solution for obtaining a more representative measurement of soil moisture around an area of interest, such as a tree radicular system, lies in the extensive use of small sampling volume sensors to create either a discretized 2D or 3D sensors network (Bogena et al., 2007). To this end,
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a significant reduction of the cost of the sensors is essential. Capacitive sensors normally work at frequencies lower than those of TDR (< 150 MHz) (Robinson et al., 2008) and this makes them more prone to be affected by conduction and polarisation phenomena in soils with high clay content and salinity. However, the greater simplicity of their circuitry and lower operating frequency results in a much lower cost (Kelleners et al., 2005), thus making them the starting point to obtain the lowest possible cost.
3.2. Parameters affecting the soil dielectric response
Topp, Davis and Annan, in their seminal paper (Topp et al., 1980), proposed a general equation that related an apparent permittivity (Ka) measured with a TDR sensor and θv with an error of estimate of 0.013, independently of soil texture, soil density, temperature and soluble salt content.
This equation has been misleadingly adopted as a standard for the calibration of all types of dielectric sensors, regardless of their principle of operation, the operation EM frequency and the experimental conditions, since the measurement conditions established in the experiments performed by Topp et al. (1980) cannot always be exactly reproduced, especially regarding the geometrical influence of the probe as it interfaces with the soil. Thus, commercial sensors that rely on Topp et al. (1980) calibration equation successfully estimate θV in the majority of mineral soils, but they provide misleading measurements in certain scenarios and soil specific calibration is generally recommended.
Several authors have experimentally shown deviations of the soil dielectric permittivity to soil water content relationship from Topp et al. (1980) equation. Jones and Friedman (2000) demonstrated that solid particles shape and orientation with respect to the applied EM field dramatically affect the bulk or effective permittivity (εeff) of the soil mixture. They used disk-shaped mica particles and a TDR system with 3-rod-based probes parallel and perpendicularly oriented to the bedding plane of the mica, in both cases the measured Ka lying well below the Topp et al. (1980) curve, thus evidencing the potential influence of high aspect ratio particles.
In mineral soils, particle shape is intrinsically associated with soil particle size distribution, since the particle shape is generally evolving from platy-like clay particles (< 0.002 mm, USDA) to more spherically shaped sand grains (0.05 to 2 mm, USDA) (Robinson and Friedman, 2002). The combined effect of oblate shape and smaller size leads the clay particles to have a greater specific surface area than silt and sand particles (Jury et al., 1991). The specific surface area of soil particles strongly influences their adsorptive abilities, since the larger the particles surface in contact with water, the higher the volume of water they can adsorb. Also, in the case of clay particles, their platy-
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like shape and mineralogy make them especially prone to held surface negative charges, which is an additional factor contributing to water bonding to the clays surface. The dipole nature of water molecules makes them held close to the solid phase surface, forming a layer of strongly bound water (Levitskaya and Sternberg, 2019). The orientation of these water molecules adsorbed on the solid phase surface and residual electrostatic forces leads to the formation of an additional loosely bound charge-oriented layer, giving rise to a Double Layer (DL) arrangement called ‘bound water’ (Wagner et al., 2013). The electrostatic forces hinder bound water dynamics, making it to have different properties than free or bulk water. Thus, bound water has greater density (1.2 – 2 g cm-3), greater viscosity, lower electrical conductivity and lower dielectric permittivity than free water (Cosenza and Tabbagh, 2004; Dyck et al., 2019; Hilhorst et al., 2001; Ishida et al., 2000; Jones and Or, 2002;
Levitskaya and Sternberg, 2019; Logsdon and Laird, 2002; Pennock and Schwan, 1969; Regalado, 2006).
Sposito (1984) exposed that according to the literature, bound water around mineral solids has an average value of ~20 for the static permittivity, with three or more layers of water being affected, depending on the mineralogy (Robinson et al., 2002) and Dirksen and Dasberg (1993) estimated that the permittivity of the first layer of bound water (the closest to the mineral) was likely similar to that of ice (εbw = 3.2). Due to the considerably reduced permittivity of bound water with respect to that of free water, the presence of bound water in soil tends to reduce εeff. Robinson et al. (2002) claimed that using a standard calibration equation such as that of Topp et al. (1980) for a soil with bound water could lead to a considerable underestimation of θV(0.05 – 0.10 m3 m-3). Bridge et al.
(1996) observed deviations from Topp et al. (1980) curve for Irving clay with θV underestimations of up to 0.08 m3 m-3 if Topp et al. (1980) equations was used and attributed this to the contribution of bound water.
Bound water is in turn affected by temperature, as it is the permittivity of free water, thus affecting εeff. The changes of air and soil solid particles permittivity with temperature is negligible in comparison to those suffered by free water. Therefore, it can be assumed that variations in εeff
because of temperature are due to changes in temperature-dependent water permittivity. However, a dual effect takes place when it comes to bound water and temperature on εeff. The static permittivity of water decreases as temperature increases (Kaatze, 1997). Hence, one would expect that a temperature decrease would lead to a reduction of εeff. Wraith and Or (1999) measured Ka in unsaturated sand and sandy clay mixture at different temperatures and observed that for the sand the effective permittivity decreased as temperature did, but found the opposite behavior for the sandy clay mixture. They suggested that in these conditions, Ka was the result of two competing
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phenomena: (i) the reduction of εeff with increased temperature; and (ii) the increase of free water proportion due to the liberation of bound water as a consequence of the temperature rise and a higher thermal molecular agitation.
Other deviations from Topp et al. (1980) equation were those shown by Dirksen and Dasberg (1993), who looking for bound water effects, ended up attributing these deviations to lower soil dry bulk density (ρb) values, whereas Bridge et al. (1996) pointed out the influence of ρb on cracking clays dielectric behavior and the proper influence of ρb on the amount of bound water.
Soil moisture dielectric sensors measurements are also affected by soil salinity. In the case of capacitive sensors and those operating at low frequencies (typically < 150 MHz), deviations from Topp et al. (1980) equation are expected for various reasons. On the one hand, the apparent permittivity (Ka) measured by Topp et al. (1980) with a TDR system is likely different from the one that can be obtained with capacitive and impedance-based sensors, since the physical derivation of the apparent permittivity responds to different principles. On the other hand, interfacial polarization, also known as Maxwell-Wagner effect (MW), typically occurs in the kHz to MHz range (Chen and Or, 2006; Sihvola, 1999) and generates a synergy effect, producing an effective permittivity of the soil mixture that can be even greater than the sum of the permittivities of the mixture components. This polarization, which occurs due to the accumulation of charge carriers at the interfaces of dielectrics (Levitskaya and Sternberg, 2019), is shown by soils with clay content, since clay particles tend to carry negative charges on their surface, and also when the soil aqueous phase presents electrical conductivity. Therefore, the permittivity measured by these low frequency sensors in saline soils, “enhanced” by the MW effect, is significantly higher than that obtained in the Topp et al. (1980) experiments, which were not affected by interfacial polarisation because TDR operates at superior frequencies (typically > 0.5 GHz (Robinson et al., 2008)), where MW effect does not show up. Nonetheless, TDR is affected by soil salinity differently. When used to measure lossy media, the length of TDR probes has proven to be critical (Robinson et al., 2003). Jones and Or (2004, 2001) demonstrated that with longer probes, the TDR waveform was so attenuated that the algorithms for obtaining the step signal travel time struggled with detecting the end reflection accurately, and therefore the soil moisture measurement was hardly reliable, requiring shorter probes and obtaining a smaller sampling volume consequently.
In view of all these parameters involved in the dielectric response of the soil, there is a clear need to propose solutions focused on trying to overcome the influence of these disturbing factors in the accurate estimation of soil moisture, but at the same time, the participation of this parameters in the soil dielectric behaviour opens a door to the estimation of other soil physical properties of
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interest different from water content. To address both paths, Reinhard Knöchel, in the foreword of Electromagnetic Aquametry, proposed the simultaneous measurement of as many independent electromagnetic parameters as there are soil properties to be estimated or controlled. In particular, he referred to the measurement of amplitude and phase of the EM signal at various frequencies.
Consequently, models that relate the dielectric permittivity with the soil water content and other soil physical properties should be further explored and enhanced, especially focusing on the frequency domain.
4. The interest of the frequency domain
The dielectric permittivity can be defined as the tendency of a medium to polarise under an electric field. When an EM field is applied to a homogeneous, isotropic, nonmagnetic medium, three different phenomena may occur: transport phenomenon, polarization phenomenon and energy dissipation (Levitskaya and Sternberg, 2019). The transport phenomenon is associated with the displacement of free or weakly bound charges and therefore with the electrical conduction. The polarization phenomenon consists in the storage of electrical energy of the medium, as a potential energy, due to the displacement and reorientation of charges under the electric field, generating dipole moments opposing the applied electric field. The energy dissipation or dielectric losses are a consequence of conduction and polarization. Part of the energy of the applied electric field is dissipated in the form of heat in the transport phenomenon, due to the so-called Joule effect, and the other part of the energy dissipation comes from polarization relaxation. Due to molecular interaction, after the electric field is applied, polarization requires a certain time to be accomplished, and different polarization mechanisms that take place in a specific medium have different associated times. This generates what is called polarization dispersion and a phase shift between the applied electric field and the polarization (Kupfer, 2004). Both conductivity and polarization relaxation depend on EM frequency in a complicated way (Levitskaya and Sternberg, 2019).
The dielectric permittivity is then frequency dependent and represented as a complex number (Robinson et al., 2005):
𝜀𝜀𝑟𝑟∗ = 𝜀𝜀𝑟𝑟′ − 𝑗𝑗𝜀𝜀𝑟𝑟′′= 𝜀𝜀𝑟𝑟′ − 𝑗𝑗(𝜀𝜀𝑟𝑟,𝑟𝑟𝑟𝑟𝑟𝑟′′ + 𝜎𝜎𝐷𝐷𝐷𝐷
𝜔𝜔𝜀𝜀0) (1)
where εr
* is the complex permittivity relative to that of a vacuum and εr' and εr'' are the real and imaginary components, respectively. The real part represents the energy storage and the imaginary part the dielectric losses. The imaginary part is in turn the addition of the losses due to conductivity (σDC/ωε0) and to polarization relaxation (εr, rel'' ), where ω is the angular frequency, σDC is the electrical
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conductivity under an applied Direct Current (DC) EM field and ε0 is the permittivity of a vacuum (ε0 = 8.854·10-12 F/m). The relationship between the absolute (ε) and relative permittivities is defined as follows:
𝜀𝜀𝑟𝑟 = 𝜀𝜀/𝜀𝜀0 (2)
Both ε’ and ε’' (and εr’ and εr’') are frequency dependent, either because of conductivity effects or polarization relaxation. Several polarization mechanisms can develop when an EM field is applied to a dielectric. In Figure 1, a schematic representation of ε’ in the frequency domain is depicted, where the possible relaxation mechanisms are presented. Note that the frequency bandwidths associated to the different polarization mechanisms in Figure 1 are approximated and can be shifted depending on the characteristics of the medium.
Figure 1.Schematic example of the polarization relaxation mechanisms on the real part of the permittivity in the frequency domain (from Levitskaya and Sternberg (2019)).
Soils are intricate media where a complex interplay between polarization mechanisms takes place.
Several authors have provided evidence that soil dielectric spectroscopy can inform about some of the soil parameters disturbing the estimation of θV and hence be used to estimate other soil physical properties or enhance the water content determination. Hallikainen et al. (1985) measured the complex permittivity of five different soil types between 1.4 and 18 GHz, showing clear influence of the soil texture in the dielectric response, especially below 5 GHz. They also tested the influence of temperature below 0 ºC, suggesting that the measured dielectric properties revealed that a fraction of the soil water phase remained liquid even at temperatures of -24 ºC. Campbell (1990) measured the complex permittivity of six different soils from 1 to 50 MHz, covering the range from sand to clay textures, by using a Vector Network Analyser (VNA) and a coaxial seven-rod probe, and showed a marked influence of soil texture in εr’ and εr’' values and in the εr’ dispersion, with