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16 pages, 50388 KiB  
Article
Ground-Penetrating Radar Full-Wave Inversion for Soil Moisture Mapping in Trench-Hill Potato Fields for Precise Irrigation
by Kaijun Wu, Henri Desesquelles, Rodolphe Cockenpot, Léon Guyard, Victor Cuisiniez and Sébastien Lambot
Remote Sens. 2022, 14(23), 6046; https://doi.org/10.3390/rs14236046 - 29 Nov 2022
Cited by 15 | Viewed by 3544
Abstract
In this paper, we analysed the effect of trench-hill soil surface on ground-penetrating radar (GPR) full-wave inversion for soil moisture measurement. We conducted numerical experiments by modelling the trench-hill surface using finite-difference time–domain (FDTD) simulations. The FDTD simulations were carried out with the [...] Read more.
In this paper, we analysed the effect of trench-hill soil surface on ground-penetrating radar (GPR) full-wave inversion for soil moisture measurement. We conducted numerical experiments by modelling the trench-hill surface using finite-difference time–domain (FDTD) simulations. The FDTD simulations were carried out with the open-source software gprMax, using different centre frequencies, namely, 150 MHz, 250 MHz and 450 MHz. The gprMax source/receiver for each centre frequency was calibrated, respectively, to transform the FDTD radar signal to normalized Green’s functions for wave propagation in multilayered media. The radar signals and inversion results of the three different frequency ranges are compared. The FDTD Green’s functions of the trench-hill surface with a flat surface are also compared. The results show that the trench-hill surface only slightly affects the inversion when frequency is lower than 190 MHz, which agrees with Rayleigh’s criterion. Field measurements were performed as well, using a prototype radar mounted on an irrigation robot. The low-frequency antenna was calibrated over a large water plane. The optimal operating frequency range was set to 130–190 MHz. TDR measurements were performed as well for comparison. The results demonstrated promising perspectives for automated and real-time determination of the root–zone soil moisture in potato fields, and thereby for precise and automatic irrigation. Full article
(This article belongs to the Special Issue Review of Application Areas of GPR)
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Graphical abstract

Graphical abstract
Full article ">Figure 1
<p>Potato trench-hill soil simulation model in gprMax. (<b>a</b>) the 3D model and (<b>b</b>) the 2D slice and configurations. Configuration i, the source/receiver moved and measured from point A to B with a step of 0.02 m, resulting in 50 measurements for each centre frequency (150 MHz, 250 MHz and 450 MHz). The soil relative permittivity stays the same, i.e., <math display="inline"><semantics> <msub> <mi>ε</mi> <mi>r</mi> </msub> </semantics></math> = 10. For configuration ii, the 150 MHz centre frequency source/receiver is situated above the centre of the top (point C), slope (point D) and bottom (point E) of the trench-hill surface, respectively, and <math display="inline"><semantics> <msub> <mi>ε</mi> <mi>r</mi> </msub> </semantics></math> varies from 5 to 22 with a step of 1. <span class="html-italic">h</span> is the distance between the source/receiver and the top of the surface. All measurements were conducted with the source/receiver at the same height, i.e., <span class="html-italic">h</span> = 1.78 m when the source/receiver above the top and <span class="html-italic">h</span> = 2 m when above the bottom.</p>
Full article ">Figure 2
<p>FDTD Green’s functions and inversion results with centre frequency (<b>a</b>) 150 MHz, (<b>b</b>) 250 MHz, and (<b>c</b>) 450 MHz. True <math display="inline"><semantics> <msub> <mi>ε</mi> <mi>r</mi> </msub> </semantics></math> = 10, <math display="inline"><semantics> <msub> <mi>h</mi> <mrow> <mi>m</mi> <mi>i</mi> <mi>n</mi> </mrow> </msub> </semantics></math> = 1.78 m, and <math display="inline"><semantics> <msub> <mi>h</mi> <mrow> <mi>m</mi> <mi>a</mi> <mi>x</mi> </mrow> </msub> </semantics></math> = 2.00 m.</p>
Full article ">Figure 3
<p>Intensity of the electric field for the three centre frequencies (150 MHz, 250 MHz and 450 MHz) and two configurations (source/receiver situated above the centre of the top (<b>a</b>–<b>c</b>) and the bottom (<b>d</b>–<b>f</b>). The propagation times as subcaptions were chosen from the peak of signals. Please note that the peaks do not correspond to the FDTD Green’s function in <a href="#remotesensing-14-06046-f002" class="html-fig">Figure 2</a> but to <math display="inline"><semantics> <mrow> <mi>b</mi> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>−</mo> <msub> <mi>h</mi> <mi>i</mi> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> </mrow> </semantics></math>.</p>
Full article ">Figure 4
<p>Simulated trench-hill and flat surface Green’s functions by gprMax, and analytical Green’s function for the flat surface in the frequency domain. (<b>a</b>) The source/receiver was situated above the central hill of the trench-hill surface. For the relevant flat surface Green’s function (the green dash line), the distance between the source/receiver and the surface <span class="html-italic">h</span> was 1.78 m. (<b>b</b>) The source/receiver was situated above the trench of the trench-hill surface, and the corresponding flat surface was with <span class="html-italic">h</span> defined as 2 m.</p>
Full article ">Figure 5
<p>Inversion results for Configuration ii, with the source/receiver situated above the hill, slope and the trench, respectively.</p>
Full article ">Figure 6
<p>Radar system with a log-periodic antenna held at several distances from a water plane to determine the antenna characteristic functions <math display="inline"><semantics> <mrow> <msub> <mi>R</mi> <mi>i</mi> </msub> <mrow> <mo>(</mo> <mi>ω</mi> <mo>)</mo> </mrow> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>T</mi> <mo>(</mo> <mi>ω</mi> <mo>)</mo> </mrow> </semantics></math>, and <math display="inline"><semantics> <mrow> <msub> <mi>R</mi> <mi>s</mi> </msub> <mrow> <mo>(</mo> <mi>ω</mi> <mo>)</mo> </mrow> </mrow> </semantics></math> (antenna calibration). The radar measurements were performed in the 80–1000 MHz frequency range.</p>
Full article ">Figure 7
<p>Magnitude and phase of the antenna characteristic functions. (<b>a</b>) the return loss <math display="inline"><semantics> <msub> <mi>R</mi> <mi>i</mi> </msub> </semantics></math>, (<b>b</b>) transmitting-receiving response <span class="html-italic">T</span> and (<b>c</b>) feedback loss <math display="inline"><semantics> <msub> <mi>R</mi> <mi>s</mi> </msub> </semantics></math>. The grey bar indicates the frequency range 130–190 MHz used for the field experiment.</p>
Full article ">Figure 8
<p>The radar prototype was set up on the irrigation robot Oscar (Osiris Agriculture, France).</p>
Full article ">Figure 9
<p>Potato field in Ferrières, Vallèe Jean Rèaux, Sains-Morainvillers, France. (<b>a</b>) volumetric soil moisture measurement points and orthophoto. Area A indicates the long profile of TDR measurements, and B indicates the short profile; (<b>b</b>) digital surface model map. Coordinates are in WGS84/UTM zone 31 N (m).</p>
Full article ">Figure 10
<p>Comparison between soil moisture results of GPR (sensitivity down to about 40 cm) and TDR (5 and 15 cm depth).</p>
Full article ">
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