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A computational model for radio wave propagation through tree orchards is presented. Trees are modeled as collections of branches, geometrically approximated by cylinders, whose dimensions are determined on the basis of measurements in a cherry orchard. Tree canopies are modeled as dielectric spheres of appropriate size. A single row of trees was modeled by creating copies of a representative tree model positioned on top of a rectangular, lossy dielectric slab that simulated the ground. The complete scattering model, including soil and trees, enhanced by periodicity conditions corresponding to the array, was characterized via a commercial computational software tool for simulating the wave propagation by means of the Finite Element Method. The attenuation of the simulated signal was compared to measurements taken in the cherry orchard, using two ZigBee receiver-transmitter modules. Near the top of the tree canopies (at 3 m), the predicted attenuation was close to the measured one—just slightly underestimated. However, at 1.5 m the solver underestimated the measured attenuation significantly, especially when leaves were present and, as distances grew longer. This suggests that the effects of scattering from neighboring tree rows need to be incorporated into the model. However, complex geometries result in ill conditioned linear systems that affect the solver's convergence.

Wireless sensor networks (WSNs) have started to gain ground in applications related to agriculture, originally for sensing and recently also for control purposes. Of particular interest are applications related to high value crops, such as fresh-market fruits grown in orchards that require high investment and intensive production measurements throughout the growing season. An important factor, which determines the effectiveness of a WSN, is the connectivity of its nodes,

In the past, several experiments have been conducted to quantify the behavior of radio signal propagation through forests [

For an EM wave propagating in free space, path loss can be calculated by the Friis equation [

The prediction of path loss in orchards is a complicated task. In addition to reflection from the ground, tree canopies, trunks, branches, and leaves cause diffraction and scattering of the radio wave. Empirical models are often used to predict path loss, in order to avoid complex analytical models that require knowledge of many parameters such as electromagnetic parameters, soil and leave moisture, geometric characteristics,

Although focusing on the aforementioned models is not the purpose of this paper, comparison among measurements against data extracted through all of them will be provided at least for one particular experimental layout, to quantify their relative accuracy with respect to the method proposed herein. In particular, the measurements and the results of the computational model proposed in this paper will be compared against the predictions of the Free Space, Fitted PE, MED, BFPED, ITU-R, and FITU-R models.

Contrary to empirical models, analytical models require knowledge of a set of propagation-related parameters regarding the environment (e.g., tree geometries), the EM properties of the soil, tree-branches and leaves (e.g., permittivity, permeability and conductivity). A well-established analytical tool is the Radiative Energy Transfer Model (RET) [

A generic model of 1–60 GHz narrowband radio signal attenuation in vegetation was suggested earlier [

Other analytical approaches for modeling the EM wave propagation include the use of the Uniform Theory of Diffraction (UTD) [

Propagation in plantations is also addressed in [

In the present approach a scattering model of a row of trees was constructed and the radio wave propagation was analyzed via a commercial Finite Element Method (FEM) solver. For this purpose, the geometry of a ‘typical’ cherry tree in an actual orchard was digitized, and a simplified Computer Aided Design (CAD) model of the tree was constructed. Estimates of the electrical properties (

The paper is organized as follows: in Section 2 material and methods are described, including tree geometry measurements, signal power measurements, and modeling through FEM. Details on the antenna characteristics, material properties and geometry discretization are provided. In Section 3, computational data are extracted and compared to measurements and analytical/empirical models. In Section 4 useful conclusions are drawn, whereas Section 5 serves as an

The orientations of the tree branches were measured using a 3D tilt sensor (InertiaCube3^{TM}, Intersense, Billerica, MA, USA). The sensor provides three degrees of freedom (yaw, pitch, roll) and angular range of 360° in all axes. In order to create a geometrical representation of cherry trees, measurements of the orientation, length and perimeter of the trunk and the main branches of a single representative tree were taken. The orchard was a commercial one and trees were similar in shapes and size.

The sensor was placed initially near the base of the trunk, thus defining the origin of a local 3D coordinate system (

Since the representation of the tree would be implemented by using cylinders for each branch, every branch that could not be considered as a unique cylinder was split into two or more shorter parts whose orientation, length and perimeter were measured separately. In total, thirty-seven tree parts were measured.

The RF module used by the receiver and the transmitter nodes was the XBee-Pro^{®} ZB (Part Number: XK-Z11-M, Digi-Key Inc., Thief River Falls, MN, USA). This RF module implements the ZigBee protocol stack, meets the IEEE 802.15.4 standards and operates within the ISM 2.4 GHz frequency band. The transmitter power was 40 mW (+16 dBm) and the receiver sensitivity was −100 dBm (1% packet error rate) and both modules used monopole integrated whip antennas with a gain equal to

The transmitter was placed 1 m away (outside the orchard) from the fourth tree of the first row; the transmitter power was set to 16 dBm. The receiver was placed inside the orchard, 1.5 m in front of every second tree, starting from the tree in the first row and first column. In total, the reception was measured at 107 trees. Each tree had a unique identification number and the numbering scheme is shown in

In both phases, three different scenarios were implemented. In each scenario the distance of the RF modules from the ground was different. In the first scenario the modules were placed 0.5 m above the ground, in the second 1.5 m above the ground, a height that is approximately near the middle of the foliage of every tree. Finally, in the third scenario, the modules were placed at a height of 3 m above the ground, which is very close to the average highest main branch of the tree.

The EM propagation through a row of cherry trees in an orchard was modeled and simulated on the basis of the Finite Element Method (FEM) [^{®}

As stated before, the transmission and reception antennas in the measurement campaign were whip monopoles. It is well known from antenna theory [_{m}_{m}

The EM properties of the cherry tree wood could not be directly measured in the field. However, fairly accurate estimates of the permittivity and conductivity could be made, based on water content measurements. To begin with, wood exhibits negligible magnetic properties, meaning that the relative permeability was set equal to _{r}_{r}_{0}_{0} = 8.85 × 10^{−12} F/M. The corresponding value for the wood conductivity at 2.4 GHz is therefore easily calculated as

The soil conductivity was directly measured at the field, and showed considerable variation with respect to the coordinates of the observation point. However, after repeated simulations, it was empirically shown that the exact value of the soil parameters did not affect significantly the EM path loss in the horizontal direction. Therefore, to simplify the simulation without significant loss of accuracy, an average value of _{r}_{0} = 4^{−7}H/m is the magnetic permeability in vacuum. This shallow penetration depth means that the soil can be simulated in COMSOL by a thin, lossy dielectric slab. To guarantee negligible propagation at a given depth, as well as acceptable behavior of the geometric mesh, the thickness of the slab was set to 2.5 m.

With respect to the foliage, again only estimates of the permittivity and conductivity could be made, based on the water content measurements that took place using the gravimetric method (weighing leaves before and after drying). The average water content was found to be 27.85%. According to [

Using the expressions above, along with the expression

These expressions have been verified for the X band, where the wavelength is on the order of 4 mm, whereas the wavelength in our application is 125 mm. An alternative model proposed in [_{SW}_{SW}_{r}=

Originally, the entire CAD model (see

To decrease the computational burden, only the main, thickest branches of the tree—including the trunk—were subsequently considered, (see

Simulation of the foliage geometry is, in general, a very complicated task [

Next, the meshing and EM simulation of an entire row of cherry trees was attempted. To simulate the row, 27 copies of the simplified cherry tree model were located at 5 m separating distances, spanning a total of 130 m. The tree models were positioned on top of a rectangular, lossy dielectric slab, 2.5 m deep, to simulate the ground, as explained in the section before. Since in the measurement campaign the transmission direction was always chosen to be along a single row, the scattering effect of the remaining rows was considered negligible, and therefore the rows were not included in the simulation, to reduce the computational burden.

As discussed in the introduction, the array of 27 trees together with the slab simulating the ground was encapsulated in a rectangular box, since in the FEM the entire space surrounding the scattering geometry is theoretically discretized (see

In this work our goal was to compare established empirical attenuation models, attenuation field measurements and the computational model developed with the _{t,r}_{t,r}^{®} Pentium I-5 Quad Core processor running at 3.10 GHz with 8 GB RAM.

In the 1.5 m height case, the main lobe of the antenna pattern for the given antenna model is intersected by the scatterers (foliage, trunk) in a way similar to the 3 m case, resulting in analogous attenuation behavior. However, for the 0.5 m height case, the main lobe is significantly affected by the tree trunks, as demonstrated by the spikes of the corresponding plot, occurring exactly at the tree positions. The slight discrepancy between measured and predicted data may be partly attributed to inexact modeling of the actual antenna, due to the lack of crucial data in the antenna documentation.

The results indicate that the predictions and measurements curves resemble each other at 3 m, and at 1.5 m only in short distances and in the absence of leaves. However the predicted path loss at 1.5 m in the presence of leaves, especially at longer ranges is consistently lower. In the

At the height of 3 m the receiver and transmitter are always close to the canopy top and the presence of leaves does not seem to greatly affect the attenuation; the predicted attenuation is slightly smaller than the measured one. However, at 1.5 m the signal propagates through the center part of the canopies and foliage and branches affect a larger portion of its travel. This is the reason why the maximum communication range decreased from 130 m to 96 m,

Finally, at longer distances from the antenna, neighboring tree rows start playing some role in the propagation, since they are increasingly ‘captured’ by the antenna lobe, as opposed to short distances, where they can safely be neglected. This observation explains partly the discrepancy in deterioration far away from the receiver. However, inclusion of neighboring rows increased the geometric complexity and resulted in an ill conditioned linear system that would not converge.

In this paper a commercial Finite Element Method solver was used to calculate the electromagnetic propagation of radio waves between a pair of ZigBee nodes at 2.4 GHz, through a row of cherry trees. The model utilized an approximation of tree geometries, and estimates of the electrical characteristics of the air, soil and foliage based on water content measurements. Clearly, it would be impractical to digitize the exact geometry of all trees in a given orchard and use it in a FEM simulation. However, given the relative uniform training and pruning of trees in commercial orchards, a ‘representative’ tree could be defined, and used for all tree positions. Then, the number of tree columns and rows and their inter-spacing would suffice to estimate attenuation using an FEM solver. This paper constitutes a first step towards this goal.

The results showed that the computed solutions were in relatively good agreement with the measured attenuation curves and the empirical models near the treetops, where a large component of the signal is in free space. However, the FEM solver consistently underestimated the actual measured attenuation at a height corresponding to the middle of the canopies; the discrepancy was larger in the presence of leaves and at longer distances. To fully understand and explain the discrepancies, further research needs to take place. The effects of more precise geometric models and neighboring tree rows should be examined and their value should be weighed against the increased computational complexity. Accurate values for the real part of the permittivity of all scatterers are also essential; it is envisioned that libraries of tree geometric models and EM properties could be developed for this purpose, which is also of general interest in precision fruticulture. It is essential that the amplitude and the phase of the three components of the electric field be computed to account for the effects of wave scattering.

The significance of the results is not limited to a certain type of modulation. The overall methodology would be almost identical for any signal type (cellular, WLAN). The essential parameter that would need to be re-defined is the frequency of operation, meaning that the material properties should also be modified accordingly, based on experimental data obtained from the bibliography. Also, the transmitting and receiving antenna models should be taken care of, affecting obviously the radiation pattern.

Despite these difficulties, the proposed method promises to offer attenuation predictions that can be used for WSN deployment planning in an orchard, without the need for extensive RF measurements in the orchard, which are required by empirical models. This is essential, since obviously orchard grow and the WSN planning is certainly done only once for an orchard.

Part of this work was supported by the ICT-AGRI project “3D-Mosaic—Advanced Monitoring of Tree Crops for Optimized Management—How to Cope with Variability in Soil and Plant Properties?”, which is funded by the European Commission's ERA-NET scheme under the 7th Framework Programme for Research.

Hristos T. Anastassiu worked on modeling, set up the COMSOL solver, wrote Section 2.3, produced

The authors declare no conflict of interest.

For an EM wave propagating in free space, path loss is described by the Friis equation:
_{r}_{t}_{r}_{t}_{t}_{r}

This equation is named as the Plane Earth (PE) propagation model. The path loss for this model is calculated by:

In reality, soil is not perfectly conducting and the PE model results in large errors. To achieve modeling of higher fidelity, the empirical Fitted Plane Earth model has been used, which is a general mathematical expression of the following form:

Calculation of _{t}_{r}

Layout of the cherry orchard.

The complete CAD model of a single cherry tree (without leaves).

The simplified CAD model for a single cherry tree (no foliage).

Row of cherry trees and soil slab embedded in a bounding box.

RSSI computations and measurements for transmitter and receiver height equal to

Attenuation computations and measurements for transmitter and receiver height equal to

Attenuation computations and measurements for transmitter and receiver height equal to

Comparison between empirical propagation models, measurements and data from simulation, for transmitter and receiver height at 1.5 m with no leaves.

Comparison between empirical propagation models, measurements and data from simulation, for transmitter and receiver height at 1.5 m, with foliage.