Attenuation of electromagnetic waves by vegetation canopies in the 100–10000 MHz frequency band

Unfortunately, we couldn't find data on dielectric properties of tree leaves and branches in the frequency range 0.1 - 1 GHz (data for corn leaves are presented in [108, 117]). Probably the open-ended coaxial probe reflection technique meets some difficulties in this frequency domain [114] and should be further developed or another technique should be suggested. There are also very few data for trunks in this band. We think that extensive measurements of in this frequency range with continuous change of frequency (like it was done in [114] in the range 1.9 - 9.1 GHz) would be extremely useful to understand the frequency dependence of attenuation by vegetation and of emission and backscattering from vegetated terrain.

5. EM waves propagation through a vegetation layer. Relation between electromagnetic and biometric vegetation parameters

To calculate radar return (or emissivity) from vegetation canopies the vector radiative transfer equation is used [96]. It is of the following form: For



(43)

where is a 4?1 column vector denoting the modified Stokes parameters in direction , is the 4?4 phase matrix denoting scattering from direction into direction , and is the extinction matrix which can be expressed in terms of the forward scattering amplitudes (see Section 3.1). For the case of thermal emission the right side of the equation is added by the term where is the absorption matrix and T is the physical temperature of the canopy.

The relation between the components of , particularly, the extinction coefficient ? for given polarization (or the optical depth ) and biometric parameters is established by expressions (26) - (30). The extinction cross sections are calculated for simple geometric elements (ellipsoid, cylinder, and disc) (see Section 3.2.1) which are characterized by their dimensions and dielectric constant (see Section 4).

For the simplest case of small chaotic ellipsoids it was obtained [3, 48] using (33) and (34)

(44)

where u = 1 for small needles and u = 2 for small discs (see the nomenclature in Section 1.1). For other cases the semi-empirical equations is used [48, 2]

(45)

where A is the coefficient (form factor) related to the plant structure, f is the frequency. Taking into account that in the microwave band weakly depends on the frequency (see Fig.1) and ~ 10 the simple equation could be obtained for attenuation by crops and foliage in the frequency range 1 - 10 GHz [3, 28, 29, 130]

(46)

where ? is the attenuation in dB, U = 2.5…5 depending on the vegetation type, ? is the wavelength in cm (?[cm] = ), W is the vegetation water content in kg per square meter. More complicated equations are given in [74].

The equations given above are very simple and can provide only rough estimates of attenuation by vegetation canopies. Nevertheless, these expressions are rather useful since they help someone to understand what the attenuation in vegetation depends on.

To obtain more accurate estimates of attenuation numerical solution of the transfer equation is used [1, 17 - 19]. The scattering amplitudes of dielectric needles, discs, and cylinders are computed on the base of generalized Rayleigh-Gans approach or other developed approaches for dimensions and dielectric constant of scatterers obtained from in-situ measurements (see Table 2 and 3). Computed data of backscattering coefficients are in good agreement with experimental data [1]. Unfortunately, when a numerical solution of transfer equation is used it is rather difficult to separate the influence of the change of model parameters (dimension of scatterers, their number density and moisture content, etc) on the value of attenuation or backscattering coefficient. In other words, it is not clear enough as to what biometric parameters determine the attenuation by a canopy and how strong they influence the attenuation.

Besides, applying the numerical solution, a researcher should remember the following.

i. Vegetation elements are substituted in the model by simple forms like circular discs and circular cylinders of finite length. However, even for these bodies the rigorous solution of the diffraction problem is not known and approximate models are used. The extinction coefficient is calculated as the sum of extinction cross sections of elements occupied a unit volume (30). That does not take into account the effects of mutual screening and correlation of scatterers [3, 74]. As a result, the error of the model can be significant.

ii. Because a vegetation canopy is an inhomogeneous medium, its coherent attenuation should be treated as a random value [8]. Calculating extinction with given dimensions, angular distributions, and number densities of scatterers we should understand that we obtain the mean value of extinction and the sampling values can change in wide limits for the given canopy. For example, variations of attenuation for corn canopy amounts to 50 % and more within the test site [8]. It shows that it is interesting to know the relative level of attenuation at different frequencies rather than absolute values of attenuation.

Theoretical models are extremely important and should play a vital role in the research process since they are indispensable for conducting sensitivity analyses and for pointing the directions of future research. But, in our opinion, because any model is based on certain assumptions, modeling process can only indicate the factors determining, for instance, attenuation by vegetation. Parameters of the model should be found by regression analysis of experimental data. For example, for a part of the frequency band considered the extinction coefficient could be found out in the form [130]

(47)

where A is the form factor determining by vegetation type, ? is the coefficient depending on the vegetation moisture content, f is the frequency, and w is vegetation water content per unit volume. Other forms of the regression models can be also suggested.

The angular dependences of attenuation by stands described in Table 1 and 2 are presented in [1] for different frequency bands. Attenuation is given as the percent of radar beam power lost (scattered and absorbed) while traveling through the canopy along the direction of propagation to the forest floor. We recalculated these data to the attenuation in decibels. These data for incident angle of 30? are presented in Table 5.

Table 5. Attenuation by the stands from Table 2 and 3.

Stand	Attenuation in dB (H polarization)
	P - band	L - band	C - band	X - band
Aspen leaf on	2.2	3.5	16	> 16
Hemlock leaf on	0.7	2.4	12.5	>16
Maple/beech	4	11	16
Red/white pine	1.7	5.5	13

One can see that the computed attenuation values differ from each other by several times for the stands. Strong frequency dependence of attenuation is present.

Polarization signatures of attenuation arise when an oriented component (stalks, trunks) is present in the vegetation canopy [6-9, 17-19, 29, 38, 58, 73, 74, 79, 83, 97, 100, 103]. The difference in attenuation of vertically and horizontally polarized waves can be large and is used in retrieving algorithms [28, 29, and 38].

Shutko



III. EXPERIMENTAL STUDIES OF EM WAVES ATTENUATION IN VEGETATION CANOPIES.

1. The methods of measurements

Measurements of attenuation by vegetation were conducted under laboratory conditions, under ground-based field conditions, and from aircrafts.

Laboratory experiments have the advantage that parameters of investigated objects can be changed and controlled. They allow examining the influence of individual parameters on the EM propagation characteristics of the medium.

Ground-based field measurements produced the largest amount of information on propagation properties of vegetation canopies. The natural conditions provide the possibility to obtain data during the whole period of canopy growth and to compare them with ground truth data.

Airborne sensors provide a possibility to gather quickly a large data set for different types of vegetation under various states and conditions.

Methods which were used to measure the attenuation can be divided into active and passive ones. In active methods, the attenuation over the path between transmitting and receiving antennas is measured. Airborne radar studies used corner reflectors and active calibrators placed on the ground at different locations within a canopy. Several typical configurations of active measurements are presented in Fig.3.

Configuration Fig.3 A) was used in [7, 8, 58, and 109] to measure attenuation in different crops such as wheat, corn, soybeans, etc. The transmitters were placed on a truck-mounted platform and the receivers were



Fig.3. Typical configurations of active measurements of attenuation.

Fig.4. Typical configurations of passive measurements of attenuation.

placed underneath the canopy. Measurements were conducted at different frequencies, polarizations, and incidence angles. Besides, measurements of the phase difference between horizontally polarized and vertically polarized simultaneously transmitted waves were presented in [8]. Calibration was provided by cutting and removing the plants to establish a free-space reference signal.

Configuration Fig.3 B) with different height of antennas above the ground is usually used for investigation of electromagnetic waves propagation in forest environment [131, 139-142, 163].

Configuration Fig.3 C) was used in laboratory measurements of attenuation by forest litter [112] and forest fragments [103]. A vector network analyzer measured the power and phase of the signal passing through the cell [112].

Attenuation constant of a layer was determined by comparing measurements of litter with that of the empty cell. In work [103], vegetation samples were placed on a Styrofoam frame, in one row or several rows with different spacing. Measurements were performed with vegetative targets and the transmitted power was recorded. After removing the targets the reference power was then recorded to find the attenuation.

Configuration Fig.3 D) is used in airborne and space borne radar studies of attenuation and backscattering [132-138, 155-158, 160, 161, 164]. Attenuation is determined by comparing signals from reflectors placed beneath the canopy and placed on the open ground.

Passive methods use the measurements of thermal emission from the investigated object in the presence of atmosphere and space emission as the background. Typical configurations used in passive (radiometric) measurements of attenuation are shown in Fig.4.

Configuration Fig 4. A) was proposed in [30, 6] for the field measurements of attenuation by corn and soybeans. The zero-order solution of the transfer equation for the emission from vegetated soil was reduced to

(48)

where T0 is the vegetation and soil physical temperature, Rs is the reflectivity of the soil surface (), and Tsky is the down welling sky (atmosphere and space) brightness temperature. The simplified equation was used to determine the reflectivity r and the transmissivity q by measuring the brightness temperature Tb for a) bare soil, b) canopy over soil, c) bare absorbing material with an emissivity close to unit, and d) canopy over the absorbing material. To increase the accuracy of measurements the soil was covered by screens which were wire meshes with an inter wire spacing of 1.6 mm and wire thickness of 0.3 mm. The brightness temperature was measured by a dual-frequency 2.7 and 5.1 GHz), dual-polarization radiometer mounted atop a truck-mounted boom. It was shown that the canopy is highly anisotropic, the emission exhibits a strong dependence on polarization and look direction, and the reflectivity is typically less than 0.1.

The technique described ensures good accuracy but it is very cumbersome. Field measurements of the transmissivity were conducted with microwave radiometers mounted on a truck [5, 11, and 134] and on a car [133]. The transmissivity was estimated by the relation that one can easy obtain from (1)

(49)

where and are the emissivity of vegetated and bare soil, respectively, with the same moisture content (and the reflectivity) within a site.

The technique proposed in [30, 6] for field measurements can be easily performed under the laboratory conditions [100, 77, 145-147] (configuration Fig. 4 B)). The fresh-cut plants were placed on the reflector located in the far zone of the antenna of the radiometer. As the reflector, a “blackbody” and a metal plate were used. The transmissivity of the vegetation layer was estimated from the expression

(50)



where is the brightness temperature contrast between the bare blackbody and the bare metal plate and is the same contrast but when the reflectors are covered by vegetation.

Configuration Fig. 4 C) was used in [74] to measure the transmissivity of a vegetation layer and in [148, 68] for field measurements of the transmissivity of trees. Attenuation values were estimated by comparing measurements of the brightness temperature with vegetation and without vegetation.

Configuration Fig. 4 D) is used for measurements of attenuation with the help of airborne radiometers [48, 150, and 151].

2. The results of measurements and their comparison with calculating data

Agricultural vegetation.

Data of measurements of attenuation by crops in the microwave band for different polarizations and look directions are presented in papers [2 - 9, 11, 26-32, 34-36, 40, 43, 48, 49, 53, 54, 58, 69, 71, 74, 81, 100, 109, 130, 143-145]. Analysis of the data shows the following [130].

The dependence of attenuation on the vegetation water content can be approximated by a linear function, i.e. expressions (44) - (46) give a satisfactory estimate for this dependence. Nonlinear dependence of the attenuation on the water content was reported in [3, 5, 40, and 74] and can be explained by mutual screening of vegetation elements [3] or by the temporal change of vegetation water status [40, 74].



Fig.5. Characteristic values of attenuation by different crops. 1 - corn, sunflower; 2 - pea, alfalfa; 3 - grains (wheat, barley, oat, etc); 4 - soybeans, cotton.



Fig.6. Experimental data on attenuation by different forests. 1, 2, 3, 4 - [64]; 5 - calculated data from [83]; 6 - [151]; 7, 8 - [154]; 9 - [135]; 10 - [134, 152]; 11 - [153].

The generalized frequency dependence of attenuation is presented in Fig. 5 [130]. Data in Fig. 5 relate to the mature state of crops and represent the maximum level of attenuation. In the microwave band, the attenuation by crops is proportional to the frequency in () power () where ? = 0…0.2 depending on the crop and vegetation moisture content.

In the microwave band, a rough estimate of attenuation can be obtained from expression (46) . The calculated dependence of attenuation for U = 3 and W = 4 kg/m2 is presented in Fig.5 by the dashed line. More accurate estimate of attenuation can be obtained from the models taking into account the vegetation structure and dimensions, orientation, and dielectric properties of leaves and stalks (Sections 4 and 5). Numerical calculation of attenuation with use of a computer is required in this case [8].

We could not find experimental data on attenuation by crops in the frequency range 100…1000 MHz. In this band, the salinity of free water contained in vegetation material (or conductivity of plant elements) could be a major factor determining the spectral dependence of attenuation. This factor is not yet sufficiently studied. Measurements and modeling of attenuation in the frequency range 100…1000 MHz and of direct current conductivity of plant elements could be a subject of future research.

Forest vegetation.

Experimental data of the extinction coefficient for different types of forests (rain, coniferous, deciduous) are presented in Fig. 6. We recalculated data on penetration depths found in [1, 83, 134, 135, 151 -153] in the values of attenuation in dB per meter; some data are reported in [64, 154].

Available data of the attenuation by forest canopies are very limited and it is rather difficult to make certain conclusions about the attenuation and its spectral dependence. Nevertheless, the data presented can give someone an idea about observed values of the attenuation and their dependence on the frequency. Analysis of the data shows the following.

There is not a big difference in attenuation values for different types of forests in 100…1000 MHz frequency range. For higher frequencies the values of extinction coefficient at a given frequency reported by different authors differ from each other by several (2…5) times.

The data in Fig. 6 show the general trend of frequency dependence of extinction. In the frequency range 100…1000 MHz this dependence can be approximated by a linear dependence [130]

? = 0.8 (51)

where is the attenuation in dB per meter, c = 8?10-4 is the regression coefficient, and f is the frequency in MHz. This dependence is shown in Fig. 6 by the dashed line. In the frequency range 1000…10000 MHz a greater slope of frequency dependence is observed.

The values of attenuation (5 in Fig.6) calculated by the model [83] are in agreement with experimental data reported by other researchers. However, the slope of model frequency dependence does not coincide with the general trend of frequency dependence for data presented in Fig.6.

The total extinction in a forest media at frequencies below 1000 MHz is mainly determined by extinction by branches and trunks [1, 64]. The last is not completely studied. A further development of attenuation models requires spectral measurements of attenuation in the wide band and measurements of dielectric constant and conductivity of branches and leaves.



IV. CONCLUSIONS

An analytical overview conducted in the paper allows us to make the following concluding remarks.

Due to the efforts of many researchers and research groups the basic questions of EM propagation and attenuation in vegetation canopies are clarified. Appropriate models are developed to describe the extinction of EM waves by plant elements and by vegetation volume as a whole. Theoretical and empirical models are available to calculate the dielectric constant of vegetation material in the microwave band. Experimental data of dielectric constant and of attenuation are well fitted by the models.

Nevertheless, several problems remain unsolved that enables one to point the directions of future research areas. In our opinion, these areas could be:

i. Extensive measurements of dielectric permittivity of plant elements in 100…1000 MHz frequency range and of the direct current conductivity of different plant elements;

ii. Extensive measurements of EM attenuation spectra by vegetation canopies under laboratory and field conditions;

iii. Verification of the known models and developing, if it is necessary, new ones to fit spectral data of attenuation.

The designated research areas are planned to be a subject of our further work.



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