A MULTI-polarized and
Multi-angle C-band Radar System for Soil Moisture Determination Under Bare
Soil Conditions Shakil A.
Romshoo*, T. Oki** and Katumi Musiake** *Earth Obervation Research
Center, NASDA, 9-9-1, Roppongi, Minato-ku, Tokyo, Japan e-mail
: shakil@aab.iis.u-tokyo.ac.jp **Musaike Lab, IIS, University of Tokyo,
B Building, 4-6-1, Komaba, Meguro-ku, Tokyo, Japan E-MAIL : prof@hydro.iis.u-tokyo.ac.jp
AbstractThis article is an attempt to
determine the soil moisture under bare soil conditions at a field scale
suing a ground based C-band radar with all the three linear polarizations,
i.e., HYPER SPECTRAL, HV, and VV and employing 4 angles of incidences,
i.e., 150, 230, 350 and 430. The experiment was concluded 12 times during
the year 1999 to monitor the soil moisture variation at a field scale at
Chiba, Japan. The field was purposefully maintained bare and smooth. The
Integral Equation Model (IEM), based on the theory of diffraction of
surfaces, was used to predict the backscattering phenomena. The model is
validated with the experiment data and a good agreement between the
modeled and the observed backscattering coefficient is obtained at HH
polarization while as the model does overestimate the backscattering at VV
polarizations. Further, a sensitivity analysis of the model reveals that
radar is sometimes more sensitive to the small changes in the roughness
characteristics than the larger changes in the soil moisture. Under
natural roughness conditions, the C-band radar, particularly with VV
polarization and lower angles of incidence, should be the ideal system for
soil moisture determination. Such a configuration has been found to be
more sensitive to soil moisture as compared to roughness
affects. IntroductionThrough a number of models based on
experiment data have been proposed (Oh et. al., 1992, Dubois et. al.,
1996) but for soil moisture retrieval, but the results are very limited.
Further, these empirical models derived from the experimental data may
sometimes lack the consistency and the universality. They may apply to
surface conditions and the radar parameters that were looked at during the
time of experiments. On the other hand, the theoretical models developed
have also some validity restrictions as for the frequency and roughness
ranges are concerned. Among the high frequency scattering models, the
Kirchoff formulation (KF) is the most commonly used. For a ground surface
whose standard deviation and correlation length are much smaller than the
wavelength, the small perturbation method, SPM (Ulaby, 1982), which is a
low frequency solution, can be used to estimate the backscattering
contribution. Attempts have also been made to unite the KF and SPM to
obtain a model applicable to a wide range of roughness scales of
frequencies. More recently, Fung et. al., 1992 has developed a surface
scattering model based on the surface field integral equations called the
Integral Equation Model (IEM). The (IEM) reduces to the SPM when the
surface is smooth and to the standard Kirchoff model when the standard
deviation is much larger than the incident wavelength. In its complete
version, the model describes the is much larger than the incident
wavelength. In its complete version, the model describes the
backscattering behavior of a random rough bare surface without any
limitation on the roughness scale and frequency range. In view of
the extended validity of the IEM model and to overcome the draw of the
other reported surface scattering models, we selected this model for
validation of our experimental results. Besides validating the model under
different surface roughness and soil moisture conditions, the simulation
studies have been carried out to the thoroughly understand the influence
of the different factors which influence the radar backscattering
behavior. Integral Equation ModelThe integral equation
model (Fung et. al., 1992), abbreviated as IEM was used in this study to
predict and understand the radar backscattering coefficients as a function
of both target and sensor parameters. This model has been applied to a
wide range of roughness for bare soil surfaces as well as sea surfaces
(Altese et. al., 1992; Chen et al., 1995). Because of complexity, it is
not practical to use the complete version of the model and in the
application usually, the approximate versions are usually considered
(Altese, et. al., 1996). The validity condition can be expressed as ks (3,
where k=2p/l, the wave number; l is the wavelength; and s is the surface
rms height. The like polarized backscattering coefficient s0 can be
expressed as follows:) Where s0pq is the radar backscattering coefficient; p, q are
vertical or horizontal polarizations; kz=k cosq and kx=ksinq ; s is the
surface rms height and W(n) (u,v)is the roughness spectrum of the surface
related to the surface correlation function. In the above equation
(4.1), R= and R^ are
the Fresnel reflections coefficients for vertical and horizontal
polarizations q is the angle of incidence; Where p(x,z) is the surface
correlation function, a stationary random process with zero mean and ()
denotes the ensemble average operator. In light of the previous research
function as exponential which gives a better fit with the experimental
data. There are several models which convert the volumetric soil
moisture to dielectric constant and vice versa (Dobson et. al., 1981,
Hallikainein et. al., 1985). I used the model given by Hallikainein et.
al., 1985 which takes into consideration the soil properties like texture
and bulk density as follows: Where Î refers to the dielectric constant, q is the
volumetric soil moisture, a and b are the shape factor and the texture
dependent coefficient respectively, r refers to density and the subscript
s, b, and fw refer to soil solids, bulk density and free water
respectively. Scatterometer Data and Field
MeasurementsA C-band Scatterometer system was used in this study
and have been described in details by Musiake et. al., (1997). The Figure
1(a) shows the van-mounted Scatterometer taking measurements of the bare
field. The radar system was employed at three polarizations, viz., HH, HV
and VV and over four angles of incidence, i.e., 150, 230, 350 and 430.
moreover, on almost every occasion of the experiment, the surface
roughness and soil moisture measurements were recorded. A lazer roughness
profile meter was employed to record a number of roughness measurements
across and along the field axis. The Fig. 1(a) shows the lazer profiler in
operation. The lazer profiler, which is driven by a stepper motor, can
measure a surface profile with 1mm horizontal resolution and 2 mm vertical
accuracy. The profiler is connected to the laptop computer to record the
measurements in X and Y directions. The horizontal resolution of the
measurements on each occasion was maintained constant as 3 mm. Though the
soil moisture measurements were recorded at the depth resolution of 2 cm,
5cm and 10 cm but in view of the penetration depth of the radar signals at
C-band wavelength (Wilheit, 1975), only the 2 cm measurements recorded by
volumetric methods were compared with the s0 measurement. Data
Analysis and Discussion The following sections would discuss
the experimental data, the relations between various surface
characteristics and the radar backscattering coefficients s0. Also the
sensitivity analysis performed would be discussed to have a thoroughly
understanding of the influence of these characteristics on the radar
response at different sensor configuration. Temporal Variations
of s0 The Table 1 shows the relationships, i.e.
coefficient of correlation and the slope obtained between the observed
surface soil moisture and the radar backscattering coefficient s0. Though,
the temporal relationship are reasonable for VV polarization and for all
the angles of incidence but the for other polarization, the relationships
are week except at an incidence angle 430. But this is in contrast to Sano
et. al., (1998) and Ulbay et al., (1979) results wherein they reported
higher coefficient of correlation but compatible sensitivity of the s0 to
soil moisture variations under varied roughness conditions. Geng et al.,
1996 reported similar relationships as obtained in this experiment. The
Figure 1(b-c) shows the temporal variation of the backscattering
coefficient s0 for HH and VV polarizations and four angles of incidence
employed in this experiment. The dynamic range of the backscattering
coefficients s0 during the conduct of the experiment is small for HH and
VV polarizations. HV has comparatively better dynamic range for all the
incidence angles used here. Also plotted on the figure is the temporal
variation of the soil moisture. We can see on 7th experiment that despite
an increase of more than 10% in the volumetric soil moisture, the
backscattering coefficient has decreased by more than 5 dB for higher
angles of incidence for HH polarization and a little less for 230
incidence angle. The decrease is in response to smooth surface roughness
condition observed on 7th experiment. The decrease is obviously more at
higher angles of incidence than at lower angles of incidence (Ulbay et
al., 1979).
Table 1 Summary of the correlation coefficient and
sensitivity of s0 using C-band Scatterometer system over bare
field
Polariastion |
Incidence Angle |
|
23o |
35o |
45o |
|
r |
Slope |
r |
Slope |
r |
Slope |
HH |
.74 |
.35 |
.26 |
.11 |
.28 |
.10 |
HV |
.67 |
.47 |
.31 |
.23 |
.30 |
.22 |
VV |
.76 |
.32 |
.62 |
.30 |
.67 |
.37 |
|
|
|
|
|
|
|
Comparison Between Measured and simulated Radar Data The
Integral Equations model was validated on three for both VV and HH
polarizations. These data are 21st May, 22nd June and 28 June. The values
of the rms height have been observed as 0.34, 0.525 and 0.30 cm
respectively while that of the correlation length as 14.5, 13.1, and 16 cm
respectively. The simulation and observed measurements for HH
polarizations are plotted in Figure 1 (d-e). We could get better agreement
between the two at HH polarizations than at VV polarizations. The pattern
is matching reasonably well for both the polarization with a decline in
the s0 as a function of incidence angle. The exponential correlation
function is assumed here. Bracaglia et al., (1995) also reported a
discrepancy when comparing the theory and experimental data over bare
soils. He attributed it to the inaccuracies of the available surface
models. While as Hoeben et al., reported of very good agreements between
the theory and the experiment for VV polarization over a range of
incidence angles from 110 to 230 and frequency of 1-10 GHz but for 350
angle of incidence, the deviation were quite higher than that observed
here for C-band. Altese et al. (1996) also reported a wide scatter between
the IEM model simulations and the ERS-1 backscattering coefficients values
for VV polarization and at an incidence angle of
230.
Sensitivity Analysis A sensitivity of the IEM
model simulations to the surface characteristics as well the radar
configurations was performed to have a better understanding of the
influence of these factors on soil moisture retrieval. The following
subsections would deal with each of these influences
separately:
The Figure 1 (g-h) shows the sensitivity of the
s0 to soil moisture variations for different frequencies, HH polarization
and two angles of incidence, i.e., 230 & 430 on 7th experiment (28
June ). The sensitivity reduces with the increase of incidence angle. For
all the four frequencies tested in this analysis, a variation of soil
moisture from 1% to 40% results in an increase of the backscattering
coefficient values of 7 to 8 dB for HH polarization at 230 incidence angle
while as at 430 angle, a similar change in soil moisture causes an
increase in s0 from 5 to 6 dB depending upon the frequency. Because of the
smooth nature of the surfaces, the s0 values are higher at lower angles of
incidence compared to the higher ones. For VV polarization, a similar
analysis results in an increase of around 8 dB for both lower (230) and
higher (350) angles of incidence. For both VV and HH polarization at both
lower and higher incidences angles, the sensitivity is quite high at lower
values of the soil moisture and as the soil moisture increases, the
sensitivity decrease.
The sensitivity analysis of
backscattering coefficient to rms height has been performed for different
dates. The plots in figure 1(i-j) show the sensitivity on 21st May for HH
polarization and two angles of incidence, when the soil moisture is lower
(13.69%). It can be seen from the Figure that the s0 sensitivity to rm
height is most strong of all the parameters tested during this sensitivity
analysis. The sensitivity is very strong at lower values strong at lower
values of the rms height and as the surface get rough and rougher, the
sensitivity decreases markedly, especially for higher frequency signals.
For L-band and above, the sensitivity is quite high even for rougher
surfaces. The IEM model looses its validity for X-band frequency beyond
the roughness values of 1.5 cm and that is reason of the discontinuity in
the X-band simulations.
The sensitivity to the correlation length
for different frequencies on 21st of May when the rms height was observed
as 3.4 mm and the surface soil moisture was 16.23% for HH polarization is
shown in Figure 1(K-1). Though the incidence angles do not affect the
dynamic range of the change in the s0 as function of correlation length, L
but the magnitude of the s0 is lower by several decibels at higher angles
of incidence that the lower angles. The polarization effects are not so
marked on the correlation length sensitivity. Further, the higher
frequencies are more sensitivity to the changes in the correlation length
at low incidence angles than the lower frequencies with X-band showing the
highest, followed by C-band, then L-band and the other one. The L-band
sensitivity at higher incidence angles (430) is equally higher for both
the polarizations. The L-band frequency shows insensitivity to the lower
values of correlation length (5 cm) for both HH and VV polarization at an
incidence angle 230. The 0.45 GHz frequency shows appreciable sensitivity
to radar backscatter at lower values of correlation length but
demonstrates week sensitivity at higher values of the
parameter.
Conclusions The radar backscattering
coefficient s0 is sometimes more sensitive to small changes in roughness
characteristics than to large change in soil moisture. As observed on 7th
experiment, a decrease of rms height from 5.25 mm to 3.0 mm bring about a
reduction of more than 5 dB for HH and HV polarization and a little
smaller change for VV polarization, despite an increase of around 10 % in
the soil moisture. The small disturbances in the field, as noticed by the
uprooting of weeds, can describe the surface roughness patterns and can
not be assumed as constant.
The better validation of the IEM
model at HH polarization lends further confidence to the model. The
disagreements between theory and experimental data at VV polarization at
higher angles of incidence may be due to the negligence of the volume
scattering term in IEM model at higher angles of incidence. At higher
angles, the volume scattering is expected to have an important influence
at such low backscatter values.
The sensitivity analysis done for
various surface characteristics have made their importance and influences
on radar backscattering phenomena a lot more clear. Under smooth surface
conditions, as observed in this field, the rms height has been observed to
be the most sensitive parameter at lower values of the surface rms height.
At higher values of rms height, for the higher frequencies, the radar
backscattering coefficients s0 gets insensitive or shows low sensitivity
to the rms height at lower angles of incidence. The s0 sensitivity to
higher values of rms height is observed even at higher angles of
incidence. The polarization effects are not so distinct. The L-band
frequency and beyond are sensitive to rms height irrespective of the angle
and the polarization.
The sensitivity to correlation length
is also equally strong especially at higher angles of incidence for both
HH and VV polarizations. The L-band frequency is noticed to be less
sensitive to the correlation length at lower angles of incidence (230).
The 0.45 GHz frequency exhibits week sensitivity to correlation length
after 5 cm, while as before that the sensitivity is
appreciable.
The sensitivity to soil moisture is equally good for
all the frequencies and both the angles tested here. But it is less than
that for the surface rms height values.
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