2.2.4. Bragg phenomenon

rð Þ¼ ξ

length is toward infinity.

36 Soil Moisture

scattering behaviors:

only incoherent scattering.

Figure 2. Scattering patterns determined by surface roughness.

response from bare soil.

2.2.3. Wave interaction with the surface roughness

P<sup>N</sup>þ1�<sup>j</sup>

where zj+i � <sup>1</sup> is a point with the spatial displacement xi from the point zi. The surface correlation length l is then defined as the displacement xi, under which the r(xi) between the two points equals 1/e. The correlation length characterizes the statistical independence of two points. In case that the distance between two points is larger than l, their heights can be considered statistically independent from each other. For very smooth surface, the correlation

Furthermore, the effective surface roughness observed by SAR system depends on microwave wavelength. For instance, a given surface that appears smooth in L-band may seem rough in C-band. The relative surface roughness status (compared with wavelength) affects the surface

• For the smooth surface, the angular radiation pattern of the reflected wave is modeled as a

• For the medium roughness surface, the angular radiation pattern is comprised of coherent component and incoherent component. The coherent component is radiated in the specular direction even though its magnitude is smaller than over the smooth surface. The incoherent scattering component consists of energy scattered in all directions, but its

• For the rough surface, the radiation pattern seems like a Lambertian surface, comprised of

Thus, in the electromagnetic models, the effective vertical and horizontal surface roughness is given in terms of the production with EM wave number (k=2 π f/c): ks and kl. It is obvious that ks and kl are decreasing with increasing wavelength. Consequently, as shown in Figure 2, the surface roughness is one of the important factors that determine the electromagnetic wave

delta function which is centered about the specular direction.

magnitude is smaller than that of the coherent component.

<sup>i</sup>¼<sup>1</sup> zjzjþi�<sup>1</sup> P<sup>N</sup> <sup>i</sup>¼<sup>1</sup> zi

<sup>2</sup> (12)

Except the surface roughness and soil moisture, the row direction also influences the backscattering SAR wave from the bare agricultural soils, because it induces the Bragg phenomenon. Bragg resonance is a type of coherent scattering, which is present in some agricultural fields due to the plowing or other row structures' tillage. The resonance occurs in case that the distance between radar and each of the periodic structures has an additional phase difference of λ/2 in the slant-range direction. Under this condition, the additional phase shift is 2π, and the signals will add in phase.
