PHASE SENSITIVITY TO SOIL MOISTURE IN CONTROLLED ANECHOIC CHAMBER: MEASUREMENTS AND FIRST RESULTS K. Ben Khadhra (1), M. Nolan (2), T. Börner (1), D. Hounam (1), M. Chandra (3) 1
German Aerospace Center (DLR) - Microwaves and Radar Institute, Oberpfaffenhofen, D-82234 Wessling, Germany (Email:
[email protected], Tel: 0049-8153-2386, Fax: 0049-8153-1449) 2 Institute of Northern Engineering, 455 Duckering Bldg, University of Alaska Fairbanks Fairbanks, AK 99775-5860 3 TU Chemnitz, Elektrotechnik und Informationstechnik, Reichenhainer Strasse 70, D-09107 Chemnitz, Germany
Abstract — in this work, we will present new Bistatic X-band (9.6 GHz) laboratory measurements, which have been carried out in the Bistatic Measurement Facility at the DLR Oberpfaffenhofen, Microwaves and Radar Institute in Germany. The Bistatic facility enables us to have full polarimetric data with different Bistatic angles and different soil moistures controlled by a TDR (Time Domain Reflectivity) system. After calibration of the measuring system using a large metal plate, the sensitivity of phase and reflectivity with regard to moisture variation and therefore the penetration depth was evaluated. Current results demonstrate a non-linear relationship between the signal phase and the soil moisture, as expected, confirming the possibility of using DInSAR to measure variations in soil moisture.
could be a reliable proxy to assess the soil moisture. The moisture variation (penetration depth variation) causes a change in path length and yields a change in phase, the socalled signal phase (eq. 2).
Keywords: bistatic measurement; signal phase; soil moisture; penetration depth; interferometry; anechoic chamber
The Hallikainen model [5,6] relates the dielectric constant to the frequency, the volumetric moisture content and the percentage of sand and clay contained in the soil. It has been used to prove the relationship between the soil moisture and the penetration depth.
I.
INTRODUCTION
To date many radar methods and models have been reported for the estimation of soil moisture, such as the Ohmodel or the Dubois model. Those models, which use only the magnitude of the backscattered signal, show results with 5 to 10% accuracy. In the last two decades SAR Interferometry (InSAR) and differential InSAR (DInSAR), which uses the phase of the backscattered signal, has been shown to be a useful tool for the creation of Digital Elevation Models (DEMs), and temporal changes due to earthquakes, subsidence, and other ground motions. Matt Nolan [1-3] also suggested the possibility to use DInSAR penetration depth as a proxy to estimate the soil moisture. The principal is based on the relationship between the penetration depth and the permittivity, which varies as a function of soil moisture. II.
THEORY
The penetration depth (eq. 1) [4] is defined as the distance over which the field amplitude decreases by a factor of 1/e. It
δp =
λ ε′ 2πε ′
φ sig = δ 2k = δ
(1)
4π
λ
ε c = (a0 + a1 S + a0 C ) + (b0 + b1 S + b2 C )mv + (c0 + c1 S + c2 C )mv 2
(2)
(3)
εc is the complex dielectric constant, S is the percentage of sand, C is the percentage of clay, mv is the volumetric moisture content, and the coefficients ai, bi and ci depend on the frequency. Because of the nonlinear relationship between soil moisture and penetration depth (fig. 1), a measurement of a change in penetration depth cannot be directly converted to a change in soil moisture unless one of the soil moisture values is known a priori or if some linearizing assumptions can be made. For example, a measured displacement of 5 mm could ambiguously mean a change in soil moisture from 1% to 2% or from 10% to 17%.
1
Figure 1. The penetration depth versus volumetric soil moisture
However, if the initial soil moisture value is known, and assuming that a phase change is fully attributable to a change in penetration, the initial value can be converted to a penetration depth using the equations presented previously. Figure 3. The bistatic measurement facility at DLR
Transmitter
Receiver
20 cm
50 cm
Figure 4. Bistatic geometry of the facility Figure 2. The signal phase versus volumetric soil moisture
BISTATIC MEASUREMENT FACILITY
The X-band Bistatic Measurement Facility (Microwaves and Radar Institute, DLR Oberpfaffenhofen, Germany) has been used to measure a full polarimetric data set for quasibistatic angles from 24° to 140° with controlled conditions in an anechoic chamber (fig. 3). The transmitting and receiving horn antennas are moving in the plane of incidence, where the azimuth angle of the transmitter is 0° and the azimuth angle of the receiver is 180°. The transmitter and the receiver can move from 12° to 70° similarly (specular case) or separately to measure the incoherent term. The chosen target was a flat soil with different moisture levels controlled by a TDR system. An average of four soil moisture measurements has been used for each target. The soil sedimentation shows that the soil contains 100% (pure) sand and no clay contributions. Therefore the swelling effect of soil caused by clay can be completely neglected.
2
HH measured VV measured HH Simulated VV Simulated
1
Reflectivity Fresh Water dB
III.
0 -1 -2 -3 -4 -5 -6 10
20
30
40
50
60
70
specular angle in degree
Figure 5. The Reflectivity of fresh water
2
The Isolated Antenna Calibration Technique (IACT) [7] has been used to calibrate the measured data. A large metal plate has been used as calibration target. The validation of the calibration has been achieved by comparing the simulated and measured reflectivity of fresh water (fig. 5). IV.
soil moistures varying form 5% to 40% (fig. 8). This means that the measured variation of the signal phase of up to 100° cannot be explained by the pure dielectric effect covered by the Fresnel equations!
MEASUREMENTS AND RESULTS
Specular measurements with different soil moistures have been carried out to prove the signal variation with the soil moisture, as the penetration depth is related to the magnitude of the signal. The variation of reflectivity with soil moisture is shown in fig. 6; the incidence angle was 20°.
HH VV
Reflectivity Flat Soil dB
-2
-4
-6
-8
-10
-12
Figure 8. The Reflectivity of flat soil versus the soil moisture 5
10
15
20
25
30
The soil moisture %
V.
Figure 6. The Reflectivity of flat soil versus the soil moisture
The reflectivity of flat soil increases as the soil moisture increases for both polarizations H and V. Apparently the penetration depth depends on soil moisture. Fig. 7 shows that the signal phase is also changing with soil moisture (for the same geometry and the same soil roughness). HH VV
The signal phase degree
160 140 120 100 80 60 40 20 5
10
15
20
25
30
The soil moisture %
INTERFEROMETRIC ANALYSIS
The assessment and interpretation of the signal phase for the different soil moistures using the complex interferometric coherence seems to be reasonable. The coherence Γ is defined as:
Si S r*
Γ= Si
2
(4) Sr
2
where Sr is the reference signal of a surface with soil moisture mv,1. Si with i ∈ {2,3,…} is the complex amplitude of the signal for the surfaces with soil moistures mv,i. 〈…〉 denotes ensemble averaging. As expected, due to the coherent nature of the surface (flat soil), the magnitude of the interfermetric coherence for two relatively wet surfaces is almost 1. However, the main purpose of this experiment was the anaylsis of the signal phase measured for different soil moistures at the same geometry and roughness. Therefore only the argument of the complex coherence, i.e. the phase shift due to the soil moisture variation, will be taken into account. From fig. 9 we can see that this phase shift can be a good proxy to assess the soil moisture variation. Due to the absence of clay in our soil (no swelling effects) the phase shift can be directly related to the penetration depth of the electromagnetic wave into the soil.
Figure 7. The signal phase versus the soil moisture
The simulation of the signal phase using the Fresnel reflection coefficient yields a variation of about 1 degree for a
3
[4] HH VV
[5]
The phase shift in degree
120
100
[6] 80
[7]
60
40
F.T. Ulaby, R.K. Moore, and A.K. Fung, Microwave Remote Sensing. Reading, MA: Addison-Wesley, 1982, vol. 2, Fundamentals and Radiometry. M.T. Hallikainen, F.T. Ulaby, M.C. Dobson, and M.A. El-Rayes, "Microwave dielectric behaviour of wet soil - Part I: Empirical models and experimental observations," IEEE Trans. Geosci. Remote Sensing, vol.GE-23, pp. 25-34, Jan. 1985. M.C. Dobson, F.T. Ulaby, M.T. Hallikainen, and M.A. El-Rayes, "Microwave dielectric behaviour of wet soil - Part II: dielectric mixing models," IEEE Trans. Geosci. Remote Sensing, vol.GE-23, pp. 35-46, Jan. 1985. K. Sarabandi, F.T. Ulaby, and M.A. Tassoudji, "Calibration of polarimetric radar systems with good polarization isolation," IEEE Trans. Geosci. Remote Sensing, vol. 28, no. 1, pp. 70-75, Jan. 1990.
20 5
10
15
20
25
The soil moisture variation in %
Figure 9. The interferoetric phase versus the soil moisture variation
VI.
CONCLUSION AND DISCUSSION
The variation of the reflectivity with regard to soil moisture could be a reliable tool to understand the relationship between the penetration depth and the soil moisture. As expected it can be seen from the measurements that the penetration depth decreases with increasing reflectivity. The dependence of signal phase on soil moisture demonstrates that the path of the electromagnetic wave through the soil is strongly related to its dielectric properties. The nonlinearity of the signal phase variation to the soil moisture variation can be clearly seen, but the biggest changes in phase are occurring at the higher ranges of soil moisture which is contrary to theory. It could be a problem of correct phase unwrapping (i.e. cycle slips), but maybe also due to unaccuracies in the measurements. The effects of surface roughness with respect to varying bistatic angles and polarisation will be subject to future studies. The clear aim is to find ways of independently estimate soil moisture and surface roughness. ACKNOWLEDGEMENTS The authors should like to thank Dr. Erich Kemptner and Stefan Thurner from the "Signatures" group for their outstanding support with the laboratory measurements and equipment. REFERENCES [1]
[2]
[3]
M. Nolan, D.R. Fatland, and L. Hinzman, "DInSAR Measurements of Soil Moisture," IEEE Trans. Geosci. Remote Sensing, vol. 41, no. 12, December 2003. M. Nolan, and D.R. Fatland, "New DEMs May Stimulate Significant Advancements in Remote Sensing of Soil Moisture," EOS Trans. AGU, vol. 84, no. 25, pp. 233-240, 24 June 2003. M. Nolan, and D.R. Fatland, "Penetration Depth as a DInSAR Observable and Proxy for Soil Moisture," IEEE Trans. Geosci. Remote Sensing, vol. 41, no. 3, pp. 532-537, March 2003.
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