Application of the Dubois-model using experimental synthetic
aperture radar data for the determination of soil moisture and
surface roughness
Tania Neusch
), Manfred Sties
Institute for Photogrammetry and Remote Sensing, UniÕersity of Karlsruhe, Englerstr. 7, D-76131, Karlsruhe, Germany
Received 30 September 1998; accepted 29 April 1999
Abstract
Many models have been developed in the active microwave domain to explain backscatter as a function of soil moisture andror surface roughness. They can be categorised in three classes: theoretical models, empirical models and semi-empirical
w
models. In this paper we will describe the semi-empirical Dubois-model Dubois, P., Van Zyl, J., Engman, T., 1995. Ž . x Measuring soil moisture with imaging radars. IEEE Transactions on Geoscience and Remote Sensing, 33 4 915–926. . The
Ž .
decisive criterion for choosing this model is its tolerance of sparsely vegetated ground surface NDVI-0.4 , whereas other models require the complete absence of vegetation. After a brief description of image acquisition and ground truth measurements, the effect of measurement and image calibration inaccuracies on the inversion of the radar measurements to infer soil moisture and surface roughness will be analysed.q1999 Elsevier Science B.V. All rights reserved.
Keywords: airborne SAR imagery; E-SAR sensor; soil moisture; surface roughness; model sensitivity
1. Introduction
Remote sensing plays a predominate role in hy-drological parameter modelling because many solu-tions of hydrological problems need area-wide or spatially distributed input data on the basis of regular
Ž .
or irregular grids. Engman and Gurney 1991 give
)Corresponding author. E-mail: [email protected]
an overview of the capabilities and advantages of remote sensing in modelling of the water cycle tak-ing into account various sensors. For example, ther-mal sensors are used for evapotranspiration aspects,
Ž .
and lasers visible and infrared for the measurement of characteristics such as vegetation height, terrain topography and chlorophyl. Engman and Gurney Ž1991 also confirmed that airborne cameras working. in the visible and infrared spectrum are unsuitable for soil moisture detection due to unfavourable sig-nal to noise ratio. On the other hand, they advocate
Ž
the use of microwave sensors especially active
mi-0924-2716r99r$ - see front matterq1999 Elsevier Science B.V. All rights reserved.
Ž .
.
crowaves to measure the dielectric properties of the soil surface. Indeed, the dielectric constant of water
Ž
is widely larger than that of dry soil ´s81 against
.
´s1 to 10, respectively and should be mirrored by
a detectable difference in the backscattering signal. Ž It has also been shown in Ulaby et al. 1981,
.
1982, 1986 , that microwaves are sensitive not only to soil moisture changes, but also to other hydrologi-cal parameters such as vegetation coverage, and relief and surface roughness. Since these interrelated parameters have an important contribution to the backscattered signal, this research examines the problem of the separation of these interrelated pa-rameters from a series of radar images.
2. Data acquisition
Image acquisition was realised on April, 17 and 21 of 1997 with an airborne system in order to acquire multi-frequency and multi-polarisation radar data. The tables and figures in this paper concern the second campaign only.
2.1. Imaging campaigns
The airborne sensor system Experimental
Syn-Ž .
thetic Aperture Radar E-SAR of DLR
Oberpfaffen-Ž .
hofen Deutsches Zentrum fur Luft- und Raumfahrt
¨
acquired radar image data in C-, L-, and P-bands over the small Weiherbachtal watershed located in Southwest Germany. Some key parameters of the sensor are provided in Table 1.
The operating conditions resulted in a pixel size of about 2.5 m=2.5 m for C- and L-bands and
Table 1
E-SAR key parameters
Band C L P
w x
Frequency GHz 5.30 1.30 0.45
Polarisation HH, VV HH, VV HH, VV
HV, VH HV, VH w x
Wavelength cm 5.66 23.07 66.66
w x
Flying height km 3–4 3–4 3–4
w x
Swath width km 6 3.50 -3.5
Table 2
Ground truth measurements averaged over each field
Ž .
Field Soil moisture in % by vol. RMS height
Žin cm.
0–4 cm 4–8 cm 8–16 cm TDR
1 28.85 32.80 27.50 25.64 1.70
2 21.20 35.21 33.23 27.90 1.49
3 21.57 30.12 27.51 23.03 1.78
4 16.52 28.42 28.10 23.51 1.45
5 8.53 22.50 24.74 20.17 1.89
6 19.53 24.86 22.59 25.43 1.56
about 10 m=10 m for the P-band. The incidence angle was approximately 558.
2.2. Soil moisture measurements
Concurrent with the imaging campaigns, soil moisture measurements were taken at 62 positions distributed over the whole test area. The test subar-eas pertain to six large agricultural fields. The 62 positions comprised of six measurements per field, 25 positions in an intensive measurement area, and one point in a forest. The coordinates of these 62 positions were measured by GPS, and thus they could be easily identified in the geocoded radar images. Fields 1 and 3 contained medium developed winter wheat, field 2 bare soil, field 4 almost bare soil, field 5 bare and freshly ploughed soil, and field 6 weakly developed winter wheat.
It has been demonstrated that microwaves have the capability of penetrating into the ground and thus providing subsurface information, whereby the sur-face penetration extent depends on both sensor and surface properties. For this reason, soil moisture measurements were taken at more than one depth.
Ž .
Time-Domain-Reflectometry TDR instruments were used for measuring soil moisture in the layer 0–15 cm. On the other hand, gravimetric measure-ments were taken in the depth layers 0–4, 4–8, 8–16 cm.
2.3. Roughness measurements
The digitisation of the height differences to the average height led to the calculation of the roughness variance presented in Table 2. This roughness vari-ance is also known as Root Mean Square height ŽRMS height . Plant row direction, row distance,. ploughing width, plant height and the estimated veg-etation coverage density were also noted.
2.4. Image preprocessing
After slant-to-ground range transformation and georeferencing, the radar image data were processed to reduce the speckle effects, with regard to the available ground truth data. For this purpose, we decided to smooth the raw radar data within object
Ž .
boundaries as detailed in Neusch and Sties 1998 .
3. The Dubois-model
The Dubois-model algorithm is described in sev-Ž
eral articles Dubois and Van Zyl, 1994; Dubois et .
al., 1995 and was developed using scatterometer data. It was also tested on datasets acquired with airborne systems. The model is semi-empirical, i.e., theoretical models for the main structure of the model are used, while some model coefficients are determined by a fit to experimental measurements.
The inversion of the model expresses the dielec-tric constant as a function of the HH- and VV-polarised backscattering cross-sections and radar
Ž .
characteristics local incidence angle, frequency . The surface roughness can also be determined indepen-dently from the soil moisture and as a function of the same parameters. The HH- and VV-polarised backscattering cross-sections were found to fulfil the equations:
the dielectric constant, h: the RMS height of the surface, k: the wave number, and l: the wavelength.
Best results were achieved by the model of Dubois
Ž .
et al. 1995 with bare and sparsely vegetated areas ŽNDVI-0.4 , at a frequency between 1.5 and 11. GHz, for khF2.5 and incidence anglesuG308. The
Ž .
inversion RMS error RMSE was 4.2% by vol. for the estimates of soil moisture and 0.34 cm for the estimates of the RMS height.
Ž .
Dubois et al. 1995 have found a relation be-tween the NDVI calculated from optical images and the cross-polarised ratio s 8rs 8 defined as q in
hv vv
Oh et al., 1992. To fulfil the validity conditions of the Dubois-model, this ratio should be less thany11
Ž
dB according to Dubois et al., 1995, q-y11 dB .
corresponds to NDVI-0.4 . For NDVI)0.4, the vegetation level can no longer be disregarded by the Dubois-model. Further image processing in a related study revealed that the NDVI values of our fields are betweeny0.03 and 0.11.
3.1. Application of the model
From the availables 8ands 8measurements in
hh vv
each image, we derived the surface roughness and the real part of the dielectric constant. Then, using the known sand and clay parts of the soil composi-tion, the dielectric constant values were converted into soil moisture values and vice versa through the
Ž
set of Hallikainen empirical curves Hallikainen et .
al., 1985 . The RMSE values obtained with the C-band are 0.36 cm for the estimates of surface roughness and 7.4% by vol. for the estimates of soil moisture. An accurate roughness estimation could be
Ž .
obtained with the L-band too RMSEf0.4 cm . The results, however, were less satisfying for the soil moisture estimation, which was extremely
underesti-Ž .
mated RMSEf14% by vol. . Hence, we decided to analyse more precisely the radar returns measured by the sensor and those expected by the model.
In order to determine the backscattering values
Ž .
expected by Dubois et al. 1995 and to compare them to the effectively measured returns, soil
mois-Ž Ž ..
ture taken in the layers 0–4 and 0–15 cm TDR and roughness measurements were introduced into
Ž .
Eq. 1 to derive the expected s 8, s 8values. The
hh v v
expected values were estimated using the backscat-Ž tering coefficients at each measuring position and a
.
Fig. 1. Measured and expected C-band returns.
Žsix points per field and the difference of the aver-. ages was computed. The results are presented in Figs. 1 and 2 for the C- and L-band, respectively and are summarised in Table 3.
3.2. Interpretation of the results
3.2.1. C-band
The C-band cross-sections derived with the mea-surements taken in the 0–4 cm layer approximate our backscatter coefficients better than those derived with the TDR measurements. This first result is consistent, because a short wavelength such as C Žls5.66 cm penetrates the soil surface only to a. small extent. In the case of L-band wavelength,
Ž .
Ulaby et al. 1981, 1982, 1986 calculated a penetra-tion depth of about 8 cm for a loamy soil with
Fig. 2. Measured and expected L-band returns.
moisture values of 0.3 grcm3, although most studies
Žsee Engman and Gurney, 1991 mentioned penetra-. tion depths of less than 8 cm.
The RMSE values for both polarisations are less than 2 dB, although they are much better for the
Ž .
HH-polarisation Table 3 . Consequently, the C-band will offer better results in surface roughness than in soil moisture estimation. The reason for this is that roughness is influenced more by s 8 than by s 8
hh vv
and the expected signals in HH-polarisation do not differ substantially from the HH-polarisation signals measured.
Fields 4 and 5 correspond to almost bare soil field and a freshly ploughed field, respectively. However, they present the worst expected returns. The other
Table 3
Ž .
Differences of backscattering coefficients expected–measured for various layer depths
Ž . Ž .
Field C-band dB L-band dB
0–4 cm 0–4 cm TDR
HH VV HH VV HH VV
1 y0.20 1.17 3.04 6.10 2.06 4.53
2 0.12 y0.41 y0.92 0.42 1.21 3.27
3 0.05 0.23 3.06 4.80 3.79 5.68
4 1.62 0.81 3.80 4.32 4.41 5.63
5 y0.70 y2.66 y0.32 1.12 1.18 3.49
6 y0.74 y0.28 2.65 4.24 4.02 6.13
differences are less than 1.2 dB, even though some fields are covered by medium developed winter wheat Že.g., field 3 ..
Furthermore, the Dubois-model predicts s 8r
hh
s 8-1 for fields 1, 2, 3, 4, 6 and s 8rs 8)1 for
vv hh vv
field 5. The phenomenon occurring for field 5 can be
Ž .
explained by the low soil moisture values ´-5
Ž .
and the large surface roughness RMS hs1.89 cm for this field, and the different incidence angles for
Ž
the calculation of C-HH and C-VV signals u /
C-HH
.
u .
C-VV
3.3. L-band
The general behaviour in Table 3 and Fig. 2 is an extreme underestimation of the measured backscat-tering values and the estimated values. Compared to the RMSE values for the HH-polarisation, the RMSE for the VV-polarisation is worse by about 1.5 dB. The only fields that provide acceptable values are fields 2 and 5. Fields 3 and 4 need further examina-tion. Field 4, in particular, shows unexplained and very low backscattering values.
Although a long wavelength like L-band should penetrate the soil surface much more than C-band, the measured backscatter values of the C-band with the 0–4 cm measurements are at all events closer to the expected values than the L-band values with the
Ž . Ž .
0–15 cm TDR measurements see Table 3 . In summary, the Dubois-model expects higher return values than ours and predicts pss 8rs 8
hh vv
-1 over all fields. This cannot be explained by the input of different incidence angles for the calculation of L-HH and L-VV signals, because the sensor acquires both signals simultaneously.
Fig. 3. Errors introduced by RMS height measurement.
Fig. 4. Errors introduced by soil moisture measurement inaccura-cies.
Other published tests using the Dubois-model can
Ž . Ž .
be found in O’ Neill et al. 1995 , Ji et al. 1996 and
Ž .
Weimann 1996 .
4. Model accuracy
Fixing all parameters by a reference average value Žus468, ´s12, RMS hs1.6 cm , except one. which varies over a defined interval, it is possible to calculate the effect of ground measurement errors ŽRMS height, moisture on the expected cross-sec-. tion returns and, alternatively, to derive the effect of calibration errors on the estimated soil moisture and surface roughness. In this case, the study is limited to the L-Band.
4.1. Errors introduced by ground measurement inac-curacies
Fig. 3 displays the errors introduced by inaccurate RMS height measurements. If 0.34 cm are accepted as the RMSE of the RMS height estimates, the same error made in the ground measurement produces an error of about 1.2 dB for the L-HH expected radar backscattering. The L-VV will be less affected by this error.
Errors introduced by inaccurate soil moisture measurement are presented in Fig. 4. For about 4.5%
Ž .
by vol. overestimated measurement mean ´s12 ,
the Dubois-model predicts errors of 1.67 dB for the L-VV expected radar backscattering.
Another remarkable effect is coupled with the local incidence angle measurement accuracy. Fig. 5 shows that a 58error in local incidence angle affects
Fig. 5. Errors introduced by local incidence angle inaccuracies.
1.3 dB. In summary, errors in the absolute values of the signal due to inaccuracies occurring during mea-surement campaigns can only reach a maximum of 2 dB.
4.2. Errors introduced by calibration errors
In addition to errors due to ground measurements, the errors introduced by eventual calibration errors must be taken into account. For this study, we calculated the estimation errors for moisture and roughness as a function of relative or absolute
cali-Ž Ž ..
bration errors as calculated in Dubois et al. 1995 for our imaging conditions.
Based on these calculations, if the absolute cali-Ž
bration error is about 3 dB i.e., both polarisation .
signals are 3 dB lower than expected , then the soil moisture will be underestimated by 4.25% by vol. and the roughness will be underestimated by about
Ž 0.5 cm. A 1 dB relative calibration error i.e., the VV-polarisation signal is 1 dB lower than expected
.
and ps0.69 , however, will cause an underestima-tion of about 6.7% by vol. In the case of ps
s 8rs 8s1, an underestimation in the soil
mois-hh vv
ture greater than 10% by vol. was obtained.
5. Conclusion
In this paper, we analysed the semi-empirical Dubois-model by comparison of the expected and measured backscattering values. Measured and ex-pected values show a better agreement for C-band Žespecially for the HH-polarisation than for the L-. band. The reason for this may be inaccuracies in the soil moisture and roughness measurements andror calibration errors of the data, whereby absolute
cali-bration errors have a weaker influence than relative ones.
Further research is needed to clarify whether the attenuation in the L-band signals is caused by the presence of vegetation. However, the biggest soil moisture underestimation in this study was realised in an almost bare soil field, although the ratio q was less than y11 dB, i.e., the validity condition of the Dubois-model was fulfilled.
Based on these results, the model needs further refinement to be acceptable in the case of a
catch-Ž
ment area where relief introduced by the local
inci-. Ž
dence angle and vegetation coverage introduced by .
the ratio q play a predominant role.
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