Progress 12/01/17 to 11/30/18
Outputs
Target Audience:A presentation on this project was made at the Annual Meeting of the Agronomy Society of America, in Baltimore, MD on November 5, 2018. The Abstract of this presentation reads: "Predicting plant traits (Phenotypes) from Genetics in a site-specific Environment modified by Management (GEM2P) is a key problem for crop modeling. GEM2P modeling is as critical to farmers managing one variety in one field as it is to breeders seeking to optimize crossing programs relative to a target population of environments given data on lines tested to date. While genetic data are exploding exponentially, plant trait data have lagged, leading to keen interest in high throughput phenotyping, especially via imaging. Imagery has multifaceted value in early crop stages but options for its use decline when canopy closure cuts lines of sight. This project explores whether this impediment can be ameliorated by microwave (2-18 GHz) radar scans to which canopies are partially transparent. To enable both small plot testing with many target plant morphologies and function and also to aid breeders in establishing GEM2P links, this study uses wheat breeding trial plots (1m x 5m), and a newly developed mapping population. The radar is cart-mounted and manually pushed over the plots. Antenna position is continuously tracked by GPS. Radar data can be processed in many ways. We are currently extracting echograms (10.9 MB/plot) that show signal return strength as a function of depth into the canopy and distance along the plot, and genetically mapping echogram features. Near-term work will combine simulation of within-canopy radar propagation with machine learning to explore the estimation of plant morphology model parameters which can then, themselves, be genetically mapped. Current scanning covers 300 plots in ca. two hours, which can likely be cut in half by robotic automation. If high throughput systems reach a point where they can safely and reliably operate in a fully autonomous mode then, unlike optical systems, radar would be able to collect phenotype data at any time of day or night." Additionally, at that same meeting, material from this project formed part of a longer presentation entitled "Co-design of Gene-based Ecophysiological Crop Models for Breeding and Management". That presentation was one of five invited talks in a special symposium entitled "The Modeling Road Less Travelled - Alternative Paradigms for Crop Modeling". The paper containing material from this project was titled "Co-design of Gene-based Ecophysiological Crop Models for Breeding and Management" and emphasized that the next generation of crop models must both drive the evolution of novel sensing modalities as well as directly exploit their measurements. This project was presented as one of two novel electromagnetic technologies that appear to be very promising in this regard. Changes/Problems:Year 2 was extremely informative regarding all aspects of the project from the design and operation of the field apparatus through the modeling and use of brightness histograms for feature extraction. We will continue to refine our efforts using the insights gained. We therefore do not anticipate any major changes during the unfunded extension (Year 3) that would be comparable in scale to the alterations made during Year 2. What opportunities for training and professional development has the project provided?This project has supported two graduate research assistants at KU including a Ph.D. candidate and M.S. student. The project has provided mentoring for these student by faculty and staff from both KU and KSU in the disciplines of Engineering, Agronomy, and Mathematics. It has also provided field experience in an agricultural environment to these as well as a few other students during the radar experiments. The Ph.D. student is expected to graduate during the Fall 2018 semester and is planning to continue as a Post-Doc to work primarily on this work. Other students have gained experience in conducting field work during the surveys in Viola. In the area of professional development, the radar expertise at KU has substantially increased the understanding of electromagnetic scattering and radar technology among the faculty participants at KSU. How have the results been disseminated to communities of interest?An invited presentation was made to the 2018 Coalition for Advancing Digital Research & Education) conference (CADRE) held at Oklahoma State University. As described at its website (https://hpcc.okstate.edu/cadre-conference), the CADRE conference "brings together regional research computing professionals, librarians, researchers, educators, and students interested in advancing digital research and education across all disciplines". According to the conference website (https://hpcc.okstate.edu/cadre-conference), over 200 people participated in this conference from several states, 23 academic institutions, 12 commercial organizations, 2 government agencies, and 3 non-governmental organizations. The abstract for the CADRE presentation read: "Annual rates of gain in crop yields are far below those needed to meet global food needs at 2050. Accelerating progress depends on finding highly efficient methods for measuring plant traits in crop improvement programs. While great progress is being made in using image-based approaches, especially from unmanned aerial vehicles, these methods become limited when the canopy becomes too dense to see into. The work to be reported shows the potential to overcome this problem by using microwave radar to which plant canopies are moderately transparent. Exploiting this technology requires a combination of 3D modeling, microwave scattering calculations, and scattering inversion methods, all of which are computationally intensive (e.g. repeated pseudoinverse solving of 80K x 40K matrices for each plot). An overview of the computational methods will be included in the talk." What do you plan to do during the next reporting period to accomplish the goals?NOTE: This project has elements that are highly visual. Therefore, this text references figures that can be found at https://www.math.ksu.edu/~albin/rpt/USDA.NIFA.1011409.2018/figures.pdf. Plans for Year 3 (an unfunded project extension) will focus primarily on radar simulations, field-data processing and overall interpretation and analysis. Information obtained under each of the objectives in Years 1 and 2 will be brought together in a cohesive and highly integrated manner. For example, we will use the radar wheat simulator to investigate relationships (sensitivity analysis) between plant structure and radar wave forms from both the simulations and actual field data. The now documented ability to extract genetically mappable features from brightness histograms of selected echogram areas provides a powerful probe. Such histograms should be linkable to the simulator by simulating random realizations of the canopy such as was done in Year 1. This establishes the existence of a concrete and complete analytic pipeline from morphological constructs to radar signatures to genetic map features. Proving that such a pipeline could be constructed was the major aim of the project. In the coming year we will seek to both broaden and sharpen that connection. Doing so will entail improvements at all three pipeline stages, including the application of more refined mapping procedures to the extant data, now that we have shown that radar measurements do, indeed, contain concrete genetic signals to be deciphered. This process can, in effect, be worked from both ends. In the forward direction, once we have identified a measureable relationship between a plant feature and a waveform parameter, the parameters will be determined from all the 300 wheat plots measured during Year 2, and analyzed to see if there are any genetic correlations. In the reverse direction, candidate features to examine can be identified from QTL already established in the published literature. Additionally, we will take advantage of opportunities to collect additional data with the current cart/radar configuration. Any potential modifications to the current cart/radar design will be to experiment with alternative viewing geometries and improve survey efficiency. One set of data from Year 2 that has received only qualitative attention to this point is the imagery that was collected (Figure 8). These image will be further exploited in the analyses detailed in the preceding paragraph. A potential cart modification would add an additional form of photography able to produce images such as in Figure 9. Watershed algorithms operate on single, monochromatic images to extract information correlated with distance and/or surface angles. Such imagery from areas visible to both cameras and the radar might aid in formulating simulator inputs (e.g. flake distributions) that could identify exceptionally revealing radar signatures applicable throughout the canopy. The simulator will also be used to investigate how different measurement/viewing geometries (other than nadir sounding as was done in the field surveys) can potentially be used to extract complementary data for inclusion in the analysis. These simulations will provide guidance on future cart and radar configuration. Additionally, if a specific geometry does appears to provide additional information, we will, if possible, attempt to collect such data from field plots during Year 3. We will also prepare and submit publications describing project results.
Impacts
What was accomplished under these goals?
This project has highly visual elements. Therefore, to maximize clarity, the figures referenced in the text are at: https://www.math.ksu.edu/~albin/rpt/PhenomicsEAGER_2nd_Annual_Rept_2018/figures.pdf. To provide the most readable flow, Objectives 2 and 1 are presented in reverse order. Objective 2. During the second year of the project, the radar simulator for plant models was completed and simulations were conducted for individual plant components (stems, leaves, and heads), single plants and collections of multiple plants. Simulation results were compared against full-wave simulations and measurements to test accuracy and to find its validity region. First, the simulation results were compared against those of a full-wave commercial simulator (Ansys HFSS-IE solver). This full-wave simulator is exact in the sense that it does not make analytic approximations, but it is significantly time-consuming. This comparison verified that our simulator, based on analytic approximations, is valid over a significant range of plant dimensions. In order to import the same geometry from our simulator to the full-wave simulator, a translator was developed to convert the original geometric model to the STL format, which uses closed polygon meshes to describe solids. The full-wave simulator verifies the performance of our simulator for a given geometry, but it does not test the geometric model itself. For this purpose, we performed laboratory radar measurements of the individual plant components and whole plants and compared them against simulations. These samples were collected from plants grown in-doors. The plant dimensions were measured with a micrometer, rulers and a protractor. The relative dielectric of the plant materials were measured with a dielectric probe. The laboratory radar measurements of the heads, leaves and stems were performed at different angles of illumination with respect to their main axis. The leaves were also measured at various curvature values. The measurements of the leaves and stems agreed very well with simulations. The geometric model of the head had to be modified from a single cylinder to a stack of cylinders with varying radii so that the measurements agree with the simulations. Relevant features of laboratory procedures and the resulting agreement between simulated and actual radar cross section measurements are shown in Figure 1 in the pdf file at the URL given above. Figure 2 shows the head modeled as a set of cylinders. Objective 1 is to extend the Analytic Element Method (AEM) used in hydrology to solve the Laplace fluid flow equation to the vector Helmholtz equation for electromagnetic scattering. This was accomplished in Year 1 for large numbers of spherical elements. Methods were developed to overcome severe numeric instabilities that used both preconditioning methods and techniques for efficiently reordering matrix elements. As work began this year on the elliptic cylinder, which to be the basic AEM primitive for modeling whole wheat plants, we realized that the sharp edges at the ends of each element created numeric problems not shared by the solvers being developed at KU. This moved us toward shapes such as the versatile polynomial "flake" in Figure 3. It also seemed likely that some numerical issues could be avoided by simply not attempting to simulate the fields in places that are not "real" - such as the spaces "between" the flakes. Before we could test this notion, however, we realized there was another problem - what was the curvature of the leaf? The shapes of leaf blades are well established via growth dynamics. Functional structural models like ADEL-Wheat have modeled the leaf midrib curvature using measured combinations of linear and parabolic segments, generating realistic-looking results. The simulations used herein have employed beam deflection equations using flexural rigidity (FR) values we measured in the lab and an assumption of uniform leaf loading. However, more general approaches might have value in capturing the elements of 3D leaf curvature in the field. This issue will be discussed in the section on the next reporting period. Objective 3 was to conduct microwave backscatter experiments in a large (24' x 24' x 38') anechoic chamber (www.chamber.cresis.ku.edu) at KU to obtain basic design data in an electrically quiet environment. The initial experiments were accomplished by constructing a mobile planting box (ca. 4' x 4' x 2' box on casters) to grow a small plot of wheat in a greenhouse on the roof of the building housing the anechoic chamber. The box was periodically transported to the chamber where antennas were mounted above the wheat and backscatter measurements were collected, a process that became increasing difficult to accomplish due to the large size of the box. As an alternative, a growing area was created in the basement of another KU building with sufficient lighting to grow a stationary wheat plot. Hard red spring wheat (Kelby) was grown in a 1.4mx3m plot indoors with proper illumination and watering. Due to shallow planting, plants did not develop evenly and full canopy measurements did not yield useful results. Fortunately, some plants developed normally, from which radar measurements of individual plant components were performed. These provided adequate information to evaluate the simulator. In addition to backscatter measurements from the wheat plot, other tools have been developed. A small test fixture was designed and built to measure the dielectric properties of leaves. Additionally, a computer simulator was developed to model the electromagnetic response of individual components of a wheat plant (stalk, leaves, head) as well as a combination of components to construct a single plant or plot of multiple plants - as described in objective (2). Objective 4 activities significantly increased during the second year of the project, focusing on achieving the ability to collect field data over for a complete mapping panel experiment involving 300 plots. Measurements from the first year validated the ability of the radar system to measure plant characteristics, but the wooden structure prohibited rapid data collection and limited the surveys to a maximum of 30 plots. A new version of a more mobile platform was developed as shown in Figure 4. The platform was also equipped to collect DGPS as well as both downward looking and side looking optical images of the wheat plots using small camera systems. The optical images provide addition context for data interpretation. Project team members collected data with the new platform in Viola, Kansas five times during the growing period on the specific dates of 04/16, 05/07, 05/22, 06/06, and 06/16. The data were processed to generate Level-2 products along with the necessary ancillary position data, and all products were documented and posted on a team FTP site for access. Initial features were extracted from the Level-2 products to include plant height and scattering intensities. Echograms (Figure 5) were filtered and analyzed to obtain isolate the ground and microwave-visible canopy tops. Brightness histograms (Figure 6) were tabulated and a heuristic model fit to separate canopy, ground, and noise data. A variety of direct and synthetic features were then extracted for correlation studies with agronomic data (yield, grain test weight, etc.) and genetic mapping. Figure 7 (top panel) shows a map of one such feature, namely the average brightness in the top half of the canopy in the 06/06 sampling. A variety of significant QTL are present. One of these (red arrow) appears to collocate with a QTL obtained from mapping final yield. At the present time, however, this cannot be confirmed because this figure is a low-resolution single-marker map. More powerful mapping methods will be applied shortly to this and to QTL obtained for other radar features.
Publications
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Progress 12/01/16 to 11/30/17
Outputs
Target Audience:The main target audience for the technology being evaluated in this proof-of-concept project is plant breeders needing to be able to assess phenotypes that cannot be seen optically as canopies become denser. Candidly, until we collected the first field data this year, we were not sure that there was a "there there". As a consequence, it would have been premature to engage in the kind of formal informational outreach efforts described in the "REEprot Guide for Project Directors" (pg. 40). However, do note the items described in the Dissemination section. With the first year's results in hand, there will be greater effort in this area. Two activities are already in the docket - invited invitations to present at this year's Agronomy Society of America annual meeting and at the 2018 CADRE (Coalition for Advancing Digital Research & Education) conference to be held at Oklahoma State University. The ASA presentation will be in the context of new approaches to crop modeling. It will emphasize an end-to-end modeling approach wherein phenotyping, model development (including genetic aspects), and model delivery/use are designed as an integrated whole. The opportunity to include radar-based sensing will be included as part of this package. As described at its website (https://hpcc.okstate.edu/cadre-conference), the CADRE conference "brings together regional research computing professionals, librarians, researchers, educators, and students interested in advancing digital research and education across all disciplines". The 200 attendees at the 2017 conference represented "16 higher educational institutions, 11 commercial, four governmental, and four nongovernmental organizations". The (not yet web posted) abstract for the CADRE presentation reads: "Annual rates of gain in crop yields are far below those needed to meet global food needs at 2050. Accelerating progress depends on finding highly efficient methods for measuring plant traits in crop improvement programs. While great progress is being made in using image-based approaches, especially from unmanned aerial vehicles, these methods become limited when the canopy becomes too dense to see into. The work to be reported shows the potential to overcome this problem by using microwave radar to which plant canopies are moderately transparent. Exploiting this technology requires a combination of 3D modeling, microwave scattering calculations, and scattering inversion methods, all of which are computationally intensive (e.g. repeated pseudoinverse solving of 80K x 40K matrices for each plot). An overview of the computational methods will be included in the talk." Changes/Problems:We do not intend to perform additional measurements in the anechoic chamber, as we seem to be getting accurate results with the time gating setup discussed in the Work section. In addition to the analytic methods in the original proposal, we will investigate the use of deep neural networks as a method for inverting the radar signals. The scattering models reported herein will be used to generate training samples. What opportunities for training and professional development has the project provided?This project has supported two graduate research assistants at KU including a Ph.D. candidate and M.S. student. The project has provided mentoring for these student by faculty and staff from both KU and KSU in the disciplines of Engineering, Agronomy, and Mathematics. It has also provided field experience in an agricultural environment to these as well as a few other students during the radar experiments. In the area of professional development, the radar expertise at KU has substantially increased the understanding of electromagnetic scattering and radar technology among the faculty participants at KSU. How have the results been disseminated to communities of interest?Presentations were made in conjunction with the National Association of Plant Breeders in Davis, California (NIFA Project Directors meeting, August 2017) and at the Plant Animal Genome meeting in San Diego, California (January 2018). Both meetings entailed oral presentations and, at the former, a poster was shown. The presentation abstract for the former meeting reads "Wheat is achieving barely 50% of the gain rate needed to meet food needs at 2050. However, technology limits collection of the massive phenotype data, especially canopy geometry, needed to accelerate progress. This proof-of-concept project is combining microwave radar sensing with a novel, inversion algorithm to ameliorate the situation. We believe (1) it is unnecessary to sense the 3D position, angle, and size of all plant parts in a plot - rather one desires the genetic markers and effect sizes associated with statistical distributions of these quantities; (2) suitable morphological models exist; (3) if field radar data from plant canopies can be obtained and calculations accelerated, then such models can be inverted to yield genetics; and (4) extending the Analytical Element Method from hydrology to electromagnetic wave propagation can provide such a speed up. A prototype system has been built and tested in a wheat breeding field trial. Echograms clearly show canopy tops, the ground surface and dry down effects. As yet undiagnosed within-canopy features reflect morphological differences. Preliminary mathematical derivations and numerical work are underway. Using the observed distribution of radar returns and radiation boundary conditions, we seek to solve for plant phenotype probability density functions. Current work is 2D and we will move to 3D next year." At the January meeting this report was updated to include results obtained during the interim. One project-related paper has been accepted for publication. Steward, D. R., Wave resonance and dissipation in collections of partially reflecting vertical cylinders, Journal of Waterway, Port, Coastal and Ocean Engineering (ASCE), in press. This paper assumes that cylindrical scattering elements are arranged in rows and that the incident wave is planar with an electrical polarization vector parallel to the cylindrical axis. The spatially variable but temporally static target function is the wave potential. These simplifying assumptions enable initial bridging from hydrology, wherein the Analytical Element Method (AEM) originated, to electromagnetics. This is a natural first extension of existing theory from Graf's addition theorem for wave propagation, and has resulted in a model capable of very accurately reproducing the wave field caused by reflection and adsorption along sets of circular boundaries. This AEM model was exercised across a range of conditions and, as noted in the Work section, was found that extremely high amplification factors occur due to full wave reflection within sets of elements. In many cases, this causes convergence failures in the commonly used Gauss-Seidel solution algorithm, similar to what has been observed at discrete frequencies in boundary element solutions that utilize singular integrals (which is discussed in Steward, 2018). And, so the model is being adapted to reproduce not only the wave field outside a set of elements, but also the electrostatic wave field within the sets of elements and their solutions that satisfy sets of interface conditions. This paper does include the required NIFA acknowledgement for work supported by this project. What do you plan to do during the next reporting period to accomplish the goals?NOTE: This project has elements that are highly visual. Therefore, this text references figures that can be found at https://www.math.ksu.edu/~albin/rpt/USDA.NIFA.1011409.2018/figures.pdf. Objective 1. As originally stated in the proposal, this objective was to develop an exact solution to the vector Helmholtz equation for electromagnetic scattering from an elliptic cylinder using the Analytic Element Method. The idea was to first use this element to first build realistic 3D wheat plants. Then, second, inverse methods would be developed able to extract probability distributions of phenotypes like biomass, leaf angle distributions, etc., that are hidden from optical view in closed canopies. These probability distributions are all that are needed for genetics work and were deemed much simpler targets than full 3D morphology, which is an ill-posed problem for electromagnetic scattering. This said, the progress that both KU and KSU have made this year on solving for the scattered fields creates more opportunities than were envisioned in the original proposal as regards to the all-important inverse problem. First, an AEM-based inversion algorithm was, in fact, designed for the 2D cylinder problem but we did not report it in the "Work" section because the numeric computation problems alluded to therein prevented its full testing. While those issues have been resolved in 2D they are even more pronounced in 3D as noted in the Work section. It is probably worth noting that our long 2D learning curve is resulting in an ability to move much faster in 3D even though it is more difficult. KSU will take this experience forward and expand from the elliptical cylinder, alone, looking more broadly toward AEM Helmholtz solutions for other shapes (technically, isosurfaces of orthogonal coordinate systems). However, two other options are now seen to be additional possible lines of attack. First, the KU radar simulator will be used to determine a set of signal parameters that characterize the radar returns based on survey and target parameters. A regression algorithm will then be implemented to determine the relationship between these waveform parameters and some target characteristics. A second approach is based on a new idea. Workers in image-based sensing have been investigating whether deep neural networks can be used to extract plant data from pictures. A microwave example is shown in Fig 8. An impediment to this approach is the difficulty of obtaining enough network images whose plant trait scores are known. This is, of course, just exactly the manual phenotyping problem in another guise. One method is to use 3D models to generate the training set as shown at the bottom of Fig 8 for Arabidopsis. KSU will begin investigating this approach to wave field inversion by first using field images from the 2D cylinder solution in Fig 4. This will permit comparison with both true results and with the 2D inversion algorithm just mentioned. If that proves successful, then 3D work can be undertaken with training examples sourced either from the KU model, a 3D AEM model, or both. It is anticipated that preparing a training set from any of the models will require a cluster computing run of 80-160K CPU-hours. This is not an intimidating amount as such things go. Objective 2. Although the ADEL-Wheat model will not be used for reasons described in the Work section, both KU and KSU will work to improve 3D models. For example, KU will experiment with calculating leaf curvature from cantilever beam deflection theory under the assumption of uniform weight loading. A needed parameter is flexural rigidity (FR). Values for FR will be obtained from measurements of real leaf leaves. Biologically, FR integrates midrib characteristics, leaf dihedral angles, amounts of structural carbon, etc. making it of potential phenotypic interest. KSU will work on ways to make accurate 3D wheat plant models with whatever selection of AEM components prove readily derivable. Objective 3. Originally planned work under this objective was to obtain both design and validation data using the anechoic chamber at KU. However, as noted in the Work section, it proved sufficient to create a separate facility where non-target reflections could be removed from the data via time gating. Thus, no more work will be done using that chamber. The following forms of validation will be done. The simulator developed by KU will be validated by comparing its results against those generated using a much less computationally efficient commercial full-wave numerical simulator. This validation method will be used to check the accuracy of backscattering from individual elements and single plants. A similar comparison will be done between the AEM and KU simulators to test the sensitivity to the types of scattering elements used. Additionally, the KU simulator output will also be compared against laboratory measurements of the radar-cross-section of individual plants and plant elements. Objective 4. Based on experiences in 2017, a redesigned platform (Fig 9) will be used in the field. A major advantage of this design is that the transverse manual scanning has been replaced. Instead, the forward, GPS monitored motion of the device will carry the antenna mount lengthwise along the plot. This will dramatically increase the speed of operation from the move-stop-scan-reset and repeat mode of last year to nearly continuous scanning. Larger wheels combined with a three-point rather than four-point suspension will make it easier for the apparatus to conform to the somewhat uneven ground within a breeding trial. The frame of the platform will be formed from pre-fabricated aluminum rails. In contrast to the 2017 wooden structure (Fig 7), which weighed ca. 140 kg including the radar. The new aluminum structure will weigh half as much (70 kg). The wooden I-beam crossbar was ca. 5 m long but the longest piece of the new design is just over 3 m. This means that the 20-foot truck used to transport the apparatus in 2017 will no longer be needed. The new design's larger wheels, rotatable front wheel, lighter weight, and increased rigidity will enable a single person to operate the platform without assistance. We will monitor 188 recombinant inbred lines (RILs) at several points in time during the spring growing season. The lines are from a HV9W03-596R x TX04M410164 cross that captures central vs. southern Great Plains wheat variation in tillering capacity, height, and leaf angle - all traits to which our first year studies have revealed radar sensitivity. The plants have been planted in a partially replicated design with ca. 300 plots. They are located in Sumner Co. Kansas, near the Oklahoma line. (We originally planned to use a closer site in Reno Co. but the plots overwintered in unacceptable shape.) The data will be used in several ways. The first will be to genetically map information directly extracted from the returned radar signals (i.e. without any attempt to use inversion algorithms). Illustrative examples are shown in Fig 10. These will be based on longitudinal statistical moments of the depth profiles such as means, variances, etc. Whole profile indices will include the average strength of the returns, plant height, and so on. Additionally, microwave polarization studies have a proven capability to classify plant canopies as to crop, thus indicating that morphological information is contained in such data. We will compute polarization indices and map it to see if associated genomic regions can be identified. We will compare all mapping results to the extensive wheat mapping literature to identify candidate associations with known genetics. Similar mapping operations will be applied to the outputs of all inversion methods developed under Objective 1.
Impacts
What was accomplished under these goals?
NOTE: This project has elements that are highly visual. Therefore, this text references figures that can be found at https://www.math.ksu.edu/~albin/rpt/USDA.NIFA.1011409.2018/figures.pdf. For readability, Objectives 2 and 1 are presented in reverse order. Objective 2. Originally, the CERES-Wheat model was to be used as a stepping stone to the ADEL-Wheat model to parameterize some 5000 genotyped wheat lines. However, given the short project length, it was critical to focus modeling efforts on plant morphology rather than working with the extensive ecophysiological elements in such models. We therefore decided to concentrate on the mathematical approachs to be used in the scattering parts of the project. For the work at KU, a simulator first generates a structural description of individual plants and, in multi-plant runs, the entire canopy. A logistic equation was used to grade the change in leaf angle from that at the collar to the angle at the tip as a function of distance along the leaf. Leaf length and initial leaf angle are important plant phenotypes that influence light interception. Fig 1 in the linked pdf shows a single resulting plant along with simulated radar returns (line graphs) and tables of plant parameters. The line graphs are for a single plant and for an average of 40 plants with slight differences created by Monte Carlo simulation. For comparison, Fig 2 shows plants from ADEL-Wheat (image supplied by J. Evers, Wageningen Univ). Note that the leaves in Fig 2 have no thickness and so are unusable in our study. Each plant's leaves, stems, and heads were divided into small canonical objects located and oriented via parametric geometry based on the position and alignment of each plant part. Small circular cylinders were used for stems and flat rectangular cuboids for leaves. Tissue scattering properties were selected based on inputs from plant experts. Individual plant locations mimicked cultural practice. Fig 3 shows a resulting architectural model for a 1m x 1m plot. Ten cuboidal segments / leaf, four leaves / plant, ten cylinders / stem, and 200 plants / square meter gives 10K segments per simulation. Because of the antenna field-of-view, 2m x 2m is the smallest simulated target that can be used to generate realistic returns. The line graph is a depth profile of reflected field strength. (Note: To facilitate drawing, Fig 3 was produced from a mesh rendering rather than a voxel display (Fig 1). Next, each canonical object's scattering dyads are calculated via analytic approximations.As rotated in space, the scattering dyads for each object are used to calculate the forward scattering amplitudes, which combine to find the effective propagation constant. These various quantities, along with the antenna parameters are merged via a coherent radar equation to determine total radar returns. Objective 1. This aim is to extend the Analytic Element Method (AEM) from hydrology where it is used to calculate fluid flows and adapt it to the vector Helmholtz equation for solving electromagnetic scattering equations. Initial information from KSU related to 2D cylinders is presented below under publications. A next step was to expand to large collections of such cylinders. This proved to be numerically challenging. The most commonly used method for solving AEM equations is the Gauss-Seidel (GS) algorithm which is very efficient in terms of computer memory. However, GS requires that the spectral radius of the problem matrix be less than unity - a condition rarely met for large numbers of scatterers, especially when they are closely packed. A combination of matrix preconditioning and methods for reordering matrix elements so as to permit nested submatrix inversion were researched, developed, and implemented. Currently, we can compute the required AEM scattering coefficients for a set of 960 2D cylinders - the largest number tried - in less than two minutes. Fig 4 shows a close up of the scattered field. We have begun work on 3D elements, starting, as proposed, with elliptic cylinders. Figure 5 shows how sets of control points (yellow) on an object's surface can be used to solve for the Helmholtz scalar field scalar field from which the vector field can be calculated in the surround. The accompanying paragraph describes some of the numerical problems which are far more difficult in this system than they are for spheres. Fig 6 (from the proposal) shows our concept of how such cylinders might be used to construct wheat plants. Two issues are affecting this work. The first are the numeric issues just mentioned. The second and more fundamental is the realization that not all 11 coordinate systems in which the Helmholtz equation solves "nicely" may be suited for electromagnetic work. In particular, it is possible that some of the functions used in this system might not meet the "radiation conditions", i.e. the scattered waves might not dissipate at long distances. We have tarted looking at other coordinate systems to find ones that (1) solve easily, (2) satisfy the radiation condition and (3) have the geometric potential to represent plant parts. In any event, along with the more advanced KU work, we now have two approaches to predicting the scattering field whose efficiency and accuracy can be compared. Such models are the key to radar sensitivity and inversion analysis. More will be said about the latter, mission critical inversion problem under Plans. Objective 3 was to conduct microwave backscatter experiments in a large (24' x 24' x 38') anechoic chamber (www.chamber.cresis.ku.edu) at KU to obtain basic design data in an electrically quiet environment. Initially we constructed a mobile "wheat plot" (ca. 4' x 4' x 2') on casters in a greenhouse on the roof of the building housing the anechoic chamber. The box was periodically transported to the chamber where antennas were mounted above the wheat and backscatter measurements were collected. However, this process became increasingly difficult due to the large size of the box. As an alternative, a growing area was created in the basement of another KU building with sufficient lighting to grow a stationary wheat plot. Measurements can now be easily collected in a controlled way, wherein the radar data can be time-gated to remove unwanted reflection from walls or other nearby items. In addition to backscatter measurements from the wheat plot, other tools have been developed including a small test fixture to measure the dielectric properties of leaves and other wheat plant parts. Consideration is being given to measuring other leaf properties such as, for example, flexural rigidity so as to be able to calculate leaf curvature via cantilevered beam deflection equations. Objective 4 was to take field measurements in a breeding trial to link radar features to plant genetics. In 2017, a mobile, wooden structure scanned radar antennas across field plots to collect data. Two field trials were conducted with an ultra-wideband radar (2-8 GHz and 12-18 GHz). On 5 May, a proof-of-concept test scanned five wheat plots exhibiting different visual characteristics (height, heading status, leaf angles). Ca. 20 GB of radar measurements were collected from 5 m linear traverses over each plot. The data were processed to provide a cross-sectional reflection profiles (echograms) through the canopy to the soil. Fig 7 shows an echogram inserted into a picture of the apparatus. The line graph in Fig 3 (see also Fig 1) conceptually equates to one vertical cut through the echogram. A second experiment on 19 June looked at ca. 30 plots to provide additional measurements on dried wheat. This experiment included a second receiving antenna oriented at right angles so that cross polarization data could be collected. The May-to-June drying effects were obvious in the data. Because of the small number of plots sampled, no attempt was made this year to make a genetic connection.
Publications
- Type:
Journal Articles
Status:
Accepted
Year Published:
2018
Citation:
Steward, D. R., Wave resonance and dissipation in collections of partially reflecting vertical cylinders, Journal of Waterway, Port, Coastal and Ocean Engineering (ASCE), in press.
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