Indi an Journal of Radio & Space Physics Vol. 33, June 2004, pp. 196-200

Esti1nation of dielectric constant of soil from the given texture at microwave frequency

0 P N Calla

International Centre for Radi o Science, "OM-NJWAS " A-23, Shastri Nagar, Jodhpur 342 003, Rajasthan , Indi a

and

Vivek Ranjan 1, Chetan Bohra 1 & Gangadhar L Naik2

1 Department of Electronics and Communicatio n 2Department o f Electrica l and Electronics

Hirasugar Rural Eng ineering Co llege, Nidasoshi , Belgaum 591 236, Karnataka, India

and

Waseem Hasan & Harmeet Singh Bali

Department of Elec tro nics and Com munica ti on, Nati onal Institute of Technology, Hazarthbal , Sri nagar 190 006, Jammu & Kashm ir, India

Received 18 March 2003; revised 16 Februwy 2004; accepted 17 March 2004

Value o f the die lec tric constant of a give n sample o f soil has been est imated from its know n texture by multip lying the g iven tex ture with the constants at different mi crowave frequencies. The model is tested fo r four sa mples of so il: one sample from Uttar Pradesh and three samples from Kashmir in India.

Keywords: Di elec tric con tan t, Soil , Microwave frequency PACS No: 95.75 Rs; 84.40 Xb lPC Code: G 0 I N 33/24

1 Introduction Over the past two decades, microwave remote

sensing has evol ved into an important tool for monitoring the atmosphere and surfaces of planetary objects, with especial emphasis on the pl anet earth. Remote sensing using microwave techniques is the emerging fi e ld for the study of natural resources of the planet earth . It encompasses the physics of the radiowave propagation and its inte rac tion with materi al med ia, thJ.t inc ludes surface and volume scattering and emi ss ion , which helps in providing information about the temporal or spatial variation of atmosphere and surface feat ures.

Microwave remote sensing of natu ral emth material such as soi l and water has a very c lose dependence on their e lectri ca l parameters. The most important parameter is the d ie lectric constant. T he knowledge o f dielectric constant 1 helps in the study of dry and wet so il s using microwave sensors. The dependence of emissivity2 and backscatter coefficient3

.4 of the soil on th is particu lar parameter is used fo r design ing the passive and acti ve microwave sensors. Th us dry and wet soil properties can be studi ed from different

platforms and the sensors, which will give knowledge of variability of so il moi sture, which is important for agriculture .

2 Properties of soi15

Soils are composed of solids, liquids and gases mi xed together in variable proportions. The re lative amount of ai r and water present depends on the way the soil particles are packed together. T he so il texture depends upon the s ize of the particle and the structure o f soi l depends on the way the partic les are mnnged. Both of them infl uence the amount of pore space and its distributio n in the soil.

Soil tex ture is characterized by percen tage sand , silt and clay in it. Depending upon the percentage of each cons tituent the soil texture is differently named5

. It is observed that the sandy soil lacks the water holding capacity as in the case of soi l of Rajasthan. Soil o f Kashmir, o n the other hand has more silt and bette r water ho ld ing capacity.

T he determination of dielectric constant of the soi I of known con~t itu e nts has been done us ing the wavegui de cell method and the model has been

CALLA eta/. : ESTIMATION OF DIELECTRIC CONSTANT 0 f SOIL AT MICROWAVE FREQUENCY 197

generated for the determination of dielectric constant of a given sample of soil by knowing its constituents. The verification of the model is done using four samples, obtained from different locations.

The four samples used in the present study for generation of the model are from Rajasthan and have different constituents, thus dividing them in four categories, i.e. Clay loam, Loamy sand, Sandy loam and Pure sand, thus giving a spectrum of soils from texture point of view and for an useful study. The soils of Kashmir and Uttar Pradesh, India have been used in the present study for verification of the model.

Table I presents the texture of the soil samples of Rajasthan, India.

3 Sample preparation The following sequence of steps were taken:

(a) The samples of soils were first sieved to get fine particles.

(b) The samples were then oven dried at ll0°C for about 30 min.

(c) Equal amounts of oven-dried samples were taken for measurements .

4 Measurement of dielectric constant The choice of method of measurement depends on

many factors such as the physical properties including shape and size of the sample, temperature, humidity and the field of measurement. There are four methods of measurement of dielectric constant of soil at microwave frequencies6

. They are as follows:

(i) Transmission Method (ii) Cavity Method (iii) Free Space Method (iv) Waveguide Cell Method

We have used the waveguide cell method for the measurement of dielectric constant of the different soil samples. It is a simple method for the

Table !- Physical properties of soil samples from Rajasthan

S::~mple A 13 c D

Co lour Dark Gr::~y i s h Brown Yell owish ye llow brown Brown

Co::~ rse sand % 26.40 29.80 43.80 44.30 Fine sand % 34.70 28 .60 28.00 42.20 Silt % 17.6 16.60 10.80 4 .20 Clay % 21.30 10.70 12.30 3.70 Tex lllre Clay Loamy Sandy S::~ nd

loam sand lo ::~ m

measurement of dielectric constant of a solid material , like soil. The dielectric constant is obtained by using the shift in minima of standing wave pattern inside a slotted section of rectangular waveguide. This shift takes place due to the change in guide wavelength when dielectric material ts introduced 111 the waveguide.

Here, the measurement of guide wavelength is carried out at different microwave frequencies in the X-band. The relevant equation used for determining the dielectric constant in the frequency range 8.2-10 GHz is given as

. . . (I )

where, Age is found by solving the following equation :

. .. (2)

where a = width of waveguide Aa = wavelength in free space Aga =guide wavelength when waveguide is filled with air Age = guide wavelength when waveguide i filled with lossless dielectric material. d = shift in minima L = thickness of the samples

5 Experimental results In order to determine the variability of dielectric

constant with frequency , the measurements were made at different frequencies . The measurements have been made at eight different frequencies in the range 8-10 GHz. The values of dielectric constant of different samples at various frequencies are given in Table 2 and presented in Fig. 1. From Fig. I and

T::~ble 2- Dielectric constant of different smnples of so il of Rajasth::~n :Jt different frequencies

Frequency Dielectric constant (E) GH z Sample Sample S ::~ mple Sample

A B c D

8.3 175 2.53 2.53 2.53 2.53 8.5900 2.482 2.46 2.503 2A6 8.8950 2.4 2.4 2.4 2.53 9.0500 2.35 2.49 2.35 2. 19 9.6 100 2.52 2.26 2.52 2.52 9.7070 2.5 1 '").,

-· -' 2.50 1 ')., -·-'

9.8500 2.22 2.48 2 .22 2.35 10.000 2.46 2.335 2.46 2.57

198 INDIAN J RADIO & SPACE PHYS, JUNE 2004

Table 2, it is observed that dielectric constant of the four samples is different due to the difference in their physical properties. The data have been obtained by taking ten sets of readings for each sample and each set comprising of three values of the shift in minima obtained th roughout the length of the slotted wave­guide. ln all , 30 readings were taken for each sample for each freq uency. The procedure is repeated in order to check the accuracy and precision of the microwave system used. These sets of readings were taken for eight different frequencies as mentioned in Table 2. Theoretically there should not be much difference in the value of dielectric constant for dry soi l, but it was observed that there is sli ght va riati on in the value of dielectric constant with the increasing freq uency, as is clear from Fig. I . This variabil ity in dielectric constant can be attributed to the presence of moisture

2.6 ~-----------------,

2.5 1-z < ~ 2.4 z 0 u u 2.3

" 1-:il 2.2 ...J w 0

2.1

• • • Sample-A

--e-- sample-8

-w-sample-C

2 .0 L-'----'------'---J__--"----'-~===s=am=ple:=':·D::!.....I 8.3175 8.59 8.895 9.0 5 9.61 9.707 9.85 10

FREQUENCY, GHz

Fig. !- Variation of dielectric constan t of Rajasthan soils with frequency

Table 3-Minimum and maximum values of dielec tric constant of soil s of Rajasthan

Sample Minimum Maximum % Variation Value Value

A 2.22 2.53 12.2 B 2.26 2.53 10.60 c 2.22 2.53 12.2 D 2.19 2.57 14.78

Table 4-Measured values of the die lectric constant of soils of Rajasthan

Frequency Sample Value of Values GHz No. dielectric occurring out o f

constant 30 readings

8.3 175 A 2.53 18 times 'J .707 B 2.30 19times 10.00 c 2.46 16times 8.59 D 2.46 18 times

in the samples, which they absorb when kept exposed to the atmosphere.

Table 3 gives the maximum and minimum values of the dielectric constant of different samples along with the percentage variation in their values. Table 4 gives the values of dielectric constant obtained by adopti ng the methodology discussed earlier in thi s paper. It gives an idea about how the calcu lations have been made for different frequencies to know the range of accuracies with which the dielectric constant can be measured.

6 Model generation For the model samples the texture and the

percentage of its constituents, e.g. sand, silt and clay is given in Table I . The measured values of the dielectric constant for these soils are given in Table 2. Now, using the texture value one can estimate the value of dielectric constant (c) using the following equation:

c =a*(% sand) + b*(% silt)+ c* (% clay)

where a, b and c are constants. Thus, for the four soi l samples under consideration ,

one can have following linear equations:

c 1 = a*(61.l) + b*(l7 .6) + c* (21.3) c2 = a*(68.4) + b*(l6.6) + c* (10.7) c3 = a*(71.8) + b*(l0.8) + c* (12.3) c4 = a*(86 .5) + b*(4 .2) + c* (3.7)

Now, as shown in Table 2, at each freq uency there are four different va lues of c for the four' different samples. Using the texture of the soil samples from Table 1 and the va lues of c at each frequency from Table 2, the four equations so obtained are solved and the values of a, b and c are obtained at each frequency. In all , we got 32 values of a, band c each. But we selected only those combinations of a, band c which were the best fit to our approximation model , as given in Table 3. Thus for known texture of the soil, one can estimate the value of dielectric constant at different frequencies using the values of the constan ts a, band c from Table 5.

7 Results and discussion The c values plotted in Fig. I show the variation of

c with frequency for four samples of soil of Rajasthan. The different samples have different texture and hence values of c show variabi lity with freq uency.

CALLA eta/.: ESTIMATION OF DIELECTRIC CONSTANT OF SOIL AT MICROWA YE FREQUENCY 199

The variability of dielectric constant is related to soil texture, which is a function of the constituents of soil, viz. sand, si lt and clay. Thus it is possible to generate a theoretical model using the measured £ and the measured constituents of soi l. Assuming that it is a linear relation , using the measured values of £ for different samples and the constituents of soi l, one can establish a linear equation as follows:

£ = a*(o/o sand)+ h*(% silt) + c*(% clay)

where a, band care constants. Then using the above equation and constants

derived by Calla, Yivek, Chetan and Gangadhar (CYCG) given in Table 5, the values of dielectric constants were estimated for different soi I texture given in Table 6 for UP soil, at different microwave frequencies. The estimated and measured values of the dielectric constant of UP soi l are given in Table 7. The percentage variation of dielectric constant at the frequency 9.05 GHz is shown in Table 7. This value is within the percentage error expected from the waveguide cell method6

. Table 8 gives the physical properties of soil samples obtained from Kashmir.

The dielectric cons tant of Kashmir so il samples was measured using waveguide cell method presented in Table 9. Figure 2 presents measured values of

Table 5-Yalues of the constants

Frequency Constant GHz a b c

8.3 175 0.02689 0.023473 0.027949 8.59 0.026306 0.028518 0.017501

8.895 0.027543 0.020082 0.0 17074 9.05 0.02243 0.043547 - 0.023154 9.6 1 0.027524 - 0.00564 0.044015

9.707 0.024348 0.015276 0.03561 9.85 0.025106 0.05547 - 0.01477 10.0 0.026782 0.096504 0.03234:

Table 6- Soil tex ture of UP soil

Soi l Type

Fine sa nd Coarse sand Silt Clay

Const ituent % of soil

83.3 3.4

3.33 9.847

Table 7-Comparison of estimated values and mea ured values of dielect ric constant for UP so il s

Frequency. GHz Estimated Measured

values values

9.05 9.0

Die lectric constant Estimated Measured

values values

1.86 2.1

Error %

12.9

dielectric constant with frequencies for samples of soil from Kashmir. The dielectric constant was measured a number of times at the same frequency. The maximum and minimum values of dielectric constant obtained are shown in Table 10. There is a certain percentage variation in the measured values of dielectric constant using waveguide cell method. Table II gives the comparison between the measured and estimated values of dielectric constant for 3 samples of Kashmir soil, each at three different freq uencies. Variation of dielectric constant for different soils ranges from -3.99% to 17.46%, one value out of nine values being 23.8%. The values li e within measurement errors.

Table 8-Physical properties of samples of soil from Kashmir

Samples A B c

Colour Brownish Dark Dark silt brownish brownish

silt clay silt clay Sand % 4 2 1 20 Silt % 85 75 72 Clay % 11 4 8

Table 9-Measured dielectric constant of sa mpl es of soil from Kashmir at different frequencies

Freq. GH z

8.46 8.61

8.657 8.875 9.085 9.54 9.73

9.865 9.89

Sample I

2.50 2.45 2.09 2.36 2.28 2.27 2.07 2.08 2.33

Dielectric constant Sample 2 Sample 3

2.14 2.04 2.10 2.45 2.09 2.09 2.07 2.40 2.02 2.20 2.12 2.27 2.1 2.07

2.33 2.22 2.07 2.07

3.00-,-----------------------,

2.75 1-z <{

~ 250 z 0 u u 2.25 0:: 1-u ~ 2.00 w i5

1.75

..

1.50 - , _ 8.46

..

- •- Sanli

----sam:

-8.61 8.6575 8.875 9.085 9.54 9.73 9.865 9.89

FREQUENCY, GHz

Fig. 2-Variati on of dielectric constant of Kashmir soil s wi th freq uency

200 INDIAN J RADIO & SPACE PHYS, JUNE 2004

Table tO-Minimum and maximum values o f measured dielectric constant of Kashmir soil s

Sample Minimum Maximum % value value Variation

A 2.04 2.52 19.04 B 2.024 2.33 13.13 c 2.035 2.45 16.93

Table It-Comparison o f estimated values and measured values of dielectric constant for Kashmir soil

Sample Frequency. GHz Dielectric constant, Ea % Estimated Measured Estimated Measured Error

8.59 8.61 2.721 2.45 I 1.822 Sample A 8.895 8.875 2.004 2.355 17.46

9.707 9.73 1.787 2.07 15.8 8.59 8.61 2.76 2.10 23.8

Sample B 8.895 8.875 2.15 2.067 -3.99 9.707 9.73 1.80 2.1 16.7 8.59 8.61 2.71 2.45 -9.9

SampleC 8.895 8.875 2.13 2.4 12.5 9.707 9.73 1.87 2.07 10.6

8 Conclusions Here an attempt is made to see with how much

accurately one can measure the dielectric constant of soil using waveguide cell method. The waveguide cell method has certain sources of error and taking into account all these factors a number of readings were taken at each frequency and the value of E which appears maximum number of times was taken as the true value of dielectric constant. Sometimes where two or three values of E appear for a number of sets very closely, the average of these values of E was taken as true value of E. Table 2 gives these values of dielectric constant for Rajasthan soils and Table 9 gives those for Kashmir soils. Table 3 gives the percentage error in values of E for Rajasthan soils and Table 10 give percentage errors in values of E for Kashmir soils. The percentage variation for Rajasthan and Kashmir soils range from 10.6% to 14.78% and from 13.3% to 17.2%, respectively . These variations are attributed to the sources of error in the waveguide cell method . It is possible to improve the accuracy

further by taking more sets of readings and also by getting the best minimum on the slotted section.

The constants a, b and c obtained using the four samples of Rajasthan soils were then used to estimate the dielectric constant of UP soil as given in Table 10. The dielectric constant of Kashmir soils using the values of the constituents and the constants a, b and c were obtained at different frequencies and compared with the measured values of the dielectric constant at three typical frequencies as shown in Table 11. Tt is observed that the values of the estimated dielectric constant are within the errors of measurement of the waveguide cell method.

The dielectric constant of dry soil is independent of frequency. The variation is due to the absorption o f moisture by the soil. The accuracy of the measurement can be improved by minimizing enors. More accurate values of the dielectric constant will help proper designing of the sensors for microwave remote sensing.

The model is generated for the purpose of estimating the dielectric constant from the soil constituents, which can be ascertained easily from the soil samples in the field. These estimated values of dielectric constant then can be used for estimation of emissivity (e) and scattering coefficient (cr0). Using these estimated values of e and cr0, the first cut design can be done for passive and active sensors to be used in microwave remote sensing.

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