# On the Soil Roughness Parameterization Problem in Soil Moisture Retrieval of Bare Surfaces from Synthetic Aperture Radar

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## Abstract

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## 1. Introduction

## 2. Soil moisture retrieval

#### 2.1. Empirical models

#### 2.2. Semi-empirical models

^{0}

_{HV}/σ

^{0}

_{VV}) and co-polarized (p = σ

^{0}

_{HH}/σ

^{0}

_{VV}) ratios did not correspond to the ones obtained by the radar imagery. When the algorithm was applied to the entire test site, only a small percentage of pixels resulted in a normal solution. A similar problem was reported by Ji et al. [92], and was related to larger uncertainty of the cross-polarized compared to the co-polarized backscatter because of the poorer signal-to-noise ratio. Using airborne C-band SAR data, van Oevelen and Hoekman [93] obtained soil moisture estimates that in general were too high. Boisvert et al. [57] found that Oh's model systematically underestimated the backscattering coefficient for Ku-, C- and L-band data, applied to incidence angles ranging between 15° and 30°. Baghdadi and Zribi [94] found a systematic overestimation of the cross-polarization ratio which was independent on the RMS height, soil moisture or incidence angle, whereas the co-polarized ratio was correctly simulated for C-band SAR. Álvarez-Mozos et al. [95] reported an underestimation of the backscattering coefficient at HH polarization and C-band for smooth surfaces observed at low incidence angles, whereas the model yielded adequate results for rough surfaces and large incidence angles. D'Urso and Minacapilli [96] carried out a calibration procedure in order to use Oh's model to retrieve soil moisture values without a priori knowledge of roughness parameters. They used a SIR-C/X-SAR scene and calibrated the model for two agricultural fields where soil moisture data were available. Results were compared to moisture estimates obtained from a hydrological model, yielding better results for L-band data than for C-band. The results obtained were strongly influenced by the vegetated cover of the fields. Fung and Chen [97] reported that Oh's model fitted observations well over large angles of incidence, but less well over small incidence angles, especially for low frequency data. They observed that the largest errors were obtained at incidence angles of about 10°. At higher frequencies, the model performed better.

#### 2.3. Physically-based models

^{0}of a bare soil, given the radar properties (wavelength, polarization), surface characteristics (dielectric constant and surface roughness) and local incidence angle. The theoretical derivation of the IEM starts from the Stratton-Chu integral which describes the scattered electric field E

_{s}observed at the sensor in terms of the tangential electric and magnetic fields at the soil surface. Because the Stratton-Chu integral is complex some approximations as described in Fung [15] have to be made in order to arrive at an analytical solution. As noted by Hsieh et al. [109], the validity of these simplifying assumptions has to be justified by comparisons with measurements from statistically known surfaces. IEM also neglects scattering from the sub-surface soil volume which may be important for dry soil conditions and long wavelengths [110].

## 3. Soil roughness characterization

#### 3.1. RMS height

_{i}, the RMS height, s, is calculated as [4]:

#### 3.2. Correlation length

#### 3.3. Autocorrelation function

## 4. Impact of in situ roughness characterization on soil moisture retrieval

#### 4.1. Techniques

^{2}) of 0.6. For meshboards, a significant error was found in the roughness measurements (compared to laser profiler measurements), which, according to Mattia et al. [21], is most likely to be attributed to errors introduced during the image processing on the digital photos and the subsequent digitization process.

#### 4.2. Preprocessing

#### 4.3. Measurement accuracy

#### 4.3.1. Horizontal resolution

#### 4.3.2. Vertical resolution

#### 4.3.3. Digitization error

#### 4.4. Profile length

^{2}) is proportional to the profile length. Baghdadi et al. [50] discovered a relationship of the form:

#### 4.5. Number of measurements

#### 4.6. Spatial variability of soil roughness

#### 4.7. Temporal changes of soil roughness

## 5. Alternative approaches to the roughness problem

#### 5.1. Multi-scale processes

^{ν}where ν = (7 − 2D) and D is the surface fractal dimension). For these random processes, traditional roughness parameters, namely the profile height rms (s) and profile correlation length (l) are not intrinsic properties of the surface, but depend on the measured profile length [177]. This property can be employed to simply identify multi-scale roughness profiles, provided the profiles are sufficiently long (see for instance [19,21,178,179]). It is worth noting that 1/f surfaces always possess more important high frequency components than single-scale Gaussian correlated surfaces. On the contrary, they may possess larger or smaller high frequency components than single-scale exponentially correlated surfaces, depending on ν (more details can be found in [180,181]).

#### 5.2. Calibration of parameters

#### 5.3. Two-dimensional surface roughness characterization

#### 5.4. Multi-image approach

^{0}) generated by the IEM model with two different incidence angles, keeping all other parameters constant, was proportional to roughness only, expressed as a ratio of s

^{2}/l termed the Z-index. Rahman et al. [41] showed that it was possible to derive s and l separately from the Z-index using the IEM with a SAR image acquired with dry soil conditions. The resulting maps of distributed roughness can be used to parameterize IEM for producing surface soil moisture maps without the need for ancillary data [68]. The approach required the use of a SAR image acquired with dry soil conditions and two SAR images from two different view angles. During the time span of the two multi-angular image acquisitions, the surface soil moisture should remain nominally constant. This is an obvious constraint with currently orbiting radar systems which cannot acquire multi-angular imagery during a single overpass. On the other hand, it may be possible to replace two-angle imagery with two-polarization imagery (which can be obtained in a single overpass) in the Zribi-Dechambre formulization.

#### 5.5. Using polarimetric data

#### 5.6. Using prior knowledge on roughness state

## 6. Conclusions

## Acknowledgments

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**Figure 2.**Modeled backscattering coefficient as a function of local incidence angle for C- and L-band VV-configurations and different shapes (exponential and Gaussian) of the autocorrelation function, for a soil having a moisture content of 20 vol%, and roughness parameters (s,l) = (1 cm,10 cm).

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**MDPI and ACS Style**

Verhoest, N.E.C.; Lievens, H.; Wagner, W.; Álvarez-Mozos, J.; Moran, M.S.; Mattia, F.
On the Soil Roughness Parameterization Problem in Soil Moisture Retrieval of Bare Surfaces from Synthetic Aperture Radar. *Sensors* **2008**, *8*, 4213-4248.
https://doi.org/10.3390/s8074213

**AMA Style**

Verhoest NEC, Lievens H, Wagner W, Álvarez-Mozos J, Moran MS, Mattia F.
On the Soil Roughness Parameterization Problem in Soil Moisture Retrieval of Bare Surfaces from Synthetic Aperture Radar. *Sensors*. 2008; 8(7):4213-4248.
https://doi.org/10.3390/s8074213

**Chicago/Turabian Style**

Verhoest, Niko E.C, Hans Lievens, Wolfgang Wagner, Jesús Álvarez-Mozos, M. Susan Moran, and Francesco Mattia.
2008. "On the Soil Roughness Parameterization Problem in Soil Moisture Retrieval of Bare Surfaces from Synthetic Aperture Radar" *Sensors* 8, no. 7: 4213-4248.
https://doi.org/10.3390/s8074213