ASSESSING ROOTS DISTRIBUTION OF TART CHERRY TREE USING GROUND PENETRATING RADAR (GPR) AND ARTIFICIAL INTELLIGENCE By John Oludemilade Salako A THESIS Submitted to Michigan State University in partial fulfillment of the requirements for the degree of Geological Sciences – Master of Science 2023 ABSTRACT The importance of tree cultivation and management is necessary for the 21st century, given the need to sequestrate carbon and secure adequate food and raw materials productivity, which are part of the ecosystem services trees provide. This study improves upon previous studies and bridges the gap in assessing the roots of trees using non-invasive approaches. This study assessed the root distribution of Tart cherry trees using ground-penetrating radar (GPR) and artificial intelligence. Grid and cylindrical data collection and processing methodology were employed using the 800 MHz antenna frequency. Three mature trees were sampled from two Tart cherry fields in Michigan State (Clarksville and Traverse City). The reconstruction results revealed that the roots extend 30-45 cm deep in the soil. Furthermore, an Unmanned Aerial Vehicle (Matrix 100 drone) was used to obtain RGB aerial images from both fields. The findings of this study show that Tart cherry tree roots extend farther than the canopy size, as discussed extensively in this Thesis. A controlled experiment was developed to serve as ground truth in assessing the GPR's accuracy. The reconstructed result showed that the GPR accurately reconstructed and measured the depth the proxies were buried and the length of the root proxies. The biomass weight model estimator was another novel idea developed in this study. The model was developed using 115 root proxies, where the measured biomass length, width, and circumference were used as independent variables in predicting the weight of the biomass. Four regressor algorithms were used in developing the weight model. 5-fold cross-validation showed that the model performed optimally with an error of about 6% in the weight prediction. This study highlights the potential of GPR and artificial intelligence in assessing root distribution in Tart cherry trees, offering valuable insights for optimizing tree management and growth. This Thesis is dedicated to the only Majestic Potentate, JESUS CHRIST, the savior and LORD of my life, the wisdom before time began, and the wind beneath my wings. iii ACKNOWLEDGMENTS I want to express my deepest gratitude to my advisor, Professor Bruno Basso, for his comprehensive mentorship and guidance throughout my master’s program and this project. His wisdom and research acumen greatly assisted me in addressing challenges and answering specific research questions. I also extend my heartfelt appreciation to my committee members, Professor Allen McNamara and Dr. Anthony Kendall, whose invaluable input, teaching, and resource assistance contributed immensely to the success of this project. Furthermore, I would like to acknowledge Dr. Mine Dogan (Western Michigan University) for her assistance in helping me understand GPR principles and mentoring me on the collection and processing of the cylindrical data in particular. I am deeply grateful to Professor Michael Murillo, a distinguished Computational Scientist in the Department of Computational Mathematics, Science, and Engineering (CMSE), for his tireless efforts in mentoring and guiding me during the reconstruction and interpolation of the cylindrical coordinate. He was consistently available for impromptu Zoom calls to address my concerns, and I truly appreciate his kindness and dedication. I would also like to recognize and celebrate my colleagues and lab technicians who assisted me, especially during the data collection phase of this project. Their efforts significantly contributed to the completion of my thesis. I want to acknowledge Mukta Sharma, Susana Albarenque, Brian Baer, Richard Price, Ruben Ulbrich, Blair Van Agen, Ryan Jayne, Juliana Hanle, Paul Ojo, and Jac Stelly. My heartfelt appreciation goes to my parents, Pastor Abel Salako and Mrs. Juliana Salako, for their unwavering support, prayers, and encouragement throughout these two years and for passionately supporting my career growth from childhood. I pray that God Almighty protects iv them, keeps them healthy and strong, and enables me to care for them as they age. I would also like to thank my siblings, Mr. Isaiah Salako, Mr. Jude Salako, Mrs. Rhoda Oyerinde, and Ms. Faith Salako, for their immense support. I have had the pleasure of meeting some wonderful friends who contributed greatly to my well- being, including Chidiogo Azuka, Michael Alowakennu, Oluwafemi Abubakar, Prateek Sharma, Sunday Imosemi, Samin Abolmaali, and Ebenezar Okoyeocha. Thank you for your kindness and friendship. Finally, I would like to acknowledge my spiritual mentors, Pastor Gary Gauthier, and his wife, Mrs. Talisa Gauthier, whose weekly teachings of JESUS CHRIST helped me maintain my spiritual well-being during this period. I also acknowledge the music team and the entire congregation of the Pentecostals of East Lansing. v TABLE OF CONTENTS INTRODUCTION .......................................................................................................................... 1 CHAPTER 1: GPR DATA PROCESSES AND INTERPRETATION OF TART CHERRY TREE............................................................................................................................................... 7 1.1 Literature Review ............................................................................................................. 7 1.2 Data Collection Methodology ........................................................................................ 21 1.3 Data Processing Methodology ....................................................................................... 27 1.4 Results and Discussions ................................................................................................. 54 CHAPTER 2: CONTROLLED EXPERIMENT AND WEIGHT MODEL ESTIMATION OF BIOMASS ..................................................................................................................................... 61 2.1 Literature Review on Root Weight Model ..................................................................... 61 2.2 Materials and Methods ................................................................................................... 63 2.3 Results and Discussions ................................................................................................. 73 CHAPTER 3: SPATIAL RELATIONSHIP BETWEEN THE TART CHERRY TREE CANOPY AND ROOT .................................................................................................................................. 85 3.1 Site Location .................................................................................................................. 85 3.2 Materials and Methods ................................................................................................... 86 3.3 Results and Discussions ................................................................................................. 88 CHAPTER 4: CONCLUSIONS ................................................................................................... 92 BIBLIOGRAPHY ......................................................................................................................... 96 APPENDIX A: PYTHON CODE FOR USING THE VGG-16 CNN MODEL ........................ 100 APPENDIX B: AUTOMATION CODE FOR EXTRACTING TRACE NUMBER ................ 101 APPENDIX C: PYTHON CODE FOR RENAMING TRANSECTS ........................................ 102 vi INTRODUCTION Earth is home to a vast collection of plants and animals that contribute significantly to human growth and population, providing several ecosystem services. On a larger scale, trees offer provisioning, regulating, and cultural services to man and the environment (Boyd et al., 2013). Specifically, plants are responsible for generating oxygen for human consumption, extracting carbon dioxide we produce, and giving food and shelter to animals and humans. Also, plants are the basis of almost all world ecosystems. Consequently, plants play a huge role in keeping the planet’s atmosphere and climate balanced through photosynthesis. Furthermore, plants play crucial roles in air purification, water cycle, and soil management (Baró et al., 2014; McCarthy et al., 2011). Another vital ecosystem service tree offers is carbon sequestration. Agroforestry systems hold promise for sustaining productivity and capturing atmospheric carbon in trees and soil. The capacity to sequester carbon in tropical and temperate regions through agroforestry systems appears substantial. It is estimated that the above-ground components of the agroforestry systems can capture 2.1 x 109 Mg of carbon per year and 1.9 x 109 Mg of carbon per year in tropical and temperate biomes, respectively (Oelbermann et al., 2004). Furthermore, in a review of soil organic carbon sequestration, Lorenz & Lal (2014) gave an overview of soil organic carbon stored through different parts of trees. Their study explained how trees possess expansive root systems capable of growing deep into the soil. The carbon inputs derived from roots are essential for accumulating soil organic carbon in lower soil horizons. The Physicochemical interactions of root-derived carbon with soil particles tend to be more stabilized in the soil than the carbon derived from the stems of trees. Their research further provided more detail on the carbon stored in the soil by the roots. They explained how a particular European tree 1 root stores almost twice as much carbon in the soil than in the above-ground biomass. In addition to the proportion of carbon stored by both above-ground and below-ground biomass, they further explained that an elevated soil organic carbon pool could be achieved based on two strategies: firstly, by supplementing the quantity of biomass carbon that is reciprocated to the soil, and secondly, by enhancing the stability of soil organic matter (SOM) or reducing the biomass decomposition rate. Therefore, given the importance of plants and the various ecosystems plants offer, it is imperative to understudy the nature and components of plants. Plants receive essential nutrients by absorbing water and minerals from the soil through their roots. Root hairs are responsible for improving this absorption process by extending from the root's surface, allowing for a larger area for water and mineral uptake. Essentially, root hairs aid in extracting nutrients from the soil (Raven et al., 2005; Taiz & Zeiger, 2010). Their relationship with their roots influences plants’ development and growth. Mycorrhizal symbiosis is the process by which roots interact with microorganisms in the soil, and this interaction is a critical aspect of plant development (Smith & Read, 2008). The process involves the development of a mutually beneficial association between the plant's roots and fungi. This symbiotic relationship entails the fungi providing the plant with nutrients while the plant, in turn, supplies carbohydrates to the fungi. As a result of this relationship, the plant's capacity to absorb nutrients from the soil is significantly improved (Pirozynski & Malloch, 1975). The tree root system comprises two predominant root types: woody and fine roots. The woody roots are larger and firmer and have undergone secondary growth, providing stability to the tree (Lantini, Tosti, et al., 2020a). Conversely, the fine roots absorb water and nutrients, synthesize rooting hormones, and participate in root exudation and symbiotic relationships with soil microorganisms. The lateral extension of tree roots varies widely, depending on the site and the 2 soil type. The extent can reach or even surpass the width of the crown. This variance is demonstrated by the root spread of fruit trees growing in different soil types. For instance, fruit trees grown in sand tend to have roots that spread three times the canopy’s width laterally, while those produced in loam spread twice as far, and those in clay spread one and a half times as far (Pallardy, 2010). Given the significance of roots to plant growth, it is essential to understand their structure and how they interact with the soil. Assessing tree roots’ position, length, and depth is important for various reasons, including protecting the natural environment and ensuring safety in urban settings (Lantini et al., 2020). By reconstructing the roots' structure, we can quantitatively analyze the root diameter, root water content, and the distances between roots (Zhu et al., 2014). Observing tree roots is essential in recognizing potential harm and early deterioration (Alani et al., 2018). Accurate measurements of roots are necessary to quantify how much carbon is stored and how it changes spatially and over time, as roots are the primary means of carbon sequestration. Also, these measurements will help determine the root system's mass and shape (Wielopolski et al., 2000). Several methods have been used to measure roots, from destructive techniques, such as digging out the trees, to non-destructive detection methods. In recent years, non-destructive root detection methods have become increasingly popular because they do not involve digging up or harming trees. These methods include minirhizotron techniques, high-resolution X-ray CT scans, nuclear magnetic resonance (NMR), the sap flow method, acoustic methods, electrical resistivity tomography (ERT), and ground penetrating radar (GPR) (Cui et al., 2011; Lantini, Tosti, et al., 2020a). Broadly, near-surface geophysical methods have been used to explore the Physico- chemical properties of the soil. There have been huge successes in identifying and assessing soil properties such as porosity, electrical conductivity in soil, and, even most recently, soil moisture 3 content. The most commonly used geophysical method in the description and characterization of soil heterogeneity has been Electrical Resistivity tomography (ERT). In 2020, Alani & Lantini did a comprehensive study to cover recent advances in tree roots mapping and were apt in demonstrating how near-surface geophysical methods such as ERT were used in detecting soil compaction, rate of water content, and flow in plants and soil, amongst other studies. Also, (Basso et al., 2010) used ERT to study the tillage effect on the soil by looking at the soil resistivity at different tillage practices using a two-dimensional spatial and temporal variation of the soil’s physical properties. While ERT has been used to characterize soil properties quantitatively and give an insight into the qualitative comparison of soil properties, it does not match up to the success of the (GPR) in its application in reconstructing root distribution in the soil. In application, GPR can precisely locate the depth and spatial extent of roots in the soil in a much higher resolution than any other geophysical method, which is why the GPR was selected as the geophysical method for this project. GPR application in the investigation of root architecture commenced about two decades ago and has since gained popularity in identifying and describing the trees’ roots in the soil’s vadose zone (Lantini et al., 2020). The GPR was selected for studying and reconstructing the Tart cherry trees’ roots because of its high resolution, non-invasive, and non-destructive application method. GPR is a near-surface geophysical method that functions through the principle of scattering electromagnetic (EM) waves in identifying buried objects (in this case, roots of trees). RADAR, also known as “RAdio Detection And Ranging,” is the technology powering the GPR, in which the radio waves in the air propagate at the speed of light (~0.3 m/ns). The speed of light, which is the equivalent of the speed of a radio wave in space, is often a predictive variable in estimating the GPR velocity in the soil. In applying GPR, RADAR is achieved when EM pulses are sent 4 from a preselected antenna, and the reflected echoes are detected and timed. These timed echoes are stored, and the time range is kept in traces which will later be stacked into a radargram. RADARs operate between the radio and the microwave frequency of the electromagnetic spectrum. More specifically, their frequency could span from 300 kHz to 300 GHz, resulting in EM wavelengths ranging from 1 km to 1 mm (Oristaglio et al., 2000). GPR operation is time- dependent in its technique, and it uses the variation of the travel time of the EM waves to identify and reconstruct the materials in the subsurface (J. J. Daniels, 2000). The result of GPR data collection is presented in the form of a radargram, which is a stacked representation of echoes from pulses received by the receiver. The velocity of the transmitted EM energy in the soil is usually a function of the electric permittivity of the material, where the electric permittivity is the capacity of a material to store and radiate electromagnetic energy in the form of electrical charges, and usually the higher the electric permittivity of the medium the lower the velocity in m/µs or ns and vice versa. The electric permittivity is also termed the dielectric permittivity or the relative permittivity, which is the proportion of the electric permittivity of the material to the electric permittivity in free space (D. J. Daniels, 2004). The detection of subsurface objects using GPR is facilitated by the contrast in the electric permittivity between the targeted object and its surrounding soil, allowing for accurate and precise identification. When the EM wave is emitted from the transmitter and encounters a boundary between the object and the soil of different permittivity, the wave “reflects, refracts, and diffracts” from the boundary depending on the angle of contact with the boundary in a predictable manner. The receiving antenna records the wave reflected and returned to the surface, and the object’s depth can be obtained from the velocity and time of the reflected waves (Wielopolski et al., 2000). 5 In light of the significance of roots and the potential benefits of accurately measuring them, our objective is to explore methods for measuring roots, reconstructing their 3D architecture, and gaining insight into the interaction between the roots and canopy of the Tart Cherry Tree. This study aims to advance our knowledge and experience of this important tree component by comprehensively understanding the root structure. The objectives of this research are: 1. Measure roots using the ground-penetrating radar (GPR) 2. 3D reconstruction of roots using GPR and advanced processing algorithms. 3. Relate roots to the canopy by linking GPR to remote sensing. 4. Estimating roots' length, weight, and other quantitative attributes via controlled experiments. For this research, I hypothesize that the GPR signal can detect roots because of the differing dielectric permittivity values of roots and soil. 6 CHAPTER 1: GPR DATA PROCESSES AND INTERPRETATION OF TART CHERRY TREE 1.1 Literature Review This subsection is segmented into two subsections. The first outlines previous works done on root reconstruction using the GPR, and the subsequent subsection itemizes the important components of the principles of GPR. 1.1.1 Previous Studies Hruska et al. (1999) pioneered ground-penetrating radar (GPR) for mapping root systems. In their study, they applied GPR to investigate the three-dimensional distribution of root systems in large oak trees using a 450 MHz signal frequency. The results showed that the density of coarse roots was estimated, and the maximum rooting depth of the oak trees was determined to be 2 meters. The diameter of roots detected by the GPR system corresponded well to the measured diameter of roots obtained through excavation, with an error of 1 to 2 cm. The GPR system was also found to accurately determine the length of individual roots from the stem to the smallest detectable width, with an error of approximately 0.2 to 0.3 dm. Jeff Daniel has been a strong authority in exploring the fundamentals of GPR and researching the wide applicability of the GPR in environmental studies and other fields of applications. His research on “Imaging Tree Root Systems In Situ” was the second publicly sighted application of GPR in Imaging Roots (Wielopolski et al., 2000). Their research evaluated the GPR’s suitability to image roots using a relatively higher central antenna frequency of 1.5 GHz. They performed two experiments- sandbox laboratory experiments and a field experiment. They buried a “1 mm metal wire, plastic tubes filled with water, and a fresh 2.5 mm tree twigs” in a sandbox of volume (8’ x 5’ x 3’) at known depths. 7 The fresh tree twigs used in the sandbox laboratory experiments were used to simulate new roots. The 2.5 mm twig was buried 25.4 cm deep in the sandbox producing a hyperbola with a peak at an approximate depth of 3 nanoseconds. Subsequently, the field experiment survey was conducted using grids (x and y transects lines), where the “XY position data set for the antenna was used for image reconstruction purposes.” The field experiment was conducted on a large apple tree at an area of 1.5 m long and 0.8 m wide, extending from the stem of the apple tree. The experiment determined if GPR could be used to estimate the roots' mass and subsequent carbon content. Their investigation proved promising even though the 2.5 mm twig diameter could not be reconstructed due to the brevity of the sample used and the type of reconstruction algorithm used. In contrast to the twigs, these researchers reconstructed an actual large tree root and calculated the volume of the root. After using limited signal processing, they constructed a 3D volume cube from the X-Y transects and used a data explorer visualization software (OpenDX) to extract the roots from the volume. They used two methods to remove the roots. The first was the thresholding method- where the background amplitude is masked, and only the roots amplitude is made visible and isolated. The latter method used was Isosurfacing- where “the marching cube algorithm for isosurface extraction” was used in reconstructing the root image. More recent research and study on the use of GPR in reconstructing the architecture of roots have led to higher accuracy and precision in rooting system reconstruction. Some of the works done but not exclusive are Zhu et al. (2014), Cheng et al. (2014), Alani et al. (2018), Zhang et al. (2019), Alani & Lantini (2020), Lantini, Tosti, et al. (2020), Lantini, Giannakis, et al. (2020), and Fan et al. (2022). 8 Zhu et al. (2014) created a 3D volume from the result of the detected roots of larch trees using 500 MHz and 800 MHz GPR antenna frequencies. The 800 MHz produced a higher resolution and was used to construct the 3D root structure of the larch trees. They proposed a search algorithm to reconstruct the tree roots based on the continuity of the pixel intensity along the root in 3D space. The estimates with the measured root biomass had a total error of less than 10 %. Their research led to the development of a linear regression model they used for estimating the total root biomass in 10 cm depth ranges. In addition, a new index termed “magnitude width” was proposed to estimate the root diameter of the tree, which showed a good correlation with the measured root diameter with a 13 % - 16 % error. Further, Zhu et al. (2014) made a significant contribution to the field of tree root system analysis by demonstrating the capability of (GPR) to capture the coarse roots of trees with high accuracy. To validate their findings, they conducted an in-depth excavation process, where they dug the soil at 10 cm intervals to reveal the visible roots. These roots were then carefully dried and weighed to determine their physical attributes. The data collected from this process was used to develop a linear regression model that could accurately predict the dried weight of the roots based on the pixel values obtained from the 3D volume. With about 90% accuracy in total biomass validation, their research marked a first-of-its-kind achievement by successfully reconstructing a full-resolution 3D image of a larch tree root system. Cheng et al. (2014) used 270 MHz and 400 MHz for a controlled buried experiment where “ several freshly harvested root segments as calibration markers ranging from 0.5 to 5.5 cm in diameter (mean diameter = 2.1 cm) and at least 45 cm long were buried in different orientations over a flat sandy soil area, belowground at a depth of 50 cm in a 1 m by 1 m with 50 cm spacing apart”. Their research could affirm GPR accuracy in object depth. 9 The previously mentioned researchers used the grid survey method and were very successful in their delivery. However, recent researchers have developed a relatively more convenient approach for obtaining GPR data around the tree. This methodology is often called cylindrical or circular scan data collection. Alani et al. (2018) used a combination of 600 MHz and 1600 MHz antenna frequencies to study a matured fir tree using circular scans and an isolated oak tree using semi-circular scans to reconstruct the roots of these trees to understudy the tree’s health. They developed a methodological approach that reconstructed the deep and shallow roots using the mentioned antenna frequencies. Similar to the Alani et al. study, Lantini et al. (2020) collected circular measurements around a street tree in Ealing, London, to reconstruct the roots under the pavements in 3D. They used the 250 and 700 MHz antenna frequencies for the analysis, and their methodology was able to reconstruct the roots of the trees using singular value decomposition (SVD) that aided the automatic reconstruction of trees. Their main objective was to create an approach to limit the destruction of road pavements by uncontrolled street tree root growth and assess the roots' health under the asphalt. They were quite successful in reconstructing the roots in 3D with the use of circular measurements. Furthermore, Zhang et al. (2019) performed two experiments to assess the GPR capability in detecting infected citrus (orchard) tree roots. They used 900 and 1600 MHz antenna frequencies to detect roots and root proxies ranging from 0.5 to 3 cm in diameter. The root proxies they used were tree branches. They buried dead and live root proxies and tested if the GPR could detect the differences. Also, several factors were tested, such as, could the GPR detects varying root diameters, root positions, and the influence of root water content. Their results were interesting, as the signal of the dead root proxies had a weak signal compared to the live roots, which 10 produced distinct hyperbola structures. Furthermore, the root diameter was obtained by measuring the hyperbola’s width and had an optimal accuracy with an error of 1.5 cm for the horizontal distance (distance between two consecutive roots) and 0.8 cm for the depth. As expected, the result for the 1600 MHz had the highest accuracy and precision compared to the 900 MHz antenna frequency. Lastly, Lantini et al. (2020) used the circular method of collecting the GPR data creating a quasi- perpendicular tangent from the trunk of the sycamore tree. They were able to reconstruct the tree roots and also estimate the root biomass using developed quantitative algorithms. The references cited above show the ability of the GPR to assess the spatial distribution of the roots of trees. The selection of the antenna frequency is hinged on the diameter of the roots under investigation. The GPR will always give accurate results if the conditions set for success are implemented. In this study, I implemented most of the ideas obtained from the literature, such as the data collection techniques used and conducting a controlled experiment. Some of the novel contributions that was introduced are using a deep learning model in processing the GPR reconstructed roots and predicting biomass weight from the root proxies geometry, discussed extensively in Chapter 2. 1.1.2 Principles of Ground Penetrating Radar This section was adapted from two main textbooks written by authorities in Ground Penetrating Radars. The authors are D. J. Daniels (2004) and Jol (2008). 1.1.2.1 Electromagnetic Theory As the introduction explains, GPR works with the Electromagnetic (EM) theory principles and operates within the radio wave spectrum. From the literature review, the range of GPR 11 frequencies used could span from as low as 2 MHz (Berthelier et al., 2003) to several 10s or 100s of GHz. Practically, the choice of frequency depends on the object size and the depth of investigation, as the wavelength is inversely proportional to the frequency. Invariably, higher frequencies are used in detecting smaller objects, as seen from past studies in subsection 1.1.1, while lower frequencies are used in detecting larger targets and probing deeper depths. The GPR theory is further explained in the following paragraphs. Maxwell's equation captures and theoretically explains the physics of electromagnetic fields (Jol, 2009). Consider an electric field strength, magnetic flux density, electrical current density, and electric displacement vectors, E (V/m), B (T), J (A/m2), and D (C/m2), respectively. Where the electric charge density is q (C/m3), the magnetic field strength is H (A/m), and time is t (s), the electromagnetic fields and the associations can be described as follows 𝜕𝐵 ∇ ×E= − (1.1) 𝜕𝑡 𝜕𝐷 ∇ ×H= J+ (1.2) 𝜕𝑡 ∇. D = q (1.3) ∇. B = 0 (1.4) When the EM wave propagates through the soil, it interacts with the materials below the surface. Depending on the electromagnetic properties present in the materials, the EM wave is either restrained (absorbed), reflected, or transmitted. Constitutive equations often describe the material's feedback to electromagnetic fields, which provide an overview explanation of how ions (electrons and atoms) and molecules react to the 12 deployment of EM fields. These constitutive equations are explained in the definition of the electrical current density vector (J), electric displacement vector (D), and magnetic flux density vector (B). Consider electrical conductivity (σ), dielectric permittivity (ε), and magnetic permeability (µ) quantities. Where σ represents free charge movements when an electric field is present, ε measures charge displacement constrained by an electric field in a material structure, and µ defines how molecular magnetic moments react to a magnetic field. These scalar quantities are often interpreted as field-independent. That is, σ and ε correspond to the electric field, and µ corresponds to the magnetic field. The relationship of these quantities with their associated fields are defined below. 𝐽 = 𝜎𝐸 (1.5) 𝐷 = 𝜀𝐸 (1.6) 𝐵 = µ𝐻 (1.7) The dielectric permittivity is also called relative permittivity (ε𝑟 ) because its value in a material is measured relative to the permittivity of a vacuum. The permittivity of vacuum or absolute electric permittivity of free space (ε0) is given as 8.89x10-12 Fm-1 (Jol, 2009) or 8.86x10-12 Fm-1 (D. J. Daniels, 2004). The dielectric permittivity of a material is given as 𝜀 ε𝑟 = (1.8). ε0 The interaction between the electromagnetic waves and the material properties of the subsurface, which are electrical conductivity, magnetic permeability, and dielectric permeability, creates images of structures and objects beneath the surface. The electrical conductivity of the host 13 environment (soil) is the most crucial of the three material properties. Electrical conductivity estimates the number of water-soluble sodium chloride in soils. It is correlated with the type of cations exchange and the extent to which these ion salts dissociate on soil particles (D. J. Daniels, 2004). The salts and clay content are the primary factors influencing the soil's electrical conductivity. The GPR effectiveness is highly impacted by the soil's conductivity, where high conductivity leads to the quick attenuation of radar energy, limiting the capacity of the GPR to probe deeper depth and reducing the resolution of the imaging. Furthermore, the dielectric permittivity measures how charges within a material structure are displaced when an electric field is present. When charges are displaced, it leads to energy storage in the material (Jol, 2009). In contrast to electrical conductivity and dielectric permittivity, magnetic permeability has minimal effect on the GPR signal and is often assumed to be negligible (Jol, 2009). Magnetic permeability is the magnetic counterpart to dielectric permittivity and quantifies the energy of magnetic fields reserved and dissipated through induced magnetization. The dielectric and magnetic permittivity of a medium are expressed in comparison to the permittivity of a vacuum (Neal, 2004). At the boundary of contrasting below-ground material characteristics such as dielectric permittivity (Dong & Ansari, 2011), density, or moisture content of the medium or objects, a portion of the electromagnetic wave is reflected to the surface. The time taken between when the wave is sent and received is captured by the transmitter as the two-way travel time (TWTT). 1.1.2.2 EM Wave Propagation in a Material Electromagnetic waves are composed of two corresponding components: electric and magnetic fields that move perpendicularly to each other within a material (Jol, 2009). As these waves propagate, they exhibit several defining characteristics, such as wavelength, amplitude, 14 frequency, and velocity. The wavelength, expressed in meters (m), corresponds to the distance between successive crests or troughs and is influenced by the antenna frequency, as discussed in subsection 1.1.2.1. Frequency, measured in Hertz (Hz), signifies the number of oscillations per second and can be modified in Ground Penetrating Radar (GPR) systems. Amplitude, also given in meters (m), is the distance between the average signal position and the peak (positive amplitude) or trough (negative amplitude) of a wave. It strongly correlates with the energy transported by the propagating wave, with larger amplitudes representing higher energy levels. Typically, amplitudes are greater at shallower depths than deeper ones due to energy attenuation during wave propagation. Amplitude is essential when compensating for attenuation by applying energy gain to the traces of each transect collected, as illustrated in the data processing subsection 1.3.2.4. The interaction between these EM wave attributes is crucial for effectively analyzing and interpreting electromagnetic wave behavior across various applications. Since the velocity is highly dependent on the medium's dielectric permittivity, the wave propagation velocity is usually calculated using 𝑐 𝑣= (1.9). √𝜀𝑟 Where c is the speed of light, and its value is approximated to 3 × 108 𝑚/𝑠 (Kong, 2000). Once the velocity can be estimated from the above calculation, the wavelength of the EM wave can then be calculated using the commonly used relationship between the frequency, wavelength, and velocity. Such that 𝑣 𝜆= (1.10). 𝑓 Figure 1.1 shows the theoretical representation of the electrical and magnetic field and the associative components during wave propagation in a material. 15 Amplitude Velocity - v Amplitude Frequency - f Figure 1. 1: Electric and magnetic field components of EM wave propagation in a medium. Adapted from (Kong, 2000). 1.1.2.3 GPR System Description The MALA ProfessionalExplorer (ProEx) system was used for the survey, and its features are effectively described in this subsection. The write-ups were adapted from the MALA ProEx manual (For more details, see guidelinegeo.com). The MALA ProEx system consists of: • ProEx Control Unit: The MALA ProEx manages the radar data collection. It is made up of a power supply, which is an analog section that generates critical commands and signals to the antenna. Three inbuilt processors control transmitter and receiver pacing, trace intervals, and sampling frequency. The control unit is also responsible for creating temporary buffer storage of raw radar data and transferring the data to the MALA Ground Vision 2. The three controllers transmit and receive information for the transmitter, receiver, and data. They are communicated internally via fast, dual-port memories and externally via a high-speed Ethernet link. The ProEx control system can be used for a 16 range of antenna frequencies, and two antennae can be used simultaneously using the ProEx control system. • Shielded Antenna: The shielded antenna comprises a transmitting and receiving antenna called a transmitter and receiver, juxtaposed in the shielded antenna. The electromagnetic waves generated by the signal generator are transmitted from the transmitter, while the receiver collects the reflected waves from the subsurface objects. The MALA ProEx system comes with 100, 250, 500, and 800 MHz antenna frequencies. For this research and because of the relatively small diameter of roots, the 800 MHz antenna frequency was selected for this project. • Display Screen: A Dell rugged fieldwork laptop was used for the data collection, but any display device that can install the MALA Ground vision software 2 can store and display the data collected. • Accessories: Other accessories accompanying the functionality of the GPR system are two 12-volt lithium batteries to power the control unit and the antenna and an ethernet cable to connect the display unit or screen to the control unit. • Mobility Accessories: This study used two means of deploying the GPR system along a transect. The first was the rugged terrain cart (RTC) shown in Figure 1.2 and the one- wheel chain. An odometer (O-ring) is attached to both the RTC and the one-wheel chain. It is used to measure the horizontal distance traveled and control the pulse timing if the distance is selected as the reference for the transmission of the EM wave. 17 Figure 1. 2: Showing the GPR system deployed on the RTC with all the components needed for data collection. GPR system deployment using the one-wheel chain follows the same connection arrangement as the RTC. The only difference is that the RTC has a four-wheel, and the chain configuration has a one-wheel. 18 1.1.2.4 Buried Object Detection Discussed in the two previous subsections were the governing principles of the GPR and the components of the GPR system that enables data collection. This subsection aims at connecting the concepts of GPR. When a wave is transmitted from the antenna, it interacts with the material below it. Based on the nature of the materials, the EM waves are reflected, refracted, or absorbed according to the scattering theory. In the case of GPR, the reflected waves are the most considered. As highlighted in the previous sections, the EM waves are reflected at the boundary of contrasting dielectric material. The reflection from these materials produces additional spikes in the signal received by the GPR receiver (Benedetto & Benedetto, 2014). Because of the additional spike on the reflected waves, the object's (root's) shape and nature within a fairly homogenous medium (such as the soil) can be reconstructed based on the field survey chosen and through data processing. As Jol (2008) mentioned, energy is stored in the materials when charges are displaced, influencing the travel time. Also, as highlighted by Benedetto & Benedetto (2014), as the GPR antenna moves above the soil, any object greater than one-fourth of wavelength within the soil produces additional spikes in the reflection, resulting in a hyperbola feature seen in the processed GPR data (radargram). Figure 1.3 depicts the above explanation perfectly, as the three subfigures explain the interaction of the GPR wave at the boundaries or interfaces (A), the representation of the reflective signal when a circular object is buried in the soil (B), and the illustration of how the radargram is formed through the staking of individual traces. The radargram is what is processed effectively to image the subsurface. 19 Figure 1. 3: Adapted from (Benedetto & Benedetto, 2014), illustrates the EM signal interacting with the environment with different dielectric properties. Subfigure A shows the interaction of the EM wave at interfaces; subfigure B shows the interaction with an object in the soil; and subfigure C displays how individual traces are combined into forming the radargram. 20 1.2 Data Collection Methodology The literature review revealed two main approaches for collecting GPR data around the tree. These methods are: i. Grid Survey Method (GSM). ii. Cylindrical Survey Method (CM). These methods were used to investigate and reconstruct the Tart cherry tree roots. Two locations were selected for this study: the MSU AgBio Research Center, Clarksville, and the Growers Field, Traverse City. 1.2.1 Grid Survey Method (GSM) The 3D reconstruction of the tree's roots utilized the GSM, with grid lines placed on the soil and the root trunk at the grid's center. Four measuring tapes created the grid's outline border to verify the survey's dimensional accuracy. A 5m x 5m grid was constructed around the trunk, featuring inlines in the W-E direction and crosslines in the S-N direction, spaced 0.5m apart within the grid. During data collection, a separate line was placed at 0.1m or 0.15m (for a 6m x 6m grid) spacing using the inlines and crosslines as references. This approach greatly improved the time taken for the data collection and was better than prograding the grid at 10cm (0.1m) spacing for a 5m x 5m grid and also ensured a smoother soil surface for data collection. After constructing the gridlines, the next task involved calibrating the RTC's wheel with a measuring tape and confirming the distance accuracy before beginning data collection. The data was then collected from the inlines in the W-E direction, with the crossline transects following the inlines in the S-N direction. 21 Figure 1. 4: Showing the gridlines constructed around the Tart Cherry Tree using the GPR system. The inlines and crosslines were constructed in a fixed spacing within the grid. 22 1.2.2 Cylindrical Survey Method (CSM) The CSM was used for the data collection of eight tart cherry trees in Clarksville. The analysis will present a correlation between the canopy and the spatial distribution of the roots. The CSM data collection method utilized materials that enabled radial data collection around the tree trunk. These materials included a flexible strap tied around the tree, a meter rule extending from the trunk's circumference, a rope connecting the trunk to the antenna system, and a GPR system with a one-wheel chain. The strap facilitated circular data collection by allowing mobility around the tree. The setup process began by determining the trunk's radius by measuring its circumference and dividing the result by 2π. Next, a meter rule was positioned at the tree trunk and extended outward to a desired distance. A rope, connected to both the strap and the one-wheel chain system, ensured the antenna remained in contact with the soil while maintaining the selected distance on the meter rule as it moved around the tree. Once the rope between the strap and the GPR system was tight enough, the distance measured around the tree equaled the circumference calculation using the trunk's radius and the selected length on the meter rule. As in the GSM, the subsequent task involved calibrating the wheel and verifying that the measured distance matched the meter rule's length used for calibration, typically a 10m mark on the tape. Two personnel are usually needed during the data collection process. The first personnel carries the ProEx system and the display unit while dragging the antenna on the soil. Similarly, the second personnel keeps the rope tightly connected to the trunk and the antenna while ensuring that the antenna is positioned on the soil at all times. Figure 1.5 shows the CSM deployment. 23 Figure 1. 5: Showing the deployment of the CSM around the Tart cherry tree, with all the instrumentations required. 24 The entire one-wheel chain deployment is shown in Figure 1.6, where the MALA ProEx system is bagged on the shoulders, the display unit is held with one hand, and the antenna is dragged with the other hand. Figure 1. 6: Showing the overall equipment used for the CSM data collection process. 1.2.3 Measurement Parameter Settings The MALA ProEx system's Slot B channel was the data transfer port between the control unit and the antenna. The following settings were used during the GPR data collection in the GroundVision 2 software used for the interface in reading the data collected via the control unit. The 800 MHz shielded antenna was selected as the preset, with the wheel acquisition mode applied. The 25 measurement wheels included the "Cart wheel 16x2.125 (346.80-)" for the RTC and a post- registered, calibrated measurement for the one-wheel chain. As depicted in Figure 1.7, the antenna settings feature a default separation provided by the MALA manufacturer. The 800 MHz antenna transmitter and receiver have a separation of 0.14 m within the shielded antenna. A trig interval of 0.02 m was selected, meaning that after every 2 cm measured by the odometer attached to the wheel, an EM wave is sent into the soil. The data collection time window was 45 ns, with 454 samples. In this context, samples represent the number of digitized points in a trace. A higher sample count typically increases resolution and object detection within the soil. A sampling frequency of approximately 10,000 MHz was used. Four traces were stacked for each EM wave trigger to reduce noise in the signals further. 26 Figure 1. 7: Captures the GPR settings used for the data collection for both the GSM and CSM. Based on the antenna frequency used, speed of light, and estimated dielectric permittivity of the soil, the EM wavelength is approximately 12 cm. According to Guha et al. (2005), the target must be larger than one-fourth of the wavelength size to be resolved. Therefore, the root sizes that will be captured from our results are roots whose sizes are greater than 3 cm. 1.3 Data Processing Methodology Two software were used to process the GPR data. The cloud-based MALA vision software was used to process the GSM data, while ReflexW was used to process the CSM data. The necessary processing required necessitated the kind of software used. For instance, the CSM dataset required adjusting the horizontal profile distance, which is not part of the MALA vision software 27 functionality. In contrast, the RefelexW is quite robust in performing a wide range of processing and was used for the CSM. The MALA vision software was designed to expedite the processing of the GPR dataset with inbuilt functionality that facilitates rapid processing of the GPR dataset. The MALA vision software was used for the 3D reconstruction of the tree, particularly using the GSM dataset, because it presents a very flexible approach to interpolating the gridlines (inlines and crosslines). 1.3.1 Grid Data Processing Methodology The gridlines collected around the tree were imported to MALA vision, and each transect can be viewed using the 2D window of the software. Each transect was processed in the 2D window using the inherent functionalities in the software. A common practice with almost all GPR processing software (as seen in the two software used in this study) is that the processing applied to one transect can be applied to the rest of the transects, holding to the fact that the soil is assumed to be fairly homogenous around the grid region. Figure 1.8 shows the raw radargram for one of the transects collected around the Tart cherry tree, and the following subsections are the subsequent processing step used in processing the radargram. 28 Figure 1. 8: Showing the raw radargram for transect -inline_1006 collected around the tart cherry tree. The horizontal profile for each transect is 5m, and the vertical distance is prograded in time ns. 1.3.1.1 Time Zero Correction The time zero correction is crucial for accurately measuring the distance by removing the airwave measurement and can be done using the first spike on the traces representing the boundary between the air and the soil representing the soil surface. Once this is done, the 0 ns 29 will be at the exact position of the soil surface, as shown in Figure 1.9. For reference purpose, the trace shown in Figure 1.9 is trace number 266. Figure 1. 9: Showing the adjustment of the Time Zero based on the first spike seen on the traces. 30 1.3.1.2 DC Offset DC Offset correction in MALA vision software performs the exact functionality as the Dewow function in ReflexW. This function corrects the distortion in the low-frequency signal. The distortion results in the average trace amplitude having a non-zero value (Lantini, Tosti, et al., 2020a). Applying the DC Offset or Dewow function corrects this effect and positions each trace at a zero amplitude mean value. The corrected result is seen in Figure 1.10. Figure 1. 10: Showing the radargram after the application of the DC Offset filter. 31 1.3.1.3 Automatic Gain Correction (AGC) AGC is also called time gain or Gain (as seen in the ReflexW filter in subsection 1.3.2). The AGC filter applies a time-dependent gain method to equalize the amplitude at a deeper depth, effectively compensating for signal attenuation (Jol, 2009). AGC applied filter is seen in Figure 1.11. Figure 1. 11: Showing the resulting radargram after the AGC filter is applied. 32 1.3.1.4 Background Removal Background removal is done on the radargram to eliminate constant noise by increasing the signal-to-noise ratio. The background noise is represented by horizontal lines and is eradicated from the signal by subtracting their average horizontal signal (D. J. Daniels, 2004). Figure 1. 12: Showing the Radargram after the Background Removal Filter has been added. 33 1.3.1.5 Velocity Analysis As discussed extensively in subsection 1.1.2.2, the velocity depends on the medium's dielectric permittivity and the speed of light. Although there are empirical relationships to estimating the dielectric permittivity of the soil, many factors come into play, such as getting the average dielectric value of the constituting materials of the soil, such as the proportion of clay, sand, and water content, which is cumbersome to estimate. An intrinsic function based on direct estimation or multiple measurements of the distance from the surface to a physical target on the radargram is used to estimate the velocity in the processing software correctly (D. J. Daniels, 2004). Equation 1.11 is the governing hyperbolic spreading function used to estimate the velocity, 2 𝑥𝑛−1 − 𝑥02 𝑣𝑟 = 2√ 2 1.11 𝑡𝑛−1 − 𝑡02 and Equation 1.12 is the depth derivation formula of the depth to the target using TWTT, 𝑣𝑟 𝑡0 𝑑0 = 𝑚 1.12 2 Figure 1. 13: Showing the derivation of the velocity from the surface to the hyperbola. 34 Figure 1. 14: Showing the addition of the hyperbola in calculating the velocity. The velocity calculated for the Tart cherry tree in the Traverse location was 130 m/µs. The vertical profile was converted to depth in the software using the velocity in Equation 1.12. The converted vertical profile to depth can be seen in Figure 1.15. 35 Figure 1. 15: Showing the radargram vertical profile in depth. 1.3.1.6 FK Migration Migration refers to the process of spatial deconvolution that aims to eliminate both source and receiver directionality present in reflection data. Its objective is to recreate the radar reflectivity distribution beneath the surface accurately. To achieve this, migration necessitates understanding the velocity structure, frequently leading to an interactive procedure in which the background velocity is repeatedly modified to enhance the resulting image (Jol, 2009). 36 In summary, the FK migration is used to reconstruct or see the exact object width or diameter as measured and reflected on the radargram. Figure 1. 16: L-R showing the unmigrated and migrated radargram. 1.3.1.7 Gridlines Arrangement and Interpolation After the 2D processing was completed by performing the operations in subsections 1.3.1.1 – 1.3.1.6, the inlines and crosslines were arranged according to the data collection survey design on the Site map window, as seen in Figure 1.17. The arrangement of the gridlines aided the 3D reconstruction of the soil, as seen in Figure 1.18. The gridlines were interpolated using the bilinear interpolation function in the MALA vision software. The bilinear interpolation matches the related signal intensity and produces images that best represent the objects buried in the soil. 37 Figure 1. 17: Showing the gridlines in the exact spacing as they were arranged during the data collection phase. 38 Figure 1. 18: Showing the 3D reconstructed soil showing the GPR reflectance representing the roots of the Tart Cherry Tree. 39 1.3.1.8 Validating the 3D Reconstructed Roots from the Radargram The validation of the 3D reconstructed distribution of the roots is done by crosschecking the migrated signal on the 2D radargram with the timeslice generated images in the 3D cube. Figure 1.19 shows that the radargram's roots' dimension matches the cube's generated images. Figure 1. 19: Showing the correlation of the reflections in the 2D and 3D window. 1.3.1.9 Timeslice Processing and Root Extraction The timeslices, which displayed the root's reflection, were captured as screenshots and analyzed using a convolutional neural network (CNN) model and ImageJ software. These timeslices revealed the root's length and diameter, accompanied by some noise typical of soil conditions. The subsequent task involved identifying a method capable of accurately extracting the roots from the timeslices. After testing several techniques, I found the VGG16 CNN model highly effective. Developed by Google, the VGG16 is a deep-learning model in the Keras library equipped to recognize several patterns in an image, as explained (Simonyan & Zisserman, 2014). For this study, I utilized the weights of the first CNN layer of the VGG16 to create a new model 40 for root extraction from the timeslices. Among the sixty-four filters available in the layer, filter 26 demonstrated the highest accuracy in resolving root patterns and was used for extraction. Figure 1.20 shows the application of the VGG16 in extracting the root patterns and compares the result with the original timeslice. The algorithms and codes utilized to develop the root extraction model using the VGG16 can be found in Appendix A. Figure 1. 20: L-R showing the original timeslice and the extracted root pattern using the VGG16 model. ImageJ, an advanced processing software, was utilized to refine the image obtained from the VGG16 model. This refinement involved converting the image into a binary format to emphasize the roots, overlaying the binary images onto the original image to compensate for any pixel loss during previous processes, and ultimately employing the brush tool in ImageJ to reproduce the root pattern observed in the original image. Figure 1.21A presents the outcomes of the binary conversion and image overlay, while Figure 1.21B displays the final result compared to the original. 41 Figure 1. 21: Showing the processing steps in ImageJ. Subfigure A, L-R shows the binary converted VGG16 image and the overlaying process of accurately reconstructing the roots as seen in the original timeslice. Subfigure B, L-R displays the original timeslice and the extracted roots. 1.3.2 Cylindrical Data Processing Methodology As explained in subsection 1.2.1, the cylindrical data was collected radially from the tree trunk. The first process was to correct the measured profile length. Some of the profiles had longer, or shorter lengths than the estimated length due to the topography of the area or some other factors encountered during the data collection. Theoretically, the circumference as a factor of the radius 42 (radius of the trunk + distance from the trunk) is equivalent to the length of the profile. The circumference will always be equal to the measured profile length in perfectly flat soil conditions. Therefore, all the profiles were corrected to ensure that the measured distance was adjusted to the estimated distance. This correction is required because an incremented distance is essential for interpolating the transects collected for each tree. ReflexW software was used for the primary data processing of the cylindrical transects (radargram), and either Python or MATLAB can be used to interpolate the profiles of each tree. The following subsections highlight the cylindrical data processing for each tree. 1.3.2.1 Profile Distance Correction The trace interval, which is the horizontal distance to which the EM waves are pinged and stored in the transmitter, was set to 0.02 m, and this is the basis for the length of each profile distance measured. A new trace interval was calculated using the last trace number measured by the GPR system to correct the measured distance. Given that the measured distance is equal to the trace interval multiplied by the last trace number, the new trace interval can be obtained for the estimated distance by dividing the last trace from the estimated distance as written below 𝐸𝑠𝑡𝑖𝑚𝑎𝑡𝑒𝑑 𝐷𝑖𝑠𝑡𝑎𝑛𝑐𝑒 𝑁𝑒𝑤 𝑇𝑟𝑎𝑐𝑒 𝐼𝑛𝑡𝑒𝑟𝑣𝑎𝑙 = (1.13). 𝐿𝑎𝑠𝑡 𝑇𝑟𝑎𝑐𝑒 − 1 Given that an average of approximately 20 transects were collected for the eight trees used for this study, manually extracting the 'Last Trace' number from each transect file would be time- consuming and redundant. To optimize the extraction process, a Python script was developed to efficiently access the files, extract the 'Last Trace' number, and store the values for all transects associated with each tree in an Excel file. This method enabled the convenient calculation of the 43 'Estimated Distance' and the 'New Trace Interval' using Excel's capabilities. The code used for this automated process is outlined in Appendix B. The measured distance was adjusted by replacing the original trace interval with the newly calculated trace interval, effectively converting the measured distance into the estimated distance. In ReflexW, the trace interval can be modified by accessing the 'Trace Interpolation / Resorting' dialogue box, selecting the 'fix tracenumber' option and then navigating to the 'traceincr-resampling' section to choose the 'trace increment' field. Modifying the trace number to adjust for the measured distance will distort the original trace number used during the data collection phase. In order to rectify this issue, the modified profile length is fixed, and the trace number is reverted to 0.02 m. Figure 1.22 displays the original trace and the corrected horizontal profile. 44 Figure 1. 22: Showing the original radargram above and the corrected horizontal distance below. 1.3.2.2 Radargram Processing The discussion in subsection 1.3.1 explains the background basis of the filters used in processing the radargram and is not repeated in this subsection. This section describes the filters' location in ReflexW and details of the filters not used in the MALA vision software 1.3.1. The time zero correction was made by navigating to the "StaticCorrection/muting" dialogue box and selecting the "move starttime" by editing the "manual input" option. The actual time obtained from the traces was imputed in the "move time [ns]" field. The actual time is chosen based on the time the signal hits the ground, and it is subtracted from the profile by entering "-" 45 before the time zero point in the "move time" field. Figure 1.22A shows the result of the time zero correction. The Parameter for Dewow used was 1.25 ns in the 'timewindow' field. In ReflexW, the Dewow filter is present in the 1D-Filter dialogue box. The resulting radargram is seen in Figure 1.22B. The Gain filter was applied next, as seen in Figure 1.22C. Subsequently, the Bandpass Butterworth filter and the average XY filters in the 2D filter of the processing dialogue box were applied to enhance the radargram. The bandpass Butterworth filter processes the signal by cutting off certain non-essential frequencies in the traces. For most of the profiles, the lower and upper cutoff values are 200 and 1700 MHz. The resulting radargram after applying the Bandbutterworth filter is seen in Figure 1.22D. The average XY Filter is used to smoothen the traces. The Filter Parameters are "nr. of traces(x)" and "nr. of sample(y)". The value of two was entered in both parameters for all the trees. Figure 1.22E shows the resulting radargram after the Average filter was applied. Subtracting Average Trace and Background removal filters are used in removing the background noise from the radargram. Both filters can be accessed by navigating to the "2D filter processing" dialogue box. First, the "subtracting average" option is selected, and value fifty is assigned for the average traces to be subtracted. Subsequently, the "background removal" filter is applied for the background removal. Figures 1.22F and G are the resulting radargrams after applying the background removal filters. 46 Figure 1. 23: Showing the radargram processing using ReflexW. Where subfigure A is the resulting radargram after time zero correction, subfigure B is the resulting radargram after the Dewow filter has been applied, subfigure C is the output after the gain filter has been applied, subfigure D is the result of the bandpass Butterworth filter, subfigure E is the output after the average traces filter has been applied, subfigures F and G are the output of the subtracted average and background removal filters, and subfigure H is the resulting radargram after the f-k migration has been done which follows the same principle as included in subsection 1.3.1. 47 1.3.2.3 F-k Migration and Data Exporting F-k Migration, as seen in subsection 1.3.1, is used to highlight the exact width of the feature and to migrate the hyperbola legs to the peak of the hyperbola. Before the migration is done, the velocity is identified using the hyperbola tuning settings. Once the velocity is known, the f-k migration can be done by navigating to the ‘Migration/time-depth conversion’ dialogue box. The velocity obtained from the hyperbola tuning is imputed into the ‘velocity m/ns’ field. Apart from the length correction of each transect, the remaining processes are saved in batches and used to process the rest of the transects for a particular tree. Two sets of processed data are exported for plotting and interpretation. The first is the unmigrated data, which consists of all the processes up to the background removal step, and the second is the migrated data, including the f-k migration step. The processes for successfully reconstructing the cylindrical structure of the soil are extensively discussed in subsection 1.3.2.4. The exporting step involves saving each set of radargram (transects) as a set of traces in ASCII- MATRIX format, where each trace is saved as a column and exported. Again, automation was used to expedite saving the filenames correctly. The filenames are saved as "Migrated_radius" or "Unmigrated_radius." Instead of manually typing and estimating the radius of each transect, number 1 to the number of transects collected for each tree was used to save the files, while a short code that sorts and renames the file was written to expedite the process of exporting the files from ReflexW, as seen in Appendix C. 1.3.2.4 3D Reconstruction of the Tree Transects Using Python The resulting exported file for each transect comprises a two-dimensional (2D) array corresponding to the transect's horizontal distance and depth profile. The array contains integer amplitude values ranging from negative to positive amplitudes in data units (Dinh et al., 2016). 48 The objective is to reconstruct the transect in a manner that replicates the data collection process during the field survey. Given the extensive range of amplitude values, normalization was performed to ensure that the values ranged from -1 to +1, utilizing the MinMaxScaler function from the Scikit-learn library. The transect's depth in both time (ns) and depth (m) can be reconstructed from the provided array by employing the array column size and the time window specified in subsection 1.2.3, which is 45 nanoseconds (ns). The Linspace function from the NumPy library is utilized to create an array with an input range from 0 to 45 and the size corresponding to the size of the array column, which also represents the sample points or the number of digitized points. Figure 1. 24: Showing the original and normalized amplitude of a selected trace in time (ns). The depth profile can be converted to depth in meters by using the two-way travel time (TWTT), and the estimated velocity, which for the analysis of this study, ranged from 0.1 - 0.15 m/ns. For this tree, the velocity used was 0.1 m/ns, and the resulting depth by multiplying half the time value with the velocity is 2.25 m. 49 Figure 1. 25: Showing the amplitudes converted to depth (m). As the data were collected using the cylindrical method around the tree, converting them into cartesian coordinates was necessary to facilitate visualization in the x-y plane. Equation 1.14 - 1.15 maps each transect from polar coordinates to the x and y axes. 𝑥𝑖 = 𝑟. 𝑐𝑜𝑠𝜃𝑖 (1.14) 𝑦𝑖 = 𝑟𝑠𝑖𝑛𝜃𝑖 (1.15). Here, the radius (𝑟) and angle (𝜃𝑖 ) are considered, where the radius (𝑟) of a transect remains constant throughout, while theta, the angle relative to the radius, varies as the arc length increases. Theta can be determined by dividing the arc length by the radius. In practice, the arc length for each trace can be computed by creating a linear space function using the NumPy library, with a range of 0.02 and the product of the total trace number and 0.02, along with the size of the total trace number in the transect. 50 With the depth profile and the x and y coordinates created, the transect shape can be constructed as seen in Figure 1.26. Depth (m) Figure 1. 26: Showing the cylindrical coordinate reconstructed in the 3D cartesian plane for a transect. An iterative method is developed to append the rest of the transects in an array in order to map the cylindrical coordinate on the cartesian plane for all the transects collected around the tree. 51 Figure 1. 27: Showing the top view of the reconstructed cylindrical transects on the cartesian plane. Upon compiling an array containing the Cartesian coordinates for all the transects associated with a tree, the subsequent step involves creating a mesh function that maps the amplitude to the Cartesian coordinates, ensuring that each 𝑥𝑖 , 𝑦𝑖 , and 𝑧𝑖 point corresponds to an amplitude value from the collected transects. Once this mapping is accomplished, the entire set of amplitudes can be plotted with colors in the 𝑥𝑖 , 𝑦𝑖 , and 𝑧𝑖 coordinates, allowing for the observation of roots at certain depths. 52 Figure 1. 28 shows the 3D reconstructed amplitude around the tree. The results of the roots seen at certain depths are presented in subsection 1.4.2. 53 1.4 Results and Discussions 1.4.1 Grid data Results using ImageJ Processing Software The processed time slices, as discussed in subsection 1.3.1.9, were corrected to represent the exact dimensions of the grid (i.e., 5 m x 5 m) using the pixel-to-meter conversion. Each time slice taken from the soil's surface was stacked according to the depth of each time slice, using the 3D reconstructed cube in MALA vision as a reference. The 3D volume of the extracted roots was created using ImageJ software. Due to the computational resources used in this study, the dimensions of each processed time slice were downscaled to twenty times the original dimension to expedite the interpolation process using ImageJ's 3D volume viewer. The results, as shown in Figure 1, display the 3D reconstructed roots. The mature Tart cherry tree roots extended to a depth of 0.3 m in the soil and were observed to spread out laterally in the 5 m x 5 m grid. From our results, the root length and width at each depth can be estimated, and the area and volume of the roots can be obtained using ImageJ functionality. The width of the smallest root measured was approximately 5 cm - 6 cm in diameter, which corresponds to the object detection capability of the 800 MHz antenna frequency. 54 Figure 1. 29: Showing the 3D reconstructed roots of the Tart cherry tree, spatially distributed in the 5 m x 5 m grid. 55 1.4.1 Cylindrical data Results Showing the distribution of the roots at a certain depth The results from the two mature trees (Tree 2 and Tree 7) measured using the cylindrical methodology are discussed in this section. The trees were named based on the order in which the data were collected. After extrapolating the amplitude values to their respective XYZ points, depth slices were obtained by masking the arrays (X, Y, and Amplitude array) with the specified constrained depth. A 2D plot was created using the masked array as the X and Y points and the masked amplitude as the color map in the Plotly scatter plot function. High amplitude reflections indicate the roots, as seen in Figure 1.30. Figure 1.30 displays the reflection of the mature tart cherry tree (Tree 2). Tree 2 trunk radius was 15.12 cm, and the first transect was 40 cm apart from the tree diameter, making the first transect radius 55.12 cm. Subsequent transects were taken at 10 cm intervals up to a radius of 3 m from the trunk. The roots are seen to appear at a depth of 10 cm and continuously till 45 cm deep. The roots extend to the end of the last transect, taken at a radius of 3.1512 meters, indicating a lateral diameter of approximately 6.4 meters. Furthermore, to smooth the amplitude points and better visualize the roots' spatial distribution, the RBFInterpolator from the SciPy interpolation module was employed, as shown in Figure 1.31. 56 Figure 1. 30: Showing the results of Tree 2 roots' reflection using the Plotly Scatter plot. 57 Figure 1. 31: Showing the interpolation results of the depth slices of Tree 2 using the RBFInterpolator. 58 Similarly, the same processes were applied to Tree 7, as illustrated in Figure 1.32 and Figure 1.33. The roots were observed at depths ranging from 5 cm to 45 cm. Tree 7's trunk had a radius of 14 cm, and the first transect was 40 cm away from the tree's diameter, resulting in a 54 cm radius for the first transect. Following transects were taken at 10 cm intervals, up to a radius of 2.4 m from the trunk. Regarding the root's spatial distribution, it was observed that the roots extended to the full extent of the last transects, with a total radius of 2.54 m and a lateral diameter of 5.8 m. Figure 1. 32: Showing the Plotly Scatter plot of the Amplitude of Tree7. The high amplitudes are the roots and are seen to extend from the tree's trunk. 59 Figure 1. 33: Showing the interpolation results of the depth slices of Tree 7 using the RBFInterpolator. 60 CHAPTER 2: CONTROLLED EXPERIMENT AND WEIGHT MODEL ESTIMATION OF BIOMASS In this chapter, a controlled experiment is conducted to validate the GPR results by burying biomass with known parameters (length, width, and circumference). These parameters were estimated from the reconstructed GPR results and were compared with the parameters measured from the wood directly to assess the GPR's accuracy in reconstructing the roots of the Tart cherry tree. A weight estimation model was also developed by collecting over a hundred biomass samples with varying lengths and widths. The biomass width, length, circumference, and weight were measured and used to create a machine-learning model. In this model, the length, width, and circumference served as independent variables (predictors) for estimating the weight of the roots. 2.1 Literature Review on Root Weight Model Biomass estimation, including root weight estimation, has been an active area of research for several decades. Some researchers have used direct destructive methods to assess these quantities, while others have used novel approaches, such as using trees' phenological attributes to predict biomass. In 2010, Black et al. reviewed and discussed different methods for studying orchards' root growth and distribution patterns, including entire tree excavation, root sampling techniques, observation windows, and indirect procedures like making guestimates about root-to-shoot ratio. They used the soil core sampling technique, which involved the collection of soil samples (including roots) around the tree at a distance of 90 and 135 cm from the trunk, with a maximum depth of 90 cm. In summary, they used a destructive method in sampling the root distribution. 61 The direct measurement of roots via excavation or core sampling is a common practice in the study of spatial root distribution, as seen in (Black et al., 2008; Das et al., 2011; Li et al., 2019; San-Martino et al., 2010; Shoop et al., 2015). While this approach has proved effective in estimating the roots, it is not sustainable as the destruction of trees has several chronic effects on the environment. In 2011, Das et al. did a nine-year study of destructively harvesting twenty-seven trees annually, segmenting the trees into several parts, and weighing the biomass components such as the twig, branch, lateral root, and fine roots. Their analysis discovered that the “Diameter at breast height” sufficiently predicted the dry weight and can be used as an independent variable in weight prediction. A non-destructive approach to estimating tree biomass can be achieved by developing a predictive model. Sanogo et al. (2021) conducted a comprehensive study using functional branch analysis (FBA) to estimate below-ground biomass. They found that allometric equations can establish a direct relationship between the roots and shoots and that predicting the roots based on above-ground measurements, such as shoots, differed by about 6%. Their approach involved exposing the roots by carefully digging the soil without destroying them, and they were apt to cover the soil after validation. Furthermore, in a recent study by Ku et al. (2022) on the optimal method for biomass estimation, the physical properties of zooplankton, such as length, width, and lateral area, were used to derive body weight. While this study was applied to an animal species, the relationship between physical properties and weight can be established for any object, living or non-living, through data-driven machine-learning approaches. 62 2.2 Materials and Methods The experimental designs for the controlled experiments and weight model are described in this subsection. The biomass collected for these experiments can be nicknamed root proxies, and these terms were used interchangeably throughout this chapter. 2.2.1 Controlled Experiment for Validating GPR Results A 2 m x 2 m grid was constructed in a growing field at Michigan State University (coordinates 42.71490N, 84.46328W) to bury root proxies to reconstruct the root geometry using the grid method described in Chapter 1. According to the United States Department of Agriculture (USDA) web soil survey application, the soil type within the first 1.5 m is loam. The experiment consisted of two stages. In the first stage, biomass with varying diameters between 3 cm and 5 cm was buried. It was observed that biomass with a diameter lower than 4 cm was not properly detected, which informed the formulation of the second stage of the experiment. In the second stage, biomasses with average widths ranging from 4.3 cm to 4.9 cm were buried. Table 1 provides the measured diameter and depth of each biomass. The measured weight in the table is the weight before drying. The root proxies varied in moisture content as most of the woods were relatively dryer than the wet biomass used in training the wet weight model. 63 Table 1: Showing the buried root proxies measured parameter before burial. Root Proxies Length (cm) Width (cm) Circumference (cm) Weight (g) Depth (cm) RP 1 84 4.90 16.5 544 16-20 RP 2 97 4.30 14.0 786 10-15 RP 3 104 4.55 15.5 1206.2 20-30 RP 4 51 4.30 15.0 406 15-24 RP 5 56 4.86 16.5 478.6 22-25 RP 6 64 4.33 14.0 523.0 17-20 RP 7 68 4.8 16.0 610.8 17-20 The root proxies were strategically placed to simulate the spatial distribution of roots, as observed from the Tart cherry tree study presented in Chapter 1. In summary, this controlled experiment aims to achieve two goals: first, to verify the accuracy of Ground Penetrating Radar (GPR) in reconstructing root length, width, and positions, and second, to estimate root weights using the model developed in subsection 2.2.4. As depicted in Table 1, root proxies were situated at depths ranging from 10 to 30 cm in the soil. Initially introduced in Chapter 1, the grid methodology was employed within a 2 m x 2 m outer gridline, with an inner spacing of 10 cm for collecting inlines and crossline transects. Figure 2.1 illustrates the precise positioning of root proxies in the soil and the construction of gridlines. In this experiment, root proxies were placed at specific locations to emulate natural root distribution patterns, which allowed for an assessment of the GPR's accuracy in detecting root positions from various angles. 64 Figure 2. 1: Showing the controlled experimental setup. Subfigure A: R-L shows the position of RP 1 and 2; Subfigure B- shows the position of RP 3; Subfigure C: L-R shows the position of RP 4 and 5; Subfigure D: L-R shows the position of RP 6 and 7; Subfigure E illustrates how the depth of burial for each root proxy was obtained; Subfigure F shows the soil properly covered and stamped to enforce compaction; Subfigure G shows the constructed 2 m x 2 m grid; and Subfigure H shows the GPR data collection. 65 2.2.2 Weight Model Root Proxies Collation A non-destructive method for estimating biomass weight is hypothesized using biomass length, width, and circumference. Given that the GPR can asses the roots' diameter and length, I developed a machine-learning model that takes biomass length, width, and circumference as independent variables and uses it to predict biomass weight. I collated as much as 115 biomass, collected from shredded branches of trees. To create a generalizable model, I ensured that the woods collected were highly variated (i.e., woods that had longer lengths and smaller widths, smaller widths and smaller lengths, wider widths and smaller lengths, and so on). Two weight models were created using the wood's weight measurement immediately after collation and after the woods were oven-dried. Figure 2.1 shows the collation and sorting of the biomass used in setting up the weight estimation model. Importantly, I ensured the individual wood was fairly uniform, which was necessary to have a representable width and circumference of the biomass. Furthermore, the average of two to three readings taken at slightly different locations on the individual wood was used to represent the overall width and circumference of the biomass. In validating and assessing the generalization of the weight model, the parameters for the buried root proxies were not used in training or testing the data. Apart from RP 3, the rest of the root proxies buried came from a different tree species. 66 Figure 2. 2: Showing the Collation of the biomass from the shredded trees. Subfigures A and B show the pile of wood shredded from the tree; Subfigure C shows the collected and trimmed biomass; and Subfigure D shows the biomass positioned for measurement. After obtaining the initial weight readings, I placed the biomass in an oven for six weeks at a maximum temperature of 142°F. Five root proxies were selected randomly and weighed weekly; when no significant weight loss was observed, the weights were further observed daily. The biomass was removed from the oven when the percentage daily weight change was between 0.00 % and 0.15%. Table 2 shows the weekly percentage change and the weight changes before the biomasses' dry weight was measured. 67 Table 2: Showing the weekly changes in weight and the total percentage change due to moisture content loss. WEEKS / DAYS R64 (g) R61 (g) R74 (g) R106 (g) R4 (g) Start day (3/7/2023) 590 1276 714 816 1018 Week 1 (3/15/2023) 350 780 404 550 616 Percentage Change 40.68 % 38.87 % 43.42 % 32.60 % 39.49 % Week 2 (3/23/2023) 338 736 390 534 586 Percentage Change 3.43 % 5.64 % 3.47 % 2.91 % 4.87 % Week 3 (3/27/2023) 336 728 286 532 582 Percentage Change 0.59 % 1.09 % 1.03 % 0.37 % 0.68 % Week 4 (4/4/2023) 334.8 722 384 526.2 576.8 Percentage Change 0.36 % 0.82 % 0.52 % 1.09 % 0.89 % Week 5 (4/10/2023) 333.2 716.8 3822 523.4 573 Percentage Change 0.48 % 0.72 % 0.52 % 0.53 % 0.66 % Week 5 (4/11/2023) 333.2 716 382 522.6 572.6 Percentage Change 0.00 % 0.11 % 0.00 % 0.15 % 0.07 % Total % Change 43.5 % 43.9 % 46.5 % 35.9 % 43.7 % 2.2.3 Exploratory Data Analysis (EDA) EDA is an important process in developing a machine learning model, as the data is explored, and outliers are easily detected and removed. This subsection explains the EDA steps taken before I began training the machine learning model. The measured weight before drying was plotted against each independent parameter to see the relationship between the independent parameters. 68 Figure 2. 3: Showing the relationship between the wet weight and the length. EDA aided the elimination of outliers. The Seaborn library is one of Python's most advanced visualization libraries and was used for the EDA process. Jointplot was used in plotting the relationship between the length and the weight. From the plot in Figure 2.3, some outliers were seen to be present from the collated roots. I could observe the relationship between the weight and the independently measured parameters by removing these outliers. 69 Figure 2. 4: Showing the trend between the length, width, and circumference with the weight of the biomass after the outliers had been removed in wet and dry weight. 70 Figure 2.4 illustrates the linear relationship between the independent parameters and weight. The width and circumference exhibit a more precise linear trend than the length. Additionally, since the width and circumference share a similar trend, the circumference of the buried root proxies can be estimated from the evaluated width after completing the GPR processing. The seaborn library heatmap was employed to visualize the correlation among the considered parameters, effectively showcasing the intra- and inter-relationships between the independent and dependent variables. Figure 2. 5: Showing the correlation between the variables in consideration for the wet and dry weight. 71 2.2.4 Machine Learning Estimators As a regression machine learning problem, four regression algorithms were used to construct the biomass weight model. Linear Regression, Support Vector Machine (SVM) linear regression, Neural Network (NN), and Random Forest (RF) were the regressor algorithms used. In general, linear regression assesses the relationship between a dependent variable and one or more independent variables. An example of a linear regression model with several independent variables is written in equation 2.1. Consider the intercept β0 and the slope β𝑖 and the error term epsilon (𝜀) in a linear model; the dependent or response variable can be written as 𝑦 = β0 + β1 x1 + β2 x2 + β3 x3 + ⋯ + β𝑛 x𝑛 + 𝜀 (2.1). The least squares concept computes the coefficients to reduce the total squared error between the predicted and actual values. The slope and independent variables depend on the number of predictors used. In the case of the developed model, there are three predictors (length, width, and circumference) with two response variables (wet and dried weight). The SVM, NN, and RF follow the same approach but with more sophisticated algorithms that optimize each predictor's weights (slope). The equations and explanations for the algorithms are elaborated on in the book (Aurélien, 2017). The four regressors used were imported from the Scikit learn library and were used in developing the machine learning model. 2.2.5 Mean Absolute Error (MAE) To evaluate the machine learning model developed, an error test was done to assess the model prediction accuracy using the MAE method, which compares the predicted value (Ŷ) and actual value (𝑌) and computes the sum of the absolute difference in both values divided by the total number of sample points (𝑁). 72 ∑(|Ŷ − 𝑌|) 𝑀𝐴𝐸 = 2.2. 𝑁 2.3 Results and Discussions Two interconnected experiments were conducted in this chapter. The first experiment involved burying known root proxies and assessing the GPR accuracy in identifying root depth and geometry using a non-invasive method. The second experiment focused on constructing a weight model and estimating the number of weights based on the reconstructed root proxies. Since experiment one utilizes information from experiment two, the results of experiment two are presented first. 2.3.1 Weight Model Results and Discussion Two response variables were considered in constructing the weight model: wet and dry weight. A Python class was developed consisting of methods that scale the dataset (independent and dependent variables), train the training dataset, and predict the test dataset, facilitating ease of computation and enabling the exploration of various combinations for cross-validation. The 'train_test_split' function in the 'model_selection' module of the scikit-learn library was utilized to divide the dataset into 80% for training and 20% for testing. This function includes an inherent hyperparameter called 'random_state,' which is used to randomly select data for training and validation, a necessary step for performing cross-validation on the results. The k-fold cross- validation method was applied to assess model performance. A 5-fold cross-validation method was implemented, with five random numbers inputted into the 'random_state' hyperparameter, setting k=5. By varying the 'random_state' five times, five subsets of data were created for training, and the average performance of the five models was used to evaluate the overall model performance. 73 The wet weight model was developed using length, width, and circumference variables to predict weight before the biomass was oven-dried. The Support Vector Regressor (SVR) and Random Forest Regressors performed similarly, outperforming the neural network and linear regression regressors. Table 3 displays the mean absolute error of the cross-validation model. Table 3: Showing the MAE for the four regressors used for training the model and the average model performance from the 5-fold cross-validation in grams (g) for the wet weight. RANDOM STATE (SEED) SVR MAE RF MAE MLP MAE LR MAE 20 52.62 42.78 53.39 65.34 300 42.21 28.22 42.87 48.09 2 53.60 41.57 49.36 58.82 100 83.44 32.18 94.79 98.45 5 34.01 27.08 40.52 41.96 Average 53.17 34.37 56.19 62.53 As seen in Table 3, the random forest (RF) regressor produces the lowest MAE and also was the best estimator, followed by the support vector regressor (SVR) machine, neural network (MLP), and the linear regressor (LR). The prediction of the four regressors is plotted using the ‘Random_state’=5 model result. 74 Figure 2. 6: Showing the model performance using the four regressors in predicting the wet weight in the test dataset. A residual test was conducted to ensure that the model stayed balanced and was not overfitting or underfitting by calculating the difference between the training and predicted training datasets. Figure 2.7 displays the residual results of the random forest model with a random_state value of 5. 75 Figure 2. 7: Showing the residual pattern and the convergence of the data at the zero line. As depicted in Figure 2.7, the random forest algorithm attempts to minimize the error between all data points in the given dataset. Once convergence is achieved based on the cost function threshold, the model becomes adequately trained. The same processes were applied to the dry weight measurements. However, as noted in the Exploratory Data Analysis (EDA) section, the independent variables correlate more strongly with the dry weight than the wet weight. Consequently, we can anticipate better results. Additionally, since most of the moisture content in the root proxies has been eliminated and the root proxies share similar conditions, the machine learning algorithms will effectively capture the patterns between the response and independent variables. Table 4 presents the four regression models' Mean Absolute Error (MAE). 76 Table 4: Showing the MAE values in grams (g) of the dry weight model and the average. Random_state (Seed) SVR MAE RF MAE MLP MAE LR MAE 20 38.52 38.52 38.52 38.52 300 28.08 20.97 31.36 41.31 2 37.75 26.51 39.05 38.90 100 37.75 26.51 39.05 38.90 5 26.67 16.32 29.24 38.73 Average 33.75 25.77 35.44 39.27 Table 4 shows that the machine learning models optimally minimize errors during cross- validation while learning the patterns associated with length, circumference, width, and weight. Figure 2. 8: Showing the model performance using the four regressors to predict the test dataset’s dry weight. 77 Similarly, Figure 2.8 and 2.9 display the plots depicting the predictions of dry weight in comparison to the actual weight and shows the residual information of the dry weight model. Figure 2. 9: Showing the residual pattern and the convergence of the data at the zero line for the dry weight. The minimized cost function for the dry weight is notably smaller than that of the wet weight, which explains why the dry weight model performs more accurately. As seen in Figure 2.9, the data points are more closely aligned to the zero line. At this stage of the model, it becomes evident that the root geometry can serve as an estimator for determining root weight. Furthermore, the trained model was employed to predict and estimate the weight after reconstructing the buried proxies. 78 2.3.2 Reconstructed Root Proxies Results and Weight Estimation As discussed in subsection 2.2.1, the root proxies were buried at various positions within the grid at depths ranging from 15 cm to 30 cm in the soil. The experiment aimed to assess the accuracy of Ground Penetrating Radar (GPR) in detecting roots location (depth) and evaluate the precision of GPR in reconstructing roots using the grid method described in Chapter 1. Furthermore, data were collected under three soil conditions to investigate the optimal moisture content for detecting roots. Soil moisture content and precipitation data were obtained from the MSU Enviro-Weather station, approximately 3.06 miles from the controlled experiment site. The first data set was collected on March 28, 2023, following a rainfall of 0.19 inches the previous day. The soil moisture content between 0-30 cm of the soil ranged from 0.233 to 0.255 in3/in3. The second data set was collected on April 4, 2023, after a rainfall of 0.53 inches, with data collected a few hours post-rainfall. The soil was ponded, with moisture content ranging from 0.313 to 0.346 in3/in3. The final data set was collected on April 13, 2023. The soil was relatively dry since there had been no rainfall for eight days, and the soil moisture content within the first 30 cm ranged from 0.215 to 0.226 in3/in3. The data were processed using the grid method discussed in Chapter 1. Table 5 presents the velocity of the electromagnetic (EM) wave and the depth at which each root proxy was identified after interpolating the processed, controlled experiment data. 79 Figure 2. 10: Displaying the buried root position and the reconstructed depth slices showing the root proxies on Day 1 (relative moist soil), Day 2 (ponded Soil), and Day 3 (dry soil). The data collected on Day 1 accurately represented the buried root proxies among the other datasets. This information was utilized to reconstruct the root proxies in 3D while also measuring the root proxies' geometry (length and width). 80 Table 5: Showing the reconstructed roots depths and the measured buried depth. ND means non- discernable. RP 1 RP2 RP 3 RP 4 RP 5 RP 6 RP 7 VELOCITY DAYS (cm) (cm) (cm) (cm) (cm) (cm) (cm) (m/µs) DAY 1 14 - 20 9 - 15 18 - 28 14 – 20 15 - 23 15 - 22 15 - 22 68 DAY 2 ND ND ND ND ND ND ND 62 DAY 3 13 – 21 ND 18 - 29 ND ND 16 - 22 17 - 22 84 ACTUAL 16 - 20 10 – 15 20 – 30 15 – 24 22 – 25 17 – 20 17 - 20 DEPTH The reconstructed depth correlated with the actual buried depth, with an error margin of +/- 3 cm. The controlled experiment demonstrated that the ground-penetrating radar (GPR) does not perform optimally in detecting roots when the soil is excessively wet or dry. Due to the ponded soil, the depth of the majority of root proxies was indiscernible. Therefore, in order to accurately reconstruct the roots, an appropriate level of soil moisture is required. Another observation pertains to the velocity of the electromagnetic (EM) wave. As presented in subsection 1.1.2.2, the velocity is inversely proportional to the dielectric permittivity. Water has a high dielectric permittivity (epsilon = 81), indicating that increased water content reduces velocity. The interpreted results from Day 1's depth slices were further processed using ImageJ. A direct method was used, such as uploading the depth slices directly to imageJ, since the noise level was low and the root proxies amplitude could easily be seen. The depth slices that displayed the individual root proxies were chosen. The depth slice snapshot was upscaled to 7559 x 7559 pixels, equivalent to a 2m x 2m area, and the units of the slices were converted to meters. The width and length of each proxy were obtained using the line measuring tool to draw lines along 81 the length and width of the proxies. Depth slice 13 was utilized to take measurements for RP 1, RP 2, RP 4, RP 5, RP 6, and RP 7, while depth slice 16 was used to estimate RP 3. Figure 2.11 displays the depth slices used to take the readings of the root proxies geometry, and Table 5 highlights the estimated length and width, and the percentage error with the actual measurement. Figure 2. 11: Showing the methodology employed in estimating the root proxies in ImageJ. Numerous errors may emerge when estimating the width of root proxies, including variations in interpolating the grid boxes and adjusting the color threshold. To estimate the width, the smallest possible width was chosen for each root proxy which may not be an exact representation of the width of the root. The circumference was estimated based on the relationship between the collected root proxies' width and circumference. If the roots were perfectly circular, the difference would be pi; however, due to the level of variance in root circumference, the average values of the ratio 82 between the circumference and width were utilized to approximate the predicted circumference (estimated pie = 3.37). Table 6: Showing the estimated Length and width of the associated error with the actual length and width of the biomass. Root Length % Length Width % Width Circumference Proxies (cm) Error (cm) Error (cm) RP 1 73.1 -12.98% 11.8 140.82% 39.73 RP 2 79.9 -17.63% 5.4 25.58% 18.18 RP 3 113.9 9.52% 7.8 71.43% 26.26 RP 4 54.5 6.86% 9.9 130.23% 33.34 RP 5 52.4 -6.43% 6.2 27.57% 20.88 RP 6 62 -3.13% 5.4 24.71% 18.18 RP 7 55 -19.12% 8.9 85.42% 29.97 As seen in Table 6, the length error is more tolerable than the width, as discussed earlier. To successfully estimate the weight of the biomass, an allometric equation or another validation method should be used alongside the Ground Penetrating Radar (GPR) when approximating the biomass's width. The weight of the buried biomass was estimated using actual and estimated geometry measurements. The results not included in this study revealed a significant error gap. The reason for this discrepancy is quite understandable: the root proxies buried were randomly selected and had non-uniform water content, leading to errors in predicting the actual weight. However, the 83 dry weight had a smaller error and could be generalized, as this aspect will be considered in further studies. 84 CHAPTER 3: SPATIAL RELATIONSHIP BETWEEN THE TART CHERRY TREE CANOPY AND ROOT This chapter explores the relationship between the Tart cherry tree's canopy size and its root's spatial distribution extent. Three out of the Nine sampled were big Trees and were the trees the 800 MHz antenna frequency could reconstruct. The site location, materials, and methods for measuring the canopy and root extent are discussed in this chapter. 3.1 Site Location As mentioned in Chapter 1, two locations were chosen for this study: the MSU AgBioResearch Center in Clarksville and Traverse City. Figures 3.1 and 3.2 display the geographical locations of Clarksville and Upper Bahle field in Traverse City, where the trees were sampled. Figure 3. 1: Showing Clarksville location and the number of trees sampled in the MSU AgBioResearch Center. 85 The young and old Tart cherry trees in Clarksville are distinctly separated, and data collection was conducted on six of the younger trees. This result is not discussed in this chapter due to the relatively small diameter of the roots. Two of the mature trees in Clarksville were sampled using the cylindrical methodology, and their results are combined and discussed with the grid data processing methodology from Traverse City. Figure 3. 2: Showing the Traverse City geographical location at the Bahle Upper field in Northern Michigan. 3.2 Materials and Methods The aerial photographs for both locations were captured using the Basso lab-owned Matrice 100 unmanned aerial vehicle(UAV/ Drone). This drone has a 960p resolution, an embedded GPS, and an RTK hovering accuracy of +/- 10 cm. Its positioning accuracy is 1 cm + 1 ppm (for the horizontal position) and 1.5 cm + 1 ppm (for the vertical position) Aerial images of the Bahle Upper field in Traverse City were collected on June 14, 2022, during the period of GPR data collection around the tree. Following this, aerial images of the MSU AgBio Research Center were captured on June 22, 2022. 86 The drone had eight sensors, including the Normalized Difference Vegetation Index (NDVI), Thermal, RGB, and others. However, for this study, only the RGB images were used to assess the canopy size of each tree measured using the GPR. After the images were processed, the measurement tool in ArcGIS was utilized to determine the horizontal and vertical lengths of the canopies, as well as the canopy area, for the sampled trees in both Clarksville and Traverse City. Figure 3. 3: Showing the Matrix 100 UAV. 87 Figure 3. 4: Illustrates the method employed to determine the canopy size using ArcGIS's measurement tool. The geometry (length, width, and area) of the mature Cherry tree is determined using the method depicted in Figure 3.4 and subsequently compared with the spatial root distribution of the tree. The results and discussion are presented in Subsection 3.4 of this chapter. 3.3 Results and Discussions Two subsections are presented here. The first subsection compares the canopy size with the reconstructed root distribution of the Tart Cherry tree in Traverse City using the grid methodology, and Subsection 2 compares the canopy and root distribution of the two mature trees in Clarksville, whose roots were reconstructed using the cylindrical methodology. 88 3.3.1 Spatial Relationship between the Canopy and Roots of the Tart Cherry Tree in Traverse City The length and width of the canopy size, as measured using ArcGIS, are 5.388 m and 4.181 m, respectively. The area measured was 20.408 m2. Compared with the canopy size, the reconstructed Tart Cherry tree roots extend to a 5 m x 5 m area, representing the coarse part of the roots. Furthermore, there is a higher probability that the roots extend beyond the 25 m2 area as captured by the GPR results. N Figure 3. 5: Showing the spatial relationship between the Tart Cherry Tree canopy and the roots in Traverse City. 89 3.3.2 Spatial Relationship between the Canopy and Roots of the Tart Cherry Trees in Clarksville The length and width of the canopy size of the Tree 2 are 6.733 m and 6.837 m, respectively. The area measured was 32.986 m2. Compared with the canopy size, the reconstructed Tart Cherry tree roots extend to a 6.4 m x 6.4 m grid and approximately 40.96 m2 area. As seen in Traverse City, the coarse roots extend farther than the canopy size. N Figure 3. 6: Showing the spatial relationship between Tree 2 Canopy size and its roots. 90 The length and width of the canopy size of the Tree 7 are 5.572 m and 5.486 m, respectively. The area measured was 27.221 m2. Compared with the canopy size, the reconstructed Tart Cherry tree roots extend to a 5.8 m x 5.8 m grid and approximately 33.64 m2 area. N Figure 3. 7: Showing the spatial relationship between Tree 7 Canopy size and its roots. 91 CHAPTER 4: CONCLUSIONS This research offers an in-depth analysis of the root distribution of Tart Cherry trees using Ground Penetrating Radar (GPR) and Artificial Intelligence (AI), which includes machine learning and remote sensing. As hypothesized, GPR signals can detect tree roots. The study employed two known GPR data collection methodologies, and the results revealed that both could measure roots. Based on the results of this study, the research question should determine the most appropriate data collection method to be used. The cylindrical data methodology setup is relatively easier and less time-consuming; however, it is computationally intensive. There are no free tools available to reconstruct the cylindrical setup in space. As seen in Chapter 1, Python code was utilized to convert cylindrical coordinates into Cartesian coordinates after enhancing the amplitude signal and increasing the signal-to-noise ratio. Additional processing and interpolation were performed using ten cores and a 500 GB RAM supercomputing framework of the MSU HPCC platform. The length and depth of the roots were accurately measured by the cylindrical data methodology, proving sufficient for conducting spatial distribution studies of roots, as demonstrated by (Alani et al., 2018; Lantini, Tosti, et al., 2020a; Zhang et al., 2019). Conversely, while the grid data methodology can accurately assess the lengths and depths of roots, as seen in the controlled experiment results, it can also approximate root width. Although further research must be conducted to determine the accuracy of width detection, which is subject to grid cell interpolation errors and the attenuation of the GPR signal, estimating root width using GPR should be an active area of research. The ability to reconstruct root width holds promise for estimating root weight using non-invasive approaches, as demonstrated in Chapter 2 of this study. 92 The 3D reconstruction of the roots was accomplished using the grid approach, revealing that Tart Cherry tree roots in Traverse City extend to a depth of at least 30 cm. In summary, the GPR methodologies used in this study showed that Tart Cherry tree roots extend to depths of 30 cm - 45 cm in the soil, as evidenced by the results from Traverse City and Clarksville locations. The results also indicated that coarse roots extended spatially to the length of the farthest transects collected. In Chapter 1, the AI tool utilized with the GPR was the VGG-16, a Convolutional Neural Network (CNN) model that enabled the extraction of roots from depth slices obtained from the MALA Vision software. In Chapter 2, a new approach for validating GPR results was proposed and implemented using a novel idea of burying root proxies and estimating their dimensions instead of excavating trees, as most previous research studies implemented. For the study, seven root proxies were buried in the soil at varying angles and depths. The results of the reconstructed profile using the grid methodology accurately correlated with the measured biomass dimensions before burial. The reconstructed length had an error ranging from -19.12% to 3.13%. The depth had the highest accuracy with an error of 2 to 5 cm (the RP 5 had surfaced 10cm before the measured depth and was the only proxy with such a large value discrepancy). The width had the largest error, and as explained in Chapter 2, the width accuracy largely depends on the interpolation settings and the color thresholding. Furthermore, a root weight estimator model was developed using four regressor algorithms- support vector regressor (SVR), random forest (RF), neural network (MLP), and linear regression (LR) to assess the possibility of predicting biomass weights given root length, width, and circumference. The training, testing, and cross-validation results showed a generalizable 93 model, with the dry weight model performing better than the wet weight. The wet weight validation had an average mean absolute error (MAE) of 53.17 (SVR), 34.37 (RF), 56.19 (MLP), and 62.53 (LR). In contrast, the dry weight validation had an average MAE of 33.75 (SVR), 25.77 (RF), 35.44 (MLP), and 39.27 (LR), which was less than 6% of the actual measured weight of the root proxies. The grid-search approach was used for the hyperparameter tuning, but the results did not significantly increase the accuracy of the model. Hence the default model values were used for the wet and dry weights. The controlled experiment also showed that the GPR does not perform optimally when the soil is too wet and too dry, as the GPR results that assessed the spatial distribution of the root proxies were taken a day after 0.19 inches of precipitation. The readings were collected with an average soil moisture content of 0.244 in3/in3. Also, from theory, water has the highest dielectric permittivity of 81 (apart from metallic objects). Other materials' (geological) dielectric permittivity values are between air (𝜀𝑟 = 1) and water dielectric permittivity. Since velocity has an inverse relationship with the dielectric permittivity, as presented in Chapter 1, the velocity for the different soil moisture content is seen to reduce as the moisture content of the soil increases. The weight estimator study indicates the possibility of estimating the weights of roots and other tree parts using attributes such as length, width, and circumference. In Chapter 2, the four regressor algorithms for estimating biomass weight were the AI utilized. Chapter 3 concluded the study by assessing Tart cherry trees' root distribution by comparing their canopy size's spatial distribution to the lateral root extent. According to (Pallardy, 2010), the roots of fruit trees can extend up to three times wider than the canopy. The controlled experiment revealed that an 800 MHz antenna frequency, depending on the velocity of the EM wave in the soil, could detect and reconstruct roots with diameters of 4 cm. Helmisaari et al. 94 (2000) highlighted that root widths less than 2 mm are classified as fine roots. Therefore it is safe to guestimate that the roots of the tart cherry tree would greatly exceed the canopy size since the roots up to 4 cm in diameter exceeded the canopy's spatial extent, as seen in the results of Chapter 3. Also, in a fruit tree study by Kaushal et al. (2019), the majority of fine roots of the Mulberry tree were found within the first 15 cm of the soil. In conclusion, to provide a comprehensive summary of the roots of the Tart cherry tree, a higher antenna frequency in the GHz range can be combined with the 800 MHz antenna frequency to assess the total root spatial distribution completely. My research has provided systematic studies of assessing the roots of trees using GPR methodologies, and the results obtained from the combination of AI tools used alongside the GPR were very promising in reconstructing the roots of trees. 95 BIBLIOGRAPHY Alani, A. M., Ciampoli, L. B., Lantini, L., Tosti, F., & Benedetto, A. (2018, August 20). 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